High-resolution gravity model of Venus

NASA Technical Reports Server (NTRS)

Reasenberg, R. D.; Goldberg, Z. M.

1992-01-01

The anomalous gravity field of Venus shows high correlation with surface features revealed by radar. We extract gravity models from the Doppler tracking data from the Pioneer Venus Orbiter by means of a two-step process. In the first step, we solve the nonlinear spacecraft state estimation problem using a Kalman filter-smoother. The Kalman filter has been evaluated through simulations. This evaluation and some unusual features of the filter are discussed. In the second step, we perform a geophysical inversion using a linear Bayesian estimator. To allow an unbiased comparison between gravity and topography, we use a simulation technique to smooth and distort the radar topographic data so as to yield maps having the same characteristics as our gravity maps. The maps presented cover 2/3 of the surface of Venus and display the strong topography-gravity correlation previously reported. The topography-gravity scatter plots show two distinct trends.

Real-time inverse planning for Gamma Knife radiosurgery.

PubMed

Wu, Q Jackie; Chankong, Vira; Jitprapaikulsarn, Suradet; Wessels, Barry W; Einstein, Douglas B; Mathayomchan, Boonyanit; Kinsella, Timothy J

2003-11-01

The challenges of real-time Gamma Knife inverse planning are the large number of variables involved and the unknown search space a priori. With limited collimator sizes, shots have to be heavily overlapped to form a smooth prescription isodose line that conforms to the irregular target shape. Such overlaps greatly influence the total number of shots per plan, making pre-determination of the total number of shots impractical. However, this total number of shots usually defines the search space, a pre-requisite for most of the optimization methods. Since each shot only covers part of the target, a collection of shots in different locations and various collimator sizes selected makes up the global dose distribution that conforms to the target. Hence, planning or placing these shots is a combinatorial optimization process that is computationally expensive by nature. We have previously developed a theory of shot placement and optimization based on skeletonization. The real-time inverse planning process, reported in this paper, is an expansion and the clinical implementation of this theory. The complete planning process consists of two steps. The first step is to determine an optimal number of shots including locations and sizes and to assign initial collimator size to each of the shots. The second step is to fine-tune the weights using a linear-programming technique. The objective function is to minimize the total dose to the target boundary (i.e., maximize the dose conformity). Results of an ellipsoid test target and ten clinical cases are presented. The clinical cases are also compared with physician's manual plans. The target coverage is more than 99% for manual plans and 97% for all the inverse plans. The RTOG PITV conformity indices for the manual plans are between 1.16 and 3.46, compared to 1.36 to 2.4 for the inverse plans. All the inverse plans are generated in less than 2 min, making real-time inverse planning a reality.

A three-step Maximum-A-Posterior probability method for InSAR data inversion of coseismic rupture with application to four recent large earthquakes in Asia

NASA Astrophysics Data System (ADS)

Sun, J.; Shen, Z.; Burgmann, R.; Liang, F.

2012-12-01

We develop a three-step Maximum-A-Posterior probability (MAP) method for coseismic rupture inversion, which aims at maximizing the a posterior probability density function (PDF) of elastic solutions of earthquake rupture. The method originates from the Fully Bayesian Inversion (FBI) and the Mixed linear-nonlinear Bayesian inversion (MBI) methods , shares the same a posterior PDF with them and keeps most of their merits, while overcoming its convergence difficulty when large numbers of low quality data are used and improving the convergence rate greatly using optimization procedures. A highly efficient global optimization algorithm, Adaptive Simulated Annealing (ASA), is used to search for the maximum posterior probability in the first step. The non-slip parameters are determined by the global optimization method, and the slip parameters are inverted for using the least squares method without positivity constraint initially, and then damped to physically reasonable range. This step MAP inversion brings the inversion close to 'true' solution quickly and jumps over local maximum regions in high-dimensional parameter space. The second step inversion approaches the 'true' solution further with positivity constraints subsequently applied on slip parameters using the Monte Carlo Inversion (MCI) technique, with all parameters obtained from step one as the initial solution. Then the slip artifacts are eliminated from slip models in the third step MAP inversion with fault geometry parameters fixed. We first used a designed model with 45 degree dipping angle and oblique slip, and corresponding synthetic InSAR data sets to validate the efficiency and accuracy of method. We then applied the method on four recent large earthquakes in Asia, namely the 2010 Yushu, China earthquake, the 2011 Burma earthquake, the 2011 New Zealand earthquake and the 2008 Qinghai, China earthquake, and compared our results with those results from other groups. Our results show the effectiveness of the method in earthquake studies and a number of advantages of it over other methods. The details will be reported on the meeting.

Source process of the 2016 Kumamoto earthquake (Mj7.3) inferred from kinematic inversion of strong-motion records

NASA Astrophysics Data System (ADS)

Yoshida, Kunikazu; Miyakoshi, Ken; Somei, Kazuhiro; Irikura, Kojiro

2017-05-01

In this study, we estimated source process of the 2016 Kumamoto earthquake from strong-motion data by using the multiple-time window linear kinematic waveform inversion method to discuss generation of strong motions and to explain crustal deformation pattern with a seismic source inversion model. A four-segment fault model was assumed based on the aftershock distribution, active fault traces, and interferometric synthetic aperture radar data. Three western segments were set to be northwest-dipping planes, and the most eastern segment under the Aso caldera was examined to be a southeast-dipping plane. The velocity structure models used in this study were estimated by using waveform modeling of moderate earthquakes that occurred in the source region. We applied a two-step approach of the inversions of 20 strong-motion datasets observed by K-NET and KiK-net by using band-pass-filtered strong-motion data at 0.05-0.5 Hz and then at 0.05-1.0 Hz. The rupture area of the fault plane was determined by applying the criterion of Somerville et al. (Seismol Res Lett 70:59-80, 1999) to the inverted slip distribution. From the first-step inversion, the fault length was trimmed from 52 to 44 km, whereas the fault width was kept at 18 km. The trimmed rupture area was not changed in the second-step inversion. The source model obtained from the two-step approach indicated 4.7 × 1019 Nm of the total moment release and 1.8 m average slip of the entire fault with a rupture area of 792 km2. Large slip areas were estimated in the seismogenic zone and in the shallow part corresponding to the surface rupture that occurred during the Mj7.3 mainshock. The areas of the high peak moment rate correlated roughly with those of large slip; however, the moment rate functions near the Earth surface have low peak, bell shape, and long duration. These subfaults with long-duration moment release are expected to cause weak short-period ground motions. We confirmed that the southeast dipping of the most eastern segment is more plausible rather than northwest-dipping from the observed subsidence around the central cones of the Aso volcano.[Figure not available: see fulltext.

Inverse Modelling Problems in Linear Algebra Undergraduate Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor E.

2013-01-01

This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

Efficient preconditioning of the electronic structure problem in large scale ab initio molecular dynamics simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schiffmann, Florian; VandeVondele, Joost, E-mail: Joost.VandeVondele@mat.ethz.ch

2015-06-28

We present an improved preconditioning scheme for electronic structure calculations based on the orbital transformation method. First, a preconditioner is developed which includes information from the full Kohn-Sham matrix but avoids computationally demanding diagonalisation steps in its construction. This reduces the computational cost of its construction, eliminating a bottleneck in large scale simulations, while maintaining rapid convergence. In addition, a modified form of Hotelling’s iterative inversion is introduced to replace the exact inversion of the preconditioner matrix. This method is highly effective during molecular dynamics (MD), as the solution obtained in earlier MD steps is a suitable initial guess. Filteringmore » small elements during sparse matrix multiplication leads to linear scaling inversion, while retaining robustness, already for relatively small systems. For system sizes ranging from a few hundred to a few thousand atoms, which are typical for many practical applications, the improvements to the algorithm lead to a 2-5 fold speedup per MD step.« less

Angle-domain inverse scattering migration/inversion in isotropic media

NASA Astrophysics Data System (ADS)

Li, Wuqun; Mao, Weijian; Li, Xuelei; Ouyang, Wei; Liang, Quan

2018-07-01

The classical seismic asymptotic inversion can be transformed into a problem of inversion of generalized Radon transform (GRT). In such methods, the combined parameters are linearly attached to the scattered wave-field by Born approximation and recovered by applying an inverse GRT operator to the scattered wave-field data. Typical GRT-style true-amplitude inversion procedure contains an amplitude compensation process after the weighted migration via dividing an illumination associated matrix whose elements are integrals of scattering angles. It is intuitional to some extent that performs the generalized linear inversion and the inversion of GRT together by this process for direct inversion. However, it is imprecise to carry out such operation when the illumination at the image point is limited, which easily leads to the inaccuracy and instability of the matrix. This paper formulates the GRT true-amplitude inversion framework in an angle-domain version, which naturally degrades the external integral term related to the illumination in the conventional case. We solve the linearized integral equation for combined parameters of different fixed scattering angle values. With this step, we obtain high-quality angle-domain common-image gathers (CIGs) in the migration loop which provide correct amplitude-versus-angle (AVA) behavior and reasonable illumination range for subsurface image points. Then we deal with the over-determined problem to solve each parameter in the combination by a standard optimization operation. The angle-domain GRT inversion method keeps away from calculating the inaccurate and unstable illumination matrix. Compared with the conventional method, the angle-domain method can obtain more accurate amplitude information and wider amplitude-preserved range. Several model tests demonstrate the effectiveness and practicability.

Constraining earthquake source inversions with GPS data: 2. A two-step approach to combine seismic and geodetic data sets

USGS Publications Warehouse

Custodio, S.; Page, M.T.; Archuleta, R.J.

2009-01-01

We present a new method to combine static and wavefield data to image earthquake ruptures. Our combined inversion is a two-step procedure, following the work of Hernandez et al. (1999), and takes into account the differences between the resolutions of the two data sets. The first step consists of an inversion of the static field, which yields a map of slip amplitude. This inversion exploits a special irregular grid that takes into account the resolution of the static data. The second step is an inversion of the radiated wavefield; it results in the determination of the time evolution of slip on the fault. In the second step, the slip amplitude is constrained to resemble the static slip amplitude map inferred from the GPS inversion. Using this combined inversion, we study the source process of the 2004 M6 Parkfield, California, earthquake. We conclude that slip occurred in two main regions of the fault, each of which displayed distinct rupture behaviors. Slip initiated at the hypocenter with a very strong bilateral burst of energy. Here, slip was localized in a narrow area approximately 10 km long, the rupture velocity was very fast (???3.5 km/s), and slip only lasted a short period of time (<1 s). Then the rupture proceeded to a wider region 12-20 km northwest of the hypocenter. Here, the earthquake developed in a more moderated way: the rupture velocity slowed to ???3.0 km/s and slip lasted longer (1-2 s). The maximum slip amplitude was 0.45 m. Copyright 2009 by the American Geophysical Union.

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

ERIC Educational Resources Information Center

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Reduction of a linear complex model for respiratory system during Airflow Interruption.

PubMed

Jablonski, Ireneusz; Mroczka, Janusz

2010-01-01

The paper presents methodology of a complex model reduction to its simpler version - an identifiable inverse model. Its main tool is a numerical procedure of sensitivity analysis (structural and parametric) applied to the forward linear equivalent designed for the conditions of interrupter experiment. Final result - the reduced analog for the interrupter technique is especially worth of notice as it fills a major gap in occlusional measurements, which typically use simple, one- or two-element physical representations. Proposed electrical reduced circuit, being structural combination of resistive, inertial and elastic properties, can be perceived as a candidate for reliable reconstruction and quantification (in the time and frequency domain) of dynamical behavior of the respiratory system in response to a quasi-step excitation by valve closure.

Probabilistic estimation of splitting coefficients of normal modes of the Earth, and their uncertainties, using an autoregressive technique

NASA Astrophysics Data System (ADS)

Pachhai, S.; Masters, G.; Laske, G.

2017-12-01

Earth's normal-mode spectra are crucial to studying the long wavelength structure of the Earth. Such observations have been used extensively to estimate "splitting coefficients" which, in turn, can be used to determine the three-dimensional velocity and density structure. Most past studies apply a non-linear iterative inversion to estimate the splitting coefficients which requires that the earthquake source is known. However, it is challenging to know the source details, particularly for big events as used in normal-mode analyses. Additionally, the final solution of the non-linear inversion can depend on the choice of damping parameter and starting model. To circumvent the need to know the source, a two-step linear inversion has been developed and successfully applied to many mantle and core sensitive modes. The first step takes combinations of the data from a single event to produce spectra known as "receiver strips". The autoregressive nature of the receiver strips can then be used to estimate the structure coefficients without the need to know the source. Based on this approach, we recently employed a neighborhood algorithm to measure the splitting coefficients for an isolated inner-core sensitive mode (13S2). This approach explores the parameter space efficiently without any need of regularization and finds the structure coefficients which best fit the observed strips. Here, we implement a Bayesian approach to data collected for earthquakes from early 2000 and more recent. This approach combines the data (through likelihood) and prior information to provide rigorous parameter values and their uncertainties for both isolated and coupled modes. The likelihood function is derived from the inferred errors of the receiver strips which allows us to retrieve proper uncertainties. Finally, we apply model selection criteria that balance the trade-offs between fit (likelihood) and model complexity to investigate the degree and type of structure (elastic and anelastic) required to explain the data.

Minimization of model representativity errors in identification of point source emission from atmospheric concentration measurements

NASA Astrophysics Data System (ADS)

Sharan, Maithili; Singh, Amit Kumar; Singh, Sarvesh Kumar

2017-11-01

Estimation of an unknown atmospheric release from a finite set of concentration measurements is considered an ill-posed inverse problem. Besides ill-posedness, the estimation process is influenced by the instrumental errors in the measured concentrations and model representativity errors. The study highlights the effect of minimizing model representativity errors on the source estimation. This is described in an adjoint modelling framework and followed in three steps. First, an estimation of point source parameters (location and intensity) is carried out using an inversion technique. Second, a linear regression relationship is established between the measured concentrations and corresponding predicted using the retrieved source parameters. Third, this relationship is utilized to modify the adjoint functions. Further, source estimation is carried out using these modified adjoint functions to analyse the effect of such modifications. The process is tested for two well known inversion techniques, called renormalization and least-square. The proposed methodology and inversion techniques are evaluated for a real scenario by using concentrations measurements from the Idaho diffusion experiment in low wind stable conditions. With both the inversion techniques, a significant improvement is observed in the retrieval of source estimation after minimizing the representativity errors.

Joint inversion for transponder localization and sound-speed profile temporal variation in high-precision acoustic surveys.

PubMed

Li, Zhao; Dosso, Stan E; Sun, Dajun

2016-07-01

This letter develops a Bayesian inversion for localizing underwater acoustic transponders using a surface ship which compensates for sound-speed profile (SSP) temporal variation during the survey. The method is based on dividing observed acoustic travel-time data into time segments and including depth-independent SSP variations for each segment as additional unknown parameters to approximate the SSP temporal variation. SSP variations are estimated jointly with transponder locations, rather than calculated separately as in existing two-step inversions. Simulation and sea-trial results show this localization/SSP joint inversion performs better than two-step inversion in terms of localization accuracy, agreement with measured SSP variations, and computational efficiency.

Application of neural models as controllers in mobile robot velocity control loop

NASA Astrophysics Data System (ADS)

Cerkala, Jakub; Jadlovska, Anna

2017-01-01

This paper presents the application of an inverse neural models used as controllers in comparison to classical PI controllers for velocity tracking control task used in two-wheel, differentially driven mobile robot. The PI controller synthesis is based on linear approximation of actuators with equivalent load. In order to obtain relevant datasets for training of feed-forward multi-layer perceptron based neural network used as neural model, the mathematical model of mobile robot, that combines its kinematic and dynamic properties such as chassis dimensions, center of gravity offset, friction and actuator parameters is used. Neural models are trained off-line to act as an inverse dynamics of DC motors with particular load using data collected in simulation experiment for motor input voltage step changes within bounded operating area. The performances of PI controllers versus inverse neural models in mobile robot internal velocity control loops are demonstrated and compared in simulation experiment of navigation control task for line segment motion in plane.

Computed inverse MRI for magnetic susceptibility map reconstruction

PubMed Central

Chen, Zikuan; Calhoun, Vince

2015-01-01

Objective This paper reports on a computed inverse magnetic resonance imaging (CIMRI) model for reconstructing the magnetic susceptibility source from MRI data using a two-step computational approach. Methods The forward T2*-weighted MRI (T2*MRI) process is decomposed into two steps: 1) from magnetic susceptibility source to fieldmap establishment via magnetization in a main field, and 2) from fieldmap to MR image formation by intravoxel dephasing average. The proposed CIMRI model includes two inverse steps to reverse the T2*MRI procedure: fieldmap calculation from MR phase image and susceptibility source calculation from the fieldmap. The inverse step from fieldmap to susceptibility map is a 3D ill-posed deconvolution problem, which can be solved by three kinds of approaches: Tikhonov-regularized matrix inverse, inverse filtering with a truncated filter, and total variation (TV) iteration. By numerical simulation, we validate the CIMRI model by comparing the reconstructed susceptibility maps for a predefined susceptibility source. Results Numerical simulations of CIMRI show that the split Bregman TV iteration solver can reconstruct the susceptibility map from a MR phase image with high fidelity (spatial correlation≈0.99). The split Bregman TV iteration solver includes noise reduction, edge preservation, and image energy conservation. For applications to brain susceptibility reconstruction, it is important to calibrate the TV iteration program by selecting suitable values of the regularization parameter. Conclusions The proposed CIMRI model can reconstruct the magnetic susceptibility source of T2*MRI by two computational steps: calculating the fieldmap from the phase image and reconstructing the susceptibility map from the fieldmap. The crux of CIMRI lies in an ill-posed 3D deconvolution problem, which can be effectively solved by the split Bregman TV iteration algorithm. PMID:22446372

Time-domain induced polarization - an analysis of Cole-Cole parameter resolution and correlation using Markov Chain Monte Carlo inversion

NASA Astrophysics Data System (ADS)

Madsen, Line Meldgaard; Fiandaca, Gianluca; Auken, Esben; Christiansen, Anders Vest

2017-12-01

The application of time-domain induced polarization (TDIP) is increasing with advances in acquisition techniques, data processing and spectral inversion schemes. An inversion of TDIP data for the spectral Cole-Cole parameters is a non-linear problem, but by applying a 1-D Markov Chain Monte Carlo (MCMC) inversion algorithm, a full non-linear uncertainty analysis of the parameters and the parameter correlations can be accessed. This is essential to understand to what degree the spectral Cole-Cole parameters can be resolved from TDIP data. MCMC inversions of synthetic TDIP data, which show bell-shaped probability distributions with a single maximum, show that the Cole-Cole parameters can be resolved from TDIP data if an acquisition range above two decades in time is applied. Linear correlations between the Cole-Cole parameters are observed and by decreasing the acquisitions ranges, the correlations increase and become non-linear. It is further investigated how waveform and parameter values influence the resolution of the Cole-Cole parameters. A limiting factor is the value of the frequency exponent, C. As C decreases, the resolution of all the Cole-Cole parameters decreases and the results become increasingly non-linear. While the values of the time constant, τ, must be in the acquisition range to resolve the parameters well, the choice between a 50 per cent and a 100 per cent duty cycle for the current injection does not have an influence on the parameter resolution. The limits of resolution and linearity are also studied in a comparison between the MCMC and a linearized gradient-based inversion approach. The two methods are consistent for resolved models, but the linearized approach tends to underestimate the uncertainties for poorly resolved parameters due to the corresponding non-linear features. Finally, an MCMC inversion of 1-D field data verifies that spectral Cole-Cole parameters can also be resolved from TD field measurements.

The attitude inversion method of geostationary satellites based on unscented particle filter

NASA Astrophysics Data System (ADS)

Du, Xiaoping; Wang, Yang; Hu, Heng; Gou, Ruixin; Liu, Hao

2018-04-01

The attitude information of geostationary satellites is difficult to be obtained since they are presented in non-resolved images on the ground observation equipment in space object surveillance. In this paper, an attitude inversion method for geostationary satellite based on Unscented Particle Filter (UPF) and ground photometric data is presented. The inversion algorithm based on UPF is proposed aiming at the strong non-linear feature in the photometric data inversion for satellite attitude, which combines the advantage of Unscented Kalman Filter (UKF) and Particle Filter (PF). This update method improves the particle selection based on the idea of UKF to redesign the importance density function. Moreover, it uses the RMS-UKF to partially correct the prediction covariance matrix, which improves the applicability of the attitude inversion method in view of UKF and the particle degradation and dilution of the attitude inversion method based on PF. This paper describes the main principles and steps of algorithm in detail, correctness, accuracy, stability and applicability of the method are verified by simulation experiment and scaling experiment in the end. The results show that the proposed method can effectively solve the problem of particle degradation and depletion in the attitude inversion method on account of PF, and the problem that UKF is not suitable for the strong non-linear attitude inversion. However, the inversion accuracy is obviously superior to UKF and PF, in addition, in the case of the inversion with large attitude error that can inverse the attitude with small particles and high precision.

Recursive partitioned inversion of large (1500 x 1500) symmetric matrices

NASA Technical Reports Server (NTRS)

Putney, B. H.; Brownd, J. E.; Gomez, R. A.

1976-01-01

A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models.

Recursive Factorization of the Inverse Overlap Matrix in Linear-Scaling Quantum Molecular Dynamics Simulations.

PubMed

Negre, Christian F A; Mniszewski, Susan M; Cawkwell, Marc J; Bock, Nicolas; Wall, Michael E; Niklasson, Anders M N

2016-07-12

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive, iterative refinement of an initial guess of Z (inverse square root of the overlap matrix S). The initial guess of Z is obtained beforehand by using either an approximate divide-and-conquer technique or dynamical methods, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under the incomplete, approximate, iterative refinement of Z. Linear-scaling performance is obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables efficient shared-memory parallelization. As we show in this article using self-consistent density-functional-based tight-binding MD, our approach is faster than conventional methods based on the diagonalization of overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4158-atom water-solvated polyalanine system, we find an average speedup factor of 122 for the computation of Z in each MD step.

Recursive Factorization of the Inverse Overlap Matrix in Linear Scaling Quantum Molecular Dynamics Simulations

DOE PAGES

Negre, Christian F. A; Mniszewski, Susan M.; Cawkwell, Marc Jon; ...

2016-06-06

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive iterative re nement of an initial guess Z of the inverse overlap matrix S. The initial guess of Z is obtained beforehand either by using an approximate divide and conquer technique or dynamically, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under incomplete approximate iterative re nement of Z. Linear scaling performance ismore » obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables e cient shared memory parallelization. As we show in this article using selfconsistent density functional based tight-binding MD, our approach is faster than conventional methods based on the direct diagonalization of the overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4,158 atom water-solvated polyalanine system we nd an average speedup factor of 122 for the computation of Z in each MD step.« less

Preconditioned alternating direction method of multipliers for inverse problems with constraints

NASA Astrophysics Data System (ADS)

Jiao, Yuling; Jin, Qinian; Lu, Xiliang; Wang, Weijie

2017-02-01

We propose a preconditioned alternating direction method of multipliers (ADMM) to solve linear inverse problems in Hilbert spaces with constraints, where the feature of the sought solution under a linear transformation is captured by a possibly non-smooth convex function. During each iteration step, our method avoids solving large linear systems by choosing a suitable preconditioning operator. In case the data is given exactly, we prove the convergence of our preconditioned ADMM without assuming the existence of a Lagrange multiplier. In case the data is corrupted by noise, we propose a stopping rule using information on noise level and show that our preconditioned ADMM is a regularization method; we also propose a heuristic rule when the information on noise level is unavailable or unreliable and give its detailed analysis. Numerical examples are presented to test the performance of the proposed method.

Sealing glass-ceramics with near-linear thermal strain, Part II: Sequence of crystallization and phase stability

DOE PAGES

Rodriguez, Mark A.; Griego, James J. M.; Dai, Steve

2016-08-22

The sequence of crystallization in a recrystallizable lithium silicate sealing glass-ceramic Li 2O–SiO 2–Al 2O 3–K 2O–B 2O 3–P 2O 5–ZnO was analyzed by in situ high-temperature X-ray diffraction (HTXRD). Glass-ceramic specimens have been subjected to a two-stage heat-treatment schedule, including rapid cooling from sealing temperature to a first hold temperature 650°C, followed by heating to a second hold temperature of 810°C. Notable growth and saturation of Quartz was observed at 650°C (first hold). Cristobalite crystallized at the second hold temperature of 810°C, growing from the residual glass rather than converting from the Quartz. The coexistence of quartz and cristobalitemore » resulted in a glass-ceramic having a near-linear thermal strain, as opposed to the highly nonlinear glass-ceramic where the cristobalite is the dominant silica crystalline phase. HTXRD was also performed to analyze the inversion and phase stability of the two types of fully crystallized glass-ceramics. While the inversion in cristobalite resembles the character of a first-order displacive phase transformation, i.e., step changes in lattice parameters and thermal hysteresis in the transition temperature, the inversion in quartz appears more diffuse and occurs over a much broader temperature range. Furthermore, localized tensile stresses on quartz and possible solid-solution effects have been attributed to the transition behavior of quartz crystals embedded in the glass-ceramics.« less

Two-level image authentication by two-step phase-shifting interferometry and compressive sensing

NASA Astrophysics Data System (ADS)

Zhang, Xue; Meng, Xiangfeng; Yin, Yongkai; Yang, Xiulun; Wang, Yurong; Li, Xianye; Peng, Xiang; He, Wenqi; Dong, Guoyan; Chen, Hongyi

2018-01-01

A two-level image authentication method is proposed; the method is based on two-step phase-shifting interferometry, double random phase encoding, and compressive sensing (CS) theory, by which the certification image can be encoded into two interferograms. Through discrete wavelet transform (DWT), sparseness processing, Arnold transform, and data compression, two compressed signals can be generated and delivered to two different participants of the authentication system. Only the participant who possesses the first compressed signal attempts to pass the low-level authentication. The application of Orthogonal Match Pursuit CS algorithm reconstruction, inverse Arnold transform, inverse DWT, two-step phase-shifting wavefront reconstruction, and inverse Fresnel transform can result in the output of a remarkable peak in the central location of the nonlinear correlation coefficient distributions of the recovered image and the standard certification image. Then, the other participant, who possesses the second compressed signal, is authorized to carry out the high-level authentication. Therefore, both compressed signals are collected to reconstruct the original meaningful certification image with a high correlation coefficient. Theoretical analysis and numerical simulations verify the feasibility of the proposed method.

Classifying bilinear differential equations by linear superposition principle

NASA Astrophysics Data System (ADS)

Zhang, Lijun; Khalique, Chaudry Masood; Ma, Wen-Xiu

2016-09-01

In this paper, we investigate the linear superposition principle of exponential traveling waves to construct a sub-class of N-wave solutions of Hirota bilinear equations. A necessary and sufficient condition for Hirota bilinear equations possessing this specific sub-class of N-wave solutions is presented. We apply this result to find N-wave solutions to the (2+1)-dimensional KP equation, a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation, a (3+1)-dimensional generalized BKP equation and the (2+1)-dimensional BKP equation. The inverse question, i.e., constructing Hirota Bilinear equations possessing N-wave solutions, is considered and a refined 3-step algorithm is proposed. As examples, we construct two very general kinds of Hirota bilinear equations of order 4 possessing N-wave solutions among which one satisfies dispersion relation and another does not satisfy dispersion relation.

Iterative algorithms for a non-linear inverse problem in atmospheric lidar

NASA Astrophysics Data System (ADS)

Denevi, Giulia; Garbarino, Sara; Sorrentino, Alberto

2017-08-01

We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and the data follow the Poisson distribution. Standard methods work on the log-transformed data and solve the resulting linear inverse problem, but neglect to take into account the noise statistics. In this study we show that proper modelling of the noise distribution can improve substantially the quality of the reconstructed extinction profiles. To achieve this goal, we consider the non-linear inverse problem with non-negativity constraint, and propose two iterative algorithms derived using the Karush-Kuhn-Tucker conditions. We validate the algorithms with synthetic and experimental data. As expected, the proposed algorithms out-perform standard methods in terms of sensitivity to noise and reliability of the estimated profile.

On recovering distributed IP information from inductive source time domain electromagnetic data

NASA Astrophysics Data System (ADS)

Kang, Seogi; Oldenburg, Douglas W.

2016-10-01

We develop a procedure to invert time domain induced polarization (IP) data for inductive sources. Our approach is based upon the inversion methodology in conventional electrical IP (EIP), which uses a sensitivity function that is independent of time. However, significant modifications are required for inductive source IP (ISIP) because electric fields in the ground do not achieve a steady state. The time-history for these fields needs to be evaluated and then used to define approximate IP currents. The resultant data, either a magnetic field or its derivative, are evaluated through the Biot-Savart law. This forms the desired linear relationship between data and pseudo-chargeability. Our inversion procedure has three steps: (1) Obtain a 3-D background conductivity model. We advocate, where possible, that this be obtained by inverting early-time data that do not suffer significantly from IP effects. (2) Decouple IP responses embedded in the observations by forward modelling the TEM data due to a background conductivity and subtracting these from the observations. (3) Use the linearized sensitivity function to invert data at each time channel and recover pseudo-chargeability. Post-interpretation of the recovered pseudo-chargeabilities at multiple times allows recovery of intrinsic Cole-Cole parameters such as time constant and chargeability. The procedure is applicable to all inductive source survey geometries but we focus upon airborne time domain EM (ATEM) data with a coincident-loop configuration because of the distinctive negative IP signal that is observed over a chargeable body. Several assumptions are adopted to generate our linearized modelling but we systematically test the capability and accuracy of the linearization for ISIP responses arising from different conductivity structures. On test examples we show: (1) our decoupling procedure enhances the ability to extract information about existence and location of chargeable targets directly from the data maps; (2) the horizontal location of a target body can be well recovered through inversion; (3) the overall geometry of a target body might be recovered but for ATEM data a depth weighting is required in the inversion; (4) we can recover estimates of intrinsic τ and η that may be useful for distinguishing between two chargeable targets.

Isometric Non-Rigid Shape-from-Motion with Riemannian Geometry Solved in Linear Time.

PubMed

Parashar, Shaifali; Pizarro, Daniel; Bartoli, Adrien

2017-10-06

We study Isometric Non-Rigid Shape-from-Motion (Iso-NRSfM): given multiple intrinsically calibrated monocular images, we want to reconstruct the time-varying 3D shape of a thin-shell object undergoing isometric deformations. We show that Iso-NRSfM is solvable from local warps, the inter-image geometric transformations. We propose a new theoretical framework based on the Riemmanian manifold to represent the unknown 3D surfaces as embeddings of the camera's retinal plane. This allows us to use the manifold's metric tensor and Christoffel Symbol (CS) fields. These are expressed in terms of the first and second order derivatives of the inverse-depth of the 3D surfaces, which are the unknowns for Iso-NRSfM. We prove that the metric tensor and the CS are related across images by simple rules depending only on the warps. This forms a set of important theoretical results. We show that current solvers cannot solve for the first and second order derivatives of the inverse-depth simultaneously. We thus propose an iterative solution in two steps. 1) We solve for the first order derivatives assuming that the second order derivatives are known. We initialise the second order derivatives to zero, which is an infinitesimal planarity assumption. We derive a system of two cubics in two variables for each image pair. The sum-of-squares of these polynomials is independent of the number of images and can be solved globally, forming a well-posed problem for N ≥ 3 images. 2) We solve for the second order derivatives by initialising the first order derivatives from the previous step. We solve a linear system of 4N-4 equations in three variables. We iterate until the first order derivatives converge. The solution for the first order derivatives gives the surfaces' normal fields which we integrate to recover the 3D surfaces. The proposed method outperforms existing work in terms of accuracy and computation cost on synthetic and real datasets.

Fast, Nonlinear, Fully Probabilistic Inversion of Large Geophysical Problems

NASA Astrophysics Data System (ADS)

Curtis, A.; Shahraeeni, M.; Trampert, J.; Meier, U.; Cho, G.

2010-12-01

Almost all Geophysical inverse problems are in reality nonlinear. Fully nonlinear inversion including non-approximated physics, and solving for probability distribution functions (pdf’s) that describe the solution uncertainty, generally requires sampling-based Monte-Carlo style methods that are computationally intractable in most large problems. In order to solve such problems, physical relationships are usually linearized leading to efficiently-solved, (possibly iterated) linear inverse problems. However, it is well known that linearization can lead to erroneous solutions, and in particular to overly optimistic uncertainty estimates. What is needed across many Geophysical disciplines is a method to invert large inverse problems (or potentially tens of thousands of small inverse problems) fully probabilistically and without linearization. This talk shows how very large nonlinear inverse problems can be solved fully probabilistically and incorporating any available prior information using mixture density networks (driven by neural network banks), provided the problem can be decomposed into many small inverse problems. In this talk I will explain the methodology, compare multi-dimensional pdf inversion results to full Monte Carlo solutions, and illustrate the method with two applications: first, inverting surface wave group and phase velocities for a fully-probabilistic global tomography model of the Earth’s crust and mantle, and second inverting industrial 3D seismic data for petrophysical properties throughout and around a subsurface hydrocarbon reservoir. The latter problem is typically decomposed into 104 to 105 individual inverse problems, each solved fully probabilistically and without linearization. The results in both cases are sufficiently close to the Monte Carlo solution to exhibit realistic uncertainty, multimodality and bias. This provides far greater confidence in the results, and in decisions made on their basis.

Pilots Rate Augmented Generalized Predictive Control for Reconfiguration

NASA Technical Reports Server (NTRS)

Soloway, Don; Haley, Pam

2004-01-01

The objective of this paper is to report the results from the research being conducted in reconfigurable fight controls at NASA Ames. A study was conducted with three NASA Dryden test pilots to evaluate two approaches of reconfiguring an aircraft's control system when failures occur in the control surfaces and engine. NASA Ames is investigating both a Neural Generalized Predictive Control scheme and a Neural Network based Dynamic Inverse controller. This paper highlights the Predictive Control scheme where a simple augmentation to reduce zero steady-state error led to the neural network predictor model becoming redundant for the task. Instead of using a neural network predictor model, a nominal single point linear model was used and then augmented with an error corrector. This paper shows that the Generalized Predictive Controller and the Dynamic Inverse Neural Network controller perform equally well at reconfiguration, but with less rate requirements from the actuators. Also presented are the pilot ratings for each controller for various failure scenarios and two samples of the required control actuation during reconfiguration. Finally, the paper concludes by stepping through the Generalized Predictive Control's reconfiguration process for an elevator failure.

Three-dimensional inverse modelling of damped elastic wave propagation in the Fourier domain

NASA Astrophysics Data System (ADS)

Petrov, Petr V.; Newman, Gregory A.

2014-09-01

3-D full waveform inversion (FWI) of seismic wavefields is routinely implemented with explicit time-stepping simulators. A clear advantage of explicit time stepping is the avoidance of solving large-scale implicit linear systems that arise with frequency domain formulations. However, FWI using explicit time stepping may require a very fine time step and (as a consequence) significant computational resources and run times. If the computational challenges of wavefield simulation can be effectively handled, an FWI scheme implemented within the frequency domain utilizing only a few frequencies, offers a cost effective alternative to FWI in the time domain. We have therefore implemented a 3-D FWI scheme for elastic wave propagation in the Fourier domain. To overcome the computational bottleneck in wavefield simulation, we have exploited an efficient Krylov iterative solver for the elastic wave equations approximated with second and fourth order finite differences. The solver does not exploit multilevel preconditioning for wavefield simulation, but is coupled efficiently to the inversion iteration workflow to reduce computational cost. The workflow is best described as a series of sequential inversion experiments, where in the case of seismic reflection acquisition geometries, the data has been laddered such that we first image highly damped data, followed by data where damping is systemically reduced. The key to our modelling approach is its ability to take advantage of solver efficiency when the elastic wavefields are damped. As the inversion experiment progresses, damping is significantly reduced, effectively simulating non-damped wavefields in the Fourier domain. While the cost of the forward simulation increases as damping is reduced, this is counterbalanced by the cost of the outer inversion iteration, which is reduced because of a better starting model obtained from the larger damped wavefield used in the previous inversion experiment. For cross-well data, it is also possible to launch a successful inversion experiment without laddering the damping constants. With this type of acquisition geometry, the solver is still quite effective using a small fixed damping constant. To avoid cycle skipping, we also employ a multiscale imaging approach, in which frequency content of the data is also laddered (with the data now including both reflection and cross-well data acquisition geometries). Thus the inversion process is launched using low frequency data to first recover the long spatial wavelength of the image. With this image as a new starting model, adding higher frequency data refines and enhances the resolution of the image. FWI using laddered frequencies with an efficient damping schemed enables reconstructing elastic attributes of the subsurface at a resolution that approaches half the smallest wavelength utilized to image the subsurface. We show the possibility of effectively carrying out such reconstructions using two to six frequencies, depending upon the application. Using the proposed FWI scheme, massively parallel computing resources are essential for reasonable execution times.

Recursive mass matrix factorization and inversion: An operator approach to open- and closed-chain multibody dynamics

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Kreutz, K.

1988-01-01

This report advances a linear operator approach for analyzing the dynamics of systems of joint-connected rigid bodies.It is established that the mass matrix M for such a system can be factored as M=(I+H phi L)D(I+H phi L) sup T. This yields an immediate inversion M sup -1=(I-H psi L) sup T D sup -1 (I-H psi L), where H and phi are given by known link geometric parameters, and L, psi and D are obtained recursively by a spatial discrete-step Kalman filter and by the corresponding Riccati equation associated with this filter. The factors (I+H phi L) and (I-H psi L) are lower triangular matrices which are inverses of each other, and D is a diagonal matrix. This factorization and inversion of the mass matrix leads to recursive algortihms for forward dynamics based on spatially recursive filtering and smoothing. The primary motivation for advancing the operator approach is to provide a better means to formulate, analyze and understand spatial recursions in multibody dynamics. This is achieved because the linear operator notation allows manipulation of the equations of motion using a very high-level analytical framework (a spatial operator algebra) that is easy to understand and use. Detailed lower-level recursive algorithms can readily be obtained for inspection from the expressions involving spatial operators. The report consists of two main sections. In Part 1, the problem of serial chain manipulators is analyzed and solved. Extensions to a closed-chain system formed by multiple manipulators moving a common task object are contained in Part 2. To retain ease of exposition in the report, only these two types of multibody systems are considered. However, the same methods can be easily applied to arbitrary multibody systems formed by a collection of joint-connected regid bodies.

Limited-memory BFGS based least-squares pre-stack Kirchhoff depth migration

NASA Astrophysics Data System (ADS)

Wu, Shaojiang; Wang, Yibo; Zheng, Yikang; Chang, Xu

2015-08-01

Least-squares migration (LSM) is a linearized inversion technique for subsurface reflectivity estimation. Compared to conventional migration algorithms, it can improve spatial resolution significantly with a few iterative calculations. There are three key steps in LSM, (1) calculate data residuals between observed data and demigrated data using the inverted reflectivity model; (2) migrate data residuals to form reflectivity gradient and (3) update reflectivity model using optimization methods. In order to obtain an accurate and high-resolution inversion result, the good estimation of inverse Hessian matrix plays a crucial role. However, due to the large size of Hessian matrix, the inverse matrix calculation is always a tough task. The limited-memory BFGS (L-BFGS) method can evaluate the Hessian matrix indirectly using a limited amount of computer memory which only maintains a history of the past m gradients (often m < 10). We combine the L-BFGS method with least-squares pre-stack Kirchhoff depth migration. Then, we validate the introduced approach by the 2-D Marmousi synthetic data set and a 2-D marine data set. The results show that the introduced method can effectively obtain reflectivity model and has a faster convergence rate with two comparison gradient methods. It might be significant for general complex subsurface imaging.

Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agaltsov, A. D., E-mail: agalets@gmail.com; Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr; IEPT RAS, 117997 Moscow

2014-10-15

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

Comparison of Compressed Sensing Algorithms for Inversion of 3-D Electrical Resistivity Tomography.

NASA Astrophysics Data System (ADS)

Peddinti, S. R.; Ranjan, S.; Kbvn, D. P.

2016-12-01

Image reconstruction algorithms derived from electrical resistivity tomography (ERT) are highly non-linear, sparse, and ill-posed. The inverse problem is much severe, when dealing with 3-D datasets that result in large sized matrices. Conventional gradient based techniques using L2 norm minimization with some sort of regularization can impose smoothness constraint on the solution. Compressed sensing (CS) is relatively new technique that takes the advantage of inherent sparsity in parameter space in one or the other form. If favorable conditions are met, CS was proven to be an efficient image reconstruction technique that uses limited observations without losing edge sharpness. This paper deals with the development of an open source 3-D resistivity inversion tool using CS framework. The forward model was adopted from RESINVM3D (Pidlisecky et al., 2007) with CS as the inverse code. Discrete cosine transformation (DCT) function was used to induce model sparsity in orthogonal form. Two CS based algorithms viz., interior point method and two-step IST were evaluated on a synthetic layered model with surface electrode observations. The algorithms were tested (in terms of quality and convergence) under varying degrees of parameter heterogeneity, model refinement, and reduced observation data space. In comparison to conventional gradient algorithms, CS was proven to effectively reconstruct the sub-surface image with less computational cost. This was observed by a general increase in NRMSE from 0.5 in 10 iterations using gradient algorithm to 0.8 in 5 iterations using CS algorithms.

Inverse kinematics of a dual linear actuator pitch/roll heliostat

NASA Astrophysics Data System (ADS)

Freeman, Joshua; Shankar, Balakrishnan; Sundaram, Ganesh

2017-06-01

This work presents a simple, computationally efficient inverse kinematics solution for a pitch/roll heliostat using two linear actuators. The heliostat design and kinematics have been developed, modeled and tested using computer simulation software. A physical heliostat prototype was fabricated to validate the theoretical computations and data. Pitch/roll heliostats have numerous advantages including reduced cost potential and reduced space requirements, with a primary disadvantage being the significantly more complicated kinematics, which are solved here. Novel methods are applied to simplify the inverse kinematics problem which could be applied to other similar problems.

Objectively Measured Daily Steps and Subsequent Long Term All-Cause Mortality: The Tasped Prospective Cohort Study.

PubMed

Dwyer, Terence; Pezic, Angela; Sun, Cong; Cochrane, Jenny; Venn, Alison; Srikanth, Velandai; Jones, Graeme; Shook, Robin P; Shook, Robin; Sui, Xuemei; Ortaglia, Andrew; Blair, Steven; Ponsonby, Anne-Louise

2015-01-01

Self-reported physical activity has been inversely associated with mortality but the effect of objectively measured step activity on mortality has never been evaluated. The objective is to determine the prospective association of daily step activity on mortality among free-living adults. Cohort study of free-living adults residing in Tasmania, Australia between 2000 and 2005 who participated in one of three cohort studies (n = 2 576 total participants). Daily step activity by pedometer at baseline at a mean of 58.8 years of age, and for a subset, repeated monitoring was available 3.7 (SD 1.3) years later (n = 1 679). All-cause mortality (n = 219 deaths) was ascertained by record-linkage to the Australian National Death Index; 90% of participants were followed-up over ten years, until June 2011. Higher daily step count at baseline was linearly associated with lower all-cause mortality (adjusted hazard ratio AHR, 0.94; 95% CI, 0.90 to 0.98 per 1 000 steps; P = 0.004). Risk was altered little by removing deaths occurring in the first two years. Increasing baseline daily steps from sedentary to 10 000 steps a day was associated with a 46% (95% CI, 18% to 65%; P = 0.004) lower risk of mortality in the decade of follow-up. In addition, those who increased their daily steps over the monitoring period had a substantial reduction in mortality risk, after adjusting for baseline daily step count (AHR, 0.39; 95% CI, 0.22 to 0.72; P = 0.002), or other factors (AHR, 0.38; 95% CI, 0.21-0.70; P = 0.002). Higher daily step count was linearly associated with subsequent long term mortality among free living adults. These data are the first to quantify mortality reductions using an objective measure of physical activity in a free living population. They strongly underscore the importance of physical inactivity as a major public health problem.

Probability density of spatially distributed soil moisture inferred from crosshole georadar traveltime measurements

NASA Astrophysics Data System (ADS)

Linde, N.; Vrugt, J. A.

2009-04-01

Geophysical models are increasingly used in hydrological simulations and inversions, where they are typically treated as an artificial data source with known uncorrelated "data errors". The model appraisal problem in classical deterministic linear and non-linear inversion approaches based on linearization is often addressed by calculating model resolution and model covariance matrices. These measures offer only a limited potential to assign a more appropriate "data covariance matrix" for future hydrological applications, simply because the regularization operators used to construct a stable inverse solution bear a strong imprint on such estimates and because the non-linearity of the geophysical inverse problem is not explored. We present a parallelized Markov Chain Monte Carlo (MCMC) scheme to efficiently derive the posterior spatially distributed radar slowness and water content between boreholes given first-arrival traveltimes. This method is called DiffeRential Evolution Adaptive Metropolis (DREAM_ZS) with snooker updater and sampling from past states. Our inverse scheme does not impose any smoothness on the final solution, and uses uniform prior ranges of the parameters. The posterior distribution of radar slowness is converted into spatially distributed soil moisture values using a petrophysical relationship. To benchmark the performance of DREAM_ZS, we first apply our inverse method to a synthetic two-dimensional infiltration experiment using 9421 traveltimes contaminated with Gaussian errors and 80 different model parameters, corresponding to a model discretization of 0.3 m × 0.3 m. After this, the method is applied to field data acquired in the vadose zone during snowmelt. This work demonstrates that fully non-linear stochastic inversion can be applied with few limiting assumptions to a range of common two-dimensional tomographic geophysical problems. The main advantage of DREAM_ZS is that it provides a full view of the posterior distribution of spatially distributed soil moisture, which is key to appropriately treat geophysical parameter uncertainty and infer hydrologic models.

Structural-change localization and monitoring through a perturbation-based inverse problem.

PubMed

Roux, Philippe; Guéguen, Philippe; Baillet, Laurent; Hamze, Alaa

2014-11-01

Structural-change detection and characterization, or structural-health monitoring, is generally based on modal analysis, for detection, localization, and quantification of changes in structure. Classical methods combine both variations in frequencies and mode shapes, which require accurate and spatially distributed measurements. In this study, the detection and localization of a local perturbation are assessed by analysis of frequency changes (in the fundamental mode and overtones) that are combined with a perturbation-based linear inverse method and a deconvolution process. This perturbation method is applied first to a bending beam with the change considered as a local perturbation of the Young's modulus, using a one-dimensional finite-element model for modal analysis. Localization is successful, even for extended and multiple changes. In a second step, the method is numerically tested under ambient-noise vibration from the beam support with local changes that are shifted step by step along the beam. The frequency values are revealed using the random decrement technique that is applied to the time-evolving vibrations recorded by one sensor at the free extremity of the beam. Finally, the inversion method is experimentally demonstrated at the laboratory scale with data recorded at the free end of a Plexiglas beam attached to a metallic support.

jInv: A Modular and Scalable Framework for Electromagnetic Inverse Problems

NASA Astrophysics Data System (ADS)

Belliveau, P. T.; Haber, E.

2016-12-01

Inversion is a key tool in the interpretation of geophysical electromagnetic (EM) data. Three-dimensional (3D) EM inversion is very computationally expensive and practical software for inverting large 3D EM surveys must be able to take advantage of high performance computing (HPC) resources. It has traditionally been difficult to achieve those goals in a high level dynamic programming environment that allows rapid development and testing of new algorithms, which is important in a research setting. With those goals in mind, we have developed jInv, a framework for PDE constrained parameter estimation problems. jInv provides optimization and regularization routines, a framework for user defined forward problems, and interfaces to several direct and iterative solvers for sparse linear systems. The forward modeling framework provides finite volume discretizations of differential operators on rectangular tensor product meshes and tetrahedral unstructured meshes that can be used to easily construct forward modeling and sensitivity routines for forward problems described by partial differential equations. jInv is written in the emerging programming language Julia. Julia is a dynamic language targeted at the computational science community with a focus on high performance and native support for parallel programming. We have developed frequency and time-domain EM forward modeling and sensitivity routines for jInv. We will illustrate its capabilities and performance with two synthetic time-domain EM inversion examples. First, in airborne surveys, which use many sources, we achieve distributed memory parallelism by decoupling the forward and inverse meshes and performing forward modeling for each source on small, locally refined meshes. Secondly, we invert grounded source time-domain data from a gradient array style induced polarization survey using a novel time-stepping technique that allows us to compute data from different time-steps in parallel. These examples both show that it is possible to invert large scale 3D time-domain EM datasets within a modular, extensible framework written in a high-level, easy to use programming language.

Analog design optimization methodology for ultralow-power circuits using intuitive inversion-level and saturation-level parameters

NASA Astrophysics Data System (ADS)

Eimori, Takahisa; Anami, Kenji; Yoshimatsu, Norifumi; Hasebe, Tetsuya; Murakami, Kazuaki

2014-01-01

A comprehensive design optimization methodology using intuitive nondimensional parameters of inversion-level and saturation-level is proposed, especially for ultralow-power, low-voltage, and high-performance analog circuits with mixed strong, moderate, and weak inversion metal-oxide-semiconductor transistor (MOST) operations. This methodology is based on the synthesized charge-based MOST model composed of Enz-Krummenacher-Vittoz (EKV) basic concepts and advanced-compact-model (ACM) physics-based equations. The key concept of this methodology is that all circuit and system characteristics are described as some multivariate functions of inversion-level parameters, where the inversion level is used as an independent variable representative of each MOST. The analog circuit design starts from the first step of inversion-level design using universal characteristics expressed by circuit currents and inversion-level parameters without process-dependent parameters, followed by the second step of foundry-process-dependent design and the last step of verification using saturation-level criteria. This methodology also paves the way to an intuitive and comprehensive design approach for many kinds of analog circuit specifications by optimization using inversion-level log-scale diagrams and saturation-level criteria. In this paper, we introduce an example of our design methodology for a two-stage Miller amplifier.

A full potential inverse method based on a density linearization scheme for wing design

NASA Technical Reports Server (NTRS)

Shankar, V.

1982-01-01

A mixed analysis inverse procedure based on the full potential equation in conservation form was developed to recontour a given base wing to produce density linearization scheme in applying the pressure boundary condition in terms of the velocity potential. The FL030 finite volume analysis code was modified to include the inverse option. The new surface shape information, associated with the modified pressure boundary condition, is calculated at a constant span station based on a mass flux integration. The inverse method is shown to recover the original shape when the analysis pressure is not altered. Inverse calculations for weakening of a strong shock system and for a laminar flow control (LFC) pressure distribution are presented. Two methods for a trailing edge closure model are proposed for further study.

A new approach to integrate GPU-based Monte Carlo simulation into inverse treatment plan optimization for proton therapy.

PubMed

Li, Yongbao; Tian, Zhen; Song, Ting; Wu, Zhaoxia; Liu, Yaqiang; Jiang, Steve; Jia, Xun

2017-01-07

Monte Carlo (MC)-based spot dose calculation is highly desired for inverse treatment planning in proton therapy because of its accuracy. Recent studies on biological optimization have also indicated the use of MC methods to compute relevant quantities of interest, e.g. linear energy transfer. Although GPU-based MC engines have been developed to address inverse optimization problems, their efficiency still needs to be improved. Also, the use of a large number of GPUs in MC calculation is not favorable for clinical applications. The previously proposed adaptive particle sampling (APS) method can improve the efficiency of MC-based inverse optimization by using the computationally expensive MC simulation more effectively. This method is more efficient than the conventional approach that performs spot dose calculation and optimization in two sequential steps. In this paper, we propose a computational library to perform MC-based spot dose calculation on GPU with the APS scheme. The implemented APS method performs a non-uniform sampling of the particles from pencil beam spots during the optimization process, favoring those from the high intensity spots. The library also conducts two computationally intensive matrix-vector operations frequently used when solving an optimization problem. This library design allows a streamlined integration of the MC-based spot dose calculation into an existing proton therapy inverse planning process. We tested the developed library in a typical inverse optimization system with four patient cases. The library achieved the targeted functions by supporting inverse planning in various proton therapy schemes, e.g. single field uniform dose, 3D intensity modulated proton therapy, and distal edge tracking. The efficiency was 41.6  ±  15.3% higher than the use of a GPU-based MC package in a conventional calculation scheme. The total computation time ranged between 2 and 50 min on a single GPU card depending on the problem size.

A new approach to integrate GPU-based Monte Carlo simulation into inverse treatment plan optimization for proton therapy

NASA Astrophysics Data System (ADS)

Li, Yongbao; Tian, Zhen; Song, Ting; Wu, Zhaoxia; Liu, Yaqiang; Jiang, Steve; Jia, Xun

2017-01-01

Monte Carlo (MC)-based spot dose calculation is highly desired for inverse treatment planning in proton therapy because of its accuracy. Recent studies on biological optimization have also indicated the use of MC methods to compute relevant quantities of interest, e.g. linear energy transfer. Although GPU-based MC engines have been developed to address inverse optimization problems, their efficiency still needs to be improved. Also, the use of a large number of GPUs in MC calculation is not favorable for clinical applications. The previously proposed adaptive particle sampling (APS) method can improve the efficiency of MC-based inverse optimization by using the computationally expensive MC simulation more effectively. This method is more efficient than the conventional approach that performs spot dose calculation and optimization in two sequential steps. In this paper, we propose a computational library to perform MC-based spot dose calculation on GPU with the APS scheme. The implemented APS method performs a non-uniform sampling of the particles from pencil beam spots during the optimization process, favoring those from the high intensity spots. The library also conducts two computationally intensive matrix-vector operations frequently used when solving an optimization problem. This library design allows a streamlined integration of the MC-based spot dose calculation into an existing proton therapy inverse planning process. We tested the developed library in a typical inverse optimization system with four patient cases. The library achieved the targeted functions by supporting inverse planning in various proton therapy schemes, e.g. single field uniform dose, 3D intensity modulated proton therapy, and distal edge tracking. The efficiency was 41.6  ±  15.3% higher than the use of a GPU-based MC package in a conventional calculation scheme. The total computation time ranged between 2 and 50 min on a single GPU card depending on the problem size.

A New Approach to Integrate GPU-based Monte Carlo Simulation into Inverse Treatment Plan Optimization for Proton Therapy

PubMed Central

Li, Yongbao; Tian, Zhen; Song, Ting; Wu, Zhaoxia; Liu, Yaqiang; Jiang, Steve; Jia, Xun

2016-01-01

Monte Carlo (MC)-based spot dose calculation is highly desired for inverse treatment planning in proton therapy because of its accuracy. Recent studies on biological optimization have also indicated the use of MC methods to compute relevant quantities of interest, e.g. linear energy transfer. Although GPU-based MC engines have been developed to address inverse optimization problems, their efficiency still needs to be improved. Also, the use of a large number of GPUs in MC calculation is not favorable for clinical applications. The previously proposed adaptive particle sampling (APS) method can improve the efficiency of MC-based inverse optimization by using the computationally expensive MC simulation more effectively. This method is more efficient than the conventional approach that performs spot dose calculation and optimization in two sequential steps. In this paper, we propose a computational library to perform MC-based spot dose calculation on GPU with the APS scheme. The implemented APS method performs a non-uniform sampling of the particles from pencil beam spots during the optimization process, favoring those from the high intensity spots. The library also conducts two computationally intensive matrix-vector operations frequently used when solving an optimization problem. This library design allows a streamlined integration of the MC-based spot dose calculation into an existing proton therapy inverse planning process. We tested the developed library in a typical inverse optimization system with four patient cases. The library achieved the targeted functions by supporting inverse planning in various proton therapy schemes, e.g. single field uniform dose, 3D intensity modulated proton therapy, and distal edge tracking. The efficiency was 41.6±15.3% higher than the use of a GPU-based MC package in a conventional calculation scheme. The total computation time ranged between 2 and 50 min on a single GPU card depending on the problem size. PMID:27991456

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

NASA Technical Reports Server (NTRS)

Jewell, Jeffrey B.; Raymond, C.; Smrekar, S.; Millbury, C.

2004-01-01

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

Shear wave velocity structure in North America from large-scale waveform inversions of surface waves

USGS Publications Warehouse

Alsina, D.; Woodward, R.L.; Snieder, R.K.

1996-01-01

A two-step nonlinear and linear inversion is carried out to map the lateral heterogeneity beneath North America using surface wave data. The lateral resolution for most areas of the model is of the order of several hundred kilometers. The most obvious feature in the tomographic images is the rapid transition between low velocities in the technically active region west of the Rocky Mountains and high velocities in the stable central and eastern shield of North America. The model also reveals smaller-scale heterogeneous velocity structures. A high-velocity anomaly is imaged beneath the state of Washington that could be explained as the subducting Juan de Fuca plate beneath the Cascades. A large low-velocity structure extends along the coast from the Mendocino to the Rivera triple junction and to the continental interior across the southwestern United States and northwestern Mexico. Its shape changes notably with depth. This anomaly largely coincides with the part of the margin where no lithosphere is consumed since the subduction has been replaced by a transform fault. Evidence for a discontinuous subduction of the Cocos plate along the Middle American Trench is found. In central Mexico a transition is visible from low velocities across the Trans-Mexican Volcanic Belt (TMVB) to high velocities beneath the Yucatan Peninsula. Two elongated low-velocity anomalies beneath the Yellowstone Plateau and the eastern Snake River Plain volcanic system and beneath central Mexico and the TMVB seem to be associated with magmatism and partial melting. Another low-velocity feature is seen at depths of approximately 200 km beneath Florida and the Atlantic Coastal Plain. The inversion technique used is based on a linear surface wave scattering theory, which gives tomographic images of the relative phase velocity perturbations in four period bands ranging from 40 to 150 s. In order to find a smooth reference model a nonlinear inversion based on ray theory is first performed. After correcting for the crustal thickness the phase velocity perturbations obtained from the subsequent linear waveform inversion for the different period bands are converted to a three-layer model of S velocity perturbations (layer 1, 25-100 km; layer 2, 100-200 km) layer 3, 200-300 km). We have applied this method on 275 high-quality Rayleigh waves recorded by a variety of instruments in North America (IRIS/USGS, IRIS/IDA, TERRAscope, RSTN). Sensitivity tests indicate that the lateral resolution is especially good in the densely sampled western continental United States, Mexico, and the Gulf of Mexico.

Scarp degraded by linear diffusion: inverse solution for age.

USGS Publications Warehouse

Andrews, D.J.; Hanks, T.C.

1985-01-01

Under the assumption that landforms unaffected by drainage channels are degraded according to the linear diffusion equation, a procedure is developed to invert a scarp profile to find its 'diffusion age'. The inverse procedure applied to synthetic data yields the following rules of thumb. Evidence of initial scarp shape has been lost when apparent age reaches twice its initial value. A scarp that appears to have been formed by one event may have been formed by two with an interval between them as large as apparent age. The simplicity of scarp profile measurement and this inversion makes profile analysis attractive. -from Authors

Reconstruction of local perturbations in periodic surfaces

NASA Astrophysics Data System (ADS)

Lechleiter, Armin; Zhang, Ruming

2018-03-01

This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce quasi-periodic fields in one periodic cell, are no longer available. Based on the Floquet-Bloch transform, a numerical method has been developed to solve the direct problem, that leads to a possibility to design an algorithm for the inverse problem. The numerical method introduced in this paper contains two steps. The first step is initialization, that is to locate the support of the perturbation by a simple method. This step reduces the inverse problem in an infinite domain into one periodic cell. The second step is to apply the Newton-CG method to solve the associated optimization problem. The perturbation is then approximated by a finite spline basis. Numerical examples are given at the end of this paper, showing the efficiency of the numerical method.

Time-lapse three-dimensional inversion of complex conductivity data using an active time constrained (ATC) approach

USGS Publications Warehouse

Karaoulis, M.; Revil, A.; Werkema, D.D.; Minsley, B.J.; Woodruff, W.F.; Kemna, A.

2011-01-01

Induced polarization (more precisely the magnitude and phase of impedance of the subsurface) is measured using a network of electrodes located at the ground surface or in boreholes. This method yields important information related to the distribution of permeability and contaminants in the shallow subsurface. We propose a new time-lapse 3-D modelling and inversion algorithm to image the evolution of complex conductivity over time. We discretize the subsurface using hexahedron cells. Each cell is assigned a complex resistivity or conductivity value. Using the finite-element approach, we model the in-phase and out-of-phase (quadrature) electrical potentials on the 3-D grid, which are then transformed into apparent complex resistivity. Inhomogeneous Dirichlet boundary conditions are used at the boundary of the domain. The calculation of the Jacobian matrix is based on the principles of reciprocity. The goal of time-lapse inversion is to determine the change in the complex resistivity of each cell of the spatial grid as a function of time. Each model along the time axis is called a 'reference space model'. This approach can be simplified into an inverse problem looking for the optimum of several reference space models using the approximation that the material properties vary linearly in time between two subsequent reference models. Regularizations in both space domain and time domain reduce inversion artefacts and improve the stability of the inversion problem. In addition, the use of the time-lapse equations allows the simultaneous inversion of data obtained at different times in just one inversion step (4-D inversion). The advantages of this new inversion algorithm are demonstrated on synthetic time-lapse data resulting from the simulation of a salt tracer test in a heterogeneous random material described by an anisotropic semi-variogram. ?? 2011 The Authors Geophysical Journal International ?? 2011 RAS.

Advances in the microrheology of complex fluids

NASA Astrophysics Data System (ADS)

Waigh, Thomas Andrew

2016-07-01

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.

Improved Shaping Approach to the Preliminary Design of Low-Thrust Trajectories

NASA Astrophysics Data System (ADS)

Novak, D. M.; Vasile, M.

2011-01-01

This paper presents a general framework for the development of shape-based approaches to low-thrust trajectory design. A novel shaping method, based on a three-dimensional description of the trajectory in spherical coordinates, is developed within this general framework. Both the exponential sinusoid and the inverse polynomial shaping are demonstrated to be particular two-dimensional cases of the spherical one. The pseudoequinoctial shaping is revisited within the new framework, and the nonosculating nature of the pseudoequinoctial elements is analyzed. A two-step approach is introduced to solve the time of flight constraint, related to the design of low-thrust arcs with boundary constraints for both spherical and pseudoequinoctial shaping. The solution derived from the shaping approach is improved with a feedback linear-quadratic controller and compared against a direct collocation method based on finite elements in time. The new shaping approach and the combination of shaping and linear-quadratic controller are tested on three case studies: a mission to Mars, a mission to asteroid 1989ML, a mission to comet Tempel-1, and a mission to Neptune.

Oil-in-oil emulsions stabilised solely by solid particles.

PubMed

Binks, Bernard P; Tyowua, Andrew T

2016-01-21

A brief review of the stabilisation of emulsions of two immiscible oils is given. We then describe the use of fumed silica particles coated with either hydrocarbon or fluorocarbon groups in acting as sole stabilisers of emulsions of various vegetable oils with linear silicone oils (PDMS) of different viscosity. Transitional phase inversion of emulsions, containing equal volumes of the two oils, from silicone-in-vegetable (S/V) to vegetable-in-silicone (V/S) occurs upon increasing the hydrophobicity of the particles. Close to inversion, emulsions are stable to coalescence and gravity-induced separation for at least one year. Increasing the viscosity of the silicone oil enables stable S/V emulsions to be prepared even with relatively hydrophilic particles. Predictions of emulsion type from calculated contact angles of a silica particle at the oil-oil interface are in agreement with experiment provided a small polar contribution to the surface energy of the oils is included. We also show that stable multiple emulsions of V/S/V can be prepared in a two-step procedure using two particle types of different hydrophobicity. At fixed particle concentration, catastrophic phase inversion of emulsions from V/S to S/V can be effected by increasing the volume fraction of vegetable oil. Finally, in the case of sunflower oil + 20 cS PDMS, the study is extended to particles other than silica which differ in chemical type, particle size and particle shape. Consistent with the above findings, we find that only sufficiently hydrophobic particles (clay, zinc oxide, silicone, calcium carbonate) can act as efficient V/S emulsion stabilisers.

Special Course on Inverse Methods for Airfoil Design for Aeronautical and Turbomachinery Applications (Methodes Inverses pour la Conception des Profils Porteurs pour des Applications dans les Domaines de l’Aeronautique et des Turbomachines)

DTIC Science & Technology

1990-11-01

engined jet aircraft wing MID PLA CROSS tCTO% taking into account the effects of the propulsive system. -DESIGN PAAMETERS DESTIGE PARAMETERS 5CT 0 (MC 0...AGARD Report No.780 Special Course on Inverse Methods for Airfoil Design for Aeronautical and Turbomachinery Applications (M6thodes Inverses pour la...manufacturing systems. Blade or airfoil designs are normally made in two steps, and the lectures are accordingly grouped into two parts. - - In the

Numerical Recovering of a Speed of Sound by the BC-Method in 3D

NASA Astrophysics Data System (ADS)

Pestov, Leonid; Bolgova, Victoria; Danilin, Alexandr

We develop the numerical algorithm for solving the inverse problem for the wave equation by the Boundary Control method. The problem, which we refer to as a forward one, is an initial boundary value problem for the wave equation with zero initial data in the bounded domain. The inverse problem is to find the speed of sound c(x) by the measurements of waves induced by a set of boundary sources. The time of observation is assumed to be greater then two acoustical radius of the domain. The numerical algorithm for sound reconstruction is based on two steps. The first one is to find a (sufficiently large) number of controls {f_j} (the basic control is defined by the position of the source and some time delay), which generates the same number of known harmonic functions, i.e. Δ {u_j}(.,T) = 0 , where {u_j} is the wave generated by the control {f_j} . After that the linear integral equation w.r.t. the speed of sound is obtained. The piecewise constant model of the speed is used. The result of numerical testing of 3-dimensional model is presented.

Delineating chalk sand distribution of Ekofisk formation using probabilistic neural network (PNN) and stepwise regression (SWR): Case study Danish North Sea field

NASA Astrophysics Data System (ADS)

Haris, A.; Nafian, M.; Riyanto, A.

2017-07-01

Danish North Sea Fields consist of several formations (Ekofisk, Tor, and Cromer Knoll) that was started from the age of Paleocene to Miocene. In this study, the integration of seismic and well log data set is carried out to determine the chalk sand distribution in the Danish North Sea field. The integration of seismic and well log data set is performed by using the seismic inversion analysis and seismic multi-attribute. The seismic inversion algorithm, which is used to derive acoustic impedance (AI), is model-based technique. The derived AI is then used as external attributes for the input of multi-attribute analysis. Moreover, the multi-attribute analysis is used to generate the linear and non-linear transformation of among well log properties. In the case of the linear model, selected transformation is conducted by weighting step-wise linear regression (SWR), while for the non-linear model is performed by using probabilistic neural networks (PNN). The estimated porosity, which is resulted by PNN shows better suited to the well log data compared with the results of SWR. This result can be understood since PNN perform non-linear regression so that the relationship between the attribute data and predicted log data can be optimized. The distribution of chalk sand has been successfully identified and characterized by porosity value ranging from 23% up to 30%.

Spatial interpolation schemes of daily precipitation for hydrologic modeling

USGS Publications Warehouse

Hwang, Y.; Clark, M.R.; Rajagopalan, B.; Leavesley, G.

2012-01-01

Distributed hydrologic models typically require spatial estimates of precipitation interpolated from sparsely located observational points to the specific grid points. We compare and contrast the performance of regression-based statistical methods for the spatial estimation of precipitation in two hydrologically different basins and confirmed that widely used regression-based estimation schemes fail to describe the realistic spatial variability of daily precipitation field. The methods assessed are: (1) inverse distance weighted average; (2) multiple linear regression (MLR); (3) climatological MLR; and (4) locally weighted polynomial regression (LWP). In order to improve the performance of the interpolations, the authors propose a two-step regression technique for effective daily precipitation estimation. In this simple two-step estimation process, precipitation occurrence is first generated via a logistic regression model before estimate the amount of precipitation separately on wet days. This process generated the precipitation occurrence, amount, and spatial correlation effectively. A distributed hydrologic model (PRMS) was used for the impact analysis in daily time step simulation. Multiple simulations suggested noticeable differences between the input alternatives generated by three different interpolation schemes. Differences are shown in overall simulation error against the observations, degree of explained variability, and seasonal volumes. Simulated streamflows also showed different characteristics in mean, maximum, minimum, and peak flows. Given the same parameter optimization technique, LWP input showed least streamflow error in Alapaha basin and CMLR input showed least error (still very close to LWP) in Animas basin. All of the two-step interpolation inputs resulted in lower streamflow error compared to the directly interpolated inputs. ?? 2011 Springer-Verlag.

New Global 3D Upper to Mid-mantle Electrical Conductivity Model Based on Observatory Data with Realistic Auroral Sources

NASA Astrophysics Data System (ADS)

Kelbert, A.; Egbert, G. D.; Sun, J.

2011-12-01

Poleward of 45-50 degrees (geomagnetic) observatory data are influenced significantly by auroral ionospheric current systems, invalidating the simplifying zonal dipole source assumption traditionally used for long period (T > 2 days) geomagnetic induction studies. Previous efforts to use these data to obtain the global electrical conductivity distribution in Earth's mantle have omitted high-latitude sites (further thinning an already sparse dataset) and/or corrected the affected transfer functions using a highly simplified model of auroral source currents. Although these strategies are partly effective, there remain clear suggestions of source contamination in most recent 3D inverse solutions - specifically, bands of conductive features are found near auroral latitudes. We report on a new approach to this problem, based on adjusting both external field structure and 3D Earth conductivity to fit observatory data. As an initial step towards full joint inversion we are using a two step procedure. In the first stage, we adopt a simplified conductivity model, with a thin-sheet of variable conductance (to represent the oceans) overlying a 1D Earth, to invert observed magnetic fields for external source spatial structure. Input data for this inversion are obtained from frequency domain principal components (PC) analysis of geomagnetic observatory hourly mean values. To make this (essentially linear) inverse problem well-posed we regularize using covariances for source field structure that are consistent with well-established properties of auroral ionospheric (and magnetospheric) current systems, and basic physics of the EM fields. In the second stage, we use a 3D finite difference inversion code, with source fields estimated from the first stage, to further fit the observatory PC modes. We incorporate higher latitude data into the inversion, and maximize the amount of available information by directly inverting the magnetic field components of the PC modes, instead of transfer functions such as C-responses used previously. Recent improvements in accuracy and speed of the forward and inverse finite difference codes (a secondary field formulation and parallelization over frequencies) allow us to use finer computational grid for inversion, and thus to model finer scale features, making full use of the expanded data set. Overall, our approach presents an improvement over earlier observatory data interpretation techniques, making better use of the available data, and allowing to explore the trade-offs between complications in source structure, and heterogeneities in mantle conductivity. We will also report on progress towards applying the same approach to simultaneous source/conductivity inversion of shorter period observatory data, focusing especially on the daily variation band.

[Bare Soil Moisture Inversion Model Based on Visible-Shortwave Infrared Reflectance].

PubMed

Zheng, Xiao-po; Sun, Yue-jun; Qin, Qi-ming; Ren, Hua-zhong; Gao, Zhong-ling; Wu, Ling; Meng, Qing-ye; Wang, Jin-liang; Wang, Jian-hua

2015-08-01

Soil is the loose solum of land surface that can support plants. It consists of minerals, organics, atmosphere, moisture, microbes, et al. Among its complex compositions, soil moisture varies greatly. Therefore, the fast and accurate inversion of soil moisture by using remote sensing is very crucial. In order to reduce the influence of soil type on the retrieval of soil moisture, this paper proposed a normalized spectral slope and absorption index named NSSAI to estimate soil moisture. The modeling of the new index contains several key steps: Firstly, soil samples with different moisture level were artificially prepared, and soil reflectance spectra was consequently measured using spectroradiometer produced by ASD Company. Secondly, the moisture absorption spectral feature located at shortwave wavelengths and the spectral slope of visible wavelengths were calculated after analyzing the regular spectral feature change patterns of different soil at different moisture conditions. Then advantages of the two features at reducing soil types' effects was synthesized to build the NSSAI. Thirdly, a linear relationship between NSSAI and soil moisture was established. The result showed that NSSAI worked better (correlation coefficient is 0.93) than most of other traditional methods in soil moisture extraction. It can weaken the influences caused by soil types at different moisture levels and improve the bare soil moisture inversion accuracy.

ON THE GEOSTATISTICAL APPROACH TO THE INVERSE PROBLEM. (R825689C037)

EPA Science Inventory

Abstract

The geostatistical approach to the inverse problem is discussed with emphasis on the importance of structural analysis. Although the geostatistical approach is occasionally misconstrued as mere cokriging, in fact it consists of two steps: estimation of statist...

The Relationship Between Non-Symbolic Multiplication and Division in Childhood

PubMed Central

McCrink, Koleen; Shafto, Patrick; Barth, Hilary

2016-01-01

Children without formal education in addition and subtraction are able to perform multi-step operations over an approximate number of objects. Further, their performance improves when solving approximate (but not exact) addition and subtraction problems that allow for inversion as a shortcut (e.g., a + b − b = a). The current study examines children’s ability to perform multi-step operations, and the potential for an inversion benefit, for the operations of approximate, non-symbolic multiplication and division. Children were trained to compute a multiplication and division scaling factor (*2 or /2, *4 or /4), and then tested on problems that combined two of these factors in a way that either allowed for an inversion shortcut (e.g., 8 * 4 / 4) or did not (e.g., 8 * 4 / 2). Children’s performance was significantly better than chance for all scaling factors during training, and they successfully computed the outcomes of the multi-step testing problems. They did not exhibit a performance benefit for problems with the a * b / b structure, suggesting they did not draw upon inversion reasoning as a logical shortcut to help them solve the multi-step test problems. PMID:26880261

On the Development of Multi-Step Inverse FEM with Shell Model

NASA Astrophysics Data System (ADS)

Huang, Y.; Du, R.

2005-08-01

The inverse or one-step finite element approach is increasingly used in the sheet metal stamping industry to predict strain distribution and the initial blank shape in the preliminary design stage. Based on the existing theory, there are two types of method: one is based on the principle of virtual work and the other is based on the principle of extreme work. Much research has been conducted to improve the accuracy of simulation results. For example, based on the virtual work principle, Batoz et al. developed a new method using triangular DKT shell elements. In this new method, the bending and unbending effects are considered. Based on the principle of extreme work, Majlessi and et al. proposed the multi-step inverse approach with membrane elements and applied it to an axis-symmetric part. Lee and et al. presented an axis-symmetric shell element model to solve the similar problem. In this paper, a new multi-step inverse method is introduced with no limitation on the workpiece shape. It is a shell element model based on the virtual work principle. The new method is validated by means of comparing to the commercial software system (PAMSTAMP®). The comparison results indicate that the accuracy is good.

Estimation of biological parameters of marine organisms using linear and nonlinear acoustic scattering model-based inversion methods.

PubMed

Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H

2016-05-01

The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.

Distorted Born iterative T-matrix method for inversion of CSEM data in anisotropic media

NASA Astrophysics Data System (ADS)

Jakobsen, Morten; Tveit, Svenn

2018-05-01

We present a direct iterative solutions to the nonlinear controlled-source electromagnetic (CSEM) inversion problem in the frequency domain, which is based on a volume integral equation formulation of the forward modelling problem in anisotropic conductive media. Our vectorial nonlinear inverse scattering approach effectively replaces an ill-posed nonlinear inverse problem with a series of linear ill-posed inverse problems, for which there already exist efficient (regularized) solution methods. The solution update the dyadic Green's function's from the source to the scattering-volume and from the scattering-volume to the receivers, after each iteration. The T-matrix approach of multiple scattering theory is used for efficient updating of all dyadic Green's functions after each linearized inversion step. This means that we have developed a T-matrix variant of the Distorted Born Iterative (DBI) method, which is often used in the acoustic and electromagnetic (medical) imaging communities as an alternative to contrast-source inversion. The main advantage of using the T-matrix approach in this context, is that it eliminates the need to perform a full forward simulation at each iteration of the DBI method, which is known to be consistent with the Gauss-Newton method. The T-matrix allows for a natural domain decomposition, since in the sense that a large model can be decomposed into an arbitrary number of domains that can be treated independently and in parallel. The T-matrix we use for efficient model updating is also independent of the source-receiver configuration, which could be an advantage when performing fast-repeat modelling and time-lapse inversion. The T-matrix is also compatible with the use of modern renormalization methods that can potentially help us to reduce the sensitivity of the CSEM inversion results on the starting model. To illustrate the performance and potential of our T-matrix variant of the DBI method for CSEM inversion, we performed a numerical experiments based on synthetic CSEM data associated with 2D VTI and 3D orthorombic model inversions. The results of our numerical experiment suggest that the DBIT method for inversion of CSEM data in anisotropic media is both accurate and efficient.

An arbitrary-order staggered time integrator for the linear acoustic wave equation

NASA Astrophysics Data System (ADS)

Lee, Jaejoon; Park, Hyunseo; Park, Yoonseo; Shin, Changsoo

2018-02-01

We suggest a staggered time integrator whose order of accuracy can arbitrarily be extended to solve the linear acoustic wave equation. A strategy to select the appropriate order of accuracy is also proposed based on the error analysis that quantitatively predicts the truncation error of the numerical solution. This strategy not only reduces the computational cost several times, but also allows us to flexibly set the modelling parameters such as the time step length, grid interval and P-wave speed. It is demonstrated that the proposed method can almost eliminate temporal dispersive errors during long term simulations regardless of the heterogeneity of the media and time step lengths. The method can also be successfully applied to the source problem with an absorbing boundary condition, which is frequently encountered in the practical usage for the imaging algorithms or the inverse problems.

Two-Port Representation of a Linear Transmission Line in the Time Domain.

DTIC Science & Technology

1980-01-01

which is a rational function. To use the Prony procedure it is necessary to inverse transform the admittance functions. For the transmission line, most...impulse is a constant, the inverse transform of Y0(s) contains an impulse of value ._ Therefore, if we were to numerically inverse transform Yo(s), we...would remove this im- pulse and inverse transform Y-(S) Y (S) 1’LR+C~ (23) The prony procedure would then be applied to the result. Of course, an impulse

Restricted DCJ-indel model: sorting linear genomes with DCJ and indels

PubMed Central

2012-01-01

Background The double-cut-and-join (DCJ) is a model that is able to efficiently sort a genome into another, generalizing the typical mutations (inversions, fusions, fissions, translocations) to which genomes are subject, but allowing the existence of circular chromosomes at the intermediate steps. In the general model many circular chromosomes can coexist in some intermediate step. However, when the compared genomes are linear, it is more plausible to use the so-called restricted DCJ model, in which we proceed the reincorporation of a circular chromosome immediately after its creation. These two consecutive DCJ operations, which create and reincorporate a circular chromosome, mimic a transposition or a block-interchange. When the compared genomes have the same content, it is known that the genomic distance for the restricted DCJ model is the same as the distance for the general model. If the genomes have unequal contents, in addition to DCJ it is necessary to consider indels, which are insertions and deletions of DNA segments. Linear time algorithms were proposed to compute the distance and to find a sorting scenario in a general, unrestricted DCJ-indel model that considers DCJ and indels. Results In the present work we consider the restricted DCJ-indel model for sorting linear genomes with unequal contents. We allow DCJ operations and indels with the following constraint: if a circular chromosome is created by a DCJ, it has to be reincorporated in the next step (no other DCJ or indel can be applied between the creation and the reincorporation of a circular chromosome). We then develop a sorting algorithm and give a tight upper bound for the restricted DCJ-indel distance. Conclusions We have given a tight upper bound for the restricted DCJ-indel distance. The question whether this bound can be reduced so that both the general and the restricted DCJ-indel distances are equal remains open. PMID:23281630

Imaging metallic samples using electrical capacitance tomography: forward modelling and reconstruction algorithms

NASA Astrophysics Data System (ADS)

Hosani, E. Al; Zhang, M.; Abascal, J. F. P. J.; Soleimani, M.

2016-11-01

Electrical capacitance tomography (ECT) is an imaging technology used to reconstruct the permittivity distribution within the sensing region. So far, ECT has been primarily used to image non-conductive media only, since if the conductivity of the imaged object is high, the capacitance measuring circuit will be almost shortened by the conductivity path and a clear image cannot be produced using the standard image reconstruction approaches. This paper tackles the problem of imaging metallic samples using conventional ECT systems by investigating the two main aspects of image reconstruction algorithms, namely the forward problem and the inverse problem. For the forward problem, two different methods to model the region of high conductivity in ECT is presented. On the other hand, for the inverse problem, three different algorithms to reconstruct the high contrast images are examined. The first two methods are the linear single step Tikhonov method and the iterative total variation regularization method, and use two sets of ECT data to reconstruct the image in time difference mode. The third method, namely the level set method, uses absolute ECT measurements and was developed using a metallic forward model. The results indicate that the applications of conventional ECT systems can be extended to metal samples using the suggested algorithms and forward model, especially using a level set algorithm to find the boundary of the metal.

The shifting zoom: new possibilities for inverse scattering on electrically large domains

NASA Astrophysics Data System (ADS)

Persico, Raffaele; Ludeno, Giovanni; Soldovieri, Francesco; De Coster, Alberic; Lambot, Sebastien

2017-04-01

Inverse scattering is a subject of great interest in diagnostic problems, which are in their turn of interest for many applicative problems as investigation of cultural heritage, characterization of foundations or subservices, identification of unexploded ordnances and so on [1-4]. In particular, GPR data are usually focused by means of migration algorithms, essentially based on a linear approximation of the scattering phenomenon. Migration algorithms are popular because they are computationally efficient and do not require the inversion of a matrix, neither the calculation of the elements of a matrix. In fact, they are essentially based on the adjoint of the linearised scattering operator, which allows in the end to write the inversion formula as a suitably weighted integral of the data [5]. In particular, this makes a migration algorithm more suitable than a linear microwave tomography inversion algorithm for the reconstruction of an electrically large investigation domain. However, this computational challenge can be overcome by making use of investigation domains joined side by side, as proposed e.g. in ref. [3]. This allows to apply a microwave tomography algorithm even to large investigation domains. However, the joining side by side of sequential investigation domains introduces a problem of limited (and asymmetric) maximum view angle with regard to the targets occurring close to the edges between two adjacent domains, or possibly crossing these edges. The shifting zoom is a method that allows to overcome this difficulty by means of overlapped investigation and observation domains [6-7]. It requires more sequential inversion with respect to adjacent investigation domains, but the really required extra-time is minimal because the matrix to be inverted is calculated ones and for all, as well as its singular value decomposition: what is repeated more time is only a fast matrix-vector multiplication. References [1] M. Pieraccini, L. Noferini, D. Mecatti, C. Atzeni, R. Persico, F. Soldovieri, Advanced Processing Techniques for Step-frequency Continuous-Wave Penetrating Radar: the Case Study of "Palazzo Vecchio" Walls (Firenze, Italy), Research on Nondestructive Evaluation, vol. 17, pp. 71-83, 2006. [2] N. Masini, R. Persico, E. Rizzo, A. Calia, M. T. Giannotta, G. Quarta, A. Pagliuca, "Integrated Techniques for Analysis and Monitoring of Historical Monuments: the case of S.Giovanni al Sepolcro in Brindisi (Southern Italy)." Near Surface Geophysics, vol. 8 (5), pp. 423-432, 2010. [3] E. Pettinelli, A. Di Matteo, E. Mattei, L. Crocco, F. Soldovieri, J. D. Redman, and A. P. Annan, "GPR response from buried pipes: Measurement on field site and tomographic reconstructions", IEEE Transactions on Geoscience and Remote Sensing, vol. 47, n. 8, 2639-2645, Aug. 2009. [4] O. Lopera, E. C. Slob, N. Milisavljevic and S. Lambot, "Filtering soil surface and antenna effects from GPR data to enhance landmine detection", IEEE Transactions on Geoscience and Remote Sensing, vol. 45, n. 3, pp.707-717, 2007. [5] R. Persico, "Introduction to Ground Penetrating Radar: Inverse Scattering and Data Processing". Wiley, 2014. [6] R. Persico, J. Sala, "The problem of the investigation domain subdivision in 2D linear inversions for large scale GPR data", IEEE Geoscience and Remote Sensing Letters, vol. 11, n. 7, pp. 1215-1219, doi 10.1109/LGRS.2013.2290008, July 2014. [7] R. Persico, F. Soldovieri, S. Lambot, Shifting zoom in 2D linear inversions performed on GPR data gathered along an electrically large investigation domain, Proc. 16th International Conference on Ground Penetrating Radar GPR2016, Honk-Kong, June 13-16, 2016

A surgical parallel continuum manipulator with a cable-driven grasper.

PubMed

Orekhov, Andrew L; Bryson, Caroline E; Till, John; Chung, Scotty; Rucker, D Caleb

2015-01-01

In this paper, we present the design, construction, and control of a six-degree-of-freedom (DOF), 12 mm diameter, parallel continuum manipulator with a 2-DOF, cable-driven grasper. This work is a proof-of-concept first step towards miniaturization of this type of manipulator design to provide increased dexterity and stability in confined-space surgical applications, particularly for endoscopic procedures. Our robotic system consists of six superelastic NiTi (Nitinol) tubes in a standard Stewart-Gough configuration and an end effector with 180 degree motion of its two jaws. Two Kevlar cables pass through the centers of the tube legs to actuate the end effector. A computationally efficient inverse kinematics model provides low-level control inputs to ten independent linear actuators, which drive the Stewart-Gough platform and end-effector actuation cables. We demonstrate the performance and feasibility of this design by conducting open-loop range-of-motion tests for our system.

Technical note: Avoiding the direct inversion of the numerator relationship matrix for genotyped animals in single-step genomic best linear unbiased prediction solved with the preconditioned conjugate gradient.

PubMed

Masuda, Y; Misztal, I; Legarra, A; Tsuruta, S; Lourenco, D A L; Fragomeni, B O; Aguilar, I

2017-01-01

This paper evaluates an efficient implementation to multiply the inverse of a numerator relationship matrix for genotyped animals () by a vector (). The computation is required for solving mixed model equations in single-step genomic BLUP (ssGBLUP) with the preconditioned conjugate gradient (PCG). The inverse can be decomposed into sparse matrices that are blocks of the sparse inverse of a numerator relationship matrix () including genotyped animals and their ancestors. The elements of were rapidly calculated with the Henderson's rule and stored as sparse matrices in memory. Implementation of was by a series of sparse matrix-vector multiplications. Diagonal elements of , which were required as preconditioners in PCG, were approximated with a Monte Carlo method using 1,000 samples. The efficient implementation of was compared with explicit inversion of with 3 data sets including about 15,000, 81,000, and 570,000 genotyped animals selected from populations with 213,000, 8.2 million, and 10.7 million pedigree animals, respectively. The explicit inversion required 1.8 GB, 49 GB, and 2,415 GB (estimated) of memory, respectively, and 42 s, 56 min, and 13.5 d (estimated), respectively, for the computations. The efficient implementation required <1 MB, 2.9 GB, and 2.3 GB of memory, respectively, and <1 sec, 3 min, and 5 min, respectively, for setting up. Only <1 sec was required for the multiplication in each PCG iteration for any data sets. When the equations in ssGBLUP are solved with the PCG algorithm, is no longer a limiting factor in the computations.

The advantages of logarithmically scaled data for electromagnetic inversion

NASA Astrophysics Data System (ADS)

Wheelock, Brent; Constable, Steven; Key, Kerry

2015-06-01

Non-linear inversion algorithms traverse a data misfit space over multiple iterations of trial models in search of either a global minimum or some target misfit contour. The success of the algorithm in reaching that objective depends upon the smoothness and predictability of the misfit space. For any given observation, there is no absolute form a datum must take, and therefore no absolute definition for the misfit space; in fact, there are many alternatives. However, not all misfit spaces are equal in terms of promoting the success of inversion. In this work, we appraise three common forms that complex data take in electromagnetic geophysical methods: real and imaginary components, a power of amplitude and phase, and logarithmic amplitude and phase. We find that the optimal form is logarithmic amplitude and phase. Single-parameter misfit curves of log-amplitude and phase data for both magnetotelluric and controlled-source electromagnetic methods are the smoothest of the three data forms and do not exhibit flattening at low model resistivities. Synthetic, multiparameter, 2-D inversions illustrate that log-amplitude and phase is the most robust data form, converging to the target misfit contour in the fewest steps regardless of starting model and the amount of noise added to the data; inversions using the other two data forms run slower or fail under various starting models and proportions of noise. It is observed that inversion with log-amplitude and phase data is nearly two times faster in converging to a solution than with other data types. We also assess the statistical consequences of transforming data in the ways discussed in this paper. With the exception of real and imaginary components, which are assumed to be Gaussian, all other data types do not produce an expected mean-squared misfit value of 1.00 at the true model (a common assumption) as the errors in the complex data become large. We recommend that real and imaginary data with errors larger than 10 per cent of the complex amplitude be withheld from a log-amplitude and phase inversion rather than retaining them with large error-bars.

An approach to multivariable control of manipulators

NASA Technical Reports Server (NTRS)

Seraji, H.

1987-01-01

The paper presents simple schemes for multivariable control of multiple-joint robot manipulators in joint and Cartesian coordinates. The joint control scheme consists of two independent multivariable feedforward and feedback controllers. The feedforward controller is the minimal inverse of the linearized model of robot dynamics and contains only proportional-double-derivative (PD2) terms - implying feedforward from the desired position, velocity and acceleration. This controller ensures that the manipulator joint angles track any reference trajectories. The feedback controller is of proportional-integral-derivative (PID) type and is designed to achieve pole placement. This controller reduces any initial tracking error to zero as desired and also ensures that robust steady-state tracking of step-plus-exponential trajectories is achieved by the joint angles. Simple and explicit expressions of computation of the feedforward and feedback gains are obtained based on the linearized model of robot dynamics. This leads to computationally efficient schemes for either on-line gain computation or off-line gain scheduling to account for variations in the linearized robot model due to changes in the operating point. The joint control scheme is extended to direct control of the end-effector motion in Cartesian space. Simulation results are given for illustration.

Kinematic inversion of the 2008 Mw7 Iwate-Miyagi (Japan) earthquake by two independent methods: Sensitivity and resolution analysis

NASA Astrophysics Data System (ADS)

Gallovic, Frantisek; Cirella, Antonella; Plicka, Vladimir; Piatanesi, Alessio

2013-04-01

On 14 June 2008, UTC 23:43, the border of Iwate and Miyagi prefectures was hit by an Mw7 reverse-fault type crustal earthquake. The event is known to have the largest ground acceleration observed to date (~4g), which was recorded at station IWTH25. We analyze observed strong motion data with the objective to image the event rupture process and the associated uncertainties. Two different slip inversion approaches are used, the difference between the two methods being only in the parameterization of the source model. To minimize mismodeling of the propagation effects we use crustal model obtained by full waveform inversion of aftershock records in the frequency range between 0.05-0.3 Hz. In the first method, based on linear formulation, the parameters are represented by samples of slip velocity functions along the (finely discretized) fault in a time window spanning the whole rupture duration. Such a source description is very general with no prior constraint on the nucleation point, rupture velocity, shape of the velocity function. Thus the inversion could resolve very general (unexpected) features of the rupture evolution, such as multiple rupturing, rupture-propagation reversals, etc. On the other hand, due to the relatively large number of model parameters, the inversion result is highly non-unique, with possibility of obtaining a biased solution. The second method is a non-linear global inversion technique, where each point on the fault can slip only once, following a prescribed functional form of the source time function. We invert simultaneously for peak slip velocity, slip angle, rise time and rupture time by allowing a given range of variability for each kinematic model parameter. For this reason, unlike to the linear inversion approach, the rupture process needs a smaller number of parameters to be retrieved, and is more constrained with a proper control on the allowed range of parameter values. In order to test the resolution and reliability of the retrieved models, we present a thorough analysis of the performance of the two inversion approaches. In fact, depending on the inversion strategy and the intrinsic 'non-uniqueness' of the inverse problem, the final slip maps and distribution of rupture onset times are generally different, sometimes even incompatible with each other. Great emphasis is devoted to the uncertainty estimate of both techniques. Thus we do not compare only the best fitting models, but their 'compatibility' in terms of the uncertainty limits.

Next Generation Robots for STEM Education andResearch at Huston Tillotson University

DTIC Science & Technology

2017-11-10

dynamics through the following command: roslaunch mtb_lab6_feedback_linearization gravity_compensation.launch Part B: Gravity Inversion : After...understood the system’s natural dynamics. roslaunch mtb_lab6_feedback_linearization gravity_compensation.launch Part B: Gravity Inversion ...is created using the following command: roslaunch mtb_lab6_feedback_linearization gravity_inversion.launch Gravity inversion is just one

Three-dimensional inversion of multisource array electromagnetic data

NASA Astrophysics Data System (ADS)

Tartaras, Efthimios

Three-dimensional (3-D) inversion is increasingly important for the correct interpretation of geophysical data sets in complex environments. To this effect, several approximate solutions have been developed that allow the construction of relatively fast inversion schemes. One such method that is fast and provides satisfactory accuracy is the quasi-linear (QL) approximation. It has, however, the drawback that it is source-dependent and, therefore, impractical in situations where multiple transmitters in different positions are employed. I have, therefore, developed a localized form of the QL approximation that is source-independent. This so-called localized quasi-linear (LQL) approximation can have a scalar, a diagonal, or a full tensor form. Numerical examples of its comparison with the full integral equation solution, the Born approximation, and the original QL approximation are given. The objective behind developing this approximation is to use it in a fast 3-D inversion scheme appropriate for multisource array data such as those collected in airborne surveys, cross-well logging, and other similar geophysical applications. I have developed such an inversion scheme using the scalar and diagonal LQL approximation. It reduces the original nonlinear inverse electromagnetic (EM) problem to three linear inverse problems. The first of these problems is solved using a weighted regularized linear conjugate gradient method, whereas the last two are solved in the least squares sense. The algorithm I developed provides the option of obtaining either smooth or focused inversion images. I have applied the 3-D LQL inversion to synthetic 3-D EM data that simulate a helicopter-borne survey over different earth models. The results demonstrate the stability and efficiency of the method and show that the LQL approximation can be a practical solution to the problem of 3-D inversion of multisource array frequency-domain EM data. I have also applied the method to helicopter-borne EM data collected by INCO Exploration over the Voisey's Bay area in Labrador, Canada. The results of the 3-D inversion successfully delineate the shallow massive sulfides and show that the method can produce reasonable results even in areas of complex geology and large resistivity contrasts.

Three dimensional inversion of magnetic survey data collected over kimberlite pipes in presence of remanent magnetization

NASA Astrophysics Data System (ADS)

Zhao, Pengzhi

Magnetic method is a common geophysical technique used to explore kimberlites. The analysis and interpretation of measured magnetic data provides the information of magnetic and geometric properties of potential kimberlite pipes. A crucial parameter of kimberlite magnetic interpretation is the remanent magnetization that dominates the classification of kimberlite. However, the measured magnetic data is the total field affected by the remanent magnetization and the susceptibility. The presence of remanent magnetization can pose severe challenges to the quantitative interpretation of magnetic data by skewing or laterally shifting magnetic anomalies relative to the subsurface source (Haney and Li, 2002). Therefore, identification of remanence effects and determination of remanent magnetization are important in magnetic data interpretation. This project presents a new method to determine the magnetic and geometric properties of kimberlite pipes in the presence of strong remanent magnetization. This method consists of two steps. The first step is to estimate the total magnetization and geometric properties of magnetic anomaly. The second step is to separate the remanent magnetization from the total magnetization. In the first step, a joint parametric inversion of total-field magnetic data and its analytic signal (derived from the survey data by Fourier transform method) is used. The algorithm of the joint inversion is based on the Gauss-Newton method and it is more stable and more accurate than the separate inversion method. It has been tested with synthetic data and applied to interpret the field data from the Lac de Gras, North-West Territories of Canada. The results of the synthetic examples and the field data applications show that joint inversion can recovers the total magnetization and geometric properties of magnetic anomaly with a good data fit and stable convergence. In the second step, the remanent magnetization is separated from the total magnetization by using a determined susceptibility. The susceptibility value is estimated by using the frequency domain electromagnetic data. The inversion method is achieved by a code, named “EM1DFM”, developed by University of British Columbia was designed to construct one of four types of 1D model, using any type of geophysical frequency domain loop-loop data with one of four variations of the inversion algorithm. The results show that the susceptibility of magnetic body is recovered, even if the depth and thickness are not well estimated. This two-step process provides a new way to determine magnetic and geometric properties of kimberlite pipes in the presence of strong remanent magnetization. The joint inversion of the total-field magnetic data and its analytic signal obtains the total magnetization and geometric properties. The frequency domain EM method provides the susceptibility. As a result, the remanent magnetization can be separated from the total magnetization accurately.

An algorithm for hyperspectral remote sensing of aerosols: 1. Development of theoretical framework

NASA Astrophysics Data System (ADS)

Hou, Weizhen; Wang, Jun; Xu, Xiaoguang; Reid, Jeffrey S.; Han, Dong

2016-07-01

This paper describes the first part of a series of investigations to develop algorithms for simultaneous retrieval of aerosol parameters and surface reflectance from a newly developed hyperspectral instrument, the GEOstationary Trace gas and Aerosol Sensor Optimization (GEO-TASO), by taking full advantage of available hyperspectral measurement information in the visible bands. We describe the theoretical framework of an inversion algorithm for the hyperspectral remote sensing of the aerosol optical properties, in which major principal components (PCs) for surface reflectance is assumed known, and the spectrally dependent aerosol refractive indices are assumed to follow a power-law approximation with four unknown parameters (two for real and two for imaginary part of refractive index). New capabilities for computing the Jacobians of four Stokes parameters of reflected solar radiation at the top of the atmosphere with respect to these unknown aerosol parameters and the weighting coefficients for each PC of surface reflectance are added into the UNified Linearized Vector Radiative Transfer Model (UNL-VRTM), which in turn facilitates the optimization in the inversion process. Theoretical derivations of the formulas for these new capabilities are provided, and the analytical solutions of Jacobians are validated against the finite-difference calculations with relative error less than 0.2%. Finally, self-consistency check of the inversion algorithm is conducted for the idealized green-vegetation and rangeland surfaces that were spectrally characterized by the U.S. Geological Survey digital spectral library. It shows that the first six PCs can yield the reconstruction of spectral surface reflectance with errors less than 1%. Assuming that aerosol properties can be accurately characterized, the inversion yields a retrieval of hyperspectral surface reflectance with an uncertainty of 2% (and root-mean-square error of less than 0.003), which suggests self-consistency in the inversion framework. The next step of using this framework to study the aerosol information content in GEO-TASO measurements is also discussed.

Conjecture: imines as unidirectional photodriven molecular motors-motional and constitutional dynamic devices.

PubMed

Lehn, Jean-Marie

2006-08-07

Compounds containing the C==N group, such as imines and their derivatives, may undergo syn-anti isomerization by two different routes: 1) photochemically, by out-of-plane rotation around the carbon-nitrogen double bond through a "perpendicular" form, and 2) thermally, by in-plane nitrogen inversion through a "linear" transition state. When the two interconversions occur in sequence, a full, closed process is accomplished, restoring the initial state of the system along two different steps. In a chiral imine-type compound, for example, with an asymmetric center next to the C==N function, photoinduced rotation may be expected to occur in one sense in preference to the opposite one. Thus, photoisomerization followed by thermal isomerization in a chiral imine compound generates unidirectional molecular motion. Generally, imine-type compounds represent unidirectional molecular photomotors converting light energy into mechanical motion. As they are also able to undergo exchange of the carbonyl and amine partners, they present constitutional dynamics. Thus, imine-type compounds are double dynamic, motional, and constitutional devices.

Whole head quantitative susceptibility mapping using a least-norm direct dipole inversion method.

PubMed

Sun, Hongfu; Ma, Yuhan; MacDonald, M Ethan; Pike, G Bruce

2018-06-15

A new dipole field inversion method for whole head quantitative susceptibility mapping (QSM) is proposed. Instead of performing background field removal and local field inversion sequentially, the proposed method performs dipole field inversion directly on the total field map in a single step. To aid this under-determined and ill-posed inversion process and obtain robust QSM images, Tikhonov regularization is implemented to seek the local susceptibility solution with the least-norm (LN) using the L-curve criterion. The proposed LN-QSM does not require brain edge erosion, thereby preserving the cerebral cortex in the final images. This should improve its applicability for QSM-based cortical grey matter measurement, functional imaging and venography of full brain. Furthermore, LN-QSM also enables susceptibility mapping of the entire head without the need for brain extraction, which makes QSM reconstruction more automated and less dependent on intermediate pre-processing methods and their associated parameters. It is shown that the proposed LN-QSM method reduced errors in a numerical phantom simulation, improved accuracy in a gadolinium phantom experiment, and suppressed artefacts in nine subjects, as compared to two-step and other single-step QSM methods. Measurements of deep grey matter and skull susceptibilities from LN-QSM are consistent with established reconstruction methods. Copyright © 2018 Elsevier Inc. All rights reserved.

Methods to approximate reliabilities in single-step genomic evaluation

USDA-ARS?s Scientific Manuscript database

Reliability of predictions from single-step genomic BLUP (ssGBLUP) can be calculated by inversion, but that is not feasible for large data sets. Two methods of approximating reliability were developed based on decomposition of a function of reliability into contributions from records, pedigrees, and...

The Modularized Software Package ASKI - Full Waveform Inversion Based on Waveform Sensitivity Kernels Utilizing External Seismic Wave Propagation Codes

NASA Astrophysics Data System (ADS)

Schumacher, F.; Friederich, W.

2015-12-01

We present the modularized software package ASKI which is a flexible and extendable toolbox for seismic full waveform inversion (FWI) as well as sensitivity or resolution analysis operating on the sensitivity matrix. It utilizes established wave propagation codes for solving the forward problem and offers an alternative to the monolithic, unflexible and hard-to-modify codes that have typically been written for solving inverse problems. It is available under the GPL at www.rub.de/aski. The Gauss-Newton FWI method for 3D-heterogeneous elastic earth models is based on waveform sensitivity kernels and can be applied to inverse problems at various spatial scales in both Cartesian and spherical geometries. The kernels are derived in the frequency domain from Born scattering theory as the Fréchet derivatives of linearized full waveform data functionals, quantifying the influence of elastic earth model parameters on the particular waveform data values. As an important innovation, we keep two independent spatial descriptions of the earth model - one for solving the forward problem and one representing the inverted model updates. Thereby we account for the independent needs of spatial model resolution of forward and inverse problem, respectively. Due to pre-integration of the kernels over the (in general much coarser) inversion grid, storage requirements for the sensitivity kernels are dramatically reduced.ASKI can be flexibly extended to other forward codes by providing it with specific interface routines that contain knowledge about forward code-specific file formats and auxiliary information provided by the new forward code. In order to sustain flexibility, the ASKI tools must communicate via file output/input, thus large storage capacities need to be accessible in a convenient way. Storing the complete sensitivity matrix to file, however, permits the scientist full manual control over each step in a customized procedure of sensitivity/resolution analysis and full waveform inversion.

Inverse imaging of the breast with a material classification technique.

PubMed

Manry, C W; Broschat, S L

1998-03-01

In recent publications [Chew et al., IEEE Trans. Blomed. Eng. BME-9, 218-225 (1990); Borup et al., Ultrason. Imaging 14, 69-85 (1992)] the inverse imaging problem has been solved by means of a two-step iterative method. In this paper, a third step is introduced for ultrasound imaging of the breast. In this step, which is based on statistical pattern recognition, classification of tissue types and a priori knowledge of the anatomy of the breast are integrated into the iterative method. Use of this material classification technique results in more rapid convergence to the inverse solution--approximately 40% fewer iterations are required--as well as greater accuracy. In addition, tumors are detected early in the reconstruction process. Results for reconstructions of a simple two-dimensional model of the human breast are presented. These reconstructions are extremely accurate when system noise and variations in tissue parameters are not too great. However, for the algorithm used, degradation of the reconstructions and divergence from the correct solution occur when system noise and variations in parameters exceed threshold values. Even in this case, however, tumors are still identified within a few iterations.

Observer-dependent sign inversions of polarization singularities.

PubMed

Freund, Isaac

2014-10-15

We describe observer-dependent sign inversions of the topological charges of vector field polarization singularities: C points (points of circular polarization), L points (points of linear polarization), and two virtually unknown singularities we call γ(C) and α(L) points. In all cases, the sign of the charge seen by an observer can change as she changes the direction from which she views the singularity. Analytic formulas are given for all C and all L point sign inversions.

Informativeness of Wind Data in Linear Madden-Julian Oscillation Prediction

DTIC Science & Technology

2016-08-15

Linear inverse models (LIMs) are used to explore predictability and information content of the Madden–Julian Oscillation (MJO). Hindcast skill for...mostly at the largest scales, adds 1–2 days of skill. Keywords: linear inverse modeling; Madden–Julian Oscillation; sub-seasonal prediction 1...tion that may reflect on the MJO’s incompletely under- stood dynamics. Cavanaugh et al. (2014, hereafter C14) explored the skill of linear inverse

[Determinants of pride and shame: outcome, expected success and attribution].

PubMed

Schützwohl, A

1991-01-01

In two experiments we investigated the relationship between subjective probability of success and pride and shame. According to Atkinson (1957), pride (the incentive of success) is an inverse linear function of the probability of success, shame (the incentive of failure) being a negative linear function. Attribution theory predicts an inverse U-shaped relationship between subjective probability of success and pride and shame. The results presented here are at variance with both theories: Pride and shame do not vary with subjective probability of success. However, pride and shame are systematically correlated with internal attributions of action outcome.

Combining experimental techniques with non-linear numerical models to assess the sorption of pesticides on soils

NASA Astrophysics Data System (ADS)

Magga, Zoi; Tzovolou, Dimitra N.; Theodoropoulou, Maria A.; Tsakiroglou, Christos D.

2012-03-01

The risk assessment of groundwater pollution by pesticides may be based on pesticide sorption and biodegradation kinetic parameters estimated with inverse modeling of datasets from either batch or continuous flow soil column experiments. In the present work, a chemical non-equilibrium and non-linear 2-site sorption model is incorporated into solute transport models to invert the datasets of batch and soil column experiments, and estimate the kinetic sorption parameters for two pesticides: N-phosphonomethyl glycine (glyphosate) and 2,4-dichlorophenoxy-acetic acid (2,4-D). When coupling the 2-site sorption model with the 2-region transport model, except of the kinetic sorption parameters, the soil column datasets enable us to estimate the mass-transfer coefficients associated with solute diffusion between mobile and immobile regions. In order to improve the reliability of models and kinetic parameter values, a stepwise strategy that combines batch and continuous flow tests with adequate true-to-the mechanism analytical of numerical models, and decouples the kinetics of purely reactive steps of sorption from physical mass-transfer processes is required.

Spatial operator factorization and inversion of the manipulator mass matrix

NASA Technical Reports Server (NTRS)

Rodriguez, Guillermo; Kreutz-Delgado, Kenneth

1992-01-01

This paper advances two linear operator factorizations of the manipulator mass matrix. Embedded in the factorizations are many of the techniques that are regarded as very efficient computational solutions to inverse and forward dynamics problems. The operator factorizations provide a high-level architectural understanding of the mass matrix and its inverse, which is not visible in the detailed algorithms. They also lead to a new approach to the development of computer programs or organize complexity in robot dynamics.

Step-to-Step Ankle Inversion/Eversion Torque Modulation Can Reduce Effort Associated with Balance.

PubMed

Kim, Myunghee; Collins, Steven H

2017-01-01

Below-knee amputation is associated with higher energy expenditure during walking, partially due to difficulty maintaining balance. We previously found that once-per-step push-off work control can reduce balance-related effort, both in simulation and in experiments with human participants. Simulations also suggested that changing ankle inversion/eversion torque on each step, in response to changes in body state, could assist with balance. In this study, we investigated the effects of ankle inversion/eversion torque modulation on balance-related effort among amputees ( N = 5) using a multi-actuated ankle-foot prosthesis emulator. In stabilizing conditions, changes in ankle inversion/eversion torque were applied so as to counteract deviations in side-to-side center-of-mass acceleration at the moment of intact-limb toe off; higher acceleration toward the prosthetic limb resulted in a corrective ankle inversion torque during the ensuing stance phase. Destabilizing controllers had the opposite effect, and a zero gain controller made no changes to the nominal inversion/eversion torque. To separate the balance-related effects of step-to-step control from the potential effects of changes in average mechanics, average ankle inversion/eversion torque and prosthesis work were held constant across conditions. High-gain stabilizing control lowered metabolic cost by 13% compared to the zero gain controller ( p = 0.05). We then investigated individual responses to subject-specific stabilizing controllers following an enforced exploration period. Four of five participants experienced reduced metabolic rate compared to the zero gain controller (-15, -14, -11, -6, and +4%) an average reduction of 9% ( p = 0.05). Average prosthesis mechanics were unchanged across all conditions, suggesting that improvements in energy economy might have come from changes in step-to-step corrections related to balance. Step-to-step modulation of inversion/eversion torque could be used in new, active ankle-foot prostheses to reduce walking effort associated with maintaining balance.

Seismic waveform inversion using neural networks

NASA Astrophysics Data System (ADS)

De Wit, R. W.; Trampert, J.

2012-12-01

Full waveform tomography aims to extract all available information on Earth structure and seismic sources from seismograms. The strongly non-linear nature of this inverse problem is often addressed through simplifying assumptions for the physical theory or data selection, thus potentially neglecting valuable information. Furthermore, the assessment of the quality of the inferred model is often lacking. This calls for the development of methods that fully appreciate the non-linear nature of the inverse problem, whilst providing a quantification of the uncertainties in the final model. We propose to invert seismic waveforms in a fully non-linear way by using artificial neural networks. Neural networks can be viewed as powerful and flexible non-linear filters. They are very common in speech, handwriting and pattern recognition. Mixture Density Networks (MDN) allow us to obtain marginal posterior probability density functions (pdfs) of all model parameters, conditioned on the data. An MDN can approximate an arbitrary conditional pdf as a linear combination of Gaussian kernels. Seismograms serve as input, Earth structure parameters are the so-called targets and network training aims to learn the relationship between input and targets. The network is trained on a large synthetic data set, which we construct by drawing many random Earth models from a prior model pdf and solving the forward problem for each of these models, thus generating synthetic seismograms. As a first step, we aim to construct a 1D Earth model. Training sets are constructed using the Mineos package, which computes synthetic seismograms in a spherically symmetric non-rotating Earth by summing normal modes. We train a network on the body waveforms present in these seismograms. Once the network has been trained, it can be presented with new unseen input data, in our case the body waves in real seismograms. We thus obtain the posterior pdf which represents our final state of knowledge given the information in the training set and the real data.

Application of a stochastic inverse to the geophysical inverse problem

NASA Technical Reports Server (NTRS)

Jordan, T. H.; Minster, J. B.

1972-01-01

The inverse problem for gross earth data can be reduced to an undertermined linear system of integral equations of the first kind. A theory is discussed for computing particular solutions to this linear system based on the stochastic inverse theory presented by Franklin. The stochastic inverse is derived and related to the generalized inverse of Penrose and Moore. A Backus-Gilbert type tradeoff curve is constructed for the problem of estimating the solution to the linear system in the presence of noise. It is shown that the stochastic inverse represents an optimal point on this tradeoff curve. A useful form of the solution autocorrelation operator as a member of a one-parameter family of smoothing operators is derived.

Inverse-Micelle-Encapsulated Water-Enabled Bond Breaking of Dialkyl Diselenide/Disulfide: A Critical Step for Synthesizing High- Quality Gold Nanoparticles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zaluzhna, Oksana; Li, Ying; Allison, Thomas C.

2012-10-09

Inverse-micelle-encapsulated water formed in the two-phase Brust-Schiffrin method (BSM) synthesis of Au nanoparticles (NPs) is identified as essential for dialkyl diselenide/disulfide to react with the Au(III) complex in which the Se-Se/S-S bond is broken, leading to formation of higher-quality Au NPs.

3D Elastic Wavefield Tomography

NASA Astrophysics Data System (ADS)

Guasch, L.; Warner, M.; Stekl, I.; Umpleby, A.; Shah, N.

2010-12-01

Wavefield tomography, or waveform inversion, aims to extract the maximum information from seismic data by matching trace by trace the response of the solid earth to seismic waves using numerical modelling tools. Its first formulation dates from the early 80's, when Albert Tarantola developed a solid theoretical basis that is still used today with little change. Due to computational limitations, the application of the method to 3D problems has been unaffordable until a few years ago, and then only under the acoustic approximation. Although acoustic wavefield tomography is widely used, a complete solution of the seismic inversion problem requires that we account properly for the physics of wave propagation, and so must include elastic effects. We have developed a 3D tomographic wavefield inversion code that incorporates the full elastic wave equation. The bottle neck of the different implementations is the forward modelling algorithm that generates the synthetic data to be compared with the field seismograms as well as the backpropagation of the residuals needed to form the direction update of the model parameters. Furthermore, one or two extra modelling runs are needed in order to calculate the step-length. Our approach uses a FD scheme explicit time-stepping by finite differences that are 4th order in space and 2nd order in time, which is a 3D version of the one developed by Jean Virieux in 1986. We chose the time domain because an explicit time scheme is much less demanding in terms of memory than its frequency domain analogue, although the discussion of wich domain is more efficient still remains open. We calculate the parameter gradients for Vp and Vs by correlating the normal and shear stress wavefields respectively. A straightforward application would lead to the storage of the wavefield at all grid points at each time-step. We tackled this problem using two different approaches. The first one makes better use of resources for small models of dimension equal or less than 300x300x300 nodes, and it under-samples the wavefield reducing the number of stored time-steps by an order of magnitude. For bigger models the wavefield is stored only at the boundaries of the model and then re-injected while the residuals are backpropagated allowing to compute the correlation 'on the fly'. In terms of computational resource, the elastic code is an order of magnitude more demanding than the equivalent acoustic code. We have combined shared memory with distributed memory parallelisation using OpenMP and MPI respectively. Thus, we take advantage of the increasingly common multi-core architecture processors. We have successfully applied our inversion algorithm to different realistic complex 3D models. The models had non-linear relations between pressure and shear wave velocities. The shorter wavelengths of the shear waves improve the resolution of the images obtained with respect to a purely acoustic approach.

MO-F-CAMPUS-T-03: Continuous Dose Delivery with Gamma Knife Perfexion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghobadi,; Li, W; Chung, C

2015-06-15

Purpose: We propose continuous dose delivery techniques for stereotactic treatments delivered by Gamma Knife Perfexion using inverse treatment planning system that can be applied to various tumour sites in the brain. We test the accuracy of the plans on Perfexion’s planning system (GammaPlan) to ensure the obtained plans are viable. This approach introduces continuous dose delivery for Perefxion, as opposed to the currently employed step-and-shoot approaches, for different tumour sites. Additionally, this is the first realization of automated inverse planning on GammaPlan. Methods: The inverse planning approach is divided into two steps of identifying a quality path inside the target,more » and finding the best collimator composition for the path. To find a path, we select strategic regions inside the target volume and find a path that visits each region exactly once. This path is then passed to a mathematical model which finds the best combination of collimators and their durations. The mathematical model minimizes the dose spillage to the surrounding tissues while ensuring the prescribed dose is delivered to the target(s). Organs-at-risk and their corresponding allowable doses can also be added to the model to protect adjacent organs. Results: We test this approach on various tumour sizes and sites. The quality of the obtained treatment plans are comparable or better than forward plans and inverse plans that use step- and-shoot technique. The conformity indices in the obtained continuous dose delivery plans are similar to those of forward plans while the beam-on time is improved on average (see Table 1 in supporting document). Conclusion: We employ inverse planning for continuous dose delivery in Perfexion for brain tumours. The quality of the obtained plans is similar to forward and inverse plans that use conventional step-and-shoot technique. We tested the inverse plans on GammaPlan to verify clinical relevance. This research was partially supported by Elekta, Sweden (vendor of Gamma Knife Perfexion)« less

Offset-electrode profile acquisition strategy for electrical resistivity tomography

NASA Astrophysics Data System (ADS)

Robbins, Austin R.; Plattner, Alain

2018-04-01

We present an electrode layout strategy that allows electrical resistivity profiles to image the third dimension close to the profile plane. This "offset-electrode profile" approach involves laterally displacing electrodes away from the profile line in an alternating fashion and then inverting the resulting data using three-dimensional electrical resistivity tomography software. In our synthetic and field surveys, the offset-electrode method succeeds in revealing three-dimensional structures in the vicinity of the profile plane, which we could not achieve using three-dimensional inversions of linear profiles. We confirm and explain the limits of linear electrode profiles through a discussion of the three-dimensional sensitivity patterns: For a homogeneous starting model together with a linear electrode layout, all sensitivities remain symmetric with respect to the profile plane through each inversion step. This limitation can be overcome with offset-electrode layouts by breaking the symmetry pattern among the sensitivities. Thanks to freely available powerful three-dimensional resistivity tomography software and cheap modern computing power, the requirement for full three-dimensional calculations does not create a significant burden and renders the offset-electrode approach a cost-effective method. By offsetting the electrodes in an alternating pattern, as opposed to laying the profile out in a U-shape, we minimize shortening the profile length.

TOMO3D: 3-D joint refraction and reflection traveltime tomography parallel code for active-source seismic data—synthetic test

NASA Astrophysics Data System (ADS)

Meléndez, A.; Korenaga, J.; Sallarès, V.; Miniussi, A.; Ranero, C. R.

2015-10-01

We present a new 3-D traveltime tomography code (TOMO3D) for the modelling of active-source seismic data that uses the arrival times of both refracted and reflected seismic phases to derive the velocity distribution and the geometry of reflecting boundaries in the subsurface. This code is based on its popular 2-D version TOMO2D from which it inherited the methods to solve the forward and inverse problems. The traveltime calculations are done using a hybrid ray-tracing technique combining the graph and bending methods. The LSQR algorithm is used to perform the iterative regularized inversion to improve the initial velocity and depth models. In order to cope with an increased computational demand due to the incorporation of the third dimension, the forward problem solver, which takes most of the run time (˜90 per cent in the test presented here), has been parallelized with a combination of multi-processing and message passing interface standards. This parallelization distributes the ray-tracing and traveltime calculations among available computational resources. The code's performance is illustrated with a realistic synthetic example, including a checkerboard anomaly and two reflectors, which simulates the geometry of a subduction zone. The code is designed to invert for a single reflector at a time. A data-driven layer-stripping strategy is proposed for cases involving multiple reflectors, and it is tested for the successive inversion of the two reflectors. Layers are bound by consecutive reflectors, and an initial velocity model for each inversion step incorporates the results from previous steps. This strategy poses simpler inversion problems at each step, allowing the recovery of strong velocity discontinuities that would otherwise be smoothened.

A spectral domain method for remotely probing stratified media

NASA Technical Reports Server (NTRS)

Schaubert, D. H.; Mittra, R.

1977-01-01

The problem of remotely probing a stratified, lossless, dielectric medium is formulated using the spectral domain method of probing. The response of the medium to a spectrum of plane waves incident at various angles is used to invert the unknown profile. For TE polarization, the electric field satisfies a Helmholtz equation. The inverse problem is solved by means of a new representation for the wave function. The principal step in this inversion is solving a second kind Fredholm equation which is very amenable to numerical computations. Several examples are presented including some which indicate that the method can be used with experimentally obtained data. When the fields exhibit a surface wave behavior, a unique inversion can be obtained only if information about the magnetic field is also available. In this case, the inversion is accomplished by a two-step procedure which employs a formula of Jost and Kohn. Some examples are presented, and an approach which greatly shortens the computations without greatly deteriorating the results is discussed.

Solutions to inverse plume in a crosswind problem using a predictor - corrector method

NASA Astrophysics Data System (ADS)

Vanderveer, Joseph; Jaluria, Yogesh

2013-11-01

Investigation for minimalist solutions to the inverse convection problem of a plume in a crosswind has developed a predictor - corrector method. The inverse problem is to predict the strength and location of the plume with respect to a select few downstream sampling points. This is accomplished with the help of two numerical simulations of the domain at differing source strengths, allowing the generation of two inverse interpolation functions. These functions in turn are utilized by the predictor step to acquire the plume strength. Finally, the same interpolation functions with the corrections from the plume strength are used to solve for the plume location. Through optimization of the relative location of the sampling points, the minimum number of samples for accurate predictions is reduced to two for the plume strength and three for the plume location. After the optimization, the predictor-corrector method demonstrates global uniqueness of the inverse solution for all test cases. The solution error is less than 1% for both plume strength and plume location. The basic approach could be extended to other inverse convection transport problems, particularly those encountered in environmental flows.

Integration of Visual and Joint Information to Enable Linear Reaching Motions

NASA Astrophysics Data System (ADS)

Eberle, Henry; Nasuto, Slawomir J.; Hayashi, Yoshikatsu

2017-01-01

A new dynamics-driven control law was developed for a robot arm, based on the feedback control law which uses the linear transformation directly from work space to joint space. This was validated using a simulation of a two-joint planar robot arm and an optimisation algorithm was used to find the optimum matrix to generate straight trajectories of the end-effector in the work space. We found that this linear matrix can be decomposed into the rotation matrix representing the orientation of the goal direction and the joint relation matrix (MJRM) representing the joint response to errors in the Cartesian work space. The decomposition of the linear matrix indicates the separation of path planning in terms of the direction of the reaching motion and the synergies of joint coordination. Once the MJRM is numerically obtained, the feedfoward planning of reaching direction allows us to provide asymptotically stable, linear trajectories in the entire work space through rotational transformation, completely avoiding the use of inverse kinematics. Our dynamics-driven control law suggests an interesting framework for interpreting human reaching motion control alternative to the dominant inverse method based explanations, avoiding expensive computation of the inverse kinematics and the point-to-point control along the desired trajectories.

Secret Message Decryption: Group Consulting Projects Using Matrices and Linear Programming

ERIC Educational Resources Information Center

Gurski, Katharine F.

2009-01-01

We describe two short group projects for finite mathematics students that incorporate matrices and linear programming into fictional consulting requests presented as a letter to the students. The students are required to use mathematics to decrypt secret messages in one project involving matrix multiplication and inversion. The second project…

Assessing non-uniqueness: An algebraic approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasco, Don W.

Geophysical inverse problems are endowed with a rich mathematical structure. When discretized, most differential and integral equations of interest are algebraic (polynomial) in form. Techniques from algebraic geometry and computational algebra provide a means to address questions of existence and uniqueness for both linear and non-linear inverse problem. In a sense, the methods extend ideas which have proven fruitful in treating linear inverse problems.

Eikonal-Based Inversion of GPR Data from the Vaucluse Karst Aquifer

NASA Astrophysics Data System (ADS)

Yedlin, M. J.; van Vorst, D.; Guglielmi, Y.; Cappa, F.; Gaffet, S.

2009-12-01

In this paper, we present an easy-to-implement eikonal-based travel time inversion algorithm and apply it to borehole GPR measurement data obtained from a karst aquifer located in the Vaucluse in Provence. The boreholes are situated with a fault zone deep inside the aquifer, in the Laboratoire Souterrain à Bas Bruit (LSBB). The measurements were made using 250 MHz MALA RAMAC borehole GPR antennas. The inversion formulation is unique in its application of a fast-sweeping eikonal solver (Zhao [1]) to the minimization of an objective functional that is composed of a travel time misfit and a model-based regularization [2]. The solver is robust in the presence of large velocity contrasts, efficient, easy to implement, and does not require the use of a sorting algorithm. The computation of sensitivities, which are required for the inversion process, is achieved by tracing rays backward from receiver to source following the gradient of the travel time field [2]. A user wishing to implement this algorithm can opt to avoid the ray tracing step and simply perturb the model to obtain the required sensitivities. Despite the obvious computational inefficiency of such an approach, it is acceptable for 2D problems. The relationship between travel time and the velocity profile is non-linear, requiring an iterative approach to be used. At each iteration, a set of matrix equations is solved to determine the model update. As the inversion continues, the weighting of the regularization parameter is adjusted until an appropriate data misfit is obtained. The inversion results, shown in the attached image, are consistent with previously obtained geological structure. Future work will look at improving inversion resolution and incorporating other measurement methodologies, with the goal of providing useful data for groundwater analysis. References: [1] H. Zhao, “A fast sweeping method for Eikonal equations,” Mathematics of Computation, vol. 74, no. 250, pp. 603-627, 2004. [2] D. Aldridge and D. Oldenburg, “Two-dimensional tomographic inversion with finite-difference traveltimes,” Journal of Seismic Exploration, vol. 2, pp. 257-274, 1993. Recovered Permittivity Profiles

Bayesian linearized amplitude-versus-frequency inversion for quality factor and its application

NASA Astrophysics Data System (ADS)

Yang, Xinchao; Teng, Long; Li, Jingnan; Cheng, Jiubing

2018-06-01

We propose a straightforward attenuation inversion method by utilizing the amplitude-versus-frequency (AVF) characteristics of seismic data. A new linearized approximation equation of the angle and frequency dependent reflectivity in viscoelastic media is derived. We then use the presented equation to implement the Bayesian linear AVF inversion. The inversion result includes not only P-wave and S-wave velocities, and densities, but also P-wave and S-wave quality factors. Synthetic tests show that the AVF inversion surpasses the AVA inversion for quality factor estimation. However, a higher signal noise ratio (SNR) of data is necessary for the AVF inversion. To show its feasibility, we apply both the new Bayesian AVF inversion and conventional AVA inversion to a tight gas reservoir data in Sichuan Basin in China. Considering the SNR of the field data, a combination of AVF inversion for attenuation parameters and AVA inversion for elastic parameters is recommended. The result reveals that attenuation estimations could serve as a useful complement in combination with the AVA inversion results for the detection of tight gas reservoirs.

Stability diagrams for the surface patterns of GaN(0001bar) as a function of Schwoebel barrier height

NASA Astrophysics Data System (ADS)

Krzyżewski, Filip; Załuska-Kotur, Magdalena A.

2017-01-01

Height and type of Schwoebel barriers (direct or inverse) decides about the character of the surface instability. Different surface morphologies are presented. Step bunches, double steps, meanders, mounds and irregular patterns emerge at the surface as a result of step (Schwoebel) barriers at some temperature or miscut values. The study was carried out on the two-component kinetic Monte Carlo (kMC) model of GaN(0001bar) surface grown in nitrogen rich conditions. Diffusion of gallium adatoms over N-polar surface is slow and nitrogen adatoms are almost immobile. We show that in such conditions surfaces remain smooth when gallium adatoms diffuse in the presence of low inverse Schwoebel barrier. It is illustrated by adequate stability diagrams for surface morphologies.

Steady induction effects in geomagnetism. Part 1B: Geomagnetic estimation of steady surficial core motions: A non-linear inverse problem

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1993-01-01

The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.

Estimation of pseudo-2D shear-velocity section by inversion of high frequency surface waves

USGS Publications Warehouse

Luo, Y.; Liu, J.; Xia, J.; Xu, Y.; Liu, Q.

2006-01-01

A scheme to generate pseudo-2D shear-velocity sections with high horizontal resolution and low field cost by inversion of high frequency surface waves is presented. It contains six steps. The key step is the joint method of crossed correlation and phase shift scanning. This joint method chooses only two traces to generate image of dispersion curve. For Rayleigh-wave dispersion is most important for estimation of near-surface shear-wave velocity, it can effectively obtain reliable images of dispersion curves with a couple of traces. The result of a synthetic example shows the feasibility of this scheme. ?? 2005 Society of Exploration Geophysicists.

Regularized wave equation migration for imaging and data reconstruction

NASA Astrophysics Data System (ADS)

Kaplan, Sam T.

The reflection seismic experiment results in a measurement (reflection seismic data) of the seismic wavefield. The linear Born approximation to the seismic wavefield leads to a forward modelling operator that we use to approximate reflection seismic data in terms of a scattering potential. We consider approximations to the scattering potential using two methods: the adjoint of the forward modelling operator (migration), and regularized numerical inversion using the forward and adjoint operators. We implement two parameterizations of the forward modelling and migration operators: source-receiver and shot-profile. For both parameterizations, we find requisite Green's function using the split-step approximation. We first develop the forward modelling operator, and then find the adjoint (migration) operator by recognizing a Fredholm integral equation of the first kind. The resulting numerical system is generally under-determined, requiring prior information to find a solution. In source-receiver migration, the parameterization of the scattering potential is understood using the migration imaging condition, and this encourages us to apply sparse prior models to the scattering potential. To that end, we use both a Cauchy prior and a mixed Cauchy-Gaussian prior, finding better resolved estimates of the scattering potential than are given by the adjoint. In shot-profile migration, the parameterization of the scattering potential has its redundancy in multiple active energy sources (i.e. shots). We find that a smallest model regularized inverse representation of the scattering potential gives a more resolved picture of the earth, as compared to the simpler adjoint representation. The shot-profile parameterization allows us to introduce a joint inversion to further improve the estimate of the scattering potential. Moreover, it allows us to introduce a novel data reconstruction algorithm so that limited data can be interpolated/extrapolated. The linearized operators are expensive, encouraging their parallel implementation. For the source-receiver parameterization of the scattering potential this parallelization is non-trivial. Seismic data is typically corrupted by various types of noise. Sparse coding can be used to suppress noise prior to migration. It is a method that stems from information theory and that we apply to noise suppression in seismic data.

3D electromagnetic modelling of a TTI medium and TTI effects in inversion

NASA Astrophysics Data System (ADS)

Jaysaval, Piyoosh; Shantsev, Daniil; de la Kethulle de Ryhove, Sébastien

2016-04-01

We present a numerical algorithm for 3D electromagnetic (EM) forward modelling in conducting media with general electric anisotropy. The algorithm is based on the finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid, in which all components of the electric field are collocated but half a spatial step staggered with respect to the magnetic field components, which also are collocated. This leads to a system of linear equations that is solved using a stabilized biconjugate gradient method with a multigrid preconditioner. We validate the accuracy of the numerical results for layered and 3D tilted transverse isotropic (TTI) earth models representing typical scenarios used in the marine controlled-source EM method. It is then demonstrated that not taking into account the full anisotropy of the conductivity tensor can lead to misleading inversion results. For simulation data corresponding to a 3D model with a TTI anticlinal structure, a standard vertical transverse isotropic inversion is not able to image a resistor, while for a 3D model with a TTI synclinal structure the inversion produces a false resistive anomaly. If inversion uses the proposed forward solver that can handle TTI anisotropy, it produces resistivity images consistent with the true models.

Porosity Estimation By Artificial Neural Networks Inversion . Application to Algerian South Field

NASA Astrophysics Data System (ADS)

Eladj, Said; Aliouane, Leila; Ouadfeul, Sid-Ali

2017-04-01

One of the main geophysicist's current challenge is the discovery and the study of stratigraphic traps, this last is a difficult task and requires a very fine analysis of the seismic data. The seismic data inversion allows obtaining lithological and stratigraphic information for the reservoir characterization . However, when solving the inverse problem we encounter difficult problems such as: Non-existence and non-uniqueness of the solution add to this the instability of the processing algorithm. Therefore, uncertainties in the data and the non-linearity of the relationship between the data and the parameters must be taken seriously. In this case, the artificial intelligence techniques such as Artificial Neural Networks(ANN) is used to resolve this ambiguity, this can be done by integrating different physical properties data which requires a supervised learning methods. In this work, we invert the acoustic impedance 3D seismic cube using the colored inversion method, then, the introduction of the acoustic impedance volume resulting from the first step as an input of based model inversion method allows to calculate the Porosity volume using the Multilayer Perceptron Artificial Neural Network. Application to an Algerian South hydrocarbon field clearly demonstrate the power of the proposed processing technique to predict the porosity for seismic data, obtained results can be used for reserves estimation, permeability prediction, recovery factor and reservoir monitoring. Keywords: Artificial Neural Networks, inversion, non-uniqueness , nonlinear, 3D porosity volume, reservoir characterization .

Fast intersection detection algorithm for PC-based robot off-line programming

NASA Astrophysics Data System (ADS)

Fedrowitz, Christian H.

1994-11-01

This paper presents a method for fast and reliable collision detection in complex production cells. The algorithm is part of the PC-based robot off-line programming system of the University of Siegen (Ropsus). The method is based on a solid model which is managed by a simplified constructive solid geometry model (CSG-model). The collision detection problem is divided in two steps. In the first step the complexity of the problem is reduced in linear time. In the second step the remaining solids are tested for intersection. For this the Simplex algorithm, which is known from linear optimization, is used. It computes a point which is common to two convex polyhedra. The polyhedra intersect, if such a point exists. Regarding the simplified geometrical model of Ropsus the algorithm runs also in linear time. In conjunction with the first step a resultant collision detection algorithm is found which requires linear time in all. Moreover it computes the resultant intersection polyhedron using the dual transformation.

The Form of the Solutions of the Linear Integro-Differential Equations of Subsonic Aeroelasticity.

DTIC Science & Technology

1979-09-01

coefficients w (0) are given in Table 3; it V follows that, for T > 0 and (E - K v2) non-singular, the inverse transform of M- ) has the form, using (B-I) V...degree of freedom system by expanding )M- I in the form of equation (35), obtaining its inverse transform using the v -1results of Appendix A and hence...obtaining the inverse transform of M- l . The two-dimensional case, when the characteristic equation has a zero root, is not as simple. * Assuming all

High-resolution surface wave tomography of the European crust and uppermost mantle from ambient seismic noise

NASA Astrophysics Data System (ADS)

Lu, Yang; Stehly, Laurent; Paul, Anne; AlpArray Working Group

2018-05-01

Taking advantage of the large number of seismic stations installed in Europe, in particular in the greater Alpine region with the AlpArray experiment, we derive a new high-resolution 3-D shear-wave velocity model of the European crust and uppermost mantle from ambient noise tomography. The correlation of up to four years of continuous vertical-component seismic recordings from 1293 broadband stations (10° W-35° E, 30° N-75° N) provides Rayleigh wave group velocity dispersion data in the period band 5-150 s at more than 0.8 million virtual source-receiver pairs. Two-dimensional Rayleigh wave group velocity maps are estimated using adaptive parameterization to accommodate the strong heterogeneity of path coverage. A probabilistic 3-D shear-wave velocity model, including probability densities for the depth of layer boundaries and S-wave velocity values, is obtained by non-linear Bayesian inversion. A weighted average of the probabilistic model is then used as starting model for the linear inversion step, providing the final Vs model. The resulting S-wave velocity model and Moho depth are validated by comparison with previous geophysical studies. Although surface-wave tomography is weakly sensitive to layer boundaries, vertical cross-sections through our Vs model and the associated probability of presence of interfaces display striking similarities with reference controlled-source (CSS) and receiver-function sections across the Alpine belt. Our model even provides new structural information such as a ˜8 km Moho jump along the CSS ECORS-CROP profile that was not imaged by reflection data due to poor penetration across a heterogeneous upper crust. Our probabilistic and final shear wave velocity models have the potential to become new reference models of the European crust, both for crustal structure probing and geophysical studies including waveform modeling or full waveform inversion.

Correlation and simple linear regression.

PubMed

Eberly, Lynn E

2007-01-01

This chapter highlights important steps in using correlation and simple linear regression to address scientific questions about the association of two continuous variables with each other. These steps include estimation and inference, assessing model fit, the connection between regression and ANOVA, and study design. Examples in microbiology are used throughout. This chapter provides a framework that is helpful in understanding more complex statistical techniques, such as multiple linear regression, linear mixed effects models, logistic regression, and proportional hazards regression.

Direct Reconstruction of Two-Dimensional Currents in Thin Films from Magnetic-Field Measurements

NASA Astrophysics Data System (ADS)

Meltzer, Alexander Y.; Levin, Eitan; Zeldov, Eli

2017-12-01

An accurate determination of microscopic transport and magnetization currents is of central importance for the study of the electric properties of low-dimensional materials and interfaces, of superconducting thin films, and of electronic devices. Current distribution is usually derived from the measurement of the perpendicular component of the magnetic field above the surface of the sample, followed by numerical inversion of the Biot-Savart law. The inversion is commonly obtained by deriving the current stream function g , which is then differentiated in order to obtain the current distribution. However, this two-step procedure requires filtering at each step and, as a result, oversmooths the solution. To avoid this oversmoothing, we develop a direct procedure for inversion of the magnetic field that avoids use of the stream function. This approach provides enhanced accuracy of current reconstruction over a wide range of noise levels. We further introduce a reflection procedure that allows for the reconstruction of currents that cross the boundaries of the measurement window. The effectiveness of our approach is demonstrated by several numerical examples.

Viscoelastic property identification from waveform reconstruction

NASA Astrophysics Data System (ADS)

Leymarie, N.; Aristégui, C.; Audoin, B.; Baste, S.

2002-05-01

An inverse method is proposed for the determination of the viscoelastic properties of material plates from the plane-wave transmitted acoustic field. Innovations lie in a two-step inversion scheme based on the well-known maximum-likelihood principle with an analytic signal formulation. In addition, establishing the analytical formulations of the plate transmission coefficient we implement an efficient and slightly noise-sensitive process suited to both very thin plates and strongly dispersive media.

Comparison of dynamic treatment regimes via inverse probability weighting.

PubMed

Hernán, Miguel A; Lanoy, Emilie; Costagliola, Dominique; Robins, James M

2006-03-01

Appropriate analysis of observational data is our best chance to obtain answers to many questions that involve dynamic treatment regimes. This paper describes a simple method to compare dynamic treatment regimes by artificially censoring subjects and then using inverse probability weighting (IPW) to adjust for any selection bias introduced by the artificial censoring. The basic strategy can be summarized in four steps: 1) define two regimes of interest, 2) artificially censor individuals when they stop following one of the regimes of interest, 3) estimate inverse probability weights to adjust for the potential selection bias introduced by censoring in the previous step, 4) compare the survival of the uncensored individuals under each regime of interest by fitting an inverse probability weighted Cox proportional hazards model with the dichotomous regime indicator and the baseline confounders as covariates. In the absence of model misspecification, the method is valid provided data are available on all time-varying and baseline joint predictors of survival and regime discontinuation. We present an application of the method to compare the AIDS-free survival under two dynamic treatment regimes in a large prospective study of HIV-infected patients. The paper concludes by discussing the relative advantages and disadvantages of censoring/IPW versus g-estimation of nested structural models to compare dynamic regimes.

Forward and inverse solutions for Risley prism based on the Denavit-Hartenberg methodology

NASA Astrophysics Data System (ADS)

Beltran-Gonzalez, A.; Garcia-Torales, G.; Strojnik, M.; Flores, J. L.; Garcia-Luna, J. L.

2017-08-01

In this work forward and inverse solutions for two-element Risley prism for pointing and scanning beam systems are developed. A more efficient and faster algorithm is proposed to make an analogy of the Risley prism system compared with a robotic system with two degrees of freedom. This system of equations controls each Risley prism individually as a planar manipulator arm of two links. In order to evaluate the algorithm we implement it in a pointing system. We perform popular routines such as the linear, spiral and loops traces. Using forward and inverse solutions for two-element Risley prism it is also possible to point at coordinates specified by the user, provided they are within the pointer area of work area. Experimental results are showed as a validation of our proposal.

Seismic source parameters of the induced seismicity at The Geysers geothermal area, California, by a generalized inversion approach

NASA Astrophysics Data System (ADS)

Picozzi, Matteo; Oth, Adrien; Parolai, Stefano; Bindi, Dino; De Landro, Grazia; Amoroso, Ortensia

2017-04-01

The accurate determination of stress drop, seismic efficiency and how source parameters scale with earthquake size is an important for seismic hazard assessment of induced seismicity. We propose an improved non-parametric, data-driven strategy suitable for monitoring induced seismicity, which combines the generalized inversion technique together with genetic algorithms. In the first step of the analysis the generalized inversion technique allows for an effective correction of waveforms for the attenuation and site contributions. Then, the retrieved source spectra are inverted by a non-linear sensitivity-driven inversion scheme that allows accurate estimation of source parameters. We therefore investigate the earthquake source characteristics of 633 induced earthquakes (ML 2-4.5) recorded at The Geysers geothermal field (California) by a dense seismic network (i.e., 32 stations of the Lawrence Berkeley National Laboratory Geysers/Calpine surface seismic network, more than 17.000 velocity records). We find for most of the events a non-selfsimilar behavior, empirical source spectra that requires ωγ source model with γ > 2 to be well fitted and small radiation efficiency ηSW. All these findings suggest different dynamic rupture processes for smaller and larger earthquakes, and that the proportion of high frequency energy radiation and the amount of energy required to overcome the friction or for the creation of new fractures surface changes with the earthquake size. Furthermore, we observe also two distinct families of events with peculiar source parameters that, in one case suggests the reactivation of deep structures linked to the regional tectonics, while in the other supports the idea of an important role of steeply dipping fault in the fluid pressure diffusion.

Vacuum solutions of five dimensional Einstein equations generated by inverse scattering method. II. Production of the black ring solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tomizawa, Shinya; Nozawa, Masato

2006-06-15

We study vacuum solutions of five-dimensional Einstein equations generated by the inverse scattering method. We reproduce the black ring solution which was found by Emparan and Reall by taking the Euclidean Levi-Civita metric plus one-dimensional flat space as a seed. This transformation consists of two successive processes; the first step is to perform the three-solitonic transformation of the Euclidean Levi-Civita metric with one-dimensional flat space as a seed. The resulting metric is the Euclidean C-metric with extra one-dimensional flat space. The second is to perform the two-solitonic transformation by taking it as a new seed. Our result may serve asmore » a stepping stone to find new exact solutions in higher dimensions.« less

Pre-stack full-waveform inversion of multichannel seismic data to retrieve thermohaline ocean structure. Application to the Gulf of Cadiz (SW Iberia).

NASA Astrophysics Data System (ADS)

Dagnino, Daniel; Jiménez Tejero, Clara-Estela; Meléndez, Adrià; Gras, Clàudia; Sallarès, Valentí; Ranero, César R.

2016-04-01

This work demonstrates the feasibility to retrieve high-resolution models of oceanic physical parameters by means of 2D adjoint-state full-waveform inversion (FWI). The proposed method is applied to pre-stack multi-channel seismic (MCS) data acquired in the Gulf of Cadiz (SW Iberia) in the framework of the EU GO (Geophysical Oceanography) project in 2006. We first design and apply a specific data processing flow that allows reducing data noise without modifying trace amplitudes. This step is shown to be essential to obtain accurate results due to the low signal-to-noise ratio (SNR) of water layer reflections, which are typically three-to-four orders of magnitude weaker than those in solid earth. Second, we propose new techniques to improve the inversion results by reducing the artefacts appearing in the gradient and misfit as a consequence of the low SNR. We use a weight and filter operator to focus in the regions where the gradient is reliable. The source wavelet is then inverted together with the sound speed. We demonstrate the efficiency of the proposed method and inversion strategy retrieving a 2D sound speed model along a 50 km-long MCS profile collected in the Gulf of Cadiz during the GO experiment. In this region, the Mediterranean outflow entrains the Atlantic waters, creating a salinity complex thermohaline structure that can be measured by a difference in acoustic impedance. The inverted sound speed model have a resolution of 75m for the horizontal direction, which is two orders of magnitude better than the models obtained using conventional, probe-based oceanographic techniques. In a second step, temperature and salinity are derived from the sound speed by minimizing the difference between the inverted and the theoretical sound speed estimated using the thermodynamic equation of seawater (TEOS-10 software). To apply the TEOS-10 we first calculate a linear-fitting between temperature and salinity using regional data from the National Oceanic and Atmospheric Administration (NOAA) compilation. Pressure is calculated from latitude and depth. In the final step, salinity is calculated using the Temperature-Salinity relation and the previously estimated temperature. The comparison of the inverted temperature, salinity model with measures from XBT and CTD probes deployed simultaneously to the MCS data acquisition shows that the accuracy of the inverted models is ˜0.15°C for temperature and ˜0.1psu for salinity.

Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

PubMed Central

Zatsiorsky, Vladimir M.

2011-01-01

One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423–453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem. PMID:21311907

USING LINEAR AND POLYNOMIAL MODELS TO EXAMINE THE ENVIRONMENTAL STABILITY OF VIRUSES

EPA Science Inventory

The article presents the development of model equations for describing the fate of viral infectivity in environmental samples. Most of the models were based upon the use of a two-step linear regression approach. The first step employs regression of log base 10 transformed viral t...

Calculation of earthquake rupture histories using a hybrid global search algorithm: Application to the 1992 Landers, California, earthquake

USGS Publications Warehouse

Hartzell, S.; Liu, P.

1996-01-01

A method is presented for the simultaneous calculation of slip amplitudes and rupture times for a finite fault using a hybrid global search algorithm. The method we use combines simulated annealing with the downhill simplex method to produce a more efficient search algorithm then either of the two constituent parts. This formulation has advantages over traditional iterative or linearized approaches to the problem because it is able to escape local minima in its search through model space for the global optimum. We apply this global search method to the calculation of the rupture history for the Landers, California, earthquake. The rupture is modeled using three separate finite-fault planes to represent the three main fault segments that failed during this earthquake. Both the slip amplitude and the time of slip are calculated for a grid work of subfaults. The data used consist of digital, teleseismic P and SH body waves. Long-period, broadband, and short-period records are utilized to obtain a wideband characterization of the source. The results of the global search inversion are compared with a more traditional linear-least-squares inversion for only slip amplitudes. We use a multi-time-window linear analysis to relax the constraints on rupture time and rise time in the least-squares inversion. Both inversions produce similar slip distributions, although the linear-least-squares solution has a 10% larger moment (7.3 ?? 1026 dyne-cm compared with 6.6 ?? 1026 dyne-cm). Both inversions fit the data equally well and point out the importance of (1) using a parameterization with sufficient spatial and temporal flexibility to encompass likely complexities in the rupture process, (2) including suitable physically based constraints on the inversion to reduce instabilities in the solution, and (3) focusing on those robust rupture characteristics that rise above the details of the parameterization and data set.

On the inversion-indel distance

PubMed Central

2013-01-01

Background The inversion distance, that is the distance between two unichromosomal genomes with the same content allowing only inversions of DNA segments, can be computed thanks to a pioneering approach of Hannenhalli and Pevzner in 1995. In 2000, El-Mabrouk extended the inversion model to allow the comparison of unichromosomal genomes with unequal contents, thus insertions and deletions of DNA segments besides inversions. However, an exact algorithm was presented only for the case in which we have insertions alone and no deletion (or vice versa), while a heuristic was provided for the symmetric case, that allows both insertions and deletions and is called the inversion-indel distance. In 2005, Yancopoulos, Attie and Friedberg started a new branch of research by introducing the generic double cut and join (DCJ) operation, that can represent several genome rearrangements (including inversions). Among others, the DCJ model gave rise to two important results. First, it has been shown that the inversion distance can be computed in a simpler way with the help of the DCJ operation. Second, the DCJ operation originated the DCJ-indel distance, that allows the comparison of genomes with unequal contents, considering DCJ, insertions and deletions, and can be computed in linear time. Results In the present work we put these two results together to solve an open problem, showing that, when the graph that represents the relation between the two compared genomes has no bad components, the inversion-indel distance is equal to the DCJ-indel distance. We also give a lower and an upper bound for the inversion-indel distance in the presence of bad components. PMID:24564182

MARE2DEM: a 2-D inversion code for controlled-source electromagnetic and magnetotelluric data

NASA Astrophysics Data System (ADS)

Key, Kerry

2016-10-01

This work presents MARE2DEM, a freely available code for 2-D anisotropic inversion of magnetotelluric (MT) data and frequency-domain controlled-source electromagnetic (CSEM) data from onshore and offshore surveys. MARE2DEM parametrizes the inverse model using a grid of arbitrarily shaped polygons, where unstructured triangular or quadrilateral grids are typically used due to their ease of construction. Unstructured grids provide significantly more geometric flexibility and parameter efficiency than the structured rectangular grids commonly used by most other inversion codes. Transmitter and receiver components located on topographic slopes can be tilted parallel to the boundary so that the simulated electromagnetic fields accurately reproduce the real survey geometry. The forward solution is implemented with a goal-oriented adaptive finite-element method that automatically generates and refines unstructured triangular element grids that conform to the inversion parameter grid, ensuring accurate responses as the model conductivity changes. This dual-grid approach is significantly more efficient than the conventional use of a single grid for both the forward and inverse meshes since the more detailed finite-element meshes required for accurate responses do not increase the memory requirements of the inverse problem. Forward solutions are computed in parallel with a highly efficient scaling by partitioning the data into smaller independent modeling tasks consisting of subsets of the input frequencies, transmitters and receivers. Non-linear inversion is carried out with a new Occam inversion approach that requires fewer forward calls. Dense matrix operations are optimized for memory and parallel scalability using the ScaLAPACK parallel library. Free parameters can be bounded using a new non-linear transformation that leaves the transformed parameters nearly the same as the original parameters within the bounds, thereby reducing non-linear smoothing effects. Data balancing normalization weights for the joint inversion of two or more data sets encourages the inversion to fit each data type equally well. A synthetic joint inversion of marine CSEM and MT data illustrates the algorithm's performance and parallel scaling on up to 480 processing cores. CSEM inversion of data from the Middle America Trench offshore Nicaragua demonstrates a real world application. The source code and MATLAB interface tools are freely available at http://mare2dem.ucsd.edu.

On a comparison of two schemes in sequential data assimilation

NASA Astrophysics Data System (ADS)

Grishina, Anastasiia A.; Penenko, Alexey V.

2017-11-01

This paper is focused on variational data assimilation as an approach to mathematical modeling. Realization of the approach requires a sequence of connected inverse problems with different sets of observational data to be solved. Two variational data assimilation schemes, "implicit" and "explicit", are considered in the article. Their equivalence is shown and the numerical results are given on a basis of non-linear Robertson system. To avoid the "inverse problem crime" different schemes were used to produce synthetic measurement and to solve the data assimilation problem.

A Non-linear Geodetic Data Inversion Using ABIC for Slip Distribution on a Fault With an Unknown dip Angle

NASA Astrophysics Data System (ADS)

Fukahata, Y.; Wright, T. J.

2006-12-01

We developed a method of geodetic data inversion for slip distribution on a fault with an unknown dip angle. When fault geometry is unknown, the problem of geodetic data inversion is non-linear. A common strategy for obtaining slip distribution is to first determine the fault geometry by minimizing the square misfit under the assumption of a uniform slip on a rectangular fault, and then apply the usual linear inversion technique to estimate a slip distribution on the determined fault. It is not guaranteed, however, that the fault determined under the assumption of a uniform slip gives the best fault geometry for a spatially variable slip distribution. In addition, in obtaining a uniform slip fault model, we have to simultaneously determine the values of the nine mutually dependent parameters, which is a highly non-linear, complicated process. Although the inverse problem is non-linear for cases with unknown fault geometries, the non-linearity of the problems is actually weak, when we can assume the fault surface to be flat. In particular, when a clear fault trace is observed on the EarthOs surface after an earthquake, we can precisely estimate the strike and the location of the fault. In this case only the dip angle has large ambiguity. In geodetic data inversion we usually need to introduce smoothness constraints in order to compromise reciprocal requirements for model resolution and estimation errors in a natural way. Strictly speaking, the inverse problem with smoothness constraints is also non-linear, even if the fault geometry is known. The non-linearity has been dissolved by introducing AkaikeOs Bayesian Information Criterion (ABIC), with which the optimal value of the relative weight of observed data to smoothness constraints is objectively determined. In this study, using ABIC in determining the optimal dip angle, we dissolved the non-linearity of the inverse problem. We applied the method to the InSAR data of the 1995 Dinar, Turkey earthquake and obtained a much shallower dip angle than before.

40 CFR 59.653 - How do I test portable fuel containers?

Code of Federal Regulations, 2010 CFR

2010-07-01

.... Perform the following spout actuation and inversion steps at the end on the slosh testing, and at the end of the preconditioning soak. (i) Perform one complete actuation/inversion cycle per day for ten days. (ii) One actuation/inversion cycle consists of the following steps: (A) Remove and replace the spout...

Simultaneous source and attenuation reconstruction in SPECT using ballistic and single scattering data

NASA Astrophysics Data System (ADS)

Courdurier, M.; Monard, F.; Osses, A.; Romero, F.

2015-09-01

In medical single-photon emission computed tomography (SPECT) imaging, we seek to simultaneously obtain the internal radioactive sources and the attenuation map using not only ballistic measurements but also first-order scattering measurements and assuming a very specific scattering regime. The problem is modeled using the radiative transfer equation by means of an explicit non-linear operator that gives the ballistic and scattering measurements as a function of the radioactive source and attenuation distributions. First, by differentiating this non-linear operator we obtain a linearized inverse problem. Then, under regularity hypothesis for the source distribution and attenuation map and considering small attenuations, we rigorously prove that the linear operator is invertible and we compute its inverse explicitly. This allows proof of local uniqueness for the non-linear inverse problem. Finally, using the previous inversion result for the linear operator, we propose a new type of iterative algorithm for simultaneous source and attenuation recovery for SPECT based on the Neumann series and a Newton-Raphson algorithm.

One-step formation of w/o/w multiple emulsions stabilized by single amphiphilic block copolymers.

PubMed

Hong, Liangzhi; Sun, Guanqing; Cai, Jinge; Ngai, To

2012-02-07

Multiple emulsions are complex polydispersed systems in which both oil-in-water (O/W) and water-in-oil (W/O) emulsion exists simultaneously. They are often prepared accroding to a two-step process and commonly stabilized using a combination of hydrophilic and hydrophobic surfactants. Recently, some reports have shown that multiple emulsions can also be produced through one-step method with simultaneous occurrence of catastrophic and transitional phase inversions. However, these reported multiple emulsions need surfactant blends and are usually described as transitory or temporary systems. Herein, we report a one-step phase inversion process to produce water-in-oil-in-water (W/O/W) multiple emulsions stabilized solely by a synthetic diblock copolymer. Unlike the use of small molecule surfactant combinations, block copolymer stabilized multiple emulsions are remarkably stable and show the ability to separately encapsulate both polar and nonpolar cargos. The importance of the conformation of the copolymer surfactant at the interfaces with regards to the stability of the multiple emulsions using the one-step method is discussed.

A Method to Compute the Force Signature of a Body Impacting on a Linear Elastic Structure Using Fourier Analysis

DTIC Science & Technology

1982-09-17

FK * 1PK (2) The convolution of two transforms in time domain is the inverse transform of the product in frequency domain. Thus Rp(s) - Fgc() Ipg(*) (3...its inverse transform by: R,(r)- R,(a.)e’’ do. (5)2w In order to nuke use f a very accurate numerical method to ompute Fourier "ke and coil...taorm. When the inverse transform it tken by using Eq. (15), the cosine transform, because it converges faster than the sine transform refu-ft the

Theory and Simulation of an Inverse Free Electron Laser Experiment

NASA Astrophysics Data System (ADS)

Guo, S. K.; Bhattacharjee, A.; Fang, J. M.; Marshall, T. C.

1996-11-01

An experimental demonstration of the acceleration of electrons using a high power CO2 laser in an inverse free electron laser (IFEL) is underway at the Brookhaven National Laboratory. This experiment has generated data, which we are attempting to simulate. Included in our studies are such effects as: a low-loss metallic waveguide with a dielectric coating on the walls; multi-mode coupling due to self-consistent interaction between the electrons and the optical wave; space charge (which is significant at lower laser power); energy-spread of the electrons; arbitrary wiggler field profile; and slippage. Two types of wiggler profile have been considered: a linear taper of the period, and a step-taper of the period (the period is ~ 3cm, the field is ~ 1T, and the wiggler length is 47cm). The energy increment of the electrons ( ~ 1-2%) is analyzed in detail as a function of laser power, wiggler parameters, and the initial beam energy (40MeV). For laser power ~ 0.5GW, the predictions of the simulations are in good accord with experimental results. A matter currently under study is the discrepancy between theory and observations for the electron energy distribution observed at the end of the IFEL. This work is supported by the Department of Energy.

Educational Attainment and Adult Mortality in the United States: A Systematic Analysis of Functional Form*

PubMed Central

Montez, Jennifer Karas; Hummer, Robert A.; Hayward, Mark D.

2012-01-01

A vast literature has documented the inverse association between educational attainment and U.S. adult mortality risk, but given little attention to identifying the optimal functional form of the association. A theoretical explanation of the association hinges on our ability to empirically describe it. Using the 1979–1998 National Longitudinal Mortality Study for non-Hispanic white and black adults aged 25–100 years during the mortality follow-up period (N=1,008,215), we evaluated 13 functional forms across race-gender-age subgroups to determine which form(s) best captured the association. Results revealed that a functional form that includes a linear decline in mortality risk from 0–11 years of education, followed by a step-change reduction in mortality risk upon attainment of a high school diploma, at which point mortality risk resumes a linear decline but with a steeper slope than that prior to a high school diploma was generally preferred. The findings provide important clues for theoretical development of explanatory mechanisms: an explanation for the selected functional form may require integrating a credentialist perspective to explain the step-change reduction in mortality risk upon attainment of a high school diploma, with a human capital perspective to explain the linear declines before and after a high school diploma. PMID:22246797

GALA: group analysis leads to accuracy, a novel approach for solving the inverse problem in exploratory analysis of group MEG recordings

PubMed Central

Kozunov, Vladimir V.; Ossadtchi, Alexei

2015-01-01

Although MEG/EEG signals are highly variable between subjects, they allow characterizing systematic changes of cortical activity in both space and time. Traditionally a two-step procedure is used. The first step is a transition from sensor to source space by the means of solving an ill-posed inverse problem for each subject individually. The second is mapping of cortical regions consistently active across subjects. In practice the first step often leads to a set of active cortical regions whose location and timecourses display a great amount of interindividual variability hindering the subsequent group analysis. We propose Group Analysis Leads to Accuracy (GALA)—a solution that combines the two steps into one. GALA takes advantage of individual variations of cortical geometry and sensor locations. It exploits the ensuing variability in electromagnetic forward model as a source of additional information. We assume that for different subjects functionally identical cortical regions are located in close proximity and partially overlap and their timecourses are correlated. This relaxed similarity constraint on the inverse solution can be expressed within a probabilistic framework, allowing for an iterative algorithm solving the inverse problem jointly for all subjects. A systematic simulation study showed that GALA, as compared with the standard min-norm approach, improves accuracy of true activity recovery, when accuracy is assessed both in terms of spatial proximity of the estimated and true activations and correct specification of spatial extent of the activated regions. This improvement obtained without using any noise normalization techniques for both solutions, preserved for a wide range of between-subject variations in both spatial and temporal features of regional activation. The corresponding activation timecourses exhibit significantly higher similarity across subjects. Similar results were obtained for a real MEG dataset of face-specific evoked responses. PMID:25954141

THE SUCCESSIVE LINEAR ESTIMATOR: A REVISIT. (R827114)

EPA Science Inventory

This paper examines the theoretical basis of the successive linear estimator (SLE) that has been developed for the inverse problem in subsurface hydrology. We show that the SLE algorithm is a non-linear iterative estimator to the inverse problem. The weights used in the SLE al...

Stabilization of the Inverse Laplace Transform of Multiexponential Decay through Introduction of a Second Dimension

PubMed Central

Celik, Hasan; Bouhrara, Mustapha; Reiter, David A.; Fishbein, Kenneth W.; Spencer, Richard G.

2013-01-01

We propose a new approach to stabilizing the inverse Laplace transform of a multiexponential decay signal, a classically ill-posed problem, in the context of nuclear magnetic resonance relaxometry. The method is based on extension to a second, indirectly detected, dimension, that is, use of the established framework of two-dimensional relaxometry, followed by projection onto the desired axis. Numerical results for signals comprised of discrete T1 and T2 relaxation components and experiments performed on agarose gel phantoms are presented. We find markedly improved accuracy, and stability with respect to noise, as well as insensitivity to regularization in quantifying underlying relaxation components through use of the two-dimensional as compared to the one-dimensional inverse Laplace transform. This improvement is demonstrated separately for two different inversion algorithms, nonnegative least squares and non-linear least squares, to indicate the generalizability of this approach. These results may have wide applicability in approaches to the Fredholm integral equation of the first kind. PMID:24035004

Isotropic scalar image visualization of vector differential image data using the inverse Riesz transform.

PubMed

Larkin, Kieran G; Fletcher, Peter A

2014-03-01

X-ray Talbot moiré interferometers can now simultaneously generate two differential phase images of a specimen. The conventional approach to integrating differential phase is unstable and often leads to images with loss of visible detail. We propose a new reconstruction method based on the inverse Riesz transform. The Riesz approach is stable and the final image retains visibility of high resolution detail without directional bias. The outline Riesz theory is developed and an experimentally acquired X-ray differential phase data set is presented for qualitative visual appraisal. The inverse Riesz phase image is compared with two alternatives: the integrated (quantitative) phase and the modulus of the gradient of the phase. The inverse Riesz transform has the computational advantages of a unitary linear operator, and is implemented directly as a complex multiplication in the Fourier domain also known as the spiral phase transform.

Isotropic scalar image visualization of vector differential image data using the inverse Riesz transform

PubMed Central

Larkin, Kieran G.; Fletcher, Peter A.

2014-01-01

X-ray Talbot moiré interferometers can now simultaneously generate two differential phase images of a specimen. The conventional approach to integrating differential phase is unstable and often leads to images with loss of visible detail. We propose a new reconstruction method based on the inverse Riesz transform. The Riesz approach is stable and the final image retains visibility of high resolution detail without directional bias. The outline Riesz theory is developed and an experimentally acquired X-ray differential phase data set is presented for qualitative visual appraisal. The inverse Riesz phase image is compared with two alternatives: the integrated (quantitative) phase and the modulus of the gradient of the phase. The inverse Riesz transform has the computational advantages of a unitary linear operator, and is implemented directly as a complex multiplication in the Fourier domain also known as the spiral phase transform. PMID:24688823

Stability and uncertainty of finite-fault slip inversions: Application to the 2004 Parkfield, California, earthquake

USGS Publications Warehouse

Hartzell, S.; Liu, P.; Mendoza, C.; Ji, C.; Larson, K.M.

2007-01-01

The 2004 Parkfield, California, earthquake is used to investigate stability and uncertainty aspects of the finite-fault slip inversion problem with different a priori model assumptions. We utilize records from 54 strong ground motion stations and 13 continuous, 1-Hz sampled, geodetic instruments. Two inversion procedures are compared: a linear least-squares subfault-based methodology and a nonlinear global search algorithm. These two methods encompass a wide range of the different approaches that have been used to solve the finite-fault slip inversion problem. For the Parkfield earthquake and the inversion of velocity or displacement waveforms, near-surface related site response (top 100 m, frequencies above 1 Hz) is shown to not significantly affect the solution. Results are also insensitive to selection of slip rate functions with similar duration and to subfault size if proper stabilizing constraints are used. The linear and nonlinear formulations yield consistent results when the same limitations in model parameters are in place and the same inversion norm is used. However, the solution is sensitive to the choice of inversion norm, the bounds on model parameters, such as rake and rupture velocity, and the size of the model fault plane. The geodetic data set for Parkfield gives a slip distribution different from that of the strong-motion data, which may be due to the spatial limitation of the geodetic stations and the bandlimited nature of the strong-motion data. Cross validation and the bootstrap method are used to set limits on the upper bound for rupture velocity and to derive mean slip models and standard deviations in model parameters. This analysis shows that slip on the northwestern half of the Parkfield rupture plane from the inversion of strong-motion data is model dependent and has a greater uncertainty than slip near the hypocenter.

Single-step GBLUP using APY inverse for protein yield in US Holstein with a large number of genotyped animals

USDA-ARS?s Scientific Manuscript database

The objective of this study was to provide initial results in an application of single-step genomic BLUP with a genomic relationship matrix (G^-1APY) calculated using the Algorithm of Proven and Young (APY) to 305-day protein yield for US Holsteins. Two G^-1APY were tested; one was from 139,057 geno...

Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow

NASA Astrophysics Data System (ADS)

Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar

2014-09-01

We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the plate boundary can be partially recovered, especially with TV regularization.

Field theory of the inverse cascade in two-dimensional turbulence

NASA Astrophysics Data System (ADS)

Mayo, Jackson R.

2005-11-01

A two-dimensional fluid, stirred at high wave numbers and damped by both viscosity and linear friction, is modeled by a statistical field theory. The fluid’s long-distance behavior is studied using renormalization-group (RG) methods, as begun by Forster, Nelson, and Stephen [Phys. Rev. A 16, 732 (1977)]. With friction, which dissipates energy at low wave numbers, one expects a stationary inverse energy cascade for strong enough stirring. While such developed turbulence is beyond the quantitative reach of perturbation theory, a combination of exact and perturbative results suggests a coherent picture of the inverse cascade. The zero-friction fluctuation-dissipation theorem (FDT) is derived from a generalized time-reversal symmetry and implies zero anomalous dimension for the velocity even when friction is present. Thus the Kolmogorov scaling of the inverse cascade cannot be explained by any RG fixed point. The β function for the dimensionless coupling ĝ is computed through two loops; the ĝ3 term is positive, as already known, but the ĝ5 term is negative. An ideal cascade requires a linear β function for large ĝ , consistent with a Padé approximant to the Borel transform. The conjecture that the Kolmogorov spectrum arises from an RG flow through large ĝ is compatible with other results, but the accurate k-5/3 scaling is not explained and the Kolmogorov constant is not estimated. The lack of scale invariance should produce intermittency in high-order structure functions, as observed in some but not all numerical simulations of the inverse cascade. When analogous RG methods are applied to the one-dimensional Burgers equation using an FDT-preserving dimensional continuation, equipartition is obtained instead of a cascade—in agreement with simulations.

Full waveform time domain solutions for source and induced magnetotelluric and controlled-source electromagnetic fields using quasi-equivalent time domain decomposition and GPU parallelization

NASA Astrophysics Data System (ADS)

Imamura, N.; Schultz, A.

2015-12-01

Recently, a full waveform time domain solution has been developed for the magnetotelluric (MT) and controlled-source electromagnetic (CSEM) methods. The ultimate goal of this approach is to obtain a computationally tractable direct waveform joint inversion for source fields and earth conductivity structure in three and four dimensions. This is desirable on several grounds, including the improved spatial resolving power expected from use of a multitude of source illuminations of non-zero wavenumber, the ability to operate in areas of high levels of source signal spatial complexity and non-stationarity, etc. This goal would not be obtainable if one were to adopt the finite difference time-domain (FDTD) approach for the forward problem. This is particularly true for the case of MT surveys, since an enormous number of degrees of freedom are required to represent the observed MT waveforms across the large frequency bandwidth. It means that for FDTD simulation, the smallest time steps should be finer than that required to represent the highest frequency, while the number of time steps should also cover the lowest frequency. This leads to a linear system that is computationally burdensome to solve. We have implemented our code that addresses this situation through the use of a fictitious wave domain method and GPUs to speed up the computation time. We also substantially reduce the size of the linear systems by applying concepts from successive cascade decimation, through quasi-equivalent time domain decomposition. By combining these refinements, we have made good progress toward implementing the core of a full waveform joint source field/earth conductivity inverse modeling method. From results, we found the use of previous generation of CPU/GPU speeds computations by an order of magnitude over a parallel CPU only approach. In part, this arises from the use of the quasi-equivalent time domain decomposition, which shrinks the size of the linear system dramatically.

Kinematical synthesis of an inversion of the double linked fourbar for morphing wing applications

NASA Astrophysics Data System (ADS)

Aguirrebeitia, J.; Avilés, R.; Fernández, I.; Abasolo, M.

2013-03-01

This paper presents the kinematical features of an inversion of the double linked fourbar for morphing wing purposes. The structure of the mechanism is obtained using structural synthesis concepts, from an initial conceptual schematic. Then, kinematic characteristics as instant center of rotation, lock positions, dead point positions and uncertainty positions are derived for this mechanism in order to face the last step, the dimensional synthesis; in this sense, two kinds of dimensional synthesis are arranged to guide the wing along two positions, and to fulfill with the second one some aerodynamic and minimum actuation energy related issues.

Simultaneous elastic parameter inversion in 2-D/3-D TTI medium combined later arrival times

NASA Astrophysics Data System (ADS)

Bai, Chao-ying; Wang, Tao; Yang, Shang-bei; Li, Xing-wang; Huang, Guo-jiao

2016-04-01

Traditional traveltime inversion for anisotropic medium is, in general, based on a "weak" assumption in the anisotropic property, which simplifies both the forward part (ray tracing is performed once only) and the inversion part (a linear inversion solver is possible). But for some real applications, a general (both "weak" and "strong") anisotropic medium should be considered. In such cases, one has to develop a ray tracing algorithm to handle with the general (including "strong") anisotropic medium and also to design a non-linear inversion solver for later tomography. Meanwhile, it is constructive to investigate how much the tomographic resolution can be improved by introducing the later arrivals. For this motivation, we incorporated our newly developed ray tracing algorithm (multistage irregular shortest-path method) for general anisotropic media with a non-linear inversion solver (a damped minimum norm, constrained least squares problem with a conjugate gradient approach) to formulate a non-linear inversion solver for anisotropic medium. This anisotropic traveltime inversion procedure is able to combine the later (reflected) arrival times. Both 2-D/3-D synthetic inversion experiments and comparison tests show that (1) the proposed anisotropic traveltime inversion scheme is able to recover the high contrast anomalies and (2) it is possible to improve the tomographic resolution by introducing the later (reflected) arrivals, but not as expected in the isotropic medium, because the different velocity (qP, qSV and qSH) sensitivities (or derivatives) respective to the different elastic parameters are not the same but are also dependent on the inclination angle.

Solution of the symmetric eigenproblem AX=lambda BX by delayed division

NASA Technical Reports Server (NTRS)

Thurston, G. A.; Bains, N. J. C.

1986-01-01

Delayed division is an iterative method for solving the linear eigenvalue problem AX = lambda BX for a limited number of small eigenvalues and their corresponding eigenvectors. The distinctive feature of the method is the reduction of the problem to an approximate triangular form by systematically dropping quadratic terms in the eigenvalue lambda. The report describes the pivoting strategy in the reduction and the method for preserving symmetry in submatrices at each reduction step. Along with the approximate triangular reduction, the report extends some techniques used in the method of inverse subspace iteration. Examples are included for problems of varying complexity.

The Inverse Problem for Confined Aquifer Flow: Identification and Estimation With Extensions

NASA Astrophysics Data System (ADS)

Loaiciga, Hugo A.; MariñO, Miguel A.

1987-01-01

The contributions of this work are twofold. First, a methodology for estimating the elements of parameter matrices in the governing equation of flow in a confined aquifer is developed. The estimation techniques for the distributed-parameter inverse problem pertain to linear least squares and generalized least squares methods. The linear relationship among the known heads and unknown parameters of the flow equation provides the background for developing criteria for determining the identifiability status of unknown parameters. Under conditions of exact or overidentification it is possible to develop statistically consistent parameter estimators and their asymptotic distributions. The estimation techniques, namely, two-stage least squares and three stage least squares, are applied to a specific groundwater inverse problem and compared between themselves and with an ordinary least squares estimator. The three-stage estimator provides the closer approximation to the actual parameter values, but it also shows relatively large standard errors as compared to the ordinary and two-stage estimators. The estimation techniques provide the parameter matrices required to simulate the unsteady groundwater flow equation. Second, a nonlinear maximum likelihood estimation approach to the inverse problem is presented. The statistical properties of maximum likelihood estimators are derived, and a procedure to construct confidence intervals and do hypothesis testing is given. The relative merits of the linear and maximum likelihood estimators are analyzed. Other topics relevant to the identification and estimation methodologies, i.e., a continuous-time solution to the flow equation, coping with noise-corrupted head measurements, and extension of the developed theory to nonlinear cases are also discussed. A simulation study is used to evaluate the methods developed in this study.

Geometric and frequency EMI sounding of estuarine earthen flood defence embankments in Ireland using 1D inversion models

NASA Astrophysics Data System (ADS)

Viganotti, Matteo; Jackson, Ruth; Krahn, Hartmut; Dyer, Mark

2013-05-01

Earthen flood defence embankments are linear structures, raised above the flood plain, that are commonly used as flood defences in rural settings; these are often relatively old structures constructed using locally garnered material and of which little is known in terms of design and construction. Alarmingly, it is generally reported that a number of urban developments have expanded to previously rural areas; hence, acquiring knowledge about the flood defences protecting these areas has risen significantly in the agendas of basin and asset managers. This paper focusses, by reporting two case studies, on electromagnetic induction (EMI) methods that would efficiently complement routine visual inspections and would represent a first step to more detailed investigations. Evaluation of the results is presented by comparison with ERT profiles and intrusive investigation data. The EM data, acquired using a GEM-2 apparatus for frequency sounding and an EM-31 apparatus for geometrical sounding, has been handled using the prototype eGMS software tool, being developed by the eGMS international research consortium; the depth sounding data interpretation was assisted by 1D inversions obtained with the EM1DFM software developed by the University of British Columbia. Although both sounding methods showed some limitations, the models obtained were consistent with ERT models and the techniques were useful screening methods for the identification of areas of interest, such as material interfaces or potential seepage areas, within the embankment structure: 1D modelling improved the rapid assessment of earthen flood defence embankments in an estuarine environment; evidence that EMI sounding could play an important role as a monitoring tool or as a first step towards more detailed investigations.

Extended resolvent and inverse scattering with an application to KPI

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Prinari, B.

2003-08-01

We present in detail an extended resolvent approach for investigating linear problems associated to 2+1 dimensional integrable equations. Our presentation is based as an example on the nonstationary Schrödinger equation with potential being a perturbation of the one-soliton potential by means of a decaying two-dimensional function. Modification of the inverse scattering theory as well as properties of the Jost solutions and spectral data as follows from the resolvent approach are given.

Direct integration of the inverse Radon equation for X-ray computed tomography.

PubMed

Libin, E E; Chakhlov, S V; Trinca, D

2016-11-22

A new mathematical appoach using the inverse Radon equation for restoration of images in problems of linear two-dimensional x-ray tomography is formulated. In this approach, Fourier transformation is not used, and it gives the chance to create the practical computing algorithms having more reliable mathematical substantiation. Results of software implementation show that for especially for low number of projections, the described approach performs better than standard X-ray tomographic reconstruction algorithms.

Distributed Cooperative Optimal Control for Multiagent Systems on Directed Graphs: An Inverse Optimal Approach.

PubMed

Zhang, Huaguang; Feng, Tao; Yang, Guang-Hong; Liang, Hongjing

2015-07-01

In this paper, the inverse optimal approach is employed to design distributed consensus protocols that guarantee consensus and global optimality with respect to some quadratic performance indexes for identical linear systems on a directed graph. The inverse optimal theory is developed by introducing the notion of partial stability. As a result, the necessary and sufficient conditions for inverse optimality are proposed. By means of the developed inverse optimal theory, the necessary and sufficient conditions are established for globally optimal cooperative control problems on directed graphs. Basic optimal cooperative design procedures are given based on asymptotic properties of the resulting optimal distributed consensus protocols, and the multiagent systems can reach desired consensus performance (convergence rate and damping rate) asymptotically. Finally, two examples are given to illustrate the effectiveness of the proposed methods.

Modification of the nuclear landscape in the inverse problem framework using the generalized Bethe-Weizsäcker mass formula

NASA Astrophysics Data System (ADS)

Mavrodiev, S. Cht.; Deliyergiyev, M. A.

We formalized the nuclear mass problem in the inverse problem framework. This approach allows us to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. The inverse problem was formulated for the numerically generalized semi-empirical mass formula of Bethe and von Weizsäcker. It was solved in a step-by-step way based on the AME2012 nuclear database. The established parametrization describes the measured nuclear masses of 2564 isotopes with a maximum deviation less than 2.6MeV, starting from the number of protons and number of neutrons equal to 1. The explicit form of unknown functions in the generalized mass formula was discovered in a step-by-step way using the modified least χ2 procedure, that realized in the algorithms which were developed by Lubomir Aleksandrov to solve the nonlinear systems of equations via the Gauss-Newton method, lets us to choose the better one between two functions with same χ2. In the obtained generalized model, the corrections to the binding energy depend on nine proton (2, 8, 14, 20, 28, 50, 82, 108, 124) and ten neutron (2, 8, 14, 20, 28, 50, 82, 124, 152, 202) magic numbers as well on the asymptotic boundaries of their influence. The obtained results were compared with the predictions of other models.

Solution Methods for 3D Tomographic Inversion Using A Highly Non-Linear Ray Tracer

NASA Astrophysics Data System (ADS)

Hipp, J. R.; Ballard, S.; Young, C. J.; Chang, M.

2008-12-01

To develop 3D velocity models to improve nuclear explosion monitoring capability, we have developed a 3D tomographic modeling system that traces rays using an implementation of the Um and Thurber ray pseudo- bending approach, with full enforcement of Snell's Law in 3D at the major discontinuities. Due to the highly non-linear nature of the ray tracer, however, we are forced to substantially damp the inversion in order to converge on a reasonable model. Unfortunately the amount of damping is not known a priori and can significantly extend the number of calls of the computationally expensive ray-tracer and the least squares matrix solver. If the damping term is too small the solution step-size produces either an un-realistic model velocity change or places the solution in or near a local minimum from which extrication is nearly impossible. If the damping term is too large, convergence can be very slow or premature convergence can occur. Standard approaches involve running inversions with a suite of damping parameters to find the best model. A better solution methodology is to take advantage of existing non-linear solution techniques such as Levenberg-Marquardt (LM) or quasi-newton iterative solvers. In particular, the LM algorithm was specifically designed to find the minimum of a multi-variate function that is expressed as the sum of squares of non-linear real-valued functions. It has become a standard technique for solving non-linear least squared problems, and is widely adopted in a broad spectrum of disciplines, including the geosciences. At each iteration, the LM approach dynamically varies the level of damping to optimize convergence. When the current estimate of the solution is far from the ultimate solution LM behaves as a steepest decent method, but transitions to Gauss- Newton behavior, with near quadratic convergence, as the estimate approaches the final solution. We show typical linear solution techniques and how they can lead to local minima if the damping is set too low. We also describe the LM technique and show how it automatically determines the appropriate damping factor as it iteratively converges on the best solution. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04- 94AL85000.

[Application of ordinary Kriging method in entomologic ecology].

PubMed

Zhang, Runjie; Zhou, Qiang; Chen, Cuixian; Wang, Shousong

2003-01-01

Geostatistics is a statistic method based on regional variables and using the tool of variogram to analyze the spatial structure and the patterns of organism. In simulating the variogram within a great range, though optimal simulation cannot be obtained, the simulation method of a dialogue between human and computer can be used to optimize the parameters of the spherical models. In this paper, the method mentioned above and the weighted polynomial regression were utilized to simulate the one-step spherical model, the two-step spherical model and linear function model, and the available nearby samples were used to draw on the ordinary Kriging procedure, which provided a best linear unbiased estimate of the constraint of the unbiased estimation. The sum of square deviation between the estimating and measuring values of varying theory models were figured out, and the relative graphs were shown. It was showed that the simulation based on the two-step spherical model was the best simulation, and the one-step spherical model was better than the linear function model.

TG study of the Li0.4Fe2.4Zn0.2O4 ferrite synthesis

NASA Astrophysics Data System (ADS)

Lysenko, E. N.; Nikolaev, E. V.; Surzhikov, A. P.

2016-02-01

In this paper, the kinetic analysis of Li-Zn ferrite synthesis was studied using thermogravimetry (TG) method through the simultaneous application of non-linear regression to several measurements run at different heating rates (multivariate non-linear regression). Using TG-curves obtained for the four heating rates and Netzsch Thermokinetics software package, the kinetic models with minimal adjustable parameters were selected to quantitatively describe the reaction of Li-Zn ferrite synthesis. It was shown that the experimental TG-curves clearly suggest a two-step process for the ferrite synthesis and therefore a model-fitting kinetic analysis based on multivariate non-linear regressions was conducted. The complex reaction was described by a two-step reaction scheme consisting of sequential reaction steps. It is established that the best results were obtained using the Yander three-dimensional diffusion model at the first stage and Ginstling-Bronstein model at the second step. The kinetic parameters for lithium-zinc ferrite synthesis reaction were found and discussed.

Recursive inversion of externally defined linear systems

NASA Technical Reports Server (NTRS)

Bach, Ralph E., Jr.; Baram, Yoram

1988-01-01

The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problems of system identification and compensation.

A systematic linear space approach to solving partially described inverse eigenvalue problems

NASA Astrophysics Data System (ADS)

Hu, Sau-Lon James; Li, Haujun

2008-06-01

Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

On Impedance Spectroscopy of Supercapacitors

NASA Astrophysics Data System (ADS)

Uchaikin, V. V.; Sibatov, R. T.; Ambrozevich, A. S.

2016-10-01

Supercapacitors are often characterized by responses measured by methods of impedance spectroscopy. In the frequency domain these responses have the form of power-law functions or their linear combinations. The inverse Fourier transform leads to relaxation equations with integro-differential operators of fractional order under assumption that the frequency response is independent of the working voltage. To compare long-term relaxation kinetics predicted by these equations with the observed one, charging-discharging of supercapacitors (with nominal capacitances of 0.22, 0.47, and 1.0 F) have been studied by means of registration of the current response to a step voltage signal. It is established that the reaction of devices under study to variations of the charging regime disagrees with the model of a homogeneous linear response. It is demonstrated that relaxation is well described by a fractional stretched exponent.

Frequency-dependent hydrodynamic interaction between two solid spheres

NASA Astrophysics Data System (ADS)

Jung, Gerhard; Schmid, Friederike

2017-12-01

Hydrodynamic interactions play an important role in many areas of soft matter science. In simulations with implicit solvent, various techniques such as Brownian or Stokesian dynamics explicitly include hydrodynamic interactions a posteriori by using hydrodynamic diffusion tensors derived from the Stokes equation. However, this equation assumes the interaction to be instantaneous which is an idealized approximation and only valid on long time scales. In the present paper, we go one step further and analyze the time-dependence of hydrodynamic interactions between finite-sized particles in a compressible fluid on the basis of the linearized Navier-Stokes equation. The theoretical results show that at high frequencies, the compressibility of the fluid has a significant impact on the frequency-dependent pair interactions. The predictions of hydrodynamic theory are compared to molecular dynamics simulations of two nanocolloids in a Lennard-Jones fluid. For this system, we reconstruct memory functions by extending the inverse Volterra technique. The simulation data agree very well with the theory, therefore, the theory can be used to implement dynamically consistent hydrodynamic interactions in the increasingly popular field of non-Markovian modeling.

Variable-permittivity linear inverse problem for the H(sub z)-polarized case

NASA Technical Reports Server (NTRS)

Moghaddam, M.; Chew, W. C.

1993-01-01

The H(sub z)-polarized inverse problem has rarely been studied before due to the complicated way in which the unknown permittivity appears in the wave equation. This problem is equivalent to the acoustic inverse problem with variable density. We have recently reported the solution to the nonlinear variable-permittivity H(sub z)-polarized inverse problem using the Born iterative method. Here, the linear inverse problem is solved for permittivity (epsilon) and permeability (mu) using a different approach which is an extension of the basic ideas of diffraction tomography (DT). The key to solving this problem is to utilize frequency diversity to obtain the required independent measurements. The receivers are assumed to be in the far field of the object, and plane wave incidence is also assumed. It is assumed that the scatterer is weak, so that the Born approximation can be used to arrive at a relationship between the measured pressure field and two terms related to the spatial Fourier transform of the two unknowns, epsilon and mu. The term involving permeability corresponds to monopole scattering and that for permittivity to dipole scattering. Measurements at several frequencies are used and a least squares problem is solved to reconstruct epsilon and mu. It is observed that the low spatial frequencies in the spectra of epsilon and mu produce inaccuracies in the results. Hence, a regularization method is devised to remove this problem. Several results are shown. Low contrast objects for which the above analysis holds are used to show that good reconstructions are obtained for both permittivity and permeability after regularization is applied.

A python framework for environmental model uncertainty analysis

USGS Publications Warehouse

White, Jeremy; Fienen, Michael N.; Doherty, John E.

2016-01-01

We have developed pyEMU, a python framework for Environmental Modeling Uncertainty analyses, open-source tool that is non-intrusive, easy-to-use, computationally efficient, and scalable to highly-parameterized inverse problems. The framework implements several types of linear (first-order, second-moment (FOSM)) and non-linear uncertainty analyses. The FOSM-based analyses can also be completed prior to parameter estimation to help inform important modeling decisions, such as parameterization and objective function formulation. Complete workflows for several types of FOSM-based and non-linear analyses are documented in example notebooks implemented using Jupyter that are available in the online pyEMU repository. Example workflows include basic parameter and forecast analyses, data worth analyses, and error-variance analyses, as well as usage of parameter ensemble generation and management capabilities. These workflows document the necessary steps and provides insights into the results, with the goal of educating users not only in how to apply pyEMU, but also in the underlying theory of applied uncertainty quantification.

Different methods to analyze stepped wedge trial designs revealed different aspects of intervention effects.

PubMed

Twisk, J W R; Hoogendijk, E O; Zwijsen, S A; de Boer, M R

2016-04-01

Within epidemiology, a stepped wedge trial design (i.e., a one-way crossover trial in which several arms start the intervention at different time points) is increasingly popular as an alternative to a classical cluster randomized controlled trial. Despite this increasing popularity, there is a huge variation in the methods used to analyze data from a stepped wedge trial design. Four linear mixed models were used to analyze data from a stepped wedge trial design on two example data sets. The four methods were chosen because they have been (frequently) used in practice. Method 1 compares all the intervention measurements with the control measurements. Method 2 treats the intervention variable as a time-independent categorical variable comparing the different arms with each other. In method 3, the intervention variable is a time-dependent categorical variable comparing groups with different number of intervention measurements, whereas in method 4, the changes in the outcome variable between subsequent measurements are analyzed. Regarding the results in the first example data set, methods 1 and 3 showed a strong positive intervention effect, which disappeared after adjusting for time. Method 2 showed an inverse intervention effect, whereas method 4 did not show a significant effect at all. In the second example data set, the results were the opposite. Both methods 2 and 4 showed significant intervention effects, whereas the other two methods did not. For method 4, the intervention effect attenuated after adjustment for time. Different methods to analyze data from a stepped wedge trial design reveal different aspects of a possible intervention effect. The choice of a method partly depends on the type of the intervention and the possible time-dependent effect of the intervention. Furthermore, it is advised to combine the results of the different methods to obtain an interpretable overall result. Copyright © 2016 Elsevier Inc. All rights reserved.

Inverse finite element methods for extracting elastic-poroviscoelastic properties of cartilage and other soft tissues from indentation

NASA Astrophysics Data System (ADS)

Namani, Ravi

Mechanical properties are essential for understanding diseases that afflict various soft tissues, such as osteoarthritic cartilage and hypertension which alters cardiovascular arteries. Although the linear elastic modulus is routinely measured for hard materials, standard methods are not available for extracting the nonlinear elastic, linear elastic and time-dependent properties of soft tissues. Consequently, the focus of this work is to develop indentation methods for soft biological tissues; since analytical solutions are not available for the general context, finite element simulations are used. First, parametric studies of finite indentation of hyperelastic layers are performed to examine if indentation has the potential to identify nonlinear elastic behavior. To answer this, spherical, flat-ended conical and cylindrical tips are examined and the influence of thickness is exploited. Also the influence of the specimen/substrate boundary condition (slip or non-slip) is clarified. Second, a new inverse method---the hyperelastic extraction algorithm (HPE)---was developed to extract two nonlinear elastic parameters from the indentation force-depth data, which is the basic measurement in an indentation test. The accuracy of the extracted parameters and the influence of noise in measurements on this accuracy were obtained. This showed that the standard Berkovitch tip could only extract one parameter with sufficient accuracy, since the indentation force-depth curve has limited sensitivity to both nonlinear elastic parameters. Third, indentation methods for testing tissues from small animals were explored. New methods for flat-ended conical tips are derived. These account for practical test issues like the difficulty in locating the surface or soft specimens. Also, finite element simulations are explored to elucidate the influence of specimen curvature on the indentation force-depth curve. Fourth, the influence of inhomogeneity and material anisotropy on the extracted "average" linear elastic modulus was studied. The focus here is on murine tibial cartilage, since recent experiments have shown that the modulus measured by a 15 mum tip is considerably larger than that obtained from a 90 mum tip. It is shown that a depth-dependent modulus could give rise to such a size effect. Lastly, parametric studies were performed within the small strain setting to understand the influence of permeability and viscoelastic properties on the indentation stress-relaxation response. The focus here is on cartilage, and specific test protocols (single-step vs. multi-step stress relaxation) are explored. An inverse algorithm was developed to extract the poroviscoelastic parameters. A sensitivity study using this algorithm shows that the instantaneous elastic modulus (which is a measure of the viscous relaxation) can be extracted with very good accuracy, but the permeability and long-time relaxation constant cannot be extracted with good accuracy. The thesis concludes with implications of these studies. The potential and limitations of indentation tests for studying cartilage and other soft tissues is discussed.

Anomalous Nernst and thermal Hall effects in tilted Weyl semimetals

NASA Astrophysics Data System (ADS)

Ferreiros, Yago; Zyuzin, A. A.; Bardarson, Jens H.

2017-09-01

We study the anomalous Nernst and thermal Hall effects in a linearized low-energy model of a tilted Weyl semimetal, with two Weyl nodes separated in momentum space. For inversion symmetric tilt, we give analytic expressions in two opposite limits: For a small tilt, corresponding to a type-I Weyl semimetal, the Nernst conductivity is finite and independent of the Fermi level; for a large tilt, corresponding to a type-II Weyl semimetal, it acquires a contribution depending logarithmically on the Fermi energy. This result is in a sharp contrast to the nontilted case, where the Nernst response is known to be zero in the linear model. The thermal Hall conductivity similarly acquires Fermi surface contributions, which add to the Fermi level-independent, zero-tilt result, and is suppressed as one over the tilt parameter at half filling in the type-II phase. In the case of inversion-breaking tilt, with the tilting vector of equal modulus in the two Weyl cones, all Fermi surface contributions to both anomalous responses cancel out, resulting in zero Nernst conductivity. We discuss two possible experimental setups, representing open and closed thermoelectric circuits.

Nondestructive mechanical characterization of developing biological tissues using inflation testing.

PubMed

Oomen, P J A; van Kelle, M A J; Oomens, C W J; Bouten, C V C; Loerakker, S

2017-10-01

One of the hallmarks of biological soft tissues is their capacity to grow and remodel in response to changes in their environment. Although it is well-accepted that these processes occur at least partly to maintain a mechanical homeostasis, it remains unclear which mechanical constituent(s) determine(s) mechanical homeostasis. In the current study a nondestructive mechanical test and a two-step inverse analysis method were developed and validated to nondestructively estimate the mechanical properties of biological tissue during tissue culture. Nondestructive mechanical testing was achieved by performing an inflation test on tissues that were cultured inside a bioreactor, while the tissue displacement and thickness were nondestructively measured using ultrasound. The material parameters were estimated by an inverse finite element scheme, which was preceded by an analytical estimation step to rapidly obtain an initial estimate that already approximated the final solution. The efficiency and accuracy of the two-step inverse method was demonstrated on virtual experiments of several material types with known parameters. PDMS samples were used to demonstrate the method's feasibility, where it was shown that the proposed method yielded similar results to tensile testing. Finally, the method was applied to estimate the material properties of tissue-engineered constructs. Via this method, the evolution of mechanical properties during tissue growth and remodeling can now be monitored in a well-controlled system. The outcomes can be used to determine various mechanical constituents and to assess their contribution to mechanical homeostasis. Copyright © 2017 Elsevier Ltd. All rights reserved.

Step responses of a torsional system with multiple clearances: Study of vibro-impact phenomenon using experimental and computational methods

NASA Astrophysics Data System (ADS)

Oruganti, Pradeep Sharma; Krak, Michael D.; Singh, Rajendra

2018-01-01

Recently Krak and Singh (2017) proposed a scientific experiment that examined vibro-impacts in a torsional system under a step down excitation and provided preliminary measurements and limited non-linear model studies. A major goal of this article is to extend the prior work with a focus on the examination of vibro-impact phenomena observed under step responses in a torsional system with one, two or three controlled clearances. First, new measurements are made at several locations with a higher sampling frequency. Measured angular accelerations are examined in both time and time-frequency domains. Minimal order non-linear models of the experiment are successfully constructed, using piecewise linear stiffness and Coulomb friction elements; eight cases of the generic system are examined though only three are experimentally studied. Measured and predicted responses for single and dual clearance configurations exhibit double sided impacts and time varying periods suggest softening trends under the step down torque. Non-linear models are experimentally validated by comparing results with new measurements and with those previously reported. Several metrics are utilized to quantify and compare the measured and predicted responses (including peak to peak accelerations). Eigensolutions and step responses of the corresponding linearized models are utilized to better understand the nature of the non-linear dynamic system. Finally, the effect of step amplitude on the non-linear responses is examined for several configurations, and hardening trends are observed in the torsional system with three clearances.

Integrating conventional and inverse representation for face recognition.

PubMed

Xu, Yong; Li, Xuelong; Yang, Jian; Lai, Zhihui; Zhang, David

2014-10-01

Representation-based classification methods are all constructed on the basis of the conventional representation, which first expresses the test sample as a linear combination of the training samples and then exploits the deviation between the test sample and the expression result of every class to perform classification. However, this deviation does not always well reflect the difference between the test sample and each class. With this paper, we propose a novel representation-based classification method for face recognition. This method integrates conventional and the inverse representation-based classification for better recognizing the face. It first produces conventional representation of the test sample, i.e., uses a linear combination of the training samples to represent the test sample. Then it obtains the inverse representation, i.e., provides an approximation representation of each training sample of a subject by exploiting the test sample and training samples of the other subjects. Finally, the proposed method exploits the conventional and inverse representation to generate two kinds of scores of the test sample with respect to each class and combines them to recognize the face. The paper shows the theoretical foundation and rationale of the proposed method. Moreover, this paper for the first time shows that a basic nature of the human face, i.e., the symmetry of the face can be exploited to generate new training and test samples. As these new samples really reflect some possible appearance of the face, the use of them will enable us to obtain higher accuracy. The experiments show that the proposed conventional and inverse representation-based linear regression classification (CIRLRC), an improvement to linear regression classification (LRC), can obtain very high accuracy and greatly outperforms the naive LRC and other state-of-the-art conventional representation based face recognition methods. The accuracy of CIRLRC can be 10% greater than that of LRC.

Robotic path-finding in inverse treatment planning for stereotactic radiosurgery with continuous dose delivery

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vandewouw, Marlee M., E-mail: marleev@mie.utoronto

Purpose: Continuous dose delivery in radiation therapy treatments has been shown to decrease total treatment time while improving the dose conformity and distribution homogeneity over the conventional step-and-shoot approach. The authors develop an inverse treatment planning method for Gamma Knife® Perfexion™ that continuously delivers dose along a path in the target. Methods: The authors’ method is comprised of two steps: find a path within the target, then solve a mixed integer optimization model to find the optimal collimator configurations and durations along the selected path. Robotic path-finding techniques, specifically, simultaneous localization and mapping (SLAM) using an extended Kalman filter, aremore » used to obtain a path that travels sufficiently close to selected isocentre locations. SLAM is novelly extended to explore a 3D, discrete environment, which is the target discretized into voxels. Further novel extensions are incorporated into the steering mechanism to account for target geometry. Results: The SLAM method was tested on seven clinical cases and compared to clinical, Hamiltonian path continuous delivery, and inverse step-and-shoot treatment plans. The SLAM approach improved dose metrics compared to the clinical plans and Hamiltonian path continuous delivery plans. Beam-on times improved over clinical plans, and had mixed performance compared to Hamiltonian path continuous plans. The SLAM method is also shown to be robust to path selection inaccuracies, isocentre selection, and dose distribution. Conclusions: The SLAM method for continuous delivery provides decreased total treatment time and increased treatment quality compared to both clinical and inverse step-and-shoot plans, and outperforms existing path methods in treatment quality. It also accounts for uncertainty in treatment planning by accommodating inaccuracies.« less

The impact of approximations and arbitrary choices on geophysical images

NASA Astrophysics Data System (ADS)

Valentine, Andrew P.; Trampert, Jeannot

2016-01-01

Whenever a geophysical image is to be constructed, a variety of choices must be made. Some, such as those governing data selection and processing, or model parametrization, are somewhat arbitrary: there may be little reason to prefer one choice over another. Others, such as defining the theoretical framework within which the data are to be explained, may be more straightforward: typically, an `exact' theory exists, but various approximations may need to be adopted in order to make the imaging problem computationally tractable. Differences between any two images of the same system can be explained in terms of differences between these choices. Understanding the impact of each particular decision is essential if images are to be interpreted properly-but little progress has been made towards a quantitative treatment of this effect. In this paper, we consider a general linearized inverse problem, applicable to a wide range of imaging situations. We write down an expression for the difference between two images produced using similar inversion strategies, but where different choices have been made. This provides a framework within which inversion algorithms may be analysed, and allows us to consider how image effects may arise. In this paper, we take a general view, and do not specialize our discussion to any specific imaging problem or setup (beyond the restrictions implied by the use of linearized inversion techniques). In particular, we look at the concept of `hybrid inversion', in which highly accurate synthetic data (typically the result of an expensive numerical simulation) is combined with an inverse operator constructed based on theoretical approximations. It is generally supposed that this offers the benefits of using the more complete theory, without the full computational costs. We argue that the inverse operator is as important as the forward calculation in determining the accuracy of results. We illustrate this using a simple example, based on imaging the density structure of a vibrating string.

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1989-01-01

transform provides a linearization.’ Well known systems include the Kadomtsev - Petviashvili , Davey-Stewartson and Self-Dual Yang-Mills equations . The d...which employs inverse scattering theory in order to linearize the given nonlinear equation . I.S.T. has led to new developments in both fields: inverse...scattering and nonlinear wave equations . Listed below are some of the problems studied and a short description of results. - Multidimensional

Recursive inversion of externally defined linear systems by FIR filters

NASA Technical Reports Server (NTRS)

Bach, Ralph E., Jr.; Baram, Yoram

1989-01-01

The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least-squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problem of system identification and compensation.

Shear Wave Splitting Inversion in a Complex Crust

NASA Astrophysics Data System (ADS)

Lucas, A.

2015-12-01

Shear wave splitting (SWS) inversion presents a method whereby the upper crust can be interrogated for fracture density. It is caused when a shear wave traverses an area of anisotropy, splits in two, with each wave experiencing a different velocity resulting in an observable separation in arrival times. A SWS observation consists of the first arrival polarization direction and the time delay. Given the large amount of data common in SWS studies, manual inspection for polarization and time delay is considered prohibitively time intensive. All automated techniques used can produce high amounts of observations falsely interpreted as SWS. Thus introducing error into the interpretation. The technique often used for removing these false observations is to manually inspect all SWS observations defined as high quality by the automated routine, and remove false identifications. We investigate the nature of events falsely identified compared to those correctly identified. Once this identification is complete we conduct a inversion for crack density from SWS time delay. The current body of work on linear SWS inversion utilizes an equation that defines the time delay between arriving shear waves with respect to fracture density. This equation makes the assumption that no fluid flow occurs as a result of the passing shear wave, a situation called squirt flow. We show that the assumption is not applicable in all geological situations. When it is not true, its use in an inversion produces a result which is negatively affected by the assumptions. This is shown to be the case at the test case of 6894 SWS observations gathered in a small area at Puna geothermal field, Hawaii. To rectify this situation, a series of new time delay formulae, applicable to linear inversion, are derived from velocity equations presented in literature. The new formula use a 'fluid influence parameter' which indicates the degree to which squirt flow is influencing the SWS. It is found that accounting for squirt flow better fits the data and is more applicable. The fluid influence factor that best describes the data can be identified prior to solving the inversion. Implementing this formula in a linear inversion has a significantly improved fit to the time delay observations than that of the current methods.

Global Monthly CO2 Flux Inversion Based on Results of Terrestrial Ecosystem Modeling

NASA Astrophysics Data System (ADS)

Deng, F.; Chen, J.; Peters, W.; Krol, M.

2008-12-01

Most of our understanding of the sources and sinks of atmospheric CO2 has come from inverse studies of atmospheric CO2 concentration measurements. However, the number of currently available observation stations and our ability to simulate the diurnal planetary boundary layer evolution over continental regions essentially limit the number of regions that can be reliably inverted globally, especially over continental areas. In order to overcome these restrictions, a nested inverse modeling system was developed based on the Bayesian principle for estimating carbon fluxes of 30 regions in North America and 20 regions for the rest of the globe. Inverse modeling was conducted in monthly steps using CO2 concentration measurements of 5 years (2000 - 2005) with the following two models: (a) An atmospheric transport model (TM5) is used to generate the transport matrix where the diurnal variation n of atmospheric CO2 concentration is considered to enhance the use of the afternoon-hour average CO2 concentration measurements over the continental sites. (b) A process-based terrestrial ecosystem model (BEPS) is used to produce hourly step carbon fluxes, which could minimize the limitation due to our inability to solve the inverse problem in a high resolution, as the background of our inversion. We will present our recent results achieved through a combination of the bottom-up modeling with BEPS and the top-down modeling based on TM5 driven by offline meteorological fields generated by the European Centre for Medium Range Weather Forecast (ECMFW).

Assessing performance of flaw characterization methods through uncertainty propagation

NASA Astrophysics Data System (ADS)

Miorelli, R.; Le Bourdais, F.; Artusi, X.

2018-04-01

In this work, we assess the inversion performance in terms of crack characterization and localization based on synthetic signals associated to ultrasonic and eddy current physics. More precisely, two different standard iterative inversion algorithms are used to minimize the discrepancy between measurements (i.e., the tested data) and simulations. Furthermore, in order to speed up the computational time and get rid of the computational burden often associated to iterative inversion algorithms, we replace the standard forward solver by a suitable metamodel fit on a database built offline. In a second step, we assess the inversion performance by adding uncertainties on a subset of the database parameters and then, through the metamodel, we propagate these uncertainties within the inversion procedure. The fast propagation of uncertainties enables efficiently evaluating the impact due to the lack of knowledge on some parameters employed to describe the inspection scenarios, which is a situation commonly encountered in the industrial NDE context.

Sorting signed permutations by inversions in O(nlogn) time.

PubMed

Swenson, Krister M; Rajan, Vaibhav; Lin, Yu; Moret, Bernard M E

2010-03-01

The study of genomic inversions (or reversals) has been a mainstay of computational genomics for nearly 20 years. After the initial breakthrough of Hannenhalli and Pevzner, who gave the first polynomial-time algorithm for sorting signed permutations by inversions, improved algorithms have been designed, culminating with an optimal linear-time algorithm for computing the inversion distance and a subquadratic algorithm for providing a shortest sequence of inversions--also known as sorting by inversions. Remaining open was the question of whether sorting by inversions could be done in O(nlogn) time. In this article, we present a qualified answer to this question, by providing two new sorting algorithms, a simple and fast randomized algorithm and a deterministic refinement. The deterministic algorithm runs in time O(nlogn + kn), where k is a data-dependent parameter. We provide the results of extensive experiments showing that both the average and the standard deviation for k are small constants, independent of the size of the permutation. We conclude (but do not prove) that almost all signed permutations can be sorted by inversions in O(nlogn) time.

Identification of complex stiffness tensor from waveform reconstruction

NASA Astrophysics Data System (ADS)

Leymarie, N.; Aristégui, C.; Audoin, B.; Baste, S.

2002-03-01

An inverse method is proposed in order to determine the viscoelastic properties of composite-material plates from the plane-wave transmitted acoustic field. Analytical formulations of both the plate transmission coefficient and its first and second derivatives are established, and included in a two-step inversion scheme. Two objective functions to be minimized are then designed by considering the well-known maximum-likelihood principle and by using an analytic signal formulation. Through these innovative objective functions, the robustness of the inversion process against high level of noise in waveforms is improved and the method can be applied to a very thin specimen. The suitability of the inversion process for viscoelastic property identification is demonstrated using simulated data for composite materials with different anisotropy and damping degrees. A study of the effect of the rheologic model choice on the elastic property identification emphasizes the relevance of using a phenomenological description considering viscosity. Experimental characterizations show then the good reliability of the proposed approach. Difficulties arise experimentally for particular anisotropic media.

Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe5

PubMed Central

Chen, Zhi-Guo; Chen, R. Y.; Zhong, R. D.; Schneeloch, John; Zhang, C.; Huang, Y.; Qu, Fanming; Yu, Rui; Gu, G. D.; Wang, N. L.

2017-01-01

Three-dimensional topological insulators (3D TIs) represent states of quantum matters in which surface states are protected by time-reversal symmetry and an inversion occurs between bulk conduction and valence bands. However, the bulk-band inversion, which is intimately tied to the topologically nontrivial nature of 3D Tis, has rarely been investigated by experiments. Besides, 3D massive Dirac fermions with nearly linear band dispersions were seldom observed in TIs. Recently, a van der Waals crystal, ZrTe5, was theoretically predicted to be a TI. Here, we report an infrared transmission study of a high-mobility [∼33,000 cm2/(V ⋅ s)] multilayer ZrTe5 flake at magnetic fields (B) up to 35 T. Our observation of a linear relationship between the zero-magnetic-field optical absorption and the photon energy, a bandgap of ∼10 meV and a B dependence of the Landau level (LL) transition energies at low magnetic fields demonstrates 3D massive Dirac fermions with nearly linear band dispersions in this system. More importantly, the reemergence of the intra-LL transitions at magnetic fields higher than 17 T reveals the energy cross between the two zeroth LLs, which reflects the inversion between the bulk conduction and valence bands. Our results not only provide spectroscopic evidence for the TI state in ZrTe5 but also open up a new avenue for fundamental studies of Dirac fermions in van der Waals materials. PMID:28096330

Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe 5

DOE PAGES

Chen, Zhi -Guo; Chen, R. Y.; Zhong, R. D.; ...

2017-01-17

Three-dimensional topological insulators (3D TIs) represent states of quantum matters in which surface states are protected by time-reversal symmetry and an inversion occurs between bulk conduction and valence bands. However, the bulk-band inversion, which is intimately tied to the topologically nontrivial nature of 3D Tis, has rarely been investigated by experiments. Besides, 3D massive Dirac fermions with nearly linear band dispersions were seldom observed in TIs. Recently, a van der Waals crystal, ZrTe 5, was theoretically predicted to be a TI. Here, we report an infrared transmission study of a high-mobility [~33,000 cm 2/(V • s)] multilayer ZrTe 5 flakemore » at magnetic fields (B) up to 35 T. Our observation of a linear relationship between the zero-magnetic-field optical absorption and the photon energy, a bandgap of ~10 meV and a √B dependence of the Landau level (LL) transition energies at low magnetic fields demonstrates 3D massive Dirac fermions with nearly linear band dispersions in this system. More importantly, the reemergence of the intra-LL transitions at magnetic fields higher than 17 T reveals the energy cross between the two zeroth LLs, which reflects the inversion between the bulk conduction and valence bands. Finally, our results not only provide spectroscopic evidence for the TI state in ZrTe 5 but also open up a new avenue for fundamental studies of Dirac fermions in van der Waals materials.« less

Invariant-based inverse engineering for fluctuation transfer between membranes in an optomechanical cavity system

NASA Astrophysics Data System (ADS)

Chen, Ye-Hong; Shi, Zhi-Cheng; Song, Jie; Xia, Yan

2018-02-01

In this paper, by invariant-based inverse engineering, we design classical driving fields to transfer quantum fluctuations between two suspended membranes in an optomechanical cavity system. The transfer can be quickly attained through a nonadiabatic evolution path determined by a so-called dynamical invariant. Such an evolution path allows one to optimize the occupancies of the unstable "intermediate" states; thus, the influence of cavity decays can be suppressed. Numerical simulation demonstrates that a perfect fluctuation transfer between two membranes can be rapidly achieved in one step, and the transfer is robust to both the amplitude noises and cavity decays.

Physical properties of asteroids derived from a novel approach to modeling of optical lightcurves and WISE thermalinfrared data

NASA Astrophysics Data System (ADS)

Durech, Josef; Hanus, Josef; Delbo, Marco; Ali-Lagoa, Victor; Carry, Benoit

2014-11-01

Convex shape models and spin vectors of asteroids are now routinely derived from their disk-integrated lightcurves by the lightcurve inversion method of Kaasalainen et al. (2001, Icarus 153, 37). These shape models can be then used in combination with thermal infrared data and a thermophysical model to derive other physical parameters - size, albedo, macroscopic roughness and thermal inertia of the surface. In this classical two-step approach, the shape and spin parameters are kept fixed during the thermophysical modeling when the emitted thermal flux is computed from the surface temperature, which is computed by solving a 1-D heat diffusion equation in sub-surface layers. A novel method of simultaneous inversion of optical and infrared data was presented by Durech et al. (2012, LPI Contribution No. 1667, id.6118). The new algorithm uses the same convex shape representation as the lightcurve inversion but optimizes all relevant physical parameters simultaneously (including the shape, size, rotation vector, thermal inertia, albedo, surface roughness, etc.), which leads to a better fit to the thermal data and a reliable estimation of model uncertainties. We applied this method to selected asteroids using their optical lightcurves from archives and thermal infrared data observed by the Wide-field Infrared Survey Explorer (WISE) satellite. We will (i) show several examples of how well our model fits both optical and infrared data, (ii) discuss the uncertainty of derived parameters (namely the thermal inertia), (iii) compare results obtained with the two-step approach with those obtained by our method, (iv) discuss the advantages of this simultaneous approach with respect to the classical two-step approach, and (v) advertise the possibility to use this approach to tens of thousands asteroids for which enough WISE and optical data exist.

Stabilization of a three-dimensional limit cycle walking model through step-to-step ankle control.

PubMed

Kim, Myunghee; Collins, Steven H

2013-06-01

Unilateral, below-knee amputation is associated with an increased risk of falls, which may be partially related to a loss of active ankle control. If ankle control can contribute significantly to maintaining balance, even in the presence of active foot placement, this might provide an opportunity to improve balance using robotic ankle-foot prostheses. We investigated ankle- and hip-based walking stabilization methods in a three-dimensional model of human gait that included ankle plantarflexion, ankle inversion-eversion, hip flexion-extension, and hip ad/abduction. We generated discrete feedback control laws (linear quadratic regulators) that altered nominal actuation parameters once per step. We used ankle push-off, lateral ankle stiffness and damping, fore-aft foot placement, lateral foot placement, or all of these as control inputs. We modeled environmental disturbances as random, bounded, unexpected changes in floor height, and defined balance performance as the maximum allowable disturbance value for which the model walked 500 steps without falling. Nominal walking motions were unstable, but were stabilized by all of the step-to-step control laws we tested. Surprisingly, step-by-step modulation of ankle push-off alone led to better balance performance (3.2% leg length) than lateral foot placement (1.2% leg length) for these control laws. These results suggest that appropriate control of robotic ankle-foot prosthesis push-off could make balancing during walking easier for individuals with amputation.

Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sevastianov, L. A., E-mail: sevast@sci.pfu.edu.ru; Egorov, A. A.; Sevastyanov, A. L.

2013-02-15

Basic steps in developing an original method of adiabatic modes that makes it possible to solve the direct and inverse problems of simulating and designing three-dimensional multilayered smoothly irregular open waveguide structures are described. A new element in the method is that an approximate solution of Maxwell's equations is made to obey 'inclined' boundary conditions at the interfaces between themedia being considered. These boundary conditions take into account the obliqueness of planes tangent to nonplanar boundaries between the media and lead to new equations for coupled vector quasiwaveguide hybrid adiabatic modes. Solutions of these equations describe the phenomenon of 'entanglement'more » of two linear polarizations of an irregular multilayered waveguide, the appearance of a new mode in an entangled state, and the effect of rotation of the polarization plane of quasiwaveguide modes. The efficiency of the method is demonstrated by considering the example of numerically simulating a thin-film generalized waveguide Lueneburg lens.« less

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, Longxiao; Gu, Hanming

2018-03-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor series expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain the P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion doesn't need certain assumptions and can estimate more parameters simultaneously. It has a better applicability. Meanwhile, by using the generalized linear method, the inversion is easily implemented and its calculation cost is small. We use the theoretical model to generate synthetic seismic records to test and analyze the influence of random noise. The results can prove the availability and anti-noise-interference ability of our method. We also apply the inversion to actual field data and prove the feasibility of our method in actual situation.

Single-Step 3-D Image Reconstruction in Magnetic Induction Tomography: Theoretical Limits of Spatial Resolution and Contrast to Noise Ratio

PubMed Central

Hollaus, Karl; Rosell-Ferrer, Javier; Merwa, Robert

2006-01-01

Magnetic induction tomography (MIT) is a low-resolution imaging modality for reconstructing the changes of the complex conductivity in an object. MIT is based on determining the perturbation of an alternating magnetic field, which is coupled from several excitation coils to the object. The conductivity distribution is reconstructed from the corresponding voltage changes induced in several receiver coils. Potential medical applications comprise the continuous, non-invasive monitoring of tissue alterations which are reflected in the change of the conductivity, e.g. edema, ventilation disorders, wound healing and ischemic processes. MIT requires the solution of an ill-posed inverse eddy current problem. A linearized version of this problem was solved for 16 excitation coils and 32 receiver coils with a model of two spherical perturbations within a cylindrical phantom. The method was tested with simulated measurement data. Images were reconstructed with a regularized single-step Gauss–Newton approach. Theoretical limits for spatial resolution and contrast/noise ratio were calculated and compared with the empirical results from a Monte-Carlo study. The conductivity perturbations inside a homogeneous cylinder were localized for a SNR between 44 and 64 dB. The results prove the feasibility of difference imaging with MIT and give some quantitative data on the limitations of the method. PMID:17031597

Fractional Gaussian model in global optimization

NASA Astrophysics Data System (ADS)

Dimri, V. P.; Srivastava, R. P.

2009-12-01

Earth system is inherently non-linear and it can be characterized well if we incorporate no-linearity in the formulation and solution of the problem. General tool often used for characterization of the earth system is inversion. Traditionally inverse problems are solved using least-square based inversion by linearizing the formulation. The initial model in such inversion schemes is often assumed to follow posterior Gaussian probability distribution. It is now well established that most of the physical properties of the earth follow power law (fractal distribution). Thus, the selection of initial model based on power law probability distribution will provide more realistic solution. We present a new method which can draw samples of posterior probability density function very efficiently using fractal based statistics. The application of the method has been demonstrated to invert band limited seismic data with well control. We used fractal based probability density function which uses mean, variance and Hurst coefficient of the model space to draw initial model. Further this initial model is used in global optimization inversion scheme. Inversion results using initial models generated by our method gives high resolution estimates of the model parameters than the hitherto used gradient based liner inversion method.

A Glimpse in the Third Dimension for Electrical Resistivity Profiles

NASA Astrophysics Data System (ADS)

Robbins, A. R.; Plattner, A.

2017-12-01

We present an electrode layout strategy designed to enhance the popular two-dimensional electrical resistivity profile. Offsetting electrodes from the traditional linear layout and using 3-D inversion software allows for mapping the three-dimensional electrical resistivity close to the profile plane. We established a series of synthetic tests using simulated data generated from chosen resistivity distributions with a three-dimensional target feature. All inversions and simulations were conducted using freely-available ERT software, BERT and E4D. Synthetic results demonstrate the effectiveness of the offset electrode approach, whereas the linear layout failed to resolve the three-dimensional character of our subsurface feature. A field survey using trench backfill as a known resistivity contrast confirmed our synthetic tests. As we show, 3-D inversions of linear layouts for starting models without previously known structure are futile ventures because they generate symmetric resistivity solutions with respect to the profile plane. This is a consequence of the layout's inherent symmetrical sensitivity patterns. An offset electrode layout is not subject to the same limitation, as the collective measurements do not share a common sensitivity symmetry. For practitioners, this approach presents a low-cost improvement of a traditional geophysical method which is simple to use yet may provide critical information about the three dimensional structure of the subsurface close to the profile.

The Lanchester square-law model extended to a (2,2) conflict

NASA Astrophysics Data System (ADS)

Colegrave, R. K.; Hyde, J. M.

1993-01-01

A natural extension of the Lanchester (1,1) square-law model is the (M,N) linear model in which M forces oppose N forces with constant attrition rates. The (2,2) model is treated from both direct and inverse viewpoints. The inverse problem means that the model is to be fitted to a minimum number of observed force levels, i.e. the attrition rates are to be found from the initial force levels together with the levels observed at two subsequent times. An approach based on Hamiltonian dynamics has enabled the authors to derive a procedure for solving the inverse problem, which is readily computerized. Conflicts in which participants unexpectedly rally or weaken must be excluded.

Approximate non-linear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-03-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-waves scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform (GRT). After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic non-linear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P-wave and S-wave information.

Zinc oxide inverse opal enzymatic biosensor

NASA Astrophysics Data System (ADS)

You, Xueqiu; Pikul, James H.; King, William P.; Pak, James J.

2013-06-01

We report ZnO inverse opal- and nanowire (NW)-based enzymatic glucose biosensors with extended linear detection ranges. The ZnO inverse opal sensors have 0.01-18 mM linear detection range, which is 2.5 times greater than that of ZnO NW sensors and 1.5 times greater than that of other reported ZnO sensors. This larger range is because of reduced glucose diffusivity through the inverse opal geometry. The ZnO inverse opal sensors have an average sensitivity of 22.5 μA/(mM cm2), which diminished by 10% after 35 days, are more stable than ZnO NW sensors whose sensitivity decreased by 10% after 7 days.

Polynomial compensation, inversion, and approximation of discrete time linear systems

NASA Technical Reports Server (NTRS)

Baram, Yoram

1987-01-01

The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.

Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and the KPI equation

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.; Polivanov, M. C.

1992-11-01

The resolvent operator of the linear problem is determined as the full Green function continued in the complex domain in two variables. An analog of the known Hilbert identity is derived. We demonstrate the role of this identity in the study of two-dimensional scattering. Considering the nonstationary Schrödinger equation as an example, we show that all types of solutions of the linear problems, as well as spectral data known in the literature, are given as specific values of this unique function — the resolvent function. A new form of the inverse problem is formulated.

A novel post-processing scheme for two-dimensional electrical impedance tomography based on artificial neural networks

PubMed Central

2017-01-01

Objective Electrical Impedance Tomography (EIT) is a powerful non-invasive technique for imaging applications. The goal is to estimate the electrical properties of living tissues by measuring the potential at the boundary of the domain. Being safe with respect to patient health, non-invasive, and having no known hazards, EIT is an attractive and promising technology. However, it suffers from a particular technical difficulty, which consists of solving a nonlinear inverse problem in real time. Several nonlinear approaches have been proposed as a replacement for the linear solver, but in practice very few are capable of stable, high-quality, and real-time EIT imaging because of their very low robustness to errors and inaccurate modeling, or because they require considerable computational effort. Methods In this paper, a post-processing technique based on an artificial neural network (ANN) is proposed to obtain a nonlinear solution to the inverse problem, starting from a linear solution. While common reconstruction methods based on ANNs estimate the solution directly from the measured data, the method proposed here enhances the solution obtained from a linear solver. Conclusion Applying a linear reconstruction algorithm before applying an ANN reduces the effects of noise and modeling errors. Hence, this approach significantly reduces the error associated with solving 2D inverse problems using machine-learning-based algorithms. Significance This work presents radical enhancements in the stability of nonlinear methods for biomedical EIT applications. PMID:29206856

Nonexpansiveness of a linearized augmented Lagrangian operator for hierarchical convex optimization

NASA Astrophysics Data System (ADS)

Yamagishi, Masao; Yamada, Isao

2017-04-01

Hierarchical convex optimization concerns two-stage optimization problems: the first stage problem is a convex optimization; the second stage problem is the minimization of a convex function over the solution set of the first stage problem. For the hierarchical convex optimization, the hybrid steepest descent method (HSDM) can be applied, where the solution set of the first stage problem must be expressed as the fixed point set of a certain nonexpansive operator. In this paper, we propose a nonexpansive operator that yields a computationally efficient update when it is plugged into the HSDM. The proposed operator is inspired by the update of the linearized augmented Lagrangian method. It is applicable to characterize the solution set of recent sophisticated convex optimization problems found in the context of inverse problems, where the sum of multiple proximable convex functions involving linear operators must be minimized to incorporate preferable properties into the minimizers. For such a problem formulation, there has not yet been reported any nonexpansive operator that yields an update free from the inversions of linear operators in cases where it is utilized in the HSDM. Unlike previously known nonexpansive operators, the proposed operator yields an inversion-free update in such cases. As an application of the proposed operator plugged into the HSDM, we also present, in the context of the so-called superiorization, an algorithmic solution to a convex optimization problem over the generalized convex feasible set where the intersection of the hard constraints is not necessarily simple.

Inferring global upper-mantle shear attenuation structure by waveform tomography using the spectral element method

NASA Astrophysics Data System (ADS)

Karaoǧlu, Haydar; Romanowicz, Barbara

2018-06-01

We present a global upper-mantle shear wave attenuation model that is built through a hybrid full-waveform inversion algorithm applied to long-period waveforms, using the spectral element method for wavefield computations. Our inversion strategy is based on an iterative approach that involves the inversion for successive updates in the attenuation parameter (δ Q^{-1}_μ) and elastic parameters (isotropic velocity VS, and radial anisotropy parameter ξ) through a Gauss-Newton-type optimization scheme that employs envelope- and waveform-type misfit functionals for the two steps, respectively. We also include source and receiver terms in the inversion steps for attenuation structure. We conducted a total of eight iterations (six for attenuation and two for elastic structure), and one inversion for updates to source parameters. The starting model included the elastic part of the relatively high-resolution 3-D whole mantle seismic velocity model, SEMUCB-WM1, which served to account for elastic focusing effects. The data set is a subset of the three-component surface waveform data set, filtered between 400 and 60 s, that contributed to the construction of the whole-mantle tomographic model SEMUCB-WM1. We applied strict selection criteria to this data set for the attenuation iteration steps, and investigated the effect of attenuation crustal structure on the retrieved mantle attenuation structure. While a constant 1-D Qμ model with a constant value of 165 throughout the upper mantle was used as starting model for attenuation inversion, we were able to recover, in depth extent and strength, the high-attenuation zone present in the depth range 80-200 km. The final 3-D model, SEMUCB-UMQ, shows strong correlation with tectonic features down to 200-250 km depth, with low attenuation beneath the cratons, stable parts of continents and regions of old oceanic crust, and high attenuation along mid-ocean ridges and backarcs. Below 250 km, we observe strong attenuation in the southwestern Pacific and eastern Africa, while low attenuation zones fade beneath most of the cratons. The strong negative correlation of Q^{-1}_μ and VS anomalies at shallow upper-mantle depths points to a common dominant origin for the two, likely due to variations in thermal structure. A comparison with two other global upper-mantle attenuation models shows promising consistency. As we updated the elastic 3-D model in alternate iterations, we found that the VS part of the model was stable, while the ξ structure evolution was more pronounced, indicating that it may be important to include 3-D attenuation effects when inverting for ξ, possibly due to the influence of dispersion corrections on this less well-constrained parameter.

Acoustic-articulatory mapping in vowels by locally weighted regression

PubMed Central

McGowan, Richard S.; Berger, Michael A.

2009-01-01

A method for mapping between simultaneously measured articulatory and acoustic data is proposed. The method uses principal components analysis on the articulatory and acoustic variables, and mapping between the domains by locally weighted linear regression, or loess [Cleveland, W. S. (1979). J. Am. Stat. Assoc. 74, 829–836]. The latter method permits local variation in the slopes of the linear regression, assuming that the function being approximated is smooth. The methodology is applied to vowels of four speakers in the Wisconsin X-ray Microbeam Speech Production Database, with formant analysis. Results are examined in terms of (1) examples of forward (articulation-to-acoustics) mappings and inverse mappings, (2) distributions of local slopes and constants, (3) examples of correlations among slopes and constants, (4) root-mean-square error, and (5) sensitivity of formant frequencies to articulatory change. It is shown that the results are qualitatively correct and that loess performs better than global regression. The forward mappings show different root-mean-square error properties than the inverse mappings indicating that this method is better suited for the forward mappings than the inverse mappings, at least for the data chosen for the current study. Some preliminary results on sensitivity of the first two formant frequencies to the two most important articulatory principal components are presented. PMID:19813812

Errors in Tsunami Source Estimation from Tide Gauges

NASA Astrophysics Data System (ADS)

Arcas, D.

2012-12-01

Linearity of tsunami waves in deep water can be assessed as a comparison of flow speed, u to wave propagation speed √gh. In real tsunami scenarios this evaluation becomes impractical due to the absence of observational data of tsunami flow velocities in shallow water. Consequently the extent of validity of the linear regime in the ocean is unclear. Linearity is the fundamental assumption behind tsunami source inversion processes based on linear combinations of unit propagation runs from a deep water propagation database (Gica et al., 2008). The primary tsunami elevation data for such inversion is usually provided by National Oceanic and Atmospheric (NOAA) deep-water tsunami detection systems known as DART. The use of tide gauge data for such inversions is more controversial due to the uncertainty of wave linearity at the depth of the tide gauge site. This study demonstrates the inaccuracies incurred in source estimation using tide gauge data in conjunction with a linear combination procedure for tsunami source estimation.

Influence of phase inversion on the formation and stability of one-step multiple emulsions.

PubMed

Morais, Jacqueline M; Rocha-Filho, Pedro A; Burgess, Diane J

2009-07-21

A novel method of preparation of water-in-oil-in-micelle-containing water (W/O/W(m)) multiple emulsions using the one-step emulsification method is reported. These multiple emulsions were normal (not temporary) and stable over a 60 day test period. Previously, reported multiple emulsion by the one-step method were abnormal systems that formed at the inversion point of simple emulsion (where there is an incompatibility in the Ostwald and Bancroft theories, and typically these are O/W/O systems). Pseudoternary phase diagrams and bidimensional process-composition (phase inversion) maps were constructed to assist in process and composition optimization. The surfactants used were PEG40 hydrogenated castor oil and sorbitan oleate, and mineral and vegetables oils were investigated. Physicochemical characterization studies showed experimentally, for the first time, the significance of the ultralow surface tension point on multiple emulsion formation by one-step via phase inversion processes. Although the significance of ultralow surface tension has been speculated previously, to the best of our knowledge, this is the first experimental confirmation. The multiple emulsion system reported here was dependent not only upon the emulsification temperature, but also upon the component ratios, therefore both the emulsion phase inversion and the phase inversion temperature were considered to fully explain their formation. Accordingly, it is hypothesized that the formation of these normal multiple emulsions is not a result of a temporary incompatibility (at the inversion point) during simple emulsion preparation, as previously reported. Rather, these normal W/O/W(m) emulsions are a result of the simultaneous occurrence of catastrophic and transitional phase inversion processes. The formation of the primary emulsions (W/O) is in accordance with the Ostwald theory ,and the formation of the multiple emulsions (W/O/W(m)) is in agreement with the Bancroft theory.

A Computationally Efficient Parallel Levenberg-Marquardt Algorithm for Large-Scale Big-Data Inversion

NASA Astrophysics Data System (ADS)

Lin, Y.; O'Malley, D.; Vesselinov, V. V.

2015-12-01

Inverse modeling seeks model parameters given a set of observed state variables. However, for many practical problems due to the facts that the observed data sets are often large and model parameters are often numerous, conventional methods for solving the inverse modeling can be computationally expensive. We have developed a new, computationally-efficient Levenberg-Marquardt method for solving large-scale inverse modeling. Levenberg-Marquardt methods require the solution of a dense linear system of equations which can be prohibitively expensive to compute for large-scale inverse problems. Our novel method projects the original large-scale linear problem down to a Krylov subspace, such that the dimensionality of the measurements can be significantly reduced. Furthermore, instead of solving the linear system for every Levenberg-Marquardt damping parameter, we store the Krylov subspace computed when solving the first damping parameter and recycle it for all the following damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved by using these computational techniques. We apply this new inverse modeling method to invert for a random transitivity field. Our algorithm is fast enough to solve for the distributed model parameters (transitivity) at each computational node in the model domain. The inversion is also aided by the use regularization techniques. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). Julia is an advanced high-level scientific programing language that allows for efficient memory management and utilization of high-performance computational resources. By comparing with a Levenberg-Marquardt method using standard linear inversion techniques, our Levenberg-Marquardt method yields speed-up ratio of 15 in a multi-core computational environment and a speed-up ratio of 45 in a single-core computational environment. Therefore, our new inverse modeling method is a powerful tool for large-scale applications.

Secondary Structure Predictions for Long RNA Sequences Based on Inversion Excursions and MapReduce.

PubMed

Yehdego, Daniel T; Zhang, Boyu; Kodimala, Vikram K R; Johnson, Kyle L; Taufer, Michela; Leung, Ming-Ying

2013-05-01

Secondary structures of ribonucleic acid (RNA) molecules play important roles in many biological processes including gene expression and regulation. Experimental observations and computing limitations suggest that we can approach the secondary structure prediction problem for long RNA sequences by segmenting them into shorter chunks, predicting the secondary structures of each chunk individually using existing prediction programs, and then assembling the results to give the structure of the original sequence. The selection of cutting points is a crucial component of the segmenting step. Noting that stem-loops and pseudoknots always contain an inversion, i.e., a stretch of nucleotides followed closely by its inverse complementary sequence, we developed two cutting methods for segmenting long RNA sequences based on inversion excursions: the centered and optimized method. Each step of searching for inversions, chunking, and predictions can be performed in parallel. In this paper we use a MapReduce framework, i.e., Hadoop, to extensively explore meaningful inversion stem lengths and gap sizes for the segmentation and identify correlations between chunking methods and prediction accuracy. We show that for a set of long RNA sequences in the RFAM database, whose secondary structures are known to contain pseudoknots, our approach predicts secondary structures more accurately than methods that do not segment the sequence, when the latter predictions are possible computationally. We also show that, as sequences exceed certain lengths, some programs cannot computationally predict pseudoknots while our chunking methods can. Overall, our predicted structures still retain the accuracy level of the original prediction programs when compared with known experimental secondary structure.

Numerical solution of inverse scattering for near-field optics.

PubMed

Bao, Gang; Li, Peijun

2007-06-01

A novel regularized recursive linearization method is developed for a two-dimensional inverse medium scattering problem that arises in near-field optics, which reconstructs the scatterer of an inhomogeneous medium located on a substrate from data accessible through photon scanning tunneling microscopy experiments. Based on multiple frequency scattering data, the method starts from the Born approximation corresponding to weak scattering at a low frequency, and each update is obtained by continuation on the wavenumber from solutions of one forward problem and one adjoint problem of the Helmholtz equation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, Yongbin; White, R. D.

In the calculation of the linearized Boltzmann collision operator for an inverse-square force law interaction (Coulomb interaction) F(r)=κ/r{sup 2}, we found the widely used scattering angle cutoff θ≥θ{sub min} is a wrong practise since the divergence still exists after the cutoff has been made. When the correct velocity change cutoff |v′−v|≥δ{sub min} is employed, the scattering angle can be integrated. A unified linearized Boltzmann collision operator for both inverse-square force law and rigid-sphere interactions is obtained. Like many other unified quantities such as transition moments, Fokker-Planck expansion coefficients and energy exchange rates obtained recently [Y. B. Chang and L. A.more » Viehland, AIP Adv. 1, 032128 (2011)], the difference between the two kinds of interactions is characterized by a parameter, γ, which is 1 for rigid-sphere interactions and −3 for inverse-square force law interactions. When the cutoff is removed by setting δ{sub min}=0, Hilbert's well known kernel for rigid-sphere interactions is recovered for γ = 1.« less

Controllable rotational inversion in nanostructures with dual chirality.

PubMed

Dai, Lu; Zhu, Ka-Di; Shen, Wenzhong; Huang, Xiaojiang; Zhang, Li; Goriely, Alain

2018-04-05

Chiral structures play an important role in natural sciences due to their great variety and potential applications. A perversion connecting two helices with opposite chirality creates a dual-chirality helical structure. In this paper, we develop a novel model to explore quantitatively the mechanical behavior of normal, binormal and transversely isotropic helical structures with dual chirality and apply these ideas to known nanostructures. It is found that both direction and amplitude of rotation can be finely controlled by designing the cross-sectional shape. A peculiar rotational inversion of overwinding followed by unwinding, observed in some gourd and cucumber tendril perversions, not only exists in transversely isotropic dual-chirality helical nanobelts, but also in the binormal/normal ones when the cross-sectional aspect ratio is close to 1. Beyond this rotational inversion region, the binormal and normal dual-chirality helical nanobelts exhibit a fixed directional rotation of unwinding and overwinding, respectively. Moreover, in the binormal case, the rotation of these helical nanobelts is nearly linear, which is promising as a possible design for linear-to-rotary motion converters. The present work suggests new designs for nanoscale devices.

Time domain localization technique with sparsity constraint for imaging acoustic sources

NASA Astrophysics Data System (ADS)

Padois, Thomas; Doutres, Olivier; Sgard, Franck; Berry, Alain

2017-09-01

This paper addresses source localization technique in time domain for broadband acoustic sources. The objective is to accurately and quickly detect the position and amplitude of noise sources in workplaces in order to propose adequate noise control options and prevent workers hearing loss or safety risk. First, the generalized cross correlation associated with a spherical microphone array is used to generate an initial noise source map. Then a linear inverse problem is defined to improve this initial map. Commonly, the linear inverse problem is solved with an l2 -regularization. In this study, two sparsity constraints are used to solve the inverse problem, the orthogonal matching pursuit and the truncated Newton interior-point method. Synthetic data are used to highlight the performances of the technique. High resolution imaging is achieved for various acoustic sources configurations. Moreover, the amplitudes of the acoustic sources are correctly estimated. A comparison of computation times shows that the technique is compatible with quasi real-time generation of noise source maps. Finally, the technique is tested with real data.

Asymmetrical, inversely graded, upstream-migrating cyclic steps in marine settings: Late Miocene-early Pliocene Fish Creek-Vallecito Basin, southern California

NASA Astrophysics Data System (ADS)

Gong, Chenglin; Chen, Liuqin; West, Logan

2017-10-01

Cyclic steps are ubiquitous in modern sedimentary environments, yet their recognition remains sparse in the rock record. Here, we interpret three sets of undulating backsets (1 to 3) recognized in the late Miocene-early Pliocene Latrania Formation in the Anza-Borrego Desert, the Fish Creek-Vallecito Basin, southern California, USA as the first cm- to dm-scale outcrop record of cyclic steps, based on asymmetrical cross-sections, upstream migration, and inversely graded laminae. Upstream migration and asymmetrical cross-sections of backsets and concomitant backset laminae are attributed to supercritical-to-subcritical flow transitions through weak hydraulic jumps, which are composed of: (i) thin (tens of centimetres) and slower (reported as flow velocities (Ū) of 0.45 to 1.45 m s- 1, with mean value of Ū = 0.89 m s- 1) subcritical (represented by internal Froude numbers (Fr) of 0.67 to 0.99, with mean value of Fr = 0.84) turbidity currents on the stoss sides, and (ii) thin (tens of centimetres) and faster (reported as Ū of 0.99 to 4.03 m s- 1, with mean value of Ū = 2.24 m s- 1) supercritical (represented by Fr of 1.84 to 3.07, with mean value of Fr = 2.42) turbidity flows on the lee sides. The inversely graded laminae in the troughs of backsets are 2 to 5 cm thick, and consist of two discrete divisions: (i) 1 to 2 cm thick, lower finer-grained divisions made up of parallel laminated siltstones, overlain by very fine- to fine-grained sandstones, and (ii) 2 to 3 cm thick, upper divisions composed of medium- to coarse-grained sandstones, with sporadic occurrence of subrounded pebbles. These inversely graded laminae are related to stratified, collisional and/or frictional traction carpets under conditions of high fall-out rates. Due to the poor preservation potential of cyclic steps, the rock record of cyclic steps is generally considered to be rare. The present outcrop-based study presents a detailed analysis of sedimentary facies, growth patterns, and flow dynamics of marine cyclic steps, thereby contributing to better understand architectural styles and lithological properties of cyclic steps in the geological record.

Coarse mesh and one-cell block inversion based diffusion synthetic acceleration

NASA Astrophysics Data System (ADS)

Kim, Kang-Seog

DSA (Diffusion Synthetic Acceleration) has been developed to accelerate the SN transport iteration. We have developed solution techniques for the diffusion equations of FLBLD (Fully Lumped Bilinear Discontinuous), SCB (Simple Comer Balance) and UCB (Upstream Corner Balance) modified 4-step DSA in x-y geometry. Our first multi-level method includes a block Gauss-Seidel iteration for the discontinuous diffusion equation, uses the continuous diffusion equation derived from the asymptotic analysis, and avoids void cell calculation. We implemented this multi-level procedure and performed model problem calculations. The results showed that the FLBLD, SCB and UCB modified 4-step DSA schemes with this multi-level technique are unconditionally stable and rapidly convergent. We suggested a simplified multi-level technique for FLBLD, SCB and UCB modified 4-step DSA. This new procedure does not include iterations on the diffusion calculation or the residual calculation. Fourier analysis results showed that this new procedure was as rapidly convergent as conventional modified 4-step DSA. We developed new DSA procedures coupled with 1-CI (Cell Block Inversion) transport which can be easily parallelized. We showed that 1-CI based DSA schemes preceded by SI (Source Iteration) are efficient and rapidly convergent for LD (Linear Discontinuous) and LLD (Lumped Linear Discontinuous) in slab geometry and for BLD (Bilinear Discontinuous) and FLBLD in x-y geometry. For 1-CI based DSA without SI in slab geometry, the results showed that this procedure is very efficient and effective for all cases. We also showed that 1-CI based DSA in x-y geometry was not effective for thin mesh spacings, but is effective and rapidly convergent for intermediate and thick mesh spacings. We demonstrated that the diffusion equation discretized on a coarse mesh could be employed to accelerate the transport equation. Our results showed that coarse mesh DSA is unconditionally stable and is as rapidly convergent as fine mesh DSA in slab geometry. For x-y geometry our coarse mesh DSA is very effective for thin and intermediate mesh spacings independent of the scattering ratio, but is not effective for purely scattering problems and high aspect ratio zoning. However, if the scattering ratio is less than about 0.95, this procedure is very effective for all mesh spacing.

Total-variation based velocity inversion with Bregmanized operator splitting algorithm

NASA Astrophysics Data System (ADS)

Zand, Toktam; Gholami, Ali

2018-04-01

Many problems in applied geophysics can be formulated as a linear inverse problem. The associated problems, however, are large-scale and ill-conditioned. Therefore, regularization techniques are needed to be employed for solving them and generating a stable and acceptable solution. We consider numerical methods for solving such problems in this paper. In order to tackle the ill-conditioning of the problem we use blockiness as a prior information of the subsurface parameters and formulate the problem as a constrained total variation (TV) regularization. The Bregmanized operator splitting (BOS) algorithm as a combination of the Bregman iteration and the proximal forward backward operator splitting method is developed to solve the arranged problem. Two main advantages of this new algorithm are that no matrix inversion is required and that a discrepancy stopping criterion is used to stop the iterations, which allow efficient solution of large-scale problems. The high performance of the proposed TV regularization method is demonstrated using two different experiments: 1) velocity inversion from (synthetic) seismic data which is based on Born approximation, 2) computing interval velocities from RMS velocities via Dix formula. Numerical examples are presented to verify the feasibility of the proposed method for high-resolution velocity inversion.

Cubic spline anchored grid pattern algorithm for high-resolution detection of subsurface cavities by the IR-CAT method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kassab, A.J.; Pollard, J.E.

An algorithm is presented for the high-resolution detection of irregular-shaped subsurface cavities within irregular-shaped bodies by the IR-CAT method. The theoretical basis of the algorithm is rooted in the solution of an inverse geometric steady-state heat conduction problem. A Cauchy boundary condition is prescribed at the exposed surface, and the inverse geometric heat conduction problem is formulated by specifying the thermal condition at the inner cavities walls, whose unknown geometries are to be detected. The location of the inner cavities is initially estimated, and the domain boundaries are discretized. Linear boundary elements are used in conjunction with cubic splines formore » high resolution of the cavity walls. An anchored grid pattern (AGP) is established to constrain the cubic spline knots that control the inner cavity geometry to evolve along the AGP at each iterative step. A residual is defined measuring the difference between imposed and computed boundary conditions. A Newton-Raphson method with a Broyden update is used to automate the detection of inner cavity walls. During the iterative procedure, the movement of the inner cavity walls is restricted to physically realistic intermediate solutions. Numerical simulation demonstrates the superior resolution of the cubic spline AGP algorithm over the linear spline-based AGP in the detection of an irregular-shaped cavity. Numerical simulation is also used to test the sensitivity of the linear and cubic spline AGP algorithms by simulating bias and random error in measured surface temperature. The proposed AGP algorithm is shown to satisfactorily detect cavities with these simulated data.« less

Elucidation of the mechanism of N-demethylation catalyzed by cytochrome P450 monooxygenase is facilitated by exploiting nitrogen-15 heavy isotope effects.

PubMed

Kwiecień, Renata A; Molinié, Roland; Paneth, Piotr; Silvestre, Virginie; Lebreton, Jacques; Robins, Richard J

2011-06-01

(15)N heavy isotope effects are especially useful when detail is sought pertaining to the reaction mechanism for the cleavage of a C-N bond. Their potential in assisting to describe the mechanism of N-demethylation of tertiary amines by the action of cytochrome P450 monooxygenase has been investigated. As a working model for the first step, oxidation of the N-methyl group to N-methoxyl, tropine and a cytochrome P450 monooxygenase reaction centre composed of a truncated heme with sulfhydryl as the axial ligand were used. It is apparent that this first step of the reaction proceeds via a hydrogen atom transfer mechanism. Transition states for this step are described for both the high spin ((4)TS(H)) and low spin ((2)TS(H)) pathways in both gas and solvation states. Hence, overall normal secondary (15)N KIE could be calculated for the reaction path modeled in the low spin state, and inverse for the reaction modeled in the high spin state. This partial reaction has been identified as the probable rate limiting step. The model for the second step, fission of the C-N bond, consisted of N-methoxylnortropine and two molecules of water. A transition state described for this step, TS(CN), gives a strongly inverse overall theoretical (15)N KIE. Copyright © 2011 Elsevier Inc. All rights reserved.

A Crank–Nicolson Leapfrog stabilization: Unconditional stability and two applications

DOE PAGES

Jiang, Nan; Kubacki, Michaela; Layton, William; ...

2014-12-09

We propose and analyze a linear stabilization of the Crank-Nicolson Leapfrog (CNLF) method that removes all time step/CFL conditions for stability and controls the unstable mode. It also increases the SPD part of the linear system to be solved at each time step while increasing solution accuracy. We give a proof of unconditional stability of the method as well as a proof of unconditional, asymptotic stability of both the stable and unstable modes. As a result, we illustrate two applications of the method: uncoupling groundwater-surface water flows and Stokes flow plus a Coriolis term.

Product analysis illuminates the final steps of IES deletion in Tetrahymena thermophila

PubMed Central

Saveliev, Sergei V.; Cox, Michael M.

2001-01-01

DNA sequences (IES elements) eliminated from the developing macronucleus in the ciliate Tetrahymena thermophila are released as linear fragments, which have now been detected and isolated. A PCR-mediated examination of fragment end structures reveals three types of strand scission events, reflecting three steps in the deletion process. New evidence is provided for two steps proposed previously: an initiating double-stranded cleavage, and strand transfer to create a branched deletion intermediate. The fragment ends provide evidence for a previously uncharacterized third step: the branched DNA strand is cleaved at one of several defined sites located within 15–16 nucleotides of the IES boundary, liberating the deleted DNA in a linear form. PMID:11406601

Product analysis illuminates the final steps of IES deletion in Tetrahymena thermophila.

PubMed

Saveliev, S V; Cox, M M

2001-06-15

DNA sequences (IES elements) eliminated from the developing macronucleus in the ciliate Tetrahymena thermophila are released as linear fragments, which have now been detected and isolated. A PCR-mediated examination of fragment end structures reveals three types of strand scission events, reflecting three steps in the deletion process. New evidence is provided for two steps proposed previously: an initiating double-stranded cleavage, and strand transfer to create a branched deletion intermediate. The fragment ends provide evidence for a previously uncharacterized third step: the branched DNA strand is cleaved at one of several defined sites located within 15-16 nucleotides of the IES boundary, liberating the deleted DNA in a linear form.

CFORM- LINEAR CONTROL SYSTEM DESIGN AND ANALYSIS: CLOSED FORM SOLUTION AND TRANSIENT RESPONSE OF THE LINEAR DIFFERENTIAL EQUATION

NASA Technical Reports Server (NTRS)

Jamison, J. W.

1994-01-01

CFORM was developed by the Kennedy Space Center Robotics Lab to assist in linear control system design and analysis using closed form and transient response mechanisms. The program computes the closed form solution and transient response of a linear (constant coefficient) differential equation. CFORM allows a choice of three input functions: the Unit Step (a unit change in displacement); the Ramp function (step velocity); and the Parabolic function (step acceleration). It is only accurate in cases where the differential equation has distinct roots, and does not handle the case for roots at the origin (s=0). Initial conditions must be zero. Differential equations may be input to CFORM in two forms - polynomial and product of factors. In some linear control analyses, it may be more appropriate to use a related program, Linear Control System Design and Analysis (KSC-11376), which uses root locus and frequency response methods. CFORM was written in VAX FORTRAN for a VAX 11/780 under VAX VMS 4.7. It has a central memory requirement of 30K. CFORM was developed in 1987.

Transurethral Ultrasound Diffraction Tomography

DTIC Science & Technology

2007-03-01

the covariance matrix was derived. The covariance reduced to that of the X- ray CT under the assumptions of linear operator and real data.[5] The...the covariance matrix in the linear x- ray computed tomography is a special case of the inverse scattering matrix derived in this paper. The matrix was...is derived in Sec. IV, and its relation to that of the linear x- ray computed tomography appears in Sec. V. In Sec. VI, the inverse scattering

Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

NASA Astrophysics Data System (ADS)

Kabanov, Dmitry I.; Kasimov, Aslan R.

2018-03-01

We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

Computed inverse resonance imaging for magnetic susceptibility map reconstruction.

PubMed

Chen, Zikuan; Calhoun, Vince

2012-01-01

This article reports a computed inverse magnetic resonance imaging (CIMRI) model for reconstructing the magnetic susceptibility source from MRI data using a 2-step computational approach. The forward T2*-weighted MRI (T2*MRI) process is broken down into 2 steps: (1) from magnetic susceptibility source to field map establishment via magnetization in the main field and (2) from field map to MR image formation by intravoxel dephasing average. The proposed CIMRI model includes 2 inverse steps to reverse the T2*MRI procedure: field map calculation from MR-phase image and susceptibility source calculation from the field map. The inverse step from field map to susceptibility map is a 3-dimensional ill-posed deconvolution problem, which can be solved with 3 kinds of approaches: the Tikhonov-regularized matrix inverse, inverse filtering with a truncated filter, and total variation (TV) iteration. By numerical simulation, we validate the CIMRI model by comparing the reconstructed susceptibility maps for a predefined susceptibility source. Numerical simulations of CIMRI show that the split Bregman TV iteration solver can reconstruct the susceptibility map from an MR-phase image with high fidelity (spatial correlation ≈ 0.99). The split Bregman TV iteration solver includes noise reduction, edge preservation, and image energy conservation. For applications to brain susceptibility reconstruction, it is important to calibrate the TV iteration program by selecting suitable values of the regularization parameter. The proposed CIMRI model can reconstruct the magnetic susceptibility source of T2*MRI by 2 computational steps: calculating the field map from the phase image and reconstructing the susceptibility map from the field map. The crux of CIMRI lies in an ill-posed 3-dimensional deconvolution problem, which can be effectively solved by the split Bregman TV iteration algorithm.

A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations

NASA Astrophysics Data System (ADS)

Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei

2015-12-01

In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 ⁡ M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.

Elastic robot control - Nonlinear inversion and linear stabilization

NASA Technical Reports Server (NTRS)

Singh, S. N.; Schy, A. A.

1986-01-01

An approach to the control of elastic robot systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law u(d) is derived such that in the closed-loop system independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law u(s) is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u(d) + u(s).

Large-scale shear velocity structure of the upper mantle beneath Africa and surrounding regions

NASA Astrophysics Data System (ADS)

Legendre, Cédric; Meier, Thomas; Lebedev, Sergei; Friederich, Wolfgang; Egelados Working Group

2010-05-01

The automated multimode waveform inversion technique developed by Lebedev et al. (2005) was applied to available data of broadband stations in Africa and surrounding regions. It performs a fitting of the complete waveform starting from the S-wave onset to the surface wave. Assuming the location and focal mechanism of a considered earthquake as known, the first basic step is to consider each available seismogram separately and to find the velocity perturbations that can explain the filtered seismogram best. In a second step, each velocity perturbations serves as a linear constraint in an inversion for a 3D S-wave velocity model of the upper mantle. We collected data for the years from 1990 to 2006 from all permanent stations for which data were available via the data centers of ORFEUS, GEOFON and IRIS, and from others that build the Virtual European Seismological Network (VEBSN) as well as all available African stations. Just recently we were also able to add the data recorded by the temporary broadband EGELADOS network in the southern Aegean. This represents a huge dataset with all available stations in Africa and surroundings regions. The resulting models exhibit an overwhelming structural detail in relation to the size of the region considered in the inversion. They are to our knowledge the most detailed models of shear wave velocity currently available for the African upper mantle and surroundings. Most prominent features are an extremely sharp demarcation of the Dead Sea Rift System. Narrow high velocity regions follow the Hellenic arc and the Ionian trench toward the north. Low velocity zones are found at depths around 150 km in the Middle East region. The hotspots in North Africa are also clearly imaged.

Novel linear piezoelectric motor for precision position stage

NASA Astrophysics Data System (ADS)

Chen, Chao; Shi, Yunlai; Zhang, Jun; Wang, Junshan

2016-03-01

Conventional servomotor and stepping motor face challenges in nanometer positioning stages due to the complex structure, motion transformation mechanism, and slow dynamic response, especially directly driven by linear motor. A new butterfly-shaped linear piezoelectric motor for linear motion is presented. A two-degree precision position stage driven by the proposed linear ultrasonic motor possesses a simple and compact configuration, which makes the system obtain shorter driving chain. Firstly, the working principle of the linear ultrasonic motor is analyzed. The oscillation orbits of two driving feet on the stator are produced successively by using the anti-symmetric and symmetric vibration modes of the piezoelectric composite structure, and the slider pressed on the driving feet can be propelled twice in only one vibration cycle. Then with the derivation of the dynamic equation of the piezoelectric actuator and transient response model, start-upstart-up and settling state characteristics of the proposed linear actuator is investigated theoretically and experimentally, and is applicable to evaluate step resolution of the precision platform driven by the actuator. Moreover the structure of the two-degree position stage system is described and a special precision displacement measurement system is built. Finally, the characteristics of the two-degree position stage are studied. In the closed-loop condition the positioning accuracy of plus or minus <0.5 μm is experimentally obtained for the stage propelled by the piezoelectric motor. A precision position stage based the proposed butterfly-shaped linear piezoelectric is theoretically and experimentally investigated.

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, L.; Gu, H.

2017-12-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion has a better applicability. It doesn't need some assumptions and can estimate more parameters simultaneously. Meanwhile, by using the generalized linear method, the inversion is easily realized and its calculation amount is small. We use the Marmousi model to generate synthetic seismic records to test and analyze the influence of random noise. Without noise, all estimation results are relatively accurate. With the increase of noise, P-wave velocity change and oil saturation change are stable and less affected by noise. S-wave velocity change is most affected by noise. Finally we use the actual field data of time-lapse seismic prospecting to process and the results can prove the availability and feasibility of our method in actual situation.

Effects of anisotropy on the two-dimensional inversion procedure

NASA Astrophysics Data System (ADS)

Heise, Wiebke; Pous, Jaume

2001-12-01

In this paper we show some of the effects that appear in magnetotelluric measurements over 2-D anisotropic structures, and propose a procedure to recover the anisotropy using 2-D inversion algorithms for isotropic models. First, we see how anisotropy affects the usual interpretation steps: dimensionality analysis and 2-D inversion. Two models containing general 2-D azimuthal anisotropic features were chosen to illustrate this approach: an anisotropic block and an anisotropic layer, both forming part of general 2-D models. In addition, a third model with dipping anisotropy was studied. For each model we examined the influence of various anisotropy strikes and resistivity contrasts on the dimensionality analysis and on the behaviour of the induction arrows. We found that, when the anisotropy ratio is higher than five, even if the strike is frequency-dependent it is possible to decide on a direction close to the direction of anisotropy. Then, if the data are rotated to this angle, a 2-D inversion reproduces the anisotropy reasonably well by means of macro-anisotropy. This strategy was tested on field data where anisotropy had been previously recognized.

Role of step size and max dwell time in anatomy based inverse optimization for prostate implants

PubMed Central

Manikandan, Arjunan; Sarkar, Biplab; Rajendran, Vivek Thirupathur; King, Paul R.; Sresty, N.V. Madhusudhana; Holla, Ragavendra; Kotur, Sachin; Nadendla, Sujatha

2013-01-01

In high dose rate (HDR) brachytherapy, the source dwell times and dwell positions are vital parameters in achieving a desirable implant dose distribution. Inverse treatment planning requires an optimal choice of these parameters to achieve the desired target coverage with the lowest achievable dose to the organs at risk (OAR). This study was designed to evaluate the optimum source step size and maximum source dwell time for prostate brachytherapy implants using an Ir-192 source. In total, one hundred inverse treatment plans were generated for the four patients included in this study. Twenty-five treatment plans were created for each patient by varying the step size and maximum source dwell time during anatomy-based, inverse-planned optimization. Other relevant treatment planning parameters were kept constant, including the dose constraints and source dwell positions. Each plan was evaluated for target coverage, urethral and rectal dose sparing, treatment time, relative target dose homogeneity, and nonuniformity ratio. The plans with 0.5 cm step size were seen to have clinically acceptable tumor coverage, minimal normal structure doses, and minimum treatment time as compared with the other step sizes. The target coverage for this step size is 87% of the prescription dose, while the urethral and maximum rectal doses were 107.3 and 68.7%, respectively. No appreciable difference in plan quality was observed with variation in maximum source dwell time. The step size plays a significant role in plan optimization for prostate implants. Our study supports use of a 0.5 cm step size for prostate implants. PMID:24049323

The relationship between job stressors, hardy personality, coping resources and burnout in a sample of nurses: a correlational study at two time points.

PubMed

Garrosa, Eva; Rainho, Conceição; Moreno-Jiménez, Bernardo; Monteiro, Maria João

2010-02-01

Nursing is considered as a risk profession with high levels of stress and burnout, and these levels are probably increasing. This study assessed temporal and cross-sectional relationships between job stressors, hardy personality and coping resources on burnout dimensions among nurses. Temporal and cross-sectional effects were evaluated. A sample of 98 nurses from Portugal completed the Nursing Burnout Scale at two time points. The data were analysed using descriptive statistics, Pearson correlations, and hierarchical linear regression analyses regressing Wave 2 burnout dimensions. The study confirmed the specific contribution of control and challenged hardy personality dimensions as the explanation of burnout. However, commitment did not show any effects in this study. Social support and active coping were also relevant predictors of burnout dimensions. Specifically, active coping had an inverse temporal effect on depersonalisation and lack of personal accomplishment. In relation to the burnout process, depersonalisation appeared as an antecedent of lack of personal accomplishment. The present study is an initial step to comprehend the link between job stressors, hardy personality, coping resources and diminishing burnout. Copyright 2009 Elsevier Ltd. All rights reserved.

Inversion for the driving forces of plate tectonics

NASA Technical Reports Server (NTRS)

Richardson, R. M.

1983-01-01

Inverse modeling techniques have been applied to the problem of determining the roles of various forces that may drive and resist plate tectonic motions. Separate linear inverse problems have been solved to find the best fitting pole of rotation for finite element grid point velocities and to find the best combination of force models to fit the observed relative plate velocities for the earth's twelve major plates using the generalized inverse operator. Variance-covariance data on plate motion have also been included. Results emphasize the relative importance of ridge push forces in the driving mechanism. Convergent margin forces are smaller by at least a factor of two, and perhaps by as much as a factor of twenty. Slab pull, apparently, is poorly transmitted to the surface plate as a driving force. Drag forces at the base of the plate are smaller than ridge push forces, although the sign of the force remains in question.

Termination Proofs for String Rewriting Systems via Inverse Match-Bounds

NASA Technical Reports Server (NTRS)

Butler, Ricky (Technical Monitor); Geser, Alfons; Hofbauer, Dieter; Waldmann, Johannes

2004-01-01

Annotating a letter by a number, one can record information about its history during a reduction. A string rewriting system is called match-bounded if there is a global upper bound to these numbers. In earlier papers we established match-boundedness as a strong sufficient criterion for both termination and preservation of regular languages. We show now that the string rewriting system whose inverse (left and right hand sides exchanged) is match-bounded, also have exceptional properties, but slightly different ones. Inverse match-bounded systems effectively preserve context-free languages; their sets of normalized strings and their sets of immortal strings are effectively regular. These sets of strings can be used to decide the normalization, the termination and the uniform termination problems of inverse match-bounded systems. We also show that the termination problem is decidable in linear time, and that a certain strong reachability problem is deciable, thus solving two open problems of McNaughton's.

Constraining gross primary production and ecosystem respiration estimates for North America using atmospheric observations of carbonyl sulfide (OCS) and CO2

NASA Astrophysics Data System (ADS)

He, W.; Ju, W.; Chen, H.; Peters, W.; van der Velde, I.; Baker, I. T.; Andrews, A. E.; Zhang, Y.; Launois, T.; Campbell, J. E.; Suntharalingam, P.; Montzka, S. A.

2016-12-01

Carbonyl sulfide (OCS) is a promising novel atmospheric tracer for studying carbon cycle processes. OCS shares a similar pathway as CO2 during photosynthesis but not released through a respiration-like process, thus could be used to partition Gross Primary Production (GPP) from Net Ecosystem-atmosphere CO2 Exchange (NEE). This study uses joint atmospheric observations of OCS and CO2 to constrain GPP and ecosystem respiration (Re). Flask data from tower and aircraft sites over North America are collected. We employ our recently developed CarbonTracker (CT)-Lagrange carbon assimilation system, which is based on the CT framework and the Weather Research and Forecasting - Stochastic Time-Inverted Lagrangian Transport (WRF-STILT) model, and the Simple Biosphere model with simulated OCS (SiB3-OCS) that provides prior GPP, Re and plant uptake fluxes of OCS. Derived plant OCS fluxes from both process model and GPP-scaled model are tested in our inversion. To investigate the ability of OCS to constrain GPP and understand the uncertainty propagated from OCS modeling errors to constrained fluxes in a dual-tracer system including OCS and CO2, two inversion schemes are implemented and compared: (1) a two-step scheme, which firstly optimizes GPP using OCS observations, and then simultaneously optimizes GPP and Re using CO2 observations with OCS-constrained GPP in the first step as prior; (2) a joint scheme, which simultaneously optimizes GPP and Re using OCS and CO2 observations. We will evaluate the result using an estimated GPP from space-borne solar-induced fluorescence observations and a data-driven GPP upscaled from FLUXNET data with a statistical model (Jung et al., 2011). Preliminary result for the year 2010 shows the joint inversion makes simulated mole fractions more consistent with observations for both OCS and CO2. However, the uncertainty of OCS simulation is larger than that of CO2. The two-step and joint schemes perform similarly in improving the consistence with observations for OCS, implicating that OCS could provide independent constraint in joint inversion. Optimization makes less total GPP and Re but more NEE, when testing with prior CO2 fluxes from two biosphere models. This study gives an in-depth insight into the role of joint atmospheric OCS and CO2 observations in constraining CO2 fluxes.

Identifying pleiotropic genes in genome-wide association studies from related subjects using the linear mixed model and Fisher combination function.

PubMed

Yang, James J; Williams, L Keoki; Buu, Anne

2017-08-24

A multivariate genome-wide association test is proposed for analyzing data on multivariate quantitative phenotypes collected from related subjects. The proposed method is a two-step approach. The first step models the association between the genotype and marginal phenotype using a linear mixed model. The second step uses the correlation between residuals of the linear mixed model to estimate the null distribution of the Fisher combination test statistic. The simulation results show that the proposed method controls the type I error rate and is more powerful than the marginal tests across different population structures (admixed or non-admixed) and relatedness (related or independent). The statistical analysis on the database of the Study of Addiction: Genetics and Environment (SAGE) demonstrates that applying the multivariate association test may facilitate identification of the pleiotropic genes contributing to the risk for alcohol dependence commonly expressed by four correlated phenotypes. This study proposes a multivariate method for identifying pleiotropic genes while adjusting for cryptic relatedness and population structure between subjects. The two-step approach is not only powerful but also computationally efficient even when the number of subjects and the number of phenotypes are both very large.

Three-dimensional inverse problem of geometrical optics: a mathematical comparison between Fermat's principle and the eikonal equation.

PubMed

Borghero, Francesco; Demontis, Francesco

2016-09-01

In the framework of geometrical optics, we consider the following inverse problem: given a two-parameter family of curves (congruence) (i.e., f(x,y,z)=c₁,g(x,y,z)=c₂), construct the refractive-index distribution function n=n(x,y,z) of a 3D continuous transparent inhomogeneous isotropic medium, allowing for the creation of the given congruence as a family of monochromatic light rays. We solve this problem by following two different procedures: 1. By applying Fermat's principle, we establish a system of two first-order linear nonhomogeneous PDEs in the unique unknown function n=n(x,y,z) relating the assigned congruence of rays with all possible refractive-index profiles compatible with this family. Moreover, we furnish analytical proof that the family of rays must be a normal congruence. 2. By applying the eikonal equation, we establish a second system of two first-order linear homogeneous PDEs whose solutions give the equation S(x,y,z)=const. of the geometric wavefronts and, consequently, all pertinent refractive-index distribution functions n=n(x,y,z). Finally, we make a comparison between the two procedures described above, discussing appropriate examples having exact solutions.

United States Medical Licensing Examination and American Board of Pediatrics Certification Examination Results: Does the Residency Program Contribute to Trainee Achievement.

PubMed

Welch, Thomas R; Olson, Brad G; Nelsen, Elizabeth; Beck Dallaghan, Gary L; Kennedy, Gloria A; Botash, Ann

2017-09-01

To determine whether training site or prior examinee performance on the US Medical Licensing Examination (USMLE) step 1 and step 2 might predict pass rates on the American Board of Pediatrics (ABP) certifying examination. Data from graduates of pediatric residency programs completing the ABP certifying examination between 2009 and 2013 were obtained. For each, results of the initial ABP certifying examination were obtained, as well as results on National Board of Medical Examiners (NBME) step 1 and step 2 examinations. Hierarchical linear modeling was used to nest first-time ABP results within training programs to isolate program contribution to ABP results while controlling for USMLE step 1 and step 2 scores. Stepwise linear regression was then used to determine which of these examinations was a better predictor of ABP results. A total of 1110 graduates of 15 programs had complete testing results and were subject to analysis. Mean ABP scores for these programs ranged from 186.13 to 214.32. The hierarchical linear model suggested that the interaction of step 1 and 2 scores predicted ABP performance (F[1,1007.70] = 6.44, P = .011). By conducting a multilevel model by training program, both USMLE step examinations predicted first-time ABP results (b = .002, t = 2.54, P = .011). Linear regression analyses indicated that step 2 results were a better predictor of ABP performance than step 1 or a combination of the two USMLE scores. Performance on the USMLE examinations, especially step 2, predicts performance on the ABP certifying examination. The contribution of training site to ABP performance was statistically significant, though contributed modestly to the effect compared with prior USMLE scores. Copyright © 2017 Elsevier Inc. All rights reserved.

Comparison of the Effect of Horizontal Vibrations on Interfacial Waves in a Two-Layer System of Inviscid Liquids to Effective Gravity Inversion

NASA Astrophysics Data System (ADS)

Pimenova, Anastasiya V.; Goldobin, Denis S.; Lyubimova, Tatyana P.

2018-02-01

We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and arbitrary ratio of layer thicknesses. The derivation is performed within the framework of the long-wavelength approximation, which is relevant as the linear instability of a thin-layers system is long-wavelength. The dynamics of equations is integrable and the equations themselves can be compared to the Boussinesq equation for the gravity waves in shallow water, which allows one to compare the action of the vibrational field to the action of the gravity and its possible effective inversion.

Comparative transduction mechanisms of hair cells in the bullfrog utriculus. II. Sensitivity and response dynamics to hair bundle displacement

NASA Technical Reports Server (NTRS)

Baird, R. A.

1994-01-01

1. Hair cells in whole-mount in vitro preparations of the utricular macula of the bullfrog (Rana catesbeiana) were selected according to their macular location and hair bundle morphology. The sensitivity and response dynamics of selected hair cells to natural stimulation were examined by recording their voltage responses to step and sinusoidal hair bundle displacements applied to their longest stereocilia. 2. The voltage responses of 31 hair cells to sinusoidal hair bundle displacements were characterized by their gains and phases, taken with respect to peak hair bundle displacement. The gains of Type B and Type C cells at both 0.5 and 5.0 Hz were markedly lower than those of Type F and Type E cells. Phases, with the exception of Type C cells, lagged hair bundle displacement at 0.5 Hz. Type C cells had phase leads of 25-40 degrees. At 5.0 Hz, response phases in all cells were phase lagged with respect to those at 0.5 Hz. Type C cells had larger gains and smaller phase leads at 5.0 Hz than at 0.5 Hz, suggesting the presence of low-frequency adaptation. 3. Displacement-response curves, derived from the voltage responses to 5.0-Hz sinusoids, were sigmoidal in shape and asymmetrical, with the depolarizing response having a greater magnitude and saturating less abruptly than the hyperpolarizing response. When normalized to their largest displacement the linear ranges of these curves varied from < 0.5 to 1.25 microns and were largest in Type B and smallest in Type F and Type E cells. Sensitivity, defined as the slope of the normalized displacement-response curve, was inversely correlated with linear range. 4. The contribution of geometric factors associated with the hair bundle to linear range and sensitivity were predicted from realistic models of utricular hair bundles created using morphological data obtained from light and electron microscopy. Three factors, including 1) the inverse ratio of the lengths of the kinocilium and longest stereocilia, representing the lever arm between kinociliary and stereociliary displacement; 2) tip link extension/linear displacement, largely a function of stereociliary height and separation; and 3) stereociliary number, an estimate of the number of transduction channels, were considered in this analysis. The first of these factors was quantitatively more important than the latter two factors and their total contribution was largest in Type B and Type C cells. Theoretical models were also used to calculate the relation between rotary and linear displacement.(ABSTRACT TRUNCATED AT 400 WORDS).

Towards "Inverse" Character Tables? A One-Step Method for Decomposing Reducible Representations

ERIC Educational Resources Information Center

Piquemal, J.-Y.; Losno, R.; Ancian, B.

2009-01-01

In the framework of group theory, a new procedure is described for a one-step automated reduction of reducible representations. The matrix inversion tool, provided by standard spreadsheet software, is applied to the central part of the character table that contains the characters of the irreducible representation. This method is not restricted to…

Comparison of IMRT planning with two-step and one-step optimization: a strategy for improving therapeutic gain and reducing the integral dose

NASA Astrophysics Data System (ADS)

Abate, A.; Pressello, M. C.; Benassi, M.; Strigari, L.

2009-12-01

The aim of this study was to evaluate the effectiveness and efficiency in inverse IMRT planning of one-step optimization with the step-and-shoot (SS) technique as compared to traditional two-step optimization using the sliding windows (SW) technique. The Pinnacle IMRT TPS allows both one-step and two-step approaches. The same beam setup for five head-and-neck tumor patients and dose-volume constraints were applied for all optimization methods. Two-step plans were produced converting the ideal fluence with or without a smoothing filter into the SW sequence. One-step plans, based on direct machine parameter optimization (DMPO), had the maximum number of segments per beam set at 8, 10, 12, producing a directly deliverable sequence. Moreover, the plans were generated whether a split-beam was used or not. Total monitor units (MUs), overall treatment time, cost function and dose-volume histograms (DVHs) were estimated for each plan. PTV conformality and homogeneity indexes and normal tissue complication probability (NTCP) that are the basis for improving therapeutic gain, as well as non-tumor integral dose (NTID), were evaluated. A two-sided t-test was used to compare quantitative variables. All plans showed similar target coverage. Compared to two-step SW optimization, the DMPO-SS plans resulted in lower MUs (20%), NTID (4%) as well as NTCP values. Differences of about 15-20% in the treatment delivery time were registered. DMPO generates less complex plans with identical PTV coverage, providing lower NTCP and NTID, which is expected to reduce the risk of secondary cancer. It is an effective and efficient method and, if available, it should be favored over the two-step IMRT planning.

Analytic reconstruction of magnetic resonance imaging signal obtained from a periodic encoding field.

PubMed

Rybicki, F J; Hrovat, M I; Patz, S

2000-09-01

We have proposed a two-dimensional PERiodic-Linear (PERL) magnetic encoding field geometry B(x,y) = g(y)y cos(q(x)x) and a magnetic resonance imaging pulse sequence which incorporates two fields to image a two-dimensional spin density: a standard linear gradient in the x dimension, and the PERL field. Because of its periodicity, the PERL field produces a signal where the phase of the two dimensions is functionally different. The x dimension is encoded linearly, but the y dimension appears as the argument of a sinusoidal phase term. Thus, the time-domain signal and image spin density are not related by a two-dimensional Fourier transform. They are related by a one-dimensional Fourier transform in the x dimension and a new Bessel function integral transform (the PERL transform) in the y dimension. The inverse of the PERL transform provides a reconstruction algorithm for the y dimension of the spin density from the signal space. To date, the inverse transform has been computed numerically by a Bessel function expansion over its basis functions. This numerical solution used a finite sum to approximate an infinite summation and thus introduced a truncation error. This work analytically determines the basis functions for the PERL transform and incorporates them into the reconstruction algorithm. The improved algorithm is demonstrated by (1) direct comparison between the numerically and analytically computed basis functions, and (2) reconstruction of a known spin density. The new solution for the basis functions also lends proof of the system function for the PERL transform under specific conditions.

Statistical modeling of the reactions Fe(+) + N2O → FeO(+) + N2 and FeO(+) + CO → Fe(+) + CO2.

PubMed

Ushakov, Vladimir G; Troe, Jürgen; Johnson, Ryan S; Guo, Hua; Ard, Shaun G; Melko, Joshua J; Shuman, Nicholas S; Viggiano, Albert A

2015-08-14

The rates of the reactions Fe(+) + N2O → FeO(+) + N2 and FeO(+) + CO → Fe(+) + CO2 are modeled by statistical rate theory accounting for energy- and angular momentum-specific rate constants for formation of the primary and secondary cationic adducts and their backward and forward reactions. The reactions are both suggested to proceed on sextet and quartet potential energy surfaces with efficient, but probably not complete, equilibration by spin-inversion of the populations of the sextet and quartet adducts. The influence of spin-inversion on the overall reaction rate is investigated. The differences of the two reaction rates mostly are due to different numbers of entrance states (atom + linear rotor or linear rotor + linear rotor, respectively). The reaction Fe(+) + N2O was studied either with (6)Fe(+) or with (4)Fe(+) reactants. Differences in the rate constants of (6)Fe(+) and (4)Fe(+) reacting with N2O are attributed to different contributions from electronically excited potential energy surfaces, such as they originate from the open-electronic shell reactants.

Towards the mechanical characterization of abdominal wall by inverse analysis.

PubMed

Simón-Allué, R; Calvo, B; Oberai, A A; Barbone, P E

2017-02-01

The aim of this study is to characterize the passive mechanical behaviour of abdominal wall in vivo in an animal model using only external cameras and numerical analysis. The main objective lies in defining a methodology that provides in vivo information of a specific patient without altering mechanical properties. It is demonstrated in the mechanical study of abdomen for hernia purposes. Mechanical tests consisted on pneumoperitoneum tests performed on New Zealand rabbits, where inner pressure was varied from 0mmHg to 12mmHg. Changes in the external abdominal surface were recorded and several points were tracked. Based on their coordinates we reconstructed a 3D finite element model of the abdominal wall, considering an incompressible hyperelastic material model defined by two parameters. The spatial distributions of these parameters (shear modulus and non linear parameter) were calculated by inverse analysis, using two different types of regularization: Total Variation Diminishing (TVD) and Tikhonov (H 1 ). After solving the inverse problem, the distribution of the material parameters were obtained along the abdominal surface. Accuracy of the results was evaluated for the last level of pressure. Results revealed a higher value of the shear modulus in a wide stripe along the craneo-caudal direction, associated with the presence of linea alba in conjunction with fascias and rectus abdominis. Non linear parameter distribution was smoother and the location of higher values varied with the regularization type. Both regularizations proved to yield in an accurate predicted displacement field, but H 1 obtained a smoother material parameter distribution while TVD included some discontinuities. The methodology here presented was able to characterize in vivo the passive non linear mechanical response of the abdominal wall. Copyright © 2016 Elsevier Ltd. All rights reserved.

Joint inversion of multiple geophysical and petrophysical data using generalized fuzzy clustering algorithms

NASA Astrophysics Data System (ADS)

Sun, Jiajia; Li, Yaoguo

2017-02-01

Joint inversion that simultaneously inverts multiple geophysical data sets to recover a common Earth model is increasingly being applied to exploration problems. Petrophysical data can serve as an effective constraint to link different physical property models in such inversions. There are two challenges, among others, associated with the petrophysical approach to joint inversion. One is related to the multimodality of petrophysical data because there often exist more than one relationship between different physical properties in a region of study. The other challenge arises from the fact that petrophysical relationships have different characteristics and can exhibit point, linear, quadratic, or exponential forms in a crossplot. The fuzzy c-means (FCM) clustering technique is effective in tackling the first challenge and has been applied successfully. We focus on the second challenge in this paper and develop a joint inversion method based on variations of the FCM clustering technique. To account for the specific shapes of petrophysical relationships, we introduce several different fuzzy clustering algorithms that are capable of handling different shapes of petrophysical relationships. We present two synthetic and one field data examples and demonstrate that, by choosing appropriate distance measures for the clustering component in the joint inversion algorithm, the proposed joint inversion method provides an effective means of handling common petrophysical situations we encounter in practice. The jointly inverted models have both enhanced structural similarity and increased petrophysical correlation, and better represent the subsurface in the spatial domain and the parameter domain of physical properties.

Grid-Independent Compressive Imaging and Fourier Phase Retrieval

ERIC Educational Resources Information Center

Liao, Wenjing

2013-01-01

This dissertation is composed of two parts. In the first part techniques of band exclusion(BE) and local optimization(LO) are proposed to solve linear continuum inverse problems independently of the grid spacing. The second part is devoted to the Fourier phase retrieval problem. Many situations in optics, medical imaging and signal processing call…

Focal mechanisms and tidal modulation for tectonic tremors in Taiwan

NASA Astrophysics Data System (ADS)

Ide, S.; Yabe, S.; Tai, H. J.; Chen, K. H.

2015-12-01

Tectonic tremors in Taiwan have been discovered beneath the southern Central Range, but their hosting structure has been unknown. Here we constrain the focal mechanism of underground deformation related to tremors, using moment tensor inversion in the very low frequency band and tidal stress analysis. Three types of seismic data are used for two analysis steps: detection of tremors and the moment tensor inversion. Short-period seismograms from CWBSN are used for tremor detection. Broadband seismograms from BATS and the TAIGER project are used for both steps. About 1000 tremors were detected using an envelope correlation method in the high frequency band (2-8 Hz). Broadband seismograms are stacked relative to the tremor timing, and inverted for a moment tensor in the low frequency band (0.02-0.05 Hz). The best solution was obtained at 32 km depth, as a double-couple consistent with a low-angle thrust fault dipping to the east-southeast, or a high-angle thrust with a south-southwest strike. Almost all tremors occur when tidal shear stress is positive and normal stress is negative (clamping). Since the clamping stress is high for a high-angle thrust fault, the low-angle thrust fault is more likely to be the fault plane. Tremor rate increases non-linearly with increasing shear stress, suggesting a velocity strengthening friction law. The high tidal sensitivity is inconsistent with horizontal slip motion suggested by previous studies, and normal faults that dominates regional shallow earthquakes. Our results favor thrust slip on a low-angle fault dipping to the east-southeast, consistent with the subduction of the Eurasian plate. The tremor region is characterized by a deep thermal anomaly with decrease normal stress. This region has also experienced enough subduction to produce metamorphic fluids. A large amount of fluid and low vertical stress may explain the high tidal sensitivity.

Development of the WRF-CO2 4D-Var assimilation system v1.0

NASA Astrophysics Data System (ADS)

Zheng, Tao; French, Nancy H. F.; Baxter, Martin

2018-05-01

Regional atmospheric CO2 inversions commonly use Lagrangian particle trajectory model simulations to calculate the required influence function, which quantifies the sensitivity of a receptor to flux sources. In this paper, an adjoint-based four-dimensional variational (4D-Var) assimilation system, WRF-CO2 4D-Var, is developed to provide an alternative approach. This system is developed based on the Weather Research and Forecasting (WRF) modeling system, including the system coupled to chemistry (WRF-Chem), with tangent linear and adjoint codes (WRFPLUS), and with data assimilation (WRFDA), all in version 3.6. In WRF-CO2 4D-Var, CO2 is modeled as a tracer and its feedback to meteorology is ignored. This configuration allows most WRF physical parameterizations to be used in the assimilation system without incurring a large amount of code development. WRF-CO2 4D-Var solves for the optimized CO2 flux scaling factors in a Bayesian framework. Two variational optimization schemes are implemented for the system: the first uses the limited memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization algorithm (L-BFGS-B) and the second uses the Lanczos conjugate gradient (CG) in an incremental approach. WRFPLUS forward, tangent linear, and adjoint models are modified to include the physical and dynamical processes involved in the atmospheric transport of CO2. The system is tested by simulations over a domain covering the continental United States at 48 km × 48 km grid spacing. The accuracy of the tangent linear and adjoint models is assessed by comparing against finite difference sensitivity. The system's effectiveness for CO2 inverse modeling is tested using pseudo-observation data. The results of the sensitivity and inverse modeling tests demonstrate the potential usefulness of WRF-CO2 4D-Var for regional CO2 inversions.

Adaptive dynamic programming for discrete-time linear quadratic regulation based on multirate generalised policy iteration

NASA Astrophysics Data System (ADS)

Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

2018-06-01

In this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.

Towards quantifying uncertainty in Greenland's contribution to 21st century sea-level rise

NASA Astrophysics Data System (ADS)

Perego, M.; Tezaur, I.; Price, S. F.; Jakeman, J.; Eldred, M.; Salinger, A.; Hoffman, M. J.

2015-12-01

We present recent work towards developing a methodology for quantifying uncertainty in Greenland's 21st century contribution to sea-level rise. While we focus on uncertainties associated with the optimization and calibration of the basal sliding parameter field, the methodology is largely generic and could be applied to other (or multiple) sets of uncertain model parameter fields. The first step in the workflow is the solution of a large-scale, deterministic inverse problem, which minimizes the mismatch between observed and computed surface velocities by optimizing the two-dimensional coefficient field in a linear-friction sliding law. We then expand the deviation in this coefficient field from its estimated "mean" state using a reduced basis of Karhunen-Loeve Expansion (KLE) vectors. A Bayesian calibration is used to determine the optimal coefficient values for this expansion. The prior for the Bayesian calibration can be computed using the Hessian of the deterministic inversion or using an exponential covariance kernel. The posterior distribution is then obtained using Markov Chain Monte Carlo run on an emulator of the forward model. Finally, the uncertainty in the modeled sea-level rise is obtained by performing an ensemble of forward propagation runs. We present and discuss preliminary results obtained using a moderate-resolution model of the Greenland Ice sheet. As demonstrated in previous work, the primary difficulty in applying the complete workflow to realistic, high-resolution problems is that the effective dimension of the parameter space is very large.

Evaluation of interpolation techniques for the creation of gridded daily precipitation (1 × 1 km2); Cyprus, 1980-2010

NASA Astrophysics Data System (ADS)

Camera, Corrado; Bruggeman, Adriana; Hadjinicolaou, Panos; Pashiardis, Stelios; Lange, Manfred A.

2014-01-01

High-resolution gridded daily data sets are essential for natural resource management and the analyses of climate changes and their effects. This study aims to evaluate the performance of 15 simple or complex interpolation techniques in reproducing daily precipitation at a resolution of 1 km2 over topographically complex areas. Methods are tested considering two different sets of observation densities and different rainfall amounts. We used rainfall data that were recorded at 74 and 145 observational stations, respectively, spread over the 5760 km2 of the Republic of Cyprus, in the Eastern Mediterranean. Regression analyses utilizing geographical copredictors and neighboring interpolation techniques were evaluated both in isolation and combined. Linear multiple regression (LMR) and geographically weighted regression methods (GWR) were tested. These included a step-wise selection of covariables, as well as inverse distance weighting (IDW), kriging, and 3D-thin plate splines (TPS). The relative rank of the different techniques changes with different station density and rainfall amounts. Our results indicate that TPS performs well for low station density and large-scale events and also when coupled with regression models. It performs poorly for high station density. The opposite is observed when using IDW. Simple IDW performs best for local events, while a combination of step-wise GWR and IDW proves to be the best method for large-scale events and high station density. This study indicates that the use of step-wise regression with a variable set of geographic parameters can improve the interpolation of large-scale events because it facilitates the representation of local climate dynamics.

Frequency-domain full-waveform inversion with non-linear descent directions

NASA Astrophysics Data System (ADS)

Geng, Yu; Pan, Wenyong; Innanen, Kristopher A.

2018-05-01

Full-waveform inversion (FWI) is a highly non-linear inverse problem, normally solved iteratively, with each iteration involving an update constructed through linear operations on the residuals. Incorporating a flexible degree of non-linearity within each update may have important consequences for convergence rates, determination of low model wavenumbers and discrimination of parameters. We examine one approach for doing so, wherein higher order scattering terms are included within the sensitivity kernel during the construction of the descent direction, adjusting it away from that of the standard Gauss-Newton approach. These scattering terms are naturally admitted when we construct the sensitivity kernel by varying not the current but the to-be-updated model at each iteration. Linear and/or non-linear inverse scattering methodologies allow these additional sensitivity contributions to be computed from the current data residuals within any given update. We show that in the presence of pre-critical reflection data, the error in a second-order non-linear update to a background of s0 is, in our scheme, proportional to at most (Δs/s0)3 in the actual parameter jump Δs causing the reflection. In contrast, the error in a standard Gauss-Newton FWI update is proportional to (Δs/s0)2. For numerical implementation of more complex cases, we introduce a non-linear frequency-domain scheme, with an inner and an outer loop. A perturbation is determined from the data residuals within the inner loop, and a descent direction based on the resulting non-linear sensitivity kernel is computed in the outer loop. We examine the response of this non-linear FWI using acoustic single-parameter synthetics derived from the Marmousi model. The inverted results vary depending on data frequency ranges and initial models, but we conclude that the non-linear FWI has the capability to generate high-resolution model estimates in both shallow and deep regions, and to converge rapidly, relative to a benchmark FWI approach involving the standard gradient.

Analysis of seismicity and stress before and after the Mw 8.1 Pisagua, Chile, 2014 earthquake

NASA Astrophysics Data System (ADS)

Grigoli, F.; Cesca, S.; Dahm, T.; Hainzl, S.

2014-12-01

On April 1st, 2014 at 23:46:50 UTC, a powerful earthquake of magnitude Mw 8.1 occurred offshore the Northern Chile in the region of the North Chilean seismic gap. The epicenter of the earthquake was approximately 50 km offshore the Chilean coast, near the town of Pisagua. Two days after the main event a Mw 7.6 aftershock struck approximately the same area. In order to identify spatio-temporal changes of source parameters and stress before and after the mainshock, we analyzed in detail the local seismicity above magnitude Mw 3.0 within the time period 01/01/2013-30/04/2014 and estimated long term trends in b-values and earthquake productivity. We used data from the IPOC (Integrated Plate boundary Observatory Chile) regional seismic network, consisting of 20 "in land" broadband station deployed and managed by the GFZ-Potsdam. The recorded earthquake catalog shows an intense foreshock activity consisting of more than 1000 M3+ events in the source region. Full waveform techniques are used to derive both locations and focal mechanisms of about 435 seismic events. The location process has been performed by using a waveform stacking method (Grigoli et al 2013, 2014) with a layered velocity model based on CRUST 2.0 (see the attached figure for the location results of one of these events). Moment tensor inversion has been performed by using the KIWI tool software (Cesca et al. 2010), which is based on a two-step inversion approach. The first step consists in the inversion of the amplitude spectra to retrieve the best fitting focal planes, while the second inversion step is carried out in time domain to solve the focal mechanism polarity and to obtain the centroid location and time. Both location and moment tensor inversion resulted in agreement with the geodynamical settings of the region. Mapping the b-value reveals a spatiotemporal anomaly of low b-values characterizing the frequency-magnitude distribution of the foreshocks in the source area of the mainshock. Finally, clustering analysis of the retrieved focal mechanism and a stress tensor inversion has been performed in order to analyze the spatio-temporal evolution of the stress, before and after the mainshock. This work has been funded by the German BMBF "Geothecnologien" project MINE (BMBF03G0737A) and by Hazard and Risk Team (HART) and PBO-Chile of GFZ.

A new theory for multistep discretizations of stiff ordinary differential equations: Stability with large step sizes

NASA Technical Reports Server (NTRS)

Majda, G.

1985-01-01

A large set of variable coefficient linear systems of ordinary differential equations which possess two different time scales, a slow one and a fast one is considered. A small parameter epsilon characterizes the stiffness of these systems. A system of o.d.e.s. in this set is approximated by a general class of multistep discretizations which includes both one-leg and linear multistep methods. Sufficient conditions are determined under which each solution of a multistep method is uniformly bounded, with a bound which is independent of the stiffness of the system of o.d.e.s., when the step size resolves the slow time scale, but not the fast one. This property is called stability with large step sizes. The theory presented lets one compare properties of one-leg methods and linear multistep methods when they approximate variable coefficient systems of stiff o.d.e.s. In particular, it is shown that one-leg methods have better stability properties with large step sizes than their linear multistep counter parts. The theory also allows one to relate the concept of D-stability to the usual notions of stability and stability domains and to the propagation of errors for multistep methods which use large step sizes.

Inverse cascades and resonant triads in rotating and stratified turbulence

NASA Astrophysics Data System (ADS)

Oks, D.; Mininni, P. D.; Marino, R.; Pouquet, A.

2017-11-01

Kraichnan's seminal ideas on inverse cascades yielded new tools to study common phenomena in geophysical turbulent flows. In the atmosphere and the oceans, rotation and stratification result in a flow that can be approximated as two-dimensional at very large scales but which requires considering three-dimensional effects to fully describe turbulent transport processes and non-linear phenomena. Motions can thus be classified into two classes: fast modes consisting of inertia-gravity waves and slow quasi-geostrophic modes for which the Coriolis force and horizontal pressure gradients are close to balance. In this paper, we review previous results on the strength of the inverse cascade in rotating and stratified flows and then present new results on the effect of varying the strength of rotation and stratification (measured by the inverse Prandtl ratio N/f, of the Coriolis frequency to the Brunt-Väisäla frequency) on the amplitude of the waves and on the flow quasi-geostrophic behavior. We show that the inverse cascade is more efficient in the range of N/f for which resonant triads do not exist, 1 /2 ≤N /f ≤2 . We then use the spatio-temporal spectrum to show that in this range slow modes dominate the dynamics, while the strength of the waves (and their relevance in the flow dynamics) is weaker.

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Feedback control by online learning an inverse model.

PubMed

Waegeman, Tim; Wyffels, Francis; Schrauwen, Francis

2012-10-01

A model, predictor, or error estimator is often used by a feedback controller to control a plant. Creating such a model is difficult when the plant exhibits nonlinear behavior. In this paper, a novel online learning control framework is proposed that does not require explicit knowledge about the plant. This framework uses two learning modules, one for creating an inverse model, and the other for actually controlling the plant. Except for their inputs, they are identical. The inverse model learns by the exploration performed by the not yet fully trained controller, while the actual controller is based on the currently learned model. The proposed framework allows fast online learning of an accurate controller. The controller can be applied on a broad range of tasks with different dynamic characteristics. We validate this claim by applying our control framework on several control tasks: 1) the heating tank problem (slow nonlinear dynamics); 2) flight pitch control (slow linear dynamics); and 3) the balancing problem of a double inverted pendulum (fast linear and nonlinear dynamics). The results of these experiments show that fast learning and accurate control can be achieved. Furthermore, a comparison is made with some classical control approaches, and observations concerning convergence and stability are made.

Interferometric inverse synthetic aperture radar imaging for space targets based on wideband direct sampling using two antennas

NASA Astrophysics Data System (ADS)

Tian, Biao; Liu, Yang; Xu, Shiyou; Chen, Zengping

2014-01-01

Interferometric inverse synthetic aperture radar (InISAR) imaging provides complementary information to monostatic inverse synthetic aperture radar (ISAR) imaging. This paper proposes a new InISAR imaging system for space targets based on wideband direct sampling using two antennas. The system is easy to realize in engineering since the motion trajectory of space targets can be known in advance, which is simpler than that of three receivers. In the preprocessing step, high speed movement compensation is carried out by designing an adaptive matched filter containing speed that is obtained from the narrow band information. Then, the coherent processing and keystone transform for ISAR imaging are adopted to reserve the phase history of each antenna. Through appropriate collocation of the system, image registration and phase unwrapping can be avoided. Considering the situation not to be satisfied, the influence of baseline variance is analyzed and compensation method is adopted. The corresponding size can be achieved by interferometric processing of the two complex ISAR images. Experimental results prove the validity of the analysis and the three-dimensional imaging algorithm.

Cryptosystem based on two-step phase-shifting interferometry and the RSA public-key encryption algorithm

NASA Astrophysics Data System (ADS)

Meng, X. F.; Peng, X.; Cai, L. Z.; Li, A. M.; Gao, Z.; Wang, Y. R.

2009-08-01

A hybrid cryptosystem is proposed, in which one image is encrypted to two interferograms with the aid of double random-phase encoding (DRPE) and two-step phase-shifting interferometry (2-PSI), then three pairs of public-private keys are utilized to encode and decode the session keys (geometrical parameters, the second random-phase mask) and interferograms. In the stage of decryption, the ciphered image can be decrypted by wavefront reconstruction, inverse Fresnel diffraction, and real amplitude normalization. This approach can successfully solve the problem of key management and dispatch, resulting in increased security strength. The feasibility of the proposed cryptosystem and its robustness against some types of attack are verified and analyzed by computer simulations.

[Baseline correction of spectrum for the inversion of chlorophyll-a concentration in the turbidity water].

PubMed

Wei, Yu-Chun; Wang, Guo-Xiang; Cheng, Chun-Mei; Zhang, Jing; Sun, Xiao-Peng

2012-09-01

Suspended particle material is the main factor affecting remote sensing inversion of chlorophyll-a concentration (Chla) in turbidity water. According to the optical property of suspended material in water, the present paper proposed a linear baseline correction method to weaken the suspended particle contribution in the spectrum above turbidity water surface. The linear baseline was defined as the connecting line of reflectance from 450 to 750 nm, and baseline correction is that spectrum reflectance subtracts the baseline. Analysis result of field data in situ of Meiliangwan, Taihu Lake in April, 2011 and March, 2010 shows that spectrum linear baseline correction can improve the inversion precision of Chl a and produce the better model diagnoses. As the data in March, 2010, RMSE of band ratio model built by original spectrum is 4.11 mg x m(-3), and that built by spectrum baseline correction is 3.58 mg x m(-3). Meanwhile, residual distribution and homoscedasticity in the model built by baseline correction spectrum is improved obviously. The model RMSE of April, 2011 shows the similar result. The authors suggest that using linear baseline correction as the spectrum processing method to improve Chla inversion accuracy in turbidity water without algae bloom.

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

NASA Astrophysics Data System (ADS)

Wu, Sheng-Jhih; Chu, Moody T.

2017-08-01

An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.

Effect of Processing Parameters on Pore Structure and Thickness of Anodic Aluminum Oxide (AAO) Tubular Membranes.

PubMed

Belwalkar, A; Grasing, E; Van Geertruyden, W; Huang, Z; Misiolek, W Z

2008-07-01

Nanoporous anodic aluminum oxide (AAO) tubular membranes were fabricated from aluminum alloy tubes in sulfuric and oxalic acid electrolytes using a two-step anodization process. The membranes were investigated for characteristics such as pore size, interpore distance and thickness by varying applied voltage and electrolyte concentration. Morphology of the membranes was examined using light optical and scanning electron microscopy and characterized using ImageJ software. Results showed that membranes having narrow pore size and uniform pore distribution with parallel channel arrays were obtained. The pore sizes were ranging from 14 to 24 nm and the wall thicknesses as high as 76 microm. It was found that the pore size increased in direct proportion with the applied voltage and inversely with the electrolyte concentration while the interpore distance increased linearly with the applied voltage. It was also observed that increase in acid concentration increased tubular membrane wall thickness that improved mechanical handling. By using anodic alumina technology, robust ceramic tubes with uniformly distributed pore-structure and parallel nano-channels of lengths and sizes practical for industrial applications were reliably produced in quantity.

Effect of Processing Parameters on Pore Structure and Thickness of Anodic Aluminum Oxide (AAO) Tubular Membranes

PubMed Central

Belwalkar, A.; Grasing, E.; Huang, Z.; Misiolek, W.Z.

2008-01-01

Nanoporous anodic aluminum oxide (AAO) tubular membranes were fabricated from aluminum alloy tubes in sulfuric and oxalic acid electrolytes using a two-step anodization process. The membranes were investigated for characteristics such as pore size, interpore distance and thickness by varying applied voltage and electrolyte concentration. Morphology of the membranes was examined using light optical and scanning electron microscopy and characterized using ImageJ software. Results showed that membranes having narrow pore size and uniform pore distribution with parallel channel arrays were obtained. The pore sizes were ranging from 14 to 24 nm and the wall thicknesses as high as 76 µm. It was found that the pore size increased in direct proportion with the applied voltage and inversely with the electrolyte concentration while the interpore distance increased linearly with the applied voltage. It was also observed that increase in acid concentration increased tubular membrane wall thickness that improved mechanical handling. By using anodic alumina technology, robust ceramic tubes with uniformly distributed pore-structure and parallel nano-channels of lengths and sizes practical for industrial applications were reliably produced in quantity. PMID:19578471

Efficient mixing scheme for self-consistent all-electron charge density

NASA Astrophysics Data System (ADS)

Shishidou, Tatsuya; Weinert, Michael

2015-03-01

In standard ab initio density-functional theory calculations, the charge density ρ is gradually updated using the ``input'' and ``output'' densities of the current and previous iteration steps. To accelerate the convergence, Pulay mixing has been widely used with great success. It expresses an ``optimal'' input density ρopt and its ``residual'' Ropt by a linear combination of the densities of the iteration sequences. In large-scale metallic systems, however, the long range nature of Coulomb interaction often causes the ``charge sloshing'' phenomenon and significantly impacts the convergence. Two treatments, represented in reciprocal space, are known to suppress the sloshing: (i) the inverse Kerker metric for Pulay optimization and (ii) Kerker-type preconditioning in mixing Ropt. In all-electron methods, where the charge density does not have a converging Fourier representation, treatments equivalent or similar to (i) and (ii) have not been described so far. In this work, we show that, by going through the calculation of Hartree potential, one can accomplish the procedures (i) and (ii) without entering the reciprocal space. Test calculations are done with a FLAPW method.

Support Minimized Inversion of Acoustic and Elastic Wave Scattering

NASA Astrophysics Data System (ADS)

Safaeinili, Ali

Inversion of limited data is common in many areas of NDE such as X-ray Computed Tomography (CT), Ultrasonic and eddy current flaw characterization and imaging. In many applications, it is common to have a bias toward a solution with minimum (L^2)^2 norm without any physical justification. When it is a priori known that objects are compact as, say, with cracks and voids, by choosing "Minimum Support" functional instead of the minimum (L^2)^2 norm, an image can be obtained that is equally in agreement with the available data, while it is more consistent with what is most probably seen in the real world. We have utilized a minimum support functional to find a solution with the smallest volume. This inversion algorithm is most successful in reconstructing objects that are compact like voids and cracks. To verify this idea, we first performed a variational nonlinear inversion of acoustic backscatter data using minimum support objective function. A full nonlinear forward model was used to accurately study the effectiveness of the minimized support inversion without error due to the linear (Born) approximation. After successful inversions using a full nonlinear forward model, a linearized acoustic inversion was developed to increase speed and efficiency in imaging process. The results indicate that by using minimum support functional, we can accurately size and characterize voids and/or cracks which otherwise might be uncharacterizable. An extremely important feature of support minimized inversion is its ability to compensate for unknown absolute phase (zero-of-time). Zero-of-time ambiguity is a serious problem in the inversion of the pulse-echo data. The minimum support inversion was successfully used for the inversion of acoustic backscatter data due to compact scatterers without the knowledge of the zero-of-time. The main drawback to this type of inversion is its computer intensiveness. In order to make this type of constrained inversion available for common use, work needs to be performed in three areas: (1) exploitation of state-of-the-art parallel computation, (2) improvement of theoretical formulation of the scattering process for better computation efficiency, and (3) development of better methods for guiding the non-linear inversion. (Abstract shortened by UMI.).

Adaptive multi-step Full Waveform Inversion based on Waveform Mode Decomposition

NASA Astrophysics Data System (ADS)

Hu, Yong; Han, Liguo; Xu, Zhuo; Zhang, Fengjiao; Zeng, Jingwen

2017-04-01

Full Waveform Inversion (FWI) can be used to build high resolution velocity models, but there are still many challenges in seismic field data processing. The most difficult problem is about how to recover long-wavelength components of subsurface velocity models when seismic data is lacking of low frequency information and without long-offsets. To solve this problem, we propose to use Waveform Mode Decomposition (WMD) method to reconstruct low frequency information for FWI to obtain a smooth model, so that the initial model dependence of FWI can be reduced. In this paper, we use adjoint-state method to calculate the gradient for Waveform Mode Decomposition Full Waveform Inversion (WMDFWI). Through the illustrative numerical examples, we proved that the low frequency which is reconstructed by WMD method is very reliable. WMDFWI in combination with the adaptive multi-step inversion strategy can obtain more faithful and accurate final inversion results. Numerical examples show that even if the initial velocity model is far from the true model and lacking of low frequency information, we still can obtain good inversion results with WMD method. From numerical examples of anti-noise test, we see that the adaptive multi-step inversion strategy for WMDFWI has strong ability to resist Gaussian noise. WMD method is promising to be able to implement for the land seismic FWI, because it can reconstruct the low frequency information, lower the dominant frequency in the adjoint source, and has a strong ability to resist noise.

Analysis of longitudinal marginal structural models.

PubMed

Bryan, Jenny; Yu, Zhuo; Van Der Laan, Mark J

2004-07-01

In this article we construct and study estimators of the causal effect of a time-dependent treatment on survival in longitudinal studies. We employ a particular marginal structural model (MSM), proposed by Robins (2000), and follow a general methodology for constructing estimating functions in censored data models. The inverse probability of treatment weighted (IPTW) estimator of Robins et al. (2000) is used as an initial estimator and forms the basis for an improved, one-step estimator that is consistent and asymptotically linear when the treatment mechanism is consistently estimated. We extend these methods to handle informative censoring. The proposed methodology is employed to estimate the causal effect of exercise on mortality in a longitudinal study of seniors in Sonoma County. A simulation study demonstrates the bias of naive estimators in the presence of time-dependent confounders and also shows the efficiency gain of the IPTW estimator, even in the absence such confounding. The efficiency gain of the improved, one-step estimator is demonstrated through simulation.

Determination of intrinsic mode and linear mode coupling in solar microwave bursts

NASA Astrophysics Data System (ADS)

Huang, Guangli; Song, Qiwu; Li, Jianping

2013-05-01

An explicit equation of the propagational angle of microwave emission between the line-of-sight and the local magnetic field is newly derived based on the approximated formulae of nonthermal gyrosynchrotron emission (Dulk and Marsh in Astrophys. J. 259, 350, 1982). The existence of the solution of propagational angle is clearly shown under a series of typical parameters in solar microwave observations. It could be used to determine the intrinsic mode and linear mode coupling in solar microwave bursts by three steps. (1) The mode coupling may happen only when the angle approximately equals to 90 degrees, i.e., when the emission propagates through the quasi-transverse region (Cohen in Astrophys. J. 131, 664, 1960). (2) The inversion of polarization sense due to the weakly mode coupling takes place only when the transition frequency defined by Cohen (1960) is larger than the frequency of microwave emission, and an observable criterion of the weakly mode coupling in flaring loops was indicated by the same polarization sense in the two footpoints of a flaring loop (Melrose and Robinson in Proc. Astron. Soc. Aust. 11, 16, 1994). (3) Finally, the intrinsic mode of microwave emission is determined by the observed polarization and the calculated direction of local magnetic field according to the general plasma dispersion relation, together with the mode coupling process. However, a 180-degree ambiguity still exists in the direction of longitudinal magnetic field, to produce an uncertainty of the intrinsic mode. One example is selected to check the feasibility of the method in the 2001 September 25 event with a loop-like structure nearby the central meridian passage observed by Nobeyama Radio Heliograph and Polarimeters. The calculated angle in one footpoint (FP) varied around 90∘ in two time intervals of the maximum phase, which gives a direct evidence of the emission propagating through a quasi-transverse region where the linear mode coupling took place, while, the angle in another FP was always smaller than 90∘ where the mode coupling did not happen. Moreover, the right-circular sense at 17 GHz was always observed in both two FPs during the event, which supports that the transition frequency should be larger than 17 GHz in the first FP together with strong magnetic field of over 2000 Gauses in photosphere, where the weakly coupled case should happen. Moreover, there are two possibilities of the intrinsic mode in the two FPs due to the 180-degree ambiguity. (1) The emission of extraordinary (X) mode from the first FP turns to the ordinary (O) mode in the two time intervals of the maximum phase, while, the X-mode is always emitted from the second FP. (2) The inversion from O-mode to X-mode takes place in the first FP, while the O-mode keeps in the second FP. If the magnetic polarities in photosphere and corona are coincident in this event, the intrinsic mode belongs to the second case.

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

NASA Astrophysics Data System (ADS)

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

2016-09-01

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace such that the dimensionality of the problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2-D and a random hydraulic conductivity field in 3-D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ˜101 to ˜102 in a multicore computational environment. Therefore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate to large-scale problems.

Influence of Gridded Standoff Measurement Resolution on Numerical Bathymetric Inversion

NASA Astrophysics Data System (ADS)

Hesser, T.; Farthing, M. W.; Brodie, K.

2016-02-01

The bathymetry from the surfzone to the shoreline incurs frequent, active movement due to wave energy interacting with the seafloor. Methodologies to measure bathymetry range from point-source in-situ instruments, vessel-mounted single-beam or multi-beam sonar surveys, airborne bathymetric lidar, as well as inversion techniques from standoff measurements of wave processes from video or radar imagery. Each type of measurement has unique sources of error and spatial and temporal resolution and availability. Numerical bathymetry estimation frameworks can use these disparate data types in combination with model-based inversion techniques to produce a "best-estimate of bathymetry" at a given time. Understanding how the sources of error and varying spatial or temporal resolution of each data type affect the end result is critical for determining best practices and in turn increase the accuracy of bathymetry estimation techniques. In this work, we consider an initial step in the development of a complete framework for estimating bathymetry in the nearshore by focusing on gridded standoff measurements and in-situ point observations in model-based inversion at the U.S. Army Corps of Engineers Field Research Facility in Duck, NC. The standoff measurement methods return wave parameters computed using linear wave theory from the direct measurements. These gridded datasets can range in temporal and spatial resolution that do not match the desired model parameters and therefore could lead to a reduction in the accuracy of these methods. Specifically, we investigate the affect of numerical resolution on the accuracy of an Ensemble Kalman Filter bathymetric inversion technique in relation to the spatial and temporal resolution of the gridded standoff measurements. The accuracies of the bathymetric estimates are compared with both high-resolution Real Time Kinematic (RTK) single-beam surveys as well as alternative direct in-situ measurements using sonic altimeters.

Software to compute elastostatic Green's functions for sources in 3D homogeneous elastic layers above a (visco)elastic halfspace

NASA Astrophysics Data System (ADS)

Bradley, A. M.; Segall, P.

2012-12-01

We describe software, in development, to calculate elastostatic displacement Green's functions and their derivatives for point and polygonal dislocations in three-dimensional homogeneous elastic layers above an elastic or a viscoelastic halfspace. The steps to calculate a Green's function for a point source at depth zs are as follows. 1. A grid in wavenumber space is chosen. 2. A six-element complex rotated stress-displacement vector x is obtained at each grid point by solving a two-point boundary value problem (2P-BVP). If the halfspace is viscoelastic, the solution is inverse Laplace transformed. 3. For each receiver, x is propagated to the receiver depth zr (often zr = 0) and then, 4, inverse Fourier transformed, with the Fourier component corresponding to the receiver's horizontal position. 5. The six elements are linearly combined into displacements and their derivatives. The dominant work is in step 2. The grid is chosen to represent the wavenumber-space solution with as few points as possible. First, the wavenumber space is transformed to increase sampling density near 0 wavenumber. Second, a tensor-product grid of Chebyshev points of the first kind is constructed in each quadrant of the transformed wavenumber space. Moment-tensor-dependent symmetries further reduce work. The numerical solution of the 2P-BVP problem in step 2 involves solving a linear equation A x = b. Half of the elements of x are of geophysical interest; the subset depends on whether zr ≤ zs. Denote these \\hat x. As wavenumber k increases, \\hat x can become inaccurate in finite precision arithmetic for two reasons: 1. The condition number of A becomes too large. 2. The norm-wise relative error (NWRE) in \\hat x is large even though it is small in x. To address this problem, a number of researchers have used determinants to obtain x. This may be the best approach for 6-dimensional or smaller 2P-BVP, where the combinatorial increase in work is still moderate. But there is an alternative. Let \\bar A be the matrix after scaling its columns to unit infinity norm and \\bar x the scaled x. If \\bar A is well conditioned, as it often is in (visco)elastostatic problems, then using determinants is unnecessary. Multiply each side of A x = b by a propagator matrix to the computation depth zcd prior to storing the matrix in finite precision. zcd is determined by the rule that zr and zcd must be on opposite sides of zs. Let the resulting matrix be A(zcd). Three facts imply that this rule controls the NWRE in \\hat x: 1. Diagonally scaling a matrix changes the accuracy of an element of the solution by about one ULP (unit in the last place). 2. If the NWRE of \\bar x is small, then the largest elements are accurate. 3. zcd controls the magnitude of elements in \\bar x. In step 4, to avoid numerically Fourier transforming the (nearly) non-square-integrable functions that arise when the receiver and source depths are (nearly) the same, a function is divided into an analytical part and a numerical part that goes quickly to 0 as k -> ∞ . Our poster will describe these calculations, present a preliminary interface to a C-language package in development, and show some physical results.

An Inquiry-Based Learning Approach to the Introduction of the Improper Rotation-Reflection Operation, S[subscript n

ERIC Educational Resources Information Center

Graham, John P.

2014-01-01

Symmetry properties of molecules are generally introduced in second-year or third-year-level inorganic or physical chemistry courses. Students generally adapt readily to understanding and applying the operations of rotation (C[subscript n]), reflection (s), and inversion (i). However, the two-step operation of improper rotation-reflection…

Relative sensitivity of depth discrimination for ankle inversion and plantar flexion movements.

PubMed

Black, Georgia; Waddington, Gordon; Adams, Roger

2014-02-01

25 participants (20 women, 5 men) were tested for sensitivity in discrimination between sets of six movements centered on 8 degrees, 11 degrees, and 14 degrees, and separated by 0.3 degrees. Both inversion and plantar flexion movements were tested. Discrimination of the extent of inversion movement was observed to decline linearly with increasing depth; however, for plantar flexion, the discrimination function for movement extent was found to be non-linear. The relatively better discrimination of plantar flexion movements than inversion movements at around 11 degrees from horizontal is interpreted as an effect arising from differential amounts of practice through use, because this position is associated with the plantar flexion movement made in normal walking. The fact that plantar flexion movements are discriminated better than inversion at one region but not others argues against accounts of superior proprioceptive sensitivity for plantar flexion compared to inversion that are based on general properties of plantar flexion such as the number of muscle fibres on stretch.

Geostatistical regularization of inverse models for the retrieval of vegetation biophysical variables

NASA Astrophysics Data System (ADS)

Atzberger, C.; Richter, K.

2009-09-01

The robust and accurate retrieval of vegetation biophysical variables using radiative transfer models (RTM) is seriously hampered by the ill-posedness of the inverse problem. With this research we further develop our previously published (object-based) inversion approach [Atzberger (2004)]. The object-based RTM inversion takes advantage of the geostatistical fact that the biophysical characteristics of nearby pixel are generally more similar than those at a larger distance. A two-step inversion based on PROSPECT+SAIL generated look-up-tables is presented that can be easily implemented and adapted to other radiative transfer models. The approach takes into account the spectral signatures of neighboring pixel and optimizes a common value of the average leaf angle (ALA) for all pixel of a given image object, such as an agricultural field. Using a large set of leaf area index (LAI) measurements (n = 58) acquired over six different crops of the Barrax test site, Spain), we demonstrate that the proposed geostatistical regularization yields in most cases more accurate and spatially consistent results compared to the traditional (pixel-based) inversion. Pros and cons of the approach are discussed and possible future extensions presented.

Linear Approximation to Optimal Control Allocation for Rocket Nozzles with Elliptical Constraints

NASA Technical Reports Server (NTRS)

Orr, Jeb S.; Wall, Johnm W.

2011-01-01

In this paper we present a straightforward technique for assessing and realizing the maximum control moment effectiveness for a launch vehicle with multiple constrained rocket nozzles, where elliptical deflection limits in gimbal axes are expressed as an ensemble of independent quadratic constraints. A direct method of determining an approximating ellipsoid that inscribes the set of attainable angular accelerations is derived. In the case of a parameterized linear generalized inverse, the geometry of the attainable set is computationally expensive to obtain but can be approximated to a high degree of accuracy with the proposed method. A linear inverse can then be optimized to maximize the volume of the true attainable set by maximizing the volume of the approximating ellipsoid. The use of a linear inverse does not preclude the use of linear methods for stability analysis and control design, preferred in practice for assessing the stability characteristics of the inertial and servoelastic coupling appearing in large boosters. The present techniques are demonstrated via application to the control allocation scheme for a concept heavy-lift launch vehicle.

A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Jinglai, E-mail: jinglaili@sjtu.edu.cn; Lin, Guang, E-mail: lin491@purdue.edu; Computational Sciences and Mathematics Division, Pacific Northwest National Laboratory, Richland, WA 99352

2015-09-01

In this paper, we propose a frozen Gaussian approximation (FGA)-based multi-level particle swarm optimization (MLPSO) method for seismic inversion of high-frequency wave data. The method addresses two challenges in it: First, the optimization problem is highly non-convex, which makes hard for gradient-based methods to reach global minima. This is tackled by MLPSO which can escape from undesired local minima. Second, the character of high-frequency of seismic waves requires a large number of grid points in direct computational methods, and thus renders an extremely high computational demand on the simulation of each sample in MLPSO. We overcome this difficulty by threemore » steps: First, we use FGA to compute high-frequency wave propagation based on asymptotic analysis on phase plane; Then we design a constrained full waveform inversion problem to prevent the optimization search getting into regions of velocity where FGA is not accurate; Last, we solve the constrained optimization problem by MLPSO that employs FGA solvers with different fidelity. The performance of the proposed method is demonstrated by a two-dimensional full-waveform inversion example of the smoothed Marmousi model.« less

Towards a Full Waveform Ambient Noise Inversion

NASA Astrophysics Data System (ADS)

Sager, K.; Ermert, L. A.; Boehm, C.; Fichtner, A.

2015-12-01

Noise tomography usually works under the assumption that the inter-station ambient noise correlation is equal to a scaled version of the Green's function between the two receivers. This assumption, however, is only met under specific conditions, for instance, wavefield diffusivity and equipartitioning, zero attenuation, etc., that are typically not satisfied in the Earth. This inconsistency inhibits the exploitation of the full waveform information contained in noise correlations regarding Earth structure and noise generation. To overcome this limitation we attempt to develop a method that consistently accounts for noise distribution, 3D heterogeneous Earth structure and the full seismic wave propagation physics in order to improve the current resolution of tomographic images of the Earth. As an initial step towards a full waveform ambient noise inversion we develop a preliminary inversion scheme based on a 2D finite-difference code simulating correlation functions and on adjoint techniques. With respect to our final goal, a simultaneous inversion for noise distribution and Earth structure, we address the following two aspects: (1) the capabilities of different misfit functionals to image wave speed anomalies and source distribution and (2) possible source-structure trade-offs, especially to what extent unresolvable structure could be mapped into the inverted noise source distribution and vice versa.

Multidimensional FEM-FCT schemes for arbitrary time stepping

NASA Astrophysics Data System (ADS)

Kuzmin, D.; Möller, M.; Turek, S.

2003-05-01

The flux-corrected-transport paradigm is generalized to finite-element schemes based on arbitrary time stepping. A conservative flux decomposition procedure is proposed for both convective and diffusive terms. Mathematical properties of positivity-preserving schemes are reviewed. A nonoscillatory low-order method is constructed by elimination of negative off-diagonal entries of the discrete transport operator. The linearization of source terms and extension to hyperbolic systems are discussed. Zalesak's multidimensional limiter is employed to switch between linear discretizations of high and low order. A rigorous proof of positivity is provided. The treatment of non-linearities and iterative solution of linear systems are addressed. The performance of the new algorithm is illustrated by numerical examples for the shock tube problem in one dimension and scalar transport equations in two dimensions.

tomo3d: a new 3-D joint refraction and reflection travel-time tomography code for active-source seismic data

NASA Astrophysics Data System (ADS)

Meléndez, A.; Korenaga, J.; Sallares, V.; Ranero, C. R.

2012-12-01

We present the development state of tomo3d, a code for three-dimensional refraction and reflection travel-time tomography of wide-angle seismic data based on the previous two-dimensional version of the code, tomo2d. The core of both forward and inverse problems is inherited from the 2-D version. The ray tracing is performed by a hybrid method combining the graph and bending methods. The graph method finds an ordered array of discrete model nodes, which satisfies Fermat's principle, that is, whose corresponding travel time is a global minimum within the space of discrete nodal connections. The bending method is then applied to produce a more accurate ray path by using the nodes as support points for an interpolation with beta-splines. Travel time tomography is formulated as an iterative linearized inversion, and each step is solved using an LSQR algorithm. In order to avoid the singularity of the sensitivity kernel and to reduce the instability of inversion, regularization parameters are introduced in the inversion in the form of smoothing and damping constraints. Velocity models are built as 3-D meshes, and velocity values at intermediate locations are obtained by trilinear interpolation within the corresponding pseudo-cubic cell. Meshes are sheared to account for topographic relief. A floating reflector is represented by a 2-D grid, and depths at intermediate locations are calculated by bilinear interpolation within the corresponding square cell. The trade-off between the resolution of the final model and the associated computational cost is controlled by the relation between the selected forward star for the graph method (i.e. the number of nodes that each node considers as its neighbors) and the refinement of the velocity mesh. Including reflected phases is advantageous because it provides a better coverage and allows us to define the geometry of those geological interfaces with velocity contrasts sharp enough to be observed on record sections. The code also offers the possibility of including water-layer multiples in the modeling, which is useful whenever these phases can be followed to greater offsets than the primary ones. This increases the amount of information available from the data, yielding more extensive and better constrained velocity and geometry models. We will present synthetic results from benchmark tests for the forward and inverse problems, as well as from more complex inversion tests for different inversions possibilities such as one with travel times from refracted waves only (i.e. first arrivals) and one with travel-times from both refracted and reflected waves. In addition, we will show some preliminary results for the inversion of real 3-D OBS data acquired off-shore Ecuador and Colombia.

Three-Dimensional Anisotropic Acoustic and Elastic Full-Waveform Seismic Inversion

NASA Astrophysics Data System (ADS)

Warner, M.; Morgan, J. V.

2013-12-01

Three-dimensional full-waveform inversion is a high-resolution, high-fidelity, quantitative, seismic imaging technique that has advanced rapidly within the oil and gas industry. The method involves the iterative improvement of a starting model using a series of local linearized updates to solve the full non-linear inversion problem. During the inversion, forward modeling employs the full two-way three-dimensional heterogeneous anisotropic acoustic or elastic wave equation to predict the observed raw field data, wiggle-for-wiggle, trace-by-trace. The method is computationally demanding; it is highly parallelized, and runs on large multi-core multi-node clusters. Here, we demonstrate what can be achieved by applying this newly practical technique to several high-density 3D seismic datasets that were acquired to image four contrasting sedimentary targets: a gas cloud above an oil reservoir, a radially faulted dome, buried fluvial channels, and collapse structures overlying an evaporate sequence. We show that the resulting anisotropic p-wave velocity models match in situ measurements in deep boreholes, reproduce detailed structure observed independently on high-resolution seismic reflection sections, accurately predict the raw seismic data, simplify and sharpen reverse-time-migrated reflection images of deeper horizons, and flatten Kirchhoff-migrated common-image gathers. We also show that full-elastic 3D full-waveform inversion of pure pressure data can generate a reasonable shear-wave velocity model for one of these datasets. For two of the four datasets, the inclusion of significant transversely isotropic anisotropy with a vertical axis of symmetry was necessary in order to fit the kinematics of the field data properly. For the faulted dome, the full-waveform-inversion p-wave velocity model recovers the detailed structure of every fault that can be seen on coincident seismic reflection data. Some of the individual faults represent high-velocity zones, some represent low-velocity zones, some have more-complex internal structure, and some are visible merely as offsets between two regions with contrasting velocity. Although this has not yet been demonstrated quantitatively for this dataset, it seems likely that at least some of this fine structure in the recovered velocity model is related to the detailed lithology, strain history and fluid properties within the individual faults. We have here applied this technique to seismic data that were acquired by the extractive industries, however this inversion scheme is immediately scalable and applicable to a much wider range of problems given sufficient quality and density of observed data. Potential targets range from shallow magma chambers beneath active volcanoes, through whole-crustal sections across plate boundaries, to regional and whole-Earth models.

Neural-Based Compensation of Nonlinearities in an Airplane Longitudinal Model with Dynamic-Inversion Control

PubMed Central

Li, YuHui; Jin, FeiTeng

2017-01-01

The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller. PMID:29410680

Peeling linear inversion of upper mantle velocity structure with receiver functions

NASA Astrophysics Data System (ADS)

Shen, Xuzhang; Zhou, Huilan

2012-02-01

A peeling linear inversion method is presented to study the upper mantle (from Moho to 800 km depth) velocity structures with receiver functions. The influences of the crustal and upper mantle velocity ratio error on the inversion results are analyzed, and three valid measures are taken for its reduction. This method is tested with the IASP91 and the PREM models, and the upper mantle structures beneath the stations GTA, LZH, and AXX in northwestern China are then inverted. The results indicate that this inversion method is feasible to quantify upper mantle discontinuities, besides the discontinuities between 3 h M ( h M denotes the depth of Moho) and 5 h M due to the interference of multiples from Moho. Smoothing is used to overcome possible false discontinuities from the multiples and ensure the stability of the inversion results, but the detailed information on the depth range between 3 h M and 5 h M is sacrificed.

Limited-memory fast gradient descent method for graph regularized nonnegative matrix factorization.

PubMed

Guan, Naiyang; Wei, Lei; Luo, Zhigang; Tao, Dacheng

2013-01-01

Graph regularized nonnegative matrix factorization (GNMF) decomposes a nonnegative data matrix X[Symbol:see text]R(m x n) to the product of two lower-rank nonnegative factor matrices, i.e.,W[Symbol:see text]R(m x r) and H[Symbol:see text]R(r x n) (r < min {m,n}) and aims to preserve the local geometric structure of the dataset by minimizing squared Euclidean distance or Kullback-Leibler (KL) divergence between X and WH. The multiplicative update rule (MUR) is usually applied to optimize GNMF, but it suffers from the drawback of slow-convergence because it intrinsically advances one step along the rescaled negative gradient direction with a non-optimal step size. Recently, a multiple step-sizes fast gradient descent (MFGD) method has been proposed for optimizing NMF which accelerates MUR by searching the optimal step-size along the rescaled negative gradient direction with Newton's method. However, the computational cost of MFGD is high because 1) the high-dimensional Hessian matrix is dense and costs too much memory; and 2) the Hessian inverse operator and its multiplication with gradient cost too much time. To overcome these deficiencies of MFGD, we propose an efficient limited-memory FGD (L-FGD) method for optimizing GNMF. In particular, we apply the limited-memory BFGS (L-BFGS) method to directly approximate the multiplication of the inverse Hessian and the gradient for searching the optimal step size in MFGD. The preliminary results on real-world datasets show that L-FGD is more efficient than both MFGD and MUR. To evaluate the effectiveness of L-FGD, we validate its clustering performance for optimizing KL-divergence based GNMF on two popular face image datasets including ORL and PIE and two text corpora including Reuters and TDT2. The experimental results confirm the effectiveness of L-FGD by comparing it with the representative GNMF solvers.

DETAILED DATA ANALYSIS OF ECHO I, ECHO II AND MOON REFLECTED SIGNALS. VOLUME 2. AUTOCORRELATION FUNCTIONS OF ECHO II REFLECTED SIGNALS,

DTIC Science & Technology

techniques is presented. Two methods for linearizing the data are given. An expression for the specular-to-spattered power ratio is derived, and the inverse ... transform of the autocorrelation function is discussed. The surface roughness of the reflector, the discrete fading rates, and fading frequencies

Incorporation of diet information derived from Bayesian stable isotope mixing models into mass-balanced marine ecosystem models: A case study from the Marennes-Oleron Estuary, France

EPA Science Inventory

We investigated the use of output from Bayesian stable isotope mixing models as constraints for a linear inverse food web model of a temperate intertidal seagrass system in the Marennes-Oléron Bay, France. Linear inverse modeling (LIM) is a technique that estimates a complete net...

GWAS with longitudinal phenotypes: performance of approximate procedures

PubMed Central

Sikorska, Karolina; Montazeri, Nahid Mostafavi; Uitterlinden, André; Rivadeneira, Fernando; Eilers, Paul HC; Lesaffre, Emmanuel

2015-01-01

Analysis of genome-wide association studies with longitudinal data using standard procedures, such as linear mixed model (LMM) fitting, leads to discouragingly long computation times. There is a need to speed up the computations significantly. In our previous work (Sikorska et al: Fast linear mixed model computations for genome-wide association studies with longitudinal data. Stat Med 2012; 32.1: 165–180), we proposed the conditional two-step (CTS) approach as a fast method providing an approximation to the P-value for the longitudinal single-nucleotide polymorphism (SNP) effect. In the first step a reduced conditional LMM is fit, omitting all the SNP terms. In the second step, the estimated random slopes are regressed on SNPs. The CTS has been applied to the bone mineral density data from the Rotterdam Study and proved to work very well even in unbalanced situations. In another article (Sikorska et al: GWAS on your notebook: fast semi-parallel linear and logistic regression for genome-wide association studies. BMC Bioinformatics 2013; 14: 166), we suggested semi-parallel computations, greatly speeding up fitting many linear regressions. Combining CTS with fast linear regression reduces the computation time from several weeks to a few minutes on a single computer. Here, we explore further the properties of the CTS both analytically and by simulations. We investigate the performance of our proposal in comparison with a related but different approach, the two-step procedure. It is analytically shown that for the balanced case, under mild assumptions, the P-value provided by the CTS is the same as from the LMM. For unbalanced data and in realistic situations, simulations show that the CTS method does not inflate the type I error rate and implies only a minimal loss of power. PMID:25712081

Linearized inversion of multiple scattering seismic energy

NASA Astrophysics Data System (ADS)

Aldawood, Ali; Hoteit, Ibrahim; Zuberi, Mohammad

2014-05-01

Internal multiples deteriorate the quality of the migrated image obtained conventionally by imaging single scattering energy. So, imaging seismic data with the single-scattering assumption does not locate multiple bounces events in their actual subsurface positions. However, imaging internal multiples properly has the potential to enhance the migrated image because they illuminate zones in the subsurface that are poorly illuminated by single scattering energy such as nearly vertical faults. Standard migration of these multiples provides subsurface reflectivity distributions with low spatial resolution and migration artifacts due to the limited recording aperture, coarse sources and receivers sampling, and the band-limited nature of the source wavelet. The resultant image obtained by the adjoint operator is a smoothed depiction of the true subsurface reflectivity model and is heavily masked by migration artifacts and the source wavelet fingerprint that needs to be properly deconvolved. Hence, we proposed a linearized least-square inversion scheme to mitigate the effect of the migration artifacts, enhance the spatial resolution, and provide more accurate amplitude information when imaging internal multiples. The proposed algorithm uses the least-square image based on single-scattering assumption as a constraint to invert for the part of the image that is illuminated by internal scattering energy. Then, we posed the problem of imaging double-scattering energy as a least-square minimization problem that requires solving the normal equation of the following form: GTGv = GTd, (1) where G is a linearized forward modeling operator that predicts double-scattered seismic data. Also, GT is a linearized adjoint operator that image double-scattered seismic data. Gradient-based optimization algorithms solve this linear system. Hence, we used a quasi-Newton optimization technique to find the least-square minimizer. In this approach, an estimate of the Hessian matrix that contains curvature information is modified at every iteration by a low-rank update based on gradient changes at every step. At each iteration, the data residual is imaged using GT to determine the model update. Application of the linearized inversion to synthetic data to image a vertical fault plane demonstrate the effectiveness of this methodology to properly delineate the vertical fault plane and give better amplitude information than the standard migrated image using the adjoint operator that takes into account internal multiples. Thus, least-square imaging of multiple scattering enhances the spatial resolution of the events illuminated by internal scattering energy. It also deconvolves the source signature and helps remove the fingerprint of the acquisition geometry. The final image is obtained by the superposition of the least-square solution based on single scattering assumption and the least-square solution based on double scattering assumption.

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Time-lapse ERT interpretation methodology for leachate injection monitoring based on multiple inversions and a clustering strategy (MICS)

NASA Astrophysics Data System (ADS)

Audebert, M.; Clément, R.; Touze-Foltz, N.; Günther, T.; Moreau, S.; Duquennoi, C.

2014-12-01

Leachate recirculation is a key process in municipal waste landfills functioning as bioreactors. To quantify the water content and to assess the leachate injection system, in-situ methods are required to obtain spatially distributed information, usually electrical resistivity tomography (ERT). This geophysical method is based on the inversion process, which presents two major problems in terms of delimiting the infiltration area. First, it is difficult for ERT users to choose an appropriate inversion parameter set. Indeed, it might not be sufficient to interpret only the optimum model (i.e. the model with the chosen regularisation strength) because it is not necessarily the model which best represents the physical process studied. Second, it is difficult to delineate the infiltration front based on resistivity models because of the smoothness of the inversion results. This paper proposes a new methodology called MICS (multiple inversions and clustering strategy), which allows ERT users to improve the delimitation of the infiltration area in leachate injection monitoring. The MICS methodology is based on (i) a multiple inversion step by varying the inversion parameter values to take a wide range of resistivity models into account and (ii) a clustering strategy to improve the delineation of the infiltration front. In this paper, MICS was assessed on two types of data. First, a numerical assessment allows us to optimise and test MICS for different infiltration area sizes, contrasts and shapes. Second, MICS was applied to a field data set gathered during leachate recirculation on a bioreactor.

Kolmogorov-Kraichnan Scaling in the Inverse Energy Cascade of Two-Dimensional Plasma Turbulence

NASA Astrophysics Data System (ADS)

Antar, G. Y.

2003-08-01

Turbulence in plasmas that are magnetically confined, such as tokamaks or linear devices, is two dimensional or at least quasi two dimensional due to the strong magnetic field, which leads to extreme elongation of the fluctuations, if any, in the direction parallel to the magnetic field. These plasmas are also compressible fluid flows obeying the compressible Navier-Stokes equations. This Letter presents the first comprehensive scaling of the structure functions of the density and velocity fields up to 10th order in the PISCES linear plasma device and up to 6th order in the Mega-Ampère Spherical Tokamak (MAST). In the two devices, it is found that the scaling of the turbulent fields is in good agreement with the prediction of the Kolmogorov-Kraichnan theory for two-dimensional turbulence in the energy cascade subrange.

A Kalman filter for a two-dimensional shallow-water model

NASA Technical Reports Server (NTRS)

Parrish, D. F.; Cohn, S. E.

1985-01-01

A two-dimensional Kalman filter is described for data assimilation for making weather forecasts. The filter is regarded as superior to the optimal interpolation method because the filter determines the forecast error covariance matrix exactly instead of using an approximation. A generalized time step is defined which includes expressions for one time step of the forecast model, the error covariance matrix, the gain matrix, and the evolution of the covariance matrix. Subsequent time steps are achieved by quantifying the forecast variables or employing a linear extrapolation from a current variable set, assuming the forecast dynamics are linear. Calculations for the evolution of the error covariance matrix are banded, i.e., are performed only with the elements significantly different from zero. Experimental results are provided from an application of the filter to a shallow-water simulation covering a 6000 x 6000 km grid.

Linear analysis near a steady-state of biochemical networks: control analysis, correlation metrics and circuit theory.

PubMed

Heuett, William J; Beard, Daniel A; Qian, Hong

2008-05-15

Several approaches, including metabolic control analysis (MCA), flux balance analysis (FBA), correlation metric construction (CMC), and biochemical circuit theory (BCT), have been developed for the quantitative analysis of complex biochemical networks. Here, we present a comprehensive theory of linear analysis for nonequilibrium steady-state (NESS) biochemical reaction networks that unites these disparate approaches in a common mathematical framework and thermodynamic basis. In this theory a number of relationships between key matrices are introduced: the matrix A obtained in the standard, linear-dynamic-stability analysis of the steady-state can be decomposed as A = SRT where R and S are directly related to the elasticity-coefficient matrix for the fluxes and chemical potentials in MCA, respectively; the control-coefficients for the fluxes and chemical potentials can be written in terms of RTBS and STBS respectively where matrix B is the inverse of A; the matrix S is precisely the stoichiometric matrix in FBA; and the matrix eAt plays a central role in CMC. One key finding that emerges from this analysis is that the well-known summation theorems in MCA take different forms depending on whether metabolic steady-state is maintained by flux injection or concentration clamping. We demonstrate that if rate-limiting steps exist in a biochemical pathway, they are the steps with smallest biochemical conductances and largest flux control-coefficients. We hypothesize that biochemical networks for cellular signaling have a different strategy for minimizing energy waste and being efficient than do biochemical networks for biosynthesis. We also discuss the intimate relationship between MCA and biochemical systems analysis (BSA).

One-step production of multiple emulsions: microfluidic, polymer-stabilized and particle-stabilized approaches.

PubMed

Clegg, Paul S; Tavacoli, Joe W; Wilde, Pete J

2016-01-28

Multiple emulsions have great potential for application in food science as a means to reduce fat content or for controlled encapsulation and release of actives. However, neither production nor stability is straightforward. Typically, multiple emulsions are prepared via two emulsification steps and a variety of approaches have been deployed to give long-term stability. It is well known that multiple emulsions can be prepared in a single step by harnessing emulsion inversion, although the resulting emulsions are usually short lived. Recently, several contrasting methods have been demonstrated which give rise to stable multiple emulsions via one-step production processes. Here we review the current state of microfluidic, polymer-stabilized and particle-stabilized approaches; these rely on phase separation, the role of electrolyte and the trapping of solvent with particles respectively.

Kinematic predictors of loading during running differ by demographic group.

PubMed

Harrison, Kathryn; Thakkar, Bhushan; Kwon, Yong Ung; Crosswell, Gregory; Morgan, Jacqueline; Williams, D S Blaise

2018-05-24

To investigate whether previously-determined kinematic predictors of kinetics during running differ between demographic groups. Young male (n = 13, age = 22 (2) yrs), young female (n = 13, age = 25 (4) yrs), older male (n = 13, age = 50 (4) yrs) and older female (n = 13, age = 52 (3) yrs) runners. Sagittal plane kinematics and kinetics were assessed while participants ran at their preferred pace. Linear regression models were developed to predict kinetics in each group using kinematics as independent variables. Step length was positively associated with magnitude of at least one kinetic variable in all groups. Step position was inversely associated with vertical ground reaction force variables in all groups. Step frequency and CoM excursion were also important to all groups, however direction of the associations varied. Foot angle at initial contact was important to all groups except older females. Peak knee flexion was most important to older females, but was not important to any other groups. Optimal parameters for gait analysis of runners may depend on demographics of the individual. This provides insight for clinicians into the most effective evaluation and interventions strategies for different types of runners. Copyright © 2018. Published by Elsevier Ltd.

Nested Global Inversion for the Carbon Flux Distribution in Canada and USA from 1994 to 2003

NASA Astrophysics Data System (ADS)

Chen, J. M.; Deng, F.; Ishizawa, M.; Ju, W.; Mo, G.; Chan, D.; Higuchi, K.; Maksyutov, S.

2007-12-01

Based on TransCom inverse modeling for 22 global regions, we developed a nested global inversion system for estimating carbon fluxes of 30 regions in North America (2 of the 22 regions are divided into 30). Irregular boundaries of these 30 regions are delineated based on ecosystem types and provincial/state borders. Synthesis Bayesian inversion is conducted in monthly steps using CO2 concentration measurements at 88 coastal and continental stations of the globe for the 1994-2003 period (NOAA GlobalView database). Responses of these stations to carbon fluxes from the 50 regions are simulated using the transport model of National Institute for Environmental Studies of Japan and reanalysis wind fields of the National Centers for Environmental Prediction (NCEP). Terrestrial carbon flux fields modeled using BEPS and Biome-BGC driven by NCEP reanalysis meteorological data are used as two different a priori to constrain the inversion. The inversion (top- down) results are compared with remote sensing-based ecosystem modeling (bottom-up) results in Canada's forests and wetlands. There is a broad consistency in the spatial pattern of the carbon source and sink distributions obtained using these two independent methods. Both sets of results also indicate that Canada's forests and wetlands are carbon sinks in 1994-2003, but the top-down method produces consistently larger sinks than the bottom-up results. Reasons for this discrepancy may lie in both methods, and several issues are identified for further investigation.

Krylov Subspace Methods for Complex Non-Hermitian Linear Systems. Thesis

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1991-01-01

We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Round-off errors in cutting plane algorithms based on the revised simplex procedure

NASA Technical Reports Server (NTRS)

Moore, J. E.

1973-01-01

This report statistically analyzes computational round-off errors associated with the cutting plane approach to solving linear integer programming problems. Cutting plane methods require that the inverse of a sequence of matrices be computed. The problem basically reduces to one of minimizing round-off errors in the sequence of inverses. Two procedures for minimizing this problem are presented, and their influence on error accumulation is statistically analyzed. One procedure employs a very small tolerance factor to round computed values to zero. The other procedure is a numerical analysis technique for reinverting or improving the approximate inverse of a matrix. The results indicated that round-off accumulation can be effectively minimized by employing a tolerance factor which reflects the number of significant digits carried for each calculation and by applying the reinversion procedure once to each computed inverse. If 18 significant digits plus an exponent are carried for each variable during computations, then a tolerance value of 0.1 x 10 to the minus 12th power is reasonable.

Secretory immunoglobulin purification from whey by chromatographic techniques.

PubMed

Matlschweiger, Alexander; Engelmaier, Hannah; Himmler, Gottfried; Hahn, Rainer

2017-08-15

Secretory immunoglobulins (SIg) are a major fraction of the mucosal immune system and represent potential drug candidates. So far, platform technologies for their purification do not exist. SIg from animal whey was used as a model to develop a simple, efficient and potentially generic chromatographic purification process. Several chromatographic stationary phases were tested. A combination of two anion-exchange steps resulted in the highest purity. The key step was the use of a small-porous anion exchanger operated in flow-through mode. Diffusion of SIg into the resin particles was significantly hindered, while the main impurities, IgG and serum albumin, were bound. In this step, initial purity was increased from 66% to 89% with a step yield of 88%. In a second anion-exchange step using giga-porous material, SIg was captured and purified by step or linear gradient elution to obtain fractions with purities >95%. For the step gradient elution step yield of highly pure SIg was 54%. Elution of SIgA and SIgM with a linear gradient resulted in a step yield of 56% and 35%, respectively. Overall yields for both anion exchange steps were 43% for the combination of flow-through and step elution mode. Combination of flow-through and linear gradient elution mode resulted in a yield of 44% for SIgA and 39% for SIgM. The proposed process allows the purification of biologically active SIg from animal whey in preparative scale. For future applications, the process can easily be adopted for purification of recombinant secretory immunoglobulin species. Copyright © 2017 Elsevier B.V. All rights reserved.

A Dynamic Range Enhanced Readout Technique with a Two-Step TDC for High Speed Linear CMOS Image Sensors.

PubMed

Gao, Zhiyuan; Yang, Congjie; Xu, Jiangtao; Nie, Kaiming

2015-11-06

This paper presents a dynamic range (DR) enhanced readout technique with a two-step time-to-digital converter (TDC) for high speed linear CMOS image sensors. A multi-capacitor and self-regulated capacitive trans-impedance amplifier (CTIA) structure is employed to extend the dynamic range. The gain of the CTIA is auto adjusted by switching different capacitors to the integration node asynchronously according to the output voltage. A column-parallel ADC based on a two-step TDC is utilized to improve the conversion rate. The conversion is divided into coarse phase and fine phase. An error calibration scheme is also proposed to correct quantization errors caused by propagation delay skew within -T(clk)~+T(clk). A linear CMOS image sensor pixel array is designed in the 0.13 μm CMOS process to verify this DR-enhanced high speed readout technique. The post simulation results indicate that the dynamic range of readout circuit is 99.02 dB and the ADC achieves 60.22 dB SNDR and 9.71 bit ENOB at a conversion rate of 2 MS/s after calibration, with 14.04 dB and 2.4 bit improvement, compared with SNDR and ENOB of that without calibration.

Linear sampling method applied to non destructive testing of an elastic waveguide: theory, numerics and experiments

NASA Astrophysics Data System (ADS)

Baronian, Vahan; Bourgeois, Laurent; Chapuis, Bastien; Recoquillay, Arnaud

2018-07-01

This paper presents an application of the linear sampling method to ultrasonic non destructive testing of an elastic waveguide. In particular, the NDT context implies that both the solicitations and the measurements are located on the surface of the waveguide and are given in the time domain. Our strategy consists in using a modal formulation of the linear sampling method at multiple frequencies, such modal formulation being justified theoretically in Bourgeois et al (2011 Inverse Problems 27 055001) for rigid obstacles and in Bourgeois and Lunéville (2013 Inverse Problems 29 025017) for cracks. Our strategy requires the inversion of some emission and reception matrices which deserve some special attention due to potential ill-conditioning. The feasibility of our method is proved with the help of artificial data as well as real data.

3D non-linear inversion of magnetic anomalies caused by prismatic bodies using differential evolution algorithm

NASA Astrophysics Data System (ADS)

Balkaya, Çağlayan; Ekinci, Yunus Levent; Göktürkler, Gökhan; Turan, Seçil

2017-01-01

3D non-linear inversion of total field magnetic anomalies caused by vertical-sided prismatic bodies has been achieved by differential evolution (DE), which is one of the population-based evolutionary algorithms. We have demonstrated the efficiency of the algorithm on both synthetic and field magnetic anomalies by estimating horizontal distances from the origin in both north and east directions, depths to the top and bottom of the bodies, inclination and declination angles of the magnetization, and intensity of magnetization of the causative bodies. In the synthetic anomaly case, we have considered both noise-free and noisy data sets due to two vertical-sided prismatic bodies in a non-magnetic medium. For the field case, airborne magnetic anomalies originated from intrusive granitoids at the eastern part of the Biga Peninsula (NW Turkey) which is composed of various kinds of sedimentary, metamorphic and igneous rocks, have been inverted and interpreted. Since the granitoids are the outcropped rocks in the field, the estimations for the top depths of two prisms representing the magnetic bodies were excluded during inversion studies. Estimated bottom depths are in good agreement with the ones obtained by a different approach based on 3D modelling of pseudogravity anomalies. Accuracy of the estimated parameters from both cases has been also investigated via probability density functions. Based on the tests in the present study, it can be concluded that DE is a useful tool for the parameter estimation of source bodies using magnetic anomalies.

Computing the Moore-Penrose Inverse of a Matrix with a Computer Algebra System

ERIC Educational Resources Information Center

Schmidt, Karsten

2008-01-01

In this paper "Derive" functions are provided for the computation of the Moore-Penrose inverse of a matrix, as well as for solving systems of linear equations by means of the Moore-Penrose inverse. Making it possible to compute the Moore-Penrose inverse easily with one of the most commonly used Computer Algebra Systems--and to have the blueprint…

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

DOE PAGES

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

2016-09-01

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less

Surface and Atmospheric Parameter Retrieval From AVIRIS Data: The Importance of Non-Linear Effects

NASA Technical Reports Server (NTRS)

Green Robert O.; Moreno, Jose F.

1996-01-01

AVIRIS data represent a new and important approach for the retrieval of atmospheric and surface parameters from optical remote sensing data. Not only as a test for future space systems, but also as an operational airborne remote sensing system, the development of algorithms to retrieve information from AVIRIS data is an important step to these new approaches and capabilities. Many things have been learned since AVIRIS became operational, and the successive technical improvements in the hardware and the more sophisticated calibration techniques employed have increased the quality of the data to the point of almost meeting optimum user requirements. However, the potential capabilities of imaging spectrometry over the standard multispectral techniques have still not been fully demonstrated. Reasons for this are the technical difficulties in handling the data, the critical aspect of calibration for advanced retrieval methods, and the lack of proper models with which to invert the measured AVIRIS radiances in all the spectral channels. To achieve the potential of imaging spectrometry, these issues must be addressed. In this paper, an algorithm to retrieve information about both atmospheric and surface parameters from AVIRIS data, by using model inversion techniques, is described. Emphasis is put on the derivation of the model itself as well as proper inversion techniques, robust to noise in the data and an inadequate ability of the model to describe natural variability in the data. The problem of non-linear effects is addressed, as it has been demonstrated to be a major source of error in the numerical values retrieved by more simple, linear-based approaches. Non-linear effects are especially critical for the retrieval of surface parameters where both scattering and absorption effects are coupled, as well as in the cases of significant multiple-scattering contributions. However, sophisticated modeling approaches can handle such non-linear effects, which are especially important over vegetated surfaces. All the data used in this study were acquired during the 1991 Multisensor Airborne Campaign (MAC-Europe), as part of the European Field Experiment on a Desertification-threatened Area (EFEDA), carried out in Spain in June-July 1991.

Quantum algorithms for Gibbs sampling and hitting-time estimation

DOE PAGES

Chowdhury, Anirban Narayan; Somma, Rolando D.

2017-02-01

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. Formore » a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.« less

Development of a coupled FLEXPART-TM5 CO2 inverse modeling system

NASA Astrophysics Data System (ADS)

Monteil, Guillaume; Scholze, Marko

2017-04-01

Inverse modeling techniques are used to derive information on surface CO2 fluxes from measurements of atmospheric CO2 concentrations. The principle is to use an atmospheric transport model to compute the CO2 concentrations corresponding to a prior estimate of the surface CO2 fluxes. From the mismatches between observed and modeled concentrations, a correction of the flux estimate is computed, that represents the best statistical compromise between the prior knowledge and the new information brought in by the observations. Such "top-down" CO2 flux estimates are useful for a number of applications, such as the verification of CO2 emission inventories reported by countries in the framework of international greenhouse gas emission reduction treaties (Paris agreement), or for the validation and improvement of the bottom-up models used in future climate predictions. Inverse modeling CO2 flux estimates are limited in resolution (spatial and temporal) by the lack of observational constraints and by the very heavy computational cost of high-resolution inversions. The observational limitation is however being lifted, with the expansion of regional surface networks such as ICOS in Europe, and with the launch of new satellite instruments to measure tropospheric CO2 concentrations. To make an efficient use of these new observations, it is necessary to step up the resolution of atmospheric inversions. We have developed an inverse modeling system, based on a coupling between the TM5 and the FLEXPART transport models. The coupling follows the approach described in Rodenbeck et al., 2009: a first global, coarse resolution, inversion is performed using TM5-4DVAR, and is used to provide background constraints to a second, regional, fine resolution inversion, using FLEXPART as a transport model. The inversion algorithm is adapted from the 4DVAR algorithm used by TM5, but has been developed to be model-agnostic: it would be straightforward to replace TM5 and/or FLEXPART by other transport models, thus making it well suited to study transport model uncertainties. We will present preliminary European CO2 inversions using ICOS observations, and comparisons with TM5-4DVAR and TM3-STILT inversions. Reference: Rödenbeck, C., Gerbig, C., Trusilova, K., & Heimann, M. (2009). A two-step scheme for high-resolution regional atmospheric trace gas inversions based on independent models. Atmospheric Chemistry and Physics Discussions, 9(1), 1727-1756. http://doi.org/10.5194/acpd-9-1727-2009

Time-reversed, flow-reversed ballistics simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zernow, L.; Chapyak, E. J.; Scheffler, D. R.

2001-01-01

Two-dimensional simulations of planar sheet jet formation are studied to examine the hydrodynamic issues involved when simulations are carried out in the inverse direction, that is, with reversed time and flow. Both a realistic copper equation of state and a shockless equation of state were used. These studies are an initial step in evaluating this technique as a ballistics design tool.

Spontaneously broken spacetime symmetries and the role of inessential Goldstones

NASA Astrophysics Data System (ADS)

Klein, Remko; Roest, Diederik; Stefanyszyn, David

2017-10-01

In contrast to internal symmetries, there is no general proof that the coset construction for spontaneously broken spacetime symmetries leads to universal dynamics. One key difference lies in the role of Goldstone bosons, which for spacetime symmetries includes a subset which are inessential for the non-linear realisation and hence can be eliminated. In this paper we address two important issues that arise when eliminating inessential Goldstones. The first concerns the elimination itself, which is often performed by imposing so-called inverse Higgs constraints. Contrary to claims in the literature, there are a series of conditions on the structure constants which must be satisfied to employ the inverse Higgs phenomenon, and we discuss which parametrisation of the coset element is the most effective in this regard. We also consider generalisations of the standard inverse Higgs constraints, which can include integrating out inessential Goldstones at low energies, and prove that under certain assumptions these give rise to identical effective field theories for the essential Goldstones. Secondly, we consider mappings between non-linear realisations that differ both in the coset element and the algebra basis. While these can always be related to each other by a point transformation, remarkably, the inverse Higgs constraints are not necessarily mapped onto each other under this transformation. We discuss the physical implications of this non-mapping, with a particular emphasis on the coset space corresponding to the spontaneous breaking of the Anti-De Sitter isometries by a Minkowski probe brane.

The San Andreas fault in the San Francisco Bay region, California: Structure and kinematics of a Young plate boundary

USGS Publications Warehouse

Jachens, R.C.; Zoback, M.L.

1999-01-01

Recently acquired high-resolution aeromagnetic data delineate offset and/or truncated magnetic rock bodies of the Franciscan Complex that define the location and structure of, and total offset across, the San Andreas fault in the San Francisco Bay region. Two distinctive magnetic anomalies caused by ultramafic rocks and metabasalts east of, and truncated at, the San Andreas fault have clear counterparts west of the fault that indicate a total right-lateral offset of only 22 km on the Peninsula segment, the active strand that ruptured in 1906. The location of the Peninsula segment is well defined magnetically on the northern peninsula where it goes offshore, and can be traced along strike an additional ~6 km to the northwest. Just offshore from Lake Merced, the inferred fault trace steps right (northeast) 3 km onto a nearly parallel strand that can be traced magnetically northwest more than 20 km as the linear northeast edge of a magnetic block bounded by the San Andreas fault, the Pilarcitos fault, and the San Gregorio-Hosgri fault zone. This right-stepping strand, the Golden Gate segment, joins the eastern mapped trace of the San Andreas fault at Bolinas Lagoon and projects back onshore to the southeast near Lake Merced. Inversion of detailed gravity data on the San Francisco Peninsula reveals a 3 km wide basin situated between the two strands of the San Andreas fault, floored by Franciscan basement and filled with Plio-Quaternary sedimentary deposits of the Merced and Colma formations. The basin, ~1 km deep at the coast, narrows and becomes thinner to the southeast along the fault over a distance of ~12 km. The length, width, and location of the basin between the two strands are consistent with a pull-apart basin formed behind the right step in the right-lateral strike-slip San Andreas fault system and currently moving southeast with the North American plate. Slight nonparallelism of the two strands bounding the basin (implying a small component of convergence with continued strike-slip movement) may explain the progressive narrowing of the basin to the southeast and the puzzling recent uplift of the Merced Formation in a predominantly extensional (pull-apart basin) setting. The 1906 San Francisco earthquake may have nucleated within the step-over region, and the step-over places a strand of the San Andreas fault 3 km closer to downtown San Francisco than previously thought.

Iterative direct inversion: An exact complementary solution for inverting fault-slip data to obtain palaeostresses

NASA Astrophysics Data System (ADS)

Mostafa, Mostafa E.

2005-10-01

The present study shows that reconstructing the reduced stress tensor (RST) from the measurable fault-slip data (FSD) and the immeasurable shear stress magnitudes (SSM) is a typical iteration problem. The result of direct inversion of FSD presented by Angelier [1990. Geophysical Journal International 103, 363-376] is considered as a starting point (zero step iteration) where all SSM are assigned constant value ( λ=√{3}/2). By iteration, the SSM and RST update each other until they converge to fixed values. Angelier [1990. Geophysical Journal International 103, 363-376] designed the function upsilon ( υ) and the two estimators: relative upsilon (RUP) and (ANG) to express the divergence between the measured and calculated shear stresses. Plotting individual faults' RUP at successive iteration steps shows that they tend to zero (simulated data) or to fixed values (real data) at a rate depending on the orientation and homogeneity of the data. FSD of related origin tend to aggregate in clusters. Plots of the estimators ANG versus RUP show that by iteration, labeled data points are disposed in clusters about a straight line. These two new plots form the basis of a technique for separating FSD into homogeneous clusters.

Fully anisotropic 3-D EM modelling on a Lebedev grid with a multigrid pre-conditioner

NASA Astrophysics Data System (ADS)

Jaysaval, Piyoosh; Shantsev, Daniil V.; de la Kethulle de Ryhove, Sébastien; Bratteland, Tarjei

2016-12-01

We present a numerical algorithm for 3-D electromagnetic (EM) simulations in conducting media with general electric anisotropy. The algorithm is based on the finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid, in which all components of the electric field are collocated but half a spatial step staggered with respect to the magnetic field components, which also are collocated. This leads to a system of linear equations that is solved using a stabilized biconjugate gradient method with a multigrid preconditioner. We validate the accuracy of the numerical results for layered and 3-D tilted transverse isotropic (TTI) earth models representing typical scenarios used in the marine controlled-source EM method. It is then demonstrated that not taking into account the full anisotropy of the conductivity tensor can lead to misleading inversion results. For synthetic data corresponding to a 3-D model with a TTI anticlinal structure, a standard vertical transverse isotropic (VTI) inversion is not able to image a resistor, while for a 3-D model with a TTI synclinal structure it produces a false resistive anomaly. However, if the VTI forward solver used in the inversion is replaced by the proposed TTI solver with perfect knowledge of the strike and dip of the dipping structures, the resulting resistivity images become consistent with the true models.

tomo3d: a new 3-D joint refraction and reflection travel-time tomography code for active-source seismic data

NASA Astrophysics Data System (ADS)

Meléndez, A.; Korenaga, J.; Sallarès, V.; Ranero, C. R.

2012-04-01

We present the development state of tomo3d, a code for three-dimensional refraction and reflection travel-time tomography of wide-angle seismic data based on the previous two-dimensional version of the code, tomo2d. The core of both forward and inverse problems is inherited from the 2-D version. The ray tracing is performed by a hybrid method combining the graph and bending methods. The graph method finds an ordered array of discrete model nodes, which satisfies Fermat's principle, that is, whose corresponding travel time is a global minimum within the space of discrete nodal connections. The bending method is then applied to produce a more accurate ray path by using the nodes as support points for an interpolation with beta-splines. Travel time tomography is formulated as an iterative linearized inversion, and each step is solved using an LSQR algorithm. In order to avoid the singularity of the sensitivity kernel and to reduce the instability of inversion, regularization parameters are introduced in the inversion in the form of smoothing and damping constraints. Velocity models are built as 3-D meshes, and velocity values at intermediate locations are obtained by trilinear interpolation within the corresponding pseudo-cubic cell. Meshes are sheared to account for topographic relief. A floating reflector is represented by a 2-D grid, and depths at intermediate locations are calculated by bilinear interpolation within the corresponding square cell. The trade-off between the resolution of the final model and the associated computational cost is controlled by the relation between the selected forward star for the graph method (i.e. the number of nodes that each node considers as its neighbors) and the refinement of the velocity mesh. Including reflected phases is advantageous because it provides a better coverage and allows us to define the geometry of those geological interfaces with velocity contrasts sharp enough to be observed on record sections. The code also offers the possibility of including water-layer multiples in the modeling, whenever this phase can be followed to greater offsets than the primary phases. This increases the quantity of useful information in the data and yields more extensive and better constrained velocity and geometry models. We will present results from benchmark tests for forward and inverse problems, as well as synthetic tests comparing an inversion with refractions only and another one with both refractions and reflections.

An evolutive real-time source inversion based on a linear inverse formulation

NASA Astrophysics Data System (ADS)

Sanchez Reyes, H. S.; Tago, J.; Cruz-Atienza, V. M.; Metivier, L.; Contreras Zazueta, M. A.; Virieux, J.

2016-12-01

Finite source inversion is a steppingstone to unveil earthquake rupture. It is used on ground motion predictions and its results shed light on seismic cycle for better tectonic understanding. It is not yet used for quasi-real-time analysis. Nowadays, significant progress has been made on approaches regarding earthquake imaging, thanks to new data acquisition and methodological advances. However, most of these techniques are posterior procedures once seismograms are available. Incorporating source parameters estimation into early warning systems would require to update the source build-up while recording data. In order to go toward this dynamic estimation, we developed a kinematic source inversion formulated in the time-domain, for which seismograms are linearly related to the slip distribution on the fault through convolutions with Green's functions previously estimated and stored (Perton et al., 2016). These convolutions are performed in the time-domain as we progressively increase the time window of records at each station specifically. Selected unknowns are the spatio-temporal slip-rate distribution to keep the linearity of the forward problem with respect to unknowns, as promoted by Fan and Shearer (2014). Through the spatial extension of the expected rupture zone, we progressively build-up the slip-rate when adding new data by assuming rupture causality. This formulation is based on the adjoint-state method for efficiency (Plessix, 2006). The inverse problem is non-unique and, in most cases, underdetermined. While standard regularization terms are used for stabilizing the inversion, we avoid strategies based on parameter reduction leading to an unwanted non-linear relationship between parameters and seismograms for our progressive build-up. Rise time, rupture velocity and other quantities can be extracted later on as attributs from the slip-rate inversion we perform. Satisfactory results are obtained on a synthetic example (FIgure 1) proposed by the Source Inversion Validation project (Mai et al. 2011). A real case application is currently being explored. Our specific formulation, combined with simple prior information, as well as numerical results obtained so far, yields interesting perspectives for a real-time implementation.

Targeted next generation sequencing for the detection of ciprofloxacin resistance markers using molecular inversion probes

DTIC Science & Technology

2016-07-06

1 Targeted next-generation sequencing for the detection of ciprofloxacin resistance markers using molecular inversion probes Christopher P...development and evaluation of a panel of 44 single-stranded molecular inversion probes (MIPs) coupled to next-generation sequencing (NGS) for the...padlock and molecular inversion probes as upfront enrichment steps for use with NGS showed the specificity and multiplexability of these techniques

SAR System for UAV Operation with Motion Error Compensation beyond the Resolution Cell

PubMed Central

González-Partida, José-Tomás; Almorox-González, Pablo; Burgos-García, Mateo; Dorta-Naranjo, Blas-Pablo

2008-01-01

This paper presents an experimental Synthetic Aperture Radar (SAR) system that is under development in the Universidad Politécnica de Madrid. The system uses Linear Frequency Modulated Continuous Wave (LFM-CW) radar with a two antenna configuration for transmission and reception. The radar operates in the millimeter-wave band with a maximum transmitted bandwidth of 2 GHz. The proposed system is being developed for Unmanned Aerial Vehicle (UAV) operation. Motion errors in UAV operation can be critical. Therefore, this paper proposes a method for focusing SAR images with movement errors larger than the resolution cell. Typically, this problem is solved using two processing steps: first, coarse motion compensation based on the information provided by an Inertial Measuring Unit (IMU); and second, fine motion compensation for the residual errors within the resolution cell based on the received raw data. The proposed technique tries to focus the image without using data of an IMU. The method is based on a combination of the well known Phase Gradient Autofocus (PGA) for SAR imagery and typical algorithms for translational motion compensation on Inverse SAR (ISAR). This paper shows the first real experiments for obtaining high resolution SAR images using a car as a mobile platform for our radar. PMID:27879884

SAR System for UAV Operation with Motion Error Compensation beyond the Resolution Cell.

PubMed

González-Partida, José-Tomás; Almorox-González, Pablo; Burgos-Garcia, Mateo; Dorta-Naranjo, Blas-Pablo

2008-05-23

This paper presents an experimental Synthetic Aperture Radar (SAR) system that is under development in the Universidad Politécnica de Madrid. The system uses Linear Frequency Modulated Continuous Wave (LFM-CW) radar with a two antenna configuration for transmission and reception. The radar operates in the millimeter-wave band with a maximum transmitted bandwidth of 2 GHz. The proposed system is being developed for Unmanned Aerial Vehicle (UAV) operation. Motion errors in UAV operation can be critical. Therefore, this paper proposes a method for focusing SAR images with movement errors larger than the resolution cell. Typically, this problem is solved using two processing steps: first, coarse motion compensation based on the information provided by an Inertial Measuring Unit (IMU); and second, fine motion compensation for the residual errors within the resolution cell based on the received raw data. The proposed technique tries to focus the image without using data of an IMU. The method is based on a combination of the well known Phase Gradient Autofocus (PGA) for SAR imagery and typical algorithms for translational motion compensation on Inverse SAR (ISAR). This paper shows the first real experiments for obtaining high resolution SAR images using a car as a mobile platform for our radar.

Calculation of biochemical net reactions and pathways by using matrix operations.

PubMed Central

Alberty, R A

1996-01-01

Pathways for net biochemical reactions can be calculated by using a computer program that solves systems of linear equations. The coefficients in the linear equations are the stoichiometric numbers in the biochemical equations for the system. The solution of the system of linear equations is a vector of the stoichiometric numbers of the reactions in the pathway for the net reaction; this is referred to as the pathway vector. The pathway vector gives the number of times the various reactions have to occur to produce the desired net reaction. Net reactions may involve unknown numbers of ATP, ADP, and Pi molecules. The numbers of ATP, ADP, and Pi in a desired net reaction can be calculated in a two-step process. In the first step, the pathway is calculated by solving the system of linear equations for an abbreviated stoichiometric number matrix without ATP, ADP, Pi, NADred, and NADox. In the second step, the stoichiometric numbers in the desired net reaction, which includes ATP, ADP, Pi, NADred, and NADox, are obtained by multiplying the full stoichiometric number matrix by the calculated pathway vector. PMID:8804633

Imaging of voids by means of a physical-optics-based shape-reconstruction algorithm.

PubMed

Liseno, Angelo; Pierri, Rocco

2004-06-01

We analyze the performance of a shape-reconstruction algorithm for the retrieval of voids starting from the electromagnetic scattered field. Such an algorithm exploits the physical optics (PO) approximation to obtain a linear unknown-data relationship and performs inversions by means of the singular-value-decomposition approach. In the case of voids, in addition to a geometrical optics reflection, the presence of the lateral wave phenomenon must be considered. We analyze the effect of the presence of lateral waves on the reconstructions. For the sake of shape reconstruction, we can regard the PO algorithm as one of assuming the electric and magnetic field on the illuminated side as constant in amplitude and linear in phase, as far as the dependence on the frequency is concerned. Therefore we analyze how much the lateral wave phenomenon impairs such an assumption, and we show inversions for both one single and two circular voids, for different values of the background permittivity.

Estimation of splitting functions from Earth's normal mode spectra using the neighbourhood algorithm

NASA Astrophysics Data System (ADS)

Pachhai, Surya; Tkalčić, Hrvoje; Masters, Guy

2016-01-01

The inverse problem for Earth structure from normal mode data is strongly non-linear and can be inherently non-unique. Traditionally, the inversion is linearized by taking partial derivatives of the complex spectra with respect to the model parameters (i.e. structure coefficients), and solved in an iterative fashion. This method requires that the earthquake source model is known. However, the release of energy in large earthquakes used for the analysis of Earth's normal modes is not simple. A point source approximation is often inadequate, and a more complete account of energy release at the source is required. In addition, many earthquakes are required for the solution to be insensitive to the initial constraints and regularization. In contrast to an iterative approach, the autoregressive linear inversion technique conveniently avoids the need for earthquake source parameters, but it also requires a number of events to achieve full convergence when a single event does not excite all singlets well. To build on previous improvements, we develop a technique to estimate structure coefficients (and consequently, the splitting functions) using a derivative-free parameter search, known as neighbourhood algorithm (NA). We implement an efficient forward method derived using the autoregresssion of receiver strips, and this allows us to search over a multiplicity of structure coefficients in a relatively short time. After demonstrating feasibility of the use of NA in synthetic cases, we apply it to observations of the inner core sensitive mode 13S2. The splitting function of this mode is dominated by spherical harmonic degree 2 axisymmetric structure and is consistent with the results obtained from the autoregressive linear inversion. The sensitivity analysis of multiple events confirms the importance of the Bolivia, 1994 earthquake. When this event is used in the analysis, as little as two events are sufficient to constrain the splitting functions of 13S2 mode. Apart from not requiring the knowledge of earthquake source, the newly developed technique provides an approximate uncertainty measure of the structure coefficients and allows us to control the type of structure solved for, for example to establish if elastic structure is sufficient.

A simplified competition data analysis for radioligand specific activity determination.

PubMed

Venturino, A; Rivera, E S; Bergoc, R M; Caro, R A

1990-01-01

Non-linear regression and two-step linear fit methods were developed to determine the actual specific activity of 125I-ovine prolactin by radioreceptor self-displacement analysis. The experimental results obtained by the different methods are superposable. The non-linear regression method is considered to be the most adequate procedure to calculate the specific activity, but if its software is not available, the other described methods are also suitable.

Decoherence in quantum systems in a static gravitational field

NASA Astrophysics Data System (ADS)

Shariati, Ahmad; Khorrami, Mohammad; Loran, Farhang

2016-09-01

A small quantum system is studied which is a superposition of states localized in different positions in a static gravitational field. The time evolution of the correlation between different positions is investigated, and it is seen that there are two time scales for such an evolution (decoherence). Both time scales are inversely proportional to the red shift difference between the two points. These time scales correspond to decoherences which are linear and quadratic, respectively, in time.

Gummel Symmetry Test on charge based drain current expression using modified first-order hyperbolic velocity-field expression

NASA Astrophysics Data System (ADS)

Singh, Kirmender; Bhattacharyya, A. B.

2017-03-01

Gummel Symmetry Test (GST) has been a benchmark industry standard for MOSFET models and is considered as one of important tests by the modeling community. BSIM4 MOSFET model fails to pass GST as the drain current equation is not symmetrical because drain and source potentials are not referenced to bulk. BSIM6 MOSFET model overcomes this limitation by taking all terminal biases with reference to bulk and using proper velocity saturation (v -E) model. The drain current equation in BSIM6 is charge based and continuous in all regions of operation. It, however, adopts a complicated method to compute source and drain charges. In this work we propose to use conventional charge based method formulated by Enz for obtaining simpler analytical drain current expression that passes GST. For this purpose we adopt two steps: (i) In the first step we use a modified first-order hyperbolic v -E model with adjustable coefficients which is integrable, simple and accurate, and (ii) In the second we use a multiplying factor in the modified first-order hyperbolic v -E expression to obtain correct monotonic asymptotic behavior around the origin of lateral electric field. This factor is of empirical form, which is a function of drain voltage (vd) and source voltage (vs) . After considering both the above steps we obtain drain current expression whose accuracy is similar to that obtained from second-order hyperbolic v -E model. In modified first-order hyperbolic v -E expression if vd and vs is replaced by smoothing functions for the effective drain voltage (vdeff) and effective source voltage (vseff), it will as well take care of discontinuity between linear to saturation regions of operation. The condition of symmetry is shown to be satisfied by drain current and its higher order derivatives, as both of them are odd functions and their even order derivatives smoothly pass through the origin. In strong inversion region and technology node of 22 nm the GST is shown to pass till sixth-order derivative and for weak inversion it is shown till fifth-order derivative. In the expression of drain current major short channel phenomena like vertical field mobility reduction, velocity saturation and velocity overshoot have been taken into consideration.

Enhancing Autonomy of Aerial Systems Via Integration of Visual Sensors into Their Avionics Suite

DTIC Science & Technology

2016-09-01

aerial platform for subsequent visual sensor integration. 14. SUBJECT TERMS autonomous system, quadrotors, direct method, inverse ...CONTROLLER ARCHITECTURE .....................................................43 B. INVERSE DYNAMICS IN THE VIRTUAL DOMAIN ......................45 1...control station GPS Global-Positioning System IDVD inverse dynamics in the virtual domain ILP integer linear program INS inertial-navigation system

Alternating direction implicit methods for parabolic equations with a mixed derivative

NASA Technical Reports Server (NTRS)

Beam, R. M.; Warming, R. F.

1980-01-01

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A(0)-stable linear two-step methods in conjunction with the method of approximate factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A(0)-stable method. The parameter space for which the resulting ADI schemes are second-order accurate and unconditionally stable is determined. Some numerical examples are given.

Alternating direction implicit methods for parabolic equations with a mixed derivative

NASA Technical Reports Server (NTRS)

Beam, R. M.; Warming, R. F.

1979-01-01

Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A sub 0-stable linear two-step methods in conjunction with the method of approximation factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A sub 0-stable method. The parameter space for which the resulting ADI schemes are second order accurate and unconditionally stable is determined. Some numerical examples are given.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kitanidis, Peter

As large-scale, commercial storage projects become operational, the problem of utilizing information from diverse sources becomes more critically important. In this project, we developed, tested, and applied an advanced joint data inversion system for CO 2 storage modeling with large data sets for use in site characterization and real-time monitoring. Emphasis was on the development of advanced and efficient computational algorithms for joint inversion of hydro-geophysical data, coupled with state-of-the-art forward process simulations. The developed system consists of (1) inversion tools using characterization data, such as 3D seismic survey (amplitude images), borehole log and core data, as well as hydraulic,more » tracer and thermal tests before CO 2 injection, (2) joint inversion tools for updating the geologic model with the distribution of rock properties, thus reducing uncertainty, using hydro-geophysical monitoring data, and (3) highly efficient algorithms for directly solving the dense or sparse linear algebra systems derived from the joint inversion. The system combines methods from stochastic analysis, fast linear algebra, and high performance computing. The developed joint inversion tools have been tested through synthetic CO 2 storage examples.« less

Exact solution of a linear molecular motor model driven by two-step fluctuations and subject to protein friction.

PubMed

Fogedby, Hans C; Metzler, Ralf; Svane, Axel

2004-08-01

We investigate by analytical means the stochastic equations of motion of a linear molecular motor model based on the concept of protein friction. Solving the coupled Langevin equations originally proposed by Mogilner et al. [Phys. Lett. A 237, 297 (1998)], and averaging over both the two-step internal conformational fluctuations and the thermal noise, we present explicit, analytical expressions for the average motion and the velocity-force relationship. Our results allow for a direct interpretation of details of this motor model which are not readily accessible from numerical solutions. In particular, we find that the model is able to predict physiologically reasonable values for the load-free motor velocity and the motor mobility.

Stable Lévy motion with inverse Gaussian subordinator

NASA Astrophysics Data System (ADS)

Kumar, A.; Wyłomańska, A.; Gajda, J.

2017-09-01

In this paper we study the stable Lévy motion subordinated by the so-called inverse Gaussian process. This process extends the well known normal inverse Gaussian (NIG) process introduced by Barndorff-Nielsen, which arises by subordinating ordinary Brownian motion (with drift) with inverse Gaussian process. The NIG process found many interesting applications, especially in financial data description. We discuss here the main features of the introduced subordinated process, such as distributional properties, existence of fractional order moments and asymptotic tail behavior. We show the connection of the process with continuous time random walk. Further, the governing fractional partial differential equations for the probability density function is also obtained. Moreover, we discuss the asymptotic distribution of sample mean square displacement, the main tool in detection of anomalous diffusion phenomena (Metzler et al., 2014). In order to apply the stable Lévy motion time-changed by inverse Gaussian subordinator we propose a step-by-step procedure of parameters estimation. At the end, we show how the examined process can be useful to model financial time series.

Magnetotelluric 3-D inversion—a review of two successful workshops on forward and inversion code testing and comparison

NASA Astrophysics Data System (ADS)

Miensopust, Marion P.; Queralt, Pilar; Jones, Alan G.; 3D MT modellers

2013-06-01

Over the last half decade the need for, and importance of, three-dimensional (3-D) modelling of magnetotelluric (MT) data have increased dramatically and various 3-D forward and inversion codes are in use and some have become commonly available. Comparison of forward responses and inversion results is an important step for code testing and validation prior to `production' use. The various codes use different mathematical approximations to the problem (finite differences, finite elements or integral equations), various orientations of the coordinate system, different sign conventions for the time dependence and various inversion strategies. Additionally, the obtained results are dependent on data analysis, selection and correction as well as on the chosen mesh, inversion parameters and regularization adopted, and therefore, a careful and knowledge-based use of the codes is essential. In 2008 and 2011, during two workshops at the Dublin Institute for Advanced Studies over 40 people from academia (scientists and students) and industry from around the world met to discuss 3-D MT inversion. These workshops brought together a mix of code writers as well as code users to assess the current status of 3-D modelling, to compare the results of different codes, and to discuss and think about future improvements and new aims in 3-D modelling. To test the numerical forward solutions, two 3-D models were designed to compare the responses obtained by different codes and/or users. Furthermore, inversion results of these two data sets and two additional data sets obtained from unknown models (secret models) were also compared. In this manuscript the test models and data sets are described (supplementary files are available) and comparisons of the results are shown. Details regarding the used data, forward and inversion parameters as well as computational power are summarized for each case, and the main discussion points of the workshops are reviewed. In general, the responses obtained from the various forward models are comfortingly very similar, and discrepancies are mainly related to the adopted mesh. For the inversions, the results show how the inversion outcome is affected by distortion and the choice of errors, as well as by the completeness of the data set. We hope that these compilations will become useful not only for those that were involved in the workshops, but for the entire MT community and also the broader geoscience community who may be interested in the resolution offered by MT.

A Successful Attempt to Obtain the Linear Dependence Between One-Photon and Two-Photon Spectral Properties and Hammett Parameters of Various Aromatic Substituents in New π-Extended Asymmetric Organic Chromophores.

PubMed

Hu, Nvdan; Gong, Yulong; Wang, Xinchao; Lu, Yao; Peng, Guangyue; Yang, Long; Zhang, Shengtao; Luo, Ziping; Li, Hongru; Gao, Fang

2015-11-01

A series of new asymmetric chromophores containing aromatic substituents and possessing the excellent π-extension in space were prepared through multi-steps routes. One-photon and two-photon spectral properties of these new chromophores could be tuned by these substituents finely and simultaneously. The linear correlation of the wave numbers of the one-photon absorption and emission maxima to Hammett parameters of these substituents was presented. Near infrared two-photon absorption emission integrated areas of the target chromophores were correlated linearly to Hammett constants of these substituted groups.

Stochastic sediment property inversion in Shallow Water 06.

PubMed

Michalopoulou, Zoi-Heleni

2017-11-01

Received time-series at a short distance from the source allow the identification of distinct paths; four of these are direct, surface and bottom reflections, and sediment reflection. In this work, a Gibbs sampling method is used for the estimation of the arrival times of these paths and the corresponding probability density functions. The arrival times for the first three paths are then employed along with linearization for the estimation of source range and depth, water column depth, and sound speed in the water. Propagating densities of arrival times through the linearized inverse problem, densities are also obtained for the above parameters, providing maximum a posteriori estimates. These estimates are employed to calculate densities and point estimates of sediment sound speed and thickness using a non-linear, grid-based model. Density computation is an important aspect of this work, because those densities express the uncertainty in the inversion for sediment properties.

Modeling Gross Primary Production of Agro-Forestry Ecosystems by Assimilation of Satellite-Derived Information in a Process-Based Model

PubMed Central

Migliavacca, Mirco; Meroni, Michele; Busetto, Lorenzo; Colombo, Roberto; Zenone, Terenzio; Matteucci, Giorgio; Manca, Giovanni; Seufert, Guenther

2009-01-01

In this paper we present results obtained in the framework of a regional-scale analysis of the carbon budget of poplar plantations in Northern Italy. We explored the ability of the process-based model BIOME-BGC to estimate the gross primary production (GPP) using an inverse modeling approach exploiting eddy covariance and satellite data. We firstly present a version of BIOME-BGC coupled with the radiative transfer models PROSPECT and SAILH (named PROSAILH-BGC) with the aims of i) improving the BIOME-BGC description of the radiative transfer regime within the canopy and ii) allowing the assimilation of remotely-sensed vegetation index time series, such as MODIS NDVI, into the model. Secondly, we present a two-step model inversion for optimization of model parameters. In the first step, some key ecophysiological parameters were optimized against data collected by an eddy covariance flux tower. In the second step, important information about phenological dates and about standing biomass were optimized against MODIS NDVI. Results obtained showed that the PROSAILH-BGC allowed simulation of MODIS NDVI with good accuracy and that we described better the canopy radiation regime. The inverse modeling approach was demonstrated to be useful for the optimization of ecophysiological model parameters, phenological dates and parameters related to the standing biomass, allowing good accuracy of daily and annual GPP predictions. In summary, this study showed that assimilation of eddy covariance and remote sensing data in a process model may provide important information for modeling gross primary production at regional scale. PMID:22399948

Modeling gross primary production of agro-forestry ecosystems by assimilation of satellite-derived information in a process-based model.

PubMed

Migliavacca, Mirco; Meroni, Michele; Busetto, Lorenzo; Colombo, Roberto; Zenone, Terenzio; Matteucci, Giorgio; Manca, Giovanni; Seufert, Guenther

2009-01-01

In this paper we present results obtained in the framework of a regional-scale analysis of the carbon budget of poplar plantations in Northern Italy. We explored the ability of the process-based model BIOME-BGC to estimate the gross primary production (GPP) using an inverse modeling approach exploiting eddy covariance and satellite data. We firstly present a version of BIOME-BGC coupled with the radiative transfer models PROSPECT and SAILH (named PROSAILH-BGC) with the aims of i) improving the BIOME-BGC description of the radiative transfer regime within the canopy and ii) allowing the assimilation of remotely-sensed vegetation index time series, such as MODIS NDVI, into the model. Secondly, we present a two-step model inversion for optimization of model parameters. In the first step, some key ecophysiological parameters were optimized against data collected by an eddy covariance flux tower. In the second step, important information about phenological dates and about standing biomass were optimized against MODIS NDVI. Results obtained showed that the PROSAILH-BGC allowed simulation of MODIS NDVI with good accuracy and that we described better the canopy radiation regime. The inverse modeling approach was demonstrated to be useful for the optimization of ecophysiological model parameters, phenological dates and parameters related to the standing biomass, allowing good accuracy of daily and annual GPP predictions. In summary, this study showed that assimilation of eddy covariance and remote sensing data in a process model may provide important information for modeling gross primary production at regional scale.

Electrohydraulic linear actuator with two stepping motors controlled by overshoot-free algorithm

NASA Astrophysics Data System (ADS)

Milecki, Andrzej; Ortmann, Jarosław

2017-11-01

The paper describes electrohydraulic spool valves with stepping motors used as electromechanical transducers. A new concept of a proportional valve in which two stepping motors are working differentially is introduced. Such valve changes the fluid flow proportionally to the sum or difference of the motors' steps numbers. The valve design and principle of its operation is described. Theoretical equations and simulation models are proposed for all elements of the drive, i.e., the stepping motor units, hydraulic valve and cylinder. The main features of the valve and drive operation are described; some specific problem areas covering the nature of stepping motors and their differential work in the valve are also considered. The whole servo drive non-linear model is proposed and used further for simulation investigations. The initial simulation investigations of the drive with a new valve have shown that there is a significant overshoot in the drive step response, which is not allowed in positioning process. Therefore additional effort is spent to reduce the overshoot and in consequence reduce the settling time. A special predictive algorithm is proposed to this end. Then the proposed control method is tested and further improved in simulations. Further on, the model is implemented in reality and the whole servo drive system is tested. The investigation results presented in this paper, are showing an overshoot-free positioning process which enables high positioning accuracy.

Planktonic food webs revisited: Reanalysis of results from the linear inverse approach

NASA Astrophysics Data System (ADS)

Hlaili, Asma Sakka; Niquil, Nathalie; Legendre, Louis

2014-01-01

Identification of the trophic pathway that dominates a given planktonic assemblage is generally based on the distribution of biomasses among food-web compartments, or better, the flows of materials or energy among compartments. These flows are obtained by field observations and a posteriori analyses, including the linear inverse approach. In the present study, we re-analysed carbon flows obtained by inverse analysis at 32 stations in the global ocean and one large lake. Our results do not support two "classical" views of plankton ecology, i.e. that the herbivorous food web is dominated by mesozooplankton grazing on large phytoplankton, and the microbial food web is based on microzooplankton significantly consuming bacteria; our results suggest instead that phytoplankton are generally grazed by microzooplankton, of which they are the main food source. Furthermore, we identified the "phyto-microbial food web", where microzooplankton largely feed on phytoplankton, in addition to the already known "poly-microbial food web", where microzooplankton consume more or less equally various types of food. These unexpected results led to a (re)definition of the conceptual models corresponding to the four trophic pathways we found to exist in plankton, i.e. the herbivorous, multivorous, and two types of microbial food web. We illustrated the conceptual trophic pathways using carbon flows that were actually observed at representative stations. The latter can be calibrated to correspond to any field situation. Our study also provides researchers and managers with operational criteria for identifying the dominant trophic pathway in a planktonic assemblage, these criteria being based on the values of two carbon ratios that could be calculated from flow values that are relatively easy to estimate in the field.

Theory and simulation of an inverse free-electron laser experiment

NASA Astrophysics Data System (ADS)

Gou, S. K.; Bhattacharjee, A.; Fang, J.-M.; Marshall, T. C.

1997-03-01

An experimental demonstration of the acceleration of electrons using a high-power CO2 laser interacting with a relativistic electron beam moving along a wiggler has been carried out at the Accelerator Test Facility of the Brookhaven National Laboratory [Phys. Rev. Lett. 77, 2690 (1996)]. The data generated by this inverse free-electron-laser (IFEL) experiment are studied by means of theory and simulation. Included in the simulations are such effects as: a low-loss metallic waveguide with a dielectric coating on the walls; multi-mode coupling due to self-consistent interaction between the electrons and the optical wave; space charge; energy spread of the electrons; and arbitrary wiggler-field profile. Two types of wiggler profile are considered: a linear taper of the period, and a step-taper of the period. (The period of the wiggler is ˜3 cm, its magnetic field is ˜1 T, and the wiggler length is 0.47 m.) The energy increment of the electrons (˜1-2%) is analyzed in detail as a function of laser power, wiggler parameters, and the initial beam energy (˜40 MeV). At a laser power level ˜0.5 Gw, the simulation results on energy gain are in reasonable agreement with the experimental results. Preliminary results on the electron energy distribution at the end of the IFEL are presented. Whereas the experiment produces a near-monotone distribution of electron energies with the peak shifted to higher energy, the simulation shows a more structured and non-monotonic distribution at the end of the wiggler. Effects that may help reconcile these differences are considered.

SU-C-207B-06: Comparison of Registration Methods for Modeling Pathologic Response of Esophageal Cancer to Chemoradiation Therapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Riyahi, S; Choi, W; Bhooshan, N

2016-06-15

Purpose: To compare linear and deformable registration methods for evaluation of tumor response to Chemoradiation therapy (CRT) in patients with esophageal cancer. Methods: Linear and multi-resolution BSpline deformable registration were performed on Pre-Post-CRT CT/PET images of 20 patients with esophageal cancer. For both registration methods, we registered CT using Mean Square Error (MSE) metric, however to register PET we used transformation obtained using Mutual Information (MI) from the same CT due to being multi-modality. Similarity of Warped-CT/PET was quantitatively evaluated using Normalized Mutual Information and plausibility of DF was assessed using inverse consistency Error. To evaluate tumor response four groupsmore » of tumor features were examined: (1) Conventional PET/CT e.g. SUV, diameter (2) Clinical parameters e.g. TNM stage, histology (3)spatial-temporal PET features that describe intensity, texture and geometry of tumor (4)all features combined. Dominant features were identified using 10-fold cross-validation and Support Vector Machine (SVM) was deployed for tumor response prediction while the accuracy was evaluated by ROC Area Under Curve (AUC). Results: Average and standard deviation of Normalized mutual information for deformable registration using MSE was 0.2±0.054 and for linear registration was 0.1±0.026, showing higher NMI for deformable registration. Likewise for MI metric, deformable registration had 0.13±0.035 comparing to linear counterpart with 0.12±0.037. Inverse consistency error for deformable registration for MSE metric was 4.65±2.49 and for linear was 1.32±2.3 showing smaller value for linear registration. The same conclusion was obtained for MI in terms of inverse consistency error. AUC for both linear and deformable registration was 1 showing no absolute difference in terms of response evaluation. Conclusion: Deformable registration showed better NMI comparing to linear registration, however inverse consistency of transformation was lower in linear registration. We do not expect to see significant difference when warping PET images using deformable or linear registration. This work was supported in part by the National Cancer Institute Grants R01CA172638.« less

Minimal-Inversion Feedforward-And-Feedback Control System

NASA Technical Reports Server (NTRS)

Seraji, Homayoun

1990-01-01

Recent developments in theory of control systems support concept of minimal-inversion feedforward-and feedback control system consisting of three independently designable control subsystems. Applicable to the control of linear, time-invariant plant.

ANNIT - An Efficient Inversion Algorithm based on Prediction Principles

NASA Astrophysics Data System (ADS)

Růžek, B.; Kolář, P.

2009-04-01

Solution of inverse problems represents meaningful job in geophysics. The amount of data is continuously increasing, methods of modeling are being improved and the computer facilities are also advancing great technical progress. Therefore the development of new and efficient algorithms and computer codes for both forward and inverse modeling is still up to date. ANNIT is contributing to this stream since it is a tool for efficient solution of a set of non-linear equations. Typical geophysical problems are based on parametric approach. The system is characterized by a vector of parameters p, the response of the system is characterized by a vector of data d. The forward problem is usually represented by unique mapping F(p)=d. The inverse problem is much more complex and the inverse mapping p=G(d) is available in an analytical or closed form only exceptionally and generally it may not exist at all. Technically, both forward and inverse mapping F and G are sets of non-linear equations. ANNIT solves such situation as follows: (i) joint subspaces {pD, pM} of original data and model spaces D, M, resp. are searched for, within which the forward mapping F is sufficiently smooth that the inverse mapping G does exist, (ii) numerical approximation of G in subspaces {pD, pM} is found, (iii) candidate solution is predicted by using this numerical approximation. ANNIT is working in an iterative way in cycles. The subspaces {pD, pM} are searched for by generating suitable populations of individuals (models) covering data and model spaces. The approximation of the inverse mapping is made by using three methods: (a) linear regression, (b) Radial Basis Function Network technique, (c) linear prediction (also known as "Kriging"). The ANNIT algorithm has built in also an archive of already evaluated models. Archive models are re-used in a suitable way and thus the number of forward evaluations is minimized. ANNIT is now implemented both in MATLAB and SCILAB. Numerical tests show good performance of the algorithm. Both versions and documentation are available on Internet and anybody can download them. The goal of this presentation is to offer the algorithm and computer codes for anybody interested in the solution to inverse problems.

Inverting pump-probe spectroscopy for state tomography of excitonic systems.

PubMed

Hoyer, Stephan; Whaley, K Birgitta

2013-04-28

We propose a two-step protocol for inverting ultrafast spectroscopy experiments on a molecular aggregate to extract the time-evolution of the excited state density matrix. The first step is a deconvolution of the experimental signal to determine a pump-dependent response function. The second step inverts this response function to obtain the quantum state of the system, given a model for how the system evolves following the probe interaction. We demonstrate this inversion analytically and numerically for a dimer model system, and evaluate the feasibility of scaling it to larger molecular aggregates such as photosynthetic protein-pigment complexes. Our scheme provides a direct alternative to the approach of determining all Hamiltonian parameters and then simulating excited state dynamics.

3D CSEM inversion based on goal-oriented adaptive finite element method

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.

2016-12-01

We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with complex geological scenarios by applying it to the inversion of synthetic marine controlled source EM data generated for a complex 3D offshore model with significant seafloor topography.

The impact of accelerometer wear location on the relationship between step counts and arterial stiffness in adults treated for hypertension and diabetes.

PubMed

Cooke, Alexandra B; Daskalopoulou, Stella S; Dasgupta, Kaberi

2018-04-01

Accelerometer placement at the wrist is convenient and increasingly adopted despite less accurate physical activity (PA) measurement than with waist placement. Capitalizing on a study that started with wrist placement and shifted to waist placement, we compared associations between PA measures derived from different accelerometer locations with a responsive arterial health indicator, carotid-femoral pulse wave velocity (cfPWV). Cross-sectional study. We previously demonstrated an inverse association between waist-worn pedometer-assessed step counts (Yamax SW-200, 7 days) and cfPWV (-0.20m/s, 95% CI -0.28, -0.12 per 1000 step/day increment) in 366 adults. Participants concurrently wore accelerometers (ActiGraph GT3X+), most at the waist but the first 46 at the wrist. We matched this subgroup with participants from the 'waist accelerometer' group (sex, age, and pedometer-assessed steps/day) and assessed associations with cfPWV (applanation tonometry, Sphygmocor) separately in each subgroup through linear regression models. Compared to the waist group, wrist group participants had higher step counts (mean difference 3980 steps/day; 95% CI 2517, 5443), energy expenditure (967kcal/day, 95% CI 755, 1179), and moderate-to-vigorous-PA (138min; 95% CI 114, 162). Accelerometer-assessed step counts (waist) suggested an association with cfPWV (-0.28m/s, 95% CI -0.58, 0.01); but no relationship was apparent with wrist-assessed steps (0.02m/s, 95% CI -0.24, 0.27). Waist but not wrist ActiGraph PA measures signal associations between PA and cfPWV. We urge researchers to consider the importance of wear location choice on relationships with health indicators. Copyright © 2017 Sports Medicine Australia. Published by Elsevier Ltd. All rights reserved.

First staging of two laser accelerators.

PubMed

Kimura, W D; van Steenbergen, A; Babzien, M; Ben-Zvi, I; Campbell, L P; Cline, D B; Dilley, C E; Gallardo, J C; Gottschalk, S C; He, P; Kusche, K P; Liu, Y; Pantell, R H; Pogorelsky, I V; Quimby, D C; Skaritka, J; Steinhauer, L C; Yakimenko, V

2001-04-30

Staging of two laser-driven, relativistic electron accelerators has been demonstrated for the first time in a proof-of-principle experiment, whereby two distinct and serial laser accelerators acted on an electron beam in a coherently cumulative manner. Output from a CO2 laser was split into two beams to drive two inverse free electron lasers (IFEL) separated by 2.3 m. The first IFEL served to bunch the electrons into approximately 3 fs microbunches, which were rephased with the laser wave in the second IFEL. This represents a crucial step towards the development of practical laser-driven electron accelerators.

Trajectory following and stabilization control of fully actuated AUV using inverse kinematics and self-tuning fuzzy PID.

PubMed

Hammad, Mohanad M; Elshenawy, Ahmed K; El Singaby, M I

2017-01-01

In this work a design for self-tuning non-linear Fuzzy Proportional Integral Derivative (FPID) controller is presented to control position and speed of Multiple Input Multiple Output (MIMO) fully-actuated Autonomous Underwater Vehicles (AUV) to follow desired trajectories. Non-linearity that results from the hydrodynamics and the coupled AUV dynamics makes the design of a stable controller a very difficult task. In this study, the control scheme in a simulation environment is validated using dynamic and kinematic equations for the AUV model and hydrodynamic damping equations. An AUV configuration with eight thrusters and an inverse kinematic model from a previous work is utilized in the simulation. In the proposed controller, Mamdani fuzzy rules are used to tune the parameters of the PID. Nonlinear fuzzy Gaussian membership functions are selected to give better performance and response in the non-linear system. A control architecture with two feedback loops is designed such that the inner loop is for velocity control and outer loop is for position control. Several test scenarios are executed to validate the controller performance including different complex trajectories with and without injection of ocean current disturbances. A comparison between the proposed FPID controller and the conventional PID controller is studied and shows that the FPID controller has a faster response to the reference signal and more stable behavior in a disturbed non-linear environment.

Trajectory following and stabilization control of fully actuated AUV using inverse kinematics and self-tuning fuzzy PID

PubMed Central

Elshenawy, Ahmed K.; El Singaby, M.I.

2017-01-01

In this work a design for self-tuning non-linear Fuzzy Proportional Integral Derivative (FPID) controller is presented to control position and speed of Multiple Input Multiple Output (MIMO) fully-actuated Autonomous Underwater Vehicles (AUV) to follow desired trajectories. Non-linearity that results from the hydrodynamics and the coupled AUV dynamics makes the design of a stable controller a very difficult task. In this study, the control scheme in a simulation environment is validated using dynamic and kinematic equations for the AUV model and hydrodynamic damping equations. An AUV configuration with eight thrusters and an inverse kinematic model from a previous work is utilized in the simulation. In the proposed controller, Mamdani fuzzy rules are used to tune the parameters of the PID. Nonlinear fuzzy Gaussian membership functions are selected to give better performance and response in the non-linear system. A control architecture with two feedback loops is designed such that the inner loop is for velocity control and outer loop is for position control. Several test scenarios are executed to validate the controller performance including different complex trajectories with and without injection of ocean current disturbances. A comparison between the proposed FPID controller and the conventional PID controller is studied and shows that the FPID controller has a faster response to the reference signal and more stable behavior in a disturbed non-linear environment. PMID:28683071

Preliminary evaluation of cryogenic two-phase flow imaging using electrical capacitance tomography

NASA Astrophysics Data System (ADS)

Xie, Huangjun; Yu, Liu; Zhou, Rui; Qiu, Limin; Zhang, Xiaobin

2017-09-01

The potential application of the 2-D eight-electrode electrical capacitance tomography (ECT) to the inversion imaging of the liquid nitrogen-vaporous nitrogen (LN2-VN2) flow in the tube is theoretically evaluated. The phase distribution of the computational domain is obtained using the simultaneous iterative reconstruction technique with variable iterative step size. The detailed mathematical derivations for the calculations are presented. The calculated phase distribution for the two detached LN2 column case shows the comparable results with the water-air case, regardless of the much reduced dielectric permittivity of LN2 compared with water. The inversion images of total eight different LN2-VN2 flow patterns are presented and quantitatively evaluated by calculating the relative void fraction error and the correlation coefficient. The results demonstrate that the developed reconstruction technique for ECT has the capacity to reconstruct the phase distribution of the complex LN2-VN2 flow, while the accuracy of the inversion images is significantly influenced by the size of the discrete phase. The influence of the measurement noise on the image quality is also considered in the calculations.

Accurate upwind methods for the Euler equations

NASA Technical Reports Server (NTRS)

Huynh, Hung T.

1993-01-01

A new class of piecewise linear methods for the numerical solution of the one-dimensional Euler equations of gas dynamics is presented. These methods are uniformly second-order accurate, and can be considered as extensions of Godunov's scheme. With an appropriate definition of monotonicity preservation for the case of linear convection, it can be shown that they preserve monotonicity. Similar to Van Leer's MUSCL scheme, they consist of two key steps: a reconstruction step followed by an upwind step. For the reconstruction step, a monotonicity constraint that preserves uniform second-order accuracy is introduced. Computational efficiency is enhanced by devising a criterion that detects the 'smooth' part of the data where the constraint is redundant. The concept and coding of the constraint are simplified by the use of the median function. A slope steepening technique, which has no effect at smooth regions and can resolve a contact discontinuity in four cells, is described. As for the upwind step, existing and new methods are applied in a manner slightly different from those in the literature. These methods are derived by approximating the Euler equations via linearization and diagonalization. At a 'smooth' interface, Harten, Lax, and Van Leer's one intermediate state model is employed. A modification for this model that can resolve contact discontinuities is presented. Near a discontinuity, either this modified model or a more accurate one, namely, Roe's flux-difference splitting. is used. The current presentation of Roe's method, via the conceptually simple flux-vector splitting, not only establishes a connection between the two splittings, but also leads to an admissibility correction with no conditional statement, and an efficient approximation to Osher's approximate Riemann solver. These reconstruction and upwind steps result in schemes that are uniformly second-order accurate and economical at smooth regions, and yield high resolution at discontinuities.

Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Luo, Xu-Dan; Musslimani, Ziad H.

2018-01-01

In 2013, a new nonlocal symmetry reduction of the well-known AKNS (an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, and Alan C. Newell et al. (1974)) scattering problem was found. It was shown to give rise to a new nonlocal PT symmetric and integrable Hamiltonian nonlinear Schrödinger (NLS) equation. Subsequently, the inverse scattering transform was constructed for the case of rapidly decaying initial data and a family of spatially localized, time periodic one-soliton solutions was found. In this paper, the inverse scattering transform for the nonlocal NLS equation with nonzero boundary conditions at infinity is presented in four different cases when the data at infinity have constant amplitudes. The direct and inverse scattering problems are analyzed. Specifically, the direct problem is formulated, the analytic properties of the eigenfunctions and scattering data and their symmetries are obtained. The inverse scattering problem, which arises from a novel nonlocal system, is developed via a left-right Riemann-Hilbert problem in terms of a suitable uniformization variable and the time dependence of the scattering data is obtained. This leads to a method to linearize/solve the Cauchy problem. Pure soliton solutions are discussed, and explicit 1-soliton solution and two 2-soliton solutions are provided for three of the four different cases corresponding to two different signs of nonlinearity and two different values of the phase difference between plus and minus infinity. In another case, there are no solitons.

Large-Scale Coherent Vortex Formation in Two-Dimensional Turbulence

NASA Astrophysics Data System (ADS)

Orlov, A. V.; Brazhnikov, M. Yu.; Levchenko, A. A.

2018-04-01

The evolution of a vortex flow excited by an electromagnetic technique in a thin layer of a conducting liquid was studied experimentally. Small-scale vortices, excited at the pumping scale, merge with time due to the nonlinear interaction and produce large-scale structures—the inverse energy cascade is formed. The dependence of the energy spectrum in the developed inverse cascade is well described by the Kraichnan law k -5/3. At large scales, the inverse cascade is limited by cell sizes, and a large-scale coherent vortex flow is formed, which occupies almost the entire area of the experimental cell. The radial profile of the azimuthal velocity of the coherent vortex immediately after the pumping was switched off has been established for the first time. Inside the vortex core, the azimuthal velocity grows linearly along a radius and reaches a constant value outside the core, which agrees well with the theoretical prediction.

Two-dimensional microsphere quasi-crystal: fabrication and properties

NASA Astrophysics Data System (ADS)

Noginova, Natalia E.; Venkateswarlu, Putcha; Kukhtarev, Nickolai V.; Sarkisov, Sergey S.; Noginov, Mikhail A.; Caulfield, H. John; Curley, Michael J.

1996-11-01

2D quasi-crystals were fabricated from polystyrene microspheres and characterized for their structural, diffraction, and non-linear optics properties. The quasi- crystals were produced with the method based on Langmuir- Blodgett thin film technique. Illuminating the crystal with the laser beam, we observed the diffraction pattern in the direction of the beam propagation and in the direction of the back scattering, similar to the x-ray Laue pattern observed in regular crystals with hexagonal structure. The absorption spectrum of the quasi-crystal demonstrated two series of regular maxima and minima, with the spacing inversely proportional to the microspheres diameter. Illumination of the dye-doped microspheres crystal with Q- switched radiation of Nd:YAG laser showed the enhancement of non-linear properties, in particular, second harmonic generation.

Bowhead whale localization using time-difference-of-arrival data from asynchronous recorders.

PubMed

Warner, Graham A; Dosso, Stan E; Hannay, David E

2017-03-01

This paper estimates bowhead whale locations and uncertainties using nonlinear Bayesian inversion of the time-difference-of-arrival (TDOA) of low-frequency whale calls recorded on onmi-directional asynchronous recorders in the shallow waters of the northeastern Chukchi Sea, Alaska. A Y-shaped cluster of seven autonomous ocean-bottom hydrophones, separated by 0.5-9.2 km, was deployed for several months over which time their clocks drifted out of synchronization. Hundreds of recorded whale calls are manually associated between recorders. The TDOA between hydrophone pairs are calculated from filtered waveform cross correlations and depend on the whale locations, hydrophone locations, relative recorder clock offsets, and effective waveguide sound speed. A nonlinear Bayesian inversion estimates all of these parameters and their uncertainties as well as data error statistics. The problem is highly nonlinear and a linearized inversion did not produce physically realistic results. Whale location uncertainties from nonlinear inversion can be low enough to allow accurate tracking of migrating whales that vocalize repeatedly over several minutes. Estimates of clock drift rates are obtained from inversions of TDOA data over two weeks and agree with corresponding estimates obtained from long-time averaged ambient noise cross correlations. The inversion is suitable for application to large data sets of manually or automatically detected whale calls.

Reservoir monitoring and characterization using satellite geodetic data: Interferometric Synthetic Aperture Radar observations from the Krechba field, Algeria

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasco, D.W.; Ferretti, Alessandro; Novali, Fabrizio

2008-05-01

Deformation in the material overlying an active reservoir is used to monitor pressure change at depth. A sequence of pressure field estimates, eleven in all, allow us to construct a measure of diffusive travel time throughout the reservoir. The dense distribution of travel time values means that we can construct an exactly linear inverse problem for reservoir flow properties. Application to Interferometric Synthetic Aperture Radar (InSAR) data gathered over a CO{sub 2} injection in Algeria reveals pressure propagation along two northwest trending corridors. An inversion of the travel times indicates the existence of two northwest-trending high permeability zones. The highmore » permeability features trend in the same direction as the regional fault and fracture zones. Model parameter resolution estimates indicate that the features are well resolved.« less

Jets or vortices - what flows are generated by an inverse turbulent cascade?

NASA Astrophysics Data System (ADS)

Frishman, Anna; Laurie, Jason; Falkovich, Gregory

An inverse cascade-energy transfer to progressively larger scales - is a salient feature of two-dimensional turbulence. If the cascade reaches the system scale, it creates a coherent flow expected to have the largest available scale and conform with the symmetries of the domain. In a doubly periodic rectangle, the mean flow with zero total momentum was therefore believed to be unidirectional, with two jets along the short side; while for an aspect ratio close to unity, a vortex dipole was expected. Using direct numerical simulations, we show that in fact neither the box symmetry is respected nor the largest scale is realized: the flow is never purely unidirectional since the inverse cascade produces coherent vortices, whose number and relative motion are determined by the aspect ratio. This spontaneous symmetry breaking is closely related to the hierarchy of averaging times. Long-time averaging restores translational invariance due to vortex wandering along one direction, and gives jets whose profile, however, can be deduced neither from the largest-available-scale argument, nor from the often employed maximum-entropy principle or quasi-linear approximation.

Three-Dimensional Inverse Transport Solver Based on Compressive Sensing Technique

NASA Astrophysics Data System (ADS)

Cheng, Yuxiong; Wu, Hongchun; Cao, Liangzhi; Zheng, Youqi

2013-09-01

According to the direct exposure measurements from flash radiographic image, a compressive sensing-based method for three-dimensional inverse transport problem is presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. It is always very expensive to obtain enough measurements. With limited measurements, compressive sensing sparse reconstruction technique orthogonal matching pursuit is applied to obtain the sparse coefficients by solving an optimization problem. A three-dimensional inverse transport solver is developed based on a compressive sensing-based technique. There are three features in this solver: (1) AutoCAD is employed as a geometry preprocessor due to its powerful capacity in graphic. (2) The forward projection matrix rather than Gauss matrix is constructed by the visualization tool generator. (3) Fourier transform and Daubechies wavelet transform are adopted to convert an underdetermined system to a well-posed system in the algorithm. Simulations are performed and numerical results in pseudo-sine absorption problem, two-cube problem and two-cylinder problem when using compressive sensing-based solver agree well with the reference value.

A New Quaternion-Based Kalman Filter for Real-Time Attitude Estimation Using the Two-Step Geometrically-Intuitive Correction Algorithm.

PubMed

Feng, Kaiqiang; Li, Jie; Zhang, Xiaoming; Shen, Chong; Bi, Yu; Zheng, Tao; Liu, Jun

2017-09-19

In order to reduce the computational complexity, and improve the pitch/roll estimation accuracy of the low-cost attitude heading reference system (AHRS) under conditions of magnetic-distortion, a novel linear Kalman filter, suitable for nonlinear attitude estimation, is proposed in this paper. The new algorithm is the combination of two-step geometrically-intuitive correction (TGIC) and the Kalman filter. In the proposed algorithm, the sequential two-step geometrically-intuitive correction scheme is used to make the current estimation of pitch/roll immune to magnetic distortion. Meanwhile, the TGIC produces a computed quaternion input for the Kalman filter, which avoids the linearization error of measurement equations and reduces the computational complexity. Several experiments have been carried out to validate the performance of the filter design. The results demonstrate that the mean time consumption and the root mean square error (RMSE) of pitch/roll estimation under magnetic disturbances are reduced by 45.9% and 33.8%, respectively, when compared with a standard filter. In addition, the proposed filter is applicable for attitude estimation under various dynamic conditions.

A New Quaternion-Based Kalman Filter for Real-Time Attitude Estimation Using the Two-Step Geometrically-Intuitive Correction Algorithm

PubMed Central

Feng, Kaiqiang; Li, Jie; Zhang, Xiaoming; Shen, Chong; Bi, Yu; Zheng, Tao; Liu, Jun

2017-01-01

In order to reduce the computational complexity, and improve the pitch/roll estimation accuracy of the low-cost attitude heading reference system (AHRS) under conditions of magnetic-distortion, a novel linear Kalman filter, suitable for nonlinear attitude estimation, is proposed in this paper. The new algorithm is the combination of two-step geometrically-intuitive correction (TGIC) and the Kalman filter. In the proposed algorithm, the sequential two-step geometrically-intuitive correction scheme is used to make the current estimation of pitch/roll immune to magnetic distortion. Meanwhile, the TGIC produces a computed quaternion input for the Kalman filter, which avoids the linearization error of measurement equations and reduces the computational complexity. Several experiments have been carried out to validate the performance of the filter design. The results demonstrate that the mean time consumption and the root mean square error (RMSE) of pitch/roll estimation under magnetic disturbances are reduced by 45.9% and 33.8%, respectively, when compared with a standard filter. In addition, the proposed filter is applicable for attitude estimation under various dynamic conditions. PMID:28925979

Use of Linear Prediction Uncertainty Analysis to Guide Conditioning of Models Simulating Surface-Water/Groundwater Interactions

NASA Astrophysics Data System (ADS)

Hughes, J. D.; White, J.; Doherty, J.

2011-12-01

Linear prediction uncertainty analysis in a Bayesian framework was applied to guide the conditioning of an integrated surface water/groundwater model that will be used to predict the effects of groundwater withdrawals on surface-water and groundwater flows. Linear prediction uncertainty analysis is an effective approach for identifying (1) raw and processed data most effective for model conditioning prior to inversion, (2) specific observations and periods of time critically sensitive to specific predictions, and (3) additional observation data that would reduce model uncertainty relative to specific predictions. We present results for a two-dimensional groundwater model of a 2,186 km2 area of the Biscayne aquifer in south Florida implicitly coupled to a surface-water routing model of the actively managed canal system. The model domain includes 5 municipal well fields withdrawing more than 1 Mm3/day and 17 operable surface-water control structures that control freshwater releases from the Everglades and freshwater discharges to Biscayne Bay. More than 10 years of daily observation data from 35 groundwater wells and 24 surface water gages are available to condition model parameters. A dense parameterization was used to fully characterize the contribution of the inversion null space to predictive uncertainty and included bias-correction parameters. This approach allows better resolution of the boundary between the inversion null space and solution space. Bias-correction parameters (e.g., rainfall, potential evapotranspiration, and structure flow multipliers) absorb information that is present in structural noise that may otherwise contaminate the estimation of more physically-based model parameters. This allows greater precision in predictions that are entirely solution-space dependent, and reduces the propensity for bias in predictions that are not. Results show that application of this analysis is an effective means of identifying those surface-water and groundwater data, both raw and processed, that minimize predictive uncertainty, while simultaneously identifying the maximum solution-space dimensionality of the inverse problem supported by the data.

Inversion of residual stress profiles from ultrasonic Rayleigh wave dispersion data

NASA Astrophysics Data System (ADS)

Mora, P.; Spies, M.

2018-05-01

We investigate theoretically and with synthetic data the performance of several inversion methods to infer a residual stress state from ultrasonic surface wave dispersion data. We show that this particular problem may reveal in relevant materials undesired behaviors for some methods that could be reliably applied to infer other properties. We focus on two methods, one based on a Taylor-expansion, and another one based on a piecewise linear expansion regularized by a singular value decomposition. We explain the instabilities of the Taylor-based method by highlighting singularities in the series of coefficients. At the same time, we show that the other method can successfully provide performances which only weakly depend on the material.

Reconstructing the primordial spectrum of fluctuations of the universe from the observed nonlinear clustering of galaxies

NASA Technical Reports Server (NTRS)

Hamilton, A. J. S.; Matthews, Alex; Kumar, P.; Lu, Edward

1991-01-01

It was discovered that the nonlinear evolution of the two point correlation function in N-body experiments of galaxy clustering with Omega = 1 appears to be described to good approximation by a simple general formula. The underlying form of the formula is physically motivated, but its detailed representation is obtained empirically by fitting to N-body experiments. In this paper, the formula is presented along with an inverse formula which converts a final, nonlinear correlation function into the initial linear correlation function. The inverse formula is applied to observational data from the CfA, IRAs, and APM galaxy surveys, and the initial spectrum of fluctuations of the universe, if Omega = 1.

Random hopping fermions on bipartite lattices: density of states, inverse participation ratios, and their correlations in a strong disorder regime

NASA Astrophysics Data System (ADS)

Yamada, Hiroki; Fukui, Takahiro

2004-02-01

We study Anderson localization of non-interacting random hopping fermions on bipartite lattices in two dimensions, focusing our attention to strong disorder features of the model. We concentrate ourselves on specific models with a linear dispersion in the vicinity of the band center, which can be described by a Dirac fermion in the continuum limit. Based on the recent renormalization group method developed by Carpentier and Le Doussal for the XY gauge glass model, we calculate the density of states, inverse participation ratios, and their spatial correlations. It turns out that their behavior is quite different from those expected within naive weak disorder approaches.

Bayesian inversion of surface-wave data for radial and azimuthal shear-wave anisotropy, with applications to central Mongolia and west-central Italy

NASA Astrophysics Data System (ADS)

Ravenna, Matteo; Lebedev, Sergei

2018-04-01

Seismic anisotropy provides important information on the deformation history of the Earth's interior. Rayleigh and Love surface-waves are sensitive to and can be used to determine both radial and azimuthal shear-wave anisotropies at depth, but parameter trade-offs give rise to substantial model non-uniqueness. Here, we explore the trade-offs between isotropic and anisotropic structure parameters and present a suite of methods for the inversion of surface-wave, phase-velocity curves for radial and azimuthal anisotropies. One Markov chain Monte Carlo (McMC) implementation inverts Rayleigh and Love dispersion curves for a radially anisotropic shear velocity profile of the crust and upper mantle. Another McMC implementation inverts Rayleigh phase velocities and their azimuthal anisotropy for profiles of vertically polarized shear velocity and its depth-dependent azimuthal anisotropy. The azimuthal anisotropy inversion is fully non-linear, with the forward problem solved numerically at different azimuths for every model realization, which ensures that any linearization biases are avoided. The computations are performed in parallel, in order to reduce the computing time. The often challenging issue of data noise estimation is addressed by means of a Hierarchical Bayesian approach, with the variance of the noise treated as an unknown during the radial anisotropy inversion. In addition to the McMC inversions, we also present faster, non-linear gradient-search inversions for the same anisotropic structure. The results of the two approaches are mutually consistent; the advantage of the McMC inversions is that they provide a measure of uncertainty of the models. Applying the method to broad-band data from the Baikal-central Mongolia region, we determine radial anisotropy from the crust down to the transition-zone depths. Robust negative anisotropy (Vsh < Vsv) in the asthenosphere, at 100-300 km depths, presents strong new evidence for a vertical component of asthenospheric flow. This is consistent with an upward flow from below the thick lithosphere of the Siberian Craton to below the thinner lithosphere of central Mongolia, likely to give rise to decompression melting and the scattered, sporadic volcanism observed in the Baikal Rift area, as proposed previously. Inversion of phase-velocity data from west-central Italy for azimuthal anisotropy reveals a clear change in the shear-wave fast-propagation direction at 70-100 km depths, near the lithosphere-asthenosphere boundary. The orientation of the fabric in the lithosphere is roughly E-W, parallel to the direction of stretching over the last 10 m.y. The orientation of the fabric in the asthenosphere is NW-SE, matching the fast directions inferred from shear-wave splitting and probably indicating the direction of the asthenospheric flow.

High-order Newton-penalty algorithms

NASA Astrophysics Data System (ADS)

Dussault, Jean-Pierre

2005-10-01

Recent efforts in differentiable non-linear programming have been focused on interior point methods, akin to penalty and barrier algorithms. In this paper, we address the classical equality constrained program solved using the simple quadratic loss penalty function/algorithm. The suggestion to use extrapolations to track the differentiable trajectory associated with penalized subproblems goes back to the classic monograph of Fiacco & McCormick. This idea was further developed by Gould who obtained a two-steps quadratically convergent algorithm using prediction steps and Newton correction. Dussault interpreted the prediction step as a combined extrapolation with respect to the penalty parameter and the residual of the first order optimality conditions. Extrapolation with respect to the residual coincides with a Newton step.We explore here higher-order extrapolations, thus higher-order Newton-like methods. We first consider high-order variants of the Newton-Raphson method applied to non-linear systems of equations. Next, we obtain improved asymptotic convergence results for the quadratic loss penalty algorithm by using high-order extrapolation steps.

A Fast Estimation Algorithm for Two-Dimensional Gravity Data (GEOFAST),

DTIC Science & Technology

1979-11-15

to a wide class of problems (Refs. 9 and 17). The major inhibitor to the widespread appli- ( cation of optimal gravity data processing is the severe...extends directly to two dimensions. Define the nln 2xn1 n2 diagonal window matrix W as the Kronecker product of two one-dimensional windows W = W1 0 W2 (B...Inversion of Separable Matrices Consider the linear system y = T x (B.3-1) where T is block Toeplitz of dimension nln 2xnIn 2 . Its fre- quency domain

Long-wave model for strongly anisotropic growth of a crystal step.

PubMed

Khenner, Mikhail

2013-08-01

A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the "one-sided" model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in a form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed the nonlinear dynamics. Linear stability depends on whether the stiffness is minimum or maximum in the direction of the step growth. It also depends nontrivially on the combination of the anisotropy strength parameter and the atomic flux from the terrace to the step. Computations show formation and coarsening of a hill-and-valley structure superimposed onto a long-wavelength profile, which independently coarsens. Coarsening laws for the hill-and-valley structure are computed for two principal orientations of a maximum step stiffness, the increasing anisotropy strength, and the varying atomic flux.

Trimming and procrastination as inversion techniques

NASA Astrophysics Data System (ADS)

Backus, George E.

1996-12-01

By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.

Flexible polyelectrolyte chain in a strong electrolyte solution: Insight into equilibrium properties and force-extension behavior from mesoscale simulation

NASA Astrophysics Data System (ADS)

Malekzadeh Moghani, Mahdy; Khomami, Bamin

2016-01-01

Macromolecules with ionizable groups are ubiquitous in biological and synthetic systems. Due to the complex interaction between chain and electrostatic decorrelation lengths, both equilibrium properties and micro-mechanical response of dilute solutions of polyelectrolytes (PEs) are more complex than their neutral counterparts. In this work, the bead-rod micromechanical description of a chain is used to perform hi-fidelity Brownian dynamics simulation of dilute PE solutions to ascertain the self-similar equilibrium behavior of PE chains with various linear charge densities, scaling of the Kuhn step length (lE) with salt concentration cs and the force-extension behavior of the PE chain. In accord with earlier theoretical predictions, our results indicate that for a chain with n Kuhn segments, lE ˜ cs-0.5 as linear charge density approaches 1/n. Moreover, the constant force ensemble simulation results accurately predict the initial non-linear force-extension region of PE chain recently measured via single chain experiments. Finally, inspired by Cohen's extraction of Warner's force law from the inverse Langevin force law, a novel numerical scheme is developed to extract a new elastic force law for real chains from our discrete set of force-extension data similar to Padè expansion, which accurately depicts the initial non-linear region where the total Kuhn length is less than the thermal screening length.

Flexible polyelectrolyte chain in a strong electrolyte solution: Insight into equilibrium properties and force-extension behavior from mesoscale simulation.

PubMed

Malekzadeh Moghani, Mahdy; Khomami, Bamin

2016-01-14

Macromolecules with ionizable groups are ubiquitous in biological and synthetic systems. Due to the complex interaction between chain and electrostatic decorrelation lengths, both equilibrium properties and micro-mechanical response of dilute solutions of polyelectrolytes (PEs) are more complex than their neutral counterparts. In this work, the bead-rod micromechanical description of a chain is used to perform hi-fidelity Brownian dynamics simulation of dilute PE solutions to ascertain the self-similar equilibrium behavior of PE chains with various linear charge densities, scaling of the Kuhn step length (lE) with salt concentration cs and the force-extension behavior of the PE chain. In accord with earlier theoretical predictions, our results indicate that for a chain with n Kuhn segments, lE ∼ cs (-0.5) as linear charge density approaches 1/n. Moreover, the constant force ensemble simulation results accurately predict the initial non-linear force-extension region of PE chain recently measured via single chain experiments. Finally, inspired by Cohen's extraction of Warner's force law from the inverse Langevin force law, a novel numerical scheme is developed to extract a new elastic force law for real chains from our discrete set of force-extension data similar to Padè expansion, which accurately depicts the initial non-linear region where the total Kuhn length is less than the thermal screening length.

Sensitivity Analysis of the Sheet Metal Stamping Processes Based on Inverse Finite Element Modeling and Monte Carlo Simulation

NASA Astrophysics Data System (ADS)

Yu, Maolin; Du, R.

2005-08-01

Sheet metal stamping is one of the most commonly used manufacturing processes, and hence, much research has been carried for economic gain. Searching through the literatures, however, it is found that there are still a lots of problems unsolved. For example, it is well known that for a same press, same workpiece material, and same set of die, the product quality may vary owing to a number of factors, such as the inhomogeneous of the workpice material, the loading error, the lubrication, and etc. Presently, few seem able to predict the quality variation, not to mention what contribute to the quality variation. As a result, trial-and-error is still needed in the shop floor, causing additional cost and time delay. This paper introduces a new approach to predict the product quality variation and identify the sensitive design / process parameters. The new approach is based on a combination of inverse Finite Element Modeling (FEM) and Monte Carlo Simulation (more specifically, the Latin Hypercube Sampling (LHS) approach). With an acceptable accuracy, the inverse FEM (also called one-step FEM) requires much less computation load than that of the usual incremental FEM and hence, can be used to predict the quality variations under various conditions. LHS is a statistical method, through which the sensitivity analysis can be carried out. The result of the sensitivity analysis has clear physical meaning and can be used to optimize the die design and / or the process design. Two simulation examples are presented including drawing a rectangular box and drawing a two-step rectangular box.

Implementation of genomic recursions in single-step genomic best linear unbiased predictor for US Holsteins with a large number of genotyped animals.

PubMed

Masuda, Y; Misztal, I; Tsuruta, S; Legarra, A; Aguilar, I; Lourenco, D A L; Fragomeni, B O; Lawlor, T J

2016-03-01

The objectives of this study were to develop and evaluate an efficient implementation in the computation of the inverse of genomic relationship matrix with the recursion algorithm, called the algorithm for proven and young (APY), in single-step genomic BLUP. We validated genomic predictions for young bulls with more than 500,000 genotyped animals in final score for US Holsteins. Phenotypic data included 11,626,576 final scores on 7,093,380 US Holstein cows, and genotypes were available for 569,404 animals. Daughter deviations for young bulls with no classified daughters in 2009, but at least 30 classified daughters in 2014 were computed using all the phenotypic data. Genomic predictions for the same bulls were calculated with single-step genomic BLUP using phenotypes up to 2009. We calculated the inverse of the genomic relationship matrix GAPY(-1) based on a direct inversion of genomic relationship matrix on a small subset of genotyped animals (core animals) and extended that information to noncore animals by recursion. We tested several sets of core animals including 9,406 bulls with at least 1 classified daughter, 9,406 bulls and 1,052 classified dams of bulls, 9,406 bulls and 7,422 classified cows, and random samples of 5,000 to 30,000 animals. Validation reliability was assessed by the coefficient of determination from regression of daughter deviation on genomic predictions for the predicted young bulls. The reliabilities were 0.39 with 5,000 randomly chosen core animals, 0.45 with the 9,406 bulls, and 7,422 cows as core animals, and 0.44 with the remaining sets. With phenotypes truncated in 2009 and the preconditioned conjugate gradient to solve mixed model equations, the number of rounds to convergence for core animals defined by bulls was 1,343; defined by bulls and cows, 2,066; and defined by 10,000 random animals, at most 1,629. With complete phenotype data, the number of rounds decreased to 858, 1,299, and at most 1,092, respectively. Setting up GAPY(-1) for 569,404 genotyped animals with 10,000 core animals took 1.3h and 57 GB of memory. The validation reliability with APY reaches a plateau when the number of core animals is at least 10,000. Predictions with APY have little differences in reliability among definitions of core animals. Single-step genomic BLUP with APY is applicable to millions of genotyped animals. Copyright © 2016 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Parallel algorithms for boundary value problems

NASA Technical Reports Server (NTRS)

Lin, Avi

1990-01-01

A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are two fold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.

Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations.

PubMed

Henry, B I; Langlands, T A M; Wearne, S L

2006-09-01

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term. Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term. We have also developed further extensions of the CTRW model to include more general reaction dynamics.

Multi-scale Slip Inversion Based on Simultaneous Spatial and Temporal Domain Wavelet Transform

NASA Astrophysics Data System (ADS)

Liu, W.; Yao, H.; Yang, H. Y.

2017-12-01

Finite fault inversion is a widely used method to study earthquake rupture processes. Some previous studies have proposed different methods to implement finite fault inversion, including time-domain, frequency-domain, and wavelet-domain methods. Many previous studies have found that different frequency bands show different characteristics of the seismic rupture (e.g., Wang and Mori, 2011; Yao et al., 2011, 2013; Uchide et al., 2013; Yin et al., 2017). Generally, lower frequency waveforms correspond to larger-scale rupture characteristics while higher frequency data are representative of smaller-scale ones. Therefore, multi-scale analysis can help us understand the earthquake rupture process thoroughly from larger scale to smaller scale. By the use of wavelet transform, the wavelet-domain methods can analyze both the time and frequency information of signals in different scales. Traditional wavelet-domain methods (e.g., Ji et al., 2002) implement finite fault inversion with both lower and higher frequency signals together to recover larger-scale and smaller-scale characteristics of the rupture process simultaneously. Here we propose an alternative strategy with a two-step procedure, i.e., firstly constraining the larger-scale characteristics with lower frequency signals, and then resolving the smaller-scale ones with higher frequency signals. We have designed some synthetic tests to testify our strategy and compare it with the traditional one. We also have applied our strategy to study the 2015 Gorkha Nepal earthquake using tele-seismic waveforms. Both the traditional method and our two-step strategy only analyze the data in different temporal scales (i.e., different frequency bands), while the spatial distribution of model parameters also shows multi-scale characteristics. A more sophisticated strategy is to transfer the slip model into different spatial scales, and then analyze the smooth slip distribution (larger scales) with lower frequency data firstly and more detailed slip distribution (smaller scales) with higher frequency data subsequently. We are now implementing the slip inversion using both spatial and temporal domain wavelets. This multi-scale analysis can help us better understand frequency-dependent rupture characteristics of large earthquakes.

Aerosol Size Distributions During ACE-Asia: Retrievals From Optical Thickness and Comparisons With In-situ Measurements

NASA Astrophysics Data System (ADS)

Kuzmanoski, M.; Box, M.; Box, G. P.; Schmidt, B.; Russell, P. B.; Redemann, J.; Livingston, J. M.; Wang, J.; Flagan, R. C.; Seinfeld, J. H.

2002-12-01

As part of the ACE-Asia experiment, conducted off the coast of China, Korea and Japan in spring 2001, measurements of aerosol physical, chemical and radiative characteristics were performed aboard the Twin Otter aircraft. Of particular importance for this paper were spectral measurements of aerosol optical thickness obtained at 13 discrete wavelengths, within 354-1558 nm wavelength range, using the AATS-14 sunphotometer. Spectral aerosol optical thickness can be used to obtain information about particle size distribution. In this paper, we use sunphotometer measurements to retrieve size distribution of aerosols during ACE-Asia. We focus on four cases in which layers influenced by different air masses were identified. Aerosol optical thickness of each layer was inverted using two different techniques - constrained linear inversion and multimodal. In the constrained linear inversion algorithm no assumption about the mathematical form of the distribution to be retrieved is made. Conversely, the multimodal technique assumes that aerosol size distribution is represented as a linear combination of few lognormal modes with predefined values of mode radii and geometric standard deviations. Amplitudes of modes are varied to obtain best fit of sum of optical thicknesses due to individual modes to sunphotometer measurements. In this paper we compare the results of these two retrieval methods. In addition, we present comparisons of retrieved size distributions with in situ measurements taken using an aerodynamic particle sizer and differential mobility analyzer system aboard the Twin Otter aircraft.

Passive control of coherent structures in a modified backwards-facing step flow

NASA Astrophysics Data System (ADS)

Ormonde, Pedro C.; Cavalieri, André V. G.; Silva, Roberto G. A. da; Avelar, Ana C.

2018-05-01

We study a modified backwards-facing step flow, with the addition of two different plates; one is a baseline, impermeable plate and the second a perforated one. An experimental investigation is carried out for a turbulent reattaching shear layer downstream of the two plates. The proposed setup is a model configuration to study how the plate characteristics affect the separated shear layer and how turbulent kinetic energies and large-scale coherent structures are modified. Measurements show that the perforated plate changes the mean flow field, mostly by reducing the intensity of reverse flow close to the bottom wall. Disturbance amplitudes are significantly reduced up to five step heights downstream of the trailing edge of the plate, more specifically in the recirculation region. A loudspeaker is then used to introduce phase-locked, low-amplitude perturbations upstream of the plates, and phase-averaged measurements allow a quantitative study of large-scale structures in the shear-layer. The evolution of such coherent structures is evaluated in light of linear stability theory, comparing the eigenfunction of the Kelvin-Helmholtz mode to the experimental results. We observe a close match of linear-stability eigenfunctions with phase-averaged amplitudes for the two tested Strouhal numbers. The perforated plate is found to reduce the amplitude of the Kelvin-Helmholtz coherent structures in comparison to the baseline, impermeable plate, a behavior consistent with the predicted amplification trends from linear stability.

Meshless Method with Operator Splitting Technique for Transient Nonlinear Bioheat Transfer in Two-Dimensional Skin Tissues

PubMed Central

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-01

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue. PMID:25603180

Meshless method with operator splitting technique for transient nonlinear bioheat transfer in two-dimensional skin tissues.

PubMed

Zhang, Ze-Wei; Wang, Hui; Qin, Qing-Hua

2015-01-16

A meshless numerical scheme combining the operator splitting method (OSM), the radial basis function (RBF) interpolation, and the method of fundamental solutions (MFS) is developed for solving transient nonlinear bioheat problems in two-dimensional (2D) skin tissues. In the numerical scheme, the nonlinearity caused by linear and exponential relationships of temperature-dependent blood perfusion rate (TDBPR) is taken into consideration. In the analysis, the OSM is used first to separate the Laplacian operator and the nonlinear source term, and then the second-order time-stepping schemes are employed for approximating two splitting operators to convert the original governing equation into a linear nonhomogeneous Helmholtz-type governing equation (NHGE) at each time step. Subsequently, the RBF interpolation and the MFS involving the fundamental solution of the Laplace equation are respectively employed to obtain approximated particular and homogeneous solutions of the nonhomogeneous Helmholtz-type governing equation. Finally, the full fields consisting of the particular and homogeneous solutions are enforced to fit the NHGE at interpolation points and the boundary conditions at boundary collocations for determining unknowns at each time step. The proposed method is verified by comparison of other methods. Furthermore, the sensitivity of the coefficients in the cases of a linear and an exponential relationship of TDBPR is investigated to reveal their bioheat effect on the skin tissue.

An improved interface to process GPR data by means of microwave tomography

NASA Astrophysics Data System (ADS)

Catapano, Ilaria; Affinito, Antonio; Soldovieri, Francesco

2015-04-01

Ground Penetrating Radar (GPR) systems are well assessed non-invasive diagnostic tools, which are worth being considered in civil engineering surveys since they allow to gather information on constructive materials and techniques of manmade structures as well as on the aging and risk factors affecting their healthiness. However, the practical use of GPR depends strictly on the availability of data processing tools, on one hand, capable of providing reliable and easily interpretable images of the probed scenarios and, on the other side, easy to be used by not expert users. In this frame, 2D and full 3D microwave tomographic approaches based on the Born approximation have been developed and proved to be effective in several practical conditions [1, 2]. Generally speaking, a GPR data processing chain exploiting microwave tomography is made by two main steps: the pre-processing and the data inversion. The pre-processing groups standard procedures like start time correction, muting and background removal, which are performed in time domain to remove the direct antennas coupling, to reduce noise and to improve the targets footprint. The data inversion faces the imaging as the solution of a linear inverse scattering problem in the frequency domain. Hence, a linear integral equation relating the scattered field (i.e. the data) to the unknown electric contrast function is solved by using the truncated Singular Value Decomposition (SVD) as a regularized inversion scheme. Pre-processing and the data inversion are linked by a Discrete Fourier Transform (DFT), which allows to pass from the time domain to the frequency domain. In this respect, a frequency analysis of the GPR signals (traces) is also performed to identify the actual frequency range of the data. Unfortunately, the adoption of microwave tomography is strongly subjected to the involvement of expert people capable of managing properly the processing chain. To overcome this drawback, a couple of years ago, an end-user friendly software interface was developed to make possible a simple management of 2D microwave tomographic approaches [3]. Aim of this communication, is to present a novel interface, which is a significantly improved version with respect to the previous one. In particular, the new interface allows both 2D and full 3D imaging by taking as input GPR data gathered by means of different measurement configurations, i.e. by using down looking systems, with the antenna located close to the air-medium interface or at non negligible (in terms of the probing wavelength) distance from it, as well as by means of airborne and forward looking systems. In this frame, the users can select the data format among those of the most common commercial GPR systems or process data gathered by means of GPR prototypes, provided that they are saved in ASCII format. Moreover, the users can perform all the steps, which are needed to obtain tomographic images, and select the Born approximation based approach most suitable to the adopted measurement configuration. Raw-radargrams, intermediate and final results can be displayed for users convenience. REFERENCES [1] I. Catapano, R. Di Napoli, F. Soldovieri, M. Bavusi, A. Loperte, J. Dumoulin, "Structural monitoring via microwave tomography-enhanced GPR: the Montagnole test site", J. Geophys. Eng. 9, S100-S107, 2012. [2] I. Catapano, A. Affinito, G. Gennarelli, F.di Maio, A. Loperte, F. Soldovieri, "Full three-dimensional imaging via ground penetrating radar: assessment in controlled conditions and on field for archaeological prospecting", Appl. Phys. A, 2013, DOI 10.1007/s00339-013-8053-0. [3] I. Catapano, A. Affinito, F. Soldovieri, A user friendly interface for microwave tomography enhanced GPR surveys", EGU General Assembly 2013, vol. 15.

Computer-Based Feedback in Linear Algebra: Effects on Transfer Performance and Motivation

ERIC Educational Resources Information Center

Corbalan, Gemma; Paas, Fred; Cuypers, Hans

2010-01-01

Two studies investigated the effects on students' perceptions (Study 1) and learning and motivation (Study 2) of different levels of feedback in mathematical problems. In these problems, an error made in one step of the problem-solving procedure will carry over to the following steps and consequently to the final solution. Providing immediate…

Linear analysis near a steady-state of biochemical networks: Control analysis, correlation metrics and circuit theory

PubMed Central

Heuett, William J; Beard, Daniel A; Qian, Hong

2008-01-01

Background Several approaches, including metabolic control analysis (MCA), flux balance analysis (FBA), correlation metric construction (CMC), and biochemical circuit theory (BCT), have been developed for the quantitative analysis of complex biochemical networks. Here, we present a comprehensive theory of linear analysis for nonequilibrium steady-state (NESS) biochemical reaction networks that unites these disparate approaches in a common mathematical framework and thermodynamic basis. Results In this theory a number of relationships between key matrices are introduced: the matrix A obtained in the standard, linear-dynamic-stability analysis of the steady-state can be decomposed as A = SRT where R and S are directly related to the elasticity-coefficient matrix for the fluxes and chemical potentials in MCA, respectively; the control-coefficients for the fluxes and chemical potentials can be written in terms of RTBS and STBS respectively where matrix B is the inverse of A; the matrix S is precisely the stoichiometric matrix in FBA; and the matrix eAt plays a central role in CMC. Conclusion One key finding that emerges from this analysis is that the well-known summation theorems in MCA take different forms depending on whether metabolic steady-state is maintained by flux injection or concentration clamping. We demonstrate that if rate-limiting steps exist in a biochemical pathway, they are the steps with smallest biochemical conductances and largest flux control-coefficients. We hypothesize that biochemical networks for cellular signaling have a different strategy for minimizing energy waste and being efficient than do biochemical networks for biosynthesis. We also discuss the intimate relationship between MCA and biochemical systems analysis (BSA). PMID:18482450

Fitting a Point Cloud to a 3d Polyhedral Surface

NASA Astrophysics Data System (ADS)

Popov, E. V.; Rotkov, S. I.

2017-05-01

The ability to measure parameters of large-scale objects in a contactless fashion has a tremendous potential in a number of industrial applications. However, this problem is usually associated with an ambiguous task to compare two data sets specified in two different co-ordinate systems. This paper deals with the study of fitting a set of unorganized points to a polyhedral surface. The developed approach uses Principal Component Analysis (PCA) and Stretched grid method (SGM) to substitute a non-linear problem solution with several linear steps. The squared distance (SD) is a general criterion to control the process of convergence of a set of points to a target surface. The described numerical experiment concerns the remote measurement of a large-scale aerial in the form of a frame with a parabolic shape. The experiment shows that the fitting process of a point cloud to a target surface converges in several linear steps. The method is applicable to the geometry remote measurement of large-scale objects in a contactless fashion.

On the modeling of the bottom particles segregation with non-linear diffusion equations: application to the marine sand ripples

NASA Astrophysics Data System (ADS)

Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander

2015-04-01

The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.

FAST TRACK PAPER: Non-iterative multiple-attenuation methods: linear inverse solutions to non-linear inverse problems - II. BMG approximation

NASA Astrophysics Data System (ADS)

Ikelle, Luc T.; Osen, Are; Amundsen, Lasse; Shen, Yunqing

2004-12-01

The classical linear solutions to the problem of multiple attenuation, like predictive deconvolution, τ-p filtering, or F-K filtering, are generally fast, stable, and robust compared to non-linear solutions, which are generally either iterative or in the form of a series with an infinite number of terms. These qualities have made the linear solutions more attractive to seismic data-processing practitioners. However, most linear solutions, including predictive deconvolution or F-K filtering, contain severe assumptions about the model of the subsurface and the class of free-surface multiples they can attenuate. These assumptions limit their usefulness. In a recent paper, we described an exception to this assertion for OBS data. We showed in that paper that a linear and non-iterative solution to the problem of attenuating free-surface multiples which is as accurate as iterative non-linear solutions can be constructed for OBS data. We here present a similar linear and non-iterative solution for attenuating free-surface multiples in towed-streamer data. For most practical purposes, this linear solution is as accurate as the non-linear ones.

Computer-controlled attenuator.

PubMed

Mitov, D; Grozev, Z

1991-01-01

Various possibilities for applying electronic computer-controlled attenuators for the automation of physiological experiments are considered. A detailed description is given of the design of a 4-channel computer-controlled attenuator, in two of the channels of which the output signal can change by a linear step, in the other two channels--by a logarithmic step. This, together with the existence of additional programmable timers, allows to automate a wide range of studies in different spheres of physiology and psychophysics, including vision and hearing.

Magnetically suspended stepping motors for clean room and vacuum environments

NASA Technical Reports Server (NTRS)

Higuchi, Toshiro

1994-01-01

To answer the growing needs for super-clean or contact free actuators for uses in clean rooms, vacuum chambers, and space, innovative actuators which combine the functions of stepping motors and magnetic bearings in one body were developed. The rotor of the magnetically suspended stepping motor is suspended like a magnetic bearing and rotated and positioned like a stepping motor. The important trait of the motor is that it is not a simple mixture or combination of a stepping motor and conventional magnetic bearing, but an amalgam of a stepping motor and a magnetic bearing. Owing to optimal design and feed-back control, a toothed stator and rotor are all that are needed structurewise for stable suspension. More than ten types of motors such as linear type, high accuracy rotary type, two-dimensional type, and high vacuum type were built and tested. This paper describes the structure and design of these motors and their performance for such applications as precise positioning rotary table, linear conveyor system, and theta-zeta positioner for clean room and high vacuum use.

On computational experiments in some inverse problems of heat and mass transfer

NASA Astrophysics Data System (ADS)

Bilchenko, G. G.; Bilchenko, N. G.

2016-11-01

The results of mathematical modeling of effective heat and mass transfer on hypersonic aircraft permeable surfaces are considered. The physic-chemical processes (the dissociation and the ionization) in laminar boundary layer of compressible gas are appreciated. Some algorithms of control restoration are suggested for the interpolation and approximation statements of heat and mass transfer inverse problems. The differences between the methods applied for the problem solutions search for these statements are discussed. Both the algorithms are realized as programs. Many computational experiments were accomplished with the use of these programs. The parameters of boundary layer obtained by means of the A.A.Dorodnicyn's generalized integral relations method from solving the direct problems have been used to obtain the inverse problems solutions. Two types of blowing laws restoration for the inverse problem in interpolation statement are presented as the examples. The influence of the temperature factor on the blowing restoration is investigated. The different character of sensitivity of controllable parameters (the local heat flow and local tangent friction) respectively to step (discrete) changing of control (the blowing) and the switching point position is studied.

A two-step combination of top-down and bottom-up fire emission estimates at regional and global scales: strengths and main uncertainties

NASA Astrophysics Data System (ADS)

Sofiev, Mikhail; Soares, Joana; Kouznetsov, Rostislav; Vira, Julius; Prank, Marje

2016-04-01

Top-down emission estimation via inverse dispersion modelling is used for various problems, where bottom-up approaches are difficult or highly uncertain. One of such areas is the estimation of emission from wild-land fires. In combination with dispersion modelling, satellite and/or in-situ observations can, in principle, be used to efficiently constrain the emission values. This is the main strength of the approach: the a-priori values of the emission factors (based on laboratory studies) are refined for real-life situations using the inverse-modelling technique. However, the approach also has major uncertainties, which are illustrated here with a few examples of the Integrated System for wild-land Fires (IS4FIRES). IS4FIRES generates the smoke emission and injection profile from MODIS and SEVIRI active-fire radiative energy observations. The emission calculation includes two steps: (i) initial top-down calibration of emission factors via inverse dispersion problem solution that is made once using training dataset from the past, (ii) application of the obtained emission coefficients to individual-fire radiative energy observations, thus leading to bottom-up emission compilation. For such a procedure, the major classes of uncertainties include: (i) imperfect information on fires, (ii) simplifications in the fire description, (iii) inaccuracies in the smoke observations and modelling, (iv) inaccuracies of the inverse problem solution. Using examples of the fire seasons 2010 in Russia, 2012 in Eurasia, 2007 in Australia, etc, it is pointed out that the top-down system calibration performed for a limited number of comparatively moderate cases (often the best-observed ones) may lead to errors in application to extreme events. For instance, the total emission of 2010 Russian fires is likely to be over-estimated by up to 50% if the calibration is based on the season 2006 and fire description is simplified. Longer calibration period and more sophisticated parameterization (including the smoke injection model and distinguishing all relevant vegetation types) can improve the predictions. The other significant parameter, so far weakly addressed in fire emission inventories, is the size spectrum of the emitted aerosols. Direct size-resolving measurements showed, for instance, that smoke from smouldering fires has smaller particles as compares with smoke from flaming fires. Due to dependence of the smoke optical thickness on the size distribution, such variability can lead to significant changes in the top-down calibration step. Experiments with IS4FIRES-SILAM system manifested up to a factor of two difference in AOD, depending on the assumption on particle spectrum.

Hierarchical tone mapping for high dynamic range image visualization

NASA Astrophysics Data System (ADS)

Qiu, Guoping; Duan, Jiang

2005-07-01

In this paper, we present a computationally efficient, practically easy to use tone mapping techniques for the visualization of high dynamic range (HDR) images in low dynamic range (LDR) reproduction devices. The new method, termed hierarchical nonlinear linear (HNL) tone-mapping operator maps the pixels in two hierarchical steps. The first step allocates appropriate numbers of LDR display levels to different HDR intensity intervals according to the pixel densities of the intervals. The second step linearly maps the HDR intensity intervals to theirs allocated LDR display levels. In the developed HNL scheme, the assignment of LDR display levels to HDR intensity intervals is controlled by a very simple and flexible formula with a single adjustable parameter. We also show that our new operators can be used for the effective enhancement of ordinary images.

Inverse scattering method and soliton double solution family for the general symplectic gravity model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao Yajun

A previously established Hauser-Ernst-type extended double-complex linear system is slightly modified and used to develop an inverse scattering method for the stationary axisymmetric general symplectic gravity model. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method applied fine and effective. As an application, a concrete family of soliton double solutions for the considered theory is obtained.

The incomplete inverse and its applications to the linear least squares problem

NASA Technical Reports Server (NTRS)

Morduch, G. E.

1977-01-01

A modified matrix product is explained, and it is shown that this product defiles a group whose inverse is called the incomplete inverse. It was proven that the incomplete inverse of an augmented normal matrix includes all the quantities associated with the least squares solution. An answer is provided to the problem that occurs when the data residuals are too large and when insufficient data to justify augmenting the model are available.

A sparse reconstruction method for the estimation of multiresolution emission fields via atmospheric inversion

DOE PAGES

Ray, J.; Lee, J.; Yadav, V.; ...

2014-08-20

We present a sparse reconstruction scheme that can also be used to ensure non-negativity when fitting wavelet-based random field models to limited observations in non-rectangular geometries. The method is relevant when multiresolution fields are estimated using linear inverse problems. Examples include the estimation of emission fields for many anthropogenic pollutants using atmospheric inversion or hydraulic conductivity in aquifers from flow measurements. The scheme is based on three new developments. Firstly, we extend an existing sparse reconstruction method, Stagewise Orthogonal Matching Pursuit (StOMP), to incorporate prior information on the target field. Secondly, we develop an iterative method that uses StOMP tomore » impose non-negativity on the estimated field. Finally, we devise a method, based on compressive sensing, to limit the estimated field within an irregularly shaped domain. We demonstrate the method on the estimation of fossil-fuel CO 2 (ffCO 2) emissions in the lower 48 states of the US. The application uses a recently developed multiresolution random field model and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of two. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less

Astrophysical masers - Inverse methods, precision, resolution and uniqueness

NASA Astrophysics Data System (ADS)

Lerche, I.

1986-07-01

The paper provides exact analytic solutions to the two-level, steady-state, maser problem in parametric form, with the emergent intensities expressed in terms of the incident intensities and with the maser length also given in terms of an integral over the intensities. It is shown that some assumption must be made on the emergent intensity on the nonobservable side of the astrophysical maser in order to obtain any inversion of the equations. The incident intensities can then be expressed in terms of the emergent, observable, flux. It is also shown that the inversion is nonunique unless a homogeneous linear integral equation has only a null solution. Constraints imposed by knowledge of the physical length of the maser are felt in a nonlinear manner by the parametric variable and do not appear to provide any substantive additional information to reduce the degree of nonuniqueness of the inverse solutions. It is concluded that the questions of precision, resolution and uniqueness for solutions to astrophysical maser problems will remain more of an emotional art than a logical science for some time to come.

Cloud Point and Liquid-Liquid Equilibrium Behavior of Thermosensitive Polymer L61 and Salt Aqueous Two-Phase System.

PubMed

Rao, Wenwei; Wang, Yun; Han, Juan; Wang, Lei; Chen, Tong; Liu, Yan; Ni, Liang

2015-06-25

The cloud point of thermosensitive triblock polymer L61, poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO), was determined in the presence of various electrolytes (K2HPO4, (NH4)3C6H5O7, and K3C6H5O7). The cloud point of L61 was lowered by the addition of electrolytes, and the cloud point of L61 decreased linearly with increasing electrolyte concentration. The efficacy of electrolytes on reducing cloud point followed the order: K3C6H5O7 > (NH4)3C6H5O7 > K2HPO4. With the increase in salt concentration, aqueous two-phase systems exhibited a phase inversion. In addition, increasing the temperature reduced the concentration of salt needed that could promote phase inversion. The phase diagrams and liquid-liquid equilibrium data of the L61-K2HPO4/(NH4)3C6H5O7/K3C6H5O7 aqueous two-phase systems (before the phase inversion but also after phase inversion) were determined at T = (25, 30, and 35) °C. Phase diagrams of aqueous two-phase systems were fitted to a four-parameter empirical nonlinear expression. Moreover, the slopes of the tie-lines and the area of two-phase region in the diagram have a tendency to rise with increasing temperature. The capacity of different salts to induce aqueous two-phase system formation was the same order as the ability of salts to reduce the cloud point.

A unified inversion scheme to process multifrequency measurements of various dispersive electromagnetic properties

NASA Astrophysics Data System (ADS)

Han, Y.; Misra, S.

2018-04-01

Multi-frequency measurement of a dispersive electromagnetic (EM) property, such as electrical conductivity, dielectric permittivity, or magnetic permeability, is commonly analyzed for purposes of material characterization. Such an analysis requires inversion of the multi-frequency measurement based on a specific relaxation model, such as Cole-Cole model or Pelton's model. We develop a unified inversion scheme that can be coupled to various type of relaxation models to independently process multi-frequency measurement of varied EM properties for purposes of improved EM-based geomaterial characterization. The proposed inversion scheme is firstly tested in few synthetic cases in which different relaxation models are coupled into the inversion scheme and then applied to multi-frequency complex conductivity, complex resistivity, complex permittivity, and complex impedance measurements. The method estimates up to seven relaxation-model parameters exhibiting convergence and accuracy for random initializations of the relaxation-model parameters within up to 3-orders of magnitude variation around the true parameter values. The proposed inversion method implements a bounded Levenberg algorithm with tuning initial values of damping parameter and its iterative adjustment factor, which are fixed in all the cases shown in this paper and irrespective of the type of measured EM property and the type of relaxation model. Notably, jump-out step and jump-back-in step are implemented as automated methods in the inversion scheme to prevent the inversion from getting trapped around local minima and to honor physical bounds of model parameters. The proposed inversion scheme can be easily used to process various types of EM measurements without major changes to the inversion scheme.

Reverse-Time Imaging Based on Full-Waveform Inverted Velocity Model for Nondestructive Testing of Heterogeneous Engineered Structures

NASA Astrophysics Data System (ADS)

Nguyen, L. T.; Modrak, R. T.; Saenger, E. H.; Tromp, J.

2017-12-01

Reverse-time migration (RTM) can reconstruct reflectors and scatterers by cross-correlating the source wavefield and the receiver wavefield given a known velocity model of the background. In nondestructive testing, however, the engineered structure under inspection is often composed of layers of various materials and the background material has been degraded non-uniformly because of environmental or operational effects. On the other hand, ultrasonic waveform tomography based on the principles of full-waveform inversion (FWI) has succeeded in detecting anomalous features in engineered structures. But the building of the wave velocity model of the comprehensive small-size and high-contrast defect(s) is difficult because it requires computationally expensive high-frequency numerical wave simulations and an accurate understanding of large-scale background variations of the engineered structure.To reduce computational cost and improve detection of small defects, a useful approach is to divide the waveform tomography procedure into two steps: first, a low-frequency model-building step aimed at recovering background structure using FWI, and second, a high-frequency imaging step targeting defects using RTM. Through synthetic test cases, we show that the two-step procedure appears more promising in most cases than a single-step inversion. In particular, we find that the new workflow succeeds in the challenging scenario where the defect lies along preexisting layer interface in a composite bridge deck and in related experiments involving noisy data or inaccurate source parameters. The results reveal the potential of the new wavefield imaging method and encourage further developments in data processing, enhancing computation power, and optimizing the imaging workflow itself so that the procedure can efficiently be applied to geometrically complex 3D solids and waveguides. Lastly, owing to the scale invariance of the elastic wave equation, this imaging procedure can be transferred to applications in regional scales as well.

Parallel conjugate gradient algorithms for manipulator dynamic simulation

NASA Technical Reports Server (NTRS)

Fijany, Amir; Scheld, Robert E.

1989-01-01

Parallel conjugate gradient algorithms for the computation of multibody dynamics are developed for the specialized case of a robot manipulator. For an n-dimensional positive-definite linear system, the Classical Conjugate Gradient (CCG) algorithms are guaranteed to converge in n iterations, each with a computation cost of O(n); this leads to a total computational cost of O(n sq) on a serial processor. A conjugate gradient algorithms is presented that provide greater efficiency using a preconditioner, which reduces the number of iterations required, and by exploiting parallelism, which reduces the cost of each iteration. Two Preconditioned Conjugate Gradient (PCG) algorithms are proposed which respectively use a diagonal and a tridiagonal matrix, composed of the diagonal and tridiagonal elements of the mass matrix, as preconditioners. Parallel algorithms are developed to compute the preconditioners and their inversions in O(log sub 2 n) steps using n processors. A parallel algorithm is also presented which, on the same architecture, achieves the computational time of O(log sub 2 n) for each iteration. Simulation results for a seven degree-of-freedom manipulator are presented. Variants of the proposed algorithms are also developed which can be efficiently implemented on the Robot Mathematics Processor (RMP).

Visualizing phase transition behavior of dilute stimuli responsive polymer solutions via Mueller matrix polarimetry.

PubMed

Narayanan, Amal; Chandel, Shubham; Ghosh, Nirmalya; De, Priyadarsi

2015-09-15

Probing volume phase transition behavior of superdiluted polymer solutions both micro- and macroscopically still persists as an outstanding challenge. In this regard, we have explored 4 × 4 spectral Mueller matrix measurement and its inverse analysis for excavating the microarchitectural facts about stimuli responsiveness of "smart" polymers. Phase separation behavior of thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) and pH responsive poly(N,N-(dimethylamino)ethyl methacrylate) (PDMAEMA) and their copolymers were analyzed in terms of Mueller matrix derived polarization parameters, namely, depolarization (Δ), diattenuation (d), and linear retardance (δ). The Δ, d, and δ parameters provided useful information on both macro- and microstructural alterations during the phase separation. Additionally, the two step action ((i) breakage of polymer-water hydrogen bonding and (ii) polymer-polymer aggregation) at the molecular microenvironment during the cloud point generation was successfully probed via these parameters. It is demonstrated that, in comparison to the present techniques available for assessing the hydrophobic-hydrophilic switch over of simple stimuli-responsive polymers, Mueller matrix polarimetry offers an important advantage requiring a few hundred times dilute polymer solution (0.01 mg/mL, 1.1-1.4 μM) at a low-volume format.

Seismic gradiometry using ambient seismic noise in an anisotropic Earth

NASA Astrophysics Data System (ADS)

de Ridder, S. A. L.; Curtis, A.

2017-05-01

We introduce a wavefield gradiometry technique to estimate both isotropic and anisotropic local medium characteristics from short recordings of seismic signals by inverting a wave equation. The method exploits the information in the spatial gradients of a seismic wavefield that are calculated using dense deployments of seismic arrays. The application of the method uses the surface wave energy in the ambient seismic field. To estimate isotropic and anisotropic medium properties we invert an elliptically anisotropic wave equation. The spatial derivatives of the recorded wavefield are evaluated by calculating finite differences over nearby recordings, which introduces a systematic anisotropic error. A two-step approach corrects this error: finite difference stencils are first calibrated, then the output of the wave-equation inversion is corrected using the linearized impulse response to the inverted velocity anomaly. We test the procedure on ambient seismic noise recorded in a large and dense ocean bottom cable array installed over Ekofisk field. The estimated azimuthal anisotropy forms a circular geometry around the production-induced subsidence bowl. This conforms with results from studies employing controlled sources, and with interferometry correlating long records of seismic noise. Yet in this example, the results were obtained using only a few minutes of ambient seismic noise.

Optoelectronic Control of Spin and Pseudospin in Layered WSe2

NASA Astrophysics Data System (ADS)

Jones, Aaron

2014-03-01

Coherent manipulation of spin-like quantum numbers facilitates the development of new quantum technologies. Layered transition metal dichalcogenides provide an ideal laboratory to exploit such dynamic control of spin, pseudospin, and their interplay. Here, we discuss two examples based on monolayer and bilayer WSe2. Due to the inversion asymmetry in monolayer WSe2, valley pseudospins, which index the degenerate extrema of the energy-momentum bands, possess circularly polarized optical selection rules. In addition to the generation of valley polarization through optical pumping of valley excitons, we demonstrate the creation of a coherent superposition between valley states in monolayer WSe2 by linearly polarized excitation. On the other hand, bilayer WSe2 provides an additional quantum degree of freedom, the layer pseudospin, which corresponds to layer polarization. In AB stacked bilayers, we find the real spin is locked to layer pseudospin for a given valley, which results in the suppression of spin relaxation and electrical control of spin Zeeman splitting without an applied magnetic field. Additionally, we obtain spectroscopic evidence of interlayer and intralayer trion species, an important step toward coherent optical control in van der Waals 2D heterostructures. Aaron Jones partially supported by NSF Grant No. DGE-0718124.

Synchronized LES for acoustic near-field analysis of a supersonic jet

NASA Astrophysics Data System (ADS)

S, Unnikrishnan; Gaitonde, Datta; The Ohio State University Team

2014-11-01

We develop a novel method using simultaneous, synchronized Large Eddy Simulations (LES) to examine the manner in which the plume of a supersonic jet generates the near acoustic field. Starting from a statistically stationary state, at each time-step, the first LES (Baseline) is used to obtain native perturbations, which are then localized in space, scaled to small values and injected into the second LES (Twin). At any subsequent time, the difference between the two simulations can be processed to discern how disturbances from any particular zone in the jet are modulated and filtered by the non-linear core to form the combined hydrodynamic and acoustic near field and the fully acoustic farfield. Unlike inverse techniques that use correlations between jet turbulence and far-field signals to infer causality, the current forward analysis effectively tags and tracks native perturbations as they are processed by the jet. Results are presented for a Mach 1.3 cold jet. Statistical analysis of the baseline and perturbation boost provides insight into different mechanisms of disturbance propagation, amplification, directivity, generation of intermittent wave-packet like events and the direct and indirect effect of different parts of the jet on the acoustic field. Office of Naval Research.

Analysis of Interval Changes on Mammograms for Computer Aided Diagnosis

DTIC Science & Technology

2000-05-01

tizer was calibrated so that the gray values were linearly and erage pixel values in the template and ROI, respectively. The inversely proportional to the...earlier for linearly and inversely proportional to the OD within the alignment of the breast regions, except that the regions to be range 0-4 OD...results versely proportional to the radial distance r from the nipple. in a decrease in the value of (to 20 mm. This decrease helps For the data set

Application of linearized inverse scattering methods for the inspection in steel plates embedded in concrete structures

NASA Astrophysics Data System (ADS)

Tsunoda, Takaya; Suzuki, Keigo; Saitoh, Takahiro

2018-04-01

This study develops a method to visualize the state of steel-concrete interface with ultrasonic testing. Scattered waves are obtained by the UT pitch-catch mode from the surface of the concrete. Discrete wavelet transform is applied in order to extract echoes scattered from the steel-concrete interface. Then Linearized Inverse Scattering Methods are used for imaging the interface. The results show that LISM with Born and Kirchhoff approximation provide clear images for the target.

Mixed linear-nonlinear fault slip inversion: Bayesian inference of model, weighting, and smoothing parameters

NASA Astrophysics Data System (ADS)

Fukuda, J.; Johnson, K. M.

2009-12-01

Studies utilizing inversions of geodetic data for the spatial distribution of coseismic slip on faults typically present the result as a single fault plane and slip distribution. Commonly the geometry of the fault plane is assumed to be known a priori and the data are inverted for slip. However, sometimes there is not strong a priori information on the geometry of the fault that produced the earthquake and the data is not always strong enough to completely resolve the fault geometry. We develop a method to solve for the full posterior probability distribution of fault slip and fault geometry parameters in a Bayesian framework using Monte Carlo methods. The slip inversion problem is particularly challenging because it often involves multiple data sets with unknown relative weights (e.g. InSAR, GPS), model parameters that are related linearly (slip) and nonlinearly (fault geometry) through the theoretical model to surface observations, prior information on model parameters, and a regularization prior to stabilize the inversion. We present the theoretical framework and solution method for a Bayesian inversion that can handle all of these aspects of the problem. The method handles the mixed linear/nonlinear nature of the problem through combination of both analytical least-squares solutions and Monte Carlo methods. We first illustrate and validate the inversion scheme using synthetic data sets. We then apply the method to inversion of geodetic data from the 2003 M6.6 San Simeon, California earthquake. We show that the uncertainty in strike and dip of the fault plane is over 20 degrees. We characterize the uncertainty in the slip estimate with a volume around the mean fault solution in which the slip most likely occurred. Slip likely occurred somewhere in a volume that extends 5-10 km in either direction normal to the fault plane. We implement slip inversions with both traditional, kinematic smoothing constraints on slip and a simple physical condition of uniform stress drop.

Modeling and Inverse Controller Design for an Unmanned Aerial Vehicle Based on the Self-Organizing Map

NASA Technical Reports Server (NTRS)

Cho, Jeongho; Principe, Jose C.; Erdogmus, Deniz; Motter, Mark A.

2005-01-01

The next generation of aircraft will have dynamics that vary considerably over the operating regime. A single controller will have difficulty to meet the design specifications. In this paper, a SOM-based local linear modeling scheme of an unmanned aerial vehicle (UAV) is developed to design a set of inverse controllers. The SOM selects the operating regime depending only on the embedded output space information and avoids normalization of the input data. Each local linear model is associated with a linear controller, which is easy to design. Switching of the controllers is done synchronously with the active local linear model that tracks the different operating conditions. The proposed multiple modeling and control strategy has been successfully tested in a simulator that models the LoFLYTE UAV.

Incorporation of causative quantitative trait nucleotides in single-step GBLUP.

PubMed

Fragomeni, Breno O; Lourenco, Daniela A L; Masuda, Yutaka; Legarra, Andres; Misztal, Ignacy

2017-07-26

Much effort is put into identifying causative quantitative trait nucleotides (QTN) in animal breeding, empowered by the availability of dense single nucleotide polymorphism (SNP) information. Genomic selection using traditional SNP information is easily implemented for any number of genotyped individuals using single-step genomic best linear unbiased predictor (ssGBLUP) with the algorithm for proven and young (APY). Our aim was to investigate whether ssGBLUP is useful for genomic prediction when some or all QTN are known. Simulations included 180,000 animals across 11 generations. Phenotypes were available for all animals in generations 6 to 10. Genotypes for 60,000 SNPs across 10 chromosomes were available for 29,000 individuals. The genetic variance was fully accounted for by 100 or 1000 biallelic QTN. Raw genomic relationship matrices (GRM) were computed from (a) unweighted SNPs, (b) unweighted SNPs and causative QTN, (c) SNPs and causative QTN weighted with results obtained with genome-wide association studies, (d) unweighted SNPs and causative QTN with simulated weights, (e) only unweighted causative QTN, (f-h) as in (b-d) but using only the top 10% causative QTN, and (i) using only causative QTN with simulated weight. Predictions were computed by pedigree-based BLUP (PBLUP) and ssGBLUP. Raw GRM were blended with 1 or 5% of the numerator relationship matrix, or 1% of the identity matrix. Inverses of GRM were obtained directly or with APY. Accuracy of breeding values for 5000 genotyped animals in the last generation with PBLUP was 0.32, and for ssGBLUP it increased to 0.49 with an unweighted GRM, 0.53 after adding unweighted QTN, 0.63 when QTN weights were estimated, and 0.89 when QTN weights were based on true effects known from the simulation. When the GRM was constructed from causative QTN only, accuracy was 0.95 and 0.99 with blending at 5 and 1%, respectively. Accuracies simulating 1000 QTN were generally lower, with a similar trend. Accuracies using the APY inverse were equal or higher than those with a regular inverse. Single-step GBLUP can account for causative QTN via a weighted GRM. Accuracy gains are maximum when variances of causative QTN are known and blending is at 1%.

On the value of incorporating spatial statistics in large-scale geophysical inversions: the SABRe case

NASA Astrophysics Data System (ADS)

Kokkinaki, A.; Sleep, B. E.; Chambers, J. E.; Cirpka, O. A.; Nowak, W.

2010-12-01

Electrical Resistance Tomography (ERT) is a popular method for investigating subsurface heterogeneity. The method relies on measuring electrical potential differences and obtaining, through inverse modeling, the underlying electrical conductivity field, which can be related to hydraulic conductivities. The quality of site characterization strongly depends on the utilized inversion technique. Standard ERT inversion methods, though highly computationally efficient, do not consider spatial correlation of soil properties; as a result, they often underestimate the spatial variability observed in earth materials, thereby producing unrealistic subsurface models. Also, these methods do not quantify the uncertainty of the estimated properties, thus limiting their use in subsequent investigations. Geostatistical inverse methods can be used to overcome both these limitations; however, they are computationally expensive, which has hindered their wide use in practice. In this work, we compare a standard Gauss-Newton smoothness constrained least squares inversion method against the quasi-linear geostatistical approach using the three-dimensional ERT dataset of the SABRe (Source Area Bioremediation) project. The two methods are evaluated for their ability to: a) produce physically realistic electrical conductivity fields that agree with the wide range of data available for the SABRe site while being computationally efficient, and b) provide information on the spatial statistics of other parameters of interest, such as hydraulic conductivity. To explore the trade-off between inversion quality and computational efficiency, we also employ a 2.5-D forward model with corrections for boundary conditions and source singularities. The 2.5-D model accelerates the 3-D geostatistical inversion method. New adjoint equations are developed for the 2.5-D forward model for the efficient calculation of sensitivities. Our work shows that spatial statistics can be incorporated in large-scale ERT inversions to improve the inversion results without making them computationally prohibitive.

Determination of rock-sample anisotropy from P- and S-wave traveltime inversion

NASA Astrophysics Data System (ADS)

Pšenčík, Ivan; Růžek, Bohuslav; Lokajíček, Tomáš; Svitek, Tomáš

2018-04-01

We determine anisotropy of a rock sample from laboratory measurements of P- and S-wave traveltimes using weak-anisotropy approximation and parametri-zation of the medium by a special set of anisotropy parameters. For the traveltime inversion we use first-order velocity expressions in the weak-anisotropy approximation, which allow to deal with P and S waves separately. Each wave is described by 15 anisotropy parameters, 9 of which are common for both waves. The parameters allow an approximate construction of separate P- or common S-wave phase-velocity surfaces. Common S wave concept is used to simplify the treatment of S waves. In order to obtain all 21 anisotropy parameters, P- and S-wave traveltimes must be inverted jointly. The proposed inversion scheme has several advantages. As a consequence of the use of weak-anisotropy approximation and assumed homogeneity of the rock sample, equations used for the inversion are linear. Thus the inversion procedure is non-iterative. In the approximation used, phase and ray velocities are equal in their magnitude and direction. Thus analysis whether the measured velocity is the ray or phase velocity is unnecessary. Another advantage of the proposed inversion scheme is that, thanks to the use of the common S-wave concept, it does not require identification of S-wave modes. It is sufficient to know the two S-wave traveltimes without specification, to which S-wave mode they belong. The inversion procedure is tested first on synthetic traveltimes and then used for the inversion of traveltimes measured in laboratory. In both cases, we perform first the inversion of P-wave traveltimes alone and then joint inversion of P- and S-wave traveltimes, and compare the results.

On the analysis of para-ammonia observations

NASA Technical Reports Server (NTRS)

Kuiper, T. B. H.

1994-01-01

The intensities and optical depths of the (1, 1), (2, 2), and (2, 1) inversion transitions of ammonia can be calculated quite accurately without solving the equations of statistical equilibrium. A two-temperature partition function suffices. The excitation of the K-ladders can be approximated by using a temperature obtained from a two-level model with the (2, 1) and (1, 1) levels. Distribution of populations between the ladders is described with the kinetic temperature. This enables one to compute the (1, 1) and (2, 1) inversion transition excitation temperatures and optical depths. To compute the (2, 2) brightness temperatures, the fractional population of the (2, 2) doublet is computed from the population of the (1, 1) doublet using the 'true rotation temperature,' which is calculated using a three-level model with the (2, 1), (2, 2), and (1, 1) levels. In spite of some iterative steps, the calculation is quite fast.

Iterative methods for mixed finite element equations

NASA Technical Reports Server (NTRS)

Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.

1985-01-01

Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.

Fault gouge evolution during rupture and healing: Continual active-seismic observations across laboratory-scale fault zones

NASA Astrophysics Data System (ADS)

Krysta, M.; Kusmierczyk-Michulec, J.; Nikkinen, M.; Carter, J. A.

2011-12-01

In order to support its mission of monitoring compliance with the treaty banning nuclear explosions, the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) operates four global networks of, respectively, seismic, infrasound, hydroacoustic sensors and air samplers accompanied with radionuclide detectors. The role of the International Data Centre (IDC) of CTBTO is to associate the signals detected in the monitoring networks with the physical phenomena which emitted these signals, by forming events. One of the aspects of associating detections with emitters is the problem of inferring the sources of radionuclides from the detections made at CTBTO radionuclide network stations. This task is particularly challenging because the average transport distance between a release point and detectors is large. Complex processes of turbulent diffusion are responsible for efficient mixing and consequently for decreasing the information content of detections with an increasing distance from the source. The problem is generally addressed in a two-step process. In the first step, an atmospheric transport model establishes a link between the detections and the regions of possible source location. In the second step this link is inverted to infer source information from the detections. In this presentation, we will discuss enhancements of the presently used regression-based inversion algorithm to reconstruct a source of radionuclides. To this aim, modern inversion algorithms accounting for prior information and appropriately regularizing an under-determined reconstruction problem will be briefly introduced. Emphasis will be on the CTBTO context and the choice of inversion methods. An illustration of the first tests will be provided using a framework of twin experiments, i.e. fictitious detections in the CTBTO radionuclide network generated with an atmospheric transport model.

An Approach for Automatic Generation of Adaptive Hypermedia in Education with Multilingual Knowledge Discovery Techniques

ERIC Educational Resources Information Center

Alfonseca, Enrique; Rodriguez, Pilar; Perez, Diana

2007-01-01

This work describes a framework that combines techniques from Adaptive Hypermedia and Natural Language processing in order to create, in a fully automated way, on-line information systems from linear texts in electronic format, such as textbooks. The process is divided into two steps: an "off-line" processing step, which analyses the source text,…

The Continuized Log-Linear Method: An Alternative to the Kernel Method of Continuization in Test Equating

ERIC Educational Resources Information Center

Wang, Tianyou

2008-01-01

Von Davier, Holland, and Thayer (2004) laid out a five-step framework of test equating that can be applied to various data collection designs and equating methods. In the continuization step, they presented an adjusted Gaussian kernel method that preserves the first two moments. This article proposes an alternative continuization method that…

An approach to predict Sudden Cardiac Death (SCD) using time domain and bispectrum features from HRV signal.

PubMed

Houshyarifar, Vahid; Chehel Amirani, Mehdi

2016-08-12

In this paper we present a method to predict Sudden Cardiac Arrest (SCA) with higher order spectral (HOS) and linear (Time) features extracted from heart rate variability (HRV) signal. Predicting the occurrence of SCA is important in order to avoid the probability of Sudden Cardiac Death (SCD). This work is a challenge to predict five minutes before SCA onset. The method consists of four steps: pre-processing, feature extraction, feature reduction, and classification. In the first step, the QRS complexes are detected from the electrocardiogram (ECG) signal and then the HRV signal is extracted. In second step, bispectrum features of HRV signal and time-domain features are obtained. Six features are extracted from bispectrum and two features from time-domain. In the next step, these features are reduced to one feature by the linear discriminant analysis (LDA) technique. Finally, KNN and support vector machine-based classifiers are used to classify the HRV signals. We used two database named, MIT/BIH Sudden Cardiac Death (SCD) Database and Physiobank Normal Sinus Rhythm (NSR). In this work we achieved prediction of SCD occurrence for six minutes before the SCA with the accuracy over 91%.

A Joint Method of Envelope Inversion Combined with Hybrid-domain Full Waveform Inversion

NASA Astrophysics Data System (ADS)

CUI, C.; Hou, W.

2017-12-01

Full waveform inversion (FWI) aims to construct high-precision subsurface models by fully using the information in seismic records, including amplitude, travel time, phase and so on. However, high non-linearity and the absence of low frequency information in seismic data lead to the well-known cycle skipping problem and make inversion easily fall into local minima. In addition, those 3D inversion methods that are based on acoustic approximation ignore the elastic effects in real seismic field, and make inversion harder. As a result, the accuracy of final inversion results highly relies on the quality of initial model. In order to improve stability and quality of inversion results, multi-scale inversion that reconstructs subsurface model from low to high frequency are applied. But, the absence of very low frequencies (< 3Hz) in field data is still bottleneck in the FWI. By extracting ultra low-frequency data from field data, envelope inversion is able to recover low wavenumber model with a demodulation operator (envelope operator), though the low frequency data does not really exist in field data. To improve the efficiency and viability of the inversion, in this study, we proposed a joint method of envelope inversion combined with hybrid-domain FWI. First, we developed 3D elastic envelope inversion, and the misfit function and the corresponding gradient operator were derived. Then we performed hybrid-domain FWI with envelope inversion result as initial model which provides low wavenumber component of model. Here, forward modeling is implemented in the time domain and inversion in the frequency domain. To accelerate the inversion, we adopt CPU/GPU heterogeneous computing techniques. There were two levels of parallelism. In the first level, the inversion tasks are decomposed and assigned to each computation node by shot number. In the second level, GPU multithreaded programming is used for the computation tasks in each node, including forward modeling, envelope extraction, DFT (discrete Fourier transform) calculation and gradients calculation. Numerical tests demonstrated that the combined envelope inversion + hybrid-domain FWI could obtain much faithful and accurate result than conventional hybrid-domain FWI. The CPU/GPU heterogeneous parallel computation could improve the performance speed.

An Efficient Spectral Method for Ordinary Differential Equations with Rational Function Coefficients

NASA Technical Reports Server (NTRS)

Coutsias, Evangelos A.; Torres, David; Hagstrom, Thomas

1994-01-01

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple three-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e. matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation N, is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers.

Parallel processing architecture for computing inverse differential kinematic equations of the PUMA arm

NASA Technical Reports Server (NTRS)

Hsia, T. C.; Lu, G. Z.; Han, W. H.

1987-01-01

In advanced robot control problems, on-line computation of inverse Jacobian solution is frequently required. Parallel processing architecture is an effective way to reduce computation time. A parallel processing architecture is developed for the inverse Jacobian (inverse differential kinematic equation) of the PUMA arm. The proposed pipeline/parallel algorithm can be inplemented on an IC chip using systolic linear arrays. This implementation requires 27 processing cells and 25 time units. Computation time is thus significantly reduced.

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

DOE PAGES

Li, Ruipeng; Saad, Yousef

2017-08-01

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Ruipeng; Saad, Yousef

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

Silicon-carbon bond inversions driven by 60-keV electrons in graphene.

PubMed

Susi, Toma; Kotakoski, Jani; Kepaptsoglou, Demie; Mangler, Clemens; Lovejoy, Tracy C; Krivanek, Ondrej L; Zan, Recep; Bangert, Ursel; Ayala, Paola; Meyer, Jannik C; Ramasse, Quentin

2014-09-12

We demonstrate that 60-keV electron irradiation drives the diffusion of threefold-coordinated Si dopants in graphene by one lattice site at a time. First principles simulations reveal that each step is caused by an electron impact on a C atom next to the dopant. Although the atomic motion happens below our experimental time resolution, stochastic analysis of 38 such lattice jumps reveals a probability for their occurrence in a good agreement with the simulations. Conversions from three- to fourfold coordinated dopant structures and the subsequent reverse process are significantly less likely than the direct bond inversion. Our results thus provide a model of nondestructive and atomically precise structural modification and detection for two-dimensional materials.

Real-time solution of linear computational problems using databases of parametric reduced-order models with arbitrary underlying meshes

NASA Astrophysics Data System (ADS)

Amsallem, David; Tezaur, Radek; Farhat, Charbel

2016-12-01

A comprehensive approach for real-time computations using a database of parametric, linear, projection-based reduced-order models (ROMs) based on arbitrary underlying meshes is proposed. In the offline phase of this approach, the parameter space is sampled and linear ROMs defined by linear reduced operators are pre-computed at the sampled parameter points and stored. Then, these operators and associated ROMs are transformed into counterparts that satisfy a certain notion of consistency. In the online phase of this approach, a linear ROM is constructed in real-time at a queried but unsampled parameter point by interpolating the pre-computed linear reduced operators on matrix manifolds and therefore computing an interpolated linear ROM. The proposed overall model reduction framework is illustrated with two applications: a parametric inverse acoustic scattering problem associated with a mockup submarine, and a parametric flutter prediction problem associated with a wing-tank system. The second application is implemented on a mobile device, illustrating the capability of the proposed computational framework to operate in real-time.

Striatal dopamine release codes uncertainty in pathological gambling.

PubMed

Linnet, Jakob; Mouridsen, Kim; Peterson, Ericka; Møller, Arne; Doudet, Doris Jeanne; Gjedde, Albert

2012-10-30

Two mechanisms of midbrain and striatal dopaminergic projections may be involved in pathological gambling: hypersensitivity to reward and sustained activation toward uncertainty. The midbrain-striatal dopamine system distinctly codes reward and uncertainty, where dopaminergic activation is a linear function of expected reward and an inverse U-shaped function of uncertainty. In this study, we investigated the dopaminergic coding of reward and uncertainty in 18 pathological gambling sufferers and 16 healthy controls. We used positron emission tomography (PET) with the tracer [(11)C]raclopride to measure dopamine release, and we used performance on the Iowa Gambling Task (IGT) to determine overall reward and uncertainty. We hypothesized that we would find a linear function between dopamine release and IGT performance, if dopamine release coded reward in pathological gambling. If, on the other hand, dopamine release coded uncertainty, we would find an inversely U-shaped function. The data supported an inverse U-shaped relation between striatal dopamine release and IGT performance if the pathological gambling group, but not in the healthy control group. These results are consistent with the hypothesis of dopaminergic sensitivity toward uncertainty, and suggest that dopaminergic sensitivity to uncertainty is pronounced in pathological gambling, but not among non-gambling healthy controls. The findings have implications for understanding dopamine dysfunctions in pathological gambling and addictive behaviors. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Joint Inversion of Vp, Vs, and Resistivity at SAFOD

NASA Astrophysics Data System (ADS)

Bennington, N. L.; Zhang, H.; Thurber, C. H.; Bedrosian, P. A.

2010-12-01

Seismic and resistivity models at SAFOD have been derived from separate inversions that show significant spatial similarity between the main model features. Previous work [Zhang et al., 2009] used cluster analysis to make lithologic inferences from trends in the seismic and resistivity models. We have taken this one step further by developing a joint inversion scheme that uses the cross-gradient penalty function to achieve structurally similar Vp, Vs, and resistivity images that adequately fit the seismic and magnetotelluric MT data without forcing model similarity where none exists. The new inversion code, tomoDDMT, merges the seismic inversion code tomoDD [Zhang and Thurber, 2003] and the MT inversion code Occam2DMT [Constable et al., 1987; deGroot-Hedlin and Constable, 1990]. We are exploring the utility of the cross-gradients penalty function in improving models of fault-zone structure at SAFOD on the San Andreas Fault in the Parkfield, California area. Two different sets of end-member starting models are being tested. One set is the separately inverted Vp, Vs, and resistivity models. The other set consists of simple, geologically based block models developed from borehole information at the SAFOD drill site and a simplified version of features seen in geophysical models at Parkfield. For both starting models, our preliminary results indicate that the inversion produces a converging solution with resistivity, seismic, and cross-gradient misfits decreasing over successive iterations. We also compare the jointly inverted Vp, Vs, and resistivity models to borehole information from SAFOD to provide a "ground truth" comparison.

Integrated Analytic and Linearized Inverse Kinematics for Precise Full Body Interactions

NASA Astrophysics Data System (ADS)

Boulic, Ronan; Raunhardt, Daniel

Despite the large success of games grounded on movement-based interactions the current state of full body motion capture technologies still prevents the exploitation of precise interactions with complex environments. This paper focuses on ensuring a precise spatial correspondence between the user and the avatar. We build upon our past effort in human postural control with a Prioritized Inverse Kinematics framework. One of its key advantage is to ease the dynamic combination of postural and collision avoidance constraints. However its reliance on a linearized approximation of the problem makes it vulnerable to the well-known full extension singularity of the limbs. In such context the tracking performance is reduced and/or less believable intermediate postural solutions are produced. We address this issue by introducing a new type of analytic constraint that smoothly integrates within the prioritized Inverse Kinematics framework. The paper first recalls the background of full body 3D interactions and the advantages and drawbacks of the linearized IK solution. Then the Flexion-EXTension constraint (FLEXT in short) is introduced for the partial position control of limb-like articulated structures. Comparative results illustrate the interest of this new type of integrated analytical and linearized IK control.

Reversed inverse regression for the univariate linear calibration and its statistical properties derived using a new methodology

NASA Astrophysics Data System (ADS)

Kang, Pilsang; Koo, Changhoi; Roh, Hokyu

2017-11-01

Since simple linear regression theory was established at the beginning of the 1900s, it has been used in a variety of fields. Unfortunately, it cannot be used directly for calibration. In practical calibrations, the observed measurements (the inputs) are subject to errors, and hence they vary, thus violating the assumption that the inputs are fixed. Therefore, in the case of calibration, the regression line fitted using the method of least squares is not consistent with the statistical properties of simple linear regression as already established based on this assumption. To resolve this problem, "classical regression" and "inverse regression" have been proposed. However, they do not completely resolve the problem. As a fundamental solution, we introduce "reversed inverse regression" along with a new methodology for deriving its statistical properties. In this study, the statistical properties of this regression are derived using the "error propagation rule" and the "method of simultaneous error equations" and are compared with those of the existing regression approaches. The accuracy of the statistical properties thus derived is investigated in a simulation study. We conclude that the newly proposed regression and methodology constitute the complete regression approach for univariate linear calibrations.

Coexistence of type-II Dirac point and weak topological phase in Pt 3 Sn

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Minsung; Wang, Cai -Zhuang; Ho, Kai -Ming

Intriguing topological phases may appear in both insulating and semimetallic states. Topological insulators exhibit topologically nontrivial band inversion, while topological Dirac/Weyl semimetals show “relativistic” linear band crossings. Here, we report an unusual topological state of Pt 3Sn, where the two topological features appear simultaneously. Based on first-principles calculations, we show that Pt 3Sn is a three-dimensional weak topological semimetal with topologically nontrivial band inversion between the valence and conduction bands, where the band structure also possesses type-II Dirac points at the boundary of two electron pockets. The formation of the Dirac points can be understood in terms of the representationsmore » of relevant symmetry groups and the compatibility relations. The topological surface states appear in accordance with the nontrivial bulk band topology. As a result, the unique coexistence of the two distinct topological features in Pt 3Sn enlarges the material scope in topological physics, and is potentially useful for spintronics.« less

Coexistence of type-II Dirac point and weak topological phase in Pt 3 Sn

DOE PAGES

Kim, Minsung; Wang, Cai -Zhuang; Ho, Kai -Ming

2017-11-06

Intriguing topological phases may appear in both insulating and semimetallic states. Topological insulators exhibit topologically nontrivial band inversion, while topological Dirac/Weyl semimetals show “relativistic” linear band crossings. Here, we report an unusual topological state of Pt 3Sn, where the two topological features appear simultaneously. Based on first-principles calculations, we show that Pt 3Sn is a three-dimensional weak topological semimetal with topologically nontrivial band inversion between the valence and conduction bands, where the band structure also possesses type-II Dirac points at the boundary of two electron pockets. The formation of the Dirac points can be understood in terms of the representationsmore » of relevant symmetry groups and the compatibility relations. The topological surface states appear in accordance with the nontrivial bulk band topology. As a result, the unique coexistence of the two distinct topological features in Pt 3Sn enlarges the material scope in topological physics, and is potentially useful for spintronics.« less

Electronic structure and molecular dynamics of Na2Li

NASA Astrophysics Data System (ADS)

Malcolm, Nathaniel O. J.; McDouall, Joseph J. W.

Following the first report (Mile, B., Sillman, P. D., Yacob, A. R. and Howard, J. A., 1996, J. chem. Soc. Dalton Trans , 653) of the EPR spectrum of the mixed alkali-metal trimer Na2Li a detailed study has been made of the electronic structure and structural dynamics of this species. Two isomeric forms have been found: one of the type, Na-Li-Na, of C , symmetry and another, Li-Na-Na, of C symmetry. Also, there are two linear saddle points which correspond to 'inversion' transition structures, and a saddle point of C symmetry which connects the two minima. A molecular dynamics investigation of these species shows that, at the temperature of the reported experiments (170 K), the C minimum is not 'static', but undergoes quite rapid inversion. At higher temperatures the C minimum converts to the C form, but by a mechanism very different from that suggested by minimum energy path considerations. 2 2v s s 2v 2v s

On the use of the Reciprocity Gap Functional in inverse scattering with near-field data: An application to mammography

NASA Astrophysics Data System (ADS)

Delbary, Fabrice; Aramini, Riccardo; Bozza, Giovanni; Brignone, Massimo; Piana, Michele

2008-11-01

Microwave tomography is a non-invasive approach to the early diagnosis of breast cancer. However the problem of visualizing tumors from diffracted microwaves is a difficult nonlinear ill-posed inverse scattering problem. We propose a qualitative approach to the solution of such a problem, whereby the shape and location of cancerous tissues can be detected by means of a combination of the Reciprocity Gap Functional method and the Linear Sampling method. We validate this approach to synthetic near-fields produced by a finite element method for boundary integral equations, where the breast is mimicked by the axial view of two nested cylinders, the external one representing the skin and the internal one representing the fat tissue.

The excitation of long period seismic waves by a source spanning a structural discontinuity

NASA Astrophysics Data System (ADS)

Woodhouse, J. H.

Simple theoretical results are obtained for the excitation of seismic waves by an indigenous seismic source in the case that the source volume is intersected by a structural discontinuity. In the long wavelength approximation the seismic radiation is identical to that of a point source placed on one side of the discontinuity or of a different point source placed on the other side. The moment tensors of these two equivalent sources are related by a specific linear transformation and may differ appreciably both in magnitude and geometry. Either of these sources could be obtained by linear inversion of seismic data but the physical interpretation is more complicated than in the usual case. A source which involved no volume change would, for example, yield an isotropic component if, during inversion, it were assumed to lie on the wrong side of the discontinuity. The problem of determining the true moment tensor of the source is indeterminate unless further assumptions are made about the stress glut distribution; one way to resolve this indeterminancy is to assume proportionality between the integrated stress glut on each side of the discontinuity.

Two-step reconstruction method using global optimization and conjugate gradient for ultrasound-guided diffuse optical tomography.

PubMed

Tavakoli, Behnoosh; Zhu, Quing

2013-01-01

Ultrasound-guided diffuse optical tomography (DOT) is a promising method for characterizing malignant and benign lesions in the female breast. We introduce a new two-step algorithm for DOT inversion in which the optical parameters are estimated with the global optimization method, genetic algorithm. The estimation result is applied as an initial guess to the conjugate gradient (CG) optimization method to obtain the absorption and scattering distributions simultaneously. Simulations and phantom experiments have shown that the maximum absorption and reduced scattering coefficients are reconstructed with less than 10% and 25% errors, respectively. This is in contrast with the CG method alone, which generates about 20% error for the absorption coefficient and does not accurately recover the scattering distribution. A new measure of scattering contrast has been introduced to characterize benign and malignant breast lesions. The results of 16 clinical cases reconstructed with the two-step method demonstrates that, on average, the absorption coefficient and scattering contrast of malignant lesions are about 1.8 and 3.32 times higher than the benign cases, respectively.

Improved characterisation of measurement errors in electrical resistivity tomography (ERT) surveys

NASA Astrophysics Data System (ADS)

Tso, C. H. M.; Binley, A. M.; Kuras, O.; Graham, J.

2016-12-01

Measurement errors can play a pivotal role in geophysical inversion. Most inverse models require users to prescribe a statistical model of data errors before inversion. Wrongly prescribed error levels can lead to over- or under-fitting of data, yet commonly used models of measurement error are relatively simplistic. With the heightening interests in uncertainty estimation across hydrogeophysics, better characterisation and treatment of measurement errors is needed to provide more reliable estimates of uncertainty. We have analysed two time-lapse electrical resistivity tomography (ERT) datasets; one contains 96 sets of direct and reciprocal data collected from a surface ERT line within a 24h timeframe, while the other is a year-long cross-borehole survey at a UK nuclear site with over 50,000 daily measurements. Our study included the characterisation of the spatial and temporal behaviour of measurement errors using autocorrelation and covariance analysis. We find that, in addition to well-known proportionality effects, ERT measurements can also be sensitive to the combination of electrodes used. This agrees with reported speculation in previous literature that ERT errors could be somewhat correlated. Based on these findings, we develop a new error model that allows grouping based on electrode number in additional to fitting a linear model to transfer resistance. The new model fits the observed measurement errors better and shows superior inversion and uncertainty estimates in synthetic examples. It is robust, because it groups errors together based on the number of the four electrodes used to make each measurement. The new model can be readily applied to the diagonal data weighting matrix commonly used in classical inversion methods, as well as to the data covariance matrix in the Bayesian inversion framework. We demonstrate its application using extensive ERT monitoring datasets from the two aforementioned sites.

Differential occurrence of chromosome inversion polymorphisms among Muller's elements in three species of the tripunctata group of Drosophila, including a species with fast chromosomal evolution.

PubMed

Brianti, Mitsue T; Ananina, Galina; Klaczko, Louis B

2013-01-01

Detailed chromosome maps with reliable homologies among chromosomes of different species are the first step to study the evolution of the genetic architecture in any set of species. Here, we present detailed photo maps of the polytene chromosomes of three closely related species of the tripunctata group (subgenus Drosophila): Drosophila mediopunctata, D. roehrae, and D. unipunctata. We identified Muller's elements in each species, using FISH, establishing reliable chromosome homologies among species and D. melanogaster. The simultaneous analysis of chromosome inversions revealed a distribution pattern for the inversion polymorphisms among Muller's elements in the three species. Element E is the most polymorphic, with many inversions in each species. Element C follows; while the least polymorphic elements are B and D. While interesting, it remains to be determined how general this pattern is among species of the tripunctata group. Despite previous studies showing that D. mediopunctata and D. unipunctata are phylogenetically closer to each other than to D. roehrae, D. unipunctata shows rare karyotypic changes. It has two chromosome fusions: an additional heterochromatic chromosome pair and a pericentric inversion in the X chromosome. This especial conformation suggests a fast chromosomal evolution that deserves further study.

Two-step Raman spectroscopy method for tumor diagnosis

NASA Astrophysics Data System (ADS)

Zakharov, V. P.; Bratchenko, I. A.; Kozlov, S. V.; Moryatov, A. A.; Myakinin, O. O.; Artemyev, D. N.

2014-05-01

Two-step Raman spectroscopy phase method was proposed for differential diagnosis of malignant tumor in skin and lung tissue. It includes detection of malignant tumor in healthy tissue on first step with identification of concrete cancer type on the second step. Proposed phase method analyze spectral intensity alteration in 1300-1340 and 1640-1680 cm-1 Raman bands in relation to the intensity of the 1450 cm-1 band on first step, and relative differences between RS intensities for tumor area and healthy skin closely adjacent to the lesion on the second step. It was tested more than 40 ex vivo samples of lung tissue and more than 50 in vivo skin tumors. Linear Discriminant Analysis, Quadratic Discriminant Analysis and Support Vector Machine were used for tumors type classification on phase planes. It is shown that two-step phase method allows to reach 88.9% sensitivity and 87.8% specificity for malignant melanoma diagnosis (skin cancer); 100% sensitivity and 81.5% specificity for adenocarcinoma diagnosis (lung cancer); 90.9% sensitivity and 77.8% specificity for squamous cell carcinoma diagnosis (lung cancer).

Toward an efficient inverse characterization of the viscoelastic properties of anisotropic media based on the ultrasonic polar scan

NASA Astrophysics Data System (ADS)

Martens, A.; Kersemans, M.; Daemen, J.; Verboven, E.; Van Paepegem, W.; Degrieck, J.; Delrue, S.; Van Den Abeele, K.

2018-04-01

Composite materials (e.g., carbon fiber reinforced plastics (CFRP)) are increasingly used for critical components in several industrial sectors (e.g. aerospace, automotive). Their anisotropic nature makes it difficult to accurately determine material properties or to assess internal damages. To resolve these challenges, the Ultrasonic Polar Scan (UPS) technique has been introduced. In a UPS experiment, a fixed material spot is insonified at a multitude of incidence angles Ψ(θ,φ) for which the transmission amplitude as well as the associated arrival time (time-of-flight) are measured. Mapping these quantities on a polar diagram represents a fingerprint of the local viscoelasticity of the investigated material. In the present study, we propose a novel two-stage inversion scheme that is able to infer both the elastic and the viscous properties. In the first step, we solve the inverse problem of determining the elastic constants from time-of-flight UPS recordings. The second stage handles a similar inverse problem, but now operates on the amplitude landscape of a UPS experiment for determining the viscous part of the viscoelastic tensor. This two-stage procedure thus yields the viscoelastic tensor of the insonified material spot. The developed characterization scheme has been employed on both virtual (numerical) UPS recordings, to test the effectiveness of the method, and experimental UPS recordings of unidirectional C/E plates.

On the calibration process of film dosimetry: OLS inverse regression versus WLS inverse prediction.

PubMed

Crop, F; Van Rompaye, B; Paelinck, L; Vakaet, L; Thierens, H; De Wagter, C

2008-07-21

The purpose of this study was both putting forward a statistically correct model for film calibration and the optimization of this process. A reliable calibration is needed in order to perform accurate reference dosimetry with radiographic (Gafchromic) film. Sometimes, an ordinary least squares simple linear (in the parameters) regression is applied to the dose-optical-density (OD) curve with the dose as a function of OD (inverse regression) or sometimes OD as a function of dose (inverse prediction). The application of a simple linear regression fit is an invalid method because heteroscedasticity of the data is not taken into account. This could lead to erroneous results originating from the calibration process itself and thus to a lower accuracy. In this work, we compare the ordinary least squares (OLS) inverse regression method with the correct weighted least squares (WLS) inverse prediction method to create calibration curves. We found that the OLS inverse regression method could lead to a prediction bias of up to 7.3 cGy at 300 cGy and total prediction errors of 3% or more for Gafchromic EBT film. Application of the WLS inverse prediction method resulted in a maximum prediction bias of 1.4 cGy and total prediction errors below 2% in a 0-400 cGy range. We developed a Monte-Carlo-based process to optimize calibrations, depending on the needs of the experiment. This type of thorough analysis can lead to a higher accuracy for film dosimetry.

Improved characterisation and modelling of measurement errors in electrical resistivity tomography (ERT) surveys

NASA Astrophysics Data System (ADS)

Tso, Chak-Hau Michael; Kuras, Oliver; Wilkinson, Paul B.; Uhlemann, Sebastian; Chambers, Jonathan E.; Meldrum, Philip I.; Graham, James; Sherlock, Emma F.; Binley, Andrew

2017-11-01

Measurement errors can play a pivotal role in geophysical inversion. Most inverse models require users to prescribe or assume a statistical model of data errors before inversion. Wrongly prescribed errors can lead to over- or under-fitting of data; however, the derivation of models of data errors is often neglected. With the heightening interest in uncertainty estimation within hydrogeophysics, better characterisation and treatment of measurement errors is needed to provide improved image appraisal. Here we focus on the role of measurement errors in electrical resistivity tomography (ERT). We have analysed two time-lapse ERT datasets: one contains 96 sets of direct and reciprocal data collected from a surface ERT line within a 24 h timeframe; the other is a two-year-long cross-borehole survey at a UK nuclear site with 246 sets of over 50,000 measurements. Our study includes the characterisation of the spatial and temporal behaviour of measurement errors using autocorrelation and correlation coefficient analysis. We find that, in addition to well-known proportionality effects, ERT measurements can also be sensitive to the combination of electrodes used, i.e. errors may not be uncorrelated as often assumed. Based on these findings, we develop a new error model that allows grouping based on electrode number in addition to fitting a linear model to transfer resistance. The new model explains the observed measurement errors better and shows superior inversion results and uncertainty estimates in synthetic examples. It is robust, because it groups errors together based on the electrodes used to make the measurements. The new model can be readily applied to the diagonal data weighting matrix widely used in common inversion methods, as well as to the data covariance matrix in a Bayesian inversion framework. We demonstrate its application using extensive ERT monitoring datasets from the two aforementioned sites.

Automated rapid finite fault inversion for megathrust earthquakes: Application to the Maule (2010), Iquique (2014) and Illapel (2015) great earthquakes

NASA Astrophysics Data System (ADS)

Benavente, Roberto; Cummins, Phil; Dettmer, Jan

2016-04-01

Rapid estimation of the spatial and temporal rupture characteristics of large megathrust earthquakes by finite fault inversion is important for disaster mitigation. For example, estimates of the spatio-temporal evolution of rupture can be used to evaluate population exposure to tsunami waves and ground shaking soon after the event by providing more accurate predictions than possible with point source approximations. In addition, rapid inversion results can reveal seismic source complexity to guide additional, more detailed subsequent studies. This work develops a method to rapidly estimate the slip distribution of megathrust events while reducing subjective parameter choices by automation. The method is simple yet robust and we show that it provides excellent preliminary rupture models as soon as 30 minutes for three great earthquakes in the South-American subduction zone. This may slightly change for other regions depending on seismic station coverage but method can be applied to any subduction region. The inversion is based on W-phase data since it is rapidly and widely available and of low amplitude which avoids clipping at close stations for large events. In addition, prior knowledge of the slab geometry (e.g. SLAB 1.0) is applied and rapid W-phase point source information (time delay and centroid location) is used to constrain the fault geometry and extent. Since the linearization by multiple time window (MTW) parametrization requires regularization, objective smoothing is achieved by the discrepancy principle in two fully automated steps. First, the residuals are estimated assuming unknown noise levels, and second, seeking a subsequent solution which fits the data to noise level. The MTW scheme is applied with positivity constraints and a solution is obtained by an efficient non-negative least squares solver. Systematic application of the algorithm to the Maule (2010), Iquique (2014) and Illapel (2015) events illustrates that rapid finite fault inversion with teleseismic data is feasible and provides meaningful results. The results for the three events show excellent data fits and are consistent with other solutions showing most of the slip occurring close to the trench for the Maule an Illapel events and some deeper slip for the Iquique event. Importantly, the Illapel source model predicts tsunami waveforms of close agreement with observed waveforms. Finally, we develop a new Bayesian approach to approximate uncertainties as part of the rapid inversion scheme with positivity constraints. Uncertainties are estimated by approximating the posterior distribution as a multivariate log-normal distribution. While solving for the posterior adds some additional computational cost, we illustrate that uncertainty estimation is important for meaningful interpretation of finite fault models.

Reverse Flood Routing with the Lag-and-Route Storage Model

NASA Astrophysics Data System (ADS)

Mazi, K.; Koussis, A. D.

2010-09-01

This work presents a method for reverse routing of flood waves in open channels, which is an inverse problem of the signal identification type. Inflow determination from outflow measurements is useful in hydrologic forensics and in optimal reservoir control, but has been seldom studied. Such problems are ill posed and their solution is sensitive to small perturbations present in the data, or to any related uncertainty. Therefore the major difficulty in solving this inverse problem consists in controlling the amplification of errors that inevitably befall flow measurements, from which the inflow signal is to be determined. The lag-and-route model offers a convenient framework for reverse routing, because not only is formal deconvolution not required, but also reverse routing is through a single linear reservoir. In addition, this inversion degenerates to calculating the intermediate inflow (prior to the lag step) simply as the sum of the outflow and of its time derivative multiplied by the reservoir’s time constant. The remaining time shifting (lag) of the intermediate, reversed flow presents no complications, as pure translation causes no error amplification. Note that reverse routing with the inverted Muskingum scheme (Koussis et al., submitted to the 12th Plinius Conference) fails when that scheme is specialised to the Kalinin-Miljukov model (linear reservoirs in series). The principal functioning of the reverse routing procedure was verified first with perfect field data (outflow hydrograph generated by forward routing of a known inflow hydrograph). The field data were then seeded with random error. To smooth the oscillations caused by the imperfect (measured) outflow data, we applied a multipoint Savitzky-Golay low-pass filter. The combination of reverse routing and filtering achieved an effective recovery of the inflow signal extremely efficiently. Specifically, we compared the reverse routing results of the inverted lag-and-route model and of the inverted Kalinin-Miljukov model. The latter applies the lag-and-route model’s single-reservoir inversion scheme sequentially to its cascade of linear reservoirs, the number of which is related to the stream's hydromorphology. For this purpose, we used the example of Bruen & Dooge (2007), who back-routed flow hydrographs in a 100-km long prismatic channel using a scheme for the reverse solution of the St. Venant equations of flood wave motion. The lag-and-route reverse routing model recovered the inflow hydrograph with comparable accuracy to that of the multi-reservoir, inverted Kalinin-Miljukov model, both performing as well as the box-scheme for reverse routing with the St. Venant equations. In conclusion, the success in the regaining of the inflow signal by the devised single-reservoir reverse routing procedure, with multipoint low-pass filtering, can be attributed to its simple computational structure that endows it with remarkable robustness and exceptional efficiency.

Estimating pole/zero errors in GSN-IRIS/USGS network calibration metadata

USGS Publications Warehouse

Ringler, A.T.; Hutt, C.R.; Aster, R.; Bolton, H.; Gee, L.S.; Storm, T.

2012-01-01

Mapping the digital record of a seismograph into true ground motion requires the correction of the data by some description of the instrument's response. For the Global Seismographic Network (Butler et al., 2004), as well as many other networks, this instrument response is represented as a Laplace domain pole–zero model and published in the Standard for the Exchange of Earthquake Data (SEED) format. This Laplace representation assumes that the seismometer behaves as a linear system, with any abrupt changes described adequately via multiple time-invariant epochs. The SEED format allows for published instrument response errors as well, but these typically have not been estimated or provided to users. We present an iterative three-step method to estimate the instrument response parameters (poles and zeros) and their associated errors using random calibration signals. First, we solve a coarse nonlinear inverse problem using a least-squares grid search to yield a first approximation to the solution. This approach reduces the likelihood of poorly estimated parameters (a local-minimum solution) caused by noise in the calibration records and enhances algorithm convergence. Second, we iteratively solve a nonlinear parameter estimation problem to obtain the least-squares best-fit Laplace pole–zero–gain model. Third, by applying the central limit theorem, we estimate the errors in this pole–zero model by solving the inverse problem at each frequency in a two-thirds octave band centered at each best-fit pole–zero frequency. This procedure yields error estimates of the 99% confidence interval. We demonstrate the method by applying it to a number of recent Incorporated Research Institutions in Seismology/United States Geological Survey (IRIS/USGS) network calibrations (network code IU).

Decoupling control of vehicle chassis system based on neural network inverse system

NASA Astrophysics Data System (ADS)

Wang, Chunyan; Zhao, Wanzhong; Luan, Zhongkai; Gao, Qi; Deng, Ke

2018-06-01

Steering and suspension are two important subsystems affecting the handling stability and riding comfort of the chassis system. In order to avoid the interference and coupling of the control channels between active front steering (AFS) and active suspension subsystems (ASS), this paper presents a composite decoupling control method, which consists of a neural network inverse system and a robust controller. The neural network inverse system is composed of a static neural network with several integrators and state feedback of the original chassis system to approach the inverse system of the nonlinear systems. The existence of the inverse system for the chassis system is proved by the reversibility derivation of Interactor algorithm. The robust controller is based on the internal model control (IMC), which is designed to improve the robustness and anti-interference of the decoupled system by adding a pre-compensation controller to the pseudo linear system. The results of the simulation and vehicle test show that the proposed decoupling controller has excellent decoupling performance, which can transform the multivariable system into a number of single input and single output systems, and eliminate the mutual influence and interference. Furthermore, it has satisfactory tracking capability and robust performance, which can improve the comprehensive performance of the chassis system.

Advancements and challenges in crosshole GPR full-waveform inversion for hydrological applications

NASA Astrophysics Data System (ADS)

Klotzsche, A.; Van Der Kruk, J.; Vereecken, H.

2016-12-01

Crosshole ground penetrating radar (GPR) full-waveform inversion (FWI) demonstrated over the last decade a high potential to detect, map, and resolve decimeter-small-scale structures within aquifers. GPR FWI uses Maxwell's equations to find a model that fits the measurements with the entire measured waveform. One big advantage is that by applying one method, we can derive two soil properties: dielectric permittivity and electrical conductivity. Both parameters are sensitive to different soil properties such as soil water content and porosity, or, clay content. Hence, an improved characterization of the critical zone is possible. The application of the FWI to aquifers in Germany, Switzerland, Denmark, and USA showed for all sites improved and higher resolution images than standard ray-based methods and provided new insights in the aquifers' structures. Furthermore, small-scale high contrast layers caused by changes in porosity were characterize and enhanced our understanding of the electromagnetic wave propagation related to these features. However, to obtain reliable and accurate inversion results from experimental data and hence porosity estimates, many detailed steps in acquiring the data, pre-processing and inverting the data need to be carefully followed. Here, we provide an overview of recent developments and advancements of the 2D crosshole GPR FWI that provide improved inversion results for permittivity and electrical conductivity. In addition, we will provide guidelines and point out important challenges and pitfalls that can occur during the inversion of experimental data. We will illustrate the necessary steps that are required to achieve reliable FWI results, which are indicated by e.g. a good fit of the measured and modelled traces, and, absence of a remaining gradient for the final models. Important requirements for a successful application are an accurate time zero correction, good starting models for the FWI, and, a well-estimated source wavelet.

Female Literacy Rate is a Better Predictor of Birth Rate and Infant Mortality Rate in India.

PubMed

Saurabh, Suman; Sarkar, Sonali; Pandey, Dhruv K

2013-01-01

Educated women are known to take informed reproductive and healthcare decisions. These result in population stabilization and better infant care reflected by lower birth rates and infant mortality rates (IMRs), respectively. Our objective was to study the relationship of male and female literacy rates with crude birth rates (CBRs) and IMRs of the states and union territories (UTs) of India. The data were analyzed using linear regression. CBR and IMR were taken as the dependent variables; while the overall literacy rates, male, and female literacy rates were the independent variables. CBRs were inversely related to literacy rates (slope parameter = -0.402, P < 0.001). On multiple linear regression with male and female literacy rates, a significant inverse relationship emerged between female literacy rate and CBR (slope = -0.363, P < 0.001), while male literacy rate was not significantly related to CBR (P = 0.674). IMR of the states were also inversely related to their literacy rates (slope = -1.254, P < 0.001). Multiple linear regression revealed a significant inverse relationship between IMR and female literacy (slope = -0.816, P = 0.031), whereas male literacy rate was not significantly related (P = 0.630). Female literacy is relatively highly important for both population stabilization and better infant health.

Comparative Study of Three Data Assimilation Methods for Ice Sheet Model Initialisation

NASA Astrophysics Data System (ADS)

Mosbeux, Cyrille; Gillet-Chaulet, Fabien; Gagliardini, Olivier

2015-04-01

The current global warming has direct consequences on ice-sheet mass loss contributing to sea level rise. This loss is generally driven by an acceleration of some coastal outlet glaciers and reproducing these mechanisms is one of the major issues in ice-sheet and ice flow modelling. The construction of an initial state, as close as possible to current observations, is required as a prerequisite before producing any reliable projection of the evolution of ice-sheets. For this step, inverse methods are often used to infer badly known or unknown parameters. For instance, the adjoint inverse method has been implemented and applied with success by different authors in different ice flow models in order to infer the basal drag [ Schafer et al., 2012; Gillet-chauletet al., 2012; Morlighem et al., 2010]. Others data fields, such as ice surface and bedrock topography, are easily measurable with more or less uncertainty but only locally along tracks and interpolated on finer model grid. All these approximations lead to errors on the data elevation model and give rise to an ill-posed problem inducing non-physical anomalies in flux divergence [Seroussi et al, 2011]. A solution to dissipate these divergences of flux is to conduct a surface relaxation step at the expense of the accuracy of the modelled surface [Gillet-Chaulet et al., 2012]. Other solutions, based on the inversion of ice thickness and basal drag were proposed [Perego et al., 2014; Pralong & Gudmundsson, 2011]. In this study, we create a twin experiment to compare three different assimilation algorithms based on inverse methods and nudging to constrain the bedrock friction and the bedrock elevation: (i) cyclic inversion of friction parameter and bedrock topography using adjoint method, (ii) cycles coupling inversion of friction parameter using adjoint method and nudging of bedrock topography, (iii) one step inversion of both parameters with adjoint method. The three methods show a clear improvement in parameters knowledge leading to a significant reduction of flux divergence of the model before forecasting.

Method and apparatus for adaptive force and position control of manipulators

NASA Technical Reports Server (NTRS)

Seraji, Homayoun (Inventor)

1989-01-01

The present invention discloses systematic methods and apparatus for the design of real time controllers. Real-time control employs adaptive force/position by use of feedforward and feedback controllers, with the feedforward controller being the inverse of the linearized model of robot dynamics and containing only proportional-double-derivative terms is disclosed. The feedback controller, of the proportional-integral-derivative type, ensures that manipulator joints follow reference trajectories and the feedback controller achieves robust tracking of step-plus-exponential trajectories, all in real time. The adaptive controller includes adaptive force and position control within a hybrid control architecture. The adaptive controller, for force control, achieves tracking of desired force setpoints, and the adaptive position controller accomplishes tracking of desired position trajectories. Circuits in the adaptive feedback and feedforward controllers are varied by adaptation laws.

Precision Linear Actuator for Space Interferometry Mission (SIM) Siderostat Pointing

NASA Technical Reports Server (NTRS)

Cook, Brant; Braun, David; Hankins, Steve; Koenig, John; Moore, Don

2008-01-01

'SIM PlanetQuest will exploit the classical measuring tool of astrometry (interferometry) with unprecedented precision to make dramatic advances in many areas of astronomy and astrophysics'(1). In order to obtain interferometric data two large steerable mirrors, or Siderostats, are used to direct starlight into the interferometer. A gimbaled mechanism actuated by linear actuators is chosen to meet the unprecedented pointing and angle tracking requirements of SIM. A group of JPL engineers designed, built, and tested a linear ballscrew actuator capable of performing submicron incremental steps for 10 years of continuous operation. Precise, zero backlash, closed loop pointing control requirements, lead the team to implement a ballscrew actuator with a direct drive DC motor and a precision piezo brake. Motor control commutation using feedback from a precision linear encoder on the ballscrew output produced an unexpected incremental step size of 20 nm over a range of 120 mm, yielding a dynamic range of 6,000,000:1. The results prove linear nanometer positioning requires no gears, levers, or hydraulic converters. Along the way many lessons have been learned and will subsequently be shared.

An Inverse Method to Estimate the Root Water Uptake Source-Sink Term in Soil Water Transport Equation under the Effect of Superabsorbent Polymer

PubMed Central

Liao, Renkuan; Yang, Peiling; Wu, Wenyong; Ren, Shumei

2016-01-01

The widespread use of superabsorbent polymers (SAPs) in arid regions improves the efficiency of local land and water use. However, SAPs’ repeated absorption and release of water has periodic and unstable effects on both soil’s physical and chemical properties and on the growth of plant roots, which complicates modeling of water movement in SAP-treated soils. In this paper, we proposea model of soil water movement for SAP-treated soils. The residence time of SAP in the soil and the duration of the experiment were considered as the same parameter t. This simplifies previously proposed models in which the residence time of SAP in the soil and the experiment’s duration were considered as two independent parameters. Numerical testing was carried out on the inverse method of estimating the source/sink term of root water uptake in the model of soil water movement under the effect of SAP. The test results show that time interval, hydraulic parameters, test error, and instrument precision had a significant influence on the stability of the inverse method, while time step, layering of soil, and boundary conditions had relatively smaller effects. A comprehensive analysis of the method’s stability, calculation, and accuracy suggests that the proposed inverse method applies if the following conditions are satisfied: the time interval is between 5 d and 17 d; the time step is between 1000 and 10000; the test error is ≥ 0.9; the instrument precision is ≤ 0.03; and the rate of soil surface evaporation is ≤ 0.6 mm/d. PMID:27505000

Deconvolutions based on singular value decomposition and the pseudoinverse: a guide for beginners.

PubMed

Hendler, R W; Shrager, R I

1994-01-01

Singular value decomposition (SVD) is deeply rooted in the theory of linear algebra, and because of this is not readily understood by a large group of researchers who could profit from its application. In this paper, we discuss the subject on a level that should be understandable to scientists who are not well versed in linear algebra. However, because it is necessary that certain key concepts in linear algebra be appreciated in order to comprehend what is accomplished by SVD, we present the section, 'Bare basics of linear algebra'. This is followed by a discussion of the theory of SVD. Next we present step-by-step examples to illustrate how SVD is applied to deconvolute a titration involving a mixture of three pH indicators. One noiseless case is presented as well as two cases where either a fixed or varying noise level is present. Finally, we discuss additional deconvolutions of mixed spectra based on the use of the pseudoinverse.

One step linear reconstruction method for continuous wave diffuse optical tomography

NASA Astrophysics Data System (ADS)

Ukhrowiyah, N.; Yasin, M.

2017-09-01

The method one step linear reconstruction method for continuous wave diffuse optical tomography is proposed and demonstrated for polyvinyl chloride based material and breast phantom. Approximation which used in this method is selecting regulation coefficient and evaluating the difference between two states that corresponding to the data acquired without and with a change in optical properties. This method is used to recovery of optical parameters from measured boundary data of light propagation in the object. The research is demonstrated by simulation and experimental data. Numerical object is used to produce simulation data. Chloride based material and breast phantom sample is used to produce experimental data. Comparisons of results between experiment and simulation data are conducted to validate the proposed method. The results of the reconstruction image which is produced by the one step linear reconstruction method show that the image reconstruction almost same as the original object. This approach provides a means of imaging that is sensitive to changes in optical properties, which may be particularly useful for functional imaging used continuous wave diffuse optical tomography of early diagnosis of breast cancer.

Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Scheid, R. E., Jr.

1987-01-01

This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

The AFLOW Standard for High-throughput Materials Science Calculations

DTIC Science & Technology

2015-01-01

84602, USA fDepartment of Physics and Department of Chemistry, University of North Texas, Denton, TX 76203, USA gMaterials Science, Electrical ...inversion in the iterative subspace (RMM– DIIS ) [10]. Of the two, DBS is known to be the slower and more stable option. Additionally, the subspace...RMM– DIIS steps as needed to fulfill the dEelec condition. Later determinations of system forces are performed by a similar sequence, but only a single

Inverse Force Determination on a Small Scale Launch Vehicle Model Using a Dynamic Balance

NASA Technical Reports Server (NTRS)

Ngo, Christina L.; Powell, Jessica M.; Ross, James C.

2017-01-01

A launch vehicle can experience large unsteady aerodynamic forces in the transonic regime that, while usually only lasting for tens of seconds during launch, could be devastating if structural components and electronic hardware are not designed to account for them. These aerodynamic loads are difficult to experimentally measure and even harder to computationally estimate. The current method for estimating buffet loads is through the use of a few hundred unsteady pressure transducers and wind tunnel test. Even with a large number of point measurements, the computed integrated load is not an accurate enough representation of the total load caused by buffeting. This paper discusses an attempt at using a dynamic balance to experimentally determine buffet loads on a generic scale hammer head launch vehicle model tested at NASA Ames Research Center's 11' x 11' transonic wind tunnel. To use a dynamic balance, the structural characteristics of the model needed to be identified so that the natural modal response could be and removed from the aerodynamic forces. A finite element model was created on a simplified version of the model to evaluate the natural modes of the balance flexures, assist in model design, and to compare to experimental data. Several modal tests were conducted on the model in two different configurations to check for non-linearity, and to estimate the dynamic characteristics of the model. The experimental results were used in an inverse force determination technique with a psuedo inverse frequency response function. Due to the non linearity, the model not being axisymmetric, and inconsistent data between the two shake tests from different mounting configuration, it was difficult to create a frequency response matrix that satisfied all input and output conditions for wind tunnel configuration to accurately predict unsteady aerodynamic loads.

Adapting Better Interpolation Methods to Model Amphibious MT Data Along the Cascadian Subduction Zone.

NASA Astrophysics Data System (ADS)

Parris, B. A.; Egbert, G. D.; Key, K.; Livelybrooks, D.

2016-12-01

Magnetotellurics (MT) is an electromagnetic technique used to model the inner Earth's electrical conductivity structure. MT data can be analyzed using iterative, linearized inversion techniques to generate models imaging, in particular, conductive partial melts and aqueous fluids that play critical roles in subduction zone processes and volcanism. For example, the Magnetotelluric Observations of Cascadia using a Huge Array (MOCHA) experiment provides amphibious data useful for imaging subducted fluids from trench to mantle wedge corner. When using MOD3DEM(Egbert et al. 2012), a finite difference inversion package, we have encountered problems inverting, particularly, sea floor stations due to the strong, nearby conductivity gradients. As a work-around, we have found that denser, finer model grids near the land-sea interface produce better inversions, as characterized by reduced data residuals. This is partly to be due to our ability to more accurately capture topography and bathymetry. We are experimenting with improved interpolation schemes that more accurately track EM fields across cell boundaries, with an eye to enhancing the accuracy of the simulated responses and, thus, inversion results. We are adapting how MOD3DEM interpolates EM fields in two ways. The first seeks to improve weighting functions for interpolants to better address current continuity across grid boundaries. Electric fields are interpolated using a tri-linear spline technique, where the eight nearest electrical field estimates are each given weights determined by the technique, a kind of weighted average. We are modifying these weights to include cross-boundary conductivity ratios to better model current continuity. We are also adapting some of the techniques discussed in Shantsev et al (2014) to enhance the accuracy of the interpolated fields calculated by our forward solver, as well as to better approximate the sensitivities passed to the software's Jacobian that are used to generate a new forward model during each iteration of the inversion.

The inverse problem: Ocean tides derived from earth tide observations

NASA Technical Reports Server (NTRS)

Kuo, J. T.

1978-01-01

Indirect mapping ocean tides by means of land and island-based tidal gravity measurements is presented. The inverse scheme of linear programming is used for indirect mapping of ocean tides. Open ocean tides were measured by the numerical integration of Laplace's tidal equations.

A note on convergence of solutions of total variation regularized linear inverse problems

NASA Astrophysics Data System (ADS)

Iglesias, José A.; Mercier, Gwenael; Scherzer, Otmar

2018-05-01

In a recent paper by Chambolle et al (2017 Inverse Problems 33 015002) it was proven that if the subgradient of the total variation at the noise free data is not empty, the level-sets of the total variation denoised solutions converge to the level-sets of the noise free data with respect to the Hausdorff distance. The condition on the subgradient corresponds to the source condition introduced by Burger and Osher (2007 Multiscale Model. Simul. 6 365–95), who proved convergence rates results with respect to the Bregman distance under this condition. We generalize the result of Chambolle et al to total variation regularization of general linear inverse problems under such a source condition. As particular applications we present denoising in bounded and unbounded, convex and non convex domains, deblurring and inversion of the circular Radon transform. In all these examples the convergence result applies. Moreover, we illustrate the convergence behavior through numerical examples.

Inverse dynamics of a 3 degree of freedom spatial flexible manipulator

NASA Technical Reports Server (NTRS)

Bayo, Eduardo; Serna, M.

1989-01-01

A technique is presented for solving the inverse dynamics and kinematics of 3 degree of freedom spatial flexible manipulator. The proposed method finds the joint torques necessary to produce a specified end effector motion. Since the inverse dynamic problem in elastic manipulators is closely coupled to the inverse kinematic problem, the solution of the first also renders the displacements and rotations at any point of the manipulator, including the joints. Furthermore the formulation is complete in the sense that it includes all the nonlinear terms due to the large rotation of the links. The Timoshenko beam theory is used to model the elastic characteristics, and the resulting equations of motion are discretized using the finite element method. An iterative solution scheme is proposed that relies on local linearization of the problem. The solution of each linearization is carried out in the frequency domain. The performance and capabilities of this technique are tested through simulation analysis. Results show the potential use of this method for the smooth motion control of space telerobots.

A large inversion in the linear chromosome of Streptomyces griseus caused by replicative transposition of a new Tn3 family transposon.

PubMed

Murata, M; Uchida, T; Yang, Y; Lezhava, A; Kinashi, H

2011-04-01

We have comprehensively analyzed the linear chromosomes of Streptomyces griseus mutants constructed and kept in our laboratory. During this study, macrorestriction analysis of AseI and DraI fragments of mutant 402-2 suggested a large chromosomal inversion. The junctions of chromosomal inversion were cloned and sequenced and compared with the corresponding target sequences in the parent strain 2247. Consequently, a transposon-involved mechanism was revealed. Namely, a transposon originally located at the left target site was replicatively transposed to the right target site in an inverted direction, which generated a second copy and at the same time caused a 2.5-Mb chromosomal inversion. The involved transposon named TnSGR was grouped into a new subfamily of the resolvase-encoding Tn3 family transposons based on its gene organization. At the end, terminal diversity of S. griseus chromosomes is discussed by comparing the sequences of strains 2247 and IFO13350.

Real-time localization of mobile device by filtering method for sensor fusion

NASA Astrophysics Data System (ADS)

Fuse, Takashi; Nagara, Keita

2017-06-01

Most of the applications with mobile devices require self-localization of the devices. GPS cannot be used in indoor environment, the positions of mobile devices are estimated autonomously by using IMU. Since the self-localization is based on IMU of low accuracy, and then the self-localization in indoor environment is still challenging. The selflocalization method using images have been developed, and the accuracy of the method is increasing. This paper develops the self-localization method without GPS in indoor environment by integrating sensors, such as IMU and cameras, on mobile devices simultaneously. The proposed method consists of observations, forecasting and filtering. The position and velocity of the mobile device are defined as a state vector. In the self-localization, observations correspond to observation data from IMU and camera (observation vector), forecasting to mobile device moving model (system model) and filtering to tracking method by inertial surveying and coplanarity condition and inverse depth model (observation model). Positions of a mobile device being tracked are estimated by system model (forecasting step), which are assumed as linearly moving model. Then estimated positions are optimized referring to the new observation data based on likelihood (filtering step). The optimization at filtering step corresponds to estimation of the maximum a posterior probability. Particle filter are utilized for the calculation through forecasting and filtering steps. The proposed method is applied to data acquired by mobile devices in indoor environment. Through the experiments, the high performance of the method is confirmed.

Combined sphere-spheroid particle model for the retrieval of the microphysical aerosol parameters via regularized inversion of lidar data

NASA Astrophysics Data System (ADS)

Samaras, Stefanos; Böckmann, Christine; Nicolae, Doina

2016-06-01

In this work we propose a two-step advancement of the Mie spherical-particle model accounting for particle non-sphericity. First, a naturally two-dimensional (2D) generalized model (GM) is made, which further triggers analogous 2D re-definitions of microphysical parameters. We consider a spheroidal-particle approach where the size distribution is additionally dependent on aspect ratio. Second, we incorporate the notion of a sphere-spheroid particle mixture (PM) weighted by a non-sphericity percentage. The efficiency of these two models is investigated running synthetic data retrievals with two different regularization methods to account for the inherent instability of the inversion procedure. Our preliminary studies show that a retrieval with the PM model improves the fitting errors and the microphysical parameter retrieval and it has at least the same efficiency as the GM. While the general trend of the initial size distributions is captured in our numerical experiments, the reconstructions are subject to artifacts. Finally, our approach is applied to a measurement case yielding acceptable results.

The turbomachine blading design using S2-S1 approach

NASA Technical Reports Server (NTRS)

Luu, T. S.; Bencherif, L.; Viney, B.; Duc, J. M. Nguyen

1991-01-01

The boundary conditions corresponding to the design problem when the blades being simulated by the bound vorticity distribution are presented. The 3D flow is analyzed by the two steps S2 - S1 approach. In the first step, the number of blades is supposed to be infinite, the vortex distribution is transformed into an axisymmetric one, so that the flow field can be analyzed in a meridional plane. The thickness distribution of the blade producing the flow channel striction is taken into account by the modification of metric tensor in the continuity equation. Using the meridional stream function to define the flow field, the mass conservation is satisfied automatically. The governing equation is deduced from the relation between the azimuthal component of the vorticity and the meridional velocity. The value of the azimuthal component of the vorticity is provided by the hub to shroud equilibrium condition. This step leads to the determination of the axisymmetric stream sheets as well as the approximate camber surface of the blade. In the second step, the finite number of blades is taken into account, the inverse problem corresponding to the blade to blade flow confined in each stream sheet is analyzed. The momentum equation implies that the free vortex of the absolute velocity must be tangential to the stream sheet. The governing equation for the blade to blade flow stream function is deduced from this condition. At the beginning, the upper and the lower surfaces of the blades are created from the camber surface obtained from the first step with the assigned thickness distribution. The bound vorticity distribution and the penetrating flux conservation applied on the presumed blade surface constitute the boundary conditions of the inverse problem. The detection of this flux leads to the rectification of the geometry of the blades.

Supporting second grade lower secondary school students’ understanding of linear equation system in two variables using ethnomathematics

NASA Astrophysics Data System (ADS)

Nursyahidah, F.; Saputro, B. A.; Rubowo, M. R.

2018-03-01

The aim of this research is to know the students’ understanding of linear equation system in two variables using Ethnomathematics and to acquire learning trajectory of linear equation system in two variables for the second grade of lower secondary school students. This research used methodology of design research that consists of three phases, there are preliminary design, teaching experiment, and retrospective analysis. Subject of this study is 28 second grade students of Sekolah Menengah Pertama (SMP) 37 Semarang. The result of this research shows that the students’ understanding in linear equation system in two variables can be stimulated by using Ethnomathematics in selling buying tradition in Peterongan traditional market in Central Java as a context. All of strategies and model that was applied by students and also their result discussion shows how construction and contribution of students can help them to understand concept of linear equation system in two variables. All the activities that were done by students produce learning trajectory to gain the goal of learning. Each steps of learning trajectory of students have an important role in understanding the concept from informal to the formal level. Learning trajectory using Ethnomathematics that is produced consist of watching video of selling buying activity in Peterongan traditional market to construct linear equation in two variables, determine the solution of linear equation in two variables, construct model of linear equation system in two variables from contextual problem, and solving a contextual problem related to linear equation system in two variables.

Imaging electrical conductivity, permeability, and/or permittivity contrasts using the Born Scattering Inversion (BSI)

NASA Astrophysics Data System (ADS)

Darrh, A.; Downs, C. M.; Poppeliers, C.

2017-12-01

Born Scattering Inversion (BSI) of electromagnetic (EM) data is a geophysical imaging methodology for mapping weak conductivity, permeability, and/or permittivity contrasts in the subsurface. The high computational cost of full waveform inversion is reduced by adopting the First Born Approximation for scattered EM fields. This linearizes the inverse problem in terms of Born scattering amplitudes for a set of effective EM body sources within a 3D imaging volume. Estimation of scatterer amplitudes is subsequently achieved by solving the normal equations. Our present BSI numerical experiments entail Fourier transforming real-valued synthetic EM data to the frequency-domain, and minimizing the L2 residual between complex-valued observed and predicted data. We are testing the ability of BSI to resolve simple scattering models. For our initial experiments, synthetic data are acquired by three-component (3C) electric field receivers distributed on a plane above a single point electric dipole within a homogeneous and isotropic wholespace. To suppress artifacts, candidate Born scatterer locations are confined to a volume beneath the receiver array. Also, we explore two different numerical linear algebra algorithms for solving the normal equations: Damped Least Squares (DLS), and Non-Negative Least Squares (NNLS). Results from NNLS accurately recover the source location only for a large dense 3C receiver array, but fail when the array is decimated, or is restricted to horizontal component data. Using all receiver stations and all components per station, NNLS results are relatively insensitive to a sub-sampled frequency spectrum, suggesting that coarse frequency-domain sampling may be adequate for good target resolution. Results from DLS are insensitive to diminishing array density, but contain spatially oscillatory structure. DLS-generated images are consistently centered at the known point source location, despite an abundance of surrounding structure.

Role of zonal flows in trapped electron mode turbulence through nonlinear gyrokinetic particle and continuum simulationa)

NASA Astrophysics Data System (ADS)

Ernst, D. R.; Lang, J.; Nevins, W. M.; Hoffman, M.; Chen, Y.; Dorland, W.; Parker, S.

2009-05-01

Trapped electron mode (TEM) turbulence exhibits a rich variety of collisional and zonal flow physics. This work explores the parametric variation of zonal flows and underlying mechanisms through a series of linear and nonlinear gyrokinetic simulations, using both particle-in-cell and continuum methods. A new stability diagram for electron modes is presented, identifying a critical boundary at ηe=1, separating long and short wavelength TEMs. A novel parity test is used to separate TEMs from electron temperature gradient driven modes. A nonlinear scan of ηe reveals fine scale structure for ηe≳1, consistent with linear expectation. For ηe<1, zonal flows are the dominant saturation mechanism, and TEM transport is insensitive to ηe. For ηe>1, zonal flows are weak, and TEM transport falls inversely with a power law in ηe. The role of zonal flows appears to be connected to linear stability properties. Particle and continuum methods are compared in detail over a range of ηe=d ln Te/d ln ne values from zero to five. Linear growth rate spectra, transport fluxes, fluctuation wavelength spectra, zonal flow shearing spectra, and correlation lengths and times are in close agreement. In addition to identifying the critical parameter ηe for TEM zonal flows, this paper takes a challenging step in code verification, directly comparing very different methods of simulating simultaneous kinetic electron and ion dynamics in TEM turbulence.

Transverse Cascade and Sustenance of Turbulence in Keplerian Disks with an Azimuthal Magnetic Field

NASA Astrophysics Data System (ADS)

Gogichaishvili, D.; Mamatsashvili, G.; Horton, W.; Chagelishvili, G.; Bodo, G.

2017-10-01

The magnetorotational instability (MRI) in the sheared rotational Keplerian explains fundamental problems for both astrophysics and toroidal laboratory plasmas. The turbulence occurs before the threshold for the linear eigen modes. The work shows the turbulence occurs in nonzero toroidal magnetic field with a sheared toroidal flow velocity. We analyze the turbulence in Fourier k-space and x-space each time step to clarify the nonlinear energy-momentum transfers that produce the sustenance in the linearly stable plasma. The nonlinear process is a type 3D angular redistribution of modes in Fourier space - a transverse cascade - rather than the direct/inverse cascades. The turbulence is sustained an interplay of the linear transient growth from the radial gradient of the toroidal velocity (which is the only energy supply for the turbulence) and the transverse cascade. There is a relatively small ``vital area in Fourier space'' is crucial for the sustenance. Outside the vital area the direct cascade dominates. The interplay of the linear and nonlinear processes is generally too intertwined in k-space for a classical turbulence characterization. Subcycles occur from the interactions that maintain self-organization nonlinear turbulence. The spectral characteristics in four simulations are similar showing the universality of the sustenance mechanism of the shear flow driven MHDs-turbulence. Funded by the US Department of Energy under Grant DE-FG02-04ER54742 and the Space and Geophysics Laboratory at the University of Texas at Austin. G. Mamatsashvili is supported by the Alexander von Humboldt Foundation, Germany.

Slope tomography based on eikonal solvers and the adjoint-state method

NASA Astrophysics Data System (ADS)

Tavakoli F., B.; Operto, S.; Ribodetti, A.; Virieux, J.

2017-06-01

Velocity macromodel building is a crucial step in the seismic imaging workflow as it provides the necessary background model for migration or full waveform inversion. In this study, we present a new formulation of stereotomography that can handle more efficiently long-offset acquisition, complex geological structures and large-scale data sets. Stereotomography is a slope tomographic method based upon a semi-automatic picking of local coherent events. Each local coherent event, characterized by its two-way traveltime and two slopes in common-shot and common-receiver gathers, is tied to a scatterer or a reflector segment in the subsurface. Ray tracing provides a natural forward engine to compute traveltime and slopes but can suffer from non-uniform ray sampling in presence of complex media and long-offset acquisitions. Moreover, most implementations of stereotomography explicitly build a sensitivity matrix, leading to the resolution of large systems of linear equations, which can be cumbersome when large-scale data sets are considered. Overcoming these issues comes with a new matrix-free formulation of stereotomography: a factored eikonal solver based on the fast sweeping method to compute first-arrival traveltimes and an adjoint-state formulation to compute the gradient of the misfit function. By solving eikonal equation from sources and receivers, we make the computational cost proportional to the number of sources and receivers while it is independent of picked events density in each shot and receiver gather. The model space involves the subsurface velocities and the scatterer coordinates, while the dips of the reflector segments are implicitly represented by the spatial support of the adjoint sources and are updated through the joint localization of nearby scatterers. We present an application on the complex Marmousi model for a towed-streamer acquisition and a realistic distribution of local events. We show that the estimated model, built without any prior knowledge of the velocities, provides a reliable initial model for frequency-domain FWI of long-offset data for a starting frequency of 4 Hz, although some artefacts at the reservoir level result from a deficit of illumination. This formulation of slope tomography provides a computationally efficient alternative to waveform inversion method such as reflection waveform inversion or differential-semblance optimization to build an initial model for pre-stack depth migration and conventional FWI.

Linear Estimation of Particle Bulk Parameters from Multi-Wavelength Lidar Measurements

NASA Technical Reports Server (NTRS)

Veselovskii, Igor; Dubovik, Oleg; Kolgotin, A.; Korenskiy, M.; Whiteman, D. N.; Allakhverdiev, K.; Huseyinoglu, F.

2012-01-01

An algorithm for linear estimation of aerosol bulk properties such as particle volume, effective radius and complex refractive index from multiwavelength lidar measurements is presented. The approach uses the fact that the total aerosol concentration can well be approximated as a linear combination of aerosol characteristics measured by multiwavelength lidar. Therefore, the aerosol concentration can be estimated from lidar measurements without the need to derive the size distribution, which entails more sophisticated procedures. The definition of the coefficients required for the linear estimates is based on an expansion of the particle size distribution in terms of the measurement kernels. Once the coefficients are established, the approach permits fast retrieval of aerosol bulk properties when compared with the full regularization technique. In addition, the straightforward estimation of bulk properties stabilizes the inversion making it more resistant to noise in the optical data. Numerical tests demonstrate that for data sets containing three aerosol backscattering and two extinction coefficients (so called 3 + 2 ) the uncertainties in the retrieval of particle volume and surface area are below 45% when input data random uncertainties are below 20 %. Moreover, using linear estimates allows reliable retrievals even when the number of input data is reduced. To evaluate the approach, the results obtained using this technique are compared with those based on the previously developed full inversion scheme that relies on the regularization procedure. Both techniques were applied to the data measured by multiwavelength lidar at NASA/GSFC. The results obtained with both methods using the same observations are in good agreement. At the same time, the high speed of the retrieval using linear estimates makes the method preferable for generating aerosol information from extended lidar observations. To demonstrate the efficiency of the method, an extended time series of observations acquired in Turkey in May 2010 was processed using the linear estimates technique permitting, for what we believe to be the first time, temporal-height distributions of particle parameters.

On the solution of the generalized wave and generalized sine-Gordon equations

NASA Technical Reports Server (NTRS)

Ablowitz, M. J.; Beals, R.; Tenenblat, K.

1986-01-01

The generalized wave equation and generalized sine-Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two-dimensional versions. In this paper, a system of linear differential equations is associated with these equations, and it is shown how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial-boundary value problem is solved for these equations.

anisotropic microseismic focal mechanism inversion by waveform imaging matching

NASA Astrophysics Data System (ADS)

Wang, L.; Chang, X.; Wang, Y.; Xue, Z.

2016-12-01

The focal mechanism is one of the most important parameters in source inversion, for both natural earthquakes and human-induced seismic events. It has been reported to be useful for understanding stress distribution and evaluating the fracturing effect. The conventional focal mechanism inversion method picks the first arrival waveform of P wave. This method assumes the source as a Double Couple (DC) type and the media isotropic, which is usually not the case for induced seismic focal mechanism inversion. For induced seismic events, the inappropriate source and media model in inversion processing, by introducing ambiguity or strong simulation errors, will seriously reduce the inversion effectiveness. First, the focal mechanism contains significant non-DC source type. Generally, the source contains three components: DC, isotropic (ISO) and the compensated linear vector dipole (CLVD), which makes focal mechanisms more complicated. Second, the anisotropy of media will affect travel time and waveform to generate inversion bias. The common way to describe focal mechanism inversion is based on moment tensor (MT) inversion which can be decomposed into the combination of DC, ISO and CLVD components. There are two ways to achieve MT inversion. The wave-field migration method is applied to achieve moment tensor imaging. This method can construct elements imaging of MT in 3D space without picking the first arrival, but the retrieved MT value is influenced by imaging resolution. The full waveform inversion is employed to retrieve MT. In this method, the source position and MT can be reconstructed simultaneously. However, this method needs vast numerical calculation. Moreover, the source position and MT also influence each other in the inversion process. In this paper, the waveform imaging matching (WIM) method is proposed, which combines source imaging with waveform inversion for seismic focal mechanism inversion. Our method uses the 3D tilted transverse isotropic (TTI) elastic wave equation to approximate wave propagating in anisotropic media. First, a source imaging procedure is employed to obtain the source position. Second, we refine a waveform inversion algorithm to retrieve MT. We also use a microseismic data set recorded in surface acquisition to test our method.

Manipulating the Rate-Limiting Step in Water Oxidation Catalysis by Ruthenium Bipyridine–Dicarboxylate Complexes

DOE PAGES

Shaffer, David W.; Xie, Yan; Szalda, David J.; ...

2016-11-01

In order to gain a deeper mechanistic understanding of water oxidation by [(bda)Ru(L) 2] catalysts (bdaH 2 = [2,2'-bipyridine]-6,6'-dicarboxylic acid; L = pyridine-type ligand), a series of modified catalysts with one and two trifluoromethyl groups in the 4 position of the bda 2– ligand was synthesized and studied using stopped-flow kinetics. The additional $-$CF 3 groups increased the oxidation potentials for the catalysts and enhanced the rate of electrocatalytic water oxidation at low pH. Stopped-flow measurements of cerium(IV)-driven water oxidation at pH 1 revealed two distinct kinetic regimes depending on catalyst concentration. At relatively high catalyst concentration (ca. ≥10 –4more » M), the rate-determining step (RDS) was a proton-coupled oxidation of the catalyst by cerium(IV) with direct kinetic isotope effects (KIE > 1). At low catalyst concentration (ca. ≤10 –6 M), the RDS was a bimolecular step with k H/k D ≈ 0.8. The results support a catalytic mechanism involving coupling of two catalyst molecules. The rate constants for both RDSs were determined for all six catalysts studied. The presence of $-$CF 3 groups had inverse effects on the two steps, with the oxidation step being fastest for the unsubstituted complexes and the bimolecular step being faster for the most electron-deficient complexes. Finally, though the axial ligands studied here did not significantly affect the oxidation potentials of the catalysts, the nature of the ligand was found to be important not only in the bimolecular step but also in facilitating electron transfer from the metal center to the sacrificial oxidant.« less

Prevalence of gestational diabetes mellitus according to the different criterias

PubMed Central

Akgöl, Evren; Abuşoğlu, Sedat; Gün, Faik Deniz; Ünlü, Ali

2017-01-01

Objective: The two-step approach recommended by the National Diabetes Data Group (NDDG), Carpenter and Coustan (C&C), and O’Sullivan, and the single-step approach recommended by the International Association of Diabetes and Pregnancy Study Group (IADPSG) are used to diagnose gestational diabetes mellitus (GDM). We aimed to determine GDM prevalence and to compare the two-step and single-step approaches used in the southeastern region of Turkey. Materials and Methods: In total, 3048 records of pregnant women screened for GDM between 2008 and 2014 were retrospectively extracted from our laboratory information system. GDM was defined according to the criteria of NDDG, C&C, and O’Sullivan between in 2008 and 2011, and according to those of the IADPSG between 2012 and 2014. Demographic variables were compared using student’s t-test. The linear trends in GDM prevalence with age were calculated using logistic regression. Results: GDM prevalence was found as 4.8%, 8%, and 13.4% using the NDDG, C&C, and O’Sullivan two-step approach, respectively, and 22.3% with the IADPSG single-step approach. GDM prevalence increased with increasing age in both approaches. Conclusion: GDM prevalence was higher using the single-step approach than with the two-step approach. There was a significant increase in GDM prevalence using the IADPSG criteria. PMID:28913130

A variable-step-size robust delta modulator.

NASA Technical Reports Server (NTRS)

Song, C. L.; Garodnick, J.; Schilling, D. L.

1971-01-01

Description of an analytically obtained optimum adaptive delta modulator-demodulator configuration. The device utilizes two past samples to obtain a step size which minimizes the mean square error for a Markov-Gaussian source. The optimum system is compared, using computer simulations, with a linear delta modulator and an enhanced Abate delta modulator. In addition, the performance is compared to the rate distortion bound for a Markov source. It is shown that the optimum delta modulator is neither quantization nor slope-overload limited. The highly nonlinear equations obtained for the optimum transmitter and receiver are approximated by piecewise-linear equations in order to obtain system equations which can be transformed into hardware. The derivation of the experimental system is presented.

Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology.

PubMed

Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F

2010-07-01

Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

INFO-RNA--a fast approach to inverse RNA folding.

PubMed

Busch, Anke; Backofen, Rolf

2006-08-01

The structure of RNA molecules is often crucial for their function. Therefore, secondary structure prediction has gained much interest. Here, we consider the inverse RNA folding problem, which means designing RNA sequences that fold into a given structure. We introduce a new algorithm for the inverse folding problem (INFO-RNA) that consists of two parts; a dynamic programming method for good initial sequences and a following improved stochastic local search that uses an effective neighbor selection method. During the initialization, we design a sequence that among all sequences adopts the given structure with the lowest possible energy. For the selection of neighbors during the search, we use a kind of look-ahead of one selection step applying an additional energy-based criterion. Afterwards, the pre-ordered neighbors are tested using the actual optimization criterion of minimizing the structure distance between the target structure and the mfe structure of the considered neighbor. We compared our algorithm to RNAinverse and RNA-SSD for artificial and biological test sets. Using INFO-RNA, we performed better than RNAinverse and in most cases, we gained better results than RNA-SSD, the probably best inverse RNA folding tool on the market. www.bioinf.uni-freiburg.de?Subpages/software.html.

Efficient computation of the genomic relationship matrix and other matrices used in single-step evaluation.

PubMed

Aguilar, I; Misztal, I; Legarra, A; Tsuruta, S

2011-12-01

Genomic evaluations can be calculated using a unified procedure that combines phenotypic, pedigree and genomic information. Implementation of such a procedure requires the inverse of the relationship matrix based on pedigree and genomic relationships. The objective of this study was to investigate efficient computing options to create relationship matrices based on genomic markers and pedigree information as well as their inverses. SNP maker information was simulated for a panel of 40 K SNPs, with the number of genotyped animals up to 30 000. Matrix multiplication in the computation of the genomic relationship was by a simple 'do' loop, by two optimized versions of the loop, and by a specific matrix multiplication subroutine. Inversion was by a generalized inverse algorithm and by a LAPACK subroutine. With the most efficient choices and parallel processing, creation of matrices for 30 000 animals would take a few hours. Matrices required to implement a unified approach can be computed efficiently. Optimizations can be either by modifications of existing code or by the use of efficient automatic optimizations provided by open source or third-party libraries. © 2011 Blackwell Verlag GmbH.

3D linear inversion of magnetic susceptibility data acquired by frequency domain EMI

NASA Astrophysics Data System (ADS)

Thiesson, J.; Tabbagh, A.; Simon, F.-X.; Dabas, M.

2017-01-01

Low induction number EMI instruments are able to simultaneously measure a soil's apparent magnetic susceptibility and electrical conductivity. This family of dual measurement instruments is highly useful for the analysis of soils and archeological sites. However, the electromagnetic properties of soils are found to vary over considerably different ranges: whereas their electrical conductivity varies from ≤ 0.1 to ≥ 100 mS/m, their relative magnetic permeability remains within a very small range, between 1.0001 and 1.01 SI. Consequently, although apparent conductivity measurements need to be inverted using non-linear processes, the variations of the apparent magnetic susceptibility can be approximated through the use of linear processes, as in the case of the magnetic prospection technique. Our proposed 3D inversion algorithm starts from apparent susceptibility data sets, acquired using different instruments over a given area. A reference vertical profile is defined by considering the mode of the vertical distributions of both the electrical resistivity and of the magnetic susceptibility. At each point of the mapped area, the reference vertical profile response is subtracted to obtain the apparent susceptibility variation dataset. A 2D horizontal Fourier transform is applied to these variation datasets and to the dipole (impulse) response of each instrument, a (vertical) 1D inversion is performed at each point in the spectral domain, and finally the resulting dataset is inverse transformed to restore the apparent 3D susceptibility variations. It has been shown that when applied to synthetic results, this method is able to correct the apparent deformations of a buried object resulting from the geometry of the instrument, and to restore reliable quantitative susceptibility contrasts. It also allows the thin layer solution, similar to that used in magnetic prospection, to be implemented. When applied to field data it initially delivers a level of contrast comparable to that obtained with a non-linear 3D inversion. Over four different sites, this method is able to produce, following an acceptably short computation time, realistic values for the lateral and vertical variations in susceptibility, which are significantly different to those given by a point-by-point 1D inversion.

Minimum number of clusters and comparison of analysis methods for cross sectional stepped wedge cluster randomised trials with binary outcomes: A simulation study.

PubMed

Barker, Daniel; D'Este, Catherine; Campbell, Michael J; McElduff, Patrick

2017-03-09

Stepped wedge cluster randomised trials frequently involve a relatively small number of clusters. The most common frameworks used to analyse data from these types of trials are generalised estimating equations and generalised linear mixed models. A topic of much research into these methods has been their application to cluster randomised trial data and, in particular, the number of clusters required to make reasonable inferences about the intervention effect. However, for stepped wedge trials, which have been claimed by many researchers to have a statistical power advantage over the parallel cluster randomised trial, the minimum number of clusters required has not been investigated. We conducted a simulation study where we considered the most commonly used methods suggested in the literature to analyse cross-sectional stepped wedge cluster randomised trial data. We compared the per cent bias, the type I error rate and power of these methods in a stepped wedge trial setting with a binary outcome, where there are few clusters available and when the appropriate adjustment for a time trend is made, which by design may be confounding the intervention effect. We found that the generalised linear mixed modelling approach is the most consistent when few clusters are available. We also found that none of the common analysis methods for stepped wedge trials were both unbiased and maintained a 5% type I error rate when there were only three clusters. Of the commonly used analysis approaches, we recommend the generalised linear mixed model for small stepped wedge trials with binary outcomes. We also suggest that in a stepped wedge design with three steps, at least two clusters be randomised at each step, to ensure that the intervention effect estimator maintains the nominal 5% significance level and is also reasonably unbiased.

Age and neurodegeneration imaging biomarkers in persons with Alzheimer disease dementia

PubMed Central

Jack, Clifford R.; Wiste, Heather J.; Weigand, Stephen D.; Vemuri, Prashanthi; Lowe, Val J.; Kantarci, Kejal; Gunter, Jeffrey L.; Senjem, Matthew L.; Mielke, Michelle M.; Machulda, Mary M.; Roberts, Rosebud O.; Boeve, Bradley F.; Jones, David T.; Petersen, Ronald C.

2016-01-01

Objective: To examine neurodegenerative imaging biomarkers in Alzheimer disease (AD) dementia from middle to old age. Methods: Persons with AD dementia and elevated brain β-amyloid with Pittsburgh compound B (PiB)-PET imaging underwent [18F]-fluorodeoxyglucose (FDG)-PET and structural MRI. We evaluated 3 AD-related neurodegeneration biomarkers: hippocampal volume adjusted for total intracranial volume (HVa), FDG standardized uptake value ratio (SUVR) in regions of interest linked to AD, and cortical thickness in AD-related regions of interest. We examined associations of each biomarker with age and evaluated age effects on cutpoints defined by the 90th percentile in AD dementia. We assembled an age-, sex-, and intracranial volume-matched group of 194 similarly imaged clinically normal (CN) persons. Results: The 97 participants with AD dementia (aged 49–93 years) had PiB SUVR ≥1.8. A nonlinear (inverted-U) relationship between FDG SUVR and age was seen in the AD group but an inverse linear relationship with age was seen in the CN group. Cortical thickness had an inverse linear relationship with age in AD but a nonlinear (flat, then inverse linear) relationship in the CN group. HVa showed an inverse linear relationship with age in both AD and CN groups. Age effects on 90th percentile cutpoints were small for FDG SUVR and cortical thickness, but larger for HVa. Conclusions: In persons with AD dementia with elevated PiB SUVR, values of each neurodegeneration biomarker were associated with age. Cortical thickness had the smallest differences in 90th percentile cutpoints from middle to old age, and HVa the largest differences. PMID:27421543

Age and neurodegeneration imaging biomarkers in persons with Alzheimer disease dementia.

PubMed

Knopman, David S; Jack, Clifford R; Wiste, Heather J; Weigand, Stephen D; Vemuri, Prashanthi; Lowe, Val J; Kantarci, Kejal; Gunter, Jeffrey L; Senjem, Matthew L; Mielke, Michelle M; Machulda, Mary M; Roberts, Rosebud O; Boeve, Bradley F; Jones, David T; Petersen, Ronald C

2016-08-16

To examine neurodegenerative imaging biomarkers in Alzheimer disease (AD) dementia from middle to old age. Persons with AD dementia and elevated brain β-amyloid with Pittsburgh compound B (PiB)-PET imaging underwent [(18)F]-fluorodeoxyglucose (FDG)-PET and structural MRI. We evaluated 3 AD-related neurodegeneration biomarkers: hippocampal volume adjusted for total intracranial volume (HVa), FDG standardized uptake value ratio (SUVR) in regions of interest linked to AD, and cortical thickness in AD-related regions of interest. We examined associations of each biomarker with age and evaluated age effects on cutpoints defined by the 90th percentile in AD dementia. We assembled an age-, sex-, and intracranial volume-matched group of 194 similarly imaged clinically normal (CN) persons. The 97 participants with AD dementia (aged 49-93 years) had PiB SUVR ≥1.8. A nonlinear (inverted-U) relationship between FDG SUVR and age was seen in the AD group but an inverse linear relationship with age was seen in the CN group. Cortical thickness had an inverse linear relationship with age in AD but a nonlinear (flat, then inverse linear) relationship in the CN group. HVa showed an inverse linear relationship with age in both AD and CN groups. Age effects on 90th percentile cutpoints were small for FDG SUVR and cortical thickness, but larger for HVa. In persons with AD dementia with elevated PiB SUVR, values of each neurodegeneration biomarker were associated with age. Cortical thickness had the smallest differences in 90th percentile cutpoints from middle to old age, and HVa the largest differences. © 2016 American Academy of Neurology.

Ankle instability effects on joint position sense when stepping across the active movement extent discrimination apparatus.

PubMed

Witchalls, Jeremy; Waddington, Gordon; Blanch, Peter; Adams, Roger

2012-01-01

Individuals with and without functional ankle instability have been tested for deficits in lower limb proprioception with varied results. To determine whether a new protocol for testing participants' joint position sense during stepping is reliable and can detect differences between participants with unstable and stable ankles. Descriptive laboratory study. University clinical laboratory. Sample of convenience involving 21 young adult university students and staff. Ankle stability was categorized by score on the Cumberland Ankle Instability Tool; 13 had functional ankle instability, 8 had healthy ankles. Test-retest of ankle joint position sense when stepping onto and across the Active Movement Extent Discrimination Apparatus twice, separated by an interim test, standing still on the apparatus and moving only 1 ankle into inversion. Difference in scores between groups with stable and unstable ankles and between test repeats. Participants with unstable ankles were worse at differentiating between inversion angles underfoot in both testing protocols. On repeated testing with the stepping protocol, performance of the group with unstable ankles was improved (Cohen d = 1.06, P = .006), whereas scores in the stable ankle group did not change in the second test (Cohen d = 0.04, P = .899). Despite this improvement, the unstable group remained worse at differentiating inversion angles on the stepping retest (Cohen d = 0.99, P = .020). The deficits on proprioceptive tests shown by individuals with functional ankle instability improved with repeated exposure to the test situation. The learning effect may be the result of systematic exposure to ankle-angle variation that led to movement-specific learning or increased confidence when stepping across the apparatus.

Ion acoustic wave assisted laser beat wave terahertz generation in a plasma channel

NASA Astrophysics Data System (ADS)

Tyagi, Yachna; Tripathi, Deepak; Walia, Keshav; Garg, Deepak

2018-04-01

Resonant excitation of terahertz (THz) radiation by non-linear mixing of two lasers in the presence of an electrostatic wave is investigated. The electrostatic wave assists in k matching and contributes to non-linear coupling. In this plasma channel, the electron plasma frequency becomes minimum on the axis. The beat frequency ponderomotive force imparts an oscillating velocity to the electrons. In the presence of an ion-acoustic wave, density perturbation due to the ion-acoustic wave couples with the oscillating velocity of the electrons and give rise to non-linear current that gives rise to an ion-acoustic wave frequency assisted THz radiation field. The normalized field amplitude of ion acoustic wave assisted THz varies inversely for ω/ωp . The field amplitude of ion acoustic wave assisted THz decreases as ω/ωp increases.

A General Method for Solving Systems of Non-Linear Equations

NASA Technical Reports Server (NTRS)

Nachtsheim, Philip R.; Deiss, Ron (Technical Monitor)

1995-01-01

The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.

Interactive Inverse Groundwater Modeling - Addressing User Fatigue

NASA Astrophysics Data System (ADS)

Singh, A.; Minsker, B. S.

2006-12-01

This paper builds on ongoing research on developing an interactive and multi-objective framework to solve the groundwater inverse problem. In this work we solve the classic groundwater inverse problem of estimating a spatially continuous conductivity field, given field measurements of hydraulic heads. The proposed framework is based on an interactive multi-objective genetic algorithm (IMOGA) that not only considers quantitative measures such as calibration error and degree of regularization, but also takes into account expert knowledge about the structure of the underlying conductivity field expressed as subjective rankings of potential conductivity fields by the expert. The IMOGA converges to the optimal Pareto front representing the best trade- off among the qualitative as well as quantitative objectives. However, since the IMOGA is a population-based iterative search it requires the user to evaluate hundreds of solutions. This leads to the problem of 'user fatigue'. We propose a two step methodology to combat user fatigue in such interactive systems. The first step is choosing only a few highly representative solutions to be shown to the expert for ranking. Spatial clustering is used to group the search space based on the similarity of the conductivity fields. Sampling is then carried out from different clusters to improve the diversity of solutions shown to the user. Once the expert has ranked representative solutions from each cluster a machine learning model is used to 'learn user preference' and extrapolate these for the solutions not ranked by the expert. We investigate different machine learning models such as Decision Trees, Bayesian learning model, and instance based weighting to model user preference. In addition, we also investigate ways to improve the performance of these models by providing information about the spatial structure of the conductivity fields (which is what the expert bases his or her rank on). Results are shown for each of these machine learning models and the advantages and disadvantages for each approach are discussed. These results indicate that using the proposed two-step methodology leads to significant reduction in user-fatigue without deteriorating the solution quality of the IMOGA.

A comprehensive inversion approach for feedforward compensation of piezoactuator system at high frequency

NASA Astrophysics Data System (ADS)

Tian, Lizhi; Xiong, Zhenhua; Wu, Jianhua; Ding, Han

2016-09-01

Motion control of the piezoactuator system over broadband frequencies is limited due to its inherent hysteresis and system dynamics. One of the suggested ways is to use feedforward controller to linearize the input-output relationship of the piezoactuator system. Although there have been many feedforward approaches, it is still a challenge to develop feedforward controller for the piezoactuator system at high frequency. Hence, this paper presents a comprehensive inversion approach in consideration of the coupling of hysteresis and dynamics. In this work, the influence of dynamics compensation on the input-output relationship of the piezoactuator system is investigated first. With system dynamics compensation, the input-output relationship of the piezoactuator system will be further represented as rate-dependent nonlinearity due to the inevitable dynamics compensation error, especially at high frequency. Base on this result, the feedforward controller composed by a cascade of linear dynamics inversion and rate-dependent nonlinearity inversion is developed. Then, the system identification of the comprehensive inversion approach is proposed. Finally, experimental results show that the proposed approach can improve the performance on tracking of both periodic and non-periodic trajectories at medium and high frequency compared with the conventional feedforward approaches.

Remote sensing of environmental particulate pollutants - Optical methods for determinations of size distribution and complex refractive index

NASA Technical Reports Server (NTRS)

Fymat, A. L.

1978-01-01

A unifying approach, based on a generalization of Pearson's differential equation of statistical theory, is proposed for both the representation of particulate size distribution and the interpretation of radiometric measurements in terms of this parameter. A single-parameter gamma-type distribution is introduced, and it is shown that inversion can only provide the dimensionless parameter, r/ab (where r = particle radius, a = effective radius, b = effective variance), at least when the distribution vanishes at both ends. The basic inversion problem in reconstructing the particle size distribution is analyzed, and the existing methods are reviewed (with emphasis on their capabilities) and classified. A two-step strategy is proposed for simultaneously determining the complex refractive index and reconstructing the size distribution of atmospheric particulates.

Direct and inverse theorems on approximation by root functions of a regular boundary-value problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Radzievskii, G V

2006-08-31

One considers the spectral problem x{sup (n)}+ Fx={lambda}x with boundary conditions U{sub j}(x)=0, j=1,...,n, for functions x on [0,1]. It is assumed that F is a linear bounded operator from the Hoelder space C{sup {gamma}}, {gamma} element of [0,n-1), into L{sub 1} and the U{sub j} are bounded linear functionals on C{sup k{sub j}} with k{sub j} element of {l_brace}0,...,n- 1{r_brace}. Let P{sub {zeta}} be the linear span of the root functions of the problem x{sup (n)}+ Fx={lambda}x, U{sub j}(x)=0, j=1,...,n, corresponding to the eigenvalues {lambda}{sub k} with |{lambda}{sub k}|<{zeta}{sup n}, and let E{sub {zeta}}(f){sub W{sub p}{sup l}}:=inf{l_brace}||f-g||{sub W{sub p}{supmore » l}}:g element of P{sub {zeta}}{r_brace}. An estimate of E{sub {zeta}}(f){sub W{sub p}{sup l}} is obtained in terms of the K-functional K({zeta}{sup -m},f;W{sub p}{sup l},W{sub p,U}{sup l+m}):= inf{l_brace}||f-x||{sub W{sub p}{sup l}}+{zeta}{sup -m}||x||{sub W{sub p}{sup l}{sup +}{sup m}}:x element of W{sub p}{sup l+m}, U{sub j}(x)=0 for k{sub j}

A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

NASA Astrophysics Data System (ADS)

Rawy, E. K.

2018-06-01

We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.

New methodology for mechanical characterization of human superficial facial tissue anisotropic behaviour in vivo.

PubMed

Then, C; Stassen, B; Depta, K; Silber, G

2017-07-01

Mechanical characterization of human superficial facial tissue has important applications in biomedical science, computer assisted forensics, graphics, and consumer goods development. Specifically, the latter may include facial hair removal devices. Predictive accuracy of numerical models and their ability to elucidate biomechanically relevant questions depends on the acquisition of experimental data and mechanical tissue behavior representation. Anisotropic viscoelastic behavioral characterization of human facial tissue, deformed in vivo with finite strain, however, is sparse. Employing an experimental-numerical approach, a procedure is presented to evaluate multidirectional tensile properties of superficial tissue layers of the face in vivo. Specifically, in addition to stress relaxation, displacement-controlled multi-step ramp-and-hold protocols were performed to separate elastic from inelastic properties. For numerical representation, an anisotropic hyperelastic material model in conjunction with a time domain linear viscoelasticity formulation with Prony series was employed. Model parameters were inversely derived, employing finite element models, using multi-criteria optimization. The methodology provides insight into mechanical superficial facial tissue properties. Experimental data shows pronounced anisotropy, especially with large strain. The stress relaxation rate does not depend on the loading direction, but is strain-dependent. Preconditioning eliminates equilibrium hysteresis effects and leads to stress-strain repeatability. In the preconditioned state tissue stiffness and hysteresis insensitivity to strain rate in the applied range is evident. The employed material model fits the nonlinear anisotropic elastic results and the viscoelasticity model reasonably reproduces time-dependent results. Inversely deduced maximum anisotropic long-term shear modulus of linear elasticity is G ∞,max aniso =2.43kPa and instantaneous initial shear modulus at an applied rate of ramp loading is G 0,max aniso =15.38kPa. Derived mechanical model parameters constitute a basis for complex skin interaction simulation. Copyright © 2017. Published by Elsevier Ltd.

A linear-encoding model explains the variability of the target morphology in regeneration

PubMed Central

Lobo, Daniel; Solano, Mauricio; Bubenik, George A.; Levin, Michael

2014-01-01

A fundamental assumption of today's molecular genetics paradigm is that complex morphology emerges from the combined activity of low-level processes involving proteins and nucleic acids. An inherent characteristic of such nonlinear encodings is the difficulty of creating the genetic and epigenetic information that will produce a given self-assembling complex morphology. This ‘inverse problem’ is vital not only for understanding the evolution, development and regeneration of bodyplans, but also for synthetic biology efforts that seek to engineer biological shapes. Importantly, the regenerative mechanisms in deer antlers, planarian worms and fiddler crabs can solve an inverse problem: their target morphology can be altered specifically and stably by injuries in particular locations. Here, we discuss the class of models that use pre-specified morphological goal states and propose the existence of a linear encoding of the target morphology, making the inverse problem easy for these organisms to solve. Indeed, many model organisms such as Drosophila, hydra and Xenopus also develop according to nonlinear encodings producing linear encodings of their final morphologies. We propose the development of testable models of regeneration regulation that combine emergence with a top-down specification of shape by linear encodings of target morphology, driving transformative applications in biomedicine and synthetic bioengineering. PMID:24402915

A comparison of lidar inversion methods for cirrus applications

NASA Technical Reports Server (NTRS)

Elouragini, Salem; Flamant, Pierre H.

1992-01-01

Several methods for inverting the lidar equation are suggested as means to derive the cirrus optical properties (beta backscatter, alpha extinction coefficients, and delta optical depth) at one wavelength. The lidar equation can be inverted in a linear or logarithmic form; either solution assumes a linear relationship: beta = kappa(alpha), where kappa is the lidar ratio. A number of problems prevent us from calculating alpha (or beta) with a good accuracy. Some of these are as follows: (1) the multiple scattering effect (most authors neglect it); (2) an absolute calibration of the lidar system (difficult and sometimes not possible); (3) lack of accuracy on the lidar ratio k (taken as constant, but in fact it varies with range and cloud species); and (4) the determination of boundary condition for logarithmic solution which depends on signal to noise ration (SNR) at cloud top. An inversion in a linear form needs an absolute calibration of the system. In practice one uses molecular backscattering below the cloud to calibrate the system. This method is not permanent because the lower atmosphere turbidity is variable. For a logarithmic solution, a reference extinction coefficient (alpha(sub f)) at cloud top is required. Several methods to determine alpha(sub f) were suggested. We tested these methods at low SNR. This led us to propose two new methods referenced as S1 and S2.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahn, Cheol Hyoun; Hee Kim, So; Gu Yun, Myeong

In this study, we proposed the artificially designed channel structure in oxide thin-film transistors (TFTs) called a “step-composition gradient channel.” We demonstrated Al step-composition gradient Al-Zn-O (AZO) channel structures consisting of three AZO layers with different Al contents. The effects of stacking sequence in the step-composition gradient channel on performance and electrical stability of bottom-gate TFT devices were investigated with two channels of inverse stacking order (ascending/descending step-composition). The TFT with ascending step-composition channel structure (5 → 10 → 14 at. % Al composition) showed relatively negative threshold voltage (−3.7 V) and good instability characteristics with a reduced threshold voltage shift (Δmore » 1.4 V), which was related to the alignment of the conduction band off-set within the channel layer depending on the Al contents. Finally, the reduced Al composition in the initial layer of ascending step-composition channel resulted in the best field effect mobility of 4.5 cm{sup 2}/V s. We presented a unique active layer of the “step-composition gradient channel” in the oxide TFTs and explained the mechanism of adequate channel design.« less