Reflection Matrix Method for Controlling Light After Reflection From a Diffuse Scattering Surface

DTIC Science & Technology

2016-12-22

reflective inverse diffusion, which was a proof-of-concept experiment that used phase modulation to shape the wavefront of a laser causing it to refocus...after reflection from a rough surface. By refocusing the light, reflective inverse diffusion has the potential to eliminate the complex radiometric model...photography. However, the initial reflective inverse diffusion experiments provided no mathematical background and were conducted under the premise that the

Tracer counterpermeation analysis of diffusivity in finite-length nanopores with and without single-file dynamics

DOE PAGES

Ackerman, David M.; Evans, James W.

2017-01-19

Here, we perform a tracer counterpermeation (TCP) analysis for a stochastic model of diffusive transport through a narrow linear pore where passing of species within the pore is inhibited or even excluded (single-file diffusion). TCP involves differently labeled but otherwise identical particles from two decoupled infinite reservoirs adsorbing into opposite ends of the pore, and desorbing from either end. In addition to transient behavior, we assess steady-state concentration profiles, spatial correlations, particle number fluctuations, and diffusion fluxes through the pore. From the profiles and fluxes, we determine a generalized tracer diffusion coefficient D tr(x), at various positions x within themore » pore. D tr(x) has a plateau value in the pore center scaling inversely with the pore length, but it is enhanced near the pore openings. The latter feature reflects the effect of fluctuations in adsorption and desorption, and it is also associated with a nontrivial scaling of the concentration profiles near the pore openings.« less

Tracer counterpermeation analysis of diffusivity in finite-length nanopores with and without single-file dynamics

NASA Astrophysics Data System (ADS)

Ackerman, David M.; Evans, James W.

2017-01-01

We perform a tracer counterpermeation (TCP) analysis for a stochastic model of diffusive transport through a narrow linear pore where passing of species within the pore is inhibited or even excluded (single-file diffusion). TCP involves differently labeled but otherwise identical particles from two decoupled infinite reservoirs adsorbing into opposite ends of the pore, and desorbing from either end. In addition to transient behavior, we assess steady-state concentration profiles, spatial correlations, particle number fluctuations, and diffusion fluxes through the pore. From the profiles and fluxes, we determine a generalized tracer diffusion coefficient Dtr(x ) , at various positions x within the pore. Dtr(x ) has a plateau value in the pore center scaling inversely with the pore length, but it is enhanced near the pore openings. The latter feature reflects the effect of fluctuations in adsorption and desorption, and it is also associated with a nontrivial scaling of the concentration profiles near the pore openings.

Measuring diffusion-relaxation correlation maps using non-uniform field gradients of single-sided NMR devices.

PubMed

Nogueira d'Eurydice, Marcel; Galvosas, Petrik

2014-11-01

Single-sided NMR systems are becoming a relevant tool in industry and laboratory environments due to their low cost, low maintenance and capacity to evaluate quantity and quality of hydrogen based materials. The performance of such devices has improved significantly over the last decade, providing increased field homogeneity, field strength and even controlled static field gradients. For a class of these devices, the configuration of the permanent magnets provides a linear variation of the magnetic field and can be used in diffusion measurements. However, magnet design depends directly on its application and, according to the purpose, the field homogeneity may significantly be compromised. This may prevent the determination of diffusion properties of fluids based on the natural inhomogeneity of the field using known techniques. This work introduces a new approach that extends the applicability of diffusion-editing CPMG experiments to NMR devices with highly inhomogeneous magnetic fields, which do not vary linearly in space. Herein, we propose a method to determine a custom diffusion kernel based on the gradient distribution, which can be seen as a signature of each NMR device. This new diffusion kernel is then utilised in the 2D inverse Laplace transform (2D ILT) in order to determine diffusion-relaxation correlation maps of homogeneous multi-phasic fluids. The experiments were performed using NMR MObile Lateral Explore (MOLE), which is a single-sided NMR device designed to maximise the volume at the sweet spot with enhanced depth penetration. Copyright © 2014 Elsevier Inc. All rights reserved.

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.

Exact Solutions of Coupled Multispecies Linear Reaction–Diffusion Equations on a Uniformly Growing Domain

PubMed Central

Simpson, Matthew J.; Sharp, Jesse A.; Morrow, Liam C.; Baker, Ruth E.

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit. PMID:26407013

Exact Solutions of Coupled Multispecies Linear Reaction-Diffusion Equations on a Uniformly Growing Domain.

PubMed

Simpson, Matthew J; Sharp, Jesse A; Morrow, Liam C; Baker, Ruth E

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction-diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction-diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction-diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially-confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially-confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Undetermined Coefficient Problems for Quasi-Linear Parabolic Equations

DTIC Science & Technology

1989-12-18

a student of John Burns, spent 3 years at Brown working with Tom Banks. His speciality is in control theory, in particular for viscoelastic...diffusion equation, SIAM J. Appld Maih, 39, (2), (1980), 272-289. [ 3 ] J. R. Cannon and H. M. Yin, A uniqueness theorem for a class of parabolic inverse...2.6) where H is a C’ function. This equation is of second kind Volterra type and can be u!uiquely solved for the function 0. Thus k = A

Electron and ion acceleration in relativistic shocks with applications to GRB afterglows

NASA Astrophysics Data System (ADS)

Warren, Donald C.; Ellison, Donald C.; Bykov, Andrei M.; Lee, Shiu-Hang

2015-09-01

We have modelled the simultaneous first-order Fermi shock acceleration of protons, electrons, and helium nuclei by relativistic shocks. By parametrizing the particle diffusion, our steady-state Monte Carlo simulation allows us to follow particles from particle injection at non-relativistic thermal energies to above PeV energies, including the non-linear smoothing of the shock structure due to cosmic ray (CR) backpressure. We observe the mass-to-charge (A/Z) enhancement effect believed to occur in efficient Fermi acceleration in non-relativistic shocks and we parametrize the transfer of ion energy to electrons seen in particle-in-cell (PIC) simulations. For a given set of environmental and model parameters, the Monte Carlo simulation determines the absolute normalization of the particle distributions and the resulting synchrotron, inverse Compton, and pion-decay emission in a largely self-consistent manner. The simulation is flexible and can be readily used with a wide range of parameters typical of γ-ray burst (GRB) afterglows. We describe some preliminary results for photon emission from shocks of different Lorentz factors and outline how the Monte Carlo simulation can be generalized and coupled to hydrodynamic simulations of GRB blast waves. We assume Bohm diffusion for simplicity but emphasize that the non-linear effects we describe stem mainly from an extended shock precursor where higher energy particles diffuse further upstream. Quantitative differences will occur with different diffusion models, particularly for the maximum CR energy and photon emission, but these non-linear effects should be qualitatively similar as long as the scattering mean-free path is an increasing function of momentum.

Fast estimation of diffusion tensors under Rician noise by the EM algorithm.

PubMed

Liu, Jia; Gasbarra, Dario; Railavo, Juha

2016-01-15

Diffusion tensor imaging (DTI) is widely used to characterize, in vivo, the white matter of the central nerve system (CNS). This biological tissue contains much anatomic, structural and orientational information of fibers in human brain. Spectral data from the displacement distribution of water molecules located in the brain tissue are collected by a magnetic resonance scanner and acquired in the Fourier domain. After the Fourier inversion, the noise distribution is Gaussian in both real and imaginary parts and, as a consequence, the recorded magnitude data are corrupted by Rician noise. Statistical estimation of diffusion leads a non-linear regression problem. In this paper, we present a fast computational method for maximum likelihood estimation (MLE) of diffusivities under the Rician noise model based on the expectation maximization (EM) algorithm. By using data augmentation, we are able to transform a non-linear regression problem into the generalized linear modeling framework, reducing dramatically the computational cost. The Fisher-scoring method is used for achieving fast convergence of the tensor parameter. The new method is implemented and applied using both synthetic and real data in a wide range of b-amplitudes up to 14,000s/mm(2). Higher accuracy and precision of the Rician estimates are achieved compared with other log-normal based methods. In addition, we extend the maximum likelihood (ML) framework to the maximum a posteriori (MAP) estimation in DTI under the aforementioned scheme by specifying the priors. We will describe how close numerically are the estimators of model parameters obtained through MLE and MAP estimation. Copyright © 2015 Elsevier B.V. All rights reserved.

Anomalous current diffusion and improved confinement in the HT-6M tohamak

NASA Astrophysics Data System (ADS)

Gao, X.; Li, J. G.; Wan, Y. X.; Huo, Y. P.; Guo, W. K.; Fan, S. P.; Yu, C. X.; Luo, J. R.; Yin, F. X.; Meng, Y. D.; Zheng, L.; Yin, F.; Lin, B. L.; Zhang, S. Y.; Wang, S. Y.; Lu, H. J.; Liu, S. X.; Tong, X. D.; Ding, L. C.; Wu, Z. Y.; Yin, X. J.; Guo, Q. L.; Gong, X. Z.; Wu, X. C.; Zhao, J. Y.; Xi, J. S.

1994-10-01

Current diffusion was studied during edge ohmic heating (EOH) experiments in the HT-6M tokamak. The EOH power system makes the plasma current linearly ramp up from an initial steady state ( Ip=55kA) to a second steady state ( Ip=60kA) at a fast ramp rate of 12 MA/s. A stable discharge of an improved confinement was observed experimentally in the HT-6M tokamak after the plasma current was ramped to rise rapidly to a second steady state. The plasma current is ramped up much faster than both the classical skin time and neoclassical skin time. Fast current ramp up increases the anomalous current diffusion. The measured values of {β P+l i}/{2} and the soft X-ray sawtooth inversion radius imply the anomalous current penetration. The mechanism of anomalous penetration and improved confinement is discussed.

Optimization of the Inverse Algorithm for Estimating the Optical Properties of Biological Materials Using Spatially-resolved Diffuse Reflectance Technique

USDA-ARS?s Scientific Manuscript database

Determination of the optical properties from intact biological materials based on diffusion approximation theory is a complicated inverse problem, and it requires proper implementation of inverse algorithm, instrumentation, and experiment. This work was aimed at optimizing the procedure of estimatin...

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.

Continuous time random walk model with asymptotical probability density of waiting times via inverse Mittag-Leffler function

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Chen, Wen

2018-04-01

The mean squared displacement (MSD) of the traditional ultraslow diffusion is a logarithmic function of time. Recently, the continuous time random walk model is employed to characterize this ultraslow diffusion dynamics by connecting the heavy-tailed logarithmic function and its variation as the asymptotical waiting time density. In this study we investigate the limiting waiting time density of a general ultraslow diffusion model via the inverse Mittag-Leffler function, whose special case includes the traditional logarithmic ultraslow diffusion model. The MSD of the general ultraslow diffusion model is analytically derived as an inverse Mittag-Leffler function, and is observed to increase even more slowly than that of the logarithmic function model. The occurrence of very long waiting time in the case of the inverse Mittag-Leffler function has the largest probability compared with the power law model and the logarithmic function model. The Monte Carlo simulations of one dimensional sample path of a single particle are also performed. The results show that the inverse Mittag-Leffler waiting time density is effective in depicting the general ultraslow random motion.

Oxygen and Fuel Jet Diffusion Flame Studies in Microgravity Motivated by Spacecraft Oxygen Storage Fire Safety

NASA Technical Reports Server (NTRS)

Sunderland, P. B.; Yuan, Z.-G.; Krishnan, S. S.; Abshire, J. M.; Gore, J. P.

2003-01-01

Owing to the absence of past work involving flames similar to the Mir fire namely oxygen-enhanced, inverse gas-jet diffusion flames in microgravity the objectives of this work are as follows: 1. Observe the effects of enhanced oxygen conditions on laminar jet diffusion flames with ethane fuel. 2. Consider both earth gravity and microgravity. 3. Examine both normal and inverse flames. 4. Compare the measured flame lengths and widths with calibrated predictions of several flame shape models. This study expands on the work of Hwang and Gore which emphasized radiative emissions from oxygen-enhanced inverse flames in earth gravity, and Sunderland et al. which emphasized the shapes of normal and inverse oxygen-enhanced gas-jet diffusion flames in microgravity.

A Hybrid Seismic Inversion Method for V P/V S Ratio and Its Application to Gas Identification

NASA Astrophysics Data System (ADS)

Guo, Qiang; Zhang, Hongbing; Han, Feilong; Xiao, Wei; Shang, Zuoping

2018-03-01

The ratio of compressional wave velocity to shear wave velocity (V P/V S ratio) has established itself as one of the most important parameters in identifying gas reservoirs. However, considering that seismic inversion process is highly non-linear and geological conditions encountered may be complex, a direct estimation of V P/V S ratio from pre-stack seismic data remains a challenging task. In this paper, we propose a hybrid seismic inversion method to estimate V P/V S ratio directly. In this method, post- and pre-stack inversions are combined in which the pre-stack inversion for V P/V S ratio is driven by the post-stack inversion results (i.e., V P and density). In particular, the V P/V S ratio is considered as a model parameter and is directly inverted from the pre-stack inversion based on the exact Zoeppritz equation. Moreover, anisotropic Markov random field is employed in order to regularise the inversion process as well as taking care of geological structures (boundaries) information. Aided by the proposed hybrid inversion strategy, the directional weighting coefficients incorporated in the anisotropic Markov random field neighbourhoods are quantitatively calculated by the anisotropic diffusion method. The synthetic test demonstrates the effectiveness of the proposed inversion method. In particular, given low quality of the pre-stack data and high heterogeneity of the target layers in the field data, the proposed inversion method reveals the detailed model of V P/V S ratio that can successfully identify the gas-bearing zones.

Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

NASA Astrophysics Data System (ADS)

Fukuda, Jun'ichi; Johnson, Kaj M.

2010-06-01

We present a unified theoretical framework and solution method for probabilistic, Bayesian inversions of crustal deformation data. The inversions involve multiple data sets with unknown relative weights, model parameters that are related linearly or non-linearly through theoretic models to observations, prior information on model parameters and regularization priors to stabilize underdetermined problems. To efficiently handle non-linear inversions in which some of the model parameters are linearly related to the observations, this method combines both analytical least-squares solutions and a Monte Carlo sampling technique. In this method, model parameters that are linearly and non-linearly related to observations, relative weights of multiple data sets and relative weights of prior information and regularization priors are determined in a unified Bayesian framework. In this paper, we define the mixed linear-non-linear inverse problem, outline the theoretical basis for the method, provide a step-by-step algorithm for the inversion, validate the inversion method using synthetic data and apply the method to two real data sets. We apply the method to inversions of multiple geodetic data sets with unknown relative data weights for interseismic fault slip and locking depth. We also apply the method to the problem of estimating the spatial distribution of coseismic slip on faults with unknown fault geometry, relative data weights and smoothing regularization weight.

Combined inverse-forward artificial neural networks for fast and accurate estimation of the diffusion coefficients of cartilage based on multi-physics models.

PubMed

Arbabi, Vahid; Pouran, Behdad; Weinans, Harrie; Zadpoor, Amir A

2016-09-06

Analytical and numerical methods have been used to extract essential engineering parameters such as elastic modulus, Poisson׳s ratio, permeability and diffusion coefficient from experimental data in various types of biological tissues. The major limitation associated with analytical techniques is that they are often only applicable to problems with simplified assumptions. Numerical multi-physics methods, on the other hand, enable minimizing the simplified assumptions but require substantial computational expertise, which is not always available. In this paper, we propose a novel approach that combines inverse and forward artificial neural networks (ANNs) which enables fast and accurate estimation of the diffusion coefficient of cartilage without any need for computational modeling. In this approach, an inverse ANN is trained using our multi-zone biphasic-solute finite-bath computational model of diffusion in cartilage to estimate the diffusion coefficient of the various zones of cartilage given the concentration-time curves. Robust estimation of the diffusion coefficients, however, requires introducing certain levels of stochastic variations during the training process. Determining the required level of stochastic variation is performed by coupling the inverse ANN with a forward ANN that receives the diffusion coefficient as input and returns the concentration-time curve as output. Combined together, forward-inverse ANNs enable computationally inexperienced users to obtain accurate and fast estimation of the diffusion coefficients of cartilage zones. The diffusion coefficients estimated using the proposed approach are compared with those determined using direct scanning of the parameter space as the optimization approach. It has been shown that both approaches yield comparable results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Effect of Oxygen Enrichment in Propane Laminar Diffusion Flames under Microgravity and Earth Gravity Conditions

NASA Astrophysics Data System (ADS)

Bhatia, Pramod; Singh, Ravinder

2017-06-01

Diffusion flames are the most common type of flame which we see in our daily life such as candle flame and match-stick flame. Also, they are the most used flames in practical combustion system such as industrial burner (coal fired, gas fired or oil fired), diesel engines, gas turbines, and solid fuel rockets. In the present study, steady-state global chemistry calculations for 24 different flames were performed using an axisymmetric computational fluid dynamics code (UNICORN). Computation involved simulations of inverse and normal diffusion flames of propane in earth and microgravity condition with varying oxidizer compositions (21, 30, 50, 100 % O2, by mole, in N2). 2 cases were compared with the experimental result for validating the computational model. These flames were stabilized on a 5.5 mm diameter burner with 10 mm of burner length. The effect of oxygen enrichment and variation in gravity (earth gravity and microgravity) on shape and size of diffusion flames, flame temperature, flame velocity have been studied from the computational result obtained. Oxygen enrichment resulted in significant increase in flame temperature for both types of diffusion flames. Also, oxygen enrichment and gravity variation have significant effect on the flame configuration of normal diffusion flames in comparison with inverse diffusion flames. Microgravity normal diffusion flames are spherical in shape and much wider in comparison to earth gravity normal diffusion flames. In inverse diffusion flames, microgravity flames were wider than earth gravity flames. However, microgravity inverse flames were not spherical in shape.

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.

Effect of sorbed methanol, current, and temperature on multicomponent transport in nafion-based direct methanol fuel cells.

PubMed

Rivera, Harry; Lawton, Jamie S; Budil, David E; Smotkin, Eugene S

2008-07-24

The CO2 in the cathode exhaust of a liquid feed direct methanol fuel cell (DMFC) has two sources: methanol diffuses through the membrane electrode assembly (MEA) to the cathode where it is catalytically oxidized to CO2; additionally, a portion of the CO2 produced at the anode diffuses through the MEA to the cathode. The potential-dependent CO2 exhaust from the cathode was monitored by online electrochemical mass spectrometry (ECMS) with air and with H2 at the cathode. The precise determination of the crossover rates of methanol and CO2, enabled by the subtractive normalization of the methanol/air to the methanol/H2 ECMS data, shows that methanol decreases the membrane viscosity and thus increases the diffusion coefficients of sorbed membrane components. The crossover of CO2 initially increases linearly with the Faradaic oxidation of methanol, reaches a temperature-dependent maximum, and then decreases. The membrane viscosity progressively increases as methanol is electrochemically depleted from the anode/electrolyte interface. The crossover maximum occurs when the current dependence of the diffusion coefficients and membrane CO2 solubility dominate over the Faradaic production of CO2. The plasticizing effect of methanol is corroborated by measurements of the rotational diffusion of TEMPONE (2,2,6,6-tetramethyl-4-piperidone N-oxide) spin probe by electron spin resonance spectroscopy. A linear inverse relationship between the methanol crossover rate and current density confirms the absence of methanol electro-osmotic drag at concentrations relevant to operating DMFCs. The purely diffusive transport of methanol is explained in terms of current proton solvation and methanol-water incomplete mixing theories.

Fast reconstruction of optical properties for complex segmentations in near infrared imaging

NASA Astrophysics Data System (ADS)

Jiang, Jingjing; Wolf, Martin; Sánchez Majos, Salvador

2017-04-01

The intrinsic ill-posed nature of the inverse problem in near infrared imaging makes the reconstruction of fine details of objects deeply embedded in turbid media challenging even for the large amounts of data provided by time-resolved cameras. In addition, most reconstruction algorithms for this type of measurements are only suitable for highly symmetric geometries and rely on a linear approximation to the diffusion equation since a numerical solution of the fully non-linear problem is computationally too expensive. In this paper, we will show that a problem of practical interest can be successfully addressed making efficient use of the totality of the information supplied by time-resolved cameras. We set aside the goal of achieving high spatial resolution for deep structures and focus on the reconstruction of complex arrangements of large regions. We show numerical results based on a combined approach of wavelength-normalized data and prior geometrical information, defining a fully parallelizable problem in arbitrary geometries for time-resolved measurements. Fast reconstructions are obtained using a diffusion approximation and Monte-Carlo simulations, parallelized in a multicore computer and a GPU respectively.

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

Role of shell diffusion area in incubating eggs at simulated high altitude.

PubMed

Weiss, H S

1978-10-01

Embryonic development is inhibited when eggs are incubated at 9,100 m (0.3 atm) despite a normoxic environment. The problem apparently relates to respiratory gas exchange occurring by diffusion through gas-filled pores in the shell. Gaseous flux is therefore inversely proportional to ambient pressure and is affected by the physical characteristics of the ambient gas (Chapman-Enskog equation). Excess loss of H2O and CO2 occurs in eggs incubating at altitude and could be detrimental. Such increased loss should be correctable by decreasing diffusion area. This was tested by progressively increasing coverage of the shell with paraffin and incubating at simulated 0.3 ATA (225 Torr) in 100% O2. Uncoated eggs failed to hatch, but numbers of chicks increased with increased coverage. Maximum hatch was an extrapolated 90% of controls at 69% shell coverage. With further coverage, hatch size decreased. Egg weight loss, and estimate of H2O diffusion, was around three times controls in uncoated eggs but decreased linearly with paraffin coverage, reaching near normal at maximum hatch. Reduction of diffusion area to 0.3 normal at maximum hatch generally balanced the increased flux predicted for 0.3 ATA.

Simulations of normal and inverse laminar diffusion flames under oxygen enhancement and gravity variation

NASA Astrophysics Data System (ADS)

Bhatia, P.; Katta, V. R.; Krishnan, S. S.; Zheng, Y.; Sunderland, P. B.; Gore, J. P.

2012-10-01

Steady-state global chemistry calculations for 20 different flames were carried out using an axisymmetric Computational Fluid Dynamics (CFD) code. Computational results for 16 flames were compared with flame images obtained at the NASA Glenn Research Center. The experimental flame data for these 16 flames were taken from Sunderland et al. [4] which included normal and inverse diffusion flames of ethane with varying oxidiser compositions (21, 30, 50, 100% O2 mole fraction in N2) stabilised on a 5.5 mm diameter burner. The test conditions of this reference resulted in highly convective inverse diffusion flames (Froude numbers of the order of 10) and buoyant normal diffusion flames (Froude numbers ∼0.1). Additionally, six flames were simulated to study the effect of oxygen enhancement on normal diffusion flames. The enhancement in oxygen resulted in increased flame temperatures and the presence of gravity led to increased gas velocities. The effect of gravity-variation and oxygen enhancement on flame shape and size of normal diffusion flames was far more pronounced than for inverse diffusion flames. For normal-diffusion flames, their flame-lengths decreased (1 to 2 times) and flames-widths increased (2 to 3 times) when going from earth-gravity to microgravity, and flame height decreased by five times when going from air to a pure oxygen environment.

A non-local structural derivative model for characterization of ultraslow diffusion in dense colloids

NASA Astrophysics Data System (ADS)

Liang, Yingjie; Chen, Wen

2018-03-01

Ultraslow diffusion has been observed in numerous complicated systems. Its mean squared displacement (MSD) is not a power law function of time, but instead a logarithmic function, and in some cases grows even more slowly than the logarithmic rate. The distributed-order fractional diffusion equation model simply does not work for the general ultraslow diffusion. Recent study has used the local structural derivative to describe ultraslow diffusion dynamics by using the inverse Mittag-Leffler function as the structural function, in which the MSD is a function of inverse Mittag-Leffler function. In this study, a new stretched logarithmic diffusion law and its underlying non-local structural derivative diffusion model are proposed to characterize the ultraslow diffusion in aging dense colloidal glass at both the short and long waiting times. It is observed that the aging dynamics of dense colloids is a class of the stretched logarithmic ultraslow diffusion processes. Compared with the power, the logarithmic, and the inverse Mittag-Leffler diffusion laws, the stretched logarithmic diffusion law has better precision in fitting the MSD of the colloidal particles at high densities. The corresponding non-local structural derivative diffusion equation manifests clear physical mechanism, and its structural function is equivalent to the first-order derivative of the MSD.

HARDI denoising using nonlocal means on S2

NASA Astrophysics Data System (ADS)

Kuurstra, Alan; Dolui, Sudipto; Michailovich, Oleg

2012-02-01

Diffusion MRI (dMRI) is a unique imaging modality for in vivo delineation of the anatomical structure of white matter in the brain. In particular, high angular resolution diffusion imaging (HARDI) is a specific instance of dMRI which is known to excel in detection of multiple neural fibers within a single voxel. Unfortunately, the angular resolution of HARDI is known to be inversely proportional to SNR, which makes the problem of denoising of HARDI data be of particular practical importance. Since HARDI signals are effectively band-limited, denoising can be accomplished by means of linear filtering. However, the spatial dependency of diffusivity in brain tissue makes it impossible to find a single set of linear filter parameters which is optimal for all types of diffusion signals. Hence, adaptive filtering is required. In this paper, we propose a new type of non-local means (NLM) filtering which possesses the required adaptivity property. As opposed to similar methods in the field, however, the proposed NLM filtering is applied in the spherical domain of spatial orientations. Moreover, the filter uses an original definition of adaptive weights, which are designed to be invariant to both spatial rotations as well as to a particular sampling scheme in use. As well, we provide a detailed description of the proposed filtering procedure, its efficient implementation, as well as experimental results with synthetic data. We demonstrate that our filter has substantially better adaptivity as compared to a number of alternative methods.

Transient enhanced diffusion in preamorphized silicon: the role of the surface

NASA Astrophysics Data System (ADS)

Cowern, N. E. B.; Alquier, D.; Omri, M.; Claverie, A.; Nejim, A.

1999-01-01

Experiments on the depth dependence of transient enhanced diffusion (TED) of boron during rapid thermal annealing of Ge-preamorphized layers reveal a linear decrease in the diffusion enhancement between the end-of-range (EOR) defect band and the surface. This behavior, which indicates a quasi-steady-state distribution of excess interstitials, emitted from the EOR band and absorbed at the surface, is observed for annealing times as short as 1 s at 900°C. Using an etching procedure we vary the distance xEOR from the EOR band to the surface in the range 80-175 nm, and observe how this influences the interstitial supersaturation, s( x). The supersaturations at the EOR band and the surface remain unchanged, while the gradient d s/d x, and thus the flux to the surface, varies inversely with xEOR. This confirms the validity of earlier modelling of EOR defect evolution in terms of Ostwald ripening, and provides conclusive evidence that the surface is the dominant sink for interstitials during TED.

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

Shades of white: diffusion properties of T1- and FLAIR-defined white matter signal abnormalities differ in stages from cognitively normal to dementia.

PubMed

Riphagen, Joost M; Gronenschild, Ed H B M; Salat, David H; Freeze, Whitney M; Ivanov, Dimo; Clerx, Lies; Verhey, Frans R J; Aalten, Pauline; Jacobs, Heidi I L

2018-08-01

The underlying pathology of white matter signal abnormalities (WMSAs) is heterogeneous and may vary dependent on the magnetic resonance imaging contrast used to define them. We investigated differences in white matter diffusivity as an indicator for white matter integrity underlying WMSA based on T1-weighted and fluid-attenuated inversion recovery (FLAIR) imaging contrast. In addition, we investigated which white matter region of interest (ROI) could predict clinical diagnosis best using diffusion metrics. One hundred three older individuals with varying cognitive impairment levels were included and underwent neuroimaging. Diffusion metrics were extracted from WMSA areas based on T1 and FLAIR contrast and from their overlapping areas, the border surrounding the WMSA and the normal-appearing white matter (NAWM). Regional diffusivity differences were calculated with linear mixed effects models. Multinomial logistic regression determined which ROI diffusion values classified individuals best into clinically defined diagnostic groups. T1-based WMSA showed lower white matter integrity compared to FLAIR WMSA-defined regions. Diffusion values of NAWM predicted diagnostic group best compared to other ROI's. To conclude, T1- or FLAIR-defined WMSA provides distinct information on the underlying white matter integrity associated with cognitive decline. Importantly, not the "diseased" but the NAWM is a potentially sensitive indicator for cognitive brain health status. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

A Luenberger observer for reaction-diffusion models with front position data

NASA Astrophysics Data System (ADS)

Collin, Annabelle; Chapelle, Dominique; Moireau, Philippe

2015-11-01

We propose a Luenberger observer for reaction-diffusion models with propagating front features, and for data associated with the location of the front over time. Such models are considered in various application fields, such as electrophysiology, wild-land fire propagation and tumor growth modeling. Drawing our inspiration from image processing methods, we start by proposing an observer for the eikonal-curvature equation that can be derived from the reaction-diffusion model by an asymptotic expansion. We then carry over this observer to the underlying reaction-diffusion equation by an ;inverse asymptotic analysis;, and we show that the associated correction in the dynamics has a stabilizing effect for the linearized estimation error. We also discuss the extension to joint state-parameter estimation by using the earlier-proposed ROUKF strategy. We then illustrate and assess our proposed observer method with test problems pertaining to electrophysiology modeling, including with a realistic model of cardiac atria. Our numerical trials show that state estimation is directly very effective with the proposed Luenberger observer, while specific strategies are needed to accurately perform parameter estimation - as is usual with Kalman filtering used in a nonlinear setting - and we demonstrate two such successful strategies.

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

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.

Molecular dynamics insights into the structural and diffusive properties of ZIF-8/PDMS mixed matrix membranes in the n-butanol/water pervaporation process

NASA Astrophysics Data System (ADS)

Sun, Tao; Fang, Manquan; Wu, Zhen; Yu, Lixin; Li, Jiding

2017-04-01

Molecular dynamics (MD) simulation was used to study the structural and diffusive properties of zeolitic imidazolate framework-8 (ZIF-8)/polydimethylsiloxane (PDMS), a novel alcohol-permselective mixed matrix membrane (MMM). Simulation models of one pure PDMS membrane and three ZIF-8/PDMS MMMs with increasing loadings were successfully constructed. Non-bond energy turned out to be a strong attractive interaction between the PDMS matrix and ZIF-8 cells. The morphology and mobility of PDMS chains were characterized by mean square displacement (MSD). The fraction of free volume (FFV) of the pure membrane and MMMs was calculated and showed declining trends with increasing ZIF-8 loadings. The diffusion coefficients of n-butanol and water molecules were calculated by the Einstein relation. {D}n-\\text{butanol} first increased then decreased, while {D}{{water}} decreased with the increasing loadings. The mechanism of selective diffusion behaviour was investigated and it was found that the inner channels of ZIF-8 provided selective pathways for n-butanol. Diffusion coefficients were correlated with FFV and the results showed that the logarithm of {D}{{water}} demonstrated a good linear relation with the inverse FFV and was in agreement with the free volume theory, while {D}n-\\text{butanol} showed a significant deviation in the case of MMM-1 due to the selective diffusion channels provided by ZIF-8.

Spin-scattering rates in metallic thin films measured by ferromagnetic resonance damping enhanced by spin-pumping

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

Boone, C. T.; Shaw, J. M.; Nembach, H. T.

2015-06-14

We determined the spin-transport properties of Pd and Pt thin films by measuring the increase in ferromagnetic resonance damping due to spin-pumping in ferromagnetic (FM)-nonferromagnetic metal (NM) multilayers with varying NM thicknesses. The increase in damping with NM thickness depends strongly on both the spin- and charge-transport properties of the NM, as modeled by diffusion equations that include both momentum- and spin-scattering parameters. We use the analytical solution to the spin-diffusion equations to obtain spin-diffusion lengths for Pt and Pd. By measuring the dependence of conductivity on NM thickness, we correlate the charge- and spin-transport parameters, and validate the applicabilitymore » of various models for momentum-scattering and spin-scattering rates in these systems: constant, inverse-proportional (Dyakanov-Perel), and linear-proportional (Elliot-Yafet). We confirm previous reports that the spin-scattering time appears to be shorter than the momentum scattering time in Pt, and the Dyakanov-Perel-like model is the best fit to the data.« less

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.

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.

Addendum to foundations of multidimensional wave field signal theory: Gaussian source function

NASA Astrophysics Data System (ADS)

Baddour, Natalie

2018-02-01

Many important physical phenomena are described by wave or diffusion-wave type equations. Recent work has shown that a transform domain signal description from linear system theory can give meaningful insight to multi-dimensional wave fields. In N. Baddour [AIP Adv. 1, 022120 (2011)], certain results were derived that are mathematically useful for the inversion of multi-dimensional Fourier transforms, but more importantly provide useful insight into how source functions are related to the resulting wave field. In this short addendum to that work, it is shown that these results can be applied with a Gaussian source function, which is often useful for modelling various physical phenomena.

Brownian self-propelled particles on a sphere

NASA Astrophysics Data System (ADS)

Apaza-Pilco, Leonardo Felix; Sandoval, Mario

We present the dynamics of a Brownian self-propelled particle at low Reynolds number moving on the surface of a sphere. The effects of curvature and self-propulsion on the diffusion of the particle are elucidated by determining (numerically) the mean-square displacement of the particle's angular (azimuthal and polar) coordinates. The results show that the long time behavior of its angular mean-square displacement is linear in time. We also see that the slope of the angular MSD is proportional to the propulsion velocity and inverse to the curvature of the sphere. The angular probability distribution function (PDF) of the particle is also obtained by numerically solving its respective Smoluchowski equation.

FRACTIONAL PEARSON DIFFUSIONS.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-07-15

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.

Inverse Diffusion Curves Using Shape Optimization.

PubMed

Zhao, Shuang; Durand, Fredo; Zheng, Changxi

2018-07-01

The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color fields via a partial differential equation (PDE). We introduce a new approach complementary to previous methods by optimizing curve geometry. In particular, we propose a novel iterative algorithm based on the theory of shape derivatives. The resulting diffusion curves are clean and well-shaped, and the final image closely approximates the input. Our method provides a user-controlled parameter to regularize curve complexity, and generalizes to handle input color fields represented in a variety of formats.

The change of longitudinal relaxation rate in oxygen enhanced pulmonary MRI depends on age and BMI but not diffusing capacity of carbon monoxide in healthy never-smokers.

PubMed

Kindvall, Simon Sven Ivan; Diaz, Sandra; Svensson, Jonas; Wollmer, Per; Olsson, Lars E

2017-01-01

Oxygen enhanced pulmonary MRI is a promising modality for functional lung studies and has been applied to a wide range of pulmonary conditions. The purpose of this study was to characterize the oxygen enhancement effect in the lungs of healthy, never-smokers, in light of a previously established relationship between oxygen enhancement and diffusing capacity of carbon monoxide in the lung (DL,CO) in patients with lung disease. In 30 healthy never-smoking volunteers, an inversion recovery with gradient echo read-out (Snapshot-FLASH) was used to quantify the difference in longitudinal relaxation rate, while breathing air and 100% oxygen, ΔR1, at 1.5 Tesla. Measurements were performed under multiple tidal inspiration breath-holds. In single parameter linear models, ΔR1 exhibit a significant correlation with age (p = 0.003) and BMI (p = 0.0004), but not DL,CO (p = 0.33). Stepwise linear regression of ΔR1 yields an optimized model including an age-BMI interaction term. In this healthy, never-smoking cohort, age and BMI are both predictors of the change in MRI longitudinal relaxation rate when breathing oxygen. However, DL,CO does not show a significant correlation with the oxygen enhancement. This is possibly because oxygen transfer in the lung is not diffusion limited at rest in healthy individuals. This work stresses the importance of using a physiological model to understand results from oxygen enhanced MRI.

Linear Inverse Modeling and Scaling Analysis of Drainage Inventories.

NASA Astrophysics Data System (ADS)

O'Malley, C.; White, N. J.

2016-12-01

It is widely accepted that the stream power law can be used to describe the evolution of longitudinal river profiles. Over the last 5 years, this phenomenological law has been used to develop non-linear and linear inversion algorithms that enable uplift rate histories to be calculated by minimizing the misfit between observed and calculated river profiles. Substantial, continent-wide inventories of river profiles have been successfully inverted to yield uplift as a function of time and space. Erosional parameters can be determined by independent geological calibration. Our results help to illuminate empirical scaling laws that are well known to the geomorphological community. Here we present an analysis of river profiles from Asia. The timing and magnitude of uplift events across Asia, including the Himalayas and Tibet, have long been debated. River profile analyses have played an important role in clarifying the timing of uplift events. However, no attempt has yet been made to invert a comprehensive database of river profiles from the entire region. Asian rivers contain information which allows us to investigate putative uplift events quantitatively and to determine a cumulative uplift history for Asia. Long wavelength shapes of river profiles are governed by regional uplift and moderated by erosional processes. These processes are parameterised using the stream power law in the form of an advective-diffusive equation. Our non-negative, least-squares inversion scheme was applied to an inventory of 3722 Asian river profiles. We calibrate the key erosional parameters by predicting solid sedimentary flux for a set of Asian rivers and by comparing the flux predictions against published depositional histories for major river deltas. The resultant cumulative uplift history is compared with a range of published geological constraints for uplift and palaeoelevation. We have found good agreement for many regions across Asia. Surprisingly, single values of erosional constants can be shown to produce reliable uplift histories. However, these erosional constants appear to vary from continent to continent. Future work will investigate the global relationship between our inversion results, scaling laws, climate models, lithological variation and sedimentary flux.

Curvature and bottlenecks control molecular transport in inverse bicontinuous cubic phases

NASA Astrophysics Data System (ADS)

Assenza, Salvatore; Mezzenga, Raffaele

2018-02-01

We perform a simulation study of the diffusion of small solutes in the confined domains imposed by inverse bicontinuous cubic phases for the primitive, diamond, and gyroid symmetries common to many lipid/water mesophase systems employed in experiments. For large diffusing domains, the long-time diffusion coefficient shows universal features when the size of the confining domain is renormalized by the Gaussian curvature of the triply periodic minimal surface. When bottlenecks are widely present, they become the most relevant factor for transport, regardless of the connectivity of the cubic phase.

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

Large lateral photovoltaic effect with ultrafast relaxation time in SnSe/Si junction

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

Wang, Xianjie; Zhao, Xiaofeng; Hu, Chang

In this paper, we report a large lateral photovoltaic effect (LPE) with ultrafast relaxation time in SnSe/p-Si junctions. The LPE shows a linear dependence on the position of the laser spot, and the position sensitivity is as high as 250 mV mm{sup −1}. The optical response time and the relaxation time of the LPE are about 100 ns and 2 μs, respectively. The current-voltage curve on the surface of the SnSe film indicates the formation of an inversion layer at the SnSe/p-Si interface. Our results clearly suggest that most of the excited-electrons diffuse laterally in the inversion layer at the SnSe/p-Si interface, whichmore » results in a large LPE with ultrafast relaxation time. The high positional sensitivity and ultrafast relaxation time of the LPE make the SnSe/p-Si junction a promising candidate for a wide range of optoelectronic applications.« less

Fluid pressure arrival time tomography: Estimation and assessment in the presence of inequality constraints, with an application to a producing gas field at Krechba, Algeria

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

Rucci, A.; Vasco, D.W.; Novali, F.

2010-04-01

Deformation in the overburden proves useful in deducing spatial and temporal changes in the volume of a producing reservoir. Based upon these changes we estimate diffusive travel times associated with the transient flow due to production, and then, as the solution of a linear inverse problem, the effective permeability of the reservoir. An advantage an approach based upon travel times, as opposed to one based upon the amplitude of surface deformation, is that it is much less sensitive to the exact geomechanical properties of the reservoir and overburden. Inequalities constrain the inversion, under the assumption that the fluid production onlymore » results in pore volume decreases within the reservoir. We apply the formulation to satellite-based estimates of deformation in the material overlying a thin gas production zone at the Krechba field in Algeria. The peak displacement after three years of gas production is approximately 0.5 cm, overlying the eastern margin of the anticlinal structure defining the gas field. Using data from 15 irregularly-spaced images of range change, we calculate the diffusive travel times associated with the startup of a gas production well. The inequality constraints are incorporated into the estimates of model parameter resolution and covariance, improving the resolution by roughly 30 to 40%.« less

Effect of pectin charge density on formation of multilayer films with chitosan.

PubMed

Kamburova, Kamelia; Milkova, Viktoria; Petkanchin, Ivana; Radeva, Tsetska

2008-04-01

The effect of pectin charge density on the formation of multilayer films with chitosan (PEC/CHI) is studied by means of electro-optics. Pectins of low (21%) and high (71%) degrees of esterification, which are inversely proportional to the pectin charge density, are used to form films on colloidal beta-FeOOH particles at pH 4.0 when the CHI is fully ionized. We find that, after deposition of the first 3-4 layers, the film thickness increases linearly with the number of adsorbed layers. However, the increase in the film thickness is larger when the film is terminated with CHI. Irregular increase of the film thickness is more marked for the PEC with higher density of charge. Oscillation in the electrical polarizability of the film-coated particles with the number of deposited layers is also registered in the PEC/CHI films. The charge balance of the multilayers, calculated from electrical polarizability of the film-coated particles, is positive, with larger excess of positive charge within the film constructed from CHI and less charged PEC. This is attributed to the ability of CHI to diffuse into the film at each deposition step. Despite the CHI diffusion, the film thickness increases linearly due to the dissolution of unstable PEC/CHI complexes from the film surface.

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.

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…

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.

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.

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.

Momentum and charge transport in non-relativistic holographic fluids from Hořava gravity

NASA Astrophysics Data System (ADS)

Davison, Richard A.; Grozdanov, Sašo; Janiszewski, Stefan; Kaminski, Matthias

2016-11-01

We study the linearized transport of transverse momentum and charge in a conjectured field theory dual to a black brane solution of Hořava gravity with Lifshitz exponent z = 1. As expected from general hydrodynamic reasoning, we find that both of these quantities are diffusive over distance and time scales larger than the inverse temperature. We compute the diffusion constants and conductivities of transverse momentum and charge, as well the ratio of shear viscosity to entropy density, and find that they differ from their relativistic counterparts. To derive these results, we propose how the holographic dictionary should be modified to deal with the multiple horizons and differing propagation speeds of bulk excitations in Hořava gravity. When possible, as a check on our methods and results, we use the covariant Einstein-Aether formulation of Hořava gravity, along with field redefinitions, to re-derive our results from a relativistic bulk theory.

An adjoint-based method for a linear mechanically-coupled tumor model: application to estimate the spatial variation of murine glioma growth based on diffusion weighted magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Feng, Xinzeng; Hormuth, David A.; Yankeelov, Thomas E.

2018-06-01

We present an efficient numerical method to quantify the spatial variation of glioma growth based on subject-specific medical images using a mechanically-coupled tumor model. The method is illustrated in a murine model of glioma in which we consider the tumor as a growing elastic mass that continuously deforms the surrounding healthy-appearing brain tissue. As an inverse parameter identification problem, we quantify the volumetric growth of glioma and the growth component of deformation by fitting the model predicted cell density to the cell density estimated using the diffusion-weighted magnetic resonance imaging data. Numerically, we developed an adjoint-based approach to solve the optimization problem. Results on a set of experimentally measured, in vivo rat glioma data indicate good agreement between the fitted and measured tumor area and suggest a wide variation of in-plane glioma growth with the growth-induced Jacobian ranging from 1.0 to 6.0.

A non-Linear transport model for determining shale rock characteristics

NASA Astrophysics Data System (ADS)

Ali, Iftikhar; Malik, Nadeem

2016-04-01

Unconventional hydrocarbon reservoirs consist of tight porous rocks which are characterised by nano-scale size porous networks with ultra-low permeability [1,2]. Transport of gas through them is not well understood at the present time, and realistic transport models are needed in order to determine rock properties and for estimating future gas pressure distribution in the reservoirs. Here, we consider a recently developed non-linear gas transport equation [3], ∂p-+ U ∂p- = D ∂2p-, t > 0, (1) ∂t ∂x ∂x2 complimented with suitable initial and boundary conditions, in order to determine shale rock properties such as the permeability K, the porosity φ and the tortuosity, τ. In our new model, the apparent convection velocity, U = U(p,px), and the apparent diffusivity D = D(p), are both highly non-linear functions of the pressure. The model incorporate various flow regimes (slip, surface diffusion, transition, continuum) based upon the Knudsen number Kn, and also includes Forchchiemers turbulence correction terms. In application, the model parameters and associated compressibility factors are fully pressure dependent, giving the model more realism than previous models. See [4]. Rock properties are determined by solving an inverse problem, with model parameters adjustment to minimise the error between the model simulation and available data. It is has been found that the proposed model performs better than previous models. Results and details of the model will be presented at the conference. Corresponding author: namalik@kfupm.edu.sa and nadeem_malik@cantab.net References [1] Cui, X., Bustin, A.M. and Bustin, R., "Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications", Geofluids 9, 208-223 (2009). [2] Chiba R., Fomin S., Chugunov V., Niibori Y. and Hashida T., "Numerical Simulation of Non Fickian Diffusion and Advection in a Fractured Porous Aquifer", AIP Conference Proceedings 898, 75 (2007); doi: 10.1063/1.2721253 [3] Ali, I. "A numerical study of shale gas flow in tight porous media through non-linear transport model", PhD Dissertation, King Fahd University of Petroleum and Minerals. Submitted (2016). [4]. Civan, F., Rai, C.S., Sondergeld, C.H.: Shale-gas permeability and diffusivity inferred by improved formulation of relevant retention and transport mechanisms. Transport in Porous Media, 86(3), 925-944 (2011). Acknowledgement: The authors would like to acknowledge the support provided by King Abdulaziz City for Science and Technology (KACST) through the Science Technology Unit at King Fahd University of Petroleum and Minerals (KFUPM) for funding this work through project No. 14-OIL280-04.

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...

Quantifying Multistate Cytoplasmic Molecular Diffusion in Bacterial Cells via Inverse Transform of Confined Displacement Distribution.

PubMed

Chen, Tai-Yen; Jung, Won; Santiago, Ace George; Yang, Feng; Krzemiński, Łukasz; Chen, Peng

2015-11-12

Single-molecule tracking (SMT) of fluorescently tagged cytoplasmic proteins can provide valuable information on the underlying biological processes in living cells via subsequent analysis of the displacement distributions; however, the confinement effect originated from the small size of a bacterial cell skews the protein's displacement distribution and complicates the quantification of the intrinsic diffusive behaviors. Using the inverse transformation method, we convert the skewed displacement distribution (for both 2D and 3D imaging conditions) back to that in free space for systems containing one or multiple (non)interconverting Brownian diffusion states, from which we can reliably extract the number of diffusion states as well as their intrinsic diffusion coefficients and respective fractional populations. We further demonstrate a successful application to experimental SMT data of a transcription factor in living E. coli cells. This work allows a direct quantitative connection between cytoplasmic SMT data with diffusion theory for analyzing molecular diffusive behavior in live bacteria.

Quantifying Multistate Cytoplasmic Molecular Diffusion in Bacterial Cells via Inverse Transform of Confined Displacement Distribution

PubMed Central

2016-01-01

Single-molecule tracking (SMT) of fluorescently tagged cytoplasmic proteins can provide valuable information on the underlying biological processes in living cells via subsequent analysis of the displacement distributions; however, the confinement effect originated from the small size of a bacterial cell skews the protein’s displacement distribution and complicates the quantification of the intrinsic diffusive behaviors. Using the inverse transformation method, we convert the skewed displacement distribution (for both 2D and 3D imaging conditions) back to that in free space for systems containing one or multiple (non)interconverting Brownian diffusion states, from which we can reliably extract the number of diffusion states as well as their intrinsic diffusion coefficients and respective fractional populations. We further demonstrate a successful application to experimental SMT data of a transcription factor in living E. coli cells. This work allows a direct quantitative connection between cytoplasmic SMT data with diffusion theory for analyzing molecular diffusive behavior in live bacteria. PMID:26491971

Ion radial diffusion in an electrostatic impulse model for stormtime ring current formation

NASA Technical Reports Server (NTRS)

Chen, Margaret W.; Schulz, Michael; Lyons, Larry R.; Gorney, David J.

1992-01-01

Two refinements to the quasi-linear theory of ion radial diffusion are proposed and examined analytically with simulations of particle trajectories. The resonance-broadening correction by Dungey (1965) is applied to the quasi-linear diffusion theory by Faelthammar (1965) for an individual model storm. Quasi-linear theory is then applied to the mean diffusion coefficients resulting from simulations of particle trajectories in 20 model storms. The correction for drift-resonance broadening results in quasi-linear diffusion coefficients with discrepancies from the corresponding simulated values that are reduced by a factor of about 3. Further reductions in the discrepancies are noted following the averaging of the quasi-linear diffusion coefficients, the simulated coefficients, and the resonance-broadened coefficients for the 20 storms. Quasi-linear theory provides good descriptions of particle transport for a single storm but performs even better in conjunction with the present ensemble-averaging.

Fundamentals of diffusion MRI physics.

PubMed

Kiselev, Valerij G

2017-03-01

Diffusion MRI is commonly considered the "engine" for probing the cellular structure of living biological tissues. The difficulty of this task is threefold. First, in structurally heterogeneous media, diffusion is related to structure in quite a complicated way. The challenge of finding diffusion metrics for a given structure is equivalent to other problems in physics that have been known for over a century. Second, in most cases the MRI signal is related to diffusion in an indirect way dependent on the measurement technique used. Third, finding the cellular structure given the MRI signal is an ill-posed inverse problem. This paper reviews well-established knowledge that forms the basis for responding to the first two challenges. The inverse problem is briefly discussed and the reader is warned about a number of pitfalls on the way. Copyright © 2017 John Wiley & Sons, Ltd.

Regolith thermal property inversion in the LUNAR-A heat-flow experiment

NASA Astrophysics Data System (ADS)

Hagermann, A.; Tanaka, S.; Yoshida, S.; Fujimura, A.; Mizutani, H.

2001-11-01

In 2003, two penetrators of the LUNAR--A mission of ISAS will investigate the internal structure of the Moon by conducting seismic and heat--flow experiments. Heat-flow is the product of thermal gradient tial T / tial z, and thermal conductivity λ of the lunar regolith. For measuring the thermal conductivity (or dissusivity), each penetrator will carry five thermal property sensors, consisting of small disc heaters. The thermal response Ts(t) of the heater itself to the constant known power supply of approx. 50 mW serves as the data for the subsequent data interpretation. Horai et al. (1991) found a forward analytical solution to the problem of determining the thermal inertia λ ρ c of the regolith for constant thermal properties and a simplyfied geometry. In the inversion, the problem of deriving the unknown thermal properties of a medium from known heat sources and temperatures is an Identification Heat Conduction Problem (IDHCP), an ill--posed inverse problem. Assuming that thermal conductivity λ and heat capacity ρ c are linear functions of temperature (which is reasonable in most cases), one can apply a Kirchhoff transformation to linearize the heat conduction equation, which minimizes computing time. Then the error functional, i.e. the difference between the measured temperature response of the heater and the predicted temperature response, can be minimized, thus solving for thermal dissusivity κ = λ / (ρ c), wich will complete the set of parameters needed for a detailed description of thermal properties of the lunar regolith. Results of model calculations will be presented, in which synthetic data and calibration data are used to invert the unknown thermal diffusivity of the unknown medium by means of a modified Newton Method. Due to the ill-posedness of the problem, the number of parameters to be solved for should be limited. As the model calculations reveal, a homogeneous regolith allows for a fast and accurate inversion.

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…

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

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.

Inversion of Atmospheric Tracer Measurements, Localization of Sources

NASA Astrophysics Data System (ADS)

Issartel, J.-P.; Cabrit, B.; Hourdin, F.; Idelkadi, A.

When abnormal concentrations of a pollutant are observed in the atmosphere, the question of its origin arises immediately. The radioactivity from Tchernobyl was de- tected in Sweden before the accident was announced. This situation emphasizes the psychological, political and medical stakes of a rapid identification of sources. In tech- nical terms, most industrial sources can be modeled as a fixed point at ground level with undetermined duration. The classical method of identification involves the cal- culation of a backtrajectory departing from the detector with an upstream integration of the wind field. We were first involved in such questions as we evaluated the ef- ficiency of the international monitoring network planned in the frame of the Com- prehensive Test Ban Treaty. We propose a new approach of backtracking based upon the use of retroplumes associated to available measurements. Firstly the retroplume is related to inverse transport processes, describing quantitatively how the air in a sam- ple originates from regions that are all the more extended and diffuse as we go back far in the past. Secondly it clarifies the sensibility of the measurement with respect to all potential sources. It is therefore calculated by adjoint equations including of course diffusive processes. Thirdly, the statistical interpretation, valid as far as sin- gle particles are concerned, should not be used to investigate the position and date of a macroscopic source. In that case, the retroplume rather induces a straightforward constraint between the intensity of the source and its position. When more than one measurements are available, including zero valued measurements, the source satisfies the same number of linear relations tightly related to the retroplumes. This system of linear relations can be handled through the simplex algorithm in order to make the above intensity-position correlation more restrictive. This method enables to manage in a quantitative manner the unavoidable ambiguity of atmospheric phenomena. When several measurements are available the ambiguity about the identification of a source is reduced significantly.

Determination of Diffusion Coefficients in Cement-Based Materials: An Inverse Problem for the Nernst-Planck and Poisson Models

NASA Astrophysics Data System (ADS)

Szyszkiewicz-Warzecha, Krzysztof; Jasielec, Jerzy J.; Fausek, Janusz; Filipek, Robert

2016-08-01

Transport properties of ions have significant impact on the possibility of rebars corrosion thus the knowledge of a diffusion coefficient is important for reinforced concrete durability. Numerous tests for the determination of diffusion coefficients have been proposed but analysis of some of these tests show that they are too simplistic or even not valid. Hence, more rigorous models to calculate the coefficients should be employed. Here we propose the Nernst-Planck and Poisson equations, which take into account the concentration and electric potential field. Based on this model a special inverse method is presented for determination of a chloride diffusion coefficient. It requires the measurement of concentration profiles or flux on the boundary and solution of the NPP model to define the goal function. Finding the global minimum is equivalent to the determination of diffusion coefficients. Typical examples of the application of the presented method are given.

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.

Inverse design of centrifugal compressor vaned diffusers in inlet shear flows

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

Zangeneh, M.

1996-04-01

A three-dimensional inverse design method in which the blade (or vane) geometry is designed for specified distributions of circulation and blade thickness is applied to the design of centrifugal compressor vaned diffusers. Two generic diffusers are designed, one with uniform inlet flow (equivalent to a conventional design) and the other with a sheared inlet flow. The inlet shear flow effects are modeled in the design method by using the so-called ``Secondary Flow Approximation`` in which the Bernoulli surfaces are convected by the tangentially mean inviscid flow field. The difference between the vane geometry of the uniform inlet flow and nonuniformmore » inlet flow diffusers is found to be most significant from 50 percent chord to the trailing edge region. The flows through both diffusers are computed by using Denton`s three-dimensional inviscid Euler solver and Dawes` three-dimensional Navier-Stokes solver under sheared in-flow conditions. The predictions indicate improved pressure recovery and internal flow field for the diffuser designed for shear inlet flow conditions.« less

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.

Random walk on lattices: Graph-theoretic approach to simulating long-range diffusion-attachment growth models

NASA Astrophysics Data System (ADS)

Limkumnerd, Surachate

2014-03-01

Interest in thin-film fabrication for industrial applications have driven both theoretical and computational aspects of modeling its growth. One of the earliest attempts toward understanding the morphological structure of a film's surface is through a class of solid-on-solid limited-mobility growth models such as the Family, Wolf-Villain, or Das Sarma-Tamborenea models, which have produced fascinating surface roughening behaviors. These models, however, restrict the motion of an incidence atom to be within the neighborhood of its landing site, which renders them inept for simulating long-distance surface diffusion such as that observed in thin-film growth using a molecular-beam epitaxy technique. Naive extension of these models by repeatedly applying the local diffusion rules for each hop to simulate large diffusion length can be computationally very costly when certain statistical aspects are demanded. We present a graph-theoretic approach to simulating a long-range diffusion-attachment growth model. Using the Markovian assumption and given a local diffusion bias, we derive the transition probabilities for a random walker to traverse from one lattice site to the others after a large, possibly infinite, number of steps. Only computation with linear-time complexity is required for the surface morphology calculation without other probabilistic measures. The formalism is applied, as illustrations, to simulate surface growth on a two-dimensional flat substrate and around a screw dislocation under the modified Wolf-Villain diffusion rule. A rectangular spiral ridge is observed in the latter case with a smooth front feature similar to that obtained from simulations using the well-known multiple registration technique. An algorithm for computing the inverse of a class of substochastic matrices is derived as a corollary.

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.

Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations

NASA Astrophysics Data System (ADS)

Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro

2017-05-01

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

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.

Hipergeometric solutions to some nonhomogeneous equations of fractional order

NASA Astrophysics Data System (ADS)

Olivares, Jorge; Martin, Pablo; Maass, Fernando

2017-12-01

In this paper a study is performed to the solution of the linear non homogeneous fractional order alpha differential equation equal to I 0(x), where I 0(x) is the modified Bessel function of order zero, the initial condition is f(0)=0 and 0 < alpha < 1. Caputo definition for the fractional derivatives is considered. Fractional derivatives have become important in physical and chemical phenomena as visco-elasticity and visco-plasticity, anomalous diffusion and electric circuits. In particular in this work the values of alpha=1/2, 1/4 and 3/4. are explicitly considered . In these cases Laplace transform is applied, and later the inverse Laplace transform leads to the solutions of the differential equation, which become hypergeometric functions.

From the Rendering Equation to Stratified Light Transport Inversion

DTIC Science & Technology

2010-12-09

iteratively. These approaches relate closely to the radiosity method for diffuse global illumination in forward rendering (Hanrahan et al, 1991; Gortler et...currently simply use sparse matrices to represent T, we are also interested in exploring connections with hierar- chical and wavelet radiosity as in...Seidel iterative methods used in radiosity . 2.4 Inverse Light Transport Previous work on inverse rendering has considered inversion of the direct

Dependence of image quality on image operator and noise for optical diffusion tomography

NASA Astrophysics Data System (ADS)

Chang, Jenghwa; Graber, Harry L.; Barbour, Randall L.

1998-04-01

By applying linear perturbation theory to the radiation transport equation, the inverse problem of optical diffusion tomography can be reduced to a set of linear equations, W(mu) equals R, where W is the weight function, (mu) are the cross- section perturbations to be imaged, and R is the detector readings perturbations. We have studied the dependence of image quality on added systematic error and/or random noise in W and R. Tomographic data were collected from cylindrical phantoms, with and without added inclusions, using Monte Carlo methods. Image reconstruction was accomplished using a constrained conjugate gradient descent method. Result show that accurate images containing few artifacts are obtained when W is derived from a reference states whose optical thickness matches that of the unknown teste medium. Comparable image quality was also obtained for unmatched W, but the location of the target becomes more inaccurate as the mismatch increases. Results of the noise study show that image quality is much more sensitive to noise in W than in R, and the impact of noise increase with the number of iterations. Images reconstructed after pure noise was substituted for R consistently contain large peaks clustered about the cylinder axis, which was an initially unexpected structure. In other words, random input produces a non- random output. This finding suggests that algorithms sensitive to the evolution of this feature could be developed to suppress noise effects.

Sparseness- and continuity-constrained seismic imaging

NASA Astrophysics Data System (ADS)

Herrmann, Felix J.

2005-04-01

Non-linear solution strategies to the least-squares seismic inverse-scattering problem with sparseness and continuity constraints are proposed. Our approach is designed to (i) deal with substantial amounts of additive noise (SNR < 0 dB); (ii) use the sparseness and locality (both in position and angle) of directional basis functions (such as curvelets and contourlets) on the model: the reflectivity; and (iii) exploit the near invariance of these basis functions under the normal operator, i.e., the scattering-followed-by-imaging operator. Signal-to-noise ratio and the continuity along the imaged reflectors are significantly enhanced by formulating the solution of the seismic inverse problem in terms of an optimization problem. During the optimization, sparseness on the basis and continuity along the reflectors are imposed by jointly minimizing the l1- and anisotropic diffusion/total-variation norms on the coefficients and reflectivity, respectively. [Joint work with Peyman P. Moghaddam was carried out as part of the SINBAD project, with financial support secured through ITF (the Industry Technology Facilitator) from the following organizations: BG Group, BP, ExxonMobil, and SHELL. Additional funding came from the NSERC Discovery Grants 22R81254.

Numerical Procedures for Inlet/Diffuser/Nozzle Flows

NASA Technical Reports Server (NTRS)

Rubin, Stanley G.

1998-01-01

Two primitive variable, pressure based, flux-split, RNS/NS solution procedures for viscous flows are presented. Both methods are uniformly valid across the full Mach number range, Le., from the incompressible limit to high supersonic speeds. The first method is an 'optimized' version of a previously developed global pressure relaxation RNS procedure. Considerable reduction in the number of relatively expensive matrix inversion, and thereby in the computational time, has been achieved with this procedure. CPU times are reduced by a factor of 15 for predominantly elliptic flows (incompressible and low subsonic). The second method is a time-marching, 'linearized' convection RNS/NS procedure. The key to the efficiency of this procedure is the reduction to a single LU inversion at the inflow cross-plane. The remainder of the algorithm simply requires back-substitution with this LU and the corresponding residual vector at any cross-plane location. This method is not time-consistent, but has a convective-type CFL stability limitation. Both formulations are robust and provide accurate solutions for a variety of internal viscous flows to be provided herein.

Design and Evaluation of a Personal Diffusion Battery.

PubMed

Vosburgh, Donna J H; Klein, Timothy; Sheehan, Maura; Anthony, T Renee; Peters, Thomas M

A four-stage personal diffusion battery (pDB) was designed and constructed to measure submicron particle size distributions. The pDB consisted of a screen-type diffusion battery, solenoid valve system, and electronic controller. A data inversion spreadsheet was created to solve for the number median diameter (NMD), geometric standard deviation (GSD), and particle number concentration of unimodal aerosols using stage number concentrations from the pDB combined with a handheld condensation particle counter (pDB+CPC). The inversion spreadsheet included particle entry losses, theoretical penetrations across screens, the detection efficiency of the CPC, and constraints so the spreadsheet solved to values within the pDB range. Size distribution parameters (NMD, GSD, and number concentration) measured with the pDB+CPC with inversion spreadsheet were within 25% of those measured with a scanning mobility particle sizer (SMPS) for 5 of 12 polydisperse combustion aerosols. For three tests conducted with propylene torch exhaust, the pDB+CPC with inversion spreadsheet successfully identified that the NMD was smaller than the constraint value of 16 nm. The ratio of the nanoparticle portion of the aerosol compared to the reference ( R nano ) was calculated to determine the ability of pDB+CPC with inversion spreadsheet to measure the nanoparticle portion of the aerosols. The R nano ranged from 0.87 to 1.01 when the inversion solved and from 0.06 to 2.01 when the inversion solved to a constraint. The pDB combined with CPC has limited use as a personal monitor but combining the pDB with a different detector would allow for the pDB to be used as a personal monitor.

Design and Evaluation of a Personal Diffusion Battery

PubMed Central

Vosburgh, Donna J. H.; Klein, Timothy; Sheehan, Maura; Anthony, T. Renee; Peters, Thomas M.

2016-01-01

A four-stage personal diffusion battery (pDB) was designed and constructed to measure submicron particle size distributions. The pDB consisted of a screen-type diffusion battery, solenoid valve system, and electronic controller. A data inversion spreadsheet was created to solve for the number median diameter (NMD), geometric standard deviation (GSD), and particle number concentration of unimodal aerosols using stage number concentrations from the pDB combined with a handheld condensation particle counter (pDB+CPC). The inversion spreadsheet included particle entry losses, theoretical penetrations across screens, the detection efficiency of the CPC, and constraints so the spreadsheet solved to values within the pDB range. Size distribution parameters (NMD, GSD, and number concentration) measured with the pDB+CPC with inversion spreadsheet were within 25% of those measured with a scanning mobility particle sizer (SMPS) for 5 of 12 polydisperse combustion aerosols. For three tests conducted with propylene torch exhaust, the pDB+CPC with inversion spreadsheet successfully identified that the NMD was smaller than the constraint value of 16 nm. The ratio of the nanoparticle portion of the aerosol compared to the reference (R nano) was calculated to determine the ability of pDB+CPC with inversion spreadsheet to measure the nanoparticle portion of the aerosols. The R nano ranged from 0.87 to 1.01 when the inversion solved and from 0.06 to 2.01 when the inversion solved to a constraint. The pDB combined with CPC has limited use as a personal monitor but combining the pDB with a different detector would allow for the pDB to be used as a personal monitor. PMID:26900207

The tracer diffusion coefficient of soft nanoparticles in a linear polymer matrix

DOE PAGES

Imel, Adam E.; Rostom, Sahar; Holley, Wade; ...

2017-03-09

The diffusion properties of nanoparticles in polymer nanocomposites are largely unknown and are often difficult to determine experimentally. To address this shortcoming, we have developed a novel method to determine the tracer diffusion coefficient of soft polystyrene nanoparticles in a linear polystyrene matrix. Monitoring the interdiffusion of soft nanoparticles into a linear polystyrene matrix provides the mutual diffusion coefficient of this system, from which the tracer diffusion coefficient of the soft nanoparticle can be determined using the slow mode theory. Utilizing this protocol, the role of nanoparticle molecular weight and rigidity on its tracer diffusion coefficient is provided. These resultsmore » demonstrate that the diffusive behavior of these soft nanoparticles differ from that of star polymers, which is surprising since our recent studies suggest that the nanoparticle interacts with a linear polymer similarly to that of a star polymer. It appears that these deformable nanoparticles mostly closely mimic the diffusive behavior of fractal macromolecular architectures or microgels, where the transport of the nanoparticle relies on the cooperative motion of neighboring linear chains. Finally, the less cross-linked, and thus more deformable, nanoparticles diffuse faster than the more highly crosslinked nanoparticles, presumably because the increased deformability allows the nanoparticle to distort and fit into available space.« less

Adiabatic and fast passage ultra-wideband inversion in pulsed EPR.

PubMed

Doll, Andrin; Pribitzer, Stephan; Tschaggelar, René; Jeschke, Gunnar

2013-05-01

We demonstrate that adiabatic and fast passage ultra-wideband (UWB) pulses can achieve inversion over several hundreds of MHz and thus enhance the measurement sensitivity, as shown by two selected experiments. Technically, frequency-swept pulses are generated by a 12 GS/s arbitrary waveform generator and upconverted to X-band frequencies. This pulsed UWB source is utilized as an incoherent channel in an ordinary pulsed EPR spectrometer. We discuss experimental methodologies and modeling techniques to account for the response of the resonator, which can strongly limit the excitation bandwidth of the entire non-linear excitation chain. Aided by these procedures, pulses compensated for bandwidth or variations in group delay reveal enhanced inversion efficiency. The degree of bandwidth compensation is shown to depend critically on the time available for excitation. As a result, we demonstrate optimized inversion recovery and double electron electron resonance (DEER) experiments. First, virtually complete inversion of the nitroxide spectrum with an adiabatic pulse of 128ns length is achieved. Consequently, spectral diffusion between inverted and non-inverted spins is largely suppressed and the observation bandwidth can be increased to increase measurement sensitivity. Second, DEER is performed on a terpyridine-based copper (II) complex with a nitroxide-copper distance of 2.5nm. As previously demonstrated on this complex, when pumping copper spins and observing nitroxide spins, the modulation depth is severely limited by the excitation bandwidth of the pump pulse. By using fast passage UWB pulses with a maximum length of 64ns, we achieve up to threefold enhancement of the modulation depth. Associated artifacts in distance distributions when increasing the bandwidth of the pump pulse are shown to be small. Copyright © 2013 Elsevier Inc. All rights reserved.

Relativistic diffusive motion in random electromagnetic fields

NASA Astrophysics Data System (ADS)

Haba, Z.

2011-08-01

We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Jüttner equilibrium at the inverse temperature β-1 = mc2. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).

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.

Macro and micro rate zonal analytical centrifugation of polydisperse and slowly diffusing sedimenting systems in isovolumetric density gradients. Application to cartilage proteoglycans.

PubMed

Müller, F J; Pezon, C F; Pita, J C

1989-06-13

A method to study the polydispersity of zonally sedimenting and slowly diffusing macromolecules or particles in isokinetic or isovolumetric density gradients is presented. First, a brief theory is given for predicting the zonal profile after a "triangular" (or "inverse") zone is centrifuged. This type of zone is essential to preserve hydrodynamic stability of the very slowly diffusing polydisperse solutes. It is proven, both by semitheoretical considerations and by computer calculations, that the resulting concentration profile of macrosolute is almost identical with that obtainable with a rectangular zone coextensive with the triangular one and carrying the same total mass. Next, practical procedures are described for the convectionless layering of very small triangular zones (50 microL or less). The linearity and stability of the zones are experimentally tested and verified. Finally, the method is applied to cartilage proteoglycan preparations that included either the monomeric molecules only or both the monomeric and the aggregated ones. The zonal results are compared with those obtained by using conventional boundary sedimentation. The two sets of results are seen to coincide fairly well, thus proving that the present technique can add to preparative zonal centrifugation the analytical precision of boundary sedimentation. A multimodal polydisperse system is suggested to describe the aggregated proteoglycan macromolecules.

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.

Stability of stationary inverse transport equation in diffusion scaling

NASA Astrophysics Data System (ADS)

Chen, Ke; Li, Qin; Wang, Li

2018-02-01

We consider the inverse problem of reconstructing the optical parameters for the stationary radiative transfer equation (RTE) from velocity-averaged measurement. The RTE often contains multiple scales, characterized by the magnitude of a dimensionless parameter—the Knudsen number ( \

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.

Evaluation of the inverse dispersion modelling method for estimating ammonia multi-source emissions using low-cost long time averaging sensor

NASA Astrophysics Data System (ADS)

Loubet, Benjamin; Carozzi, Marco

2015-04-01

Tropospheric ammonia (NH3) is a key player in atmospheric chemistry and its deposition is a threat for the environment (ecosystem eutrophication, soil acidification and reduction in species biodiversity). Most of the NH3 global emissions derive from agriculture, mainly from livestock manure (storage and field application) but also from nitrogen-based fertilisers. Inverse dispersion modelling has been widely used to infer emission sources from a homogeneous source of known geometry. When the emission derives from different sources inside of the measured footprint, the emission should be treated as multi-source problem. This work aims at estimating whether multi-source inverse dispersion modelling can be used to infer NH3 emissions from different agronomic treatment, composed of small fields (typically squares of 25 m side) located near to each other, using low-cost NH3 measurements (diffusion samplers). To do that, a numerical experiment was designed with a combination of 3 x 3 square field sources (625 m2), and a set of sensors placed at the centre of each field at several heights as well as at 200 m away from the sources in each cardinal directions. The concentration at each sensor location was simulated with a forward Lagrangian Stochastic (WindTrax) and a Gaussian-like (FIDES) dispersion model. The concentrations were averaged over various integration times (3 hours to 28 days), to mimic the diffusion sampler behaviour with several sampling strategy. The sources were then inferred by inverse modelling using the averaged concentration and the same models in backward mode. The sources patterns were evaluated using a soil-vegetation-atmosphere model (SurfAtm-NH3) that incorporates the response of the NH3 emissions to surface temperature. A combination emission patterns (constant, linear decreasing, exponential decreasing and Gaussian type) and strengths were used to evaluate the uncertainty of the inversion method. Each numerical experiment covered a period of 28 days. The meteorological dataset of the fluxnet FR-Gri site (Grignon, FR) in 2008 was employed. Several sensor heights were tested, from 0.25 m to 2 m. The multi-source inverse problem was solved based on several sampling and field trial strategies: considering 1 or 2 heights over each field, considering the background concentration as known or unknown, and considering block-repetitions in the field set-up (3 repetitions). The inverse modelling approach demonstrated to be adapted for discriminating large differences in NH3 emissions from small agronomic plots using integrating sensors. The method is sensitive to sensor heights. The uncertainties and systematic biases are evaluated and discussed.

A hydraulic tomography approach coupling travel time inversion with steady shape analysis based on aquifer analogue study in coarsely clastic fluvial glacial deposit

NASA Astrophysics Data System (ADS)

Hu, R.; Brauchler, R.; Herold, M.; Bayer, P.; Sauter, M.

2009-04-01

Rarely is it possible to draw a significant conclusion about the geometry and the properties of geological structures of the underground using the information which is typically obtained from boreholes, since soil exploration is only representative of the position where the soil sample is taken from. Conventional aquifer investigation methods like pumping tests can provide hydraulic properties of a larger area; however, they lead to integral information. This information is insufficient to develop groundwater models, especially contaminant transport models, which require information about the spatial distribution of the hydraulic properties of the subsurface. Hydraulic tomography is an innovative method which has the potential to spatially resolve three dimensional structures of natural aquifer bodies. The method employs hydraulic short term tests performed between two or more wells, whereby the pumped intervals (sources) and the observation points (receivers) are separated by double packer systems. In order to optimize the computationally intensive tomographic inversion of transient hydraulic data we have decided to couple two inversion approaches (a) hydraulic travel time inversion and (b) steady shape inversion. (a) Hydraulic travel time inversion is based on the solution of the travel time integral, which describes the relationship between travel time of maximum signal variation of a transient hydraulic signal and the diffusivity between source and receiver. The travel time inversion is computationally extremely effective and robust, however, it is limited to the determination of diffusivity. In order to overcome this shortcoming we use the estimated diffusivity distribution as starting model for the steady shape inversion with the goal to separate the estimated diffusivity distribution into its components, hydraulic conductivity and specific storage. (b) The steady shape inversion utilizes the fact that at steady shape conditions, drawdown varies with time but the hydraulic gradient does not. By this trick, transient data can be analyzed with the computational efficiency of a steady state model, which proceeds hundreds of times faster than transient models. Finally, a specific storage distribution can be calculated from the diffusivity and hydraulic conductivity reconstructions derived from travel time and steady shape inversion. The groundwork of this study is the aquifer-analogue study from BAYER (1999), in which six parallel profiles of a natural sedimentary body with a size of 16m x 10m x 7m were mapped in high resolution with respect to structural and hydraulic parameters. Based on these results and using geostatistical interpolation methods, MAJI (2005) designed a three dimensional hydraulic model with a resolution of 5cm x 5cm x 5cm. This hydraulic model was used to simulate a large number of short term pumping tests in a tomographical array. The high resolution parameter reconstructions gained from the inversion of simulated pumping test data demonstrate that the proposed inversion scheme allows reconstructing the individual architectural elements and their hydraulic properties with a higher resolution compared to conventional hydraulic and geological investigation methods. Bayer P (1999) Aquifer-Analog-Studium in grobklastischen braided river Ablagerungen: Sedimentäre/hydrogeologische Wandkartierung und Kalibrierung von Georadarmessungen, Diplomkartierung am Lehrstuhl für Angewandte Geologie, Universität Tübingen, 25 pp. Maji, R. (2005) Conditional Stochastic Modelling of DNAPL Migration and Dissolution in a High-resolution Aquifer Analog, Ph.D. thesis at the University of Waterloo, 187 pp.

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.

Particle size segregation in granular avalanches: A brief review of recent progress

NASA Astrophysics Data System (ADS)

Gray, J. M. N. T.

2010-05-01

Hazardous natural flows such as snow avalanches, debris-flows, lahars and pyroclastic flows are part of a much wider class of granular avalanches, that frequently occur in industrial processes and in our kitchens! Granular avalanches are very efficient at sorting particles by size, with the smaller ones percolating down towards the base and squeezing the larger grains up towards the free-surface, to create inversely-graded layers. This paper provides a short introduction and review of recent theoretical advances in describing segregation and remixing with relatively simple hyperbolic and parabolic models. The derivation from two phase mixture theory is briefly summarized and links are drawn to earlier models of Savage & Lun and Dolgunin & Ukolov. The more complex parabolic version of the theory has a diffusive force that competes against segregation and yields S-shaped steady-state concentration profiles through the avalanche depth, that are able to reproduce results obtained from particle dynamics simulations. Time-dependent exact solutions can be constructed by using the Cole-Hopf transformation to linearize the segregation-remixing equation and the nonlinear surface and basal boundary conditions. In the limit of no diffusion, the theory is hyperbolic and the grains tend to separate out into completely segregated inversely graded layers. A series of elementary problems are used to demonstrate how concentration shocks, expansion fans, breaking waves and the large and small particles paths can be computed exactly using the model. The theory is able to capture the key features of the size distribution observed in stratification experiments, and explains how a large particle rich front is connected to an inversely graded avalanche in the interior. The theory is simple enough to couple it to the bulk flow field to investigate segregation-mobility feedback effects that spontaneously generate self-channelizing leveed avalanches, which can significantly enhance the total run-out distance of geophysical mass flows.

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

DOE PAGES

Kolev, Tzanio V.; Xu, Jinchao; Zhu, Yunrong

2015-08-23

In this study, we extend some of the multilevel convergence results obtained by Xu and Zhu, to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners for solving the linear systems arising from the linear finite element approximation of the problem, where both diffusion and reaction coefficients are piecewise-constant functions. We discuss in detail the influence of both the discontinuous reaction and diffusion coefficients to the performance of the classical BPX and multigrid V-cycle preconditioner.

Diffusion by one wave and by many waves

NASA Astrophysics Data System (ADS)

Albert, J. M.

2010-03-01

Radiation belt electrons and chorus waves are an outstanding instance of the important role cyclotron resonant wave-particle interactions play in the magnetosphere. Chorus waves are particularly complex, often occurring with large amplitude, narrowband but drifting frequency and fine structure. Nevertheless, modeling their effect on radiation belt electrons with bounce-averaged broadband quasi-linear theory seems to yield reasonable results. It is known that coherent interactions with monochromatic waves can cause particle diffusion, as well as radically different phase bunching and phase trapping behavior. Here the two formulations of diffusion, while conceptually different, are shown to give identical diffusion coefficients, in the narrowband limit of quasi-linear theory. It is further shown that suitably averaging the monochromatic diffusion coefficients over frequency and wave normal angle parameters reproduces the full broadband quasi-linear results. This may account for the rather surprising success of quasi-linear theory in modeling radiation belt electrons undergoing diffusion by chorus waves.

Combined Tensor Fitting and TV Regularization in Diffusion Tensor Imaging Based on a Riemannian Manifold Approach.

PubMed

Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir

2016-08-01

In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.

Methods for characterizing subsurface volatile contaminants using in-situ sensors

DOEpatents

Ho, Clifford K [Albuquerque, NM

2006-02-21

An inverse analysis method for characterizing diffusion of vapor from an underground source of volatile contaminant using data taken by an in-situ sensor. The method uses one-dimensional solutions to the diffusion equation in Cartesian, cylindrical, or spherical coordinates for isotropic and homogenous media. If the effective vapor diffusion coefficient is known, then the distance from the source to the in-situ sensor can be estimated by comparing the shape of the predicted time-dependent vapor concentration response curve to the measured response curve. Alternatively, if the source distance is known, then the effective vapor diffusion coefficient can be estimated using the same inverse analysis method. A triangulation technique can be used with multiple sensors to locate the source in two or three dimensions. The in-situ sensor can contain one or more chemiresistor elements housed in a waterproof enclosure with a gas permeable membrane.

Weighted linear least squares estimation of diffusion MRI parameters: strengths, limitations, and pitfalls.

PubMed

Veraart, Jelle; Sijbers, Jan; Sunaert, Stefan; Leemans, Alexander; Jeurissen, Ben

2013-11-01

Linear least squares estimators are widely used in diffusion MRI for the estimation of diffusion parameters. Although adding proper weights is necessary to increase the precision of these linear estimators, there is no consensus on how to practically define them. In this study, the impact of the commonly used weighting strategies on the accuracy and precision of linear diffusion parameter estimators is evaluated and compared with the nonlinear least squares estimation approach. Simulation and real data experiments were done to study the performance of the weighted linear least squares estimators with weights defined by (a) the squares of the respective noisy diffusion-weighted signals; and (b) the squares of the predicted signals, which are reconstructed from a previous estimate of the diffusion model parameters. The negative effect of weighting strategy (a) on the accuracy of the estimator was surprisingly high. Multi-step weighting strategies yield better performance and, in some cases, even outperformed the nonlinear least squares estimator. If proper weighting strategies are applied, the weighted linear least squares approach shows high performance characteristics in terms of accuracy/precision and may even be preferred over nonlinear estimation methods. Copyright © 2013 Elsevier Inc. All rights reserved.

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.

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.

Estimating the spin diffusion length and the spin Hall angle from spin pumping induced inverse spin Hall voltages

NASA Astrophysics Data System (ADS)

Roy, Kuntal

2017-11-01

There exists considerable confusion in estimating the spin diffusion length of materials with high spin-orbit coupling from spin pumping experiments. For designing functional devices, it is important to determine the spin diffusion length with sufficient accuracy from experimental results. An inaccurate estimation of spin diffusion length also affects the estimation of other parameters (e.g., spin mixing conductance, spin Hall angle) concomitantly. The spin diffusion length for platinum (Pt) has been reported in the literature in a wide range of 0.5-14 nm, and in particular it is a constant value independent of Pt's thickness. Here, the key reasonings behind such a wide range of reported values of spin diffusion length have been identified comprehensively. In particular, it is shown here that a thickness-dependent conductivity and spin diffusion length is necessary to simultaneously match the experimental results of effective spin mixing conductance and inverse spin Hall voltage due to spin pumping. Such a thickness-dependent spin diffusion length is tantamount to the Elliott-Yafet spin relaxation mechanism, which bodes well for transitional metals. This conclusion is not altered even when there is significant interfacial spin memory loss. Furthermore, the variations in the estimated parameters are also studied, which is important for technological applications.

The Stokes-Einstein relation at moderate Schmidt number.

PubMed

Balboa Usabiaga, Florencio; Xie, Xiaoyi; Delgado-Buscalioni, Rafael; Donev, Aleksandar

2013-12-07

The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently developed minimally resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The mismatch arises because thermal fluctuations affect the drag coefficient for a particle due to the nonlinear nature of the fluid-particle coupling. The numerical data are in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.

An inverse moisture diffusion algorithm for the determination of diffusion coefficient

Treesearch

Jen Y. Liu; William T. Simpson; Steve P. Verrill

2000-01-01

The finite difference approximation is applied to estimate the moisture-dependent diffusion coefficient by utilizing test data of isothermal moisture desorption in northern red oak (Quercus rubra). The test data contain moisture distributions at discrete locations across the thickness of specimens, which coincides with the radial direction of northern red oak, and at...

An inverse moisture diffusion algorithm for the determination of diffusion coefficient

Treesearch

Jen Y. Liu; William T. Simpson; Steve P. Verrill

2001-01-01

The finite difference approximation is applied to estimate the moisture-dependent diffusion coefficient by utilizing test data of isothermal moisture desorption in northern red oak (Quercus rubra). The test data contain moisture distributions at discrete locations across the thickness of specimens, which coincides with the radial direction of northern red oak, and at...

Absorption features of chromophoric dissolved organic matter (CDOM) and tracing implication for dissolved organic carbon (DOC) in Changjiang Estuary, China

NASA Astrophysics Data System (ADS)

Zhang, X. Y.; Chen, X.; Deng, H.; Du, Y.; Jin, H. Y.

2013-07-01

Chromophoric dissolved organic matter (CDOM) represents the light absorbing fraction of dissolved organic carbon (DOC). Studies have shown that the optical properties of CDOM can be used to infer the distribution and diffusion characteristics of DOC in the estuary and coastal zone. The inversion of DOC concentrations from remote sensing has been implemented in certain regions. In this study we investigate the potential of tracing DOC from CDOM by the measurement of DOC, absorption spectrum of CDOM, Chla concentration, suspended sediment (SS), and salinity from cruises in different seasons around the Changjiang estuary. Our results show that around the Changjiang estuary the absorption coefficients of CDOM in general have the similar spatial and temporal characteristics as that of DOC, but the strength of the correlation between CDOM and DOC varies locally and seasonally. The input of pollutants from outside the estuary, the bloom of phytoplankton in spring, re-suspension of deposited sediment, and light bleaching all contribute to the local and seasonal variation of the correlation between DOC and CDOM. An inversion model for the determination of DOC from CDOM is established, but the stability of model parameters and its application in different environments need further study. We find that relative to the absorption coefficient of CDOM, the fitted parameters of the absorption spectrum of DOM are better indictors for the composition of DOC. In addition, it is found that the terrestrial input of DOC to Changjiang estuary is a typical two-stage dilution process instead of a linear diffusion process.

Photothermal depth profiling: Comparison between genetic algorithms and thermal wave backscattering (abstract)

NASA Astrophysics Data System (ADS)

Li Voti, R.; Sibilia, C.; Bertolotti, M.

2003-01-01

Photothermal depth profiling has been the subject of many papers in the last years. Inverse problems on different kinds of materials have been identified, classified, and solved. A first classification has been done according to the type of depth profile: the physical quantity to be reconstructed is the optical absorption in the problems of type I, the thermal effusivity for type II, and both of them for type III. Another classification may be done depending on the time scale of the pump beam heating (frequency scan, time scan), or on its geometrical symmetry (one- or three-dimensional). In this work we want to discuss two different approaches, the genetic algorithms (GA) [R. Li Voti, C. Melchiorri, C. Sibilia, and M. Bertolotti, Anal. Sci. 17, 410 (2001); R. Li Voti, Proceedings, IV Int. Workshop on Advances in Signal Processing for Non-Destructive Evaluation of Materials, Quebec, August 2001] and the thermal wave backscattering (TWBS) [R. Li Voti, G. L. Liakhou, S. Paoloni, C. Sibilia, and M. Bertolotti, Anal. Sci. 17, 414 (2001); J. C. Krapez and R. Li Voti, Anal. Sci. 17, 417 (2001)], showing their performances and limits of validity for several kinds of photothermal depth profiling problems: The two approaches are based on different mechanisms and exhibit obviously different features. GA may be implemented on the exact heat diffusion equation as follows: one chromosome is associated to each profile. The genetic evolution of the chromosome allows one to find better and better profiles, eventually converging towards the solution of the inverse problem. The main advantage is that GA may be applied to any arbitrary profile, but several disadvantages exist; for example, the complexity of the algorithm, the slow convergence, and consequently the computer time consumed. On the contrary, TWBS uses a simplified theoretical model of heat diffusion in inhomogeneous materials. According to such a model, the photothermal signal depends linearly on the thermal effusivity inhomogeneities, which may be detected because they act as backscattering centers for the heat flux. The physical problem is reduced to the inversion of a algebraic linear system. The advantage is that TWBS allows excellent reconstructions, but only within the limits of validity of the approximate model, which include any slowly varying profile. Recently we have tested the perfomance of both TWBS and GA on linear conductivity profiles. In other words, we have done the numerical simulations of the photothermal measurements coming from a film over a substrate, where the conductivity in the film changes linearly from k1 at the surface, to k2 at the substrate. TWBS and GA have been used to reconstruct the original profiles. If the conductivity mismatch ranges as 0.2

DIFF--A 7090 Fortran Program to Determine Neutron Diffusion Constants Relating to a Six-Group Calculation; DIFF--UN PROGRAMME FOR TRAN 7090 POUR DETERMINER LES CONSTANTES DE DIFFUSION NEUTRONIQUE RELATIVES A UN CALCUL A SIX GROUPES

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

Plelnevaux, C.

The computer program DIFF, in Fortran for the IBM 7090, for calculating the neutron diffusion coefficients and attenuation areas (L/sup 2/) necessary for multigroup diffusion calculations for reactor shielding is described. Diffusion coefficients and values of the inverse attenuation length are given for a six group calculation for several interesting shielding materials. (D.C.W.)

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

Demonstrating Diffusion

ERIC Educational Resources Information Center

Foy, Barry G.

1977-01-01

Two demonstrations are described. Materials and instructions for demonstrating movement of molecules into cytoplasm using agar blocks, phenolphthalein, and sodium hydroxide are given. A simple method for demonstrating that the rate of diffusion of a gas is inversely proportional to its molecular weight is also presented. (AJ)

Color-coded fluid-attenuated inversion recovery images improve inter-rater reliability of fluid-attenuated inversion recovery signal changes within acute diffusion-weighted image lesions.

PubMed

Kim, Bum Joon; Kim, Yong-Hwan; Kim, Yeon-Jung; Ahn, Sung Ho; Lee, Deok Hee; Kwon, Sun U; Kim, Sang Joon; Kim, Jong S; Kang, Dong-Wha

2014-09-01

Diffusion-weighted image fluid-attenuated inversion recovery (FLAIR) mismatch has been considered to represent ischemic lesion age. However, the inter-rater agreement of diffusion-weighted image FLAIR mismatch is low. We hypothesized that color-coded images would increase its inter-rater agreement. Patients with ischemic stroke <24 hours of a clear onset were retrospectively studied. FLAIR signal change was rated as negative, subtle, or obvious on conventional and color-coded FLAIR images based on visual inspection. Inter-rater agreement was evaluated using κ and percent agreement. The predictive value of diffusion-weighted image FLAIR mismatch for identification of patients <4.5 hours of symptom onset was evaluated. One hundred and thirteen patients were enrolled. The inter-rater agreement of FLAIR signal change improved from 69.9% (k=0.538) with conventional images to 85.8% (k=0.754) with color-coded images (P=0.004). Discrepantly rated patients on conventional, but not on color-coded images, had a higher prevalence of cardioembolic stroke (P=0.02) and cortical infarction (P=0.04). The positive predictive value for patients <4.5 hours of onset was 85.3% and 71.9% with conventional and 95.7% and 82.1% with color-coded images, by each rater. Color-coded FLAIR images increased the inter-rater agreement of diffusion-weighted image FLAIR recovery mismatch and may ultimately help identify unknown-onset stroke patients appropriate for thrombolysis. © 2014 American Heart Association, Inc.

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).

Image Halftoning and Inverse Halftoning for Optimized Dot Diffusion

DTIC Science & Technology

1998-01-01

systems.caltech.edu, ppvnath@sys.caltech.edu ABSTRACT The dot diffusion method for digital halftoning has the advantage of parallelism unlike the error ... halftoning : ordered dither [3], error diffusion [4], neural-net based methods [2], and more recently direct binary search (DBS) [10]. Ordered dithering is a...patterns. On the other hand error diffused halftones do not suffer from periodicity and offer blue noise characteristic [11] which is found to be

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.

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.

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.

Accounting for magnetic diffusion in core flow inversions from geomagnetic secular variation

NASA Astrophysics Data System (ADS)

Amit, Hagay; Christensen, Ulrich R.

2008-12-01

We use numerical dynamos to investigate the possible role of magnetic diffusion at the top of the core. We find that the contribution of radial magnetic diffusion to the secular variation is correlated with that of tangential magnetic diffusion for a wide range of control parameters. The correlation between the two diffusive terms is interpreted in terms of the variation in the strength of poloidal flow along a columnar flow tube. The amplitude ratio of the two diffusive terms is used to estimate the probable contribution of radial magnetic diffusion to the secular variation at Earth-like conditions. We then apply a model where radial magnetic diffusion is proportional to tangential diffusion to core flow inversions of geomagnetic secular variation data. We find that including magnetic diffusion does not change dramatically the global flow but some significant local variations appear. In the non frozen-flux core flow models (termed `diffusive'), the hemispherical dichotomy between the active Atlantic and quiet Pacific is weaker, a cyclonic vortex below North America emerges and the vortex below Asia is stronger. Our results have several important geophysical implications. First, our diffusive flow models contain some flow activity at low latitudes in the Pacific, suggesting a local balance between magnetic field advection and diffusion in that region. Second, the cyclone below North America in our diffusive flows reconciles the difference between mantle-driven thermal wind predictions and frozen-flux core flow models, and is consistent with the prominent intense magnetic flux patch below North America in geomagnetic field models. Finally, we hypothesize that magnetic diffusion near the core surface plays a larger role in the geomagnetic secular variation than usually assumed.

A fast reconstruction algorithm for fluorescence optical diffusion tomography based on preiteration.

PubMed

Song, Xiaolei; Xiong, Xiaoyun; Bai, Jing

2007-01-01

Fluorescence optical diffusion tomography in the near-infrared (NIR) bandwidth is considered to be one of the most promising ways for noninvasive molecular-based imaging. Many reconstructive approaches to it utilize iterative methods for data inversion. However, they are time-consuming and they are far from meeting the real-time imaging demands. In this work, a fast preiteration algorithm based on the generalized inverse matrix is proposed. This method needs only one step of matrix-vector multiplication online, by pushing the iteration process to be executed offline. In the preiteration process, the second-order iterative format is employed to exponentially accelerate the convergence. Simulations based on an analytical diffusion model show that the distribution of fluorescent yield can be well estimated by this algorithm and the reconstructed speed is remarkably increased.

Warthin tumor of the parotid gland: diagnostic value of MR imaging with histopathologic correlation.

PubMed

Ikeda, Mitsuaki; Motoori, Ken; Hanazawa, Toyoyuki; Nagai, Yuichiro; Yamamoto, Seiji; Ueda, Takuya; Funatsu, Hiroyuki; Ito, Hisao

2004-08-01

The purpose of our study was to describe the MR imaging appearance of Warthin tumors multiple MR imaging techniques and to interpret the difference in appearance from that of malignant parotid tumors. T1-weighted, T2-weighted, short inversion time inversion recovery, diffusion-weighted, and contrast-enhanced dynamic MR images of 19 Warthin tumors and 17 malignant parotid tumors were reviewed. MR imaging results were compared with those of pathologic analysis. Epithelial stromata and lymphoid tissue with slitlike small cysts in Warthin tumors showed early enhancement and a high washout rate (> or =30%) on dynamic contrast-enhanced images, and accumulations of complicated cysts showed early enhancement and a low washout ratio (< 30%). The areas containing complicated cysts showed high signal intensity on T1-weighted images, whereas some foci in those areas showed low signal intensity on short tau inversion recovery images. The mean minimum signal intensity ratios (SIRmin) of Warthin tumor on short tau inversion recovery (0.29 +/- 0.22 SD) (P < .01) and T2-weighted images (0.28 +/- 0.09) (P < .05) were significantly lower than those of malignant parotid tumors (0.53 +/- 0.19, 0.48 +/- 0.19). The average washout ratio of Warthin tumors (44.0 +/- 20.4%) was higher than that of malignant parotid tumors (11.9 +/- 11.6%). The mean apparent diffusion coefficient of Warthin tumors (0.96 +/- 0.13 x 10(-3)mm2/s) was significantly lower (P < .01) than that of malignant tumors (1.19 +/- 0.19 x 10(-3)mm2/s). Detecting hypointense areas of short tau inversion recovery and T2-weighted images or low apparent diffusion coefficient values on diffusion-weighted images was useful for predicting whether salivary gland tumors were Warthin tumors. The findings of the dynamic contrast-enhanced study also were useful.

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.

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.

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.

Using Directional Diffusion Coefficients for Nonlinear Diffusion Acceleration of the First Order SN Equations in Near-Void Regions

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

Schunert, Sebastian; Hammer, Hans; Lou, Jijie

2016-11-01

The common definition of the diffusion coeffcient as the inverse of three times the transport cross section is not compat- ible with voids. Morel introduced a non-local tensor diffusion coeffcient that remains finite in voids[1]. It can be obtained by solving an auxiliary transport problem without scattering or fission. Larsen and Trahan successfully applied this diffusion coeffcient for enhancing the accuracy of diffusion solutions of very high temperature reactor (VHTR) problems that feature large, optically thin channels in the z-direction [2]. It is demonstrated that a significant reduction of error can be achieved in particular in the optically thin region.more » Along the same line of thought, non-local diffusion tensors are applied modeling the TREAT reactor confirming the findings of Larsen and Trahan [3]. Previous work of the authors have introduced a flexible Nonlinear-Diffusion Acceleration (NDA) method for the first order S N equations discretized with the discontinuous finite element method (DFEM), [4], [5], [6]. This NDA method uses a scalar diffusion coeffcient in the low-order system that is obtained as the flux weighted average of the inverse transport cross section. Hence, it su?ers from very large and potentially unbounded diffusion coeffcients in the low order problem. However, it was noted that the choice of the diffusion coeffcient does not influence consistency of the method at convergence and hence the di?usion coeffcient is essentially a free parameter. The choice of the di?usion coeffcient does, however, affect the convergence behavior of the nonlinear di?usion iterations. Within this work we use Morel’s non-local di?usion coef- ficient in the aforementioned NDA formulation in lieu of the flux weighted inverse of three times the transport cross section. The goal of this paper is to demonstrate that significant en- hancement of the spectral properties of NDA can be achieved in near void regions. For testing the spectral properties of the NDA with non-local diffusion coeffcients, the periodical horizontal interface problem is used [7]. This problem consists of alternating stripes of optically thin and thick materials both of which feature scattering ratios close to unity.« less

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.

Gas-induced friction and diffusion of rigid rotors

NASA Astrophysics Data System (ADS)

Martinetz, Lukas; Hornberger, Klaus; Stickler, Benjamin A.

2018-05-01

We derive the Boltzmann equation for the rotranslational dynamics of an arbitrary convex rigid body in a rarefied gas. It yields as a limiting case the Fokker-Planck equation accounting for friction, diffusion, and nonconservative drift forces and torques. We provide the rotranslational friction and diffusion tensors for specular and diffuse reflection off particles with spherical, cylindrical, and cuboidal shape, and show that the theory describes thermalization, photophoresis, and the inverse Magnus effect in the free molecular regime.

Global Ocean Circulation in Thermohaline Coordinates and Small-scale and Mesoscale mixing: An Inverse Estimate.

NASA Astrophysics Data System (ADS)

Groeskamp, S.; Zika, J. D.; McDougall, T. J.; Sloyan, B.

2016-02-01

I will present results of a new inverse technique that infers small-scale turbulent diffusivities and mesoscale eddy diffusivities from an ocean climatology of Salinity (S) and Temperature (T) in combination with surface freshwater and heat fluxes.First, the ocean circulation is represented in (S,T) coordinates, by the diathermohaline streamfunction. Framing the ocean circulation in (S,T) coordinates, isolates the component of the circulation that is directly related to water-mass transformation.Because water-mass transformation is directly related to fluxes of salt and heat, this framework allows for the formulation of an inverse method in which the diathermohaline streamfunction is balanced with known air-sea forcing and unknown mixing. When applying this inverse method to observations, we obtain observationally based estimates for both the streamfunction and the mixing. The results reveal new information about the component of the global ocean circulation due to water-mass transformation and its relation to surface freshwater and heat fluxes and small-scale and mesoscale mixing. The results provide global constraints on spatially varying patterns of diffusivities, in order to obtain a realistic overturning circulation. We find that mesoscale isopycnal mixing is much smaller than expected. These results are important for our understanding of the relation between global ocean circulation and mixing and may lead to improved parameterisations in numerical ocean models.

Forward and inverse functional variations in rotationally inelastic scattering

NASA Astrophysics Data System (ADS)

Guzman, Robert; Rabitz, Herschel

1986-09-01

This paper considers the response of various rotational energy transfer processes to functional variations about an assumed model intermolecular potential. Attention is focused on the scattering of an atom and a linear rigid rotor. The collision dynamics are approximated by employing both the infinite order sudden (IOS) and exponential distorted wave (EDW) methods to describe Ar-N2 and He-H2, respectively. The following cross sections are considered: state-to-state differential and integral, final state summed differential and integral, and effective diffusion and viscosity cross sections. Attention is first given to the forward sensitivity densities δ0/δV(R,r) where 0 denotes any of the aforementioned cross sections, R is the intermolecular distance, and r is the internal coordinates. These forward sensitivity densities (functional derivatives) offer a quantitative measure of the importance of different regions of the potential surface to a chosen cross section. Via knowledge of the forward sensitivities and a particular variation δV(R,r) the concomitant response δ0 is generated. It was found that locally a variation in the potential can give rise to a large response in the cross sections as measured by these forward densities. In contrast, a unit percent change in the overall potential produced a 1%-10% change in the cross sections studied indicating that the large + and - responses to local variations tend to cancel. In addition, inverse sensitivity densities δV(R,r)/δ0 are obtained. These inverse densities are of interest since they are the exact solution to the infinitesimal inverse scattering problem. Although the inverse sensitivity densities do not in themselves form an inversion algorithm, they do offer a quantitative measure of the importance of performing particular measurements for the ultimate purpose of inversion. Using a set of state-to-state integral cross sections we found that the resultant responses from the infinitesimal inversion were typically small such that ‖δV(R,r)‖≪‖V(R,r)‖. From the viewpoint of an actual inversion, these results indicate that only through an extensive effort will significant knowledge of the potential be gained from the cross sections. All of these calculations serve to illustrate the methodology, and other observables as well as dynamical schemes could be explored as desired.

A framework to analyze cerebral mean diffusivity using surface guided diffusion mapping in diffusion tensor imaging

PubMed Central

Kwon, Oh-Hun; Park, Hyunjin; Seo, Sang-Won; Na, Duk L.; Lee, Jong-Min

2015-01-01

The mean diffusivity (MD) value has been used to describe microstructural properties in Diffusion Tensor Imaging (DTI) in cortical gray matter (GM). Recently, researchers have applied a cortical surface generated from the T1-weighted volume. When the DTI data are analyzed using the cortical surface, it is important to assign an accurate MD value from the volume space to the vertex of the cortical surface, considering the anatomical correspondence between the DTI and the T1-weighted image. Previous studies usually sampled the MD value using the nearest-neighbor (NN) method or Linear method, even though there are geometric distortions in diffusion-weighted volumes. Here we introduce a Surface Guided Diffusion Mapping (SGDM) method to compensate for such geometric distortions. We compared our SGDM method with results using NN and Linear methods by investigating differences in the sampled MD value. We also projected the tissue classification results of non-diffusion-weighted volumes to the cortical midsurface. The CSF probability values provided by the SGDM method were lower than those produced by the NN and Linear methods. The MD values provided by the NN and Linear methods were significantly greater than those of the SGDM method in regions suffering from geometric distortion. These results indicate that the NN and Linear methods assigned the MD value in the CSF region to the cortical midsurface (GM region). Our results suggest that the SGDM method is an effective way to correct such mapping errors. PMID:26236180

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.

Effective scattering coefficient of the cerebral spinal fluid in adult head models for diffuse optical imaging

NASA Astrophysics Data System (ADS)

Custo, Anna; Wells, William M., III; Barnett, Alex H.; Hillman, Elizabeth M. C.; Boas, David A.

2006-07-01

An efficient computation of the time-dependent forward solution for photon transport in a head model is a key capability for performing accurate inversion for functional diffuse optical imaging of the brain. The diffusion approximation to photon transport is much faster to simulate than the physically correct radiative transport equation (RTE); however, it is commonly assumed that scattering lengths must be much smaller than all system dimensions and all absorption lengths for the approximation to be accurate. Neither of these conditions is satisfied in the cerebrospinal fluid (CSF). Since line-of-sight distances in the CSF are small, of the order of a few millimeters, we explore the idea that the CSF scattering coefficient may be modeled by any value from zero up to the order of the typical inverse line-of-sight distance, or approximately 0.3 mm-1, without significantly altering the calculated detector signals or the partial path lengths relevant for functional measurements. We demonstrate this in detail by using a Monte Carlo simulation of the RTE in a three-dimensional head model based on clinical magnetic resonance imaging data, with realistic optode geometries. Our findings lead us to expect that the diffusion approximation will be valid even in the presence of the CSF, with consequences for faster solution of the inverse problem.

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.

Specific Features in Measuring Particle Size Distributions in Highly Disperse Aerosol Systems

NASA Astrophysics Data System (ADS)

Zagaynov, V. A.; Vasyanovich, M. E.; Maksimenko, V. V.; Lushnikov, A. A.; Biryukov, Yu. G.; Agranovskii, I. E.

2018-06-01

The distribution of highly dispersed aerosols is studied. Particular attention is given to the diffusion dynamic approach, as it is the best way to determine particle size distribution. It shown that the problem can be divided into two steps: directly measuring particle penetration through diffusion batteries and solving the inverse problem (obtaining a size distribution from the measured penetrations). No reliable way of solving the so-called inverse problem is found, but it can be done by introducing a parametrized size distribution (i.e., a gamma distribution). The integral equation is therefore reduced to a system of nonlinear equations that can be solved by elementary mathematical means. Further development of the method requires an increase in sensitivity (i.e., measuring the dimensions of molecular clusters with radioactive sources, along with the activity of diffusion battery screens).

Good News for Borehole Climatology

NASA Astrophysics Data System (ADS)

Rath, Volker; Fidel Gonzalez-Rouco, J.; Goosse, Hugues

2010-05-01

Though the investigation of observed borehole temperatures has proved to be a valuable tool for the reconstruction of ground surface temperature histories, there are many open questions concerning the significance and accuracy of the reconstructions from these data. In particular, the temperature signal of the warming after the Last glacial Maximum (LGM) is still present in borehole temperature profiles. It influences the relatively shallow boreholes used in current paleoclimate inversions to estimate temperature changes in the last centuries. This is shown using Monte Carlo experiments on past surface temperature change, using plausible distributions for the most important parameters, i.e.,amplitude and timing of the glacial-interglacial transition, the prior average temperature, and petrophysical properties. It has been argued that the signature of the last glacial-interglacial transition could be responsible for the high amplitudes of millennial temperature reconstructions. However, in shallow boreholes the additional effect of past climate can reasonably approximated by a linear variation of temperature with depth, and thus be accommodated by a "biased" background heat flow. This is good news for borehole climate, but implies that the geological heat flow values have to be interpreted accordingly. Borehole climate reconstructions from these shallow are most probably underestimating past variability due to the diffusive character of the heat conduction process, and the smoothness constraints necessary for obtaining stable solutions of this ill-posed inverse problem. A simple correction based on subtracting an appropriate prior surface temperature history shows promising results reducing these errors considerably, also with deeper boreholes, where the heat flow signal can not be approximated linearly, and improves the comparisons with AOGCM modeling results.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Thermoelectric transport in two-dimensional giant Rashba systems

NASA Astrophysics Data System (ADS)

Xiao, Cong; Li, Dingping; Ma, Zhongshui; Niu, Qian

Thermoelectric transport in strongly spin-orbit coupled two-dimensional Rashba systems is studied using the analytical solution of the linearized Boltzmann equation. To highlight the effects of inter-band scattering, we assume point-like potential impurities, and obtain the band-and energy-dependent transport relaxation times. Unconventional transport behaviors arise when the Fermi level lies near or below the band crossing point (BCP), such as the non-Drude electrical conducivity below the BCP, the failure of the standard Mott relation linking the Peltier coefficient to the electrical conductivity near the BCP, the enhancement of diffusion thermopower and figure of merit below the BCP, the zero-field Hall coefficient which is not inversely proportional to and not a monotonic function of the carrier density, the enhanced Nernst coefficient below the BCP, and the enhanced current-induced spin-polarization efficiency.

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.

Performance of a low-pressure-ratio centrifugal compressor with four diffuser designs

NASA Technical Reports Server (NTRS)

Klassen, H. A.

1973-01-01

A low-pressure-ratio centrifugal compressor was tested with four different diffuser configurations. One diffuser had airfoil vanes. Two were pipe diffusers. One pipe diffuser had 7.5 deg cone diffusing passages. The other had trumpet-shaped passages designed for linear static-pressure rise from throat to exit. The fourth configuration had flat vanes with elliptical leading edges similar to those of pipe diffusers. The side walls were contoured to produce a linear pressure rise. Peak compressor efficiencies were 0.82 with the airfoil vane and conical pipe diffusers, 0.80 with the trumpet, and 0.74 with the flat-vane design. Surge margin and useful range were greater for the airfoil-vane diffuser than for the other three.

On Large Time Behavior and Selection Principle for a Diffusive Carr-Penrose Model

NASA Astrophysics Data System (ADS)

Conlon, Joseph G.; Dabkowski, Michael; Wu, Jingchen

2016-04-01

This paper is concerned with the study of a diffusive perturbation of the linear LSW model introduced by Carr and Penrose. A main subject of interest is to understand how the presence of diffusion acts as a selection principle, which singles out a particular self-similar solution of the linear LSW model as determining the large time behavior of the diffusive model. A selection principle is rigorously proven for a model which is a semiclassical approximation to the diffusive model. Upper bounds on the rate of coarsening are also obtained for the full diffusive model.

[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.

Quasi-ballistic Electronic Thermal Conduction in Metal Inverse Opals.

PubMed

Barako, Michael T; Sood, Aditya; Zhang, Chi; Wang, Junjie; Kodama, Takashi; Asheghi, Mehdi; Zheng, Xiaolin; Braun, Paul V; Goodson, Kenneth E

2016-04-13

Porous metals are used in interfacial transport applications that leverage the combination of electrical and/or thermal conductivity and the large available surface area. As nanomaterials push toward smaller pore sizes to increase the total surface area and reduce diffusion length scales, electron conduction within the metal scaffold becomes suppressed due to increased surface scattering. Here we observe the transition from diffusive to quasi-ballistic thermal conduction using metal inverse opals (IOs), which are metal films that contain a periodic arrangement of interconnected spherical pores. As the material dimensions are reduced from ∼230 nm to ∼23 nm, the thermal conductivity of copper IOs is reduced by more than 57% due to the increase in surface scattering. In contrast, nickel IOs exhibit diffusive-like conduction and have a constant thermal conductivity over this size regime. The quasi-ballistic nature of electron transport at these length scales is modeled considering the inverse opal geometry, surface scattering, and grain boundaries. Understanding the characteristics of electron conduction at the nanoscale is essential to minimizing the total resistance of porous metals for interfacial transport applications, such as the total electrical resistance of battery electrodes and the total thermal resistance of microscale heat exchangers.

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.).

Financial market dynamics: superdiffusive or not?

NASA Astrophysics Data System (ADS)

Devi, Sandhya

2017-08-01

The behavior of stock market returns over a period of 1-60 d has been investigated for S&P 500 and Nasdaq within the framework of nonextensive Tsallis statistics. Even for such long terms, the distributions of the returns are non-Gaussian. They have fat tails indicating that the stock returns do not follow a random walk model. In this work, a good fit to a Tsallis q-Gaussian distribution is obtained for the distributions of all the returns using the method of Maximum Likelihood Estimate. For all the regions of data considered, the values of the scaling parameter q, estimated from 1 d returns, lie in the range 1.4-1.65. The estimated inverse mean square deviations (beta) show a power law behavior in time with exponent values between  -0.91 and  -1.1 indicating normal to mildly subdiffusive behavior. Quite often, the dynamics of market return distributions is modelled by a Fokker-Plank (FP) equation either with a linear drift and a nonlinear diffusion term or with just a nonlinear diffusion term. Both of these cases support a q-Gaussian distribution as a solution. The distributions obtained from current estimated parameters are compared with the solutions of the FP equations. For negligible drift term, the inverse mean square deviations (betaFP) from the FP model follow a power law with exponent values between  -1.25 and  -1.48 indicating superdiffusion. When the drift term is non-negligible, the corresponding betaFP do not follow a power law and become stationary after certain characteristic times that depend on the values of the drift parameter and q. Neither of these behaviors is supported by the results of the empirical fit.

Modified chloride diffusion model for concrete under the coupling effect of mechanical load and chloride salt environment

NASA Astrophysics Data System (ADS)

Lei, Mingfeng; Lin, Dayong; Liu, Jianwen; Shi, Chenghua; Ma, Jianjun; Yang, Weichao; Yu, Xiaoniu

2018-03-01

For the purpose of investigating lining concrete durability, this study derives a modified chloride diffusion model for concrete based on the odd continuation of boundary conditions and Fourier transform. In order to achieve this, the linear stress distribution on a sectional structure is considered, detailed procedures and methods are presented for model verification and parametric analysis. Simulation results show that the chloride diffusion model can reflect the effects of linear stress distribution of the sectional structure on the chloride diffusivity with reliable accuracy. Along with the natural environmental characteristics of practical engineering structures, reference value ranges of model parameters are provided. Furthermore, a chloride diffusion model is extended for the consideration of multi-factor coupling of linear stress distribution, chloride concentration and diffusion time. Comparison between model simulation and typical current research results shows that the presented model can produce better considerations with a greater universality.

Improved algorithm for estimating optical properties of food and biological materials using spatially-resolved diffuse reflectance

USDA-ARS?s Scientific Manuscript database

In this research, the inverse algorithm for estimating optical properties of food and biological materials from spatially-resolved diffuse reflectance was optimized in terms of data smoothing, normalization and spatial region of reflectance profile for curve fitting. Monte Carlo simulation was used ...

The Fisher-KPP problem with doubly nonlinear diffusion

NASA Astrophysics Data System (ADS)

Audrito, Alessandro; Vázquez, Juan Luis

2017-12-01

The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it possesses a family of travelling waves that describe the asymptotic behaviour of a large class solutions 0 ≤ u (x , t) ≤ 1 of the problem posed in the real line. The existence of propagation waves with finite speed has been confirmed in some related models and disproved in others. We investigate here the corresponding theory when the linear diffusion is replaced by the "slow" doubly nonlinear diffusion and we find travelling waves that represent the wave propagation of more general solutions even when we extend the study to several space dimensions. A similar study is performed in the critical case that we call "pseudo-linear", i.e., when the operator is still nonlinear but has homogeneity one. With respect to the classical model and the "pseudo-linear" case, the "slow" travelling waves exhibit free boundaries.

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.

Inverse solutions for electrical impedance tomography based on conjugate gradients methods

NASA Astrophysics Data System (ADS)

Wang, M.

2002-01-01

A multistep inverse solution for two-dimensional electric field distribution is developed to deal with the nonlinear inverse problem of electric field distribution in relation to its boundary condition and the problem of divergence due to errors introduced by the ill-conditioned sensitivity matrix and the noise produced by electrode modelling and instruments. This solution is based on a normalized linear approximation method where the change in mutual impedance is derived from the sensitivity theorem and a method of error vector decomposition. This paper presents an algebraic solution of the linear equations at each inverse step, using a generalized conjugate gradients method. Limiting the number of iterations in the generalized conjugate gradients method controls the artificial errors introduced by the assumption of linearity and the ill-conditioned sensitivity matrix. The solution of the nonlinear problem is approached using a multistep inversion. This paper also reviews the mathematical and physical definitions of the sensitivity back-projection algorithm based on the sensitivity theorem. Simulations and discussion based on the multistep algorithm, the sensitivity coefficient back-projection method and the Newton-Raphson method are given. Examples of imaging gas-liquid mixing and a human hand in brine are presented.

S{sub 2}SA preconditioning for the S{sub n} equations with strictly non negative spatial discretization

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

Bruss, D. E.; Morel, J. E.; Ragusa, J. C.

2013-07-01

Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S{sub n} transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use amore » linear diffusion equation has important implications for preconditioning the S{sub n} equations with a strictly non negative spatial discretization in multiple dimensions. (authors)« less

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.

A network model of successive partitioning-limited solute diffusion through the stratum corneum.

PubMed

Schumm, Phillip; Scoglio, Caterina M; van der Merwe, Deon

2010-02-07

As the most exposed point of contact with the external environment, the skin is an important barrier to many chemical exposures, including medications, potentially toxic chemicals and cosmetics. Traditional dermal absorption models treat the stratum corneum lipids as a homogenous medium through which solutes diffuse according to Fick's first law of diffusion. This approach does not explain non-linear absorption and irregular distribution patterns within the stratum corneum lipids as observed in experimental data. A network model, based on successive partitioning-limited solute diffusion through the stratum corneum, where the lipid structure is represented by a large, sparse, and regular network where nodes have variable characteristics, offers an alternative, efficient, and flexible approach to dermal absorption modeling that simulates non-linear absorption data patterns. Four model versions are presented: two linear models, which have unlimited node capacities, and two non-linear models, which have limited node capacities. The non-linear model outputs produce absorption to dose relationships that can be best characterized quantitatively by using power equations, similar to the equations used to describe non-linear experimental data.

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.

Relationship between tissue tension and thermal diffusion to peripheral tissue using an energy device.

PubMed

Kondo, Akihiro; Nishizawa, Yuji; Ito, Masaaki; Saito, Norio; Fujii, Satoshi; Akamoto, Shintaro; Fujiwara, Masao; Okano, Keiichi; Suzuki, Yasuyuki

2016-08-01

The aim of the study was to assess the relationship between tissue tension and thermal diffusion to peripheral tissues using an electric scalpel, ultrasonically activated device, or a bipolar sealing system. The mesentery of pigs was excised with each energy device (ED) at three tissue tensions (0, 300, 600 g). The excision time and thermal diffusion area were monitored with thermography, measured for each ED, and then histologically examined. Correlations between tissue tension and thermal diffusion area were examined. The excision time was inversely correlated with tissue tension for all ED (electric scalpel, r = 0.718; ultrasonically activated device, r = 0.949; bipolar sealing system, r = 0.843), and tissue tension was inversely correlated with the thermal diffusion area with the electric scalpel (r = 0.718) and bipolar sealing system (r = 0.869). Histopathologically, limited deep thermal denaturation occurred at a tension of 600 g with all ED. We conclude that thermal damage can be avoided with adequate tissue tension when any ED is used. © 2016 Japan Society for Endoscopic Surgery, Asia Endosurgery Task Force and John Wiley & Sons Australia, Ltd.

Isotropic-resolution linear-array-based photoacoustic computed tomography through inverse Radon transform

NASA Astrophysics Data System (ADS)

Li, Guo; Xia, Jun; Li, Lei; Wang, Lidai; Wang, Lihong V.

2015-03-01

Linear transducer arrays are readily available for ultrasonic detection in photoacoustic computed tomography. They offer low cost, hand-held convenience, and conventional ultrasonic imaging. However, the elevational resolution of linear transducer arrays, which is usually determined by the weak focus of the cylindrical acoustic lens, is about one order of magnitude worse than the in-plane axial and lateral spatial resolutions. Therefore, conventional linear scanning along the elevational direction cannot provide high-quality three-dimensional photoacoustic images due to the anisotropic spatial resolutions. Here we propose an innovative method to achieve isotropic resolutions for three-dimensional photoacoustic images through combined linear and rotational scanning. In each scan step, we first elevationally scan the linear transducer array, and then rotate the linear transducer array along its center in small steps, and scan again until 180 degrees have been covered. To reconstruct isotropic three-dimensional images from the multiple-directional scanning dataset, we use the standard inverse Radon transform originating from X-ray CT. We acquired a three-dimensional microsphere phantom image through the inverse Radon transform method and compared it with a single-elevational-scan three-dimensional image. The comparison shows that our method improves the elevational resolution by up to one order of magnitude, approaching the in-plane lateral-direction resolution. In vivo rat images were also acquired.

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.

Reconstruction of stochastic temporal networks through diffusive arrival times

NASA Astrophysics Data System (ADS)

Li, Xun; Li, Xiang

2017-06-01

Temporal networks have opened a new dimension in defining and quantification of complex interacting systems. Our ability to identify and reproduce time-resolved interaction patterns is, however, limited by the restricted access to empirical individual-level data. Here we propose an inverse modelling method based on first-arrival observations of the diffusion process taking place on temporal networks. We describe an efficient coordinate-ascent implementation for inferring stochastic temporal networks that builds in particular but not exclusively on the null model assumption of mutually independent interaction sequences at the dyadic level. The results of benchmark tests applied on both synthesized and empirical network data sets confirm the validity of our algorithm, showing the feasibility of statistically accurate inference of temporal networks only from moderate-sized samples of diffusion cascades. Our approach provides an effective and flexible scheme for the temporally augmented inverse problems of network reconstruction and has potential in a broad variety of applications.

Reconstruction of stochastic temporal networks through diffusive arrival times

PubMed Central

Li, Xun; Li, Xiang

2017-01-01

Temporal networks have opened a new dimension in defining and quantification of complex interacting systems. Our ability to identify and reproduce time-resolved interaction patterns is, however, limited by the restricted access to empirical individual-level data. Here we propose an inverse modelling method based on first-arrival observations of the diffusion process taking place on temporal networks. We describe an efficient coordinate-ascent implementation for inferring stochastic temporal networks that builds in particular but not exclusively on the null model assumption of mutually independent interaction sequences at the dyadic level. The results of benchmark tests applied on both synthesized and empirical network data sets confirm the validity of our algorithm, showing the feasibility of statistically accurate inference of temporal networks only from moderate-sized samples of diffusion cascades. Our approach provides an effective and flexible scheme for the temporally augmented inverse problems of network reconstruction and has potential in a broad variety of applications. PMID:28604687

Application of mass spectrometer-inverse gas chromatography to study polymer-solvent diffusivity and solubility.

PubMed

Galdámez, J Román; Danner, Ronald P; Duda, J Larry

2007-07-20

The application of a mass spectrometer detector in capillary column inverse gas chromatography is shown to be a valuable tool in the measurement of diffusion and solubility in polymer-solvent systems. The component specific detector provides excellent results for binary polymer-solvent systems, but it is particularly valuable because it can be readily applied to multicomponent systems. Results for a number of infinitely dilute solvents in poly(vinyl acetate) (PVAc) are reported over a range of temperature from 60 to 150 degrees C. Results are also reported for finite concentrations of toluene and methanol in PVAc from 60 to 110 degrees C. Finally, the technique was applied to study the effect of finite concentrations of toluene on the diffusion coefficients of THF and cyclohexane in PVAc. The experimental data compare well with literature values for both infinite and finite concentrations, indicating that the experimental protocol described in this work is sound.

Lack of anomalous diffusion in linear translationally-invariant systems determined by only one initial condition

NASA Astrophysics Data System (ADS)

Khorrami, Mohammad; Shariati, Ahmad; Aghamohammadi, Amir; Fatollahi, Amir H.

2012-01-01

It is shown that as far as the linear diffusion equation meets both time- and space-translational invariance, the time dependence of a moment of degree α is a polynomial of degree at most equal to α, while all connected moments are at most linear functions of time. As a special case, the variance is an at most linear function of time.

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...

An extended laser flash technique for thermal diffusivity measurement of high-temperature materials

NASA Technical Reports Server (NTRS)

Shen, F.; Khodadadi, J. M.

1993-01-01

Knowledge of thermal diffusivity data for high-temperature materials (solids and liquids) is very important in analyzing a number of processes, among them solidification, crystal growth, and welding. However, reliable thermal diffusivity versus temperature data, particularly those for high-temperature liquids, are still far from complete. The main measurement difficulties are due to the presence of convection and the requirement for a container. Fortunately, the availability of levitation techniques has made it possible to solve the containment problem. Based on the feasibility of the levitation technology, a new laser flash technique which is applicable to both levitated liquid and solid samples is being developed. At this point, the analysis for solid samples is near completion and highlights of the technique are presented here. The levitated solid sample which is assumed to be a sphere is subjected to a very short burst of high power radiant energy. The temperature of the irradiated surface area is elevated and a transient heat transfer process takes place within the sample. This containerless process is a two-dimensional unsteady heat conduction problem. Due to the nonlinearity of the radiative plus convective boundary condition, an analytic solution cannot be obtained. Two options are available at this point. Firstly, the radiation boundary condition can be linearized, which then accommodates a closed-form analytic solution. Comparison of the analytic curves for the temperature rise at different points to the experimentally-measured values will then provide the thermal diffusivity values. Secondly, one may set up an inverse conduction problem whereby experimentally obtained surface temperature history is used as the boundary conditions. The thermal diffusivity can then be elevated by minimizing the difference between the real heat flux boundary condition (radiation plus convection) and the measurements. Status of an experimental study directed at measuring the thermal diffusivity of high-temperature solid samples of pure Nickel and Inconel 718 superalloys are presented. Preliminary measurements showing surface temperature histories are discussed.

Time-resolved production and detection of reactive atoms

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

Grossman, L. W.; Hurst, G. S.

1977-09-01

Cesium iodide in the presence of a buffer gas was dissociated with a pulsed ultraviolet laser, which will be referred to as the source laser. This created a population of atoms at a well defined time and in a compact, well defined volume. A second pulsed laser, with a beam that completely surrounded that of the first, photoionized the cesium after a known time delay. This laser will be referred to as the detector laser. It was determined that for short time delays, all of the cesium atoms were easily ionized. When focused, the source laser generated an extremely intensemore » fluence. By accounting for the beam intensity profile it was shown that all of the molecules in the central portion of the beam can be dissociated and detected. Besides proving the feasibility of single-molecule detection, this enabled a determination of the absolute photodissociation cross section as a function of wavelength. Initial studies of the time decay of the cesium signal at low argon pressures indicated a non-exponential decay. This was consistent with a diffusion mechanism transporting cesium atoms out of the laser beam. Therefore, it was desired to conduct further experiments using a tightly focused source beam, passing along the axis of the detector beam. The theoretical behavior of this simple geometry accounting for diffusion and reaction is easily calculated. A diffusion coefficient can then be extracted by data fitting. If reactive decay is due to impurities constituting a fixed percentage of the buffer gas, then two-body reaction rates will scale linearly with pressure and three-body reaction rates will scale quadratically. Also, the diffusion coefficient will scale inversely with pressure. At low pressures it is conceivable that decay due to diffusion would be sufficiently rapid that all other processes can be neglected. Extraction of a diffusion coefficient would then be quite direct. Finally, study of the reaction of cesium and oxygen was undertaken.« less

On the meaning of the diffusion layer thickness for slow electrode reactions.

PubMed

Molina, A; González, J; Laborda, E; Compton, R G

2013-02-21

A key concept underpinning electrochemical science is that of the diffusion layer - the zone of depletion around an electrode accompanying electrolysis. The size of this zone can be found either from the simulated or measured concentration profiles (yielding the 'true' diffusion layer thickness) or, in the case of the Nernst ('linear') diffusion layer by extrapolating the concentration gradient at the electrode surface to the distance at which the concentration takes its bulk value. The latter concept is very well developed in the case of fast (so-called reversible) electrode processes, however the study of the linear diffusion layer has received scant attention in the case of slow charge transfer processes, despite its study being of great interest in the analysis of the influence of different experimental variables which determine the electrochemical response. Analytical explicit solutions for the concentration profiles, surface concentrations and real and linear diffusion layers corresponding to the application of a potential step to a slow charge transfer process are presented. From these expressions the dependence of the diffusion layer thickness on the potential, pulse time, heterogeneous rate constant and ratio of bulk concentrations of electroactive species and of diffusion coefficients is quantified. A profound influence of the reversibility degree of the charge transfer on the diffusion layer thickness is clear, showing that for non-reversible processes the real and linear diffusion layers reveal a minimum thickness which coincides with the equilibrium potential of the redox couple in the former case and with the reversible half-wave potential in the latter one.

In-depth study of 16CygB using inversion techniques

NASA Astrophysics Data System (ADS)

Buldgen, G.; Salmon, S. J. A. J.; Reese, D. R.; Dupret, M. A.

2016-12-01

Context. The 16Cyg binary system hosts the solar-like Kepler targets with the most stringent observational constraints. Indeed, we benefit from very high quality oscillation spectra, as well as spectroscopic and interferometric observations. Moreover, this system is particularly interesting since both stars are very similar in mass but the A component is orbited by a red dwarf, whereas the B component is orbited by a Jovian planet and thus could have formed a more complex planetary system. In our previous study, we showed that seismic inversions of integrated quantities could be used to constrain microscopic diffusion in the A component. In this study, we analyse the B component in the light of a more regularised inversion. Aims: We wish to analyse independently the B component of the 16Cyg binary system using the inversion of an indicator dedicated to analyse core conditions, denoted tu. Using this independent determination, we wish to analyse any differences between both stars due to the potential influence of planetary formation on stellar structure and/or their respective evolution. Methods: First, we recall the observational constraints for 16CygB and the method we used to generate reference stellar models of this star. We then describe how we improved the inversion and how this approach could be used for future targets with a sufficient number of observed frequencies. The inversion results were then used to analyse the differences between the A and B components. Results: The inversion of the tu indicator for 16CygB shows a disagreement with models including microscopic diffusion and sharing the chemical composition previously derived for 16CygA. We show that small changes in chemical composition are insufficient to solve the problem but that extra mixing can account for the differences seen between both stars. We use a parametric approach to analyse the impact of extra mixing in the form of turbulent diffusion on the behaviour of the tu values. We conclude on the necessity of further investigations using models with a physically motivated implementation of extra mixing processes including additional constraints to further improve the accuracy with which the fundamental parameters of this system are determined.

Densities and filling factors of the diffuse ionized gas in the Solar neighbourhood

NASA Astrophysics Data System (ADS)

Berkhuijsen, E. M.; Müller, P.

2008-10-01

Aims: We analyse electron densities and filling factors of the diffuse ionized gas (DIG) in the Solar neighbourhood. Methods: We have combined dispersion measures and emission measures towards 38 pulsars at distances known to better than 50%, from which we derived the mean density in clouds, N_c, and their volume filling factor, F_v, averaged along the line of sight. The emission measures were corrected for absorption by dust and contributions from beyond the pulsar distance. Results: The scale height of the electron layer for our sample is 0.93± 0.13 kpc and the midplane electron density is 0.023± 0.004 cm-3, in agreement with earlier results. The average density along the line of sight is < n_e> = 0.018± 0.002 cm-3 and is nearly constant. Since < n_e> = F_vN_c, an inverse relationship between Fv and Nc is expected. We find F_v(N_c) = (0.011± 0.003) N_c-1.20± 0.13, which holds for the ranges N_c= 0.05-1 cm-3 and F_v= 0.4-0.01. Near the Galactic plane the dependence of Fv on Nc is significantly stronger than away from the plane. Fv does not systematically change along or perpendicular to the Galactic plane, but the spread about the mean value of 0.08± 0.02 is considerable. The total pathlength through the ionized regions increases linearly to about 80 pc towards |z| = 1 kpc. Conclusions: Our study of Fv and Nc of the DIG is the first one based on a sample of pulsars with known distances. We confirm the existence of a tight, nearly inverse correlation between Fv and Nc in the DIG. The exact form of this relation depends on the regions in the Galaxy probed by the pulsar sample. The inverse F_v-Nc relation is consistent with a hierarchical, fractal density distribution in the DIG caused by turbulence. The observed near constancy of < n_e> then is a signature of fractal structure in the ionized medium, which is most pronounced outside the thin disk.

Turbulent particle transport as a function of toroidal rotation in DIII-D H-mode plasmas

DOE PAGES

Wang, Xin; Mordijck, Saskia; Zeng, Lei; ...

2016-03-01

In this paper we show how changes in toroidal rotation, by controlling the injected torque, affect particle transport and confinement. The toroidal rotation is altered using the co- and counter neutral beam injection (NBI) in low collisionality H-mode plasmas on DIII-D with dominant electron cyclotron heating (ECH). We find that there is no correlation between the toroidal rotation shear and the inverse density gradient, which is observed on AUG whenmore » $${{T}_{\\text{e}}}/{{T}_{\\text{i}}}$$ is varied using ECH (Angioni et al 2011 Phys. Rev. Lett. 107 215003). In DIII-D, we find that in a discharge with balanced torque injection, the $$E\\times B$$ shear is smaller than the linear gyrokinetic growth rate for small $${{k}_{\\theta}}{{\\rho}_{s}}$$ for $$\\rho =0.6$$ –0.85. This results in lower particle confinement. In the co- and counter- injected discharges the $$E\\times B$$ shear is larger or close to the linear growth rate at the plasma edge and both configurations have higher particle confinement. In order to measure particle transport, we use a small periodic perturbative gas puff. This gas puff perturbs the density profiles and allows us to extract the perturbed diffusion and inward pinch coefficients. We observe a strong increase in the inward particle pinch in the counter-torque injected plasma. Lastly, the calculated quasi-linear particle flux, nor the linear growth rates using TGLF agree with experimental observations.« less

Conserved linear dynamics of single-molecule Brownian motion.

PubMed

Serag, Maged F; Habuchi, Satoshi

2017-06-06

Macromolecular diffusion in homogeneous fluid at length scales greater than the size of the molecule is regarded as a random process. The mean-squared displacement (MSD) of molecules in this regime increases linearly with time. Here we show that non-random motion of DNA molecules in this regime that is undetectable by the MSD analysis can be quantified by characterizing the molecular motion relative to a latticed frame of reference. Our lattice occupancy analysis reveals unexpected sub-modes of motion of DNA that deviate from expected random motion in the linear, diffusive regime. We demonstrate that a subtle interplay between these sub-modes causes the overall diffusive motion of DNA to appear to conform to the linear regime. Our results show that apparently random motion of macromolecules could be governed by non-random dynamics that are detectable only by their relative motion. Our analytical approach should advance broad understanding of diffusion processes of fundamental relevance.

Conserved linear dynamics of single-molecule Brownian motion

PubMed Central

Serag, Maged F.; Habuchi, Satoshi

2017-01-01

Macromolecular diffusion in homogeneous fluid at length scales greater than the size of the molecule is regarded as a random process. The mean-squared displacement (MSD) of molecules in this regime increases linearly with time. Here we show that non-random motion of DNA molecules in this regime that is undetectable by the MSD analysis can be quantified by characterizing the molecular motion relative to a latticed frame of reference. Our lattice occupancy analysis reveals unexpected sub-modes of motion of DNA that deviate from expected random motion in the linear, diffusive regime. We demonstrate that a subtle interplay between these sub-modes causes the overall diffusive motion of DNA to appear to conform to the linear regime. Our results show that apparently random motion of macromolecules could be governed by non-random dynamics that are detectable only by their relative motion. Our analytical approach should advance broad understanding of diffusion processes of fundamental relevance. PMID:28585925

Conserved linear dynamics of single-molecule Brownian motion

NASA Astrophysics Data System (ADS)

Serag, Maged F.; Habuchi, Satoshi

2017-06-01

Macromolecular diffusion in homogeneous fluid at length scales greater than the size of the molecule is regarded as a random process. The mean-squared displacement (MSD) of molecules in this regime increases linearly with time. Here we show that non-random motion of DNA molecules in this regime that is undetectable by the MSD analysis can be quantified by characterizing the molecular motion relative to a latticed frame of reference. Our lattice occupancy analysis reveals unexpected sub-modes of motion of DNA that deviate from expected random motion in the linear, diffusive regime. We demonstrate that a subtle interplay between these sub-modes causes the overall diffusive motion of DNA to appear to conform to the linear regime. Our results show that apparently random motion of macromolecules could be governed by non-random dynamics that are detectable only by their relative motion. Our analytical approach should advance broad understanding of diffusion processes of fundamental relevance.

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.

The determination of solubility and diffusion coefficient for solids in liquids by an inverse measurement technique using cylinders of amorphous glucose as a model compound

NASA Astrophysics Data System (ADS)

Hu, Chengyao; Huang, Pei

2011-05-01

The importance of sugar and sugar-containing materials is well recognized nowadays, owing to their application in industrial processes, particularly in the food, pharmaceutical and cosmetic industries. Because of the large numbers of those compounds involved and the relatively small number of solubility and/or diffusion coefficient data for each compound available, it is highly desirable to measure the solubility and/or diffusion coefficient as efficiently as possible and to be able to improve the accuracy of the methods used. In this work, a new technique was developed for the measurement of the diffusion coefficient of a stationary solid solute in a stagnant solvent which simultaneously measures solubility based on an inverse measurement problem algorithm with the real-time dissolved amount profile as a function of time. This study differs from established techniques in both the experimental method and the data analysis. The experimental method was developed in which the dissolved amount of solid solute in quiescent solvent was investigated using a continuous weighing technique. In the data analysis, the hybrid genetic algorithm is used to minimize an objective function containing a calculated and a measured dissolved amount with time. This is measured on a cylindrical sample of amorphous glucose in methanol or ethanol. The calculated dissolved amount, that is a function of the unknown physical properties of the solid solute in the solvent, is calculated by the solution of the two-dimensional nonlinear inverse natural convection problem. The estimated values of the solubility of amorphous glucose in methanol and ethanol at 293 K were respectively 32.1 g/100 g methanol and 1.48 g/100 g ethanol, in agreement with the literature values, and support the validity of the simultaneously measured diffusion coefficient. These results show the efficiency and the stability of the developed technique to simultaneously estimate the solubility and diffusion coefficient. Also the influence of the solution density change and the initial concentration conditions on the dissolved amount was investigated by the numerical results using the estimated parameters. It is found that the theoretical assumption to simplify the inverse measurement problem algorithm is reasonable for low solubility.

Parsimony and goodness-of-fit in multi-dimensional NMR inversion

NASA Astrophysics Data System (ADS)

Babak, Petro; Kryuchkov, Sergey; Kantzas, Apostolos

2017-01-01

Multi-dimensional nuclear magnetic resonance (NMR) experiments are often used for study of molecular structure and dynamics of matter in core analysis and reservoir evaluation. Industrial applications of multi-dimensional NMR involve a high-dimensional measurement dataset with complicated correlation structure and require rapid and stable inversion algorithms from the time domain to the relaxation rate and/or diffusion domains. In practice, applying existing inverse algorithms with a large number of parameter values leads to an infinite number of solutions with a reasonable fit to the NMR data. The interpretation of such variability of multiple solutions and selection of the most appropriate solution could be a very complex problem. In most cases the characteristics of materials have sparse signatures, and investigators would like to distinguish the most significant relaxation and diffusion values of the materials. To produce an easy to interpret and unique NMR distribution with the finite number of the principal parameter values, we introduce a new method for NMR inversion. The method is constructed based on the trade-off between the conventional goodness-of-fit approach to multivariate data and the principle of parsimony guaranteeing inversion with the least number of parameter values. We suggest performing the inversion of NMR data using the forward stepwise regression selection algorithm. To account for the trade-off between goodness-of-fit and parsimony, the objective function is selected based on Akaike Information Criterion (AIC). The performance of the developed multi-dimensional NMR inversion method and its comparison with conventional methods are illustrated using real data for samples with bitumen, water and clay.

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

Vapor Bubbles

NASA Astrophysics Data System (ADS)

Prosperetti, Andrea

2017-01-01

This article reviews the fundamental physics of vapor bubbles in liquids. Work on bubble growth and condensation for stationary and translating bubbles is summarized and the differences with bubbles containing a permanent gas stressed. In particular, it is shown that the natural frequency of a vapor bubble is proportional not to the inverse radius, as for a gas bubble, but to the inverse radius raised to the power 2/3. Permanent gas dissolved in the liquid diffuses into the bubble with strong effects on its dynamics. The effects of the diffusion of heat and mass on the propagation of pressure waves in a vaporous bubbly liquid are discussed. Other topics briefly touched on include thermocapillary flow, plasmonic nanobubbles, and vapor bubbles in an immiscible liquid.

Quantitative body DW-MRI biomarkers uncertainty estimation using unscented wild-bootstrap.

PubMed

Freiman, M; Voss, S D; Mulkern, R V; Perez-Rossello, J M; Warfield, S K

2011-01-01

We present a new method for the uncertainty estimation of diffusion parameters for quantitative body DW-MRI assessment. Diffusion parameters uncertainty estimation from DW-MRI is necessary for clinical applications that use these parameters to assess pathology. However, uncertainty estimation using traditional techniques requires repeated acquisitions, which is undesirable in routine clinical use. Model-based bootstrap techniques, for example, assume an underlying linear model for residuals rescaling and cannot be utilized directly for body diffusion parameters uncertainty estimation due to the non-linearity of the body diffusion model. To offset this limitation, our method uses the Unscented transform to compute the residuals rescaling parameters from the non-linear body diffusion model, and then applies the wild-bootstrap method to infer the body diffusion parameters uncertainty. Validation through phantom and human subject experiments shows that our method identify the regions with higher uncertainty in body DWI-MRI model parameters correctly with realtive error of -36% in the uncertainty values.

Diffusion phenomenon for linear dissipative wave equations in an exterior domain

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

Effective equilibrium states in mixtures of active particles driven by colored noise

NASA Astrophysics Data System (ADS)

Wittmann, René; Brader, J. M.; Sharma, A.; Marconi, U. Marini Bettolo

2018-01-01

We consider the steady-state behavior of pairs of active particles having different persistence times and diffusivities. To this purpose we employ the active Ornstein-Uhlenbeck model, where the particles are driven by colored noises with exponential correlation functions whose intensities and correlation times vary from species to species. By extending Fox's theory to many components, we derive by functional calculus an approximate Fokker-Planck equation for the configurational distribution function of the system. After illustrating the predicted distribution in the solvable case of two particles interacting via a harmonic potential, we consider systems of particles repelling through inverse power-law potentials. We compare the analytic predictions to computer simulations for such soft-repulsive interactions in one dimension and show that at linear order in the persistence times the theory is satisfactory. This work provides the toolbox to qualitatively describe many-body phenomena, such as demixing and depletion, by means of effective pair potentials.

Transient response in granular bounded heap flows

NASA Astrophysics Data System (ADS)

Xiao, Hongyi; Ottino, Julio M.; Lueptow, Richard M.; Umbanhowar, Paul B.

2017-11-01

Heap formation, a canonical granular flow, is common in industry and is also found in nature. Here, we study the transition between steady flow states in quasi-2D bounded heaps by suddenly changing the feed rate from one fixed value to another. During the transition, in both experiments and discrete element method simulations, an additional wedge of flowing particles propagates over the rising free surface. The downstream edge of the wedge - the wedge front - moves downstream with velocity inversely proportional to the square root of time. An additional longer duration transient process continues after the wedge front reaches the downstream wall. The transient flux profile during the entire transition is well modeled by a diffusion-like equation derived from local mass balance and a local linear relation between the flux and the surface slope. Scalings for the transient kinematics during the flow transitions are developed based on the flux profiles. Funded by NSF Grant CBET-1511450.

Applying a probabilistic seismic-petrophysical inversion and two different rock-physics models for reservoir characterization in offshore Nile Delta

NASA Astrophysics Data System (ADS)

Aleardi, Mattia

2018-01-01

We apply a two-step probabilistic seismic-petrophysical inversion for the characterization of a clastic, gas-saturated, reservoir located in offshore Nile Delta. In particular, we discuss and compare the results obtained when two different rock-physics models (RPMs) are employed in the inversion. The first RPM is an empirical, linear model directly derived from the available well log data by means of an optimization procedure. The second RPM is a theoretical, non-linear model based on the Hertz-Mindlin contact theory. The first step of the inversion procedure is a Bayesian linearized amplitude versus angle (AVA) inversion in which the elastic properties, and the associated uncertainties, are inferred from pre-stack seismic data. The estimated elastic properties constitute the input to the second step that is a probabilistic petrophysical inversion in which we account for the noise contaminating the recorded seismic data and the uncertainties affecting both the derived rock-physics models and the estimated elastic parameters. In particular, a Gaussian mixture a-priori distribution is used to properly take into account the facies-dependent behavior of petrophysical properties, related to the different fluid and rock properties of the different litho-fluid classes. In the synthetic and in the field data tests, the very minor differences between the results obtained by employing the two RPMs, and the good match between the estimated properties and well log information, confirm the applicability of the inversion approach and the suitability of the two different RPMs for reservoir characterization in the investigated area.

Comprehensive analysis of earthquake source spectra and swarms in the Salton Trough, California

NASA Astrophysics Data System (ADS)

Chen, X.; Shearer, P. M.

2011-09-01

We study earthquakes within California's Salton Trough from 1981 to 2009 from a precisely relocated catalog. We process the seismic waveforms to isolate source spectra, station spectra and travel-time dependent spectra. The results suggest an average P wave Q of 340, agreeing with previous results indicating relatively high attenuation in the Salton Trough. Stress drops estimated from the source spectra using an empirical Green's function (EGF) method reveal large scatter among individual events but a low median stress drop of 0.56 MPa for the region. The distribution of stress drop after applying a spatial-median filter indicates lower stress drops near geothermal sites. We explore the relationships between seismicity, stress drops and geothermal injection activities. Seismicity within the Salton Trough shows strong spatial clustering, with 20 distinct earthquake swarms with at least 50 events. They can be separated into early-Mmax and late-Mmax groups based on the normalized occurrence time of their largest event. These swarms generally have a low skew value of moment release history, ranging from -9 to 3.0. The major temporal difference between the two groups is the excess of seismicity and an inverse power law increase of seismicity before the largest event for the late-Mmax group. All swarms exhibit spatial migration of seismicity at a statistical significance greater than 85%. A weighted L1-norm inversion of linear migration parameters yields migration velocities from 0.008 to 0.8 km/hour. To explore the influence of fluid injection in geothermal sites, we also model the migration behavior with the diffusion equation, and obtain a hydraulic diffusion coefficient of approximately 0.25 m2/s for the Salton Sea geothermal site, which is within the range of expected values for a typical geothermal reservoir. The swarms with migration velocities over 0.1 km/hour cannot be explained by the diffusion curve, rather, their velocity is consistent with the propagation velocity of creep and slow slip events. These variations in migration behavior allow us to distinguish among different driving processes.

Modeling and sensitivity analysis of mass transfer in active multilayer polymeric film for food applications

NASA Astrophysics Data System (ADS)

Bedane, T.; Di Maio, L.; Scarfato, P.; Incarnato, L.; Marra, F.

2015-12-01

The barrier performance of multilayer polymeric films for food applications has been significantly improved by incorporating oxygen scavenging materials. The scavenging activity depends on parameters such as diffusion coefficient, solubility, concentration of scavenger loaded and the number of available reactive sites. These parameters influence the barrier performance of the film in different ways. Virtualization of the process is useful to characterize, design and optimize the barrier performance based on physical configuration of the films. Also, the knowledge of values of parameters is important to predict the performances. Inverse modeling and sensitivity analysis are sole way to find reasonable values of poorly defined, unmeasured parameters and to analyze the most influencing parameters. Thus, the objective of this work was to develop a model to predict barrier properties of multilayer film incorporated with reactive layers and to analyze and characterize their performances. Polymeric film based on three layers of Polyethylene terephthalate (PET), with a core reactive layer, at different thickness configurations was considered in the model. A one dimensional diffusion equation with reaction was solved numerically to predict the concentration of oxygen diffused into the polymer taking into account the reactive ability of the core layer. The model was solved using commercial software for different film layer configurations and sensitivity analysis based on inverse modeling was carried out to understand the effect of physical parameters. The results have shown that the use of sensitivity analysis can provide physical understanding of the parameters which highly affect the gas permeation into the film. Solubility and the number of available reactive sites were the factors mainly influencing the barrier performance of three layered polymeric film. Multilayer films slightly modified the steady transport properties in comparison to net PET, giving a small reduction in the permeability and oxygen transfer rate values. Scavenging capacity of the multilayer film increased linearly with the increase of the reactive layer thickness and the oxygen absorption reaction at short times decreased proportionally with the thickness of the external PET layer.

Modeling and sensitivity analysis of mass transfer in active multilayer polymeric film for food applications

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

Bedane, T.; Di Maio, L.; Scarfato, P.

The barrier performance of multilayer polymeric films for food applications has been significantly improved by incorporating oxygen scavenging materials. The scavenging activity depends on parameters such as diffusion coefficient, solubility, concentration of scavenger loaded and the number of available reactive sites. These parameters influence the barrier performance of the film in different ways. Virtualization of the process is useful to characterize, design and optimize the barrier performance based on physical configuration of the films. Also, the knowledge of values of parameters is important to predict the performances. Inverse modeling and sensitivity analysis are sole way to find reasonable values ofmore » poorly defined, unmeasured parameters and to analyze the most influencing parameters. Thus, the objective of this work was to develop a model to predict barrier properties of multilayer film incorporated with reactive layers and to analyze and characterize their performances. Polymeric film based on three layers of Polyethylene terephthalate (PET), with a core reactive layer, at different thickness configurations was considered in the model. A one dimensional diffusion equation with reaction was solved numerically to predict the concentration of oxygen diffused into the polymer taking into account the reactive ability of the core layer. The model was solved using commercial software for different film layer configurations and sensitivity analysis based on inverse modeling was carried out to understand the effect of physical parameters. The results have shown that the use of sensitivity analysis can provide physical understanding of the parameters which highly affect the gas permeation into the film. Solubility and the number of available reactive sites were the factors mainly influencing the barrier performance of three layered polymeric film. Multilayer films slightly modified the steady transport properties in comparison to net PET, giving a small reduction in the permeability and oxygen transfer rate values. Scavenging capacity of the multilayer film increased linearly with the increase of the reactive layer thickness and the oxygen absorption reaction at short times decreased proportionally with the thickness of the external PET layer.« less

A theoretical signal processing framework for linear diffusion MRI: Implications for parameter estimation and experiment design.

PubMed

Varadarajan, Divya; Haldar, Justin P

2017-11-01

The data measured in diffusion MRI can be modeled as the Fourier transform of the Ensemble Average Propagator (EAP), a probability distribution that summarizes the molecular diffusion behavior of the spins within each voxel. This Fourier relationship is potentially advantageous because of the extensive theory that has been developed to characterize the sampling requirements, accuracy, and stability of linear Fourier reconstruction methods. However, existing diffusion MRI data sampling and signal estimation methods have largely been developed and tuned without the benefit of such theory, instead relying on approximations, intuition, and extensive empirical evaluation. This paper aims to address this discrepancy by introducing a novel theoretical signal processing framework for diffusion MRI. The new framework can be used to characterize arbitrary linear diffusion estimation methods with arbitrary q-space sampling, and can be used to theoretically evaluate and compare the accuracy, resolution, and noise-resilience of different data acquisition and parameter estimation techniques. The framework is based on the EAP, and makes very limited modeling assumptions. As a result, the approach can even provide new insight into the behavior of model-based linear diffusion estimation methods in contexts where the modeling assumptions are inaccurate. The practical usefulness of the proposed framework is illustrated using both simulated and real diffusion MRI data in applications such as choosing between different parameter estimation methods and choosing between different q-space sampling schemes. Copyright © 2017 Elsevier Inc. All rights reserved.

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.

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 recovery of Markov transition probabilities from boundary value data

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

Patch, Sarah Kathyrn

1994-04-01

In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requiresmore » finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.« less

VALDRIFT 1.0: A valley atmospheric dispersion model with deposition

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

Allwine, K.J.; Bian, X.; Whiteman, C.D.

1995-05-01

VALDRIFT version 1.0 is an atmospheric transport and diffusion model for use in well-defined mountain valleys. It is designed to determine the extent of ddft from aedal pesticide spraying activities, but can also be applied to estimate the transport and diffusion of various air pollutants in valleys. The model is phenomenological -- that is, the dominant meteorological processes goveming the behavior of the valley atmosphere are formulated explicitly in the model, albeit in a highly parameterized fashion. The key meteorological processes treated are: (1) nonsteady and nonhomogeneous along-valley winds and turbulent diffusivities, (2) convective boundary layer growth, (3) inversion descent,more » (4) noctumal temperature inversion breakup, and (5) subsidence. The model is applicable under relatively cloud-free, undisturbed synoptic conditions and is configured to operate through one diumal cycle for a single valley. The inputs required are the valley topographical characteristics, pesticide release rate as a function of time and space, along-valley wind speed as a function of time and space, temperature inversion characteristics at sunrise, and sensible heat flux as a function of time following sunrise. Default values are provided for certain inputs in the absence of detailed observations. The outputs are three-dimensional air concentration and ground-level deposition fields as a function of time.« less

Joint probabilistic determination of earthquake location and velocity structure: application to local and regional events

NASA Astrophysics Data System (ADS)

Beucler, E.; Haugmard, M.; Mocquet, A.

2016-12-01

The most widely used inversion schemes to locate earthquakes are based on iterative linearized least-squares algorithms and using an a priori knowledge of the propagation medium. When a small amount of observations is available for moderate events for instance, these methods may lead to large trade-offs between outputs and both the velocity model and the initial set of hypocentral parameters. We present a joint structure-source determination approach using Bayesian inferences. Monte-Carlo continuous samplings, using Markov chains, generate models within a broad range of parameters, distributed according to the unknown posterior distributions. The non-linear exploration of both the seismic structure (velocity and thickness) and the source parameters relies on a fast forward problem using 1-D travel time computations. The a posteriori covariances between parameters (hypocentre depth, origin time and seismic structure among others) are computed and explicitly documented. This method manages to decrease the influence of the surrounding seismic network geometry (sparse and/or azimuthally inhomogeneous) and a too constrained velocity structure by inferring realistic distributions on hypocentral parameters. Our algorithm is successfully used to accurately locate events of the Armorican Massif (western France), which is characterized by moderate and apparently diffuse local seismicity.

Chemoviscosity modeling for thermosetting resins - I

NASA Technical Reports Server (NTRS)

Hou, T. H.

1984-01-01

A new analytical model for chemoviscosity variation during cure of thermosetting resins was developed. This model is derived by modifying the widely used WLF (Williams-Landel-Ferry) Theory in polymer rheology. Major assumptions involved are that the rate of reaction is diffusion controlled and is linearly inversely proportional to the viscosity of the medium over the entire cure cycle. The resultant first order nonlinear differential equation is solved numerically, and the model predictions compare favorably with experimental data of EPON 828/Agent U obtained on a Rheometrics System 4 Rheometer. The model describes chemoviscosity up to a range of six orders of magnitude under isothermal curing conditions. The extremely non-linear chemoviscosity profile for a dynamic heating cure cycle is predicted as well. The model is also shown to predict changes of glass transition temperature for the thermosetting resin during cure. The physical significance of this prediction is unclear at the present time, however, and further research is required. From the chemoviscosity simulation point of view, the technique of establishing an analytical model as described here is easily applied to any thermosetting resin. The model thus obtained is used in real-time process controls for fabricating composite materials.

Nonequilibrium transition and pattern formation in a linear reaction-diffusion system with self-regulated kinetics

NASA Astrophysics Data System (ADS)

Paul, Shibashis; Ghosh, Shyamolina; Ray, Deb Shankar

2018-02-01

We consider a reaction-diffusion system with linear, stochastic activator-inhibitor kinetics where the time evolution of concentration of a species at any spatial location depends on the relative average concentration of its neighbors. This self-regulating nature of kinetics brings in spatial correlation between the activator and the inhibitor. An interplay of this correlation in kinetics and disparity of diffusivities of the two species leads to symmetry breaking non-equilibrium transition resulting in stationary pattern formation. The role of initial noise strength and the linear reaction terms has been analyzed for pattern selection.

The role of nanoparticle rigidity on the diffusion of linear polystyrene in a polymer nanocomposite

DOE PAGES

Miller, Brad; Imel, Adam E.; Holley, Wade; ...

2015-11-12

The impact of the inclusion of a nanoparticle in a polymer matrix on the dynamics of the polymer chains is an area of recent interest. In this article, we describe the role of nanoparticle rigidity or softness on the impact of the presence of that nanoparticle on the diffusive behavior of linear polymer chains. The neutron reflectivity results clearly show that the inclusion of 10 nm soft nanoparticles in a polymer matrix (R g ~ 20 nm) increases the diffusion coefficient of the linear polymer chain. Surprisingly, thermal analysis shows that these nanocomposites exhibit an increase in their glass transitionmore » temperature, which is incommensurate with an increase in free volume. Therefore, it appears that this effect is more complex than a simple plasticizing effect. Results from small-angle neutron scattering of the nanoparticles in solution show a structure that consists of a gel like core with a corona of free chain ends and loops. Furthermore, the increase in linear polymer diffusion may be related to an increase in constraint release mechanisms in the reptation of the polymer chain, in a similar manner to that which has been reported for the diffusion of linear polymer chains in the presence of star polymers.« less

The role of nanoparticle rigidity on the diffusion of linear polystyrene in a polymer nanocomposite

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

Miller, Brad; Imel, Adam E.; Holley, Wade

The impact of the inclusion of a nanoparticle in a polymer matrix on the dynamics of the polymer chains is an area of recent interest. In this article, we describe the role of nanoparticle rigidity or softness on the impact of the presence of that nanoparticle on the diffusive behavior of linear polymer chains. The neutron reflectivity results clearly show that the inclusion of 10 nm soft nanoparticles in a polymer matrix (R g ~ 20 nm) increases the diffusion coefficient of the linear polymer chain. Surprisingly, thermal analysis shows that these nanocomposites exhibit an increase in their glass transitionmore » temperature, which is incommensurate with an increase in free volume. Therefore, it appears that this effect is more complex than a simple plasticizing effect. Results from small-angle neutron scattering of the nanoparticles in solution show a structure that consists of a gel like core with a corona of free chain ends and loops. Furthermore, the increase in linear polymer diffusion may be related to an increase in constraint release mechanisms in the reptation of the polymer chain, in a similar manner to that which has been reported for the diffusion of linear polymer chains in the presence of star polymers.« less

Understanding Coupling of Global and Diffuse Solar Radiation with Climatic Variability

NASA Astrophysics Data System (ADS)

Hamdan, Lubna

Global solar radiation data is very important for wide variety of applications and scientific studies. However, this data is not readily available because of the cost of measuring equipment and the tedious maintenance and calibration requirements. Wide variety of models have been introduced by researchers to estimate and/or predict the global solar radiations and its components (direct and diffuse radiation) using other readily obtainable atmospheric parameters. The goal of this research is to understand the coupling of global and diffuse solar radiation with climatic variability, by investigating the relationships between these radiations and atmospheric parameters. For this purpose, we applied multilinear regression analysis on the data of National Solar Radiation Database 1991--2010 Update. The analysis showed that the main atmospheric parameters that affect the amount of global radiation received on earth's surface are cloud cover and relative humidity. Global radiation correlates negatively with both variables. Linear models are excellent approximations for the relationship between atmospheric parameters and global radiation. A linear model with the predictors total cloud cover, relative humidity, and extraterrestrial radiation is able to explain around 98% of the variability in global radiation. For diffuse radiation, the analysis showed that the main atmospheric parameters that affect the amount received on earth's surface are cloud cover and aerosol optical depth. Diffuse radiation correlates positively with both variables. Linear models are very good approximations for the relationship between atmospheric parameters and diffuse radiation. A linear model with the predictors total cloud cover, aerosol optical depth, and extraterrestrial radiation is able to explain around 91% of the variability in diffuse radiation. Prediction analysis showed that the linear models we fitted were able to predict diffuse radiation with efficiency of test adjusted R2 values equal to 0.93, using the data of total cloud cover, aerosol optical depth, relative humidity and extraterrestrial radiation. However, for prediction purposes, using nonlinear terms or nonlinear models might enhance the prediction of diffuse radiation.

Nanoparticle Motion in Entangled Melts of Linear and Nonconcatenated Ring Polymers

PubMed Central

2017-01-01

The motion of nanoparticles (NPs) in entangled melts of linear polymers and nonconcatenated ring polymers are compared by large-scale molecular dynamics simulations. The comparison provides a paradigm for the effects of polymer architecture on the dynamical coupling between NPs and polymers in nanocomposites. Strongly suppressed motion of NPs with diameter d larger than the entanglement spacing a is observed in a melt of linear polymers before the onset of Fickian NP diffusion. This strong suppression of NP motion occurs progressively as d exceeds a and is related to the hopping diffusion of NPs in the entanglement network. In contrast to the NP motion in linear polymers, the motion of NPs with d > a in ring polymers is not as strongly suppressed prior to Fickian diffusion. The diffusion coefficient D decreases with increasing d much slower in entangled rings than in entangled linear chains. NP motion in entangled nonconcatenated ring polymers is understood through a scaling analysis of the coupling between NP motion and the self-similar entangled dynamics of ring polymers. PMID:28392603

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

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

A wind tunnel study of gaseous tracer dispersion in the convective boundary layer capped by a temperature inversion

NASA Astrophysics Data System (ADS)

Fedorovich, E.; Thäter, J.

Results are presented from wind tunnel simulations of gaseous pollutant dispersion in the atmospheric convective boundary layer (CBL) capped by a temperature inversion. The experiments were performed in the thermally stratified wind tunnel of the University of Karlsruhe, Germany. In the tunnel, the case of horizontally evolving, sheared CBL is reproduced. This distinguishes the employed experimental setup from the preceding laboratory and numerical CBL dispersion studies. The diffusive and mixing properties of turbulence in the studied CBL case have been found to be essentially dependent on the stage of the CBL evolution. Effects of the point source elevation on the horizontal variability of the concentration field, and on the ground level concentration as function of distance from the source have been investigated. The applicability of bottom-up/top-down diffusion concept in the simulated CBL case has been evaluated. The influence of surface wind shear and capping inversion strength on the pollutant dispersion and turbulent exchange across the CBL top has been demonstrated. The imposed positive shear across the inversion has been identified as inhibitor of the CBL growth. Comparisons of concentration patterns from the wind tunnel with water tank data are presented.

Uncertain Representations of Sub-Grid Pollutant Transport in Chemistry-Transport Models and Impacts on Long-Range Transport and Global Composition

NASA Technical Reports Server (NTRS)

Pawson, Steven; Zhu, Z.; Ott, L. E.; Molod, A.; Duncan, B. N.; Nielsen, J. E.

2009-01-01

Sub-grid transport, by convection and turbulence, is known to play an important role in lofting pollutants from their source regions. Consequently, the long-range transport and climatology of simulated atmospheric composition are impacted. This study uses the Goddard Earth Observing System, Version 5 (GEOS-5) atmospheric model to study pollutant transport. The baseline model uses a Relaxed Arakawa-Schubert (RAS) scheme that represents convection through a sequence of linearly entraining cloud plumes characterized by unique detrainment levels. Thermodynamics, moisture and trace gases are transported in the same manner. Various approximate forms of trace-gas transport are implemented, in which the box-averaged cloud mass fluxes from RAS are used with different numerical approaches. Substantial impacts on forward-model simulations of CO (using a linearized chemistry) are evident. In particular, some aspects of simulations using a diffusive form of sub-grid transport bear more resemblance to space-biased CO observations than do the baseline simulations with RAS transport. Implications for transport in the real atmosphere will be discussed. Another issue of importance is that many adjoint/inversion computations use simplified representations of sub-grid transport that may be inconsistent with the forward models: implications will be discussed. Finally, simulations using a complex chemistry model in GEOS-5 (in place of the linearized CO model) are underway: noteworthy results from this simulation will be mentioned.

Role of turbulence regime on determining the local density gradient

DOE PAGES

Wang, X.; Mordijck, Saskia; Doyle, E. J.; ...

2017-11-16

In this study we show that the local density gradient in the plasma core depends on the calculated mode-frequency of the most unstable linear mode and reaches a maximum when this frequency is close to zero. Previous theoretical and experimental work on AUG has shown that the ratio of electron to ion temperature, and as such the frequency of the dominant linear gyrokinetic mode, affects the local density gradient close to ρ = 0.3 [1, 2]. On DIII-D we find that by adding Electron Cyclotron Heating (ECH), we modify the dominant unstable linear gyro kinetic mode from an Ion Temperaturemore » Gradient (ITG) mode to a Trapped Electron Mode (TEM), which means that the frequency of the dominant mode changes sign (from the ion to the electron direction). Local density peaking around mid-radius increases by 50% right around the cross-over between the ITG and TEM regimes. By comparing how the particle flux changes, through the derivative of the electron density, n e, with respect to time, ∂n e/∂t, we find that the particle flux also exhibits the same trend versus mode frequency. As a result, we find that the changes in local particle transport are inversely proportional to the changes in electron density, indicating that the changes are driven by a change in thermo-diffusive pinch.« less

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.

3D optical tomography in the presence of void regions

NASA Astrophysics Data System (ADS)

Riley, J.; Dehghani, Hamid; Schweiger, Martin; Arridge, Simon R.; Ripoll, Jorge; Nieto-Vesperinas, Manuel

2000-12-01

We present an investigation of the effect of a 3D non-scattering gap region on image reconstruction in diffuse optical tomography. The void gap is modelled by the Radiosity-Diffusion method and the inverse problem is solved using the adjoint field method. The case of a sphere with concentric spherical gap is used as an example.

3D optical tomography in the presence of void regions.

PubMed

Riley, J; Dehghani, H; Schweiger, M; Arridge, S; Ripoll, J; Nieto-Vesperinas, M

2000-12-18

We present an investigation of the effect of a 3D non-scattering gap region on image reconstruction in diffuse optical tomography. The void gap is modelled by the Radiosity-Diffusion method and the inverse problem is solved using the adjoint field method. The case of a sphere with concentric spherical gap is used as an example.

Network diffusion accurately models the relationship between structural and functional brain connectivity networks

PubMed Central

Abdelnour, Farras; Voss, Henning U.; Raj, Ashish

2014-01-01

The relationship between anatomic connectivity of large-scale brain networks and their functional connectivity is of immense importance and an area of active research. Previous attempts have required complex simulations which model the dynamics of each cortical region, and explore the coupling between regions as derived by anatomic connections. While much insight is gained from these non-linear simulations, they can be computationally taxing tools for predicting functional from anatomic connectivities. Little attention has been paid to linear models. Here we show that a properly designed linear model appears to be superior to previous non-linear approaches in capturing the brain’s long-range second order correlation structure that governs the relationship between anatomic and functional connectivities. We derive a linear network of brain dynamics based on graph diffusion, whereby the diffusing quantity undergoes a random walk on a graph. We test our model using subjects who underwent diffusion MRI and resting state fMRI. The network diffusion model applied to the structural networks largely predicts the correlation structures derived from their fMRI data, to a greater extent than other approaches. The utility of the proposed approach is that it can routinely be used to infer functional correlation from anatomic connectivity. And since it is linear, anatomic connectivity can also be inferred from functional data. The success of our model confirms the linearity of ensemble average signals in the brain, and implies that their long-range correlation structure may percolate within the brain via purely mechanistic processes enacted on its structural connectivity pathways. PMID:24384152

Sorption-desorption equilibrium and diffusion of tetracycline in poultry litter and municipal biosolids soil amendments.

PubMed

D'Angelo, E

2017-12-01

Tetracycline (TET) is commonly used to treat bacterial diseases in humans and chickens (Gallus gallus domesticus), is largely excreted, and is found at elevated concentrations in treated sewage sludge (biosolids) and poultry litter (excrement plus bedding materials). Routine application of these nutrient-and carbon-enriched materials to soils improves fertility and other characteristics, but the presence of antibiotics (and other pharmaceuticals) in amendments raises questions about potential adverse effects on biota and development of antibiotic resistance in the environment. Hazard risks are largely dictated by sorption-desorption and diffusion behavior in amendments, so these processes were evaluated from sorption-desorption equilibrium isotherm and diffusion cell experiments with four types amendments (biosolids, poultry manure, wood chip litter, and rice hull litter) at three temperatures (8 °C, 20 °C and 32 °C). Linear sorption-desorption equilibrium distribution constants (Kd) in native amendments ranged between 124-2418 L kg -1 . TET sorption was significantly increased after treatment with alum, and there was a strong exponential relationship between Kd and the concentration of bound Al 3+ in amendments (R 2  = 0.94), which indicated that amendments contained functional groups capable of chelating Al 3+ and forming metal bridges with TET. Effective diffusion coefficients of TET in amendments ranged between 0.1 and 5.2 × 10 -6  cm 2  s -1 , which were positively related to temperature and inversely related to Kd by a multiple regression model (R 2  = 0.86). Treatment of organic amendments with alum greatly increased Kd, would decrease D s , and so would greatly reduce hazard risks of applying these organic amendments with this antibiotic to soils. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

Faster quantum searching with almost any diffusion operator

NASA Astrophysics Data System (ADS)

Tulsi, Avatar

2015-05-01

Grover's search algorithm drives a quantum system from an initial state |s > to a desired final state |t > by using selective phase inversions of these two states. Earlier, we studied a generalization of Grover's algorithm that relaxes the assumption of the efficient implementation of Is, the selective phase inversion of the initial state, also known as a diffusion operator. This assumption is known to become a serious handicap in cases of physical interest. Our general search algorithm works with almost any diffusion operator Ds with the only restriction of having |s > as one of its eigenstates. The price that we pay for using any operator is an increase in the number of oracle queries by a factor of O (B ) , where B is a characteristic of the eigenspectrum of Ds and can be large in some situations. Here we show that by using a quantum Fourier transform, we can regain the optimal query complexity of Grover's algorithm without losing the freedom of using any diffusion operator for quantum searching. However, the total number of operators required by the algorithm is still O (B ) times more than that of Grover's algorithm. So our algorithm offers an advantage only if the oracle operator is computationally more expensive than the diffusion operator, which is true in most search problems.

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.

Solution of the nonlinear Poisson-Boltzmann equation: Application to ionic diffusion in cementitious materials

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

Arnold, J.; Kosson, D.S., E-mail: david.s.kosson@vanderbilt.edu; Garrabrants, A.

2013-02-15

A robust numerical solution of the nonlinear Poisson-Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson-Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.

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.

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.

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.

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Electrochemical Impedance Imaging via the Distribution of Diffusion Times

NASA Astrophysics Data System (ADS)

Song, Juhyun; Bazant, Martin Z.

2018-03-01

We develop a mathematical framework to analyze electrochemical impedance spectra in terms of a distribution of diffusion times (DDT) for a parallel array of random finite-length Warburg (diffusion) or Gerischer (reaction-diffusion) circuit elements. A robust DDT inversion method is presented based on complex nonlinear least squares regression with Tikhonov regularization and illustrated for three cases of nanostructured electrodes for energy conversion: (i) a carbon nanotube supercapacitor, (ii) a silicon nanowire Li-ion battery, and (iii) a porous-carbon vanadium flow battery. The results demonstrate the feasibility of nondestructive "impedance imaging" to infer microstructural statistics of random, heterogeneous materials.

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

Exsolution lamellae as fast diffusion pathways in rutile: implications for U-Pb thermochronology and Zr thermometry

NASA Astrophysics Data System (ADS)

Smye, A.; Seman, S.; Roberts, N. M. W.; Condon, D. J.; Davis, B.

2017-12-01

Geophysical processes impart characteristic thermal signatures to the lithosphere. Near-continuous thermal histories can be obtained from inversion of intracrystalline U-Pb age profiles in rutile and apatite provided that it can be shown that profile formed in response to Fickian-type diffusion. Here, we present the results of a combined LA-ICPMS and ID-TIMS U-Pb study on rutile grains from two garnet-bearing granulite xenoliths from a kimberlite in the Archean Slave province. Interpreted using numerical models, we show that the rutile U-Pb isotope systematics are consistent with slow-cooling following crystallization at 1.2 Ga, contemporaneous with the Mackenzie dike swarm. However, inversion of rutile U-Pb age gradients is complicated by the ubiquitous presence of ilmenite exsolution lamellae. We show that these lamellae act as fast diffusion pathways for Pb and High Field Strength Elements, including Zr. This has important implications for the use of rutile as a U-Pb themochronometer and as a single-phase thermometer.

A computationally efficient scheme for the non-linear diffusion equation

NASA Astrophysics Data System (ADS)

Termonia, P.; Van de Vyver, H.

2009-04-01

This Letter proposes a new numerical scheme for integrating the non-linear diffusion equation. It is shown that it is linearly stable. Some tests are presented comparing this scheme to a popular decentered version of the linearized Crank-Nicholson scheme, showing that, although this scheme is slightly less accurate in treating the highly resolved waves, (i) the new scheme better treats highly non-linear systems, (ii) better handles the short waves, (iii) for a given test bed turns out to be three to four times more computationally cheap, and (iv) is easier in implementation.

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.

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.

Linear diffusion model dating of cinder cones in Central Anatolia, Turkey

NASA Astrophysics Data System (ADS)

O'Sadnick, L. G.; Reid, M. R.; Cline, M. L.; Cosca, M. A.; Kuscu, G.

2013-12-01

The progressive decrease in slope angle, cone height and cone height/width ratio over time provides the basis for geomorphic dating of cinder cones using linear diffusion models. Previous research using diffusion models to date cinder cones has focused on the cone height/width ratio as the basis for dating cones of unknown age [1,2]. Here we apply linear diffusion models to dating cinder cones. A suite of 16 cinder cones from the Hasandağ volcano area of the Neogene-Quaternary Central Anatolian Volcanic Zone, for which samples are available, were selected for morphologic dating analysis. New 40Ar/39Ar dates for five of these cones range from 62 × 4 to 517 × 9 ka. Linear diffusion models were used to model the erosional degradation of each cone. Diffusion coefficients (κ) for the 5 cinder cones with known ages were constrained by comparing various modeled slope profiles to the current slope profile. The resulting κ is 7.5×0.5 m2kyr-1. Using this κ value, eruption ages were modeled for the remaining 11 cinder cones and range from 53×3 to 455×30 ka. These ages are within the range of ages previously reported for cinder cones in the Hasandağ region. The linear diffusion model-derived ages are being compared to additional new 40Ar/39Ar dates in order to further assess the applicability of morphological dating to constrain the ages of cinder cones. The relatively well-constrained κ value we obtained by applying the linear diffusion model to cinder cones that range in age by nearly 500 ka suggests that this model can be used to date cinder cones. This κ value is higher than the well-established value of κ =3.9 for a cinder cone in a similar climate [3]. Therefore our work confirms the importance of determining appropriate κ values from nearby cones with known ages. References 1. C.A. Wood, J. Volcanol. Geotherm. Res. 8, 137 (1980) 2. D.M. Wood, M.F. Sheridan, J. Volcanol. Geotherm. Res. 83, 241 (1998) 3. J.D. Pelletier, M.L. Cline, Geology 35, 1067 (2007)

Thermal and ultrasonic evaluation of porosity in composite laminates

NASA Technical Reports Server (NTRS)

Johnston, Patrick H.; Winfree, William P.; Long, Edward R., Jr.; Kullerd, Susan M.; Nathan, N.; Partos, Richard D.

1992-01-01

The effects of porosity on damage incurred by low-velocity impact are investigated. Specimens of graphite/epoxy composite were fabricated with various volume fractions of voids. The void fraction was independently determined using optical examination and acid resin digestion methods. Thermal diffusivity and ultrasonic attenuation were measured, and these results were related to the void volume fraction. The relationship between diffusivity and fiber volume fraction was also considered. The slope of the ultrasonic attenuation coefficient was found to increase linearly with void content, and the diffusivity decreased linearly with void volume fraction, after compensation for an approximately linear dependence on the fiber volume fraction.

Spatial diffusion of influenza outbreak-related climate factors in Chiang Mai Province, Thailand.

PubMed

Nakapan, Supachai; Tripathi, Nitin Kumar; Tipdecho, Taravudh; Souris, Marc

2012-10-24

Influenza is one of the most important leading causes of respiratory illness in the countries located in the tropical areas of South East Asia and Thailand. In this study the climate factors associated with influenza incidence in Chiang Mai Province, Northern Thailand, were investigated. Identification of factors responsible for influenza outbreaks and the mapping of potential risk areas in Chiang Mai are long overdue. This work examines the association between yearly climate patterns between 2001 and 2008 and influenza outbreaks in the Chiang Mai Province. The climatic factors included the amount of rainfall, percent of rainy days, relative humidity, maximum, minimum temperatures and temperature difference. The study develops a statistical analysis to quantitatively assess the relationship between climate and influenza outbreaks and then evaluate its suitability for predicting influenza outbreaks. A multiple linear regression technique was used to fit the statistical model. The Inverse Distance Weighted (IDW) interpolation and Geographic Information System (GIS) techniques were used in mapping the spatial diffusion of influenza risk zones. The results show that there is a significance correlation between influenza outbreaks and climate factors for the majority of the studied area. A statistical analysis was conducted to assess the validity of the model comparing model outputs and actual outbreaks.

Can a one-layer optical skin model including melanin and inhomogeneously distributed blood explain spatially resolved diffuse reflectance spectra?

NASA Astrophysics Data System (ADS)

Karlsson, Hanna; Pettersson, Anders; Larsson, Marcus; Strömberg, Tomas

2011-02-01

Model based analysis of calibrated diffuse reflectance spectroscopy can be used for determining oxygenation and concentration of skin chromophores. This study aimed at assessing the effect of including melanin in addition to hemoglobin (Hb) as chromophores and compensating for inhomogeneously distributed blood (vessel packaging), in a single-layer skin model. Spectra from four humans were collected during different provocations using a twochannel fiber optic probe with source-detector separations 0.4 and 1.2 mm. Absolute calibrated spectra using data from either a single distance or both distances were analyzed using inverse Monte Carlo for light transport and Levenberg-Marquardt for non-linear fitting. The model fitting was excellent using a single distance. However, the estimated model failed to explain spectra from the other distance. The two-distance model did not fit the data well at either distance. Model fitting was significantly improved including melanin and vessel packaging. The most prominent effect when fitting data from the larger separation compared to the smaller separation was a different light scattering decay with wavelength, while the tissue fraction of Hb and saturation were similar. For modeling spectra at both distances, we propose using either a multi-layer skin model or a more advanced model for the scattering phase function.

Medium-energy electrons and heavy ions in Jupiter's magnetosphere - Effects of lower hybrid wave-particle interactions

NASA Technical Reports Server (NTRS)

Barbosa, D. D.

1986-01-01

A theory of medium-energy (about keV) electrons and heavy ions in Jupiter's magnetosphere is presented. Lower hybrid waves are generated by the combined effects of a ring instability of neutral wind pickup ions and the modified two-stream instability associated with transport of cool Iogenic plasma. The quasi-linear energy diffusion coefficient for lower hybrid wave-particle interactions is evaluated, and several solutions to the diffusion equation are given. Calculations based on measured wave properties show that the noise substantially modifies the particle distribution functions. The effects are to accelerate superthermal ions and electrons to keV energies and to thermalize the pickup ions on time scales comparable to the particle residence time. The S(2+)/S(+) ratio at medium energies is a measure of the relative contribution from Iogenic thermal plasma and neutral wind ions, and this important quantity should be determined from future measurements. The theory also predicts a preferential acceleration of heavy ions with an accleration time that scales inversely with the root of the ion mass. Electrons accelerated by the process contribute to further reionization of the neutral wind by electron impact, thus providing a possible confirmation of Alfven's critical velocity effect in the Jovian magnetosphere.

The DOSY experiment provides insights into the protegrin-lipid interaction

NASA Astrophysics Data System (ADS)

Malliavin, T. E.; Louis, V.; Delsuc, M. A.

1998-02-01

The measure of translational diffusion using PFG NMR has known a renewal of interest with the development of the DOSY experiments. The extraction of diffusion coefficients from these experiments requires an inverse Laplace transform. We present here the use of the Maximum Entropy technique to perform this transform, and an application of this method to investigate the interaction protegrin-lipid. We show that the analysis by DOSY experiments permits to determine some of the interaction features. La mesure de diffusion translationnelle par gradients de champs pulsés en RMN a connu un regain d'intérêt avec le développement des expériences de DOSY. L'extraction de coefficients de diffusion à partir de ces expériences nécessite l'application d'une transformée de Laplace inverse. Nous présentons ici l'utilisation de la méthode d'Entropie Maximum pour effectuer cette transformée, ainsi qu'une application de l'expérience de DOSY pour étudier une interaction protégrine-lipide. Nous montrons que l'analyse par l'expérience de DOSY permet de déterminer certaines des caractéristiques de cette interaction.

Influence of chain ordering on the selectivity of dipalmitoylphosphatidylcholine bilayer membranes for permeant size and shape.

PubMed Central

Xiang, T X; Anderson, B D

1998-01-01

The effects of lipid chain packing and permeant size and shape on permeability across lipid bilayers have been investigated in gel and liquid crystalline dipalmitoylphosphatidylcholine (DPPC) bilayers by a combined NMR line-broadening/dynamic light scattering method using seven short-chain monocarboxylic acids (formic acid, acetic acid, propionic acid, butyric acid, valeric acid, isovaleric acid, and trimethylacetic acid) as permeants. The experimental permeability coefficients are compared with the predictions of a bulk solubility diffusion model in which the bilayer membrane is represented as a slab of bulk hexadecane. Deviations of the observed permeability coefficients (Pm) from the values predicted from solubility diffusion theory (Po) lead to the determination of a correction factor, the permeability decrement f (= Pm/Po), to account for the effects of chain ordering. The natural logarithm of f has been found to correlate linearly with the inverse of the bilayer free surface area with slopes of 25 +/- 2, 36 +/- 3, 45 +/- 8, 32 +/- 12, 33 +/- 4, 49 +/- 12, and 75 +/- 6 A2 for formic acid, acetic acid, propionic acid, butyric acid, valeric acid, isovaleric acid, and trimethylacetic acid, respectively. The slope, which measures the sensitivity of the permeability coefficient of a given permeant to bilayer chain packing, exhibits an excellent linear correlation (r = 0.94) with the minimum cross-sectional area of the permeant and a poor correlation (r = 0.59) with molecular volume, suggesting that in the bilayer interior the permeants prefer to move with their long principal axis along the bilayer normal. Based on these studies, a permeability model combining the effects of bilayer chain packing and permeant size and shape on permeability across lipid membranes is developed. PMID:9826590

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.

Effects of molecular size and structure on self-diffusion coefficient and viscosity for saturated hydrocarbons having six carbon atoms.

PubMed

Iwahashi, Makio; Kasahara, Yasutoshi

2007-01-01

Self-diffusion coefficients and viscosities for the saturated hydrocarbons having six carbon atoms such as hexane, 2-methylpentane (2MP), 3-methylpentane (3MP), 2,2-dimethylbutane (22DMB), 2,3-dimethylbutane (23DMB), methylcyclopentane (McP) and cyclohexane (cH) were measured at various constant temperatures; obtained results were discussed in connection with their molar volumes, molecular structures and thermodynamic properties. The values of self-diffusion coefficients as the microscopic property were inversely proportional to those of viscosities as the macroscopic property. The order of their viscosities was almost same to those of their melting temperatures and enthalpies of fusion, which reflect the attractive interactions among their molecules. On the other hand, the order of the self-diffusion coefficients inversely related to the order of the melting temperatures and the enthalpies of the fusion. Namely, the compound having the larger attractive interaction mostly shows the less mobility in its liquid state, e.g., cyclohexane (cH), having the largest attractive interaction and the smallest molar volume exhibits an extremely large viscosity and small self-diffusion coefficient comparing with other hydrocarbons. However, a significant exception was 22DMB, being most close to a sphere: In spite of the smallest attractive interaction and the largest molar volume of 22DMB in the all samples, it has the thirdly larger viscosity and the thirdly smaller self-diffusion coefficient. Consequently, the dynamical properties such as self-diffusion and viscosity for the saturated hydrocarbons are determined not only by their attractive interactions but also by their molecular structures.

Diffuse colonies of human skin fibroblasts in relation to cellular senescence and proliferation.

PubMed

Zorin, Vadim; Zorina, Alla; Smetanina, Nadezhda; Kopnin, Pavel; Ozerov, Ivan V; Leonov, Sergey; Isaev, Artur; Klokov, Dmitry; Osipov, Andreyan N

2017-05-16

Development of personalized skin treatment in medicine and skin care may benefit from simple and accurate evaluation of the fraction of senescent skin fibroblasts that lost their proliferative capacity. We examined whether enriched analysis of colonies formed by primary human skin fibroblasts, a simple and widely available cellular assay, could reveal correlations with the fraction of senescent cells in heterogenic cell population. We measured fractions of senescence associated β-galactosidase (SA-βgal) positive cells in either mass cultures or colonies of various morphological types (dense, mixed and diffuse) formed by skin fibroblasts from 10 human donors. Although the donors were chosen to be within the same age group (33-54 years), the colony forming efficiency of their fibroblasts (ECO-f) and the percentage of dense, mixed and diffuse colonies varied greatly among the donors. We showed, for the first time, that the SA-βgal positive fraction was the largest in diffuse colonies, confirming that they originated from cells with the least proliferative capacity. The percentage of diffuse colonies was also found to correlate with the SA-βgal positive cells in mass culture. Using Ki67 as a cell proliferation marker, we further demonstrated a strong inverse correlation (r=-0.85, p=0.02) between the percentage of diffuse colonies and the fraction of Ki67+ cells. Moreover, a significant inverse correlation (r=-0.94, p=0.0001) between the percentage of diffuse colonies and ECO-f was found. Our data indicate that quantification of a fraction of diffuse colonies may provide a simple and useful method to evaluate the extent of cellular senescence in human skin fibroblasts.

Stochastic field-line wandering in magnetic turbulence with shear. I. Quasi-linear theory

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

Shalchi, A.; Negrea, M.; Petrisor, I.

2016-07-15

We investigate the random walk of magnetic field lines in magnetic turbulence with shear. In the first part of the series, we develop a quasi-linear theory in order to compute the diffusion coefficient of magnetic field lines. We derive general formulas for the diffusion coefficients in the different directions of space. We like to emphasize that we expect that quasi-linear theory is only valid if the so-called Kubo number is small. We consider two turbulence models as examples, namely, a noisy slab model as well as a Gaussian decorrelation model. For both models we compute the field line diffusion coefficientsmore » and we show how they depend on the aforementioned Kubo number as well as a shear parameter. It is demonstrated that the shear effect reduces all field line diffusion coefficients.« less

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

NASA Astrophysics Data System (ADS)

Broche, Rita de Cássia D. S.; de Oliveira, Luiz Augusto F.

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem.

Apparent diffusion coefficient measurement in a moving phantom simulating linear respiratory motion.

PubMed

Kwee, Thomas C; Takahara, Taro; Muro, Isao; Van Cauteren, Marc; Imai, Yutaka; Nievelstein, Rutger A J; Mali, Willem P T M; Luijten, Peter R

2010-10-01

The aim of this study was to examine the effect of simulated linear respiratory motion on apparent diffusion coefficient (ADC) measurements. Six rectangular test tubes (14 × 92 mm) filled with either water, tomato ketchup, or mayonnaise were positioned in a box containing agarose gel. This box was connected to a double-acting pneumatic cylinder, capable of inducing periodic linear motion in the long-axis direction of the magnetic bore (23-mm stroke). Diffusion-weighted magnetic resonance imaging was performed for both the static and moving phantoms, and ADC measurements were made in the six test tubes in both situations. In the three test tubes whose long axes were parallel to the direction of motion, ADCs agreed well between the moving and static phantom situations. However, in two test tubes that were filled with fluids that had a considerably lower diffusion coefficient than the surrounding agarose gel, and whose long axes were perpendicular to the direction of motion, the ADCs agreed poorly between the moving and static phantom situations. ADC measurements of large homogeneous structures are not affected by linear respiratory motion. However, ADC measurements of inhomogeneous or small structures are affected by linear respiratory motion due to partial volume effects.

Nanoparticle Motion in Entangled Melts of Linear and Nonconcatenated Ring Polymers [Nanoparticle Motion in Entangled Melts of Non-Concatenated Ring Polymers].

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

Ge, Ting; Kalathi, Jagannathan T.; Halverson, Jonathan D.

The motion of nanoparticles (NPs) in entangled melts of linear polymers and non-concatenated ring polymers are compared by large-scale molecular dynamics simulations. The comparison provides a paradigm for the effects of polymer architecture on the dynamical coupling between NPs and polymers in nanocomposites. Strongly suppressed motion of NPs with diameter d larger than the entanglement spacing a is observed in a melt of linear polymers before the onset of Fickian NP diffusion. This strong suppression of NP motion occurs progressively as d exceeds a, and is related to the hopping diffusion of NPs in the entanglement network. In contrast tomore » the NP motion in linear polymers, the motion of NPs with d > a in ring polymers is not as strongly suppressed prior to Fickian diffusion. The diffusion coefficient D decreases with increasing d much slower in entangled rings than in entangled linear chains. NP motion in entangled non-concatenated ring polymers is understood through a scaling analysis of the coupling between NP motion and the self-similar entangled dynamics of ring polymers.« less

Nanoparticle Motion in Entangled Melts of Linear and Nonconcatenated Ring Polymers [Nanoparticle Motion in Entangled Melts of Non-Concatenated Ring Polymers].

DOE PAGES

Ge, Ting; Kalathi, Jagannathan T.; Halverson, Jonathan D.; ...

2017-02-13

The motion of nanoparticles (NPs) in entangled melts of linear polymers and non-concatenated ring polymers are compared by large-scale molecular dynamics simulations. The comparison provides a paradigm for the effects of polymer architecture on the dynamical coupling between NPs and polymers in nanocomposites. Strongly suppressed motion of NPs with diameter d larger than the entanglement spacing a is observed in a melt of linear polymers before the onset of Fickian NP diffusion. This strong suppression of NP motion occurs progressively as d exceeds a, and is related to the hopping diffusion of NPs in the entanglement network. In contrast tomore » the NP motion in linear polymers, the motion of NPs with d > a in ring polymers is not as strongly suppressed prior to Fickian diffusion. The diffusion coefficient D decreases with increasing d much slower in entangled rings than in entangled linear chains. NP motion in entangled non-concatenated ring polymers is understood through a scaling analysis of the coupling between NP motion and the self-similar entangled dynamics of ring polymers.« less

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.

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.

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.

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.

Time-resolved diffusion tomographic 2D and 3D imaging in highly scattering turbid media

NASA Technical Reports Server (NTRS)

Alfano, Robert R. (Inventor); Cai, Wei (Inventor); Liu, Feng (Inventor); Lax, Melvin (Inventor); Das, Bidyut B. (Inventor)

1999-01-01

A method for imaging objects in highly scattering turbid media. According to one embodiment of the invention, the method involves using a plurality of intersecting source/detectors sets and time-resolving equipment to generate a plurality of time-resolved intensity curves for the diffusive component of light emergent from the medium. For each of the curves, the intensities at a plurality of times are then inputted into the following inverse reconstruction algorithm to form an image of the medium: ##EQU1## wherein W is a matrix relating output at source and detector positions r.sub.s and r.sub.d, at time t, to position r, .LAMBDA. is a regularization matrix, chosen for convenience to be diagonal, but selected in a way related to the ratio of the noise, to fluctuations in the absorption (or diffusion) X.sub.j that we are trying to determine: .LAMBDA..sub.ij =.lambda..sub.j .delta..sub.ij with .lambda..sub.j =/<.DELTA.Xj.DELTA.Xj> Y is the data collected at the detectors, and X.sup.k is the kth iterate toward the desired absoption information. An algorithm, which combines a two dimensional (2D) matrix inversion with a one-dimensional (1D) Fourier transform inversion is used to obtain images of three dimensional hidden objects in turbid scattering media.

Time-resolved diffusion tomographic 2D and 3D imaging in highly scattering turbid media

NASA Technical Reports Server (NTRS)

Alfano, Robert R. (Inventor); Cai, Wei (Inventor); Gayen, Swapan K. (Inventor)

2000-01-01

A method for imaging objects in highly scattering turbid media. According to one embodiment of the invention, the method involves using a plurality of intersecting source/detectors sets and time-resolving equipment to generate a plurality of time-resolved intensity curves for the diffusive component of light emergent from the medium. For each of the curves, the intensities at a plurality of times are then inputted into the following inverse reconstruction algorithm to form an image of the medium: wherein W is a matrix relating output at source and detector positions r.sub.s and r.sub.d, at time t, to position r, .LAMBDA. is a regularization matrix, chosen for convenience to be diagonal, but selected in a way related to the ratio of the noise, to fluctuations in the absorption (or diffusion) X.sub.j that we are trying to determine: .LAMBDA..sub.ij =.lambda..sub.j .delta..sub.ij with .lambda..sub.j =/<.DELTA.Xj.DELTA.Xj> Y is the data collected at the detectors, and X.sup.k is the kth iterate toward the desired absorption information. An algorithm, which combines a two dimensional (2D) matrix inversion with a one-dimensional (1D) Fourier transform inversion is used to obtain images of three dimensional hidden objects in turbid scattering media.

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.

Traumatic Brain Injury: Hope Through Research

MedlinePlus

... last decade to image milder TBI damage. For example, diffusion tensor imaging (DTI) can image white matter tracts, more sensitive tests like fluid-attenuated inversion recovery (FLAIR) can detect ...

Decoupling of rotational and translational diffusion in supercooled colloidal fluids

PubMed Central

Edmond, Kazem V.; Elsesser, Mark T.; Hunter, Gary L.; Pine, David J.; Weeks, Eric R.

2012-01-01

We use confocal microscopy to directly observe 3D translational and rotational diffusion of tetrahedral clusters, which serve as tracers in colloidal supercooled fluids. We find that as the colloidal glass transition is approached, translational and rotational diffusion decouple from each other: Rotational diffusion remains inversely proportional to the growing viscosity whereas translational diffusion does not, decreasing by a much lesser extent. We quantify the rotational motion with two distinct methods, finding agreement between these methods, in contrast with recent simulation results. The decoupling coincides with the emergence of non-Gaussian displacement distributions for translation whereas rotational displacement distributions remain Gaussian. Ultimately, our work demonstrates that as the glass transition is approached, the sample can no longer be approximated as a continuum fluid when considering diffusion. PMID:23071311

Electrochemical Impedance Imaging via the Distribution of Diffusion Times.

PubMed

Song, Juhyun; Bazant, Martin Z

2018-03-16

We develop a mathematical framework to analyze electrochemical impedance spectra in terms of a distribution of diffusion times (DDT) for a parallel array of random finite-length Warburg (diffusion) or Gerischer (reaction-diffusion) circuit elements. A robust DDT inversion method is presented based on complex nonlinear least squares regression with Tikhonov regularization and illustrated for three cases of nanostructured electrodes for energy conversion: (i) a carbon nanotube supercapacitor, (ii) a silicon nanowire Li-ion battery, and (iii) a porous-carbon vanadium flow battery. The results demonstrate the feasibility of nondestructive "impedance imaging" to infer microstructural statistics of random, heterogeneous materials.

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.

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

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.

Astrophysical gamma-ray production by inverse Compton interactions of relativistic electrons

NASA Technical Reports Server (NTRS)

Schlickeiser, R.

1979-01-01

The inverse Compton scattering of background photon gases by relativistic electrons is a good candidate for the production of high-energy gamma rays in the diffuse interstellar medium as well as in discrete sources. By discussing the special case of the scattering of the diffuse starlight in the interstellar medium by cosmic ray electrons, we demonstrate that previous derivations of the gamma ray source function for this process on the basis of the Thomson limit of the Klein-Nishina cross section lead to incorrect values for gamma-ray energies above 100 MeV. It is shown that the Thomson limit is not applicable for the calculation of gamma-ray source functions in astrophysical circumstances in which target photons with energies greater than 1 eV are scattered by relativistic electrons.

Linear response theory and transient fluctuation relations for diffusion processes: a backward point of view

NASA Astrophysics Data System (ADS)

Liu, Fei; Tong, Huan; Ma, Rui; Ou-Yang, Zhong-can

2010-12-01

A formal apparatus is developed to unify derivations of the linear response theory and a variety of transient fluctuation relations for continuous diffusion processes from a backward point of view. The basis is a perturbed Kolmogorov backward equation and the path integral representation of its solution. We find that these exact transient relations could be interpreted as a consequence of a generalized Chapman-Kolmogorov equation, which intrinsically arises from the Markovian characteristic of diffusion processes.

Cosmic ray diffusion: Report of the Workshop in Cosmic Ray Diffusion Theory

NASA Technical Reports Server (NTRS)

Birmingham, T. J.; Jones, F. C.

1975-01-01

A workshop in cosmic ray diffusion theory was held at Goddard Space Flight Center on May 16-17, 1974. Topics discussed and summarized are: (1) cosmic ray measurements as related to diffusion theory; (2) quasi-linear theory, nonlinear theory, and computer simulation of cosmic ray pitch-angle diffusion; and (3) magnetic field fluctuation measurements as related to diffusion theory.

Differences in Callosal and Forniceal Diffusion between Patients with and without Postconcussive Migraine.

PubMed

Alhilali, L M; Delic, J; Fakhran, S

2017-04-01

Posttraumatic migraines are common after mild traumatic brain injury. The purpose of this study was to determine if a specific axonal injury pattern underlies posttraumatic migraines after mild traumatic brain injury utilizing Tract-Based Spatial Statistics analysis of diffusion tensor imaging. DTI was performed in 58 patients with mild traumatic brain injury with posttraumatic migraines. Controls consisted of 17 patients with mild traumatic brain injury without posttraumatic migraines. Fractional anisotropy and diffusivity maps were generated to measure white matter integrity and were evaluated by using Tract-Based Spatial Statistics regression analysis with a general linear model. DTI findings were correlated with symptom severity, neurocognitive test scores, and time to recovery with the Pearson correlation coefficient. Patients with mild traumatic brain injury with posttraumatic migraines were not significantly different from controls in terms of age, sex, type of injury, or neurocognitive test performance. Patients with posttraumatic migraines had higher initial symptom severity ( P = .01) than controls. Compared with controls, patients with mild traumatic brain injury with posttraumatic migraines had decreased fractional anisotropy in the corpus callosum ( P = .03) and fornix/septohippocampal circuit ( P = .045). Injury to the fornix/septohippocampal circuit correlated with decreased visual memory ( r = 0.325, P = .01). Injury to corpus callosum trended toward inverse correlation with recovery ( r = -0.260, P = .05). Injuries to the corpus callosum and fornix/septohippocampal circuit were seen in patients with mild traumatic brain injury with posttraumatic migraines, with injuries in the fornix/septohippocampal circuit correlating with decreased performance on neurocognitive testing. © 2017 by American Journal of Neuroradiology.

Diffusive sensitivity to muscle architecture: a magnetic resonance diffusion tensor imaging study of the human calf.

PubMed

Galbán, Craig J; Maderwald, Stefan; Uffmann, Kai; de Greiff, Armin; Ladd, Mark E

2004-12-01

The aim of this study was to examine the diffusive properties of adjacent muscles at rest, and to determine the relationship between diffusive and architectural properties, which are task-specific to muscles. The principle, second, and third eigenvalues, trace of the diffusion tensor, and two anisotropic parameters, ellipsoid eccentricity (e) and fractional anisotropy (FA), of various muscles in the human calf were calculated by diffusion tensor imaging (DTI). Linear correlations of the calculated parameters to the muscle physiological cross-sectional area (PCSA), which is proportional to maximum muscle force, were performed to ascertain any linear relation between muscle architecture and diffusivity. Images of the left calf were acquired from six healthy male volunteers. Seven muscles were investigated in this study. These comprised the soleus, lateral gastrocnemius, medial gastrocnemius, posterior tibialis, anterior tibialis, extensor digitorum longus, and peroneus longus. All data were presented as the mean and standard error of the mean (SEM). In general, differences in diffusive parameter values occurred primarily between functionally different muscles. A strong correlation was also found between PCSA and the third eigenvalue, e, and FA. A mathematical derivation revealed a linear relationship between PCSA and the third eigenvalue as a result of their dependence on the average radius of all fibers within a single muscle. These findings demonstrated the ability of DTI to differentiate between functionally different muscles in the same region of the body on the basis of their diffusive properties.

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.

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.

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.

Self-diffusion in a stochastically heated two-dimensional dusty plasma

NASA Astrophysics Data System (ADS)

Sheridan, T. E.

2016-09-01

Diffusion in a two-dimensional dusty plasma liquid (i.e., a Yukawa liquid) is studied experimentally. The dusty plasma liquid is heated stochastically by a surrounding three-dimensional toroidal dusty plasma gas which acts as a thermal reservoir. The measured dust velocity distribution functions are isotropic Maxwellians, giving a well-defined kinetic temperature. The mean-square displacement for dust particles is found to increase linearly with time, indicating normal diffusion. The measured diffusion coefficients increase approximately linearly with temperature. The effective collision rate is dominated by collective dust-dust interactions rather than neutral gas drag, and is comparable to the dusty-plasma frequency.

Effects of superparamagnetic iron oxide nanoparticles on the longitudinal and transverse relaxation of hyperpolarized xenon gas

NASA Astrophysics Data System (ADS)

Burant, Alex; Antonacci, Michael; McCallister, Drew; Zhang, Le; Branca, Rosa Tamara

2018-06-01

SuperParamagnetic Iron Oxide Nanoparticles (SPIONs) are often used in magnetic resonance imaging experiments to enhance Magnetic Resonance (MR) sensitivity and specificity. While the effect of SPIONs on the longitudinal and transverse relaxation time of 1H spins has been well characterized, their effect on highly diffusive spins, like those of hyperpolarized gases, has not. For spins diffusing in linear magnetic field gradients, the behavior of the magnetization is characterized by the relative size of three length scales: the diffusion length, the structural length, and the dephasing length. However, for spins diffusing in non-linear gradients, such as those generated by iron oxide nanoparticles, that is no longer the case, particularly if the diffusing spins experience the non-linearity of the gradient. To this end, 3D Monte Carlo simulations are used to simulate the signal decay and the resulting image contrast of hyperpolarized xenon gas near SPIONs. These simulations reveal that signal loss near SPIONs is dominated by transverse relaxation, with little contribution from T1 relaxation, while simulated image contrast and experiments show that diffusion provides no appreciable sensitivity enhancement to SPIONs.

Characterization of Ultrasound Energy Diffusion Due to Small-Size Damage on an Aluminum Plate Using Piezoceramic Transducers

PubMed Central

Lu, Guangtao; Feng, Qian; Li, Yourong; Wang, Hao; Song, Gangbing

2017-01-01

During the propagation of ultrasonic waves in structures, there is usually energy loss due to ultrasound energy diffusion and dissipation. The aim of this research is to characterize the ultrasound energy diffusion that occurs due to small-size damage on an aluminum plate using piezoceramic transducers, for the future purpose of developing a damage detection algorithm. The ultrasonic energy diffusion coefficient is related to the damage distributed in the medium. Meanwhile, the ultrasonic energy dissipation coefficient is related to the inhomogeneity of the medium. Both are usually employed to describe the characteristics of ultrasound energy diffusion. The existence of multimodes of Lamb waves in metallic plate structures results in the asynchronous energy transport of different modes. The mode of Lamb waves has a great influence on ultrasound energy diffusion as a result, and thus has to be chosen appropriately. In order to study the characteristics of ultrasound energy diffusion in metallic plate structures, an experimental setup of an aluminum plate with a through-hole, whose diameter varies from 0.6 mm to 1.2 mm, is used as the test specimen with the help of piezoceramic transducers. The experimental results of two categories of damages at different locations reveal that the existence of damage changes the energy transport between the actuator and the sensor. Also, when there is only one dominate mode of Lamb wave excited in the structure, the ultrasound energy diffusion coefficient decreases approximately linearly with the diameter of the simulated damage. Meanwhile, the ultrasonic energy dissipation coefficient increases approximately linearly with the diameter of the simulated damage. However, when two or more modes of Lamb waves are excited, due to the existence of different group velocities between the different modes, the energy transport of the different modes is asynchronous, and the ultrasonic energy diffusion is not strictly linear with the size of the damage. Therefore, it is recommended that only one dominant mode of Lamb wave should be excited during the characterization process, in order to ensure that the linear relationship between the damage size and the characteristic parameters is maintained. In addition, the findings from this paper demonstrate the potential of developing future damage detection algorithms using the linear relationships between damage size and the ultrasound energy diffusion coefficient or ultrasonic energy dissipation coefficient when a single dominant mode is excited. PMID:29207530

Test of the diffusing-diffusivity mechanism using near-wall colloidal dynamics

NASA Astrophysics Data System (ADS)

Matse, Mpumelelo; Chubynsky, Mykyta V.; Bechhoefer, John

2017-10-01

The mechanism of diffusing diffusivity predicts that, in environments where the diffusivity changes gradually, the displacement distribution becomes non-Gaussian, even though the mean-square displacement grows linearly with time. Here, we report single-particle tracking measurements of the diffusion of colloidal spheres near a planar substrate. Because the local effective diffusivity is known, we have been able to carry out a direct test of this mechanism for diffusion in inhomogeneous media.

The effect of tissue structure and soil chemistry on trace element uptake in fossils

NASA Astrophysics Data System (ADS)

Hinz, Emily A.; Kohn, Matthew J.

2010-06-01

Trace element profiles for common divalent cations (Sr, Zn, Ba), rare-earth elements (REE), Y, U, and Th were measured in fossil bones and teeth from the c. 25 ka Merrell locality, Montana, USA, by using laser-ablation ICP-MS. Multiple traverses in teeth were transformed into 2-D trace element maps for visualizing structural influences on trace element uptake. Trace element compositions of different soils from the fossil site were also analyzed by solution ICP-MS, employing progressive leaches that included distilled H 2O, 0.1 M acetic acid, and microwave digestion in concentrated HCl-HNO 3. In teeth, trace element uptake in enamel is 2-4 orders of magnitude slower than in dentine, forming an effective trace element barrier. Uptake in dentine parallel to the dentine-enamel interface is enhanced by at least 2 orders of magnitude compared to transverse, causing trace element "plumes" down the tooth core. In bone, U, Ba and Sr are nearly homogeneous, implying diffusivities ˜5 orders of magnitude faster than in enamel and virtually complete equilibration with host soils. In contrast all REE show strong depletions inward, with stepwise linear segments in log-normal or inverse complementary error function plots; these data require a multi-medium diffusion model, with about 2 orders of magnitude difference in slowest vs. fastest diffusivities. Differences in REE diffusivities in bone (slow) vs. dentine (fast) reflect different partition coefficients ( Kd's). Although acid leaches and bulk digestion of soils yield comparable fossil-soil Kd's among different elements, natural solutions are expected to be neutral to slightly basic. Distilled H 2O leachates instead reveal radically different Kd's in bone for REE than for U-Sr-Ba, suggest orders of magnitude lower effective diffusivities for REE, and readily explain steep vs. flat profiles for REE vs. U-Sr-Ba, respectively. Differences among REE Kd's and diffusivities may explain inward changes in Ce anomalies. Acid washes and bulk soil compositions yield misleading Kd's for many trace elements, especially the REE, and H 2O-leaches are preferred. Patterns of trace element distributions indicate diagenetic alteration at all scales, including enamel, and challenge the use of trace elements in paleodietary studies.

Long-time behavior and Turing instability induced by cross-diffusion in a three species food chain model with a Holling type-II functional response.

PubMed

Haile, Dawit; Xie, Zhifu

2015-09-01

In this paper, we study a strongly coupled reaction-diffusion system describing three interacting species in a food chain model, where the third species preys on the second one and simultaneously the second species preys on the first one. An intra-species competition b2 among the second predator is introduced to the food chain model. This parameter produces some very interesting result in linear stability and Turing instability. We first show that the unique positive equilibrium solution is locally asymptotically stable for the corresponding ODE system when the intra-species competition exists among the second predator. The positive equilibrium solution remains linearly stable for the reaction diffusion system without cross diffusion, hence it does not belong to the classical Turing instability scheme. But it becomes linearly unstable only when cross-diffusion also plays a role in the reaction-diffusion system, hence the instability is driven solely from the effect of cross diffusion. Our results also exhibit some interesting combining effects of cross-diffusion, intra-species competitions and inter-species interactions. Numerically, we conduct a one parameter analysis which illustrate how the interactions change the existence of stable equilibrium, limit cycle, and chaos. Some interesting dynamical phenomena occur when we perform analysis of interactions in terms of self-production of prey and intra-species competition of the middle predator. By numerical simulations, it illustrates the existence of nonuniform steady solutions and new patterns such as spot patterns, strip patterns and fluctuations due to the diffusion and cross diffusion in two-dimension. Published by Elsevier Inc.

Anomalous dielectric relaxation with linear reaction dynamics in space-dependent force fields.

PubMed

Hong, Tao; Tang, Zhengming; Zhu, Huacheng

2016-12-28

The anomalous dielectric relaxation of disordered reaction with linear reaction dynamics is studied via the continuous time random walk model in the presence of space-dependent electric field. Two kinds of modified reaction-subdiffusion equations are derived for different linear reaction processes by the master equation, including the instantaneous annihilation reaction and the noninstantaneous annihilation reaction. If a constant proportion of walkers is added or removed instantaneously at the end of each step, there will be a modified reaction-subdiffusion 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, there will be a standard linear reaction kinetics term but a fractional order temporal derivative operating on an anomalous diffusion term. The dielectric polarization is analyzed based on the Legendre polynomials and the dielectric properties of both reactions can be expressed by the effective rotational diffusion function and component concentration function, which is similar to the standard reaction-diffusion process. The results show that the effective permittivity can be used to describe the dielectric properties in these reactions if the chemical reaction time is much longer than the relaxation time.

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.

Progression of White Matter Hyperintensities Preceded by Heterogeneous Decline of Microstructural Integrity.

PubMed

van Leijsen, Esther M C; Bergkamp, Mayra I; van Uden, Ingeborg W M; Ghafoorian, Mohsen; van der Holst, Helena M; Norris, David G; Platel, Bram; Tuladhar, Anil M; de Leeuw, Frank-Erik

2018-05-03

White matter hyperintensities (WMH) are frequently seen on neuroimaging of elderly and are associated with cognitive decline and the development of dementia. Yet, the temporal dynamics of conversion of normal-appearing white matter (NAWM) into WMH remains unknown. We examined whether and when progression of WMH was preceded by changes in fluid-attenuated inversion recovery and diffusion tensor imaging values, thereby taking into account differences between participants with mild versus severe baseline WMH. From 266 participants of the RUN DMC study (Radboud University Nijmegen Diffusion Tensor and Magnetic Resonance Imaging Cohort), we semiautomatically segmented WMH at 3 time points for 9 years. Images were registered to standard space through a subject template. We analyzed differences in baseline fluid-attenuated inversion recovery, fractional anisotropy, and mean diffusivity (MD) values and changes in MD values over time between 4 regions: (1) remaining NAWM, (2) NAWM converting into WMH in the second follow-up period, (3) NAWM converting into WMH in the first follow-up period, and (4) WMH. NAWM converting into WMH in the first or second time interval showed higher fluid-attenuated inversion recovery and MD values than remaining NAWM. MD values in NAWM converting into WMH in the first time interval were similar to MD values in WMH. When stratified by baseline WMH severity, participants with severe WMH had higher fluid-attenuated inversion recovery and MD and lower fractional anisotropy values than participants with mild WMH, in all areas including the NAWM. MD values in WMH and in NAWM that converted into WMH continuously increased over time. Impaired microstructural integrity preceded conversion into WMH and continuously declined over time, suggesting a continuous disease process of white matter integrity loss that can be detected using diffusion tensor imaging even years before WMH become visible on conventional neuroimaging. Differences in microstructural integrity between participants with mild versus severe WMH suggest heterogeneity of both NAWM and WMH, which might explain the clinical variability observed in patients with similar small vessel disease severity. © 2018 American Heart Association, Inc.

Monotonic non-linear transformations as a tool to investigate age-related effects on brain white matter integrity: A Box-Cox investigation.

PubMed

Morozova, Maria; Koschutnig, Karl; Klein, Elise; Wood, Guilherme

2016-01-15

Non-linear effects of age on white matter integrity are ubiquitous in the brain and indicate that these effects are more pronounced in certain brain regions at specific ages. Box-Cox analysis is a technique to increase the log-likelihood of linear relationships between variables by means of monotonic non-linear transformations. Here we employ Box-Cox transformations to flexibly and parsimoniously determine the degree of non-linearity of age-related effects on white matter integrity by means of model comparisons using a voxel-wise approach. Analysis of white matter integrity in a sample of adults between 20 and 89years of age (n=88) revealed that considerable portions of the white matter in the corpus callosum, cerebellum, pallidum, brainstem, superior occipito-frontal fascicle and optic radiation show non-linear effects of age. Global analyses revealed an increase in the average non-linearity from fractional anisotropy to radial diffusivity, axial diffusivity, and mean diffusivity. These results suggest that Box-Cox transformations are a useful and flexible tool to investigate more complex non-linear effects of age on white matter integrity and extend the functionality of the Box-Cox analysis in neuroimaging. Copyright © 2015 Elsevier Inc. All rights reserved.

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.

Isoprene-styrene copolymer elastomer and tetrahydrofurfuryl methacrylate mixtures for soft prosthetic applications.

PubMed

Nazhat, S N; Parker, S; Patel, M P; Braden, M

2001-09-01

Novel elastomer/methacrylate systems have been developed for potential soft prosthetic applications. Mixtures of varying compositions of an isoprene-styrene copolymer elastomer and tetrahydrofurfuryl methacrylate (SIS/THFMA) formed one-gel systems and were heat cured with a peroxide initiator. The blends were characterised in terms of sorption in deionised water and simulated body fluids (SBF), tensile properties and viscoelastic parameters of storage modulus and tan delta, as well as glass transition temperatures using dynamic mechanical analysis (DMA). DMA data gave two distinct peaks in tan delta, a lower temperature transition due to the isoprene phase in SIS and one at high temperature thought to be a combination of THFMA and the styrene phase in SIS. The tensile data showed a clear phase inversion within the mid range compositions changing from plastic to elastomeric behaviour. The sorption studies in deionised water showed a two stage uptake with an initial Fickian region that was linear to t 1/2 followed by a droplet growth/clustering system. The slope of the linear region was dependent on the composition ratio. The extent of overall uptake was osmotically dependent as all materials equilibrated at a much lower uptake in SBF. The diffusion coefficients were found to be concentration dependent.

Diffusion, Viscosity and Crystal Growth in Microgravity

NASA Technical Reports Server (NTRS)

Myerson, Allan S.

1996-01-01

The diffusivity of TriGlycine Sulfate (TGS), Potassium Dihydrogen Phosphate (KDP), Ammonium Dihydrogen Phosphate (ADF) and other compounds of interest to microgravity crystal growth, in supersaturated solutions as a function of solution concentration, 'age' and 'history was studied experimentally. The factors that affect the growth of crystals from water solutions in microgravity have been examined. Three non-linear optical materials have been studied, potassium dihydrogen phosphate (KDP), ammonium dihydrogen phosphate (ADP) and triglycine sulfate (TGC). The diffusion coefficient and viscosity of supersaturated water solutions were measured. Also theoretical model of diffusivity and viscosity in a metastable state, model of crystal growth from solution including non-linear time dependent diffusivity and viscosity effect and computer simulation of the crystal growth process which allows simulation of the microgravity crystal growth were developed.

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.

Locating and characterizing a crack in concrete with diffuse ultrasound: A four-point bending test.

PubMed

Larose, Eric; Obermann, Anne; Digulescu, Angela; Planès, Thomas; Chaix, Jean-Francois; Mazerolle, Frédéric; Moreau, Gautier

2015-07-01

This paper describes an original imaging technique, named Locadiff, that benefits from the diffuse effect of ultrasound waves in concrete to detect and locate mechanical changes associated with the opening of pre-existing cracks, and/or to the development of diffuse damage at the tip of the crack. After giving a brief overview of the theoretical model to describe the decorrelation of diffuse waveforms induced by a local change, the article introduces the inversion procedure that produces the three dimensional maps of density of changes. These maps are interpreted in terms of mechanical changes, fracture opening, and damage development. In addition, each fracture is characterized by its effective scattering cross section.

Geomorphic control of radionuclide diffusion in desert soils

USGS Publications Warehouse

Pelletier, J.D.; Harrington, C.D.; Whitney, J.W.; Cline, M.; DeLong, S.B.; Keating, G.; Ebert, T.K.

2005-01-01

Diffusion is a standard model for the vertical migration of radionuclides in soil profiles. Here we show that diffusivity values inferred from fallout 137CS profiles in soils on the Fortymile Wash alluvial fan, Nye County, Nevada, have a strong inverse correlation with the age of the geomorphic surface. This result suggests that radionuclide-bound particles are predominantly transported by infiltration rather than by bulk-mixing processes such as wetting/ drying, freeze/thaw, and bioturbation. Our results provide a preliminary basis for using soil-geomorphic mapping, point-based calibration data, and the diffusion model to predict radionuclide trans desert soils within a pedotransfer-function approach. Copyright 2005 by the American Geophysical Union.

Global uniqueness in an inverse problem for time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Kian, Y.; Oksanen, L.; Soccorsi, E.; Yamamoto, M.

2018-01-01

Given (M , g), a compact connected Riemannian manifold of dimension d ⩾ 2, with boundary ∂M, we consider an initial boundary value problem for a fractional diffusion equation on (0 , T) × M, T > 0, with time-fractional Caputo derivative of order α ∈ (0 , 1) ∪ (1 , 2). We prove uniqueness in the inverse problem of determining the smooth manifold (M , g) (up to an isometry), and various time-independent smooth coefficients appearing in this equation, from measurements of the solutions on a subset of ∂M at fixed time. In the "flat" case where M is a compact subset of Rd, two out the three coefficients ρ (density), a (conductivity) and q (potential) appearing in the equation ρ ∂tα u - div (a∇u) + qu = 0 on (0 , T) × M are recovered simultaneously.

Acoustic measurement of bubble size and position in a piezo driven inkjet printhead

NASA Astrophysics Data System (ADS)

van der Bos, Arjan; Jeurissen, Roger; de Jong, Jos; Stevens, Richard; Versluis, Michel; Reinten, Hans; van den Berg, Marc; Wijshoff, Herman; Lohse, Detlef

2008-11-01

A bubble can be entrained in the ink channel of a piezo-driven inkjet printhead, where it grows by rectified diffusion. If large enough, the bubble counteracts the pressure buildup at the nozzle, resulting in nozzle failure. Here an acoustic sizing method for the volume and position of the bubble is presented. The bubble response is detected by the piezo actuator itself, operating in a sensor mode. The method used to determine the volume and position of the bubble is based on a linear model in which the interaction between the bubble and the channel are included. This model predicts the acoustic signal for a given position and volume of the bubble. The inverse problem is to infer the position and volume of the bubble from the measured acoustic signal. By solving it, we can thus acoustically measure size and position of the bubble. The validity of the presented method is supported by time-resolved optical observations of the dynamics of the bubble within an optically accessible ink-jet channel.

Interpreting the sub-linear Kennicutt-Schmidt relationship: the case for diffuse molecular gas

NASA Astrophysics Data System (ADS)

Shetty, Rahul; Clark, Paul C.; Klessen, Ralf S.

2014-08-01

Recent statistical analysis of two extragalactic observational surveys strongly indicate a sub-linear Kennicutt-Schmidt (KS) relationship between the star formation rate (ΣSFR) and molecular gas surface density (Σmol). Here, we consider the consequences of these results in the context of common assumptions, as well as observational support for a linear relationship between ΣSFR and the surface density of dense gas. If the CO traced gas depletion time (τ_dep^CO) is constant, and if CO only traces star-forming giant molecular clouds (GMCs), then the physical properties of each GMC must vary, such as the volume densities or star formation rates. Another possibility is that the conversion between CO luminosity and Σmol, the XCO factor, differs from cloud-to-cloud. A more straightforward explanation is that CO permeates the hierarchical interstellar medium, including the filaments and lower density regions within which GMCs are embedded. A number of independent observational results support this description, with the diffuse gas comprising at least 30 per cent of the total molecular content. The CO bright diffuse gas can explain the sub-linear KS relationship, and consequently leads to an increasing τ_dep^CO with Σmol. If ΣSFR linearly correlates with the dense gas surface density, a sub-linear KS relationship indicates that the fraction of diffuse gas fdiff grows with Σmol. In galaxies where Σmol falls towards the outer disc, this description suggests that fdiff also decreases radially.

Effects of Diffusion Time on Short-Range Hyperpolarized 3He Diffusivity Measurements in Emphysema

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

Gierada, David S.; Woods, Jason C.; Bierhals, Andrew J.

2009-09-28

Purpose: To characterize the effect of diffusion time on short-range hyperpolarized 3He MR diffusion measurements across a wide range of emphysema severity. Materials and Methods: 3He diffusion MR imaging was performed on 19 lungs or lobes resected from 18 subjects with varying degrees of emphysema using 3 diffusion times (1.6 msec, 5 msec, and 10 msec) at constant b value. Emphysema severity was quantified as the mean apparent diffusion coefficient (ADC) and as the percentage of pixels with ADC higher than multiple thresholds from 0.30-0.55 cm2/sec (ADC index). Quantitative histology (mean linear intercept) was obtained in 10 of the lungmore » specimens from 10 of the subjects. Results: The mean ADCs with diffusion times of 1.6, 5.0, and 10.0 msec were 0.46, 0.40, and 0.37 cm2/sec, respectively (P <0.0001, ANOVA). There was no relationship between the ADC magnitude and the effect of diffusion time on ADC values. Mean linear intercept correlated with ADC (r=0.91-0.94, P<0.001) and ADC index (r=0.78-0.92, P<0.01) at all diffusion times.« less

Quantum State Diffusion

NASA Astrophysics Data System (ADS)

Percival, Ian

2005-10-01

1. Introduction; 2. Brownian motion and Itô calculus; 3. Open quantum systems; 4. Quantum state diffusion; 5. Localisation; 6. Numerical methods and examples; 7. Quantum foundations; 8. Primary state diffusion; 9. Classical dynamics of quantum localisation; 10. Semiclassical theory and linear dynamics.

Axial diffusivity of the corona radiata correlated with ventricular size in adult hydrocephalus.

PubMed

Cauley, Keith A; Cataltepe, Oguz

2014-07-01

Hydrocephalus causes changes in the diffusion-tensor properties of periventricular white matter. Understanding the nature of these changes may aid in the diagnosis and treatment planning of this relatively common neurologic condition. Because ventricular size is a common measure of the severity of hydrocephalus, we hypothesized that a quantitative correlation could be made between the ventricular size and diffusion-tensor changes in the periventricular corona radiata. In this article, we investigated this relationship in adult patients with hydrocephalus and in healthy adult subjects. Diffusion-tensor imaging metrics of the corona radiata were correlated with ventricular size in 14 adult patients with acute hydrocephalus, 16 patients with long-standing hydrocephalus, and 48 consecutive healthy adult subjects. Regression analysis was performed to investigate the relationship between ventricular size and the diffusion-tensor metrics of the corona radiata. Subject age was analyzed as a covariable. There is a linear correlation between fractional anisotropy of the corona radiata and ventricular size in acute hydrocephalus (r = 0.784, p < 0.001), with positive correlation with axial diffusivity (r = 0.636, p = 0.014) and negative correlation with radial diffusivity (r = 0.668, p = 0.009). In healthy subjects, axial diffusion in the periventricular corona radiata is more strongly correlated with ventricular size than with patient age (r = 0.466, p < 0.001, compared with r = 0.058, p = 0.269). Axial diffusivity of the corona radiata is linearly correlated with ventricular size in healthy adults and in patients with hydrocephalus. Radial diffusivity of the corona radiata decreases linearly with ventricular size in acute hydrocephalus but is not significantly correlated with ventricular size in healthy subjects or in patients with long-standing hydrocephalus.

Effects of convergent diffusion and charge transfer kinetics on the diffusion layer thickness of spherical micro- and nanoelectrodes.

PubMed

Molina, A; Laborda, E; González, J; Compton, R G

2013-05-21

Nuances of the linear diffusion layer approximation are examined for slow charge transfer reactions at (hemi)spherical micro- and nanoelectrodes. This approximation is widely employed in Electrochemistry to evaluate the extent of electrolyte solution perturbed by the electrode process, which is essential to the understanding of the effects arising from thin-layer diffusion, convergent diffusion, convection, coupled chemical reactions and the double layer. The concept was well established for fast charge transfer processes at macroelectrodes, but remains unclear under other conditions such that a thorough assessment of its meaning was necessary. In a previous publication [A. Molina, J. González, E. Laborda and R. G. Compton, Phys. Chem. Chem. Phys., 2013, 15, 2381-2388] we shed some light on the influence of the reversibility degree. In the present work, the meaning of the diffusion layer thickness is investigated when very small electrodes are employed and so the contribution of convergent diffusion to the mass transport is very important. An analytical expression is given to calculate the linear diffusion layer thickness at (hemi)spherical electrodes and its behaviour is studied for a wide range of conditions of reversibility (from reversible to fully-irreversible processes) and electrode size (from macro- to nano-electrodes). Rigorous analytical solutions are deduced for true concentration profiles, surface concentrations, linear diffusion layer thickness and current densities when a potential pulse is applied at (hemi)spherical electrodes. The expressions for the magnitudes mentioned above are valid for electrodes of any size (including (hemi)spherical nanoelectrodes) and for any degree of reversibility, provided that mass transport occurs exclusively via diffusion. The variation of the above with the electrode size, applied potential and charge transfer kinetics is studied.

Validation of drift and diffusion coefficients from experimental data

NASA Astrophysics Data System (ADS)

Riera, R.; Anteneodo, C.

2010-04-01

Many fluctuation phenomena, in physics and other fields, can be modeled by Fokker-Planck or stochastic differential equations whose coefficients, associated with drift and diffusion components, may be estimated directly from the observed time series. Its correct characterization is crucial to determine the system quantifiers. However, due to the finite sampling rates of real data, the empirical estimates may significantly differ from their true functional forms. In the literature, low-order corrections, or even no corrections, have been applied to the finite-time estimates. A frequent outcome consists of linear drift and quadratic diffusion coefficients. For this case, exact corrections have been recently found, from Itô-Taylor expansions. Nevertheless, model validation constitutes a necessary step before determining and applying the appropriate corrections. Here, we exploit the consequences of the exact theoretical results obtained for the linear-quadratic model. In particular, we discuss whether the observed finite-time estimates are actually a manifestation of that model. The relevance of this analysis is put into evidence by its application to two contrasting real data examples in which finite-time linear drift and quadratic diffusion coefficients are observed. In one case the linear-quadratic model is readily rejected while in the other, although the model constitutes a very good approximation, low-order corrections are inappropriate. These examples give warning signs about the proper interpretation of finite-time analysis even in more general diffusion processes.

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.

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

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

D'Elia, M.; Edwards, H. C.; Hu, J.

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble whenmore » applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.« less

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

DOE PAGES

D'Elia, M.; Edwards, H. C.; Hu, J.; ...

2018-01-18

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble whenmore » applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.« less

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.

Slaved diffusion in phospholipid bilayers

PubMed Central

Zhang, Liangfang; Granick, Steve

2005-01-01

The translational diffusion of phospholipids in supported fluid bilayers splits into two populations when polyelectrolytes adsorb at incomplete surface coverage. Spatially resolved measurements using fluorescence correlation spectroscopy show that a slow mode, whose magnitude scales inversely with the degree of polymerization of the adsorbate, coexists with a fast mode characteristic of naked lipid diffusion. Inner and outer leaflets of the bilayer are affected nearly equally. Mobility may vary from spot to spot on the membrane surface, despite the lipid composition being the same. This work offers a mechanism to explain how nanosized domains with reduced mobility arise in lipid membranes. PMID:15967988

A Monte Carlo approach to the inverse problem of diffuse pollution risk in agricultural catchments

NASA Astrophysics Data System (ADS)

Milledge, D.; Lane, S. N.; Heathwaite, A. L.; Reaney, S.

2012-04-01

The hydrological and biogeochemical processes that operate in catchments influence the ecological quality of freshwater systems through delivery of fine sediment, nutrients and organic matter. As an alternative to the, often complex, reductionist models we outline a - data-driven - approach based on 'inverse modelling'. We invert SCIMAP, a parsimonious risk based model that has an explicit treatment of hydrological connectivity, and use a Bayesian approach to determine the risk that must be assigned to different land uses in a catchment in order to explain the spatial patterns of measured in-stream nutrient concentrations. First, we apply the model to a set of eleven UK catchments to show that: 1) some land use generates a consistently high or low risk of diffuse nitrate (N) and Phosphate (P) pollution; but 2) the risks associated with different land uses vary both between catchments and between P and N delivery; and 3) that the dominant sources of P and N risk in the catchment are often a function of the spatial configuration of land uses. These results suggest that on a case by case basis, inverse modelling may be used to help prioritise the focus of interventions to reduce diffuse pollution risk for freshwater ecosystems. However, a key uncertainty in this approach is the extent to which it can recover the 'true' risks associated with a land cover given error in both the input parameters and equifinality in model outcomes. We test this using a set of synthetic scenarios in which the true risks can be pre-assigned then compared with those recovered from the inverse model. We use these scenarios to identify the number of simulations and observations required to optimize recovery of the true weights, then explore the conditions under which the inverse model becomes equifinal (hampering recovery of the true weights) We find that this is strongly dependent on the covariance in land covers between subcatchments, introducing the possibility that instream sampling could be designed or subsampled to maximize identifiability of the risks associated with a given land cover.

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

Detection of Natural Fractures from Observed Surface Seismic Data Based on a Linear-Slip Model

NASA Astrophysics Data System (ADS)

Chen, Huaizhen; Zhang, Guangzhi

2018-03-01

Natural fractures play an important role in migration of hydrocarbon fluids. Based on a rock physics effective model, the linear-slip model, which defines fracture parameters (fracture compliances) for quantitatively characterizing the effects of fractures on rock total compliance, we propose a method to detect natural fractures from observed seismic data via inversion for the fracture compliances. We first derive an approximate PP-wave reflection coefficient in terms of fracture compliances. Using the approximate reflection coefficient, we derive azimuthal elastic impedance as a function of fracture compliances. An inversion method to estimate fracture compliances from seismic data is presented based on a Bayesian framework and azimuthal elastic impedance, which is implemented in a two-step procedure: a least-squares inversion for azimuthal elastic impedance and an iterative inversion for fracture compliances. We apply the inversion method to synthetic and real data to verify its stability and reasonability. Synthetic tests confirm that the method can make a stable estimation of fracture compliances in the case of seismic data containing a moderate signal-to-noise ratio for Gaussian noise, and the test on real data reveals that reasonable fracture compliances are obtained using the proposed method.

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.

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.

Bayesian inference of radiation belt loss timescales.

NASA Astrophysics Data System (ADS)

Camporeale, E.; Chandorkar, M.

2017-12-01

Electron fluxes in the Earth's radiation belts are routinely studied using the classical quasi-linear radial diffusion model. Although this simplified linear equation has proven to be an indispensable tool in understanding the dynamics of the radiation belt, it requires specification of quantities such as the diffusion coefficient and electron loss timescales that are never directly measured. Researchers have so far assumed a-priori parameterisations for radiation belt quantities and derived the best fit using satellite data. The state of the art in this domain lacks a coherent formulation of this problem in a probabilistic framework. We present some recent progress that we have made in performing Bayesian inference of radial diffusion parameters. We achieve this by making extensive use of the theory connecting Gaussian Processes and linear partial differential equations, and performing Markov Chain Monte Carlo sampling of radial diffusion parameters. These results are important for understanding the role and the propagation of uncertainties in radiation belt simulations and, eventually, for providing a probabilistic forecast of energetic electron fluxes in a Space Weather context.

THERMOHALINE INSTABILITIES INSIDE STARS: A SYNTHETIC STUDY INCLUDING EXTERNAL TURBULENCE AND RADIATIVE LEVITATION

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

Vauclair, Sylvie; Theado, Sylvie, E-mail: sylvie.vauclair@irap.omp.eu

2012-07-01

We have derived a new expression for the thermohaline mixing coefficient in stars, including the effects of radiative levitation and external turbulence, by solving Boussinesq equations in a nearly incompressible stratified fluid with a linear approximation. It is well known that radiative levitation of individual elements can lead to their accumulation in specific stellar layers. In some cases, it can induce important effects on the stellar structure. Here we confirm that this accumulation is moderated by thermohaline convection due to the resulting inverse {mu}-gradient. The new coefficient that we have derived shows that the effect of radiative accelerations on themore » thermohaline instability itself is small. This effect must however be checked in all computations. We also confirm that the presence of large horizontal turbulence can reduce or even suppress the thermohaline convection. These results are important as they concern all the cases of heavy element accumulation in stars. Computations of radiative diffusion must be revisited to include thermohaline convection and its consequences. It may be one of the basic reasons for the fact that the observed abundances are always smaller than those predicted by pure atomic diffusion. In any case, these processes have to compete with rotation-induced mixing, but this competition is more complex than previously thought due to their mutual interaction.« less

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 Geophysical Inversion Model Enhancement Technique Based on the Blind Deconvolution

NASA Astrophysics Data System (ADS)

Zuo, B.; Hu, X.; Li, H.

2011-12-01

A model-enhancement technique is proposed to enhance the geophysical inversion model edges and details without introducing any additional information. Firstly, the theoretic correctness of the proposed geophysical inversion model-enhancement technique is discussed. An inversion MRM (model resolution matrix) convolution approximating PSF (Point Spread Function) method is designed to demonstrate the correctness of the deconvolution model enhancement method. Then, a total-variation regularization blind deconvolution geophysical inversion model-enhancement algorithm is proposed. In previous research, Oldenburg et al. demonstrate the connection between the PSF and the geophysical inverse solution. Alumbaugh et al. propose that more information could be provided by the PSF if we return to the idea of it behaving as an averaging or low pass filter. We consider the PSF as a low pass filter to enhance the inversion model basis on the theory of the PSF convolution approximation. Both the 1D linear and the 2D magnetotelluric inversion examples are used to analyze the validity of the theory and the algorithm. To prove the proposed PSF convolution approximation theory, the 1D linear inversion problem is considered. It shows the ratio of convolution approximation error is only 0.15%. The 2D synthetic model enhancement experiment is presented. After the deconvolution enhancement, the edges of the conductive prism and the resistive host become sharper, and the enhancement result is closer to the actual model than the original inversion model according the numerical statistic analysis. Moreover, the artifacts in the inversion model are suppressed. The overall precision of model increases 75%. All of the experiments show that the structure details and the numerical precision of inversion model are significantly improved, especially in the anomalous region. The correlation coefficient between the enhanced inversion model and the actual model are shown in Fig. 1. The figure illustrates that more information and details structure of the actual model are enhanced through the proposed enhancement algorithm. Using the proposed enhancement method can help us gain a clearer insight into the results of the inversions and help make better informed decisions.

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.

Effect of temperature and grain size on the dominant diffusion process for superplastic flow in an AZ61 magnesium alloy

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

Watanabe, H.; Mukai, T.; Kohzu, M.

1999-10-26

The effect of temperature and grain size on superplastic flow was investigated using a relatively coarse-grained ({approximately}20 {micro}m) Mg-Al-Zn alloy for the inclusive understanding of the dominant diffusion process. Tensile tests revealed that the strain rate was inversely proportional to the square of the grain size and to the second power of stress. The activation energy was close to that for grain boundary diffusion at 523--573 K, and was close to that for lattice diffusion at 598--673 K. From the analysis of the stress exponent, the grain size exponent and activation energy, it was suggested that the dominant diffusion processmore » was influenced by temperature and grain size. It was demonstrated that the notion of effective diffusivity explained the experimental results.« less

Relativistic analysis of stochastic kinematics

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ (w ) =(1-w2/c2) -1 /2 . Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ (w ) . The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.

Comparison of various methods for mathematical analysis of the Foucault knife edge test pattern to determine optical imperfections

NASA Technical Reports Server (NTRS)

Gatewood, B. E.

1971-01-01

The linearized integral equation for the Foucault test of a solid mirror was solved by various methods: power series, Fourier series, collocation, iteration, and inversion integral. The case of the Cassegrain mirror was solved by a particular power series method, collocation, and inversion integral. The inversion integral method appears to be the best overall method for both the solid and Cassegrain mirrors. Certain particular types of power series and Fourier series are satisfactory for the Cassegrain mirror. Numerical integration of the nonlinear equation for selected surface imperfections showed that results start to deviate from those given by the linearized equation at a surface deviation of about 3 percent of the wavelength of light. Several possible procedures for calibrating and scaling the input data for the integral equation are described.

Blocky inversion of multichannel elastic impedance for elastic parameters

NASA Astrophysics Data System (ADS)

Mozayan, Davoud Karami; Gholami, Ali; Siahkoohi, Hamid Reza

2018-04-01

Petrophysical description of reservoirs requires proper knowledge of elastic parameters like P- and S-wave velocities (Vp and Vs) and density (ρ), which can be retrieved from pre-stack seismic data using the concept of elastic impedance (EI). We propose an inversion algorithm which recovers elastic parameters from pre-stack seismic data in two sequential steps. In the first step, using the multichannel blind seismic inversion method (exploited recently for recovering acoustic impedance from post-stack seismic data), high-resolution blocky EI models are obtained directly from partial angle-stacks. Using an efficient total-variation (TV) regularization, each angle-stack is inverted independently in a multichannel form without prior knowledge of the corresponding wavelet. The second step involves inversion of the resulting EI models for elastic parameters. Mathematically, under some assumptions, the EI's are linearly described by the elastic parameters in the logarithm domain. Thus a linear weighted least squares inversion is employed to perform this step. Accuracy of the concept of elastic impedance in predicting reflection coefficients at low and high angles of incidence is compared with that of exact Zoeppritz elastic impedance and the role of low frequency content in the problem is discussed. The performance of the proposed inversion method is tested using synthetic 2D data sets obtained from the Marmousi model and also 2D field data sets. The results confirm the efficiency and accuracy of the proposed method for inversion of pre-stack seismic data.

Comments on the Diffusive Behavior of Two Upwind Schemes

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

Diffusion Characteristics of Upwind Schemes on Unstructured Triangulations

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and dimensionally-split finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the dimensionally-split finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2-3 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a 20-25 speedup over finite volume.

Antifungal susceptibility testing of Malassezia yeast: comparison of two different methodologies.

PubMed

Rojas, Florencia D; Córdoba, Susana B; de Los Ángeles Sosa, María; Zalazar, Laura C; Fernández, Mariana S; Cattana, María E; Alegre, Liliana R; Carrillo-Muñoz, Alfonso J; Giusiano, Gustavo E

2017-02-01

All Malassezia species are lipophilic; thus, modifications are required in susceptibility testing methods to ensure their growth. Antifungal susceptibility of Malassezia species using agar and broth dilution methods has been studied. Currently, few tests using disc diffusion methods are being performed. The aim was to evaluate the in vitro susceptibility of Malassezia yeast against antifungal agents using broth microdilution and disc diffusion methods, then to compare both methodologies. Fifty Malassezia isolates were studied. Microdilution method was performed as described in reference document and agar diffusion test was performed using antifungal tablets and discs. To support growth, culture media were supplemented. To correlate methods, linear regression analysis and categorical agreement was determined. The strongest linear association was observed for fluconazole and miconazole. The highest agreement between both methods was observed for itraconazole and voriconazole and the lowest for amphotericin B and fluconazole. Although modifications made to disc diffusion method allowed to obtain susceptibility data for Malassezia yeast, variables cannot be associated through a linear correlation model, indicating that inhibition zone values cannot predict MIC value. According to the results, disc diffusion assay may not represent an alternative to determine antifungal susceptibility of Malassezia yeast. © 2016 Blackwell Verlag GmbH.

Exact Solutions of Linear Reaction-Diffusion Processes on a Uniformly Growing Domain: Criteria for Successful Colonization

PubMed Central

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

PubMed

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0

[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.

Nanoprobe diffusion in entangled polymer solutions: Linear vs. unconcatenated ring chains

NASA Astrophysics Data System (ADS)

Nahali, Negar; Rosa, Angelo

2018-05-01

We employ large-scale molecular dynamics computer simulations to study the problem of nanoprobe diffusion in entangled solutions of linear polymers and unknotted and unconcatenated circular (ring) polymers. By tuning both the diameter of the nanoprobe and the density of the solution, we show that nanoprobes of diameter smaller than the entanglement distance (tube diameter) of the solution display the same (Rouse-like) behavior in solutions of both polymer architectures. Instead, nanoprobes with larger diameters appear to diffuse markedly faster in solutions of rings than in solutions of linear chains. Finally, by analysing the distribution functions of spatial displacements, we find that nanoprobe motion in rings' solutions shows both Gaussian and ergodic behaviors, in all regimes considered, while, in solutions of linear chains, nanoprobes exceeding the size of the tube diameter show a transition to non-Gaussian and non-ergodic motion. Our results emphasize the role of chain architecture in the motion of nanoprobes dispersed in polymer solutions.

Size effects in non-linear heat conduction with flux-limited behaviors

NASA Astrophysics Data System (ADS)

Li, Shu-Nan; Cao, Bing-Yang

2017-11-01

Size effects are discussed for several non-linear heat conduction models with flux-limited behaviors, including the phonon hydrodynamic, Lagrange multiplier, hierarchy moment, nonlinear phonon hydrodynamic, tempered diffusion, thermon gas and generalized nonlinear models. For the phonon hydrodynamic, Lagrange multiplier and tempered diffusion models, heat flux will not exist in problems with sufficiently small scale. The existence of heat flux needs the sizes of heat conduction larger than their corresponding critical sizes, which are determined by the physical properties and boundary temperatures. The critical sizes can be regarded as the theoretical limits of the applicable ranges for these non-linear heat conduction models with flux-limited behaviors. For sufficiently small scale heat conduction, the phonon hydrodynamic and Lagrange multiplier models can also predict the theoretical possibility of violating the second law and multiplicity. Comparisons are also made between these non-Fourier models and non-linear Fourier heat conduction in the type of fast diffusion, which can also predict flux-limited behaviors.

Female Literacy Rate is a Better Predictor of Birth Rate and Infant Mortality Rate in India

PubMed Central

Saurabh, Suman; Sarkar, Sonali; Pandey, Dhruv K.

2013-01-01

Background: 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. Materials and Methods: 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. Results: 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). Conclusion: Female literacy is relatively highly important for both population stabilization and better infant health. PMID:26664840

Studying the Transient Thermal Contact Conductance Between the Exhaust Valve and Its Seat Using the Inverse Method

NASA Astrophysics Data System (ADS)

Nezhad, Mohsen Motahari; Shojaeefard, Mohammad Hassan; Shahraki, Saeid

2016-02-01

In this study, the experiments aimed at analyzing thermally the exhaust valve in an air-cooled internal combustion engine and estimating the thermal contact conductance in fixed and periodic contacts. Due to the nature of internal combustion engines, the duration of contact between the valve and its seat is too short, and much time is needed to reach the quasi-steady state in the periodic contact between the exhaust valve and its seat. Using the methods of linear extrapolation and the inverse solution, the surface contact temperatures and the fixed and periodic thermal contact conductance were calculated. The results of linear extrapolation and inverse methods have similar trends, and based on the error analysis, they are accurate enough to estimate the thermal contact conductance. Moreover, due to the error analysis, a linear extrapolation method using inverse ratio is preferred. The effects of pressure, contact frequency, heat flux, and cooling air speed on thermal contact conductance have been investigated. The results show that by increasing the contact pressure the thermal contact conductance increases substantially. In addition, by increasing the engine speed the thermal contact conductance decreases. On the other hand, by boosting the air speed the thermal contact conductance increases, and by raising the heat flux the thermal contact conductance reduces. The average calculated error equals to 12.9 %.

Communication: Relationship between solute localization and diffusion in a dynamically constrained polymer system

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

Saylor, David M.; Jawahery, Sudi; Silverstein, Joshua S.

2016-07-21

We investigate the link between dynamic localization, characterized by the Debye–Waller factor, 〈u{sup 2}〉, and solute self-diffusivity, D, in a polymer system using atomistic molecular dynamics simulations and vapor sorption experiments. We find a linear relationship between lnD and 1/〈u{sup 2}〉 over more than four decades of D, encompassing most of the glass formation regime. The observed linearity is consistent with the Langevin dynamics in a periodically varying potential field and may offer a means to rapidly assess diffusion based on the characterization of dynamic localization.

Improvement of gray-scale representation of horizontally scanning holographic display using error diffusion.

PubMed

Matsumoto, Yuji; Takaki, Yasuhiro

2014-06-15

Horizontally scanning holography can enlarge both screen size and viewing zone angle. A microelectromechanical-system spatial light modulator, which can generate only binary images, is used to generate hologram patterns. Thus, techniques to improve gray-scale representation in reconstructed images should be developed. In this study, the error diffusion technique was used for the binarization of holograms. When the Floyd-Steinberg error diffusion coefficients were used, gray-scale representation was improved. However, the linearity in the gray-scale representation was not satisfactory. We proposed the use of a correction table and showed that the linearity was greatly improved.

An induced junction photovoltaic cell

NASA Technical Reports Server (NTRS)

Call, R. L.

1974-01-01

Silicon solar cells operating with induced junctions rather than diffused junctions have been fabricated and tested. Induced junctions were created by forming an inversion layer near the surface of the silicon by supplying a sheet of positive charge above the surface. Measurements of the response of the inversion layer cell to light of different wavelengths indicated it to be more sensitive to the shorter wavelengths of the sun's spectrum than conventional cells. The greater sensitivity occurs because of the shallow junction and the strong electric field at the surface.

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.

A Higher Order Iterative Method for Computing the Drazin Inverse

PubMed Central

Soleymani, F.; Stanimirović, Predrag S.

2013-01-01

A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper. PMID:24222747

A study on characterization of stratospheric aerosol and gas parameters with the spacecraft solar occultation experiment

NASA Technical Reports Server (NTRS)

Chu, W. P.

1977-01-01

Spacecraft remote sensing of stratospheric aerosol and ozone vertical profiles using the solar occultation experiment has been analyzed. A computer algorithm has been developed in which a two step inversion of the simulated data can be performed. The radiometric data are first inverted into a vertical extinction profile using a linear inversion algorithm. Then the multiwavelength extinction profiles are solved with a nonlinear least square algorithm to produce aerosol and ozone vertical profiles. Examples of inversion results are shown illustrating the resolution and noise sensitivity of the inversion algorithms.

Nature of electron trap states under inversion at In0.53Ga0.47As/Al2O3 interfaces

NASA Astrophysics Data System (ADS)

Colleoni, Davide; Pourtois, Geoffrey; Pasquarello, Alfredo

2017-03-01

In and Ga impurities substitutional to Al in the oxide layer resulting from diffusion out of the substrate are identified as candidates for electron traps under inversion at In0.53Ga0.47As/Al2O3 interfaces. Through density-functional calculations, these defects are found to be thermodynamically stable in amorphous Al2O3 and to be able to capture two electrons in a dangling bond upon breaking bonds with neighboring O atoms. Through a band alignment based on hybrid functional calculations, it is inferred that the corresponding defect levels lie at ˜1 eV above the conduction band minimum of In0.53Ga0.47As, in agreement with measured defect densities. These results support the technological importance of avoiding cation diffusion into the oxide layer.

Approximate Seismic Diffusive Models of Near-Receiver Geology: Applications from Lab Scale to Field

NASA Astrophysics Data System (ADS)

King, Thomas; Benson, Philip; De Siena, Luca; Vinciguerra, Sergio

2017-04-01

This paper presents a novel and simple method of seismic envelope analysis that can be applied at multiple scales, e.g. field, m to km scale and laboratory, mm to cm scale, and utilises the diffusive approximation of the seismic wavefield (Wegler, 2003). Coefficient values for diffusion and attenuation are obtained from seismic coda energies and are used to describe the rate at which seismic energy is scattered and attenuated into the local medium around a receiver. Values are acquired by performing a linear least squares inversion of coda energies calculated in successive time windows along a seismic trace. Acoustic emission data were taken from piezoelectric transducers (PZT) with typical resonance frequency of 1-5MHz glued around rock samples during deformation laboratory experiments carried out using a servo-controlled triaxial testing machine, where a shear/damage zone is generated under compression after the nucleation, growth and coalescence of microcracks. Passive field data were collected from conventional geophones during the 2004-2008 eruption of Mount St. Helens volcano (MSH), USA where a sudden reawakening of the volcanic activity and a new dome growth has occurred. The laboratory study shows a strong correlation between variations of the coefficients over time and the increase of differential stress as the experiment progresses. The field study links structural variations present in the near-surface geology, including those seen in previous geophysical studies of the area, to these same coefficients. Both studies show a correlation between frequency and structural feature size, i.e. landslide slip-planes and microcracks, with higher frequencies being much more sensitive to smaller scale features and vice-versa.

Discovery of the linear region of Near Infrared Diffuse Reflectance spectra using the Kubelka-Munk theory

NASA Astrophysics Data System (ADS)

Dai, Shengyun; Pan, Xiaoning; Ma, Lijuan; Huang, Xingguo; Du, Chenzhao; Qiao, Yanjiang; Wu, Zhisheng

2018-05-01

Particle size is of great importance for the quantitative model of the NIR diffuse reflectance. In this paper, the effect of sample particle size on the measurement of harpagoside in Radix Scrophulariae powder by near infrared diffuse (NIR) reflectance spectroscopy was explored. High-performance liquid chromatography (HPLC) was employed as a reference method to construct the quantitative particle size model. Several spectral preprocessing methods were compared, and particle size models obtained by different preprocessing methods for establishing the partial least-squares (PLS) models of harpagoside. Data showed that the particle size distribution of 125-150 μm for Radix Scrophulariae exhibited the best prediction ability with R2pre=0.9513, RMSEP=0.1029 mg·g-1, and RPD = 4.78. For the hybrid granularity calibration model, the particle size distribution of 90-180 μm exhibited the best prediction ability with R2pre=0.8919, RMSEP=0.1632 mg·g-1, and RPD = 3.09. Furthermore, the Kubelka-Munk theory was used to relate the absorption coefficient k (concentration-dependent) and scatter coefficient s (particle size-dependent). The scatter coefficient s was calculated based on the Kubelka-Munk theory to study the changes of s after being mathematically preprocessed. A linear relationship was observed between k/s and absorption A within a certain range and the value for k/s was greater than 4. According to this relationship, the model was more accurately constructed with the particle size distribution of 90-180 μm when s was kept constant or in a small linear region. This region provided a good reference for the linear modeling of diffuse reflectance spectroscopy. To establish a diffuse reflectance NIR model, further accurate assessment should be obtained in advance for a precise linear model.

Product diffusion through on-demand information-seeking behaviour.

PubMed

Riedl, Christoph; Bjelland, Johannes; Canright, Geoffrey; Iqbal, Asif; Engø-Monsen, Kenth; Qureshi, Taimur; Sundsøy, Pål Roe; Lazer, David

2018-02-01

Most models of product adoption predict S-shaped adoption curves. Here we report results from two country-scale experiments in which we find linear adoption curves. We show evidence that the observed linear pattern is the result of active information-seeking behaviour: individuals actively pulling information from several central sources facilitated by modern Internet searches. Thus, a constant baseline rate of interest sustains product diffusion, resulting in a linear diffusion process instead of the S-shaped curve of adoption predicted by many diffusion models. The main experiment seeded 70 000 (48 000 in Experiment 2) unique voucher codes for the same product with randomly sampled nodes in a social network of approximately 43 million individuals with about 567 million ties. We find that the experiment reached over 800 000 individuals with 80% of adopters adopting the same product-a winner-take-all dynamic consistent with search engine driven rankings that would not have emerged had the products spread only through a network of social contacts. We provide evidence for (and characterization of) this diffusion process driven by active information-seeking behaviour through analyses investigating (a) patterns of geographical spreading; (b) the branching process; and (c) diffusion heterogeneity. Using data on adopters' geolocation we show that social spreading is highly localized, while on-demand diffusion is geographically independent. We also show that cascades started by individuals who actively pull information from central sources are more effective at spreading the product among their peers. © 2018 The Authors.

Product diffusion through on-demand information-seeking behaviour

PubMed Central

Bjelland, Johannes; Canright, Geoffrey; Iqbal, Asif; Qureshi, Taimur; Sundsøy, Pål Roe

2018-01-01

Most models of product adoption predict S-shaped adoption curves. Here we report results from two country-scale experiments in which we find linear adoption curves. We show evidence that the observed linear pattern is the result of active information-seeking behaviour: individuals actively pulling information from several central sources facilitated by modern Internet searches. Thus, a constant baseline rate of interest sustains product diffusion, resulting in a linear diffusion process instead of the S-shaped curve of adoption predicted by many diffusion models. The main experiment seeded 70 000 (48 000 in Experiment 2) unique voucher codes for the same product with randomly sampled nodes in a social network of approximately 43 million individuals with about 567 million ties. We find that the experiment reached over 800 000 individuals with 80% of adopters adopting the same product—a winner-take-all dynamic consistent with search engine driven rankings that would not have emerged had the products spread only through a network of social contacts. We provide evidence for (and characterization of) this diffusion process driven by active information-seeking behaviour through analyses investigating (a) patterns of geographical spreading; (b) the branching process; and (c) diffusion heterogeneity. Using data on adopters' geolocation we show that social spreading is highly localized, while on-demand diffusion is geographically independent. We also show that cascades started by individuals who actively pull information from central sources are more effective at spreading the product among their peers. PMID:29467257

Influence of diffuse reflectance measurement accuracy on the scattering coefficient in determination of optical properties with integrating sphere optics (a secondary publication).

PubMed

Horibe, Takuro; Ishii, Katsunori; Fukutomi, Daichi; Awazu, Kunio

2015-12-30

An estimation error of the scattering coefficient of hemoglobin in the high absorption wavelength range has been observed in optical property calculations of blood-rich tissues. In this study, the relationship between the accuracy of diffuse reflectance measurement in the integrating sphere and calculated scattering coefficient was evaluated with a system to calculate optical properties combined with an integrating sphere setup and the inverse Monte Carlo simulation. Diffuse reflectance was measured with the integrating sphere using a small incident port diameter and optical properties were calculated. As a result, the estimation error of the scattering coefficient was improved by accurate measurement of diffuse reflectance. In the high absorption wavelength range, the accuracy of diffuse reflectance measurement has an effect on the calculated scattering coefficient.

Optimal Network Modularity for Information Diffusion

NASA Astrophysics Data System (ADS)

Nematzadeh, Azadeh; Ferrara, Emilio; Flammini, Alessandro; Ahn, Yong-Yeol

2014-08-01

We investigate the impact of community structure on information diffusion with the linear threshold model. Our results demonstrate that modular structure may have counterintuitive effects on information diffusion when social reinforcement is present. We show that strong communities can facilitate global diffusion by enhancing local, intracommunity spreading. Using both analytic approaches and numerical simulations, we demonstrate the existence of an optimal network modularity, where global diffusion requires the minimal number of early adopters.

Least squares reconstruction of non-linear RF phase encoded MR data.

PubMed

Salajeghe, Somaie; Babyn, Paul; Sharp, Jonathan C; Sarty, Gordon E

2016-09-01

The numerical feasibility of reconstructing MRI signals generated by RF coils that produce B1 fields with a non-linearly varying spatial phase is explored. A global linear spatial phase variation of B1 is difficult to produce from current confined to RF coils. Here we use regularized least squares inversion, in place of the usual Fourier transform, to reconstruct signals generated in B1 fields with non-linear phase variation. RF encoded signals were simulated for three RF coil configurations: ideal linear, parallel conductors and, circular coil pairs. The simulated signals were reconstructed by Fourier transform and by regularized least squares. The Fourier reconstruction of simulated RF encoded signals from the parallel conductor coil set showed minor distortions over the reconstruction of signals from the ideal linear coil set but the Fourier reconstruction of signals from the circular coil set produced severe geometric distortion. Least squares inversion in all cases produced reconstruction errors comparable to the Fourier reconstruction of the simulated signal from the ideal linear coil set. MRI signals encoded in B1 fields with non-linearly varying spatial phase may be accurately reconstructed using regularized least squares thus pointing the way to the use of simple RF coil designs for RF encoded MRI. Crown Copyright © 2016. Published by Elsevier Inc. All rights reserved.

An inverse finance problem for estimation of the volatility

NASA Astrophysics Data System (ADS)

Neisy, A.; Salmani, K.

2013-01-01

Black-Scholes model, as a base model for pricing in derivatives markets has some deficiencies, such as ignoring market jumps, and considering market volatility as a constant factor. In this article, we introduce a pricing model for European-Options under jump-diffusion underlying asset. Then, using some appropriate numerical methods we try to solve this model with integral term, and terms including derivative. Finally, considering volatility as an unknown parameter, we try to estimate it by using our proposed model. For the purpose of estimating volatility, in this article, we utilize inverse problem, in which inverse problem model is first defined, and then volatility is estimated using minimization function with Tikhonov regularization.

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

Sueyoshi, Eijun, E-mail: EijunSueyoshi@aol.com; Sakamoto, Ichiro; Okimoto, Tomoaki

Amyloidosis is a rare systemic disease. However, involvement of the heart is a common finding and is the most frequent cause of death in amyloidosis. We report the sonographic, scintigraphic, and MRI features of a pathologically proven case of cardiac amyloidosis. Delayed contrast-enhanced MR images, using an inversion recovery prepped gradient-echo sequence, revealed diffuse enhancement in the wall of both left and right ventricles. This enhancement suggested expansion of the extracellular space of the myocardium caused by diffuse myocardial necrosis secondary to deposition of amyloid.

A compendium of controlled diffusion blades generated by an automated inverse design procedure

NASA Technical Reports Server (NTRS)

Sanz, Jose M.

1989-01-01

A set of sample cases was produced to test an automated design procedure developed at the NASA Lewis Research Center for the design of controlled diffusion blades. The range of application of the automated design procedure is documented. The results presented include characteristic compressor and turbine blade sections produced with the automated design code as well as various other airfoils produced with the base design method prior to the incorporation of the automated procedure.

Pipe and grain boundary diffusion of He in UO 2

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

Galvin, C. O.T.; Cooper, M. W. D.; Fossati, P. C. M.

Molecular dynamics simulations have been conducted to study the effects of dislocations and grain boundaries on He diffusion inmore » $$\\text{U}{{\\text{O}}_{2}}$$ . Calculations were carried out for the {100}, {110} and {111} $$\\langle 1\\,1\\,0\\rangle $$ edge dislocations, the screw $$\\langle 1\\,1\\,0\\rangle $$ dislocation and Σ5, Σ13, Σ19 and Σ25 tilt grain boundaries. He diffusivity as a function of distance from the dislocation core and grain boundaries was investigated for the temperature range 2300–3000 K. An enhancement in diffusivity was predicted within 20 Å of the dislocations or grain boundaries. Further investigation showed that He diffusion in the edge dislocations follows anisotropic behaviour along the dislocation core, suggesting that pipe diffusion occurs. Here, an Arrhenius plot of He diffusivity against the inverse of temperature was also presented and the activation energy calculated for each structure, as a function of distance from the dislocation or grain boundary.« less

Pipe and grain boundary diffusion of He in UO 2

DOE PAGES

Galvin, C. O.T.; Cooper, M. W. D.; Fossati, P. C. M.; ...

2016-10-12

Molecular dynamics simulations have been conducted to study the effects of dislocations and grain boundaries on He diffusion inmore » $$\\text{U}{{\\text{O}}_{2}}$$ . Calculations were carried out for the {100}, {110} and {111} $$\\langle 1\\,1\\,0\\rangle $$ edge dislocations, the screw $$\\langle 1\\,1\\,0\\rangle $$ dislocation and Σ5, Σ13, Σ19 and Σ25 tilt grain boundaries. He diffusivity as a function of distance from the dislocation core and grain boundaries was investigated for the temperature range 2300–3000 K. An enhancement in diffusivity was predicted within 20 Å of the dislocations or grain boundaries. Further investigation showed that He diffusion in the edge dislocations follows anisotropic behaviour along the dislocation core, suggesting that pipe diffusion occurs. Here, an Arrhenius plot of He diffusivity against the inverse of temperature was also presented and the activation energy calculated for each structure, as a function of distance from the dislocation or grain boundary.« less

A diffusion-free and linear-energy-transfer-independent nanocomposite Fricke gel dosimeter

NASA Astrophysics Data System (ADS)

Maeyama, T.; Fukunishi, N.; Ishikawa, K. L.; Furuta, T.; Fukasaku, K.; Takagi, S.; Noda, S.; Himeno, R.; Fukuda, S.

2014-03-01

We report a new magnetic-resonance-imaging (MRI) based nanocomposite Fricke gel (NC-FG) dosimeter system, which is free from two main drawbacks of conventional Fricke gel dosimeters, namely, the diffusion of the radiation products and the linear-energy-transfer (LET) dependence of the radiation sensitivity when used for ion beams. The NC-FG dosimeter was prepared by incorporating 1% (w/w) clay nanoparticles into deaerated Fricke gel. We have dosimetrically characterized the NC-FG by using MRI measurements after irradiation with a monoenergetic 290 MeV/nucleon carbon beam. No diffusion of the radiation products was observed during nine days after the irradiation. Moreover, its response faithfully reproduced the depth-dose distribution measured by an ionization chamber, which indicates the absence of the LET dependence. Also, the NC-FG dosimeter exhibited a good linearity up to 800 Gy.

The effects of the Asselin time filter on numerical solutions to the linearized shallow-water wave equations

NASA Technical Reports Server (NTRS)

Schlesinger, R. E.; Johnson, D. R.; Uccellini, L. W.

1983-01-01

In the present investigation, a one-dimensional linearized analysis is used to determine the effect of Asselin's (1972) time filter on both the computational stability and phase error of numerical solutions for the shallow water wave equations, in cases with diffusion but without rotation. An attempt has been made to establish the approximate optimal values of the filtering parameter nu for each of the 'lagged', Dufort-Frankel, and Crank-Nicholson diffusion schemes, suppressing the computational wave mode without materially altering the physical wave mode. It is determined that in the presence of diffusion, the optimum filter length depends on whether waves are undergoing significant propagation. When moderate propagation is present, with or without diffusion, the Asselin filter has little effect on the spatial phase lag of the physical mode for the leapfrog advection scheme of the three diffusion schemes considered.

Levitation effect: Distinguishing anomalous from linear regime of guests sorbed in zeolites through the decay of intermediate scattering function and wavevector dependence of self-diffusivity.

PubMed

Ghorai, Pradip Kr; Yashonath, S

2005-03-10

Previous work investigating the dependence of self-diffusivity, D, on the size of the guest diffusing within the porous solid such as zeolite has reported the existence of an anomalous maximum in the diffusion coefficient (J. Phys. Chem. 1994, 98, 6368). Two distinct regimes of dependence of D on sigma(gg), diameter of the guest were reported. D proportional to 1/sigma(gg)2, often referred to as linear regime (LR), is found when sigma(gg) is smaller than sigma(v), the diameter of the void. A maximum in D has been observed when sigma(gg) is comparable to sigma(v) and this regime is referred to as anomalous regime (AR). Here we report the intermediate scattering function for a particle from LR and AR in zeolite faujasite. A particle from LR exhibits a biexponential decay while a particle from AR exhibits a single-exponential decay at small k. Variation with k of the full width at half-maximum of the self-part of the dynamic structure factor is nonmonotonic for a particle in the linear regime. In contrast, this variation is monotonic for a particle in the anomalous regime. These results can be understood in terms of the existence of energetic barrier at the bottleneck, the 12-ring window, in the path of diffusion. They provide additional signatures for the linear regime and anomalous regimes and therefore for levitation effect (LE).

Preview-Based Stable-Inversion for Output Tracking

NASA Technical Reports Server (NTRS)

Zou, Qing-Ze; Devasia, Santosh

1999-01-01

Stable Inversion techniques can be used to achieve high-accuracy output tracking. However, for nonminimum phase systems, the inverse is non-causal - hence the inverse has to be pre-computed using a pre-specified desired-output trajectory. This requirement for pre-specification of the desired output restricts the use of inversion-based approaches to trajectory planning problems (for nonminimum phase systems). In the present article, it is shown that preview information of the desired output can be used to achieve online inversion-based output tracking of linear systems. The amount of preview-time needed is quantified in terms of the tracking error and the internal dynamics of the system (zeros of the system). The methodology is applied to the online output tracking of a flexible structure and experimental results are presented.

Mapping diffuse photosynthetically active radiation from satellite data in Thailand

NASA Astrophysics Data System (ADS)

Choosri, P.; Janjai, S.; Nunez, M.; Buntoung, S.; Charuchittipan, D.

2017-12-01

In this paper, calculation of monthly average hourly diffuse photosynthetically active radiation (PAR) using satellite data is proposed. Diffuse PAR was analyzed at four stations in Thailand. A radiative transfer model was used for calculating the diffuse PAR for cloudless sky conditions. Differences between the diffuse PAR under all sky conditions obtained from the ground-based measurements and those from the model are representative of cloud effects. Two models are developed, one describing diffuse PAR only as a function of solar zenith angle, and the second one as a multiple linear regression with solar zenith angle and satellite reflectivity acting linearly and aerosol optical depth acting in logarithmic functions. When tested with an independent data set, the multiple regression model performed best with a higher coefficient of variance R2 (0.78 vs. 0.70), lower root mean square difference (RMSD) (12.92% vs. 13.05%) and the same mean bias difference (MBD) of -2.20%. Results from the multiple regression model are used to map diffuse PAR throughout the country as monthly averages of hourly data.

Dispersion effects in the miscible displacement of two fluids in a duct of large aspect ratio

NASA Astrophysics Data System (ADS)

Zhang, J.; Frigaard, I. A.

We study miscible displacements in long ducts in the dispersive limit of small \\varepsilon Pe, where \\varepsilon ≪ 1 is the inverse aspect ratio and Pe the Péclet number. We consider the class of generalized Newtonian fluids, with specified closure laws for the fluid properties of the concentration-dependent mixture. Regardless of viscosity ratio and the constitutive laws of the pure fluids, for sufficiently small \\varepsilon Pe these displacements are characterized by rapid cross-stream diffusion and slow streamwise dispersion, i.e. the concentration appears to be near-uniform across the duct and spreads slowly as it translates. Using the multiple-scales method we derive the leading-order asymptotic approximation to the average fluid concentration bar{c}_0. We show that bar{c}_0 evolves on the slow timescale t ˜ (\\varepsilon Pe)^{-1}, and satisfies a nonlinear diffusion equation in a frame of reference moving with the mean speed of the flow. In the case that the two fluids have identical rheologies and the concentration represents a passive tracer, the diffusion equation is linear. For Newtonian fluids we recover the classical results of Taylor (l953), Aris (1956), and for power-law fluids those of Vartuli et al. (1995). In the case that the fluids differ and/or that mixing is non-passive, bar{c}_0 satisfies a nonlinear diffusion equation in the moving frame of reference. Given a specific mixing/closure law for the rheological properties, we are able to compute the dispersive diffusivity D_T(bar{c}_0) and predict spreading along the channel. We show that D_T(bar{c}_0) can vary significantly with choice of mixing law and discuss why. This also opens the door to possibilities of controlling streamwise spreading by the rheological design of reactive mixtures, i.e. including chemical additives such that the rheology of the mixture behaves very differently to the rheology of either pure fluid. Computed examples illustrate the potential effects that might be achieved.

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.

Full analogue electronic realisation of the Hodgkin-Huxley neuronal dynamics in weak-inversion CMOS.

PubMed

Lazaridis, E; Drakakis, E M; Barahona, M

2007-01-01

This paper presents a non-linear analog synthesis path towards the modeling and full implementation of the Hodgkin-Huxley neuronal dynamics in silicon. The proposed circuits have been realized in weak-inversion CMOS technology and take advantage of both log-domain and translinear transistor-level techniques.

Recursive Inversion By Finite-Impulse-Response Filters

NASA Technical Reports Server (NTRS)

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

1991-01-01

Recursive approximation gives least-squares best fit to exact response. Algorithm yields finite-impulse-response approximation of unknown single-input/single-output, causal, time-invariant, linear, real system, response of which is sequence of impulses. Applicable to such system-inversion problems as suppression of echoes and identification of target from its scatter response to incident impulse.

Solving ill-posed inverse problems using iterative deep neural networks

NASA Astrophysics Data System (ADS)

Adler, Jonas; Öktem, Ozan

2017-12-01

We propose a partially learned approach for the solution of ill-posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularisation theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularising functional. The method results in a gradient-like iterative scheme, where the ‘gradient’ component is learned using a convolutional network that includes the gradients of the data discrepancy and regulariser as input in each iteration. We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against filtered backprojection and total variation reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the total variation reconstruction while being significantly faster, giving reconstructions of 512 × 512 pixel images in about 0.4 s using a single graphics processing unit (GPU).

Non-Linear Dynamics and Emergence in Laboratory Fusion Plasmas

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

Hnat, B.

2011-09-22

Turbulent behaviour of laboratory fusion plasma system is modelled using extended Hasegawa-Wakatani equations. The model is solved numerically using finite difference techniques. We discuss non-linear effects in such a system in the presence of the micro-instabilities, specifically a drift wave instability. We explore particle dynamics in different range of parameters and show that the transport changes from diffusive to non-diffusive when large directional flows are developed.

Time of flight dependent linearity in diffuse imaging: how effective is it to evaluate the spatial resolution by measuring the edge response function?

PubMed

Ortiz-Rascón, E; Bruce, N C; Rodríguez-Rosales, A A; Garduño-Mejía, J

2016-03-01

We describe the behavior of linearity in diffuse imaging by evaluating the differences between time-resolved images produced by photons arriving at the detector at different times. Two approaches are considered: Monte Carlo simulations and experimental results. The images of two complete opaque bars embedded in a transparent or in a turbid medium with a slab geometry are analyzed; the optical properties of the turbid medium sample are close to those of breast tissue. A simple linearity test was designed involving a direct comparison between the intensity profile produced by two bars scanned at the same time and the intensity profile obtained by adding two profiles of each bar scanned one at a time. It is shown that the linearity improves substantially when short time of flight photons are used in the imaging process, but even then the nonlinear behavior prevails. As the edge response function (ERF) has been used widely for testing the spatial resolution in imaging systems, the main implication of a time dependent linearity is the weakness of the linearity assumption when evaluating the spatial resolution through the ERF in diffuse imaging systems, and the need to evaluate the spatial resolution by other methods.

Spin pumping and inverse spin Hall effects in heavy metal/antiferromagnet/Permalloy trilayers

NASA Astrophysics Data System (ADS)

Saglam, Hilal; Zhang, Wei; Jungfleisch, M. Benjamin; Jiang, Wanjun; Pearson, John E.; Hoffmann, Axel

Recent work shows efficient spin transfer via spin waves in insulating antiferromagnets (AFMs), suggesting that AFMs can play a more active role in the manipulation of ferromagnets. We use spin pumping and inverse spin Hall effect experiments on heavy metal (Pt and W)/AFMs/Py (Ni80Fe20) trilayer structures, to examine the possible spin transfer phenomenon in metallic AFMs, i . e . , FeMn and PdMn. Previous work has studied electronic effects of the spin transport in these materials, yielding short spin diffusion length on the order of 1 nm. However, the work did not examine whether besides diffusive spin transport by the conduction electrons, there are additional spin transport contributions from spin wave excitations. We clearly observe spin transport from the Py spin reservoir to the heavy metal layer through the sandwiched AFMs with thicknesses well above the previously measured spin diffusion lengths, indicating that spin transport by spin waves may lead to non-negligible contributions This work was supported by US DOE, OS, Materials Sciences and Engineering Division. Lithographic patterning was carried out at the CNM, which is supported by DOE, OS under Contract No. DE-AC02-06CH11357.

Hybrid quantitative MRI using chemical shift displacement and recovery-based simultaneous water and lipid imaging: A preliminary study.

PubMed

Ohno, Naoki; Miyati, Tosiaki; Suzuki, Shuto; Kan, Hirohito; Aoki, Toshitaka; Nakamura, Yoshitaka; Hiramatsu, Yuki; Kobayashi, Satoshi; Gabata, Toshifumi

2018-07-01

To suppress olefinic signals and enable simultaneous and quantitative estimation of multiple functional parameters associated with water and lipid, we investigated a modified method using chemical shift displacement and recovery-based separation of lipid tissue (SPLIT) involving acquisitions with different inversion times (TIs), echo times (TEs), and b-values. Single-shot diffusion echo-planar imaging (SSD-EPI) with multiple b-values (0-3000 s/mm 2 ) was performed without fat suppression to separate water and lipid images using the chemical shift displacement of lipid signals in the phase-encoding direction. An inversion pulse (TI = 292 ms) was applied to SSD-EPI to remove olefinic signals. Consecutively, SSD-EPI (b = 0 s/mm 2 ) was performed with TI = 0 ms and TE = 31.8 ms for T 1 and T 2 measurements, respectively. Under these conditions, transverse water and lipid images at the maximum diameter of the right calf were obtained in six healthy subjects. T 1 , T 2 , and the apparent diffusion coefficients (ADC) were then calculated for the tibialis anterior (TA), gastrocnemius (GM), and soleus (SL) muscles, tibialis bone marrow (TB), and subcutaneous fat (SF). Perfusion-related (D*) and restricted diffusion coefficients (D) were calculated for the muscles. Lastly, the lipid fractions (LF) of the muscles were determined after T 1 and T 2 corrections. The modified SPLIT method facilitated sufficient separation of water and lipid images of the calf, and the inversion pulse with TI of 292 ms effectively suppressed olefinic signals. All quantitative parameters obtained with the modified SPLIT method were found to be in general agreement with those previously reported in the literature. The modified SPLIT technique enabled sufficient suppression of olefinic signals and simultaneous acquisition of quantitative parameters including diffusion, perfusion, T 1 and T 2 relaxation times, and LF. Copyright © 2018. Published by Elsevier Inc.

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography.

PubMed

Biswas, Samir Kumar; Kanhirodan, Rajan; Vasu, Ram Mohan; Roy, Debasish

2011-08-01

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data.

Diffusion of Polymers through Periodic Networks of Lipid-Based Nanochannels.

PubMed

Ghanbari, Reza; Assenza, Salvatore; Saha, Abhijit; Mezzenga, Raffaele

2017-04-11

We present an experimental investigation of the diffusion of unfolded polymers in the triply-periodic water-channel network of inverse bicontinuous cubic phases. Depending on the chain size, our results indicate the presence of two different dynamical regimes corresponding to Zimm and Rouse diffusion. We support our findings by scaling arguments based on a combination of blob and effective-medium theories and suggest the presence of a third regime where dynamics is driven by reptation. Our experimental results also show an increasing behavior of the partition coefficient as a function of the polymer molecular weight, indicative of a reduction in the conformational degrees of freedom induced by the confinement.

External and Intraparticle Diffusion of Coumarin 102 with Surfactant in the ODS-silica Gel/water System by Single Microparticle Injection and Confocal Fluorescence Microspectroscopy.

PubMed

Nakatani, Kiyoharu; Matsuta, Emi

2015-01-01

The release mechanism of coumarin 102 from a single ODS-silica gel microparticle into the water phase in the presence of Triton X-100 was investigated by confocal fluorescence microspectroscopy combined with the single microparticle injection technique. The release rate significantly depended on the Triton X-100 concentration in the water phase and was not limited by diffusion in the pores of the microparticle. The release rate constant was inversely proportional to the microparticle radius squared, indicating that the rate-determining step is the external diffusion between the microparticle and the water phase.

Is time to peak effect of neuromuscular blocking agents dependent on dose? Testing the concept of buffered diffusion.

PubMed

Proost, J H; Houwertjes, M C; Wierda, J M K H

2008-07-01

For neuromuscular blocking agents, an inverse relationship between potency and time to peak effect has been observed. To test the hypothesis that this relationship is due to buffered diffusion, we investigated the influence of dose on time to peak effect. Pharmacokinetic-pharmacodynamic simulations were performed to support the expected relationships between potency, dose, peak effect and time to peak effect. Pigs (20-28 kg body weight) were anaesthetized with ketamine and midazolam, followed by pentobarbital and fentanyl intravenously. Neuromuscular block was measured by stimulating the peroneal nerve supramaximally at 0.1 Hz and measuring the response of the tibialis anterior muscle mechanomyographically. After an initial dose to establish the individual ED90 of a neuromuscular blocking agent (rocuronium, vecuronium, pipecuronium or d-tubocurarine), five different doses of the same compound were administered to each animal, aiming at 20%, 40%, 60%, 75% or 90% block, in a random order. Doses were given 45 min after complete recovery of the twitch response. For rocuronium and pipecuronium, time to peak effect increased with dose, whereas dose did not affect time to peak effect of vecuronium and d-tubocurarine. Simulations predict that time to peak effect decreases with dose if buffered diffusion is taken into account. The results suggest that buffered diffusion does not play a dominant role in the time to peak effect of neuromuscular blocking agents. Therefore it is unlikely that the observed inverse relationship between potency and time to peak effect of neuromuscular blocking agents in the clinical range is due to buffered diffusion.

Fruit and vegetable intake and the risk of gastric adenocarcinoma: a reanalysis of the European Prospective Investigation into Cancer and Nutrition (EPIC-EURGAST) study after a longer follow-up.

PubMed

Gonzalez, Carlos A; Lujan-Barroso, Leila; Bueno-de-Mesquita, H B; Jenab, Mazda; Duell, Eric J; Agudo, Antonio; Tjønneland, Anne; Boutron-Ruault, Marie Christine; Clavel-Chapelon, Françoise; Touillaud, Marina; Teucher, Birgit; Kaaks, Rudolf; Boeing, Heiner; Steffen, Annika; Trichopoulou, Antonia; Roukos, Dimitrios; Karapetyan, Tina; Palli, Domenico; Tagliabue, Giovanna; Mattiello, Amalia; Tumino, Rosario; Ricceri, Fulvio; Siersema, Peter D; Numans, Mattijs E; Peeters, Petra P H; Parr, Christine L; Skeie, Guri; Lund, Eiliv; Quirós, J Ramón; Sánchez-Cantalejo, Emilio; Navarro, Carmen; Barricarte, Aurelio; Dorronsoro, Miren; Ehrnström, Roy; Regner, Sara; Khaw, Kay-Tee; Wareham, Nick; Key, Timothy J; Crowe, Francesca L; Blaker, Hendrik; Romieu, Isabelle; Riboli, Elio

2012-12-15

In a previous European prospective investigation into cancer and nutrition (EPIC) analysis, we found an inverse association between total intake of vegetables, onion and garlic, and risk of intestinal gastric cancer (GC) and between citrus fruit and risk of cardia GC. The aim of this study is to reanalyze the effect of fruit and vegetables (F&V), based on a longer follow-up and twice the number of GC cases. Subjects are 477,312 men and women mostly aged 35 to 70 years participating in the EPIC cohort, including 683 gastric adenocarcinomas with 11 years of follow-up. Information on diet and lifestyle was collected at baseline. A calibration study in a subsample was used to correct for dietary measurement errors. When comparing the highest vs. lowest quintile of intake, we found an inverse association between total intake of V&F and GC risk [hazard ratio (HR) 0.77; 95% confidence interval (CI) 0.57-1.04; p for trend 0.02], between fresh fruit and risk of the diffuse type (HR 0.59; 95% CI 0.36-0.97; p for trend 0.03) and an inverse association between citrus fruit and risk of cardia cancer (HR 0.61; 95% CI 0.38-1.00, p for trend 0.01). Although calibration revealed somewhat stronger inverse associations, none of the risks reached statistical significance. There was no association between total or specific vegetables intake and GC risk. The inverse association between fresh fruit and citrus fruits and risk of GC seems to be restricted to smokers and the Northern European countries. Fresh fruit and citrus fruit consumption may protect against diffuse and cardia GC, respectively. Copyright © 2012 UICC.

Imaging the Earth's anisotropic structure with Bayesian Inversion of fundamental and higher mode surface-wave dispersion data

NASA Astrophysics Data System (ADS)

Ravenna, Matteo; Lebedev, Sergei; Celli, Nicolas

2017-04-01

We develop a Markov Chain Monte Carlo inversion of fundamental and higher mode phase-velocity curves for radially and azimuthally anisotropic structure of the crust and upper mantle. In the inversions of Rayleigh- and Love-wave dispersion curves for radially anisotropic structure, we obtain probabilistic 1D radially anisotropic shear-velocity profiles of the isotropic average Vs and anisotropy (or Vsv and Vsh) as functions of depth. In the inversions for azimuthal anisotropy, Rayleigh-wave dispersion curves at different azimuths are inverted for the vertically polarized shear-velocity structure (Vsv) and the 2-phi component of azimuthal anisotropy. The strength and originality of the method is in its fully non-linear approach. Each model realization is computed using exact forward calculations. The uncertainty of the models is a part of the output. In the inversions for azimuthal anisotropy, in particular, the computation of the forward problem is performed separately at different azimuths, with no linear approximations on the relation of the Earth's elastic parameters to surface wave phase velocities. The computations are performed in parallel in order reduce the computing time. We compare inversions of the fundamental mode phase-velocity curves alone with inversions that also include overtones. The addition of higher modes enhances the resolving power of the anisotropic structure of the deep upper mantle. We apply the inversion method to phase-velocity curves in a few regions, including the Hangai dome region in Mongolia. Our models provide constraints on the Moho depth, the Lithosphere-Asthenosphere Boundary, and the alignment of the anisotropic fabric and the direction of current and past flow, from the crust down to the deep asthenosphere.

Robust, nonlinear, high angle-of-attack control design for a supermaneuverable vehicle

NASA Technical Reports Server (NTRS)

Adams, Richard J.

1993-01-01

High angle-of-attack flight control laws are developed for a supermaneuverable fighter aircraft. The methods of dynamic inversion and structured singular value synthesis are combined into an approach which addresses both the nonlinearity and robustness problems of flight at extreme operating conditions. The primary purpose of the dynamic inversion control elements is to linearize the vehicle response across the flight envelope. Structured singular value synthesis is used to design a dynamic controller which provides robust tracking to pilot commands. The resulting control system achieves desired flying qualities and guarantees a large margin of robustness to uncertainties for high angle-of-attack flight conditions. The results of linear simulation and structured singular value stability analysis are presented to demonstrate satisfaction of the design criteria. High fidelity nonlinear simulation results show that the combined dynamics inversion/structured singular value synthesis control law achieves a high level of performance in a realistic environment.

LQS_INVERSION v. 1.0

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

Weiss, Chester J

FORTRAN90 codes for inversion of electrostatic geophysical data in terms of three subsurface parameters in a single-well, oilfield environment: the linear charge density of the steel well casing (L), the point charge associated with an induced fracture filled with a conductive contrast agent (Q) and the location of said fracture (s). Theory is described in detail in Weiss et al. (Geophysics, 2016). Inversion strategy is to loop over candidate fracture locations, and at each one minimize the squared Cartesian norm of the data misfit to arrive at L and Q. Solution method is to construct the 2x2 linear system ofmore » normal equations and compute L and Q algebraically. Practical Application: Oilfield environments where observed electrostatic geophysical data can reasonably be assumed by a simple L-Q-s model. This may include hydrofracking operations, as postulated in Weiss et al. (2016), but no field validation examples have so far been provided.« less

Force sensing using 3D displacement measurements in linear elastic bodies

NASA Astrophysics Data System (ADS)

Feng, Xinzeng; Hui, Chung-Yuen

2016-07-01

In cell traction microscopy, the mechanical forces exerted by a cell on its environment is usually determined from experimentally measured displacement by solving an inverse problem in elasticity. In this paper, an innovative numerical method is proposed which finds the "optimal" traction to the inverse problem. When sufficient regularization is applied, we demonstrate that the proposed method significantly improves the widely used approach using Green's functions. Motivated by real cell experiments, the equilibrium condition of a slowly migrating cell is imposed as a set of equality constraints on the unknown traction. Our validation benchmarks demonstrate that the numeric solution to the constrained inverse problem well recovers the actual traction when the optimal regularization parameter is used. The proposed method can thus be applied to study general force sensing problems, which utilize displacement measurements to sense inaccessible forces in linear elastic bodies with a priori constraints.

Shear wave velocity variation across the Taupo Volcanic Zone, New Zealand, from receiver function inversion

USGS Publications Warehouse

Bannister, S.; Bryan, C.J.; Bibby, H.M.

2004-01-01

The Taupo Volcanic Zone (TVZ), New Zealand is a region characterized by very high magma eruption rates and extremely high heat flow, which is manifest in high-temperature geothermal waters. The shear wave velocity structure across the region is inferred using non-linear inversion of receiver functions, which were derived from teleseismic earthquake data. Results from the non-linear inversion, and from forward synthetic modelling, indicate low S velocities at ???6- 16 km depth near the Rotorua and Reporoa calderas. We infer these low-velocity layers to represent the presence of high-level bodies of partial melt associated with the volcanism. Receiver functions at other stations are complicated by reverberations associated with near-surface sedimentary layers. The receiver function data also indicate that the Moho lies between 25 and 30 km, deeper than the 15 ?? 2 km depth previously inferred for the crust-mantle boundary beneath the TVZ. ?? 2004 RAS.

A MATLAB implementation of the minimum relative entropy method for linear inverse problems

NASA Astrophysics Data System (ADS)

Neupauer, Roseanna M.; Borchers, Brian

2001-08-01

The minimum relative entropy (MRE) method can be used to solve linear inverse problems of the form Gm= d, where m is a vector of unknown model parameters and d is a vector of measured data. The MRE method treats the elements of m as random variables, and obtains a multivariate probability density function for m. The probability density function is constrained by prior information about the upper and lower bounds of m, a prior expected value of m, and the measured data. The solution of the inverse problem is the expected value of m, based on the derived probability density function. We present a MATLAB implementation of the MRE method. Several numerical issues arise in the implementation of the MRE method and are discussed here. We present the source history reconstruction problem from groundwater hydrology as an example of the MRE implementation.

Correlations, soliton modes, and non-Hermitian linear mode transmutation in the one-dimensional noisy Burgers equation.

PubMed

Fogedby, Hans C

2003-08-01

Using the previously developed canonical phase space approach applied to the noisy Burgers equation in one dimension, we discuss in detail the growth morphology in terms of nonlinear soliton modes and superimposed linear modes. We moreover analyze the non-Hermitian character of the linear mode spectrum and the associated dynamical pinning, and mode transmutation from diffusive to propagating behavior induced by the solitons. We discuss the anomalous diffusion of growth modes, switching and pathways, correlations in the multisoliton sector, and in detail the correlations and scaling properties in the two-soliton sector.

Periodic order and defects in Ni-based inverse opal-like crystals on the mesoscopic and atomic scale

NASA Astrophysics Data System (ADS)

Chumakova, A. V.; Valkovskiy, G. A.; Mistonov, A. A.; Dyadkin, V. A.; Grigoryeva, N. A.; Sapoletova, N. A.; Napolskii, K. S.; Eliseev, A. A.; Petukhov, A. V.; Grigoriev, S. V.

2014-10-01

The structure of inverse opal crystals based on nickel was probed on the mesoscopic and atomic levels by a set of complementary techniques such as scanning electron microscopy and synchrotron microradian and wide-angle diffraction. The microradian diffraction revealed the mesoscopic-scale face-centered-cubic (fcc) ordering of spherical voids in the inverse opal-like structure with unit cell dimension of 750±10nm. The diffuse scattering data were used to map defects in the fcc structure as a function of the number of layers in the Ni inverse opal-like structure. The average lateral size of mesoscopic domains is found to be independent of the number of layers. 3D reconstruction of the reciprocal space for the inverse opal crystals with different thickness provided an indirect study of original opal templates in a depth-resolved way. The microstructure and thermal response of the framework of the porous inverse opal crystal was examined using wide-angle powder x-ray diffraction. This artificial porous structure is built from nickel crystallites possessing stacking faults and dislocations peculiar for the nickel thin films.

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.

Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control

NASA Astrophysics Data System (ADS)

Syed Ali, M.; Yogambigai, J.; Kwon, O. M.

2018-03-01

Finite-time boundedness and finite-time passivity for a class of switched stochastic complex dynamical networks (CDNs) with coupling delays, parameter uncertainties, reaction-diffusion term and impulsive control are studied. Novel finite-time synchronisation criteria are derived based on passivity theory. This paper proposes a CDN consisting of N linearly and diffusively coupled identical reaction- diffusion neural networks. By constructing of a suitable Lyapunov-Krasovskii's functional and utilisation of Jensen's inequality and Wirtinger's inequality, new finite-time passivity criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.

Ground-based microwave radiometric remote sensing of the tropical atmosphere

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

Han, Yong.

1992-01-01

A partially developed 9-channel ground-based microwave radiometer for the Department of Meteorology at Penn State was completed and tested. Complementary units were added, corrections to both hardware and software were made, and system software was corrected and upgraded. Measurements from this radiometer were used to infer tropospheric temperature, water vapor and cloud liquid water. The various weighting functions at each of the 9 channels were calculated and analyzed to estimate the sensitivities of the brightness temperature to the desired atmospheric variables. The mathematical inversion problem, in a linear form, was viewed in terms of the theory of linear algebra. Severalmore » methods for solving the inversion problem were reviewed. Radiometric observations were conducted during the 1990 Tropical Cyclone Motion Experiment. The radiometer was installed on the island of Saipan in a tropical region. The radiometer was calibrated using tipping curve and radiosonde data as well as measurements of the radiation from a blackbody absorber. A linear statistical method was applied for the data inversion. The inversion coefficients in the equation were obtained using a large number of radiosonde profiles from Guam and a radiative transfer model. Retrievals were compared with those from local, Saipan, radiosonde measurements. Water vapor profiles, integrated water vapor, and integrated liquid water were retrieved successfully. For temperature profile retrievals, however, the radiometric measurements with experimental noises added no more profile information to the inversion than that they were determined mainly by the surface pressure measurements. A method was developed to derive the integrated water vapor and liquid water from combined radiometer and ceilometer measurements. Significant improvement on radiometric measurements of the integrated liquid water can be gained with this method.« less

Stimulated echo diffusion tensor imaging (STEAM-DTI) with varying diffusion times as a probe of breast tissue.

PubMed

Teruel, Jose R; Cho, Gene Y; Moccaldi Rt, Melanie; Goa, Pål E; Bathen, Tone F; Feiweier, Thorsten; Kim, Sungheon G; Moy, Linda; Sigmund, Eric E

2017-01-01

To explore the application of diffusion tensor imaging (DTI) for breast tissue and breast pathologies using a stimulated-echo acquisition mode (STEAM) with variable diffusion times. In this Health Insurance Portability and Accountability Act-compliant study, approved by the local institutional review board, eight patients and six healthy volunteers underwent an MRI examination at 3 Tesla including STEAM-DTI with several diffusion times ranging from 68.5 to 902.5 ms. A DTI model was fitted to the data for each diffusion time, and parametric maps of mean diffusivity, fractional anisotropy, axial diffusivity, and radial diffusivity were computed for healthy fibroglandular tissue (FGT) and lesions. The median value of radial diffusivity for FGT was fitted to a linear decay to obtain an estimation of the surface-to-volume ratio, from which the radial diameter was calculated. For healthy FGT, radial diffusivity presented a linear decay with the square root of the diffusion time resulting in a range of estimated radial diameters from 202 to 496 µm, while axial diffusivity presented a nearly time-independent diffusion. Residual fat signal was reduced at longer diffusion times due to the shorter T1 of fat. Residual fat signal to the overall signal in the healthy volunteers' FGT was found to range from 2.39% to 2.55% (shortest mixing time), and from 0.40% to 0.51% (longest mixing time) for the b500 images. The use of variable diffusion times may provide an in vivo noninvasive tool to probe diffusion lengths in breast tissue and breast pathology, and might aid by improving fat suppression at longer diffusion times. 2 J. Magn. Reson. Imaging 2017;45:84-93. © 2016 International Society for Magnetic Resonance in Medicine.

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.

Inversion layer solar cell fabrication and evaluation. [measurement of response of inversion layer solar cell to light of different wavelengths

NASA Technical Reports Server (NTRS)

Call, R. L.

1973-01-01

Silicon solar cells operating with induced junctions rather than diffused junctions have been fabricated and tested. Induced junctions were created by forming an inversion layer near the surface of the silicon by supplying a sheet of positive charge above the surface. This charged layer was supplied through three mechanisms: (1) applying a positive potential to a transparent electrode separated from the silicon surface by a dielectric, (2) contaminating the oxide layer with positive ions, and (3) forming donor surface states that leave a positive charge on the surface. A movable semi-infinite shadow delineated the extent of sensitivity of the cell due to the inversion region. Measurements of the response of the inversion layer cell to light of different wavelengths indicated it to be more sensitive to the shorter wavelengths of the sun's spectrum than conventional cells. The greater sensitivity occurs because of the shallow junction and the strong electric field at the surface.

White Matter Integrity, Creativity, and Psychopathology: Disentangling Constructs with Diffusion Tensor Imaging

PubMed Central

Jung, Rex E.; Grazioplene, Rachael; Caprihan, Arvind; Chavez, Robert S.; Haier, Richard J.

2010-01-01

That creativity and psychopathology are somehow linked remains a popular but controversial idea in neuroscience research. Brain regions implicated in both psychosis-proneness and creative cognition include frontal projection zones and association fibers. In normal subjects, we have previously demonstrated that a composite measure of divergent thinking (DT) ability exhibited significant inverse relationships in frontal lobe areas with both cortical thickness and metabolite concentration of N-acetyl-aspartate (NAA). These findings support the idea that creativity may reside upon a continuum with psychopathology. Here we examine whether white matter integrity, assessed by Fractional Anisotropy (FA), is related to two measures of creativity (Divergent Thinking and Openness to Experience). Based on previous findings, we hypothesize inverse correlations within fronto-striatal circuits. Seventy-two healthy, young adult (18–29 years) subjects were scanned on a 3 Tesla scanner with Diffusion Tensor Imaging. DT measures were scored by four raters (α = .81) using the Consensual Assessment Technique, from which a composite creativity index (CCI) was derived. We found that the CCI was significantly inversely related to FA within the left inferior frontal white matter (t = 5.36, p = .01), and Openness was inversely related to FA within the right inferior frontal white matter (t = 4.61, p = .04). These findings demonstrate an apparent overlap in specific white matter architecture underlying the normal variance of divergent thinking, openness, and psychotic-spectrum traits, consistent with the idea of a continuum. PMID:20339554

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.

A novel method for calculating the energy barriers for carbon diffusion in ferrite under heterogeneous stress

NASA Astrophysics Data System (ADS)

Tchitchekova, Deyana S.; Morthomas, Julien; Ribeiro, Fabienne; Ducher, Roland; Perez, Michel

2014-07-01

A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ˜3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress.

A novel method for calculating the energy barriers for carbon diffusion in ferrite under heterogeneous stress.

PubMed

Tchitchekova, Deyana S; Morthomas, Julien; Ribeiro, Fabienne; Ducher, Roland; Perez, Michel

2014-07-21

A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ∼3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress.

Standard and inverse bond percolation of straight rigid rods on square lattices

NASA Astrophysics Data System (ADS)

Ramirez, L. S.; Centres, P. M.; Ramirez-Pastor, A. J.

2018-04-01

Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse bond percolation of straight rigid rods on square lattices. In the case of standard percolation, the lattice is initially empty. Then, linear bond k -mers (sets of k linear nearest-neighbor bonds) are randomly and sequentially deposited on the lattice. Jamming coverage pj ,k and percolation threshold pc ,k are determined for a wide range of k (1 ≤k ≤120 ). pj ,k and pc ,k exhibit a decreasing behavior with increasing k , pj ,k →∞=0.7476 (1 ) and pc ,k →∞=0.0033 (9 ) being the limit values for large k -mer sizes. pj ,k is always greater than pc ,k, and consequently, the percolation phase transition occurs for all values of k . In the case of inverse percolation, the process starts with an initial configuration where all lattice bonds are occupied and, given that periodic boundary conditions are used, the opposite sides of the lattice are connected by nearest-neighbor occupied bonds. Then, the system is diluted by randomly removing linear bond k -mers from the lattice. The central idea here is based on finding the maximum concentration of occupied bonds (minimum concentration of empty bonds) for which connectivity disappears. This particular value of concentration is called the inverse percolation threshold pc,k i, and determines a geometrical phase transition in the system. On the other hand, the inverse jamming coverage pj,k i is the coverage of the limit state, in which no more objects can be removed from the lattice due to the absence of linear clusters of nearest-neighbor bonds of appropriate size. It is easy to understand that pj,k i=1 -pj ,k . The obtained results for pc,k i show that the inverse percolation threshold is a decreasing function of k in the range 1 ≤k ≤18 . For k >18 , all jammed configurations are percolating states, and consequently, there is no nonpercolating phase. In other words, the lattice remains connected even when the highest allowed concentration of removed bonds pj,k i is reached. In terms of network attacks, this striking behavior indicates that random attacks on single nodes (k =1 ) are much more effective than correlated attacks on groups of close nodes (large k 's). Finally, the accurate determination of critical exponents reveals that standard and inverse bond percolation models on square lattices belong to the same universality class as the random percolation, regardless of the size k considered.

Efficient Monte Carlo sampling of inverse problems using a neural network-based forward—applied to GPR crosshole traveltime inversion

NASA Astrophysics Data System (ADS)

Hansen, T. M.; Cordua, K. S.

2017-12-01

Probabilistically formulated inverse problems can be solved using Monte Carlo-based sampling methods. In principle, both advanced prior information, based on for example, complex geostatistical models and non-linear forward models can be considered using such methods. However, Monte Carlo methods may be associated with huge computational costs that, in practice, limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical forward response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival traveltime inversion of crosshole ground penetrating radar data. An accurate forward model, based on 2-D full-waveform modeling followed by automatic traveltime picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the accurate and computationally expensive forward model, and also considerably faster and more accurate (i.e. with better resolution), than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of non-linear and non-Gaussian inverse problems that have to be solved using Monte Carlo sampling techniques.

3-D linear inversion of gravity data: method and application to Basse-Terre volcanic island, Guadeloupe, Lesser Antilles

NASA Astrophysics Data System (ADS)

Barnoud, Anne; Coutant, Olivier; Bouligand, Claire; Gunawan, Hendra; Deroussi, Sébastien

2016-04-01

We use a Bayesian formalism combined with a grid node discretization for the linear inversion of gravimetric data in terms of 3-D density distribution. The forward modelling and the inversion method are derived from seismological inversion techniques in order to facilitate joint inversion or interpretation of density and seismic velocity models. The Bayesian formulation introduces covariance matrices on model parameters to regularize the ill-posed problem and reduce the non-uniqueness of the solution. This formalism favours smooth solutions and allows us to specify a spatial correlation length and to perform inversions at multiple scales. We also extract resolution parameters from the resolution matrix to discuss how well our density models are resolved. This method is applied to the inversion of data from the volcanic island of Basse-Terre in Guadeloupe, Lesser Antilles. A series of synthetic tests are performed to investigate advantages and limitations of the methodology in this context. This study results in the first 3-D density models of the island of Basse-Terre for which we identify: (i) a southward decrease of densities parallel to the migration of volcanic activity within the island, (ii) three dense anomalies beneath Petite Plaine Valley, Beaugendre Valley and the Grande-Découverte-Carmichaël-Soufrière Complex that may reflect the trace of former major volcanic feeding systems, (iii) shallow low-density anomalies in the southern part of Basse-Terre, especially around La Soufrière active volcano, Piton de Bouillante edifice and along the western coast, reflecting the presence of hydrothermal systems and fractured and altered rocks.

Mass Transport of Macromolecules within an In Vitro Model of Supragingival Plaque

PubMed Central

Thurnheer, Thomas; Gmür, Rudolf; Shapiro, Stuart; Guggenheim, Bernhard

2003-01-01

The aim of this study was to examine the diffusion of macromolecules through an in vitro biofilm model of supragingival plaque. Polyspecies biofilms containing Actinomyces naeslundii, Fusobacterium nucleatum, Streptococcus oralis, Streptococcus sobrinus, Veillonella dispar, and Candida albicans were formed on sintered hydroxyapatite disks and then incubated at room temperature for defined periods with fluorescent markers with molecular weights ranging from 3,000 to 900,000. Subsequent examination by confocal laser scanning microscopy revealed that the mean square penetration depths for all tested macromolecules except immunoglobulin M increased linearly with time, diffusion coefficients being linearly proportional to the cube roots of the molecular weights of the probes (range, 10,000 to 240,000). Compared to diffusion in bulk water, diffusion in the biofilms was markedly slower. The rate of diffusion for each probe appeared to be constant and not a function of biofilm depth. Analysis of diffusion phenomena through the biofilms suggested tortuosity as the most probable explanation for retarded diffusion. Selective binding of probes to receptors present in the biofilms could not explain the observed extent of retardation of diffusion. These results are relevant to oral health, as selective attenuated diffusion of fermentable carbohydrates and acids produced within dental plaque is thought to be essential for the development of carious lesions. PMID:12620862

Study of Solid-State Diffusion of Bi in Polycrystalline Sn Using Electron Probe Microanalysis

NASA Astrophysics Data System (ADS)

Delhaise, André M.; Perovic, Doug D.

2018-03-01

Current lead-free solders such as SAC305 exhibit degradation in microstructure, properties, and reliability. Current third-generation alloys containing bismuth (Bi) demonstrate preservation of strength after aging; this is accompanied by homogenization of the Bi precipitates in the tin (Sn) matrix, driven via solid-state diffusion. This study quantifies the diffusion of Bi in Sn. Diffusion couples were prepared by mating together polished samples of pure Sn and Bi. Couples were annealed at one of three temperatures, viz. 85°C for 7 days, 100°C for 2 days, or 125°C for 1 day. After cross-sectioning the couples to examine the diffusion microstructure and grain size, elemental analysis was performed using electron probe microanalysis. For this study, it was assumed that the diffusivity of Bi in Sn is concentration dependent, therefore inverse methods were used to solve Fick's non-steady-state diffusion equation. In addition, Darken analysis was used to extract the impurity diffusivity of Bi in Sn at each temperature, allowing estimation of the Arrhenius parameters D 0 and k A.

Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

PubMed

Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

2011-10-01

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

A Framework for Linear and Non-Linear Registration of Diffusion-Weighted MRIs Using Angular Interpolation

PubMed Central

Duarte-Carvajalino, Julio M.; Sapiro, Guillermo; Harel, Noam; Lenglet, Christophe

2013-01-01

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis. PMID:23596381

A Framework for Linear and Non-Linear Registration of Diffusion-Weighted MRIs Using Angular Interpolation.

PubMed

Duarte-Carvajalino, Julio M; Sapiro, Guillermo; Harel, Noam; Lenglet, Christophe

2013-01-01

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis.

Polynomial dual energy inverse functions for bone Calcium/Phosphorus ratio determination and experimental evaluation.

PubMed

Sotiropoulou, P; Fountos, G; Martini, N; Koukou, V; Michail, C; Kandarakis, I; Nikiforidis, G

2016-12-01

An X-ray dual energy (XRDE) method was examined, using polynomial nonlinear approximation of inverse functions for the determination of the bone Calcium-to-Phosphorus (Ca/P) mass ratio. Inverse fitting functions with the least-squares estimation were used, to determine calcium and phosphate thicknesses. The method was verified by measuring test bone phantoms with a dedicated dual energy system and compared with previously published dual energy data. The accuracy in the determination of the calcium and phosphate thicknesses improved with the polynomial nonlinear inverse function method, introduced in this work, (ranged from 1.4% to 6.2%), compared to the corresponding linear inverse function method (ranged from 1.4% to 19.5%). Copyright © 2016 Elsevier Ltd. All rights reserved.

Functional Effects of Parasites on Food Web Properties during the Spring Diatom Bloom in Lake Pavin: A Linear Inverse Modeling Analysis

PubMed Central

Niquil, Nathalie; Jobard, Marlène; Saint-Béat, Blanche; Sime-Ngando, Télesphore

2011-01-01

This study is the first assessment of the quantitative impact of parasitic chytrids on a planktonic food web. We used a carbon-based food web model of Lake Pavin (Massif Central, France) to investigate the effects of chytrids during the spring diatom bloom by developing models with and without chytrids. Linear inverse modelling procedures were employed to estimate undetermined flows in the lake. The Monte Carlo Markov chain linear inverse modelling procedure provided estimates of the ranges of model-derived fluxes. Model results support recent theories on the probable impact of parasites on food web function. In the lake, during spring, when ‘inedible’ algae (unexploited by planktonic herbivores) were the dominant primary producers, the epidemic growth of chytrids significantly reduced the sedimentation loss of algal carbon to the detritus pool through the production of grazer-exploitable zoospores. We also review some theories about the potential influence of parasites on ecological network properties and argue that parasitism contributes to longer carbon path lengths, higher levels of activity and specialization, and lower recycling. Considering the “structural asymmetry” hypothesis as a stabilizing pattern, chytrids should contribute to the stability of aquatic food webs. PMID:21887240

Considering the reversibility of passive and reactive transport problems: Are forward-in-time and backward-in-time models ever equivalent?

NASA Astrophysics Data System (ADS)

Engdahl, N.

2017-12-01

Backward in time (BIT) simulations of passive tracers are often used for capture zone analysis, source area identification, and generation of travel time and age distributions. The BIT approach has the potential to become an immensely powerful tool for direct inverse modeling but the necessary relationships between the processes modeled in the forward and backward models have yet to be formally established. This study explores the time reversibility of passive and reactive transport models in a variety of 2D heterogeneous domains using particle-based random walk methods for the transport and nonlinear reaction steps. Distributed forward models are used to generate synthetic observations that form the initial conditions for the backward in time models and we consider both linear-flood and point injections. The results for passive travel time distributions show that forward and backward models are not exactly equivalent but that the linear-flood BIT models are reasonable approximations. Point based BIT models fall within the travel time range of the forward models, though their distributions can be distinctive in some cases. The BIT approximation is not as robust when nonlinear reactive transport is considered and we find that this reaction system is only exactly reversible under uniform flow conditions. We use a series of simplified, longitudinally symmetric, but heterogeneous, domains to illustrate the causes of these discrepancies between the two model types. Many of the discrepancies arise because diffusion is a "self-adjoint" operator, which causes mass to spread in the forward and backward models. This allows particles to enter low velocity regions in the both models, which has opposite effects in the forward and reverse models. It may be possible to circumvent some of these limitations using an anti-diffusion model to undo mixing when time is reversed, but this is beyond the capabilities of the existing Lagrangian methods.

Anomalous changes of diffuse CO_{2} emission and seismic activity at Teide volcano, Tenerife, Canary Islands

NASA Astrophysics Data System (ADS)

García-Hernández, Rubén; Melián, Gladys; D'Auria, Luca; Asensio-Ramos, María; Alonso, Mar; Padilla, Germán D.; Rodríguez, Fátima; Padrón, Eleazar; Barrancos, José; García-Merino, Marta; Amonte, Cecilia; Pérez, Aarón; Calvo, David; Hernández, Pedro A.; Pérez, Nemesio M.

2017-04-01

Tenerife (2034 km2) is the largest of the Canary Islands and hosts four main active volcanic edifices: three volcanic rifts and a central volcanic complex, Las Cañadas, which is characterized by the eruption of differentiated magmas. Laying inside Las Cañadas a twin stratovolcanoes system, Pico Viejo and Teide, has been developed. Although there are no visible gas emanations along the volcanic rifts of Tenerife, the existence of a volcanic-hydrothermal system beneath Teide volcano is suggested by the occurrence of a weak fumarolic system, steamy ground and high rates of diffuse CO2 degassing all around the summit cone of Teide. Soil CO2 efflux surveys have been performed at the summit crater of Teide volcano since 1999, to determine the diffuse CO2 emission from the summit crater and to evaluate the temporal variations of CO2 efflux and their relationships with seismic-volcanic activity. Soil CO2 efflux and soil temperature have been always measured at the same 38 observation sites homogeneously distributed within an area of about 6,972 m2 inside the summit crater. Soil CO2 diffuse effluxes were estimated according to the accumulation chamber method by means of a non-dispersive infrared (NDIR) LICOR-820 CO2 analyzer. Historical seismic activity in Tenerife has been characterized by low- to moderate-magnitude events (M <2.5), and most of the earthquake's epicenters have been clustered in an offshore area SE of Tenerife. However, very few earthquakes have occurred in other areas, including Teide volcano. At 12:18 of January 6, 2017, the Canary Seismic Network belonged to the Instituto Volcanológico de Canarias (INVOLCAN) registered an earthquake of M 2.5 located in the vertical of Teide volcano with a depth of 6.6 km. It was the strongest earthquake located inside Cañadas caldera since 2004. Between October 11 and December 13, 2016, a continuous increase on the diffuse CO2 emission was registered, from 21.3 ± 2.0 to 101.7 ± 20.7 t d-1, suggesting the occurrence of future increase in the seismic-volcanic activity. In fact, this precursory signal preceded the occurrence of the 2.5 seismic event and no significant horizontal and vertical displacements were registered by the Canary GPS network belonged to INVOLCAN. This seismic event was probably due to the increase of fluid pressure in the hydrothermal-magmatic system of Tenerife. With the aim of investigate the relationship of the observed temporal variation on diffuse CO2 emission and the seismic event occurred beneath Teide volcano in January 6, 2016, the anomalous peak of diffuse CO2 emission was tested following the Material Failure Forecast Method (FFM). To do so, a Geochemical Window Precursory Signal (GWPS) was selected between October 11 and December 13, 2016. Plotting the inverse of diffuse CO2 emission rate versus time, the interception of the linear fit of the data with the time axis indicates the theoretical moment when seismicity is most likely to occur. Surprisingly, interception of the linear fit occurred for a time window between January 6 and 9, 2017, showing an excellent correlation with the occurrence of the M 2.5 earthquake registered at Teide in January 6, 2017.

Pickup protons and water ions at Comet Halley - Comparisons with Giotto observations

NASA Astrophysics Data System (ADS)

Ye, G.; Cravens, T. E.; Gombosi, T. I.

1993-02-01

The cometary ion pickup process along the sun-comet line at Comet Halley is investigated using a quasi-linear diffusion model including both pitch angle and energy diffusion, adiabatic compression, and convective motion with the solar wind flow. The model results are compared with energetic ion distributions observed by instruments on board the Giotto spacecraft. The observed power spectrum index of magnetic turbulence (gamma) is 2-2.5. The present simulation shows that when gamma was 2, the calculated proton distributions were much more isotropic than the observed ones. The numerical solutions of the quasi-linear diffusion equations show that the isotropization of the pickup ion distribution, particularly at the pickup velocity, is not complete even close to the bow shock. Given the observed turbulence level, quasi-linear theory yields pickup ion energy distributions that agree with the observed ones quite well and easily produces energetic ions with energies up to hundreds of keV.

Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction

NASA Astrophysics Data System (ADS)

Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh

2016-09-01

A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.

Determination of molecular diffusion coefficient in n-alkane binary mixtures: empirical correlations.

PubMed

De Mezquia, D Alonso; Bou-Ali, M Mounir; Larrañaga, M; Madariaga, J A; Santamaría, C

2012-03-08

In this work we have measured the molecular diffusion coefficient of the n-alkane binary series nC(i)-nC(6), nC(i)-nC(10), and nC(i)-nC(12) at 298 K and 1 atm and a mass fraction of 0.5 by using the so-called sliding symmetric tubes technique. The results show that the diffusion coefficient at this concentration is proportional to the inverse viscosity of the mixture. In addition, we have also measured the diffusion coefficient of the systems nC(12)-nC(6), nC(12)-nC(7), and nC(12)-nC(8) as a function of concentration. From the data obtained, it is shown that the diffusion coefficient of the n-alkane binary mixtures at any concentration can be calculated from the molecular weight of the components and the dynamic viscosity of the corresponding mixture at 50% mass fraction.

The Dynamics of Entangled DNA Networks using Single-Molecule Methods

NASA Astrophysics Data System (ADS)

Chapman, Cole David

Single molecule experiments were performed on DNA, a model polymer, and entangled DNA networks to explore diffusion within complex polymeric fluids and their linear and non-linear viscoelasticity. DNA molecules of varying length and topology were prepared using biological methods. An ensemble of individual molecules were then fluorescently labeled and tracked in blends of entangled linear and circular DNA to examine the dependence of diffusion on polymer length, topology, and blend ratio. Diffusion was revealed to possess a non-monotonic dependence on the blend ratio, which we believe to be due to a second-order effect where the threading of circular polymers by their linear counterparts greatly slows the mobility of the system. Similar methods were used to examine the diffusive and conformational behavior of DNA within highly crowded environments, comparable to that experienced within the cell. A previously unseen gamma distributed elongation of the DNA in the presence of crowders, proposed to be due to entropic effects and crowder mobility, was observed. Additionally, linear viscoelastic properties of entangled DNA networks were explored using active microrheology. Plateau moduli values verified for the first time the predicted independence from polymer length. However, a clear bead-size dependence was observed for bead radii less than ~3x the tube radius, a newly discovered limit, above which microrheology results are within the continuum limit and may access the bulk properties of the fluid. Furthermore, the viscoelastic properties of entangled DNA in the non-linear regime, where the driven beads actively deform the network, were also examined. By rapidly driving a bead through the network utilizing optical tweezers, then removing the trap and tracking the bead's subsequent motion we are able to model the system as an over-damped harmonic oscillator and find the elasticity to be dominated by stress-dependent entanglements.

A Computational Investigation of Sooting Limits of Spherical Diffusion Flames

NASA Technical Reports Server (NTRS)

Lecoustre, V. R.; Chao, B. H.; Sunderland, P. B.; Urban, D. L.; Stocker, D. P.; Axelbaum, R. L.

2007-01-01

Limiting conditions for soot particle inception in spherical diffusion flames were investigated numerically. The flames were modeled using a one-dimensional, time accurate diffusion flame code with detailed chemistry and transport and an optically thick radiation model. Seventeen normal and inverse flames were considered, covering a wide range of stoichiometric mixture fraction, adiabatic flame temperature, and residence time. These flames were previously observed to reach their sooting limits after 2 s of microgravity. Sooting-limit diffusion flames with residence times longer than 200 ms were found to have temperatures near 1190 K where C/O = 0.6, whereas flames with shorter residence times required increased temperatures. Acetylene was found to be a reasonable surrogate for soot precursor species in these flames, having peak mole fractions of about 0.01.

Effects of C/O Ratio and Temperature on Sooting Limits of Spherical Diffusion Flames

NASA Technical Reports Server (NTRS)

Lecoustre, V. R.; Sunderland, P. B.; Chao, B. H.; Urban, D. L.; Stocker, D. P.; Axelbaum, R. L.

2008-01-01

Limiting conditions for soot particle inception in spherical diffusion flames were investigated numerically. The flames were modeled using a one-dimensional, time accurate diffusion flame code with detailed chemistry and transport and an optically thick radiation model. Seventeen normal and inverse flames were considered, covering a wide range of stoichiometric mixture fraction, adiabatic flame temperature, residence time and scalar dissipation rate. These flames were previously observed to reach their sooting limits after 2 s of microgravity. Sooting-limit diffusion flames with scalar dissipation rate lower than 2/s were found to have temperatures near 1400 K where C/O = 0.51, whereas flames with greater scalar dissipation rate required increased temperatures. This finding was valid across a broad range of fuel and oxidizer compositions and convection directions.

Models of collective cell spreading with variable cell aspect ratio: a motivation for degenerate diffusion models.

PubMed

Simpson, Matthew J; Baker, Ruth E; McCue, Scott W

2011-02-01

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multiscale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (PME). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the PME to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

Gyrokinetic modelling of the quasilinear particle flux for plasmas with neutral-beam fuelling

NASA Astrophysics Data System (ADS)

Narita, E.; Honda, M.; Nakata, M.; Yoshida, M.; Takenaga, H.; Hayashi, N.

2018-02-01

A quasilinear particle flux is modelled based on gyrokinetic calculations. The particle flux is estimated by determining factors, namely, coefficients of off-diagonal terms and a particle diffusivity. In this paper, the methodology to estimate the factors is presented using a subset of JT-60U plasmas. First, the coefficients of off-diagonal terms are estimated by linear gyrokinetic calculations. Next, to obtain the particle diffusivity, a semi-empirical approach is taken. Most experimental analyses for particle transport have assumed that turbulent particle fluxes are zero in the core region. On the other hand, even in the stationary state, the plasmas in question have a finite turbulent particle flux due to neutral-beam fuelling. By combining estimates of the experimental turbulent particle flux and the coefficients of off-diagonal terms calculated earlier, the particle diffusivity is obtained. The particle diffusivity should reflect a saturation amplitude of instabilities. The particle diffusivity is investigated in terms of the effects of the linear instability and linear zonal flow response, and it is found that a formula including these effects roughly reproduces the particle diffusivity. The developed framework for prediction of the particle flux is flexible to add terms neglected in the current model. The methodology to estimate the quasilinear particle flux requires so low computational cost that a database consisting of the resultant coefficients of off-diagonal terms and particle diffusivity can be constructed to train a neural network. The development of the methodology is the first step towards a neural-network-based particle transport model for fast prediction of the particle flux.

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

Wolfram, Phillip J.; Ringler, Todd D.

Meridional diffusivity is assessed in this paper for a baroclinically unstable jet in a high-latitudeIdealized Circumpolar Current (ICC) using the Model for Prediction Across Scales-Ocean (MPAS-O) and the online Lagrangian In-situ Global High-performance particle Tracking (LIGHT) diagnostic via space-time dispersion of particle clusters over 120 monthly realizations of O(10 6) particles on 11 potential density surfaces. Diffusivity in the jet reaches values of O(6000 m 2 s -1) and is largest near the critical layer supporting mixing suppression and critical layer theory. Values in the vicinity of the shelf break are suppressed to O(100 m 2 s -1) due tomore » the presence of westward slope front currents. Diffusivity attenuates less rapidly with depth in the jet than both eddy velocity and kinetic energy scalings would suggest. Removal of the mean flow via high-pass filtering shifts the nonlinear parameter (ratio of the eddy velocity to eddy phase speed) into the linear wave regime by increasing the eddy phase speed via the depth-mean flow. Low-pass filtering, in contrast, quantifies the effect of mean shear. Diffusivity is decomposed into mean flow shear, linear waves, and the residual nonhomogeneous turbulence components, where turbulence dominates and eddy-produced filamentation strained by background mean shear enhances mixing, accounting for ≥ 80% of the total diffusivity relative to mean shear [O(100 m 2 s -1)], linear waves [O(1000 m 2 s -1)], and undecomposed full diffusivity [O(6000 m 2 s -1)]. Finally, diffusivity parameterizations accounting for both the nonhomogeneous turbulence residual and depth variability are needed.« less

Stochastic inversion of cross-borehole radar data from metalliferous vein detection

NASA Astrophysics Data System (ADS)

Zeng, Zhaofa; Huai, Nan; Li, Jing; Zhao, Xueyu; Liu, Cai; Hu, Yingsa; Zhang, Ling; Hu, Zuzhi; Yang, Hui

2017-12-01

In the exploration and evaluation of the metalliferous veins with a cross-borehole radar system, traditional linear inversion methods (least squares inversion, LSQR) only get indirect parameters (permittivity, resistivity, or velocity) to estimate the target structure. They cannot accurately reflect the geological parameters of the metalliferous veins’ media properties. In order to get the intrinsic geological parameters and internal distribution, in this paper, we build a metalliferous veins model based on the stochastic effective medium theory, and carry out stochastic inversion and parameter estimation based on the Monte Carlo sampling algorithm. Compared with conventional LSQR, the stochastic inversion can get higher resolution inversion permittivity and velocity of the target body. We can estimate more accurately the distribution characteristics of abnormality and target internal parameters. It provides a new research idea to evaluate the properties of complex target 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

Oil core microcapsules by inverse gelation technique.

PubMed

Martins, Evandro; Renard, Denis; Davy, Joëlle; Marquis, Mélanie; Poncelet, Denis

2015-01-01

A promising technique for oil encapsulation in Ca-alginate capsules by inverse gelation was proposed by Abang et al. This method consists of emulsifying calcium chloride solution in oil and then adding it dropwise in an alginate solution to produce Ca-alginate capsules. Spherical capsules with diameters around 3 mm were produced by this technique, however the production of smaller capsules was not demonstrated. The objective of this study is to propose a new method of oil encapsulation in a Ca-alginate membrane by inverse gelation. The optimisation of the method leads to microcapsules with diameters around 500 μm. In a search of microcapsules with improved diffusion characteristics, the size reduction is an essential factor to broaden the applications in food, cosmetics and pharmaceuticals areas. This work contributes to a better understanding of the inverse gelation technique and allows the production of microcapsules with a well-defined shell-core structure.

Engineering three-dimensionally electrodeposited Si-on-Ni inverse opal structure for high volumetric capacity Li-ion microbattery anode.

PubMed

Liu, Hao; Cho, Hyung-Man; Meng, Ying Shirley; Li, Quan

2014-06-25

Aiming at improving the volumetric capacity of nanostructured Li-ion battery anode, an electrodeposited Si-on-Ni inverse opal structure has been proposed in the present work. This type of electrode provides three-dimensional bi-continuous pathways for ion/electron transport and high surface area-to-volume ratios, and thus exhibits lower interfacial resistance, but higher effective Li ions diffusion coefficients, when compared to the Si-on-Ni nanocable array electrode of the same active material mass. As a result, improved volumetric capacities and rate capabilities have been demonstrated in the Si-on-Ni inverse opal anode. We also show that optimization of the volumetric capacities and the rate performance of the inverse opal electrode can be realized by manipulating the pore size of the Ni scaffold and the thickness of the Si deposit.

Cross hole GPR traveltime inversion using a fast and accurate neural network as a forward model

NASA Astrophysics Data System (ADS)

Mejer Hansen, Thomas

2017-04-01

Probabilistic formulated inverse problems can be solved using Monte Carlo based sampling methods. In principle both advanced prior information, such as based on geostatistics, and complex non-linear forward physical models can be considered. However, in practice these methods can be associated with huge computational costs that in practice limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error, that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival travel time inversion of cross hole ground-penetrating radar (GPR) data. An accurate forward model, based on 2D full-waveform modeling followed by automatic travel time picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the full forward model, and considerably faster, and more accurate, than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of the types of inverse problems that can be solved using non-linear Monte Carlo sampling techniques.

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

Lin, Chien-Chih; Hsu, Pei-Lun; Lin, Li

A particular edge-dependent inversion current behavior of metal-oxide-semiconductor (MOS) tunneling diodes was investigated utilizing square and comb-shaped electrodes. The inversion tunneling current exhibits the strong dependence on the tooth size of comb-shaped electrodes and oxide thickness. Detailed illustrations of current conduction mechanism are developed by simulation and experimental measurement results. It is found that the electron diffusion current and Schottky barrier height lowering for hole tunneling current both contribute on inversion current conduction. In MOS tunneling photodiode applications, the photoresponse can be improved by decreasing SiO{sub 2} thickness and using comb-shaped electrodes with smaller tooth spacing. Meantime, the high andmore » steady photosensitivity can also be approached by introducing HfO{sub 2} into dielectric stacks.« less

Bayesian inversion of refraction seismic traveltime data

NASA Astrophysics Data System (ADS)

Ryberg, T.; Haberland, Ch

2018-03-01

We apply a Bayesian Markov chain Monte Carlo (McMC) formalism to the inversion of refraction seismic, traveltime data sets to derive 2-D velocity models below linear arrays (i.e. profiles) of sources and seismic receivers. Typical refraction data sets, especially when using the far-offset observations, are known as having experimental geometries which are very poor, highly ill-posed and far from being ideal. As a consequence, the structural resolution quickly degrades with depth. Conventional inversion techniques, based on regularization, potentially suffer from the choice of appropriate inversion parameters (i.e. number and distribution of cells, starting velocity models, damping and smoothing constraints, data noise level, etc.) and only local model space exploration. McMC techniques are used for exhaustive sampling of the model space without the need of prior knowledge (or assumptions) of inversion parameters, resulting in a large number of models fitting the observations. Statistical analysis of these models allows to derive an average (reference) solution and its standard deviation, thus providing uncertainty estimates of the inversion result. The highly non-linear character of the inversion problem, mainly caused by the experiment geometry, does not allow to derive a reference solution and error map by a simply averaging procedure. We present a modified averaging technique, which excludes parts of the prior distribution in the posterior values due to poor ray coverage, thus providing reliable estimates of inversion model properties even in those parts of the models. The model is discretized by a set of Voronoi polygons (with constant slowness cells) or a triangulated mesh (with interpolation within the triangles). Forward traveltime calculations are performed by a fast, finite-difference-based eikonal solver. The method is applied to a data set from a refraction seismic survey from Northern Namibia and compared to conventional tomography. An inversion test for a synthetic data set from a known model is also presented.

Role of Rayleigh numbers on characteristics of double diffusive salt fingers

NASA Astrophysics Data System (ADS)

Rehman, F.; Singh, O. P.

2018-05-01

Double diffusion convection, driven by two constituents of the fluid with different molecular diffusivity, is widely applied in oceanography and large number of other fields like astrophysics, geology, chemistry and metallurgy. In case of ocean, heat (T) and salinity (S) are the two components with varying diffusivity, where heat diffuses hundred times faster than salt. Component (T) stabilizes the system whereas components (S) destabilizes the system with overall density remains stable and forms the rising and sinking fingers known as salt fingers. Recent observations suggest that salt finger characteristics such as growth rates, wavenumber, and fluxes are strongly depending on the Rayleigh numbers as major driving force. In this paper, we corroborate this observation with the help of experiments, numerical simulations and linear theory. An eigenvalue expression for growth rate is derived from the linearized governing equations with explicit dependence on Rayleigh numbers, density stability ratio, Prandtl number and diffusivity ratio. Expressions for fastest growing fingers are also derived as a function various non-dimensional parameter. The predicted results corroborate well with the data reported from the field measurements, experiments and numerical simulations.

Viscosity-dependent diffusion of fluorescent particles using fluorescence correlation spectroscopy.

PubMed

Jung, Chanbae; Lee, Jaeran; Kang, Manil; Kim, Sok Won

2014-11-01

Fluorescent particles show the variety characteristics by the interaction with other particles and solvent. In order to investigate the relationship between the dynamic properties of fluorescent particles and solvent viscosity, particle diffusion in various solvents was evaluated using a fluorescence correlation spectroscopy. Upon analyzing the correlation functions of AF-647, Q-dot, and beads with different viscosity values, the diffusion time of all particles was observed to increase with increasing solvent viscosity, and the ratio of diffusion time to solvent viscosity, τ D /η, showed a linear dependence on particle size. The particle diffusion coefficients calculated from the diffusion time decreased with increasing solvent viscosity. Further, the hydrodynamic radii of AF-647, Q-dot, and beads were 0.98 ± 0.1 nm, 64.8 ± 3.23 nm, and 89.8 ± 4.91 nm, respectively, revealing a linear dependence on τ D /η, which suggests that the hydrodynamic radius of a particle strongly depends on both the physical size of the particle and solvent viscosity.

Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

PubMed

Ackerman, David M; Wang, Jing; Wendel, Joseph H; Liu, Da-Jiang; Pruski, Marek; Evans, James W

2011-03-21

We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

Imaging and quantification of trans-membrane protein diffusion in living bacteria.

PubMed

Oswald, Felix; L M Bank, Ernst; Bollen, Yves J M; Peterman, Erwin J G

2014-07-07

The cytoplasmic membrane forms the barrier between any cell's interior and the outside world. It contains many proteins that enable essential processes such as the transmission of signals, the uptake of nutrients, and cell division. In the case of prokaryotes, which do not contain intracellular membranes, the cytoplasmic membrane also contains proteins for respiration and protein folding. Mutual interactions and specific localization of these proteins depend on two-dimensional diffusion driven by thermal fluctuations. The experimental investigation of membrane-protein diffusion in bacteria is challenging due to their small size, only a few times larger than the resolution of an optical microscope. Here, we review fluorescence microscopy-based methods to study diffusion of membrane proteins in living bacteria. The main focus is on data-analysis tools to extract diffusion coefficients from single-particle tracking data obtained by single-molecule fluorescence microscopy. We introduce a novel approach, IPODD (inverse projection of displacement distributions), to obtain diffusion coefficients from the usually obtained 2-D projected diffusion trajectories of the highly 3-D curved bacterial membrane. This method provides, in contrast to traditional mean-squared-displacement methods, correct diffusion coefficients and allows unravelling of heterogeneously diffusing populations.

Histogram analysis parameters of apparent diffusion coefficient reflect tumor cellularity and proliferation activity in head and neck squamous cell carcinoma

PubMed Central

Winter, Karsten; Richter, Cindy; Hoehn, Anna-Kathrin

2018-01-01

Our purpose was to analyze associations between apparent diffusion coefficient (ADC) histogram analysis parameters and histopathologicalfeatures in head and neck squamous cell carcinoma (HNSCC). The study involved 32 patients with primary HNSCC. For every tumor, the following histogram analysis parameters were calculated: ADCmean, ADCmax, ADCmin, ADCmedian, ADCmode, P10, P25, P75, P90, kurtosis, skewness, and entropy. Furthermore, proliferation index KI 67, cell count, total and average nucleic areas were estimated. Spearman's correlation coefficient (p) was used to analyze associations between investigated parameters. In overall sample, all ADC values showed moderate inverse correlations with KI 67. All ADC values except ADCmax correlated inversely with tumor cellularity. Slightly correlations were identified between total/average nucleic area and ADCmean, ADCmin, ADCmedian, and P25. In G1/2 tumors, only ADCmode correlated well with Ki67. No statistically significant correlations between ADC parameters and cellularity were found. In G3 tumors, Ki 67 correlated with all ADC parameters except ADCmode. Cell count correlated well with all ADC parameters except ADCmax. Total nucleic area correlated inversely with ADCmean, ADCmin, ADCmedian, P25, and P90. ADC histogram parameters reflect proliferation potential and cellularity in HNSCC. The associations between histopathology and imaging depend on tumor grading. PMID:29805759

Induced polarization: Simulation and inversion of nonlinear mineral electrodics

NASA Astrophysics Data System (ADS)

Agunloye, Olu

1983-02-01

Graph-theoretic representations are used to model nonlinear electrodics, while forward and inverse simulations are based on reaction rate theory. The electrodic responses are presented as distorted elliptical Lissajous shapes obtained from dynamic impedance over a full cycle. Simulations show that asymmetry in reaction energy barrier causes slight asymmetry in the shape of the response ellipse and hardly affects the phase angle of the complex electrode impedance. The charge transfer resistance and the diffusion constraints tend to have opposite effects. The former causes reduction in the phase angle, tending to make the impedance purely resistive. Both of these mechanisms show saturation effects. Charge transfer resistance at its limit forces a thin S-type symmetry on the Lissajous patterns, while with diffusion control the size of the Lissajous patterns begins to reduce after saturation. The fixed layer causes substantial increase in the phase angle and tends to “enlarge” the Lissajous patterns. It is responsible for the hysteresis-like shapes of the Lissajous patterns when superimposed on strong charge transfer resistance. This study shows that it is quite possible to deduce the mechanisms that control the electrodic processes by inverting electrodic parameters from “observed” distorted, nonelliptical Lissajous patterns characteristic of nonlinear electrodics. The results and qualities of the inversion technique are discussed.

Mechanism of Facilitated Diffusion during a DNA Search in Crowded Environments.

PubMed

Krepel, Dana; Gomez, David; Klumpp, Stefan; Levy, Yaakov

2016-11-03

The key feature explaining the rapid recognition of a DNA target site by its protein lies in the combination of one- and three-dimensional (1D and 3D) diffusion, which allows efficient scanning of the many alternative sites. This facilitated diffusion mechanism is expected to be affected by cellular conditions, particularly crowding, given that up to 40% of the total cellular volume may by occupied by macromolecules. Using coarse-grained molecular dynamics and Monte Carlo simulations, we show that the crowding particles can enhance facilitated diffusion and accelerate search kinetics. This effect originates from a trade-off between 3D and 1D diffusion. The 3D diffusion coefficient is lower under crowded conditions, but it has little influence because the excluded volume effect of molecular crowding restricts its use. Largely prevented from using 3D diffusion, the searching protein dramatically increases its use of the hopping search mode, which results in a higher linear diffusion coefficient. The coefficient of linear diffusion also increases under crowded conditions as a result of increased collisions between the crowding particles and the searching protein. Overall, less 3D diffusion coupled with an increase in the use of the hopping and speed of 1D diffusion results in faster search kinetics under crowded conditions. Our study shows that the search kinetics and mechanism are modulated not only by the crowding occupancy but also by the properties of the crowding particles and the salt concentration.

Diffusion in Ordered Alloys, Symposium Held in Chicago, Illinois on November 3 - 4, 1992

DTIC Science & Technology

1992-11-04

calculation of transport proneres The essence of an atomistic theory of diffusion within the linear approximation of the Onsager formalism is to derive...the pair model may be extended to the low temperature range and that this linear behavior exists nearly over the whole temperature range where SRO...being the concentration of the component X. The successive jumps of vacancies are considered to be the elementary process of orde- ring. The jump

Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations

NASA Astrophysics Data System (ADS)

Moghaderi, Hamid; Dehghan, Mehdi; Donatelli, Marco; Mazza, Mariarosa

2017-12-01

Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Grünwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.

Gold Nanoparticle Labels and Heterogeneous Immunoassays: The Case for the Inverted Substrate.

PubMed

Crawford, Alexis C; Young, Colin C; Porter, Marc D

2018-06-15

This paper examines how the difference in the spatial orientation of the capture substrate influences the analytical sensitivity and limits of detection for immunoassays that use gold nanoparticle labels (AuNPs) and rely on diffusion in quiet solution in the antigen capture and labeling steps. Ideally, the accumulation of both reactants should follow a dependence governed by the rate in which diffusion delivers reactants to the capture surface. In other words, the accumulation of reactants should increase with the square root of the incubation time, i.e., t1/2. The work herein shows, however, that this expectation is only obeyed when the capture substrate is oriented to direct the gravity-induced sedimentation of the AuNP labels away from the substrate. Using an assay for human IgG, the results show that circumventing the sedimentation of the gold nanoparticle labels by substrate inversion enables the dependence of the labeling step on diffusion, reduces nonspecific label adsorption, and improves the estimated detection limit by ~30×. High-density maps of the signal across the two types of substrates also demonstrate that inversion in the labeling step results in a more uniform distribution of AuNP labels across the surface, which translates to a greater measurement reproducibility. These results, which are supported by model simulations via the Mason-Weaver sedimentation-diffusion equation, and their potential implications when using other nanoparticle labels and related materials in diagnostic tests and other applications, are briefly discussed.

NMR Water Self–Diffusion and Relaxation Studies on Sodium Polyacrylate Solutions and Gels in Physiologic Ionic Solutions

PubMed Central

Bai, Ruiliang; Basser, Peter J.; Briber, Robert M.; Horkay, Ferenc

2013-01-01

Water self-diffusion coefficients and longitudinal relaxation rates in sodium polyacrylate solutions and gels were measured by NMR, as a function of polymer content and structure in a physiological concentration range of monovalent and divalent cations, Ca2+ and Na+. Several physical models describing the self-diffusion of the solvent were applied and compared. A free-volume model was found to be in good agreement with the experimental results over a wide range of polymer concentrations. The longitudinal relaxation rate exhibited linear dependence on polymer concentration below a critical concentration and showed non-linear behavior at higher concentrations. Both the water self-diffusion and relaxation were less influenced by the polymer in the gel state than in the uncrosslinked polymer solutions. The effect of Na+ on the mobility of water molecules was practically undetectable. By contrast, addition of Ca2+ strongly increased the longitudinal relaxation rate while its effect on the self-diffusion coefficient was much less pronounced. PMID:24409001

NMR Water Self-Diffusion and Relaxation Studies on Sodium Polyacrylate Solutions and Gels in Physiologic Ionic Solutions.

PubMed

Bai, Ruiliang; Basser, Peter J; Briber, Robert M; Horkay, Ferenc

2014-03-15

Water self-diffusion coefficients and longitudinal relaxation rates in sodium polyacrylate solutions and gels were measured by NMR, as a function of polymer content and structure in a physiological concentration range of monovalent and divalent cations, Ca 2+ and Na + . Several physical models describing the self-diffusion of the solvent were applied and compared. A free-volume model was found to be in good agreement with the experimental results over a wide range of polymer concentrations. The longitudinal relaxation rate exhibited linear dependence on polymer concentration below a critical concentration and showed non-linear behavior at higher concentrations. Both the water self-diffusion and relaxation were less influenced by the polymer in the gel state than in the uncrosslinked polymer solutions. The effect of Na + on the mobility of water molecules was practically undetectable. By contrast, addition of Ca 2+ strongly increased the longitudinal relaxation rate while its effect on the self-diffusion coefficient was much less pronounced.

The effects of nutrient chemotaxis on bacterial aggregation patterns with non-linear degenerate cross diffusion

NASA Astrophysics Data System (ADS)

Leyva, J. Francisco; Málaga, Carlos; Plaza, Ramón G.

2013-11-01

This paper studies a reaction-diffusion-chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (1997) [5] and it includes a suitable nutrient chemotactic term compatible with such type of diffusion, as suggested by Ben-Jacob et al. (2000) [20]. An asymptotic estimation predicts the growth velocity of the colony envelope as a function of both the nutrient concentration and the chemotactic sensitivity. It is shown that the growth velocity is an increasing function of the chemotactic sensitivity. High resolution numerical simulations using Graphic Processing Units (GPUs), which include noise in the diffusion coefficient for the bacteria, are presented. The numerical results verify that the chemotactic term enhances the velocity of propagation of the colony envelope. In addition, the chemotaxis seems to stabilize the formation of branches in the soft-agar, low-nutrient regime.

Cross-Diffusion Driven Instability for a Lotka-Volterra Competitive Reaction-Diffusion System

NASA Astrophysics Data System (ADS)

Gambino, G.; Lombardo, M. C.; Sammartino, M.

2008-04-01

In this work we investigate the possibility of the pattern formation for a reaction-diffusion system with nonlinear diffusion terms. Through a linear stability analysis we find the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show how cross-diffusion effects are responsible for the initiation of spatial patterns. Finally, we find a Fisher amplitude equation which describes the weakly nonlinear dynamics of the system near the marginal stability.

Hybrid finite element and Brownian dynamics method for diffusion-controlled reactions.

PubMed

Bauler, Patricia; Huber, Gary A; McCammon, J Andrew

2012-04-28

Diffusion is often the rate determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetric diffusion systems.

Effect of various binning methods and ROI sizes on the accuracy of the automatic classification system for differentiation between diffuse infiltrative lung diseases on the basis of texture features at HRCT

NASA Astrophysics Data System (ADS)

Kim, Namkug; Seo, Joon Beom; Sung, Yu Sub; Park, Bum-Woo; Lee, Youngjoo; Park, Seong Hoon; Lee, Young Kyung; Kang, Suk-Ho

2008-03-01

To find optimal binning, variable binning size linear binning (LB) and non-linear binning (NLB) methods were tested. In case of small binning size (Q <= 10), NLB shows significant better accuracy than the LB. K-means NLB (Q = 26) is statistically significant better than every LB. To find optimal binning method and ROI size of the automatic classification system for differentiation between diffuse infiltrative lung diseases on the basis of textural analysis at HRCT Six-hundred circular regions of interest (ROI) with 10, 20, and 30 pixel diameter, comprising of each 100 ROIs representing six regional disease patterns (normal, NL; ground-glass opacity, GGO; reticular opacity, RO; honeycombing, HC; emphysema, EMPH; and consolidation, CONS) were marked by an experienced radiologist from HRCT images. Histogram (mean) and co-occurrence matrix (mean and SD of angular second moment, contrast, correlation, entropy, and inverse difference momentum) features were employed to test binning and ROI effects. To find optimal binning, variable binning size LB (bin size Q: 4~30, 32, 64, 128, 144, 196, 256, 384) and NLB (Q: 4~30) methods (K-means, and Fuzzy C-means clustering) were tested. For automated classification, a SVM classifier was implemented. To assess cross-validation of the system, a five-folding method was used. Each test was repeatedly performed twenty times. Overall accuracies with every combination of variable ROIs, and binning sizes were statistically compared. In case of small binning size (Q <= 10), NLB shows significant better accuracy than the LB. K-means NLB (Q = 26) is statistically significant better than every LB. In case of 30x30 ROI size and most of binning size, the K-means method showed better than other NLB and LB methods. When optimal binning and other parameters were set, overall sensitivity of the classifier was 92.85%. The sensitivity and specificity of the system for each class were as follows: NL, 95%, 97.9%; GGO, 80%, 98.9%; RO 85%, 96.9%; HC, 94.7%, 97%; EMPH, 100%, 100%; and CONS, 100%, 100%, respectively. We determined the optimal binning method and ROI size of the automatic classification system for differentiation between diffuse infiltrative lung diseases on the basis of texture features at HRCT.

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

NASA Astrophysics Data System (ADS)

de Almeida, Valmor F.

2017-07-01

A phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equation and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.

Effect of biochar particle size on hydrophobic organic compound sorption kinetics: Applicability of using representative size.

PubMed

Kang, Seju; Jung, Jihyeun; Choe, Jong Kwon; Ok, Yong Sik; Choi, Yongju

2018-04-01

Particle size of biochar may strongly affect the kinetics of hydrophobic organic compound (HOC) sorption. However, challenges exist in characterizing the effect of biochar particle size on the sorption kinetics because of the wide size range of biochar. The present study suggests a novel method to determine a representative value that can be used to show the dependence of HOC sorption kinetics to biochar particle size on the basis of an intra-particle diffusion model. Biochars derived from three different feedstocks are ground and sieved to obtain three daughter products each having different size distributions. Phenanthrene sorption kinetics to the biochars are well described by the intra-particle diffusion model with significantly greater sorption rates observed for finer grained biochars. The time to reach 95% of equilibrium for phenanthrene sorption to biochar is reduced from 4.6-17.9days for the original biochars to <1-4.6days for the powdered biochars with <125μm in size. A moderate linear correlation is found between the inverse square of the representative biochar particle radius obtained using particle size distribution analysis and the apparent phenanthrene sorption rates determined by the sorption kinetics experiments and normalized to account for the variation of the sorption rate-determining factors other than the biochar particle radius. The results suggest that the representative biochar particle radius reasonably describes the dependence of HOC sorption rates on biochar particle size. Copyright © 2017 Elsevier B.V. All rights reserved.

Fermi LAT Observation of Diffuse Gamma Rays Produced Through Interactions Between Local Interstellar Matter and High-Energy Cosmic Rays

DOE PAGES

Abdo, A. A.; Ackermann, M.; Ajello, M.; ...

2009-09-08

Observations by the Large Area Telescope (LAT) on the Fermi mission of diffuse γ-rays in a mid-latitude region in the third quadrant (Galactic longitude l from 200° to 260° and latitude |b| from 22° to 60°) are reported in this paper. The region contains no known large molecular cloud and most of the atomic hydrogen is within 1 kpc of the solar system. The contributions of γ-ray point sources and inverse Compton scattering are estimated and subtracted. The residual γ-ray intensity exhibits a linear correlation with the atomic gas column density in energy from 100 MeV to 10 GeV. Themore » measured integrated γ-ray emissivity is (1.63 ± 0.05) × 10 –26 photons s –1sr –1 H-atom –1 and (0.66 ± 0.02) × 10 –26 photons s –1sr –1 H-atom –1 above 100 MeV and above 300 MeV, respectively, with an additional systematic error of ~10%. The differential emissivity from 100 MeV to 10 GeV agrees with calculations based on cosmic ray spectra consistent with those directly measured, at the 10% level. Finally, the results obtained indicate that cosmic ray nuclei spectra within 1 kpc from the solar system in regions studied are close to the local interstellar spectra inferred from direct measurements at the Earth within ~10%.« less

High-temperature dynamic behavior in bulk liquid water: A molecular dynamics simulation study using the OPC and TIP4P-Ew potentials

NASA Astrophysics Data System (ADS)

Gabrieli, Andrea; Sant, Marco; Izadi, Saeed; Shabane, Parviz Seifpanahi; Onufriev, Alexey V.; Suffritti, Giuseppe B.

2018-02-01

Classical molecular dynamics simulations were performed to study the high-temperature (above 300 K) dynamic behavior of bulk water, specifically the behavior of the diffusion coefficient, hydrogen bond, and nearest-neighbor lifetimes. Two water potentials were compared: the recently proposed "globally optimal" point charge (OPC) model and the well-known TIP4P-Ew model. By considering the Arrhenius plots of the computed inverse diffusion coefficient and rotational relaxation constants, a crossover from Vogel-Fulcher-Tammann behavior to a linear trend with increasing temperature was detected at T* ≈ 309 and T* ≈ 285 K for the OPC and TIP4P-Ew models, respectively. Experimentally, the crossover point was previously observed at T* ± 315-5 K. We also verified that for the coefficient of thermal expansion α P ( T, P), the isobaric α P ( T) curves cross at about the same T* as in the experiment. The lifetimes of water hydrogen bonds and of the nearest neighbors were evaluated and were found to cross near T*, where the lifetimes are about 1 ps. For T < T*, hydrogen bonds persist longer than nearest neighbors, suggesting that the hydrogen bonding network dominates the water structure at T < T*, whereas for T > T*, water behaves more like a simple liquid. The fact that T* falls within the biologically relevant temperature range is a strong motivation for further analysis of the phenomenon and its possible consequences for biomolecular systems.

Fermi LAT Observation of Diffuse Gamma-Rays Produced through Interactions Between Local Interstellar Matter and High Energy Cosmic Rays

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

Abdo, A.A.; /Naval Research Lab, Wash., D.C. /Federal City Coll.; Ackermann, M.

Observations by the Large Area Telescope (LAT) on the Fermi mission of diffuse {gamma}-rays in a mid-latitude region in the third quadrant (Galactic longitude l from 200{sup o} to 260{sup o} and latitude |b| from 22{sup o} to 60{sup o}) are reported. The region contains no known large molecular cloud and most of the atomic hydrogen is within 1 kpc of the solar system. The contributions of {gamma}-ray point sources and inverse Compton scattering are estimated and subtracted. The residual {gamma}-ray intensity exhibits a linear correlation with the atomic gas column density in energy from 100 MeV to 10 GeV.more » The measured integrated {gamma}-ray emissivity is (1.63 {+-} 0.05) x 10{sup -26} photons s{sup -1}sr{sup -1} H-atom{sup -1} and (0.66 {+-} 0.02) x 10{sup -26} photons s{sup -1}sr{sup -1} H-atom{sup -1} above 100 MeV and above 300 MeV, respectively, with an additional systematic error of {approx}10%. The differential emissivity from 100 MeV to 10 GeV agrees with calculations based on cosmic ray spectra consistent with those directly measured, at the 10% level. The results obtained indicate that cosmic ray nuclei spectra within 1 kpc from the solar system in regions studied are close to the local interstellar spectra inferred from direct measurements at the Earth within {approx}10%.« less

A fast and accurate imaging algorithm in optical/diffusion tomography

NASA Astrophysics Data System (ADS)

Klibanov, M. V.; Lucas, T. R.; Frank, R. M.

1997-10-01

An n-dimensional (n = 2,3) inverse problem for the parabolic/diffusion equation 0266-5611/13/5/015/img1, 0266-5611/13/5/015/img2, 0266-5611/13/5/015/img3, 0266-5611/13/5/015/img4 is considered. The problem consists of determining the function a(x) inside of a bounded domain 0266-5611/13/5/015/img5 given the values of the solution u(x,t) for a single source location 0266-5611/13/5/015/img6 on a set of detectors 0266-5611/13/5/015/img7, where 0266-5611/13/5/015/img8 is the boundary of 0266-5611/13/5/015/img9. A novel numerical method is derived and tested. Numerical tests are conducted for n = 2 and for ranges of parameters which are realistic for applications to early breast cancer diagnosis and the search for mines in murky shallow water using ultrafast laser pulses. The main innovation of this method lies in a new approach for a novel linearized problem (LP). Such a LP is derived and reduced to a well-posed boundary-value problem for a coupled system of elliptic partial differential equations. A principal advantage of this technique is in its speed and accuracy, since it leads to the factorization of well conditioned, sparse matrices with non-zero entries clustered in a narrow band near the diagonal. The authors call this approach the elliptic systems method (ESM). The ESM can be extended to other imaging modalities.

Teaching Linear Algebra: Proceeding More Efficiently by Staying Comfortably within Z

ERIC Educational Resources Information Center

Beaver, Scott

2015-01-01

For efficiency in a linear algebra course the instructor may wish to avoid the undue arithmetical distractions of rational arithmetic. In this paper we explore how to write fraction-free problems of various types including elimination, matrix inverses, orthogonality, and the (non-normalizing) Gram-Schmidt process.

A Nth-order linear algorithm for extracting diffuse correlation spectroscopy blood flow indices in heterogeneous tissues.

PubMed

Shang, Yu; Yu, Guoqiang

2014-09-29

Conventional semi-infinite analytical solutions of correlation diffusion equation may lead to errors when calculating blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements in tissues with irregular geometries. Very recently, we created an algorithm integrating a N th-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in homogenous tissues with arbitrary geometries for extraction of BFI (i.e., αD B ). The purpose of this study is to extend the capability of the N th-order linear algorithm for extracting BFI in heterogeneous tissues with arbitrary geometries. The previous linear algorithm was modified to extract BFIs in different types of tissues simultaneously through utilizing DCS data at multiple source-detector separations. We compared the proposed linear algorithm with the semi-infinite homogenous solution in a computer model of adult head with heterogeneous tissue layers of scalp, skull, cerebrospinal fluid, and brain. To test the capability of the linear algorithm for extracting relative changes of cerebral blood flow (rCBF) in deep brain, we assigned ten levels of αD B in the brain layer with a step decrement of 10% while maintaining αD B values constant in other layers. Simulation results demonstrate the accuracy (errors < 3%) of high-order ( N  ≥ 5) linear algorithm in extracting BFIs in different tissue layers and rCBF in deep brain. By contrast, the semi-infinite homogenous solution resulted in substantial errors in rCBF (34.5% ≤ errors ≤ 60.2%) and BFIs in different layers. The N th-order linear model simplifies data analysis, thus allowing for online data processing and displaying. Future study will test this linear algorithm in heterogeneous tissues with different levels of blood flow variations and noises.

Very Efficient High-order Hyperbolic Schemes for Time-dependent Advection Diffusion Problems: Third-, Fourth-, and Sixth-order

DTIC Science & Technology

2014-07-07

boundary condition (x ¼ 7p =2; j ¼ 2p; U ¼ 1; m ¼ 1) on N ¼ 10 uniform nodes (Dt ¼ 0:01.) Table 10 Unsteady linear advection–diffusion problem with periodic...500 3rd 55 2 4th 55 2 6th 55 2 1000 3rd 116 2 4th 116 2 6th 116 2 Table 11 Unsteady linear advection–diffusion problem with oscillatory BC (x ¼ 7p =2; a...dependent problem with oscillatory BC (x ¼ 7p =2; a ¼ 1.) using the third-order RD-GT scheme with the BDF3 time discretization. Number of nodes Dt (BDF3

Scalar rate correlation at a turbulent liquid free surface - A two-regime correlation for high Schmidt numbers

NASA Technical Reports Server (NTRS)

Khoo, Boo-Cheong; Sonin, Ain A.

1992-01-01

An experimental correlation is derived for gas absorption at a turbulent, shear-free liquid interface. The correlation is expressed in terms of the liquid-side turbulence intensity, liquid-side macroscale, and the properties of the diffusing gas and solvent. The transfer coefficient increases linearly with rms velocity up to a point where the eddy Reynolds number reaches a critical (Schmidt number dependent) value. At higher velocities, there is a more rapid linear rise. The slope of the lower Reynolds number region is proportional to the square root of the diffusivity; at Reynolds numbers much higher than that of the break point, the slope becomes independent of diffusivity.

Finite linear diffusion model for design of overcharge protection for rechargeable lithium batteries

NASA Technical Reports Server (NTRS)

Narayanan, S. R.; Surampudi, S.; Attia, A. I.

1991-01-01

The overcharge condition in secondary lithium batteries employing redox additives for overcharge protection has been theoretically analyzed in terms of a finite linear diffusion model. The analysis leads to expressions relating the steady-state overcharge current density and cell voltage to the concentration, diffusion coefficient, standard reduction potential of the redox couple, and interelectrode distance. The model permits the estimation of the maximum permissible overcharge rate for any chosen set of system conditions. The model has been experimentally verified using 1,1-prime-dimethylferrocene as a redox additive. The theoretical results may be exploited in the design and optimization of overcharge protection by the redox additive approach.

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

Building Generalized Inverses of Matrices Using Only Row and Column Operations

ERIC Educational Resources Information Center

Stuart, Jeffrey

2010-01-01

Most students complete their first and only course in linear algebra with the understanding that a real, square matrix "A" has an inverse if and only if "rref"("A"), the reduced row echelon form of "A", is the identity matrix I[subscript n]. That is, if they apply elementary row operations via the Gauss-Jordan algorithm to the partitioned matrix…

[Research on the method of interference correction for nondispersive infrared multi-component gas analysis].

PubMed

Sun, You-Wen; Liu, Wen-Qing; Wang, Shi-Mei; Huang, Shu-Hua; Yu, Xiao-Man

2011-10-01

A method of interference correction for nondispersive infrared multi-component gas analysis was described. According to the successive integral gas absorption models and methods, the influence of temperature and air pressure on the integral line strengths and linetype was considered, and based on Lorentz detuning linetypes, the absorption cross sections and response coefficients of H2O, CO2, CO, and NO on each filter channel were obtained. The four dimension linear regression equations for interference correction were established by response coefficients, the absorption cross interference was corrected by solving the multi-dimensional linear regression equations, and after interference correction, the pure absorbance signal on each filter channel was only controlled by the corresponding target gas concentration. When the sample cell was filled with gas mixture with a certain concentration proportion of CO, NO and CO2, the pure absorbance after interference correction was used for concentration inversion, the inversion concentration error for CO2 is 2.0%, the inversion concentration error for CO is 1.6%, and the inversion concentration error for NO is 1.7%. Both the theory and experiment prove that the interference correction method proposed for NDIR multi-component gas analysis is feasible.

A function space framework for structural total variation regularization with applications in inverse problems

NASA Astrophysics Data System (ADS)

Hintermüller, Michael; Holler, Martin; Papafitsoros, Kostas

2018-06-01

In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is the appropriate lower semi-continuous envelope (relaxation) of a suitable TV type functional initially defined for sufficiently smooth functions. We study examples where this relaxation can be expressed explicitly, and we also provide refinements for weighted TV for a wide range of weights. Since an integral characterization of the relaxation in function space is, in general, not always available, we show that, for a rather general linear inverse problems setting, instead of the classical Tikhonov regularization problem, one can equivalently solve a saddle-point problem where no a priori knowledge of an explicit formulation of the structural TV functional is needed. In particular, motivated by concrete applications, we deduce corresponding results for linear inverse problems with norm and Poisson log-likelihood data discrepancy terms. Finally, we provide proof-of-concept numerical examples where we solve the saddle-point problem for weighted TV denoising as well as for MR guided PET image reconstruction.

Isotropic probability measures in infinite dimensional spaces: Inverse problems/prior information/stochastic inversion

NASA Technical Reports Server (NTRS)

Backus, George

1987-01-01

Let R be the real numbers, R(n) the linear space of all real n-tuples, and R(infinity) the linear space of all infinite real sequences x = (x sub 1, x sub 2,...). Let P sub n :R(infinity) approaches R(n) be the projection operator with P sub n (x) = (x sub 1,...,x sub n). Let p(infinity) be a probability measure on the smallest sigma-ring of subsets of R(infinity) which includes all of the cylinder sets P sub n(-1) (B sub n), where B sub n is an arbitrary Borel subset of R(n). Let p sub n be the marginal distribution of p(infinity) on R(n), so p sub n(B sub n) = p(infinity)(P sub n to the -1(B sub n)) for each B sub n. A measure on R(n) is isotropic if it is invariant under all orthogonal transformations of R(n). All members of the set of all isotropic probability distributions on R(n) are described. The result calls into question both stochastic inversion and Bayesian inference, as currently used in many geophysical inverse problems.

Fast inverse scattering solutions using the distorted Born iterative method and the multilevel fast multipole algorithm

PubMed Central

Hesford, Andrew J.; Chew, Weng C.

2010-01-01

The distorted Born iterative method (DBIM) computes iterative solutions to nonlinear inverse scattering problems through successive linear approximations. By decomposing the scattered field into a superposition of scattering by an inhomogeneous background and by a material perturbation, large or high-contrast variations in medium properties can be imaged through iterations that are each subject to the distorted Born approximation. However, the need to repeatedly compute forward solutions still imposes a very heavy computational burden. To ameliorate this problem, the multilevel fast multipole algorithm (MLFMA) has been applied as a forward solver within the DBIM. The MLFMA computes forward solutions in linear time for volumetric scatterers. The typically regular distribution and shape of scattering elements in the inverse scattering problem allow the method to take advantage of data redundancy and reduce the computational demands of the normally expensive MLFMA setup. Additional benefits are gained by employing Kaczmarz-like iterations, where partial measurements are used to accelerate convergence. Numerical results demonstrate both the efficiency of the forward solver and the successful application of the inverse method to imaging problems with dimensions in the neighborhood of ten wavelengths. PMID:20707438

Azimuthal Seismic Amplitude Variation with Offset and Azimuth Inversion in Weakly Anisotropic Media with Orthorhombic Symmetry

NASA Astrophysics Data System (ADS)

Pan, Xinpeng; Zhang, Guangzhi; Yin, Xingyao

2018-01-01

Seismic amplitude variation with offset and azimuth (AVOaz) inversion is well known as a popular and pragmatic tool utilized to estimate fracture parameters. A single set of vertical fractures aligned along a preferred horizontal direction embedded in a horizontally layered medium can be considered as an effective long-wavelength orthorhombic medium. Estimation of Thomsen's weak-anisotropy (WA) parameters and fracture weaknesses plays an important role in characterizing the orthorhombic anisotropy in a weakly anisotropic medium. Our goal is to demonstrate an orthorhombic anisotropic AVOaz inversion approach to describe the orthorhombic anisotropy utilizing the observable wide-azimuth seismic reflection data in a fractured reservoir with the assumption of orthorhombic symmetry. Combining Thomsen's WA theory and linear-slip model, we first derive a perturbation in stiffness matrix of a weakly anisotropic medium with orthorhombic symmetry under the assumption of small WA parameters and fracture weaknesses. Using the perturbation matrix and scattering function, we then derive an expression for linearized PP-wave reflection coefficient in terms of P- and S-wave moduli, density, Thomsen's WA parameters, and fracture weaknesses in such an orthorhombic medium, which avoids the complicated nonlinear relationship between the orthorhombic anisotropy and azimuthal seismic reflection data. Incorporating azimuthal seismic data and Bayesian inversion theory, the maximum a posteriori solutions of Thomsen's WA parameters and fracture weaknesses in a weakly anisotropic medium with orthorhombic symmetry are reasonably estimated with the constraints of Cauchy a priori probability distribution and smooth initial models of model parameters to enhance the inversion resolution and the nonlinear iteratively reweighted least squares strategy. The synthetic examples containing a moderate noise demonstrate the feasibility of the derived orthorhombic anisotropic AVOaz inversion method, and the real data illustrate the inversion stabilities of orthorhombic anisotropy in a fractured reservoir.

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.

Influence of magnetic flutter on tearing growth in linear and nonlinear theory

NASA Astrophysics Data System (ADS)

Kreifels, L.; Hornsby, W. A.; Weikl, A.; Peeters, A. G.

2018-06-01

Recent simulations of tearing modes in turbulent regimes show an unexpected enhancement in the growth rate. In this paper the effect is investigated analytically. The enhancement is linked to the influence of turbulent magnetic flutter, which is modelled by diffusion terms in magnetohydrodynamics (MHD) momentum balance and Ohm’s law. Expressions for the linear growth rate as well as the island width in nonlinear theory for small amplitudes are derived. The results indicate an enhanced linear growth rate and a larger linear layer width compared with resistive MHD. Also the island width in the nonlinear regime grows faster in the diffusive model. These observations correspond well to simulations in which the effect of turbulence on the magnetic island width and tearing mode growth is analyzed.

Measurement of effective air diffusion coefficients for trichloroethene in undisturbed soil cores.

PubMed

Bartelt-Hunt, Shannon L; Smith, James A

2002-06-01

In this study, we measure effective diffusion coefficients for trichloroethene in undisturbed soil samples taken from Picatinny Arsenal, New Jersey. The measured effective diffusion coefficients ranged from 0.0053 to 0.0609 cm2/s over a range of air-filled porosity of 0.23-0.49. The experimental data were compared to several previously published relations that predict diffusion coefficients as a function of air-filled porosity and porosity. A multiple linear regression analysis was developed to determine if a modification of the exponents in Millington's [Science 130 (1959) 100] relation would better fit the experimental data. The literature relations appeared to generally underpredict the effective diffusion coefficient for the soil cores studied in this work. Inclusion of a particle-size distribution parameter, d10, did not significantly improve the fit of the linear regression equation. The effective diffusion coefficient and porosity data were used to recalculate estimates of diffusive flux through the subsurface made in a previous study performed at the field site. It was determined that the method of calculation used in the previous study resulted in an underprediction of diffusive flux from the subsurface. We conclude that although Millington's [Science 130 (1959) 100] relation works well to predict effective diffusion coefficients in homogeneous soils with relatively uniform particle-size distributions, it may be inaccurate for many natural soils with heterogeneous structure and/or non-uniform particle-size distributions.

Nonlinear extension of a hemodynamic linear model for coherent hemodynamics spectroscopy.

PubMed

Sassaroli, Angelo; Kainerstorfer, Jana M; Fantini, Sergio

2016-01-21

In this work, we are proposing an extension of a recent hemodynamic model (Fantini, 2014a), which was developed within the framework of a novel approach to the study of tissue hemodynamics, named coherent hemodynamics spectroscopy (CHS). The previous hemodynamic model, from a signal processing viewpoint, treats the tissue microvasculature as a linear time-invariant system, and considers changes of blood volume, capillary blood flow velocity and the rate of oxygen diffusion as inputs, and the changes of oxy-, deoxy-, and total hemoglobin concentrations (measured in near infrared spectroscopy) as outputs. The model has been used also as a forward solver in an inversion procedure to retrieve quantitative parameters that assess physiological and biological processes such as microcirculation, cerebral autoregulation, tissue metabolic rate of oxygen, and oxygen extraction fraction. Within the assumption of "small" capillary blood flow velocity oscillations the model showed that the capillary and venous compartments "respond" to this input as low pass filters, characterized by two distinct impulse response functions. In this work, we do not make the assumption of "small" perturbations of capillary blood flow velocity by solving without approximations the partial differential equation that governs the spatio-temporal behavior of hemoglobin saturation in capillary and venous blood. Preliminary comparison between the linear time-invariant model and the extended model (here identified as nonlinear model) are shown for the relevant parameters measured in CHS as a function of the oscillation frequency (CHS spectra). We have found that for capillary blood flow velocity oscillations with amplitudes up to 10% of the baseline value (which reflect typical scenarios in CHS), the discrepancies between CHS spectra obtained with the linear and nonlinear models are negligible. For larger oscillations (~50%) the linear and nonlinear models yield CHS spectra with differences within typical experimental errors, but further investigation is needed to assess the effect of these differences. Flow oscillations larger than 10-20% are not typically induced in CHS; therefore, the results presented in this work indicate that a linear hemodynamic model, combined with a method to elicit controlled hemodynamic oscillations (as done for CHS), is appropriate for the quantitative assessment of cerebral microcirculation. Copyright © 2015 Elsevier Ltd. All rights reserved.

Back-bombardment compensation in microwave thermionic electron guns

NASA Astrophysics Data System (ADS)

Kowalczyk, Jeremy M. D.; Madey, John M. J.

2014-12-01

The development of capable, reliable, and cost-effective compact electron beam sources remains a long-standing objective of the efforts to develop the accelerator systems needed for on-site research and industrial applications ranging from electron beam welding to high performance x-ray and gamma ray light sources for element-resolved microanalysis and national security. The need in these applications for simplicity, reliability, and low cost has emphasized solutions compatible with the use of the long established and commercially available pulsed microwave rf sources and L-, S- or X-band linear accelerators. Thermionic microwave electron guns have proven to be one successful approach to the development of the electron sources for these systems providing high macropulse average current beams with picosecond pulse lengths and good emittance out to macropulse lengths of 4-5 microseconds. But longer macropulse lengths are now needed for use in inverse-Compton x-ray sources and other emerging applications. We describe in this paper our approach to extending the usable macropulse current and pulse length of these guns through the use of thermal diffusion to compensate for the increase in cathode surface temperature due to back-bombardment.

White matter lesions relate to tract-specific reductions in functional connectivity.

PubMed

Langen, Carolyn D; Zonneveld, Hazel I; White, Tonya; Huizinga, Wyke; Cremers, Lotte G M; de Groot, Marius; Ikram, Mohammad Arfan; Niessen, Wiro J; Vernooij, Meike W

2017-03-01

White matter lesions play a role in cognitive decline and dementia. One presumed pathway is through disconnection of functional networks. Little is known about location-specific effects of lesions on functional connectivity. This study examined location-specific effects within anatomically-defined white matter tracts in 1584 participants of the Rotterdam Study, aged 50-95. Tracts were delineated from diffusion magnetic resonance images using probabilistic tractography. Lesions were segmented on fluid-attenuated inversion recovery images. Functional connectivity was defined across each tract on resting-state functional magnetic resonance images by using gray matter parcellations corresponding to the tract ends and calculating the correlation of the mean functional activity between the gray matter regions. A significant relationship between both local and brain-wide lesion load and tract-specific functional connectivity was found in several tracts using linear regressions, also after Bonferroni correction. Indirect connectivity analyses revealed that tract-specific functional connectivity is affected by lesions in several tracts simultaneously. These results suggest that local white matter lesions can decrease tract-specific functional connectivity, both in direct and indirect connections. Copyright © 2016 Elsevier Inc. All rights reserved.

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.

Inversion Of Jacobian Matrix For Robot Manipulators

NASA Technical Reports Server (NTRS)

Fijany, Amir; Bejczy, Antal K.

1989-01-01

Report discusses inversion of Jacobian matrix for class of six-degree-of-freedom arms with spherical wrist, i.e., with last three joints intersecting. Shows by taking advantage of simple geometry of such arms, closed-form solution of Q=J-1X, which represents linear transformation from task space to joint space, obtained efficiently. Presents solutions for PUMA arm, JPL/Stanford arm, and six-revolute-joint coplanar arm along with all singular points. Main contribution of paper shows simple geometry of this type of arms exploited in performing inverse transformation without any need to compute Jacobian or its inverse explicitly. Implication of this computational efficiency advanced task-space control schemes for spherical-wrist arms implemented more efficiently.

Recursive inverse factorization.

PubMed

Rubensson, Emanuel H; Bock, Nicolas; Holmström, Erik; Niklasson, Anders M N

2008-03-14

A recursive algorithm for the inverse factorization S(-1)=ZZ(*) of Hermitian positive definite matrices S is proposed. The inverse factorization is based on iterative refinement [A.M.N. Niklasson, Phys. Rev. B 70, 193102 (2004)] combined with a recursive decomposition of S. As the computational kernel is matrix-matrix multiplication, the algorithm can be parallelized and the computational effort increases linearly with system size for systems with sufficiently sparse matrices. Recent advances in network theory are used to find appropriate recursive decompositions. We show that optimization of the so-called network modularity results in an improved partitioning compared to other approaches. In particular, when the recursive inverse factorization is applied to overlap matrices of irregularly structured three-dimensional molecules.

Preliminary assessment of the robustness of dynamic inversion based flight control laws

NASA Technical Reports Server (NTRS)

Snell, S. A.

1992-01-01

Dynamic-inversion-based flight control laws present an attractive alternative to conventional gain-scheduled designs for high angle-of-attack maneuvering, where nonlinearities dominate the dynamics. Dynamic inversion is easily applied to the aircraft dynamics requiring a knowledge of the nonlinear equations of motion alone, rather than an extensive set of linearizations. However, the robustness properties of the dynamic inversion are questionable especially when considering the uncertainties involved with the aerodynamic database during post-stall flight. This paper presents a simple analysis and some preliminary results of simulations with a perturbed database. It is shown that incorporating integrators into the control loops helps to improve the performance in the presence of these perturbations.

Quantifying residual, eddy, and mean flow effects on mixing in an idealized circumpolar current

DOE PAGES

Wolfram, Phillip J.; Ringler, Todd D.

2017-07-13

Meridional diffusivity is assessed in this paper for a baroclinically unstable jet in a high-latitudeIdealized Circumpolar Current (ICC) using the Model for Prediction Across Scales-Ocean (MPAS-O) and the online Lagrangian In-situ Global High-performance particle Tracking (LIGHT) diagnostic via space-time dispersion of particle clusters over 120 monthly realizations of O(10 6) particles on 11 potential density surfaces. Diffusivity in the jet reaches values of O(6000 m 2 s -1) and is largest near the critical layer supporting mixing suppression and critical layer theory. Values in the vicinity of the shelf break are suppressed to O(100 m 2 s -1) due tomore » the presence of westward slope front currents. Diffusivity attenuates less rapidly with depth in the jet than both eddy velocity and kinetic energy scalings would suggest. Removal of the mean flow via high-pass filtering shifts the nonlinear parameter (ratio of the eddy velocity to eddy phase speed) into the linear wave regime by increasing the eddy phase speed via the depth-mean flow. Low-pass filtering, in contrast, quantifies the effect of mean shear. Diffusivity is decomposed into mean flow shear, linear waves, and the residual nonhomogeneous turbulence components, where turbulence dominates and eddy-produced filamentation strained by background mean shear enhances mixing, accounting for ≥ 80% of the total diffusivity relative to mean shear [O(100 m 2 s -1)], linear waves [O(1000 m 2 s -1)], and undecomposed full diffusivity [O(6000 m 2 s -1)]. Finally, diffusivity parameterizations accounting for both the nonhomogeneous turbulence residual and depth variability are needed.« less

Inverse Algorithm Optimization for Determining Optical Properties of Biological Materials from Spatially-Resolved Diffuse Reflectance

USDA-ARS?s Scientific Manuscript database

Optical characterization of biological materials is useful in many scientific and industrial applications like biomedical diagnosis and nondestructive quality evaluation of food and agricultural products. However, accurate determination of the optical properties from intact biological materials base...

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.

Choice of crystal surface finishing for a dual-ended readout depth-of-interaction (DOI) detector.

PubMed

Fan, Peng; Ma, Tianyu; Wei, Qingyang; Yao, Rutao; Liu, Yaqiang; Wang, Shi

2016-02-07

The objective of this study was to choose the crystal surface finishing for a dual-ended readout (DER) DOI detector. Through Monte Carlo simulations and experimental studies, we evaluated 4 crystal surface finishing options as combinations of crystal surface polishing (diffuse or specular) and reflector (diffuse or specular) options on a DER detector. We also tested one linear and one logarithm DOI calculation algorithm. The figures of merit used were DOI resolution, DOI positioning error, and energy resolution. Both the simulation and experimental results show that (1) choosing a diffuse type in either surface polishing or reflector would improve DOI resolution but degrade energy resolution; (2) crystal surface finishing with a diffuse polishing combined with a specular reflector appears a favorable candidate with a good balance of DOI and energy resolution; and (3) the linear and logarithm DOI calculation algorithms show overall comparable DOI error, and the linear algorithm was better for photon interactions near the ends of the crystal while the logarithm algorithm was better near the center. These results provide useful guidance in DER DOI detector design in choosing the crystal surface finishing and DOI calculation methods.

Kinetics of diffusion-controlled annihilation with sparse initial conditions

DOE PAGES

Ben-Naim, Eli; Krapivsky, Paul

2016-12-16

Here, we study diffusion-controlled single-species annihilation with sparse initial conditions. In this random process, particles undergo Brownian motion, and when two particles meet, both disappear. We also focus on sparse initial conditions where particles occupy a subspace of dimension δ that is embedded in a larger space of dimension d. Furthermore, we find that the co-dimension Δ = d - δ governs the behavior. All particles disappear when the co-dimension is sufficiently small, Δ ≤ 2; otherwise, a finite fraction of particles indefinitely survive. We establish the asymptotic behavior of the probability S(t) that a test particle survives until time t. When the subspace is a line, δ = 1, we find inverse logarithmic decay,more » $$S\\sim {(\\mathrm{ln}t)}^{-1}$$, in three dimensions, and a modified power-law decay, $$S\\sim (\\mathrm{ln}t){t}^{-1/2}$$, in two dimensions. In general, the survival probability decays algebraically when Δ < 2, and there is an inverse logarithmic decay at the critical co-dimension Δ = 2.« less

The X-ray structure of Centaurus A

NASA Technical Reports Server (NTRS)

Feigelson, E. D.; Schreier, E. J.; Delvaille, J. P.; Giacconi, R.; Grindlay, J. E.; Lightman, A. P.

1981-01-01

The Einstein X-ray observatory imaging detectors have found X-ray emission associated with several components of the nearby radio galaxy Cen A = NGC 5128: (1) the compact nucleus; (2) an X-ray jet pointed toward the NE radio lobes; (3) the middle NE radio lobe; (4) the disk or dust lane; and (5) diffuse emission extending several arcmin around the nucleus. The intensity of the nucleus changed by a factor of seven over six months. The X-ray jet is considered in terms of thermal, inverse Compton, and synchrotron models. The emission of the NE radio lobe is greater than that expected from inverse Compton or synchrotron processes. Two ridges of emission are found along each edge of the dust lane, within several arcmin of the nucleus. The diffuse X-ray component has a luminosity which is too high to be due to bulge population X-ray sources, but which may be produced by main sequence stars under appropriate circumstances.

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

Design and evaluation of an imaging spectrophotometer incorporating a uniform light source.

PubMed

Noble, S D; Brown, R B; Crowe, T G

2012-03-01

Accounting for light that is diffusely scattered from a surface is one of the practical challenges in reflectance measurement. Integrating spheres are commonly used for this purpose in point measurements of reflectance and transmittance. This solution is not directly applicable to a spectral imaging application for which diffuse reflectance measurements are desired. In this paper, an imaging spectrophotometer design is presented that employs a uniform light source to provide diffuse illumination. This creates the inverse measurement geometry to the directional illumination/diffuse reflectance mode typically used for point measurements. The final system had a spectral range between 400 and 1000 nm with a 5.2 nm resolution, a field of view of approximately 0.5 m by 0.5 m, and millimeter spatial resolution. Testing results indicate illumination uniformity typically exceeding 95% and reflectance precision better than 1.7%.

Light diffusion in N-layered turbid media: steady-state domain.

PubMed

Liemert, André; Kienle, Alwin

2010-01-01

We deal with light diffusion in N-layered turbid media. The steady-state diffusion equation is solved for N-layered turbid media having a finite or an infinitely thick N'th layer. Different refractive indices are considered in the layers. The Fourier transform formalism is applied to derive analytical solutions of the fluence rate in Fourier space. The inverse Fourier transform is calculated using four different methods to test their performance and accuracy. Further, to avoid numerical errors, approximate formulas in Fourier space are derived. Fast solutions for calculation of the spatially resolved reflectance and transmittance from the N-layered turbid media ( approximately 10 ms) with small relative differences (<10(-7)) are found. Additionally, the solutions of the diffusion equation are compared to Monte Carlo simulations for turbid media having up to 20 layers.

Easy way to determine quantitative spatial resolution distribution for a general inverse problem

NASA Astrophysics Data System (ADS)

An, M.; Feng, M.

2013-12-01

The spatial resolution computation of a solution was nontrivial and more difficult than solving an inverse problem. Most geophysical studies, except for tomographic studies, almost uniformly neglect the calculation of a practical spatial resolution. In seismic tomography studies, a qualitative resolution length can be indicatively given via visual inspection of the restoration of a synthetic structure (e.g., checkerboard tests). An effective strategy for obtaining quantitative resolution length is to calculate Backus-Gilbert resolution kernels (also referred to as a resolution matrix) by matrix operation. However, not all resolution matrices can provide resolution length information, and the computation of resolution matrix is often a difficult problem for very large inverse problems. A new class of resolution matrices, called the statistical resolution matrices (An, 2012, GJI), can be directly determined via a simple one-parameter nonlinear inversion performed based on limited pairs of random synthetic models and their inverse solutions. The total procedure were restricted to forward/inversion processes used in the real inverse problem and were independent of the degree of inverse skill used in the solution inversion. Spatial resolution lengths can be directly given during the inversion. Tests on 1D/2D/3D model inversion demonstrated that this simple method can be at least valid for a general linear inverse problem.

Is 3D true non linear traveltime tomography reasonable ?

NASA Astrophysics Data System (ADS)

Herrero, A.; Virieux, J.

2003-04-01

The data sets requiring 3D analysis tools in the context of seismic exploration (both onshore and offshore experiments) or natural seismicity (micro seismicity surveys or post event measurements) are more and more numerous. Classical linearized tomographies and also earthquake localisation codes need an accurate 3D background velocity model. However, if the medium is complex and a priori information not available, a 1D analysis is not able to provide an adequate background velocity image. Moreover, the design of the acquisition layouts is often intrinsically 3D and renders difficult even 2D approaches, especially in natural seismicity cases. Thus, the solution relies on the use of a 3D true non linear approach, which allows to explore the model space and to identify an optimal velocity image. The problem becomes then practical and its feasibility depends on the available computing resources (memory and time). In this presentation, we show that facing a 3D traveltime tomography problem with an extensive non-linear approach combining fast travel time estimators based on level set methods and optimisation techniques such as multiscale strategy is feasible. Moreover, because management of inhomogeneous inversion parameters is more friendly in a non linear approach, we describe how to perform a jointly non-linear inversion for the seismic velocities and the sources locations.

Passivity analysis for uncertain BAM neural networks with time delays and reaction-diffusions

NASA Astrophysics Data System (ADS)

Zhou, Jianping; Xu, Shengyuan; Shen, Hao; Zhang, Baoyong

2013-08-01

This article deals with the problem of passivity analysis for delayed reaction-diffusion bidirectional associative memory (BAM) neural networks with weight uncertainties. By using a new integral inequality, we first present a passivity condition for the nominal networks, and then extend the result to the case with linear fractional weight uncertainties. The proposed conditions are expressed in terms of linear matrix inequalities, and thus can be checked easily. Examples are provided to demonstrate the effectiveness of the proposed results.

Concentration-dependent changes in apparent diffusion coefficients as indicator for colloidal stability of protein solutions.

PubMed

Bauer, Katharina Christin; Göbel, Mathias; Schwab, Marie-Luise; Schermeyer, Marie-Therese; Hubbuch, Jürgen

2016-09-10

The colloidal stability of a protein solution during downstream processing, formulation, and storage is a key issue for the biopharmaceutical production process. Thus, knowledge about colloidal solution characteristics, such as the tendency to form aggregates or high viscosity, at various processing conditions is of interest. This work correlates changes in the apparent diffusion coefficient as a parameter of protein interactions with observed protein aggregation and dynamic viscosity of the respective protein samples. For this purpose, the diffusion coefficient, the protein phase behavior, and the dynamic viscosity in various systems containing the model proteins α-lactalbumin, lysozyme, and glucose oxidase were studied. Each of these experiments revealed a wide range of variations in protein interactions depending on protein type, protein concentration, pH, and the NaCl concentration. All these variations showed to be mirrored by changes in the apparent diffusion coefficient in the respective samples. Whereas stable samples with relatively low viscosity showed an almost linear dependence, the deviation from the concentration-dependent linearity indicated both an increase in the sample viscosity and probability of protein aggregation. This deviation of the apparent diffusion coefficient from concentration-dependent linearity was independent of protein type and solution properties for this study. Thus, this single parameter shows the potential to act as a prognostic tool for colloidal stability of protein solutions. Copyright © 2016 Elsevier B.V. All rights reserved.

Plasma diffusion at the magnetopause - The case of lower hybrid drift waves

NASA Technical Reports Server (NTRS)

Treumann, R. A.; Labelle, J.; Pottelette, R.

1991-01-01

The diffusion expected from the quasi-linear theory of the lower hybrid drift instability at the earth's magnetopause is recalculated. The resulting diffusion coefficient is marginally large enough to explain the thickness of the boundary layer under quiet conditions, based on observational upper limits for the wave intensities. Thus, one possible model for the boundary layer could involve equilibrium between the diffusion arising from lower hybrid waves and various loss processes.

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

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

Jin, Shi, E-mail: sjin@wisc.edu; Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240; Lu, Hanqing, E-mail: hanqing@math.wisc.edu

2017-04-01

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (inmore » the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.« less

Determination of unknown coefficient in a non-linear elliptic problem related to the elastoplastic torsion of a bar

NASA Astrophysics Data System (ADS)

Hasanov, Alemdar; Erdem, Arzu

2008-08-01

The inverse problem of determining the unknown coefficient of the non-linear differential equation of torsional creep is studied. The unknown coefficient g = g({xi}2) depends on the gradient{xi} : = |{nabla}u| of the solution u(x), x [isin] {Omega} [sub] Rn, of the direct problem. It is proved that this gradient is bounded in C-norm. This permits one to choose the natural class of admissible coefficients for the considered inverse problem. The continuity in the norm of the Sobolev space H1({Omega}) of the solution u(x;g) of the direct problem with respect to the unknown coefficient g = g({xi}2) is obtained in the following sense: ||u(x;g) - u(x;gm)||1 [->] 0 when gm({eta}) [->] g({eta}) point-wise as m [->] {infty}. Based on these results, the existence of a quasi-solution of the inverse problem in the considered class of admissible coefficients is obtained. Numerical examples related to determination of the unknown coefficient are presented.

An Inverse Modeling Approach to Estimating Phytoplankton Pigment Concentrations from Phytoplankton Absorption Spectra

NASA Technical Reports Server (NTRS)

Moisan, John R.; Moisan, Tiffany A. H.; Linkswiler, Matthew A.

2011-01-01

Phytoplankton absorption spectra and High-Performance Liquid Chromatography (HPLC) pigment observations from the Eastern U.S. and global observations from NASA's SeaBASS archive are used in a linear inverse calculation to extract pigment-specific absorption spectra. Using these pigment-specific absorption spectra to reconstruct the phytoplankton absorption spectra results in high correlations at all visible wavelengths (r(sup 2) from 0.83 to 0.98), and linear regressions (slopes ranging from 0.8 to 1.1). Higher correlations (r(sup 2) from 0.75 to 1.00) are obtained in the visible portion of the spectra when the total phytoplankton absorption spectra are unpackaged by multiplying the entire spectra by a factor that sets the total absorption at 675 nm to that expected from absorption spectra reconstruction using measured pigment concentrations and laboratory-derived pigment-specific absorption spectra. The derived pigment-specific absorption spectra were further used with the total phytoplankton absorption spectra in a second linear inverse calculation to estimate the various phytoplankton HPLC pigments. A comparison between the estimated and measured pigment concentrations for the 18 pigment fields showed good correlations (r(sup 2) greater than 0.5) for 7 pigments and very good correlations (r(sup 2) greater than 0.7) for chlorophyll a and fucoxanthin. Higher correlations result when the analysis is carried out at more local geographic scales. The ability to estimate phytoplankton pigments using pigment-specific absorption spectra is critical for using hyperspectral inverse models to retrieve phytoplankton pigment concentrations and other Inherent Optical Properties (IOPs) from passive remote sensing observations.

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.

Building generalized inverses of matrices using only row and column operations

NASA Astrophysics Data System (ADS)

Stuart, Jeffrey

2010-12-01

Most students complete their first and only course in linear algebra with the understanding that a real, square matrix A has an inverse if and only if rref(A), the reduced row echelon form of A, is the identity matrix I n . That is, if they apply elementary row operations via the Gauss-Jordan algorithm to the partitioned matrix [A | I n ] to obtain [rref(A) | P], then the matrix A is invertible exactly when rref(A) = I n , in which case, P = A -1. Many students must wonder what happens when A is not invertible, and what information P conveys in that case. That question is, however, seldom answered in a first course. We show that investigating that question emphasizes the close relationships between matrix multiplication, elementary row operations, linear systems, and the four fundamental spaces associated with a matrix. More important, answering that question provides an opportunity to show students how mathematicians extend results by relaxing hypotheses and then exploring the strengths and limitations of the resulting generalization, and how the first relaxation found is often not the best relaxation to be found. Along the way, we introduce students to the basic properties of generalized inverses. Finally, our approach should fit within the time and topic constraints of a first course in linear algebra.

Inverse transport problems in quantitative PAT for molecular imaging

NASA Astrophysics Data System (ADS)

Ren, Kui; Zhang, Rongting; Zhong, Yimin

2015-12-01

Fluorescence photoacoustic tomography (fPAT) is a molecular imaging modality that combines photoacoustic tomography with fluorescence imaging to obtain high-resolution imaging of fluorescence distributions inside heterogeneous media. The objective of this work is to study inverse problems in the quantitative step of fPAT where we intend to reconstruct physical coefficients in a coupled system of radiative transport equations using internal data recovered from ultrasound measurements. We derive uniqueness and stability results on the inverse problems and develop some efficient algorithms for image reconstructions. Numerical simulations based on synthetic data are presented to validate the theoretical analysis. The results we present here complement these in Ren K and Zhao H (2013 SIAM J. Imaging Sci. 6 2024-49) on the same problem but in the diffusive regime.

Optical inverse-square displacement sensor

DOEpatents

Howe, Robert D.; Kychakoff, George

1989-01-01

This invention comprises an optical displacement sensor that uses the inverse-square attenuation of light reflected from a diffused surface to calculate the distance from the sensor to the reflecting surface. Light emerging from an optical fiber or the like is directed onto the surface whose distance is to be measured. The intensity I of reflected light is angle dependent, but within a sufficiently small solid angle it falls off as the inverse square of the distance from the surface. At least a pair of optical detectors are mounted to detect the reflected light within the small solid angle, their ends being at different distances R and R+.DELTA.R from the surface. The distance R can then be found in terms of the ratio of the intensity measurements and the separation length as ##EQU1##

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.

Normalized sensitivities and parameter identifiability of in situ diffusion experiments on Callovo Oxfordian clay at Bure site

NASA Astrophysics Data System (ADS)

Samper, J.; Dewonck, S.; Zheng, L.; Yang, Q.; Naves, A.

Diffusion of inert and reactive tracers (DIR) is an experimental program performed by ANDRA at Bure underground research laboratory in Meuse/Haute Marne (France) to characterize diffusion and retention of radionuclides in Callovo-Oxfordian (C-Ox) argillite. In situ diffusion experiments were performed in vertical boreholes to determine diffusion and retention parameters of selected radionuclides. C-Ox clay exhibits a mild diffusion anisotropy due to stratification. Interpretation of in situ diffusion experiments is complicated by several non-ideal effects caused by the presence of a sintered filter, a gap between the filter and borehole wall and an excavation disturbed zone (EdZ). The relevance of such non-ideal effects and their impact on estimated clay parameters have been evaluated with numerical sensitivity analyses and synthetic experiments having similar parameters and geometric characteristics as real DIR experiments. Normalized dimensionless sensitivities of tracer concentrations at the test interval have been computed numerically. Tracer concentrations are found to be sensitive to all key parameters. Sensitivities are tracer dependent and vary with time. These sensitivities are useful to identify which are the parameters that can be estimated with less uncertainty and find the times at which tracer concentrations begin to be sensitive to each parameter. Synthetic experiments generated with prescribed known parameters have been interpreted automatically with INVERSE-CORE 2D and used to evaluate the relevance of non-ideal effects and ascertain parameter identifiability in the presence of random measurement errors. Identifiability analysis of synthetic experiments reveals that data noise makes difficult the estimation of clay parameters. Parameters of clay and EdZ cannot be estimated simultaneously from noisy data. Models without an EdZ fail to reproduce synthetic data. Proper interpretation of in situ diffusion experiments requires accounting for filter, gap and EdZ. Estimates of the effective diffusion coefficient and the porosity of clay are highly correlated, indicating that these parameters cannot be estimated simultaneously. Accurate estimation of De and porosities of clay and EdZ is only possible when the standard deviation of random noise is less than 0.01. Small errors in the volume of the circulation system do not affect clay parameter estimates. Normalized sensitivities as well as the identifiability analysis of synthetic experiments provide additional insight on inverse estimation of in situ diffusion experiments and will be of great benefit for the interpretation of real DIR in situ diffusion experiments.

Comparative study of inversion methods of three-dimensional NMR and sensitivity to fluids

NASA Astrophysics Data System (ADS)

Tan, Maojin; Wang, Peng; Mao, Keyu

2014-04-01

Three-dimensional nuclear magnetic resonance (3D NMR) logging can simultaneously measure transverse relaxation time (T2), longitudinal relaxation time (T1), and diffusion coefficient (D). These parameters can be used to distinguish fluids in the porous reservoirs. For 3D NMR logging, the relaxation mechanism and mathematical model, Fredholm equation, are introduced, and the inversion methods including Singular Value Decomposition (SVD), Butler-Reeds-Dawson (BRD), and Global Inversion (GI) methods are studied in detail, respectively. During one simulation test, multi-echo CPMG sequence activation is designed firstly, echo trains of the ideal fluid models are synthesized, then an inversion algorithm is carried on these synthetic echo trains, and finally T2-T1-D map is built. Futhermore, SVD, BRD, and GI methods are respectively applied into a same fluid model, and the computing speed and inversion accuracy are compared and analyzed. When the optimal inversion method and matrix dimention are applied, the inversion results are in good aggreement with the supposed fluid model, which indicates that the inversion method of 3D NMR is applieable for fluid typing of oil and gas reservoirs. Additionally, the forward modeling and inversion tests are made in oil-water and gas-water models, respectively, the sensitivity to the fluids in different magnetic field gradients is also examined in detail. The effect of magnetic gradient on fluid typing in 3D NMR logging is stuied and the optimal manetic gradient is choosen.

Efficient Inversion of Mult-frequency and Multi-Source Electromagnetic Data

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

Gary D. Egbert

2007-03-22

The project covered by this report focused on development of efficient but robust non-linear inversion algorithms for electromagnetic induction data, in particular for data collected with multiple receivers, and multiple transmitters, a situation extremely common in eophysical EM subsurface imaging methods. A key observation is that for such multi-transmitter problems each step in commonly used linearized iterative limited memory search schemes such as conjugate gradients (CG) requires solution of forward and adjoint EM problems for each of the N frequencies or sources, essentially generating data sensitivities for an N dimensional data-subspace. These multiple sensitivities allow a good approximation to themore » full Jacobian of the data mapping to be built up in many fewer search steps than would be required by application of textbook optimization methods, which take no account of the multiplicity of forward problems that must be solved for each search step. We have applied this idea to a develop a hybrid inversion scheme that combines features of the iterative limited memory type methods with a Newton-type approach using a partial calculation of the Jacobian. Initial tests on 2D problems show that the new approach produces results essentially identical to a Newton type Occam minimum structure inversion, while running more rapidly than an iterative (fixed regularization parameter) CG style inversion. Memory requirements, while greater than for something like CG, are modest enough that even in 3D the scheme should allow 3D inverse problems to be solved on a common desktop PC, at least for modest (~ 100 sites, 15-20 frequencies) data sets. A secondary focus of the research has been development of a modular system for EM inversion, using an object oriented approach. This system has proven useful for more rapid prototyping of inversion algorithms, in particular allowing initial development and testing to be conducted with two-dimensional example problems, before approaching more computationally cumbersome three-dimensional problems.« less

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.

Space, energy and anisotropy effects on effective cross sections and diffusion coefficients in the resonance region

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

Meftah, B.

1982-01-01

Present methods used in reactor analysis do not include adequately the effect of anisotropic scattering in the calculation of resonance effective cross sections. Also the assumption that the streaming term ..cap omega...del Phi is conserved when the total, absorption and transfer cross sections are conserved, is bad because the leakage from a heterogeneous cell will not be conserved and is strongly anisotropic. A third major consideration is the coupling between different regions in a multiregion reactor; currently this effect is being completely ignored. To assess the magnitude of these effects, a code based on integral transport formalism with linear anisotropicmore » scattering was developed. Also, a more adequate formulation of the diffusion coefficient in a heterogeneous cell was derived. Two reactors, one fast, ZPR-6/5, and one thermal, TRX-3, were selected for the study. The study showed that, in general, the inclusion of linear scattering anisotropy increases the cell effective capture cross section of U-238. The increase was up to 2% in TRX-3 and 0.5% in ZPR-6/5. The effect on the multiplication factor was -0.003% ..delta..k/k for ZPR-6/5 and -0.05% ..delta..k/k for TRX-3. For the case of the diffusion coefficient, the combined effect of heterogeneity and linear anisotropy gave an increase of up to 29% in the parallel diffusion coefficient of TRX-3 and 5% in the parallel diffusion coefficient of ZPR-6/5. In contrast, the change in the perpendicular diffusion coefficient did not exceed 2% in both systems.« less

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1990-09-18

to be published Proceedings: conference Chaos in Australia (February 1990). 5. On the Kadomtsev Petviashvili Equation and Associated Constraints by...Scattering Transfoni (IST). IST is a method which alows one to’solve nonlinear wave equations by solving certain related direct and inverse scattering...problems. We use these results to find solutions to nonlinear wave equations much like one uses Fourier analysis for linear problems. Moreover the

Modelling and Inverse-Modelling: Experiences with O.D.E. Linear Systems in Engineering Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor

2009-01-01

In engineering careers courses, differential equations are widely used to solve problems concerned with modelling. In particular, ordinary differential equations (O.D.E.) linear systems appear regularly in Chemical Engineering, Food Technology Engineering and Environmental Engineering courses, due to the usefulness in modelling chemical kinetics,…

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…

On the null distribution of Bayes factors in linear regression

USDA-ARS?s Scientific Manuscript database

We show that under the null, the 2 log (Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and...