Metric Identification and Protocol Development for Characterizing DNAPL Source Zone Architecture and Associated Plume Response

DTIC Science & Technology

2013-09-01

M.4.1. Two-dimensional domains cropped out of three-dimensional numerically generated realizations; (a) 3D PCE-NAPL realizations generated by UTCHEM...165 Figure R.3.2. The absolute error vs relative error scatter plots of pM and gM from SGS data set- 4 using multi-task manifold...error scatter plots of pM and gM from TP/MC data set using multi- task manifold regression

Mode-based equivalent multi-degree-of-freedom system for one-dimensional viscoelastic response analysis of layered soil deposit

NASA Astrophysics Data System (ADS)

Li, Chong; Yuan, Juyun; Yu, Haitao; Yuan, Yong

2018-01-01

Discrete models such as the lumped parameter model and the finite element model are widely used in the solution of soil amplification of earthquakes. However, neither of the models will accurately estimate the natural frequencies of soil deposit, nor simulate a damping of frequency independence. This research develops a new discrete model for one-dimensional viscoelastic response analysis of layered soil deposit based on the mode equivalence method. The new discrete model is a one-dimensional equivalent multi-degree-of-freedom (MDOF) system characterized by a series of concentrated masses, springs and dashpots with a special configuration. The dynamic response of the equivalent MDOF system is analytically derived and the physical parameters are formulated in terms of modal properties. The equivalent MDOF system is verified through a comparison of amplification functions with the available theoretical solutions. The appropriate number of degrees of freedom (DOFs) in the equivalent MDOF system is estimated. A comparative study of the equivalent MDOF system with the existing discrete models is performed. It is shown that the proposed equivalent MDOF system can exactly present the natural frequencies and the hysteretic damping of soil deposits and provide more accurate results with fewer DOFs.

Verification of Three Dimensional Triangular Prismatic Discrete Ordinates Transport Code ENSEMBLE-TRIZ by Comparison with Monte Carlo Code GMVP

NASA Astrophysics Data System (ADS)

Homma, Yuto; Moriwaki, Hiroyuki; Ohki, Shigeo; Ikeda, Kazumi

2014-06-01

This paper deals with verification of three dimensional triangular prismatic discrete ordinates transport calculation code ENSEMBLE-TRIZ by comparison with multi-group Monte Carlo calculation code GMVP in a large fast breeder reactor. The reactor is a 750 MWe electric power sodium cooled reactor. Nuclear characteristics are calculated at beginning of cycle of an initial core and at beginning and end of cycle of equilibrium core. According to the calculations, the differences between the two methodologies are smaller than 0.0002 Δk in the multi-plication factor, relatively about 1% in the control rod reactivity, and 1% in the sodium void reactivity.

Prediction of discretization error using the error transport equation

NASA Astrophysics Data System (ADS)

Celik, Ismail B.; Parsons, Don Roscoe

2017-06-01

This study focuses on an approach to quantify the discretization error associated with numerical solutions of partial differential equations by solving an error transport equation (ETE). The goal is to develop a method that can be used to adequately predict the discretization error using the numerical solution on only one grid/mesh. The primary problem associated with solving the ETE is the formulation of the error source term which is required for accurately predicting the transport of the error. In this study, a novel approach is considered which involves fitting the numerical solution with a series of locally smooth curves and then blending them together with a weighted spline approach. The result is a continuously differentiable analytic expression that can be used to determine the error source term. Once the source term has been developed, the ETE can easily be solved using the same solver that is used to obtain the original numerical solution. The new methodology is applied to the two-dimensional Navier-Stokes equations in the laminar flow regime. A simple unsteady flow case is also considered. The discretization error predictions based on the methodology presented in this study are in good agreement with the 'true error'. While in most cases the error predictions are not quite as accurate as those from Richardson extrapolation, the results are reasonable and only require one numerical grid. The current results indicate that there is much promise going forward with the newly developed error source term evaluation technique and the ETE.

TIME-DEPENDENT MULTI-GROUP MULTI-DIMENSIONAL RELATIVISTIC RADIATIVE TRANSFER CODE BASED ON SPHERICAL HARMONIC DISCRETE ORDINATE METHOD

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

Tominaga, Nozomu; Shibata, Sanshiro; Blinnikov, Sergei I., E-mail: tominaga@konan-u.ac.jp, E-mail: sshibata@post.kek.jp, E-mail: Sergei.Blinnikov@itep.ru

We develop a time-dependent, multi-group, multi-dimensional relativistic radiative transfer code, which is required to numerically investigate radiation from relativistic fluids that are involved in, e.g., gamma-ray bursts and active galactic nuclei. The code is based on the spherical harmonic discrete ordinate method (SHDOM) which evaluates a source function including anisotropic scattering in spherical harmonics and implicitly solves the static radiative transfer equation with ray tracing in discrete ordinates. We implement treatments of time dependence, multi-frequency bins, Lorentz transformation, and elastic Thomson and inelastic Compton scattering to the publicly available SHDOM code. Our code adopts a mixed-frame approach; the source functionmore » is evaluated in the comoving frame, whereas the radiative transfer equation is solved in the laboratory frame. This implementation is validated using various test problems and comparisons with the results from a relativistic Monte Carlo code. These validations confirm that the code correctly calculates the intensity and its evolution in the computational domain. The code enables us to obtain an Eddington tensor that relates the first and third moments of intensity (energy density and radiation pressure) and is frequently used as a closure relation in radiation hydrodynamics calculations.« less

SPHARA--a generalized spatial Fourier analysis for multi-sensor systems with non-uniformly arranged sensors: application to EEG.

PubMed

Graichen, Uwe; Eichardt, Roland; Fiedler, Patrique; Strohmeier, Daniel; Zanow, Frank; Haueisen, Jens

2015-01-01

Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction. We propose a new approach for spatial harmonic analysis (SPHARA) that extends the classical spatial Fourier analysis to EEG sensors positioned non-uniformly on the surface of the head. The proposed method is based on the eigenanalysis of the discrete Laplace-Beltrami operator defined on a triangular mesh. We present several ways to discretize the continuous Laplace-Beltrami operator and compare the properties of the resulting basis functions computed using these discretization methods. We apply SPHARA to somatosensory evoked potential data from eleven volunteers and demonstrate the ability of the method for spatial data decomposition, dimensionality reduction and noise suppression. When employing SPHARA for dimensionality reduction, a significantly more compact representation can be achieved using the FEM approach, compared to the other discretization methods. Using FEM, to recover 95% and 99% of the total energy of the EEG data, on average only 35% and 58% of the coefficients are necessary. The capability of SPHARA for noise suppression is shown using artificial data. We conclude that SPHARA can be used for spatial harmonic analysis of multi-sensor data at arbitrary positions and can be utilized in a variety of other applications.

On controllability of homogeneous and inhomogeneous discrete-time multi-input bilinear systems in dimension two

NASA Astrophysics Data System (ADS)

Tie, Lin

2017-08-01

In this paper, the controllability problem of two-dimensional discrete-time multi-input bilinear systems is completely solved. The homogeneous and the inhomogeneous cases are studied separately and necessary and sufficient conditions for controllability are established by using a linear algebraic method, which are easy to apply. Moreover, for the uncontrollable systems, near-controllability is considered and similar necessary and sufficient conditions are also obtained. Finally, examples are provided to demonstrate the results of this paper.

Reduction of multi-dimensional laboratory data to a two-dimensional plot: a novel technique for the identification of laboratory error.

PubMed

Kazmierczak, Steven C; Leen, Todd K; Erdogmus, Deniz; Carreira-Perpinan, Miguel A

2007-01-01

The clinical laboratory generates large amounts of patient-specific data. Detection of errors that arise during pre-analytical, analytical, and post-analytical processes is difficult. We performed a pilot study, utilizing a multidimensional data reduction technique, to assess the utility of this method for identifying errors in laboratory data. We evaluated 13,670 individual patient records collected over a 2-month period from hospital inpatients and outpatients. We utilized those patient records that contained a complete set of 14 different biochemical analytes. We used two-dimensional generative topographic mapping to project the 14-dimensional record to a two-dimensional space. The use of a two-dimensional generative topographic mapping technique to plot multi-analyte patient data as a two-dimensional graph allows for the rapid identification of potentially anomalous data. Although we performed a retrospective analysis, this technique has the benefit of being able to assess laboratory-generated data in real time, allowing for the rapid identification and correction of anomalous data before they are released to the physician. In addition, serial laboratory multi-analyte data for an individual patient can also be plotted as a two-dimensional plot. This tool might also be useful for assessing patient wellbeing and prognosis.

Toward Automatic Verification of Goal-Oriented Flow Simulations

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.

2014-01-01

We demonstrate the power of adaptive mesh refinement with adjoint-based error estimates in verification of simulations governed by the steady Euler equations. The flow equations are discretized using a finite volume scheme on a Cartesian mesh with cut cells at the wall boundaries. The discretization error in selected simulation outputs is estimated using the method of adjoint-weighted residuals. Practical aspects of the implementation are emphasized, particularly in the formulation of the refinement criterion and the mesh adaptation strategy. Following a thorough code verification example, we demonstrate simulation verification of two- and three-dimensional problems. These involve an airfoil performance database, a pressure signature of a body in supersonic flow and a launch abort with strong jet interactions. The results show reliable estimates and automatic control of discretization error in all simulations at an affordable computational cost. Moreover, the approach remains effective even when theoretical assumptions, e.g., steady-state and solution smoothness, are relaxed.

An extended sequential goodness-of-fit multiple testing method for discrete data.

PubMed

Castro-Conde, Irene; Döhler, Sebastian; de Uña-Álvarez, Jacobo

2017-10-01

The sequential goodness-of-fit (SGoF) multiple testing method has recently been proposed as an alternative to the familywise error rate- and the false discovery rate-controlling procedures in high-dimensional problems. For discrete data, the SGoF method may be very conservative. In this paper, we introduce an alternative SGoF-type procedure that takes into account the discreteness of the test statistics. Like the original SGoF, our new method provides weak control of the false discovery rate/familywise error rate but attains false discovery rate levels closer to the desired nominal level, and thus it is more powerful. We study the performance of this method in a simulation study and illustrate its application to a real pharmacovigilance data set.

Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory

NASA Astrophysics Data System (ADS)

Haegeman, Jutho; Swingle, Brian; Walter, Michael; Cotler, Jordan; Evenbly, Glen; Scholz, Volkher B.

2018-01-01

We construct entanglement renormalization schemes that provably approximate the ground states of noninteracting-fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice. These schemes give hierarchical quantum circuits that build up the states from unentangled degrees of freedom. The circuits are based on pairs of discrete wavelet transforms, which are approximately related by a "half-shift": translation by half a unit cell. The presence of the Fermi surface in the two-dimensional model requires a special kind of circuit architecture to properly capture the entanglement in the ground state. We show how the error in the approximation can be controlled without ever performing a variational optimization.

Transforming high-dimensional potential energy surfaces into sum-of-products form using Monte Carlo methods

NASA Astrophysics Data System (ADS)

Schröder, Markus; Meyer, Hans-Dieter

2017-08-01

We propose a Monte Carlo method, "Monte Carlo Potfit," for transforming high-dimensional potential energy surfaces evaluated on discrete grid points into a sum-of-products form, more precisely into a Tucker form. To this end we use a variational ansatz in which we replace numerically exact integrals with Monte Carlo integrals. This largely reduces the numerical cost by avoiding the evaluation of the potential on all grid points and allows a treatment of surfaces up to 15-18 degrees of freedom. We furthermore show that the error made with this ansatz can be controlled and vanishes in certain limits. We present calculations on the potential of HFCO to demonstrate the features of the algorithm. To demonstrate the power of the method, we transformed a 15D potential of the protonated water dimer (Zundel cation) in a sum-of-products form and calculated the ground and lowest 26 vibrationally excited states of the Zundel cation with the multi-configuration time-dependent Hartree method.

SPHARA - A Generalized Spatial Fourier Analysis for Multi-Sensor Systems with Non-Uniformly Arranged Sensors: Application to EEG

PubMed Central

Graichen, Uwe; Eichardt, Roland; Fiedler, Patrique; Strohmeier, Daniel; Zanow, Frank; Haueisen, Jens

2015-01-01

Important requirements for the analysis of multichannel EEG data are efficient techniques for signal enhancement, signal decomposition, feature extraction, and dimensionality reduction. We propose a new approach for spatial harmonic analysis (SPHARA) that extends the classical spatial Fourier analysis to EEG sensors positioned non-uniformly on the surface of the head. The proposed method is based on the eigenanalysis of the discrete Laplace-Beltrami operator defined on a triangular mesh. We present several ways to discretize the continuous Laplace-Beltrami operator and compare the properties of the resulting basis functions computed using these discretization methods. We apply SPHARA to somatosensory evoked potential data from eleven volunteers and demonstrate the ability of the method for spatial data decomposition, dimensionality reduction and noise suppression. When employing SPHARA for dimensionality reduction, a significantly more compact representation can be achieved using the FEM approach, compared to the other discretization methods. Using FEM, to recover 95% and 99% of the total energy of the EEG data, on average only 35% and 58% of the coefficients are necessary. The capability of SPHARA for noise suppression is shown using artificial data. We conclude that SPHARA can be used for spatial harmonic analysis of multi-sensor data at arbitrary positions and can be utilized in a variety of other applications. PMID:25885290

Fourth-order convergence of a compact scheme for the one-dimensional biharmonic equation

NASA Astrophysics Data System (ADS)

Fishelov, D.; Ben-Artzi, M.; Croisille, J.-P.

2012-09-01

The convergence of a fourth-order compact scheme to the one-dimensional biharmonic problem is established in the case of general Dirichlet boundary conditions. The compact scheme invokes value of the unknown function as well as Pade approximations of its first-order derivative. Using the Pade approximation allows us to approximate the first-order derivative within fourth-order accuracy. However, although the truncation error of the discrete biharmonic scheme is of fourth-order at interior point, the truncation error drops to first-order at near-boundary points. Nonetheless, we prove that the scheme retains its fourth-order (optimal) accuracy. This is done by a careful inspection of the matrix elements of the discrete biharmonic operator. A number of numerical examples corroborate this effect. We also present a study of the eigenvalue problem uxxxx = νu. We compute and display the eigenvalues and the eigenfunctions related to the continuous and the discrete problems. By the positivity of the eigenvalues, one can deduce the stability of of the related time-dependent problem ut = -uxxxx. In addition, we study the eigenvalue problem uxxxx = νuxx. This is related to the stability of the linear time-dependent equation uxxt = νuxxxx. Its continuous and discrete eigenvalues and eigenfunction (or eigenvectors) are computed and displayed graphically.

Damage Initiation in Two-Dimensional, Woven, Carbon-Carbon Composites

DTIC Science & Technology

1988-12-01

biaxial stress interaction were themselves a function of the applied biaxial stress ratio and thus the error in measuring F12 depended on F12. To find the...the supported directions. Discretizing the model will tend to induce error in the computed nodal displacements when compared to an exact continuum...solution, however, for an increasing number of elements in the structural model, the net error should converge to zero (3:94). The inherent flexibility in

Multi-Material Closure Model for High-Order Finite Element Lagrangian Hydrodynamics

DOE PAGES

Dobrev, V. A.; Kolev, T. V.; Rieben, R. N.; ...

2016-04-27

We present a new closure model for single fluid, multi-material Lagrangian hydrodynamics and its application to high-order finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous pressure equilibration, while the full pressure equilibration is achieved bymore » both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material high-velocity impact arbitrary Lagrangian–Eulerian calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.« less

Multi-Material Closure Model for High-Order Finite Element Lagrangian Hydrodynamics

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

Dobrev, V. A.; Kolev, T. V.; Rieben, R. N.

We present a new closure model for single fluid, multi-material Lagrangian hydrodynamics and its application to high-order finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous pressure equilibration, while the full pressure equilibration is achieved bymore » both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material high-velocity impact arbitrary Lagrangian–Eulerian calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.« less

Research on Signature Verification Method Based on Discrete Fréchet Distance

NASA Astrophysics Data System (ADS)

Fang, J. L.; Wu, W.

2018-05-01

This paper proposes a multi-feature signature template based on discrete Fréchet distance, which breaks through the limitation of traditional signature authentication using a single signature feature. It solves the online handwritten signature authentication signature global feature template extraction calculation workload, signature feature selection unreasonable problem. In this experiment, the false recognition rate (FAR) and false rejection rate (FRR) of the statistical signature are calculated and the average equal error rate (AEER) is calculated. The feasibility of the combined template scheme is verified by comparing the average equal error rate of the combination template and the original template.

Development and Application of Methods for Estimating Operating Characteristics of Discrete Test Item Responses without Assuming any Mathematical Form.

ERIC Educational Resources Information Center

Samejima, Fumiko

In latent trait theory the latent space, or space of the hypothetical construct, is usually represented by some unidimensional or multi-dimensional continuum of real numbers. Like the latent space, the item response can either be treated as a discrete variable or as a continuous variable. Latent trait theory relates the item response to the latent…

Numerical prediction of the energy efficiency of the three-dimensional fish school using the discretized Adomian decomposition method

NASA Astrophysics Data System (ADS)

Lin, Yinwei

2018-06-01

A three-dimensional modeling of fish school performed by a modified Adomian decomposition method (ADM) discretized by the finite difference method is proposed. To our knowledge, few studies of the fish school are documented due to expensive cost of numerical computing and tedious three-dimensional data analysis. Here, we propose a simple model replied on the Adomian decomposition method to estimate the efficiency of energy saving of the flow motion of the fish school. First, the analytic solutions of Navier-Stokes equations are used for numerical validation. The influences of the distance between the side-by-side two fishes are studied on the energy efficiency of the fish school. In addition, the complete error analysis for this method is presented.

Efficient genetic algorithms using discretization scheduling.

PubMed

McLay, Laura A; Goldberg, David E

2005-01-01

In many applications of genetic algorithms, there is a tradeoff between speed and accuracy in fitness evaluations when evaluations use numerical methods with varying discretization. In these types of applications, the cost and accuracy vary from discretization errors when implicit or explicit quadrature is used to estimate the function evaluations. This paper examines discretization scheduling, or how to vary the discretization within the genetic algorithm in order to use the least amount of computation time for a solution of a desired quality. The effectiveness of discretization scheduling can be determined by comparing its computation time to the computation time of a GA using a constant discretization. There are three ingredients for the discretization scheduling: population sizing, estimated time for each function evaluation and predicted convergence time analysis. Idealized one- and two-dimensional experiments and an inverse groundwater application illustrate the computational savings to be achieved from using discretization scheduling.

Portable laser synthesizer for high-speed multi-dimensional spectroscopy

DOEpatents

Demos, Stavros G [Livermore, CA; Shverdin, Miroslav Y [Sunnyvale, CA; Shirk, Michael D [Brentwood, CA

2012-05-29

Portable, field-deployable laser synthesizer devices designed for multi-dimensional spectrometry and time-resolved and/or hyperspectral imaging include a coherent light source which simultaneously produces a very broad, energetic, discrete spectrum spanning through or within the ultraviolet, visible, and near infrared wavelengths. The light output is spectrally resolved and each wavelength is delayed with respect to each other. A probe enables light delivery to a target. For multidimensional spectroscopy applications, the probe can collect the resulting emission and deliver this radiation to a time gated spectrometer for temporal and spectral analysis.

A multidomain spectral collocation method for the Stokes problem

NASA Technical Reports Server (NTRS)

Landriani, G. Sacchi; Vandeven, H.

1989-01-01

A multidomain spectral collocation scheme is proposed for the approximation of the two-dimensional Stokes problem. It is shown that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pressure.

Optimal Runge-Kutta Schemes for High-order Spatial and Temporal Discretizations

DTIC Science & Technology

2015-06-01

using larger time steps versus lower-order time integration with smaller time steps.4 In the present work, an attempt is made to gener - alize these... generality and because of interest in multi-speed and high Reynolds number, wall-bounded flow regimes, a dual-time framework is adopted in the present work...errors of general combinations of high-order spatial and temporal discretizations. Different Runge-Kutta time integrators are applied to central

Development of morphogen gradient: The role of dimension and discreteness

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

Teimouri, Hamid; Kolomeisky, Anatoly B.

2014-02-28

The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen gradients is a result of complex processes that involve diffusion and degradation of locally produced signaling molecules. We developed a multi-dimensional discrete-state stochastic approach for investigating the corresponding reaction-diffusion models. It provided a full analytical description for stationary profiles and for important dynamic properties such as local accumulation times, variances, and mean first-passage times. The role of discreteness in developing of morphogen gradients is analyzed by comparing with available continuummore » descriptions. It is found that the continuum models prediction about multiple time scales near the source region in two-dimensional and three-dimensional systems is not supported in our analysis. Using ideas that view the degradation process as an effective potential, the effect of dimensionality on establishment of morphogen gradients is also discussed. In addition, we investigated how these reaction-diffusion processes are modified with changing the size of the source region.« less

Effects of bathymetric lidar errors on flow properties predicted with a multi-dimensional hydraulic model

Treesearch

J. McKean; D. Tonina; C. Bohn; C. W. Wright

2014-01-01

New remote sensing technologies and improved computer performance now allow numerical flow modeling over large stream domains. However, there has been limited testing of whether channel topography can be remotely mapped with accuracy necessary for such modeling. We assessed the ability of the Experimental Advanced Airborne Research Lidar, to support a multi-dimensional...

Research on target information optics communications transmission characteristic and performance in multi-screens testing system

NASA Astrophysics Data System (ADS)

Li, Hanshan

2016-04-01

To enhance the stability and reliability of multi-screens testing system, this paper studies multi-screens target optical information transmission link properties and performance in long-distance, sets up the discrete multi-tone modulation transmission model based on geometric model of laser multi-screens testing system and visible light information communication principle; analyzes the electro-optic and photoelectric conversion function of sender and receiver in target optical information communication system; researches target information transmission performance and transfer function of the generalized visible-light communication channel; found optical information communication transmission link light intensity space distribution model and distribution function; derives the SNR model of information transmission communication system. Through the calculation and experiment analysis, the results show that the transmission error rate increases with the increment of transmission rate in a certain channel modulation depth; when selecting the appropriate transmission rate, the bit error rate reach 0.01.

Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

DOE PAGES

Moral, Pierre Del; Jasra, Ajay; Law, Kody J. H.; ...

2017-08-24

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the discrete approximation error must be balanced. A multilevel strategy is utilized to substantially reduce the cost to obtain a given error level in the approximation as compared to standard estimators. Two estimators are considered and relative variance bounds are given. The theoretical results are numerically illustrated for two Bayesian inverse problems arising from elliptic partial differential equations (PDEs). The examples involve the inversion of observations of themore » solution of (i) a 1-dimensional Poisson equation to infer the diffusion coefficient, and (ii) a 2-dimensional Poisson equation to infer the external forcing.« less

Opto-mechanical design of a dispersive artificial eye.

PubMed

Coughlan, Mark F; Mihashi, Toshifumi; Goncharov, Alexander V

2017-05-20

We present an opto-mechanical artificial eye that can be used for examining multi-wavelength ophthalmic instruments. Standard off-the-shelf lenses and a refractive-index-matching fluid were used in the creation of the artificial eye. In addition to dispersive properties, the artificial eye can be used to simulate refractive error. To analyze the artificial eye, a multi-wavelength Hartmann-Shack aberrometer was used to measure the longitudinal chromatic aberration and the possibility of inducing refractive error. Off-axis chromatic aberrations were also analyzed by imaging through the artificial eye at two discrete wavelengths. Possible extensions to the dispersive artificial eye are also discussed.

Wavepacket dynamics and the multi-configurational time-dependent Hartree approach

NASA Astrophysics Data System (ADS)

Manthe, Uwe

2017-06-01

Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.

A sparse grid based method for generative dimensionality reduction of high-dimensional data

NASA Astrophysics Data System (ADS)

Bohn, Bastian; Garcke, Jochen; Griebel, Michael

2016-03-01

Generative dimensionality reduction methods play an important role in machine learning applications because they construct an explicit mapping from a low-dimensional space to the high-dimensional data space. We discuss a general framework to describe generative dimensionality reduction methods, where the main focus lies on a regularized principal manifold learning variant. Since most generative dimensionality reduction algorithms exploit the representer theorem for reproducing kernel Hilbert spaces, their computational costs grow at least quadratically in the number n of data. Instead, we introduce a grid-based discretization approach which automatically scales just linearly in n. To circumvent the curse of dimensionality of full tensor product grids, we use the concept of sparse grids. Furthermore, in real-world applications, some embedding directions are usually more important than others and it is reasonable to refine the underlying discretization space only in these directions. To this end, we employ a dimension-adaptive algorithm which is based on the ANOVA (analysis of variance) decomposition of a function. In particular, the reconstruction error is used to measure the quality of an embedding. As an application, the study of large simulation data from an engineering application in the automotive industry (car crash simulation) is performed.

ZN graded discrete Lax pairs and Yang-Baxter maps

NASA Astrophysics Data System (ADS)

Fordy, Allan P.; Xenitidis, Pavlos

2017-05-01

We recently introduced a class of ZN graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In this paper, we introduce the corresponding Yang-Baxter maps. Many well-known examples belong to this scheme for N=2, so, for N≥3, our systems may be regarded as generalizations of these. In particular, for each N we introduce a class of multi-component Yang-Baxter maps, which include H^{B_{III (of Papageorgiou et al. 2010 SIGMA 6, 003 (9 p). (doi:10.3842/SIGMA.2010.033)), when N=2, and that associated with the discrete modified Boussinesq equation, for N=3. For N≥5 we introduce a new family of Yang-Baxter maps, which have no lower dimensional analogue. We also present new multi-component versions of the Yang-Baxter maps FIV and FV (given in the classification of Adler et al. 2004 Commun. Anal. Geom. 12, 967-1007. (doi:10.4310/CAG.2004.v12.n5.a1)).}}

[Formula: see text] graded discrete Lax pairs and Yang-Baxter maps.

PubMed

Fordy, Allan P; Xenitidis, Pavlos

2017-05-01

We recently introduced a class of [Formula: see text] graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In this paper, we introduce the corresponding Yang-Baxter maps. Many well-known examples belong to this scheme for N =2, so, for N ≥3, our systems may be regarded as generalizations of these. In particular, for each N we introduce a class of multi-component Yang-Baxter maps, which include H B III (of Papageorgiou et al. 2010 SIGMA 6, 003 (9 p). (doi:10.3842/SIGMA.2010.033)), when N =2, and that associated with the discrete modified Boussinesq equation, for N =3. For N ≥5 we introduce a new family of Yang-Baxter maps, which have no lower dimensional analogue. We also present new multi-component versions of the Yang-Baxter maps F IV and F V (given in the classification of Adler et al. 2004 Commun. Anal. Geom. 12, 967-1007. (doi:10.4310/CAG.2004.v12.n5.a1)).

ZN graded discrete Lax pairs and Yang–Baxter maps

PubMed Central

Fordy, Allan P.

2017-01-01

We recently introduced a class of ZN graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In this paper, we introduce the corresponding Yang–Baxter maps. Many well-known examples belong to this scheme for N=2, so, for N≥3, our systems may be regarded as generalizations of these. In particular, for each N we introduce a class of multi-component Yang–Baxter maps, which include HBIII (of Papageorgiou et al. 2010 SIGMA 6, 003 (9 p). (doi:10.3842/SIGMA.2010.033)), when N=2, and that associated with the discrete modified Boussinesq equation, for N=3. For N≥5 we introduce a new family of Yang–Baxter maps, which have no lower dimensional analogue. We also present new multi-component versions of the Yang–Baxter maps FIV and FV (given in the classification of Adler et al. 2004 Commun. Anal. Geom. 12, 967–1007. (doi:10.4310/CAG.2004.v12.n5.a1)). PMID:28588406

On the predictivity of pore-scale simulations: Estimating uncertainties with multilevel Monte Carlo

NASA Astrophysics Data System (ADS)

Icardi, Matteo; Boccardo, Gianluca; Tempone, Raúl

2016-09-01

A fast method with tunable accuracy is proposed to estimate errors and uncertainties in pore-scale and Digital Rock Physics (DRP) problems. The overall predictivity of these studies can be, in fact, hindered by many factors including sample heterogeneity, computational and imaging limitations, model inadequacy and not perfectly known physical parameters. The typical objective of pore-scale studies is the estimation of macroscopic effective parameters such as permeability, effective diffusivity and hydrodynamic dispersion. However, these are often non-deterministic quantities (i.e., results obtained for specific pore-scale sample and setup are not totally reproducible by another ;equivalent; sample and setup). The stochastic nature can arise due to the multi-scale heterogeneity, the computational and experimental limitations in considering large samples, and the complexity of the physical models. These approximations, in fact, introduce an error that, being dependent on a large number of complex factors, can be modeled as random. We propose a general simulation tool, based on multilevel Monte Carlo, that can reduce drastically the computational cost needed for computing accurate statistics of effective parameters and other quantities of interest, under any of these random errors. This is, to our knowledge, the first attempt to include Uncertainty Quantification (UQ) in pore-scale physics and simulation. The method can also provide estimates of the discretization error and it is tested on three-dimensional transport problems in heterogeneous materials, where the sampling procedure is done by generation algorithms able to reproduce realistic consolidated and unconsolidated random sphere and ellipsoid packings and arrangements. A totally automatic workflow is developed in an open-source code [1], that include rigid body physics and random packing algorithms, unstructured mesh discretization, finite volume solvers, extrapolation and post-processing techniques. The proposed method can be efficiently used in many porous media applications for problems such as stochastic homogenization/upscaling, propagation of uncertainty from microscopic fluid and rock properties to macro-scale parameters, robust estimation of Representative Elementary Volume size for arbitrary physics.

Pareto-optimal multi-objective dimensionality reduction deep auto-encoder for mammography classification.

PubMed

Taghanaki, Saeid Asgari; Kawahara, Jeremy; Miles, Brandon; Hamarneh, Ghassan

2017-07-01

Feature reduction is an essential stage in computer aided breast cancer diagnosis systems. Multilayer neural networks can be trained to extract relevant features by encoding high-dimensional data into low-dimensional codes. Optimizing traditional auto-encoders works well only if the initial weights are close to a proper solution. They are also trained to only reduce the mean squared reconstruction error (MRE) between the encoder inputs and the decoder outputs, but do not address the classification error. The goal of the current work is to test the hypothesis that extending traditional auto-encoders (which only minimize reconstruction error) to multi-objective optimization for finding Pareto-optimal solutions provides more discriminative features that will improve classification performance when compared to single-objective and other multi-objective approaches (i.e. scalarized and sequential). In this paper, we introduce a novel multi-objective optimization of deep auto-encoder networks, in which the auto-encoder optimizes two objectives: MRE and mean classification error (MCE) for Pareto-optimal solutions, rather than just MRE. These two objectives are optimized simultaneously by a non-dominated sorting genetic algorithm. We tested our method on 949 X-ray mammograms categorized into 12 classes. The results show that the features identified by the proposed algorithm allow a classification accuracy of up to 98.45%, demonstrating favourable accuracy over the results of state-of-the-art methods reported in the literature. We conclude that adding the classification objective to the traditional auto-encoder objective and optimizing for finding Pareto-optimal solutions, using evolutionary multi-objective optimization, results in producing more discriminative features. Copyright © 2017 Elsevier B.V. All rights reserved.

Improved numerical methods for turbulent viscous recirculating flows

NASA Technical Reports Server (NTRS)

Turan, A.

1985-01-01

The hybrid-upwind finite difference schemes employed in generally available combustor codes possess excessive numerical diffusion errors which preclude accurate quantative calculations. The present study has as its primary objective the identification and assessment of an improved solution algorithm as well as discretization schemes applicable to analysis of turbulent viscous recirculating flows. The assessment is carried out primarily in two dimensional/axisymetric geometries with a view to identifying an appropriate technique to be incorporated in a three-dimensional code.

A high-resolution Godunov method for compressible multi-material flow on overlapping grids

NASA Astrophysics Data System (ADS)

Banks, J. W.; Schwendeman, D. W.; Kapila, A. K.; Henshaw, W. D.

2007-04-01

A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on a uniform-pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on the Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of a planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.

Discrete-state representation of ion permeation coupled to fast gating in a model of ClC chloride channels: comparison to multi-ion continuous space Brownian dynamics simulations.

PubMed

Coalson, Rob D; Cheng, Mary Hongying

2010-01-28

A discrete-state model of chloride ion motion in a ClC chloride channel is constructed, following a previously developed multi-ion continuous space model of the same system (Cheng, M. H.; Mamonov, A. B.; Dukes, J. W.; Coalson, R. D. J. Phys. Chem. B 2007, 111, 5956) that included a simplistic representation of the fast gate in this channel. The reducibility of the many-body continuous space to the eight discrete-state model considered in the present work is examined in detail by performing three-dimensional Brownian dynamics simulations of each allowed state-to-state transition in order to extract the appropriate rate constant for this process, and then inserting the pairwise rate constants thereby obtained into an appropriate set of kinetic master equations. Experimental properties of interest, including the rate of Cl(-) ion permeation through the open channel and the average rate of closing of the fast gate as a function of bulk Cl(-) ion concentrations in the intracellular and extracellular electrolyte reservoirs are computed. Good agreement is found between the results obtained via the eight discrete-state model versus the multi-ion continuous space model, thereby encouraging continued development of the discrete-state model to include more complex behaviors observed experimentally in these channels.

A comparison of locally adaptive multigrid methods: LDC, FAC and FIC

NASA Technical Reports Server (NTRS)

Khadra, Khodor; Angot, Philippe; Caltagirone, Jean-Paul

1993-01-01

This study is devoted to a comparative analysis of three 'Adaptive ZOOM' (ZOom Overlapping Multi-level) methods based on similar concepts of hierarchical multigrid local refinement: LDC (Local Defect Correction), FAC (Fast Adaptive Composite), and FIC (Flux Interface Correction)--which we proposed recently. These methods are tested on two examples of a bidimensional elliptic problem. We compare, for V-cycle procedures, the asymptotic evolution of the global error evaluated by discrete norms, the corresponding local errors, and the convergence rates of these algorithms.

High-order central ENO finite-volume scheme for hyperbolic conservation laws on three-dimensional cubed-sphere grids

NASA Astrophysics Data System (ADS)

Ivan, L.; De Sterck, H.; Susanto, A.; Groth, C. P. T.

2015-02-01

A fourth-order accurate finite-volume scheme for hyperbolic conservation laws on three-dimensional (3D) cubed-sphere grids is described. The approach is based on a central essentially non-oscillatory (CENO) finite-volume method that was recently introduced for two-dimensional compressible flows and is extended to 3D geometries with structured hexahedral grids. Cubed-sphere grids feature hexahedral cells with nonplanar cell surfaces, which are handled with high-order accuracy using trilinear geometry representations in the proposed approach. Varying stencil sizes and slope discontinuities in grid lines occur at the boundaries and corners of the six sectors of the cubed-sphere grid where the grid topology is unstructured, and these difficulties are handled naturally with high-order accuracy by the multidimensional least-squares based 3D CENO reconstruction with overdetermined stencils. A rotation-based mechanism is introduced to automatically select appropriate smaller stencils at degenerate block boundaries, where fewer ghost cells are available and the grid topology changes, requiring stencils to be modified. Combining these building blocks results in a finite-volume discretization for conservation laws on 3D cubed-sphere grids that is uniformly high-order accurate in all three grid directions. While solution-adaptivity is natural in the multi-block setting of our code, high-order accurate adaptive refinement on cubed-sphere grids is not pursued in this paper. The 3D CENO scheme is an accurate and robust solution method for hyperbolic conservation laws on general hexahedral grids that is attractive because it is inherently multidimensional by employing a K-exact overdetermined reconstruction scheme, and it avoids the complexity of considering multiple non-central stencil configurations that characterizes traditional ENO schemes. Extensive numerical tests demonstrate fourth-order convergence for stationary and time-dependent Euler and magnetohydrodynamic flows on cubed-sphere grids, and robustness against spurious oscillations at 3D shocks. Performance tests illustrate efficiency gains that can be potentially achieved using fourth-order schemes as compared to second-order methods for the same error level. Applications on extended cubed-sphere grids incorporating a seventh root block that discretizes the interior of the inner sphere demonstrate the versatility of the spatial discretization method.

Multi-time-scale heat transfer modeling of turbid tissues exposed to short-pulsed irradiations.

PubMed

Kim, Kyunghan; Guo, Zhixiong

2007-05-01

A combined hyperbolic radiation and conduction heat transfer model is developed to simulate multi-time-scale heat transfer in turbid tissues exposed to short-pulsed irradiations. An initial temperature response of a tissue to an ultrashort pulse irradiation is analyzed by the volume-average method in combination with the transient discrete ordinates method for modeling the ultrafast radiation heat transfer. This response is found to reach pseudo steady state within 1 ns for the considered tissues. The single pulse result is then utilized to obtain the temperature response to pulse train irradiation at the microsecond/millisecond time scales. After that, the temperature field is predicted by the hyperbolic heat conduction model which is solved by the MacCormack's scheme with error terms correction. Finally, the hyperbolic conduction is compared with the traditional parabolic heat diffusion model. It is found that the maximum local temperatures are larger in the hyperbolic prediction than the parabolic prediction. In the modeled dermis tissue, a 7% non-dimensional temperature increase is found. After about 10 thermal relaxation times, thermal waves fade away and the predictions between the hyperbolic and parabolic models are consistent.

Calculations of axisymmetric vortex sheet roll-up using a panel and a filament model

NASA Technical Reports Server (NTRS)

Kantelis, J. P.; Widnall, S. E.

1986-01-01

A method for calculating the self-induced motion of a vortex sheet using discrete vortex elements is presented. Vortex panels and vortex filaments are used to simulate two-dimensional and axisymmetric vortex sheet roll-up. A straight forward application using vortex elements to simulate the motion of a disk of vorticity with an elliptic circulation distribution yields unsatisfactroy results where the vortex elements move in a chaotic manner. The difficulty is assumed to be due to the inability of a finite number of discrete vortex elements to model the singularity at the sheet edge and due to large velocity calculation errors which result from uneven sheet stretching. A model of the inner portion of the spiral is introduced to eliminate the difficulty with the sheet edge singularity. The model replaces the outermost portion of the sheet with a single vortex of equivalent circulation and a number of higher order terms which account for the asymmetry of the spiral. The resulting discrete vortex model is applied to both two-dimensional and axisymmetric sheets. The two-dimensional roll-up is compared to the solution for a semi-infinite sheet with good results.

Building the 3D Geological Model of Wall Rock of Salt Caverns Based on Integration Method of Multi-source data

NASA Astrophysics Data System (ADS)

Yongzhi, WANG; hui, WANG; Lixia, LIAO; Dongsen, LI

2017-02-01

In order to analyse the geological characteristics of salt rock and stability of salt caverns, rough three-dimensional (3D) models of salt rock stratum and the 3D models of salt caverns on study areas are built by 3D GIS spatial modeling technique. During implementing, multi-source data, such as basic geographic data, DEM, geological plane map, geological section map, engineering geological data, and sonar data are used. In this study, the 3D spatial analyzing and calculation methods, such as 3D GIS intersection detection method in three-dimensional space, Boolean operations between three-dimensional space entities, three-dimensional space grid discretization, are used to build 3D models on wall rock of salt caverns. Our methods can provide effective calculation models for numerical simulation and analysis of the creep characteristics of wall rock in salt caverns.

An equilibrium-preserving discretization for the nonlinear Rosenbluth-Fokker-Planck operator in arbitrary multi-dimensional geometry

NASA Astrophysics Data System (ADS)

Taitano, W. T.; Chacón, L.; Simakov, A. N.

2017-06-01

The Fokker-Planck collision operator is an advection-diffusion operator which describe dynamical systems such as weakly coupled plasmas [1,2], photonics in high temperature environment [3,4], biological [5], and even social systems [6]. For plasmas in the continuum, the Fokker-Planck collision operator supports such important physical properties as conservation of number, momentum, and energy, as well as positivity. It also obeys the Boltzmann's H-theorem [7-11], i.e., the operator increases the system entropy while simultaneously driving the distribution function towards a Maxwellian. In the discrete, when these properties are not ensured, numerical simulations can either fail catastrophically or suffer from significant numerical pollution [12,13]. There is strong emphasis in the literature on developing numerical techniques to solve the Fokker-Planck equation while preserving these properties [12-24]. In this short note, we focus on the analytical equilibrium preserving property, meaning that the Fokker-Planck collision operator vanishes when acting on an analytical Maxwellian distribution function. The equilibrium preservation property is especially important, for example, when one is attempting to capture subtle transport physics. Since transport arises from small O (ɛ) corrections to the equilibrium [25] (where ɛ is a small expansion parameter), numerical truncation error present in the equilibrium solution may dominate, overwhelming transport dynamics.

Stress Recovery and Error Estimation for Shell Structures

NASA Technical Reports Server (NTRS)

Yazdani, A. A.; Riggs, H. R.; Tessler, A.

2000-01-01

The Penalized Discrete Least-Squares (PDLS) stress recovery (smoothing) technique developed for two dimensional linear elliptic problems is adapted here to three-dimensional shell structures. The surfaces are restricted to those which have a 2-D parametric representation, or which can be built-up of such surfaces. The proposed strategy involves mapping the finite element results to the 2-D parametric space which describes the geometry, and smoothing is carried out in the parametric space using the PDLS-based Smoothing Element Analysis (SEA). Numerical results for two well-known shell problems are presented to illustrate the performance of SEA/PDLS for these problems. The recovered stresses are used in the Zienkiewicz-Zhu a posteriori error estimator. The estimated errors are used to demonstrate the performance of SEA-recovered stresses in automated adaptive mesh refinement of shell structures. The numerical results are encouraging. Further testing involving more complex, practical structures is necessary.

A High-Order Transport Scheme for Collisional-Radiative and Nonequilibrium Plasma

DTIC Science & Technology

2009-02-06

of change of the temperature is obtained, ∂E ∂T ∂T ∂t = ∂ ∂x ( κs ∂T ∂x ) (7.6) Assuming a one- dimensional discretization on a uniformly- spaced ...oscillations nor a quantitative analysis of the multi- dimensional shock structure has been provided to date. This dissertation builds upon previous...high-enthalpy nonequilibrium plasmas and is the focus of much of this work. The plasma is described as

Assessment of numerical techniques for unsteady flow calculations

NASA Technical Reports Server (NTRS)

Hsieh, Kwang-Chung

1989-01-01

The characteristics of unsteady flow motions have long been a serious concern in the study of various fluid dynamic and combustion problems. With the advancement of computer resources, numerical approaches to these problems appear to be feasible. The objective of this paper is to assess the accuracy of several numerical schemes for unsteady flow calculations. In the present study, Fourier error analysis is performed for various numerical schemes based on a two-dimensional wave equation. Four methods sieved from the error analysis are then adopted for further assessment. Model problems include unsteady quasi-one-dimensional inviscid flows, two-dimensional wave propagations, and unsteady two-dimensional inviscid flows. According to the comparison between numerical and exact solutions, although second-order upwind scheme captures the unsteady flow and wave motions quite well, it is relatively more dissipative than sixth-order central difference scheme. Among various numerical approaches tested in this paper, the best performed one is Runge-Kutta method for time integration and six-order central difference for spatial discretization.

A discrete fracture model for two-phase flow in fractured porous media

NASA Astrophysics Data System (ADS)

Gläser, Dennis; Helmig, Rainer; Flemisch, Bernd; Class, Holger

2017-12-01

A discrete fracture model on the basis of a cell-centered finite volume scheme with multi-point flux approximation (MPFA) is presented. The fractures are included in a d-dimensional computational domain as (d - 1)-dimensional entities living on the element facets, which requires the grid to have the element facets aligned with the fracture geometries. However, the approach overcomes the problem of small cells inside the fractures when compared to equi-dimensional models. The system of equations considered is solved on both the matrix and the fracture domain, where on the prior the fractures are treated as interior boundaries and on the latter the exchange term between fracture and matrix appears as an additional source/sink. This exchange term is represented by the matrix-fracture fluxes, computed as functions of the unknowns in both domains by applying adequate modifications to the MPFA scheme. The method is applicable to both low-permeable as well as highly conductive fractures. The quality of the results obtained by the discrete fracture model is studied by comparison to an equi-dimensional discretization on a simple geometry for both single- and two-phase flow. For the case of two-phase flow in a highly conductive fracture, good agreement in the solution and in the matrix-fracture transfer fluxes could be observed, while for a low-permeable fracture the discrepancies were more pronounced. The method is then applied two-phase flow through a realistic fracture network in two and three dimensions.

Evaluation of Two Crew Module Boilerplate Tests Using Newly Developed Calibration Metrics

NASA Technical Reports Server (NTRS)

Horta, Lucas G.; Reaves, Mercedes C.

2012-01-01

The paper discusses a application of multi-dimensional calibration metrics to evaluate pressure data from water drop tests of the Max Launch Abort System (MLAS) crew module boilerplate. Specifically, three metrics are discussed: 1) a metric to assess the probability of enveloping the measured data with the model, 2) a multi-dimensional orthogonality metric to assess model adequacy between test and analysis, and 3) a prediction error metric to conduct sensor placement to minimize pressure prediction errors. Data from similar (nearly repeated) capsule drop tests shows significant variability in the measured pressure responses. When compared to expected variability using model predictions, it is demonstrated that the measured variability cannot be explained by the model under the current uncertainty assumptions.

Discrete dynamical laser equation for the critical onset of bistability, entanglement and disappearance

NASA Astrophysics Data System (ADS)

Abdul, M.; Farooq, U.; Akbar, Jehan; Saif, F.

2018-06-01

We transform the semi-classical laser equation for single mode homogeneously broadened lasers to a one-dimensional nonlinear map by using the discrete dynamical approach. The obtained mapping, referred to as laser logistic mapping (LLM), characteristically exhibits convergent, cyclic and chaotic behavior depending on the control parameter. Thus, the so obtained LLM explains stable, bistable, multi-stable, and chaotic solutions for output field intensity. The onset of bistability takes place at a critical value of the effective gain coefficient. The obtained analytical results are confirmed through numerical calculations.

Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca; Ronco, Michele

2017-10-01

We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.

Universal scaling function in discrete time asymmetric exclusion processes

NASA Astrophysics Data System (ADS)

Chia, Nicholas; Bundschuh, Ralf

2005-03-01

In the universality class of the one dimensional Kardar-Parisi-Zhang surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since Derrida and Lebowitz' original publication this universality has been verified for a variety of continuous time systems in the KPZ universality class. We study the Derrida-Lebowitz scaling function for multi-particle versions of the discrete time Asymmetric Exclusion Process. We find that in this discrete time system the Derrida-Lebowitz scaling function not only properly characterizes the large system size limit, but even accurately describes surprisingly small systems. These results have immediate applications in searching biological sequence databases.

A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids

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

Banks, J W; Schwendeman, D W; Kapila, A K

2006-02-13

A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on amore » uniform pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of an planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.« less

A discrete time-varying internal model-based approach for high precision tracking of a multi-axis servo gantry.

PubMed

Zhang, Zhen; Yan, Peng; Jiang, Huan; Ye, Peiqing

2014-09-01

In this paper, we consider the discrete time-varying internal model-based control design for high precision tracking of complicated reference trajectories generated by time-varying systems. Based on a novel parallel time-varying internal model structure, asymptotic tracking conditions for the design of internal model units are developed, and a low order robust time-varying stabilizer is further synthesized. In a discrete time setting, the high precision tracking control architecture is deployed on a Voice Coil Motor (VCM) actuated servo gantry system, where numerical simulations and real time experimental results are provided, achieving the tracking errors around 3.5‰ for frequency-varying signals. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Multi-Dimensional Asymptotically Stable 4th Order Accurate Schemes for the Diffusion Equation

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Ditkowski, Adi

1996-01-01

An algorithm is presented which solves the multi-dimensional diffusion equation on co mplex shapes to 4th-order accuracy and is asymptotically stable in time. This bounded-error result is achieved by constructing, on a rectangular grid, a differentiation matrix whose symmetric part is negative definite. The differentiation matrix accounts for the Dirichlet boundary condition by imposing penalty like terms. Numerical examples in 2-D show that the method is effective even where standard schemes, stable by traditional definitions fail.

Multi-Level Adaptive Techniques (MLAT) for singular-perturbation problems

NASA Technical Reports Server (NTRS)

Brandt, A.

1978-01-01

The multilevel (multigrid) adaptive technique, a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization is described. It provides very fast general solvers, together with adaptive, nearly optimal discretization schemes. In the process, boundary layers are automatically either resolved or skipped, depending on a control function which expresses the computational goal. The global error decreases exponentially as a function of the overall computational work, in a uniform rate independent of the magnitude of the singular-perturbation terms. The key is high-order uniformly stable difference equations, and uniformly smoothing relaxation schemes.

Mixed finite-difference scheme for analysis of simply supported thick plates.

NASA Technical Reports Server (NTRS)

Noor, A. K.

1973-01-01

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

Convergence Analysis of Triangular MAC Schemes for Two Dimensional Stokes Equations

PubMed Central

Wang, Ming; Zhong, Lin

2015-01-01

In this paper, we consider the use of H(div) elements in the velocity–pressure formulation to discretize Stokes equations in two dimensions. We address the error estimate of the element pair RT0–P0, which is known to be suboptimal, and render the error estimate optimal by the symmetry of the grids and by the superconvergence result of Lagrange inter-polant. By enlarging RT0 such that it becomes a modified BDM-type element, we develop a new discretization BDM1b–P0. We, therefore, generalize the classical MAC scheme on rectangular grids to triangular grids and retain all the desirable properties of the MAC scheme: exact divergence-free, solver-friendly, and local conservation of physical quantities. Further, we prove that the proposed discretization BDM1b–P0 achieves the optimal convergence rate for both velocity and pressure on general quasi-uniform grids, and one and half order convergence rate for the vorticity and a recovered pressure. We demonstrate the validity of theories developed here by numerical experiments. PMID:26041948

A novel method for 3D measurement of RFID multi-tag network based on matching vision and wavelet

NASA Astrophysics Data System (ADS)

Zhuang, Xiao; Yu, Xiaolei; Zhao, Zhimin; Wang, Donghua; Zhang, Wenjie; Liu, Zhenlu; Lu, Dongsheng; Dong, Dingbang

2018-07-01

In the field of radio frequency identification (RFID), the three-dimensional (3D) distribution of RFID multi-tag networks has a significant impact on their reading performance. At the same time, in order to realize the anti-collision of RFID multi-tag networks in practical engineering applications, the 3D distribution of RFID multi-tag networks must be measured. In this paper, a novel method for the 3D measurement of RFID multi-tag networks is proposed. A dual-CCD system (vertical and horizontal cameras) is used to obtain images of RFID multi-tag networks from different angles. Then, the wavelet threshold denoising method is used to remove noise in the obtained images. The template matching method is used to determine the two-dimensional coordinates and vertical coordinate of each tag. The 3D coordinates of each tag are obtained subsequently. Finally, a model of the nonlinear relation between the 3D coordinate distribution of the RFID multi-tag network and the corresponding reading distance is established using the wavelet neural network. The experiment results show that the average prediction relative error is 0.71% and the time cost is 2.17 s. The values of the average prediction relative error and time cost are smaller than those of the particle swarm optimization neural network and genetic algorithm–back propagation neural network. The time cost of the wavelet neural network is about 1% of that of the other two methods. The method proposed in this paper has a smaller relative error. The proposed method can improve the real-time performance of RFID multi-tag networks and the overall dynamic performance of multi-tag networks.

Fast frequency domain method to detect skew in a document image

NASA Astrophysics Data System (ADS)

Mehta, Sunita; Walia, Ekta; Dutta, Maitreyee

2015-12-01

In this paper, a new fast frequency domain method based on Discrete Wavelet Transform and Fast Fourier Transform has been implemented for the determination of the skew angle in a document image. Firstly, image size reduction is done by using two-dimensional Discrete Wavelet Transform and then skew angle is computed using Fast Fourier Transform. Skew angle error is almost negligible. The proposed method is experimented using a large number of documents having skew between -90° and +90° and results are compared with Moments with Discrete Wavelet Transform method and other commonly used existing methods. It has been determined that this method works more efficiently than the existing methods. Also, it works with typed, picture documents having different fonts and resolutions. It overcomes the drawback of the recently proposed method of Moments with Discrete Wavelet Transform that does not work with picture documents.

SU-F-T-350: Continuous Leaf Optimization (CLO) for IMRT Leaf Sequencing

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

Long, T; Chen, M; Jiang, S

Purpose: To study a new step-and-shoot IMRT leaf sequencing model that avoids the two main pitfalls of conventional leaf sequencing: (1) target fluence being stratified into a fixed number of discrete levels and/or (2) aperture leaf positions being restricted to a discrete set of locations. These assumptions induce error into the sequence or reduce the feasible region of potential plans, respectively. Methods: We develop a one-dimensional (single leaf pair) methodology that does not make assumptions (1) or (2) that can be easily extended to a multi-row model. The proposed continuous leaf optimization (CLO) methodology takes in an existing set ofmore » apertures and associated intensities, or solution “seed,” and improves the plan without the restrictiveness of 1or (2). It then uses a first-order descent algorithm to converge onto a locally optimal solution. A seed solution can come from models that assume (1) and (2), thus allowing the CLO model to improve upon existing leaf sequencing methodologies. Results: The CLO model was applied to 208 generated target fluence maps in one dimension. In all cases for all tested sequencing strategies, the CLO model made improvements on the starting seed objective function. The CLO model also was able to keep MUs low. Conclusion: The CLO model can improve upon existing leaf sequencing methods by avoiding the restrictions of (1) and (2). By allowing for more flexible leaf positioning, error can be reduced when matching some target fluence. This study lays the foundation for future models and solution methodologies that can incorporate continuous leaf positions explicitly into the IMRT treatment planning model. Supported by Cancer Prevention & Research Institute of Texas (CPRIT) - ID RP150485.« less

Hyperbolic Positioning with Antenna Arrays and Multi-Channel Pseudolite for Indoor Localization

PubMed Central

Fujii, Kenjirou; Sakamoto, Yoshihiro; Wang, Wei; Arie, Hiroaki; Schmitz, Alexander; Sugano, Shigeki

2015-01-01

A hyperbolic positioning method with antenna arrays consisting of proximately-located antennas and a multi-channel pseudolite is proposed in order to overcome the problems of indoor positioning with conventional pseudolites (ground-based GPS transmitters). A two-dimensional positioning experiment using actual devices is conducted. The experimental result shows that the positioning accuracy varies centimeter- to meter-level according to the geometric relation between the pseudolite antennas and the receiver. It also shows that the bias error of the carrier-phase difference observables is more serious than their random error. Based on the size of the bias error of carrier-phase difference that is inverse-calculated from the experimental result, three-dimensional positioning performance is evaluated by computer simulation. In addition, in the three-dimensional positioning scenario, an initial value convergence analysis of the non-linear least squares is conducted. Its result shows that initial values that can converge to a right position exist at least under the proposed antenna setup. The simulated values and evaluation methods introduced in this work can be applied to various antenna setups; therefore, by using them, positioning performance can be predicted in advance of installing an actual system. PMID:26437405

Stress Recovery and Error Estimation for 3-D Shell Structures

NASA Technical Reports Server (NTRS)

Riggs, H. R.

2000-01-01

The C1-continuous stress fields obtained from finite element analyses are in general lower- order accurate than are the corresponding displacement fields. Much effort has focussed on increasing their accuracy and/or their continuity, both for improved stress prediction and especially error estimation. A previous project developed a penalized, discrete least squares variational procedure that increases the accuracy and continuity of the stress field. The variational problem is solved by a post-processing, 'finite-element-type' analysis to recover a smooth, more accurate, C1-continuous stress field given the 'raw' finite element stresses. This analysis has been named the SEA/PDLS. The recovered stress field can be used in a posteriori error estimators, such as the Zienkiewicz-Zhu error estimator or equilibrium error estimators. The procedure was well-developed for the two-dimensional (plane) case involving low-order finite elements. It has been demonstrated that, if optimal finite element stresses are used for the post-processing, the recovered stress field is globally superconvergent. Extension of this work to three dimensional solids is straightforward. Attachment: Stress recovery and error estimation for shell structure (abstract only). A 4-node, shear-deformable flat shell element developed via explicit Kirchhoff constraints (abstract only). A novel four-node quadrilateral smoothing element for stress enhancement and error estimation (abstract only).

Notes on Accuracy of Finite-Volume Discretization Schemes on Irregular Grids

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2011-01-01

Truncation-error analysis is a reliable tool in predicting convergence rates of discretization errors on regular smooth grids. However, it is often misleading in application to finite-volume discretization schemes on irregular (e.g., unstructured) grids. Convergence of truncation errors severely degrades on general irregular grids; a design-order convergence can be achieved only on grids with a certain degree of geometric regularity. Such degradation of truncation-error convergence does not necessarily imply a lower-order convergence of discretization errors. In these notes, irregular-grid computations demonstrate that the design-order discretization-error convergence can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all.

Discretization vs. Rounding Error in Euler's Method

ERIC Educational Resources Information Center

Borges, Carlos F.

2011-01-01

Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…

Sensitivity of the model error parameter specification in weak-constraint four-dimensional variational data assimilation

NASA Astrophysics Data System (ADS)

Shaw, Jeremy A.; Daescu, Dacian N.

2017-08-01

This article presents the mathematical framework to evaluate the sensitivity of a forecast error aspect to the input parameters of a weak-constraint four-dimensional variational data assimilation system (w4D-Var DAS), extending the established theory from strong-constraint 4D-Var. Emphasis is placed on the derivation of the equations for evaluating the forecast sensitivity to parameters in the DAS representation of the model error statistics, including bias, standard deviation, and correlation structure. A novel adjoint-based procedure for adaptive tuning of the specified model error covariance matrix is introduced. Results from numerical convergence tests establish the validity of the model error sensitivity equations. Preliminary experiments providing a proof-of-concept are performed using the Lorenz multi-scale model to illustrate the theoretical concepts and potential benefits for practical applications.

A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth-Fokker-Planck equation

NASA Astrophysics Data System (ADS)

Taitano, W. T.; Chacón, L.; Simakov, A. N.; Molvig, K.

2015-09-01

In this study, we demonstrate a fully implicit algorithm for the multi-species, multidimensional Rosenbluth-Fokker-Planck equation which is exactly mass-, momentum-, and energy-conserving, and which preserves positivity. Unlike most earlier studies, we base our development on the Rosenbluth (rather than Landau) form of the Fokker-Planck collision operator, which reduces complexity while allowing for an optimal fully implicit treatment. Our discrete conservation strategy employs nonlinear constraints that force the continuum symmetries of the collision operator to be satisfied upon discretization. We converge the resulting nonlinear system iteratively using Jacobian-free Newton-Krylov methods, effectively preconditioned with multigrid methods for efficiency. Single- and multi-species numerical examples demonstrate the advertised accuracy properties of the scheme, and the superior algorithmic performance of our approach. In particular, the discretization approach is numerically shown to be second-order accurate in time and velocity space and to exhibit manifestly positive entropy production. That is, H-theorem behavior is indicated for all the examples we have tested. The solution approach is demonstrated to scale optimally with respect to grid refinement (with CPU time growing linearly with the number of mesh points), and timestep (showing very weak dependence of CPU time with time-step size). As a result, the proposed algorithm delivers several orders-of-magnitude speedup vs. explicit algorithms.

Multi-dimensional Upwind Fluctuation Splitting Scheme with Mesh Adaption for Hypersonic Viscous Flow. Degree awarded by Virginia Polytechnic Inst. and State Univ., 9 Nov. 2001

NASA Technical Reports Server (NTRS)

Wood, William A., III

2002-01-01

A multi-dimensional upwind fluctuation splitting scheme is developed and implemented for two-dimensional and axisymmetric formulations of the Navier-Stokes equations on unstructured meshes. Key features of the scheme are the compact stencil, full upwinding, and non-linear discretization which allow for second-order accuracy with enforced positivity. Throughout, the fluctuation splitting scheme is compared to a current state-of-the-art finite volume approach, a second-order, dual mesh upwind flux difference splitting scheme (DMFDSFV), and is shown to produce more accurate results using fewer computer resources for a wide range of test cases. A Blasius flat plate viscous validation case reveals a more accurate upsilon-velocity profile for fluctuation splitting, and the reduced artificial dissipation production is shown relative to DMFDSFV. Remarkably, the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. The second half of the report develops a local, compact, anisotropic unstructured mesh adaptation scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. The adaptation strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization.

A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Zaky, M. A.

2015-01-01

In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.

Stationary Wavelet-based Two-directional Two-dimensional Principal Component Analysis for EMG Signal Classification

NASA Astrophysics Data System (ADS)

Ji, Yi; Sun, Shanlin; Xie, Hong-Bo

2017-06-01

Discrete wavelet transform (WT) followed by principal component analysis (PCA) has been a powerful approach for the analysis of biomedical signals. Wavelet coefficients at various scales and channels were usually transformed into a one-dimensional array, causing issues such as the curse of dimensionality dilemma and small sample size problem. In addition, lack of time-shift invariance of WT coefficients can be modeled as noise and degrades the classifier performance. In this study, we present a stationary wavelet-based two-directional two-dimensional principal component analysis (SW2D2PCA) method for the efficient and effective extraction of essential feature information from signals. Time-invariant multi-scale matrices are constructed in the first step. The two-directional two-dimensional principal component analysis then operates on the multi-scale matrices to reduce the dimension, rather than vectors in conventional PCA. Results are presented from an experiment to classify eight hand motions using 4-channel electromyographic (EMG) signals recorded in healthy subjects and amputees, which illustrates the efficiency and effectiveness of the proposed method for biomedical signal analysis.

Inverse Heat Conduction Methods in the CHAR Code for Aerothermal Flight Data Reconstruction

NASA Technical Reports Server (NTRS)

Oliver, A Brandon; Amar, Adam J.

2016-01-01

Reconstruction of flight aerothermal environments often requires the solution of an inverse heat transfer problem, which is an ill-posed problem of specifying boundary conditions from discrete measurements in the interior of the domain. This paper will present the algorithms implemented in the CHAR code for use in reconstruction of EFT-1 flight data and future testing activities. Implementation nuances will be discussed, and alternative hybrid-methods that are permitted by the implementation will be described. Results will be presented for a number of one-dimensional and multi-dimensional problems

Calculating and controlling the error of discrete representations of Pareto surfaces in convex multi-criteria optimization.

PubMed

Craft, David

2010-10-01

A discrete set of points and their convex combinations can serve as a sparse representation of the Pareto surface in multiple objective convex optimization. We develop a method to evaluate the quality of such a representation, and show by example that in multiple objective radiotherapy planning, the number of Pareto optimal solutions needed to represent Pareto surfaces of up to five dimensions grows at most linearly with the number of objectives. The method described is also applicable to the representation of convex sets. Copyright © 2009 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

A WENO-Limited, ADER-DT, Finite-Volume Scheme for Efficient, Robust, and Communication-Avoiding Multi-Dimensional Transport

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

Norman, Matthew R

2014-01-01

The novel ADER-DT time discretization is applied to two-dimensional transport in a quadrature-free, WENO- and FCT-limited, Finite-Volume context. Emphasis is placed on (1) the serial and parallel computational properties of ADER-DT and this framework and (2) the flexibility of ADER-DT and this framework in efficiently balancing accuracy with other constraints important to transport applications. This study demonstrates a range of choices for the user when approaching their specific application while maintaining good parallel properties. In this method, genuine multi-dimensionality, single-step and single-stage time stepping, strict positivity, and a flexible range of limiting are all achieved with only one parallel synchronizationmore » and data exchange per time step. In terms of parallel data transfers per simulated time interval, this improves upon multi-stage time stepping and post-hoc filtering techniques such as hyperdiffusion. This method is evaluated with standard transport test cases over a range of limiting options to demonstrate quantitatively and qualitatively what a user should expect when employing this method in their application.« less

Advanced graphical user interface for multi-physics simulations using AMST

NASA Astrophysics Data System (ADS)

Hoffmann, Florian; Vogel, Frank

2017-07-01

Numerical modelling of particulate matter has gained much popularity in recent decades. Advanced Multi-physics Simulation Technology (AMST) is a state-of-the-art three dimensional numerical modelling technique combining the eX-tended Discrete Element Method (XDEM) with Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) [1]. One major limitation of this code is the lack of a graphical user interface (GUI) meaning that all pre-processing has to be made directly in a HDF5-file. This contribution presents the first graphical pre-processor developed for AMST.

Landsat D Thematic Mapper image dimensionality reduction and geometric correction accuracy

NASA Technical Reports Server (NTRS)

Ford, G. E.

1986-01-01

To characterize and quantify the performance of the Landsat thematic mapper (TM), techniques for dimensionality reduction by linear transformation have been studied and evaluated and the accuracy of the correction of geometric errors in TM images analyzed. Theoretical evaluations and comparisons for existing methods for the design of linear transformation for dimensionality reduction are presented. These methods include the discrete Karhunen Loeve (KL) expansion, Multiple Discriminant Analysis (MDA), Thematic Mapper (TM)-Tasseled Cap Linear Transformation and Singular Value Decomposition (SVD). A unified approach to these design problems is presented in which each method involves optimizing an objective function with respect to the linear transformation matrix. From these studies, four modified methods are proposed. They are referred to as the Space Variant Linear Transformation, the KL Transform-MDA hybrid method, and the First and Second Version of the Weighted MDA method. The modifications involve the assignment of weights to classes to achieve improvements in the class conditional probability of error for classes with high weights. Experimental evaluations of the existing and proposed methods have been performed using the six reflective bands of the TM data. It is shown that in terms of probability of classification error and the percentage of the cumulative eigenvalues, the six reflective bands of the TM data require only a three dimensional feature space. It is shown experimentally as well that for the proposed methods, the classes with high weights have improvements in class conditional probability of error estimates as expected.

An investigation into multi-dimensional prediction models to estimate the pose error of a quadcopter in a CSP plant setting

NASA Astrophysics Data System (ADS)

Lock, Jacobus C.; Smit, Willie J.; Treurnicht, Johann

2016-05-01

The Solar Thermal Energy Research Group (STERG) is investigating ways to make heliostats cheaper to reduce the total cost of a concentrating solar power (CSP) plant. One avenue of research is to use unmanned aerial vehicles (UAVs) to automate and assist with the heliostat calibration process. To do this, the pose estimation error of each UAV must be determined and integrated into a calibration procedure. A computer vision (CV) system is used to measure the pose of a quadcopter UAV. However, this CV system contains considerable measurement errors. Since this is a high-dimensional problem, a sophisticated prediction model must be used to estimate the measurement error of the CV system for any given pose measurement vector. This paper attempts to train and validate such a model with the aim of using it to determine the pose error of a quadcopter in a CSP plant setting.

High-Order Methods for Incompressible Fluid Flow

NASA Astrophysics Data System (ADS)

Deville, M. O.; Fischer, P. F.; Mund, E. H.

2002-08-01

High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. Introductory chapters present high-order spatial and temporal discretizations for one-dimensional problems. These are extended to multiple space dimensions with a detailed discussion of tensor-product forms, multi-domain methods, and preconditioners for iterative solution techniques. Numerous discretizations of the steady and unsteady Stokes and Navier-Stokes equations are presented, with particular sttention given to enforcement of imcompressibility. Advanced discretizations. implementation issues, and parallel and vector performance are considered in the closing sections. Numerous examples are provided throughout to illustrate the capabilities of high-order methods in actual applications.

Hybrid simulation combining two space-time discretization of the discrete-velocity Boltzmann equation

NASA Astrophysics Data System (ADS)

Horstmann, Jan Tobias; Le Garrec, Thomas; Mincu, Daniel-Ciprian; Lévêque, Emmanuel

2017-11-01

Despite the efficiency and low dissipation of the stream-collide scheme of the discrete-velocity Boltzmann equation, which is nowadays implemented in many lattice Boltzmann solvers, a major drawback exists over alternative discretization schemes, i.e. finite-volume or finite-difference, that is the limitation to Cartesian uniform grids. In this paper, an algorithm is presented that combines the positive features of each scheme in a hybrid lattice Boltzmann method. In particular, the node-based streaming of the distribution functions is coupled with a second-order finite-volume discretization of the advection term of the Boltzmann equation under the Bhatnagar-Gross-Krook approximation. The algorithm is established on a multi-domain configuration, with the individual schemes being solved on separate sub-domains and connected by an overlapping interface of at least 2 grid cells. A critical parameter in the coupling is the CFL number equal to unity, which is imposed by the stream-collide algorithm. Nevertheless, a semi-implicit treatment of the collision term in the finite-volume formulation allows us to obtain a stable solution for this condition. The algorithm is validated in the scope of three different test cases on a 2D periodic mesh. It is shown that the accuracy of the combined discretization schemes agrees with the order of each separate scheme involved. The overall numerical error of the hybrid algorithm in the macroscopic quantities is contained between the error of the two individual algorithms. Finally, we demonstrate how such a coupling can be used to adapt to anisotropic flows with some gradual mesh refinement in the FV domain.

A robust computational technique for model order reduction of two-time-scale discrete systems via genetic algorithms.

PubMed

Alsmadi, Othman M K; Abo-Hammour, Zaer S

2015-01-01

A robust computational technique for model order reduction (MOR) of multi-time-scale discrete systems (single input single output (SISO) and multi-input multioutput (MIMO)) is presented in this paper. This work is motivated by the singular perturbation of multi-time-scale systems where some specific dynamics may not have significant influence on the overall system behavior. The new approach is proposed using genetic algorithms (GA) with the advantage of obtaining a reduced order model, maintaining the exact dominant dynamics in the reduced order, and minimizing the steady state error. The reduction process is performed by obtaining an upper triangular transformed matrix of the system state matrix defined in state space representation along with the elements of B, C, and D matrices. The GA computational procedure is based on maximizing the fitness function corresponding to the response deviation between the full and reduced order models. The proposed computational intelligence MOR method is compared to recently published work on MOR techniques where simulation results show the potential and advantages of the new approach.

Ensemble-type numerical uncertainty information from single model integrations

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

Rauser, Florian, E-mail: florian.rauser@mpimet.mpg.de; Marotzke, Jochem; Korn, Peter

2015-07-01

We suggest an algorithm that quantifies the discretization error of time-dependent physical quantities of interest (goals) for numerical models of geophysical fluid dynamics. The goal discretization error is estimated using a sum of weighted local discretization errors. The key feature of our algorithm is that these local discretization errors are interpreted as realizations of a random process. The random process is determined by the model and the flow state. From a class of local error random processes we select a suitable specific random process by integrating the model over a short time interval at different resolutions. The weights of themore » influences of the local discretization errors on the goal are modeled as goal sensitivities, which are calculated via automatic differentiation. The integration of the weighted realizations of local error random processes yields a posterior ensemble of goal approximations from a single run of the numerical model. From the posterior ensemble we derive the uncertainty information of the goal discretization error. This algorithm bypasses the requirement of detailed knowledge about the models discretization to generate numerical error estimates. The algorithm is evaluated for the spherical shallow-water equations. For two standard test cases we successfully estimate the error of regional potential energy, track its evolution, and compare it to standard ensemble techniques. The posterior ensemble shares linear-error-growth properties with ensembles of multiple model integrations when comparably perturbed. The posterior ensemble numerical error estimates are of comparable size as those of a stochastic physics ensemble.« less

Numerical treatment for solving two-dimensional space-fractional advection-dispersion equation using meshless method

NASA Astrophysics Data System (ADS)

Cheng, Rongjun; Sun, Fengxin; Wei, Qi; Wang, Jufeng

2018-02-01

Space-fractional advection-dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann-Liouville operator is discretized by the Grünwald formula. With center difference method, EFG method and Grünwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results by other well-known methods, the computed approximate solutions are presented in the format of tables and graphs. The presented results demonstrate the validity, efficiency and accuracy of the proposed techniques. Furthermore, the error is computed and the proposed method has reasonable convergence rates in spatial and temporal discretizations.

Differentially Private Synthesization of Multi-Dimensional Data using Copula Functions

PubMed Central

Li, Haoran; Xiong, Li; Jiang, Xiaoqian

2014-01-01

Differential privacy has recently emerged in private statistical data release as one of the strongest privacy guarantees. Most of the existing techniques that generate differentially private histograms or synthetic data only work well for single dimensional or low-dimensional histograms. They become problematic for high dimensional and large domain data due to increased perturbation error and computation complexity. In this paper, we propose DPCopula, a differentially private data synthesization technique using Copula functions for multi-dimensional data. The core of our method is to compute a differentially private copula function from which we can sample synthetic data. Copula functions are used to describe the dependence between multivariate random vectors and allow us to build the multivariate joint distribution using one-dimensional marginal distributions. We present two methods for estimating the parameters of the copula functions with differential privacy: maximum likelihood estimation and Kendall’s τ estimation. We present formal proofs for the privacy guarantee as well as the convergence property of our methods. Extensive experiments using both real datasets and synthetic datasets demonstrate that DPCopula generates highly accurate synthetic multi-dimensional data with significantly better utility than state-of-the-art techniques. PMID:25405241

Test functions for three-dimensional control-volume mixed finite-element methods on irregular grids

USGS Publications Warehouse

Naff, R.L.; Russell, T.F.; Wilson, J.D.; ,; ,; ,; ,; ,

2000-01-01

Numerical methods based on unstructured grids, with irregular cells, usually require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element methods, vector shape functions are used to approximate the distribution of velocities across cells and vector test functions are used to minimize the error associated with the numerical approximation scheme. For a logically cubic mesh, the lowest-order shape functions are chosen in a natural way to conserve intercell fluxes that vary linearly in logical space. Vector test functions, while somewhat restricted by the mapping into the logical reference cube, admit a wider class of possibilities. Ideally, an error minimization procedure to select the test function from an acceptable class of candidates would be the best procedure. Lacking such a procedure, we first investigate the effect of possible test functions on the pressure distribution over the control volume; specifically, we look for test functions that allow for the elimination of intermediate pressures on cell faces. From these results, we select three forms for the test function for use in a control-volume mixed method code and subject them to an error analysis for different forms of grid irregularity; errors are reported in terms of the discrete L2 norm of the velocity error. Of these three forms, one appears to produce optimal results for most forms of grid irregularity.

Two-dimensional straightness measurement based on optical knife-edge sensing

NASA Astrophysics Data System (ADS)

Wang, Chen; Zhong, Fenghe; Ellis, Jonathan D.

2017-09-01

Straightness error is a parasitic translation along a perpendicular direction to the primary displacement axis of a linear stage. The parasitic translations could be coupled into other primary displacement directions of a multi-axis platform. Hence, its measurement and compensation are critical in precision multi-axis metrology, calibration, and manufacturing. This paper presents a two-dimensional (2D) straightness measurement configuration based on 2D optical knife-edge sensing, which is simple, light-weight, compact, and easy to align. It applies a 2D optical knife-edge to manipulate the diffraction pattern sensed by a quadrant photodetector, whose output voltages could derive 2D straightness errors after a calibration process. This paper analyzes the physical model of the configuration and performs simulations and experiments to study the system sensitivity, measurement nonlinearity, and error sources. The results demonstrate that the proposed configuration has higher sensitivity and insensitive to beam's vibration, compared with the conventional configurations without using the knife-edge, and could achieve ±0.25 μ m within a ±40 μ m measurement range along a 40 mm primary axial motion.

A multi-resolution approach to electromagnetic modeling.

NASA Astrophysics Data System (ADS)

Cherevatova, M.; Egbert, G. D.; Smirnov, M. Yu

2018-04-01

We present a multi-resolution approach for three-dimensional magnetotelluric forward modeling. Our approach is motivated by the fact that fine grid resolution is typically required at shallow levels to adequately represent near surface inhomogeneities, topography, and bathymetry, while a much coarser grid may be adequate at depth where the diffusively propagating electromagnetic fields are much smoother. This is especially true for forward modeling required in regularized inversion, where conductivity variations at depth are generally very smooth. With a conventional structured finite-difference grid the fine discretization required to adequately represent rapid variations near the surface are continued to all depths, resulting in higher computational costs. Increasing the computational efficiency of the forward modeling is especially important for solving regularized inversion problems. We implement a multi-resolution finite-difference scheme that allows us to decrease the horizontal grid resolution with depth, as is done with vertical discretization. In our implementation, the multi-resolution grid is represented as a vertical stack of sub-grids, with each sub-grid being a standard Cartesian tensor product staggered grid. Thus, our approach is similar to the octree discretization previously used for electromagnetic modeling, but simpler in that we allow refinement only with depth. The major difficulty arose in deriving the forward modeling operators on interfaces between adjacent sub-grids. We considered three ways of handling the interface layers and suggest a preferable one, which results in similar accuracy as the staggered grid solution, while retaining the symmetry of coefficient matrix. A comparison between multi-resolution and staggered solvers for various models show that multi-resolution approach improves on computational efficiency without compromising the accuracy of the solution.

Numerical Solution of Optimal Control Problem under SPDE Constraints

DTIC Science & Technology

2011-10-14

Faure and Sobol sequences are used to evaluate high dimensional integrals, and the errors in the numerical results for over 30 dimensions become quite...sequence; right: 1000 points of dimension 26 and 27 projection for optimal Kronecker sequence. benchmark Faure and Sobol methods. 2.2 High order...J. Goodman and J. O’Rourke, Handbook of discrete and computational geome- try, CRC Press, Inc., (2004). [5] S. Joe and F. Kuo, Constructing Sobol

Optimum projection pattern generation for grey-level coded structured light illumination systems

NASA Astrophysics Data System (ADS)

Porras-Aguilar, Rosario; Falaggis, Konstantinos; Ramos-Garcia, Ruben

2017-04-01

Structured light illumination (SLI) systems are well-established optical inspection techniques for noncontact 3D surface measurements. A common technique is multi-frequency sinusoidal SLI that obtains the phase map at various fringe periods in order to estimate the absolute phase, and hence, the 3D surface information. Nevertheless, multi-frequency SLI systems employ multiple measurement planes (e.g. four phase shifted frames) to obtain the phase at a given fringe period. It is therefore an age old challenge to obtain the absolute surface information using fewer measurement frames. Grey level (GL) coding techniques have been developed as an attempt to reduce the number of planes needed, because a spatio-temporal GL sequence employing p discrete grey-levels and m frames has the potential to unwrap up to pm fringes. Nevertheless, one major disadvantage of GL based SLI techniques is that there are often errors near the border of each stripe, because an ideal stepwise intensity change cannot be measured. If the step-change in intensity is a single discrete grey-level unit, this problem can usually be overcome by applying an appropriate threshold. However, severe errors occur if the intensity change at the border of the stripe exceeds several discrete grey-level units. In this work, an optimum GL based technique is presented that generates a series of projection patterns with a minimal gradient in the intensity. It is shown that when using this technique, the errors near the border of the stripes can be significantly reduced. This improvement is achieved with the choice generated patterns, and does not involve additional hardware or special post-processing techniques. The performance of that method is validated using both simulations and experiments. The reported technique is generic, works with an arbitrary number of frames, and can employ an arbitrary number of grey-levels.

A lock-free priority queue design based on multi-dimensional linked lists

DOE PAGES

Dechev, Damian; Zhang, Deli

2015-04-03

The throughput of concurrent priority queues is pivotal to multiprocessor applications such as discrete event simulation, best-first search and task scheduling. Existing lock-free priority queues are mostly based on skiplists, which probabilistically create shortcuts in an ordered list for fast insertion of elements. The use of skiplists eliminates the need of global rebalancing in balanced search trees and ensures logarithmic sequential search time on average, but the worst-case performance is linear with respect to the input size. In this paper, we propose a quiescently consistent lock-free priority queue based on a multi-dimensional list that guarantees worst-case search time of O(logN)more » for key universe of size N. The novel multi-dimensional list (MDList) is composed of nodes that contain multiple links to child nodes arranged by their dimensionality. The insertion operation works by first injectively mapping the scalar key to a high-dimensional vector, then uniquely locating the target position by using the vector as coordinates. Nodes in MDList are ordered by their coordinate prefixes and the ordering property of the data structure is readily maintained during insertion without rebalancing nor randomization. Furthermore, in our experimental evaluation using a micro-benchmark, our priority queue achieves an average of 50% speedup over the state of the art approaches under high concurrency.« less

A lock-free priority queue design based on multi-dimensional linked lists

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

Dechev, Damian; Zhang, Deli

The throughput of concurrent priority queues is pivotal to multiprocessor applications such as discrete event simulation, best-first search and task scheduling. Existing lock-free priority queues are mostly based on skiplists, which probabilistically create shortcuts in an ordered list for fast insertion of elements. The use of skiplists eliminates the need of global rebalancing in balanced search trees and ensures logarithmic sequential search time on average, but the worst-case performance is linear with respect to the input size. In this paper, we propose a quiescently consistent lock-free priority queue based on a multi-dimensional list that guarantees worst-case search time of O(logN)more » for key universe of size N. The novel multi-dimensional list (MDList) is composed of nodes that contain multiple links to child nodes arranged by their dimensionality. The insertion operation works by first injectively mapping the scalar key to a high-dimensional vector, then uniquely locating the target position by using the vector as coordinates. Nodes in MDList are ordered by their coordinate prefixes and the ordering property of the data structure is readily maintained during insertion without rebalancing nor randomization. Furthermore, in our experimental evaluation using a micro-benchmark, our priority queue achieves an average of 50% speedup over the state of the art approaches under high concurrency.« less

Statistical Projections for Multi-resolution, Multi-dimensional Visual Data Exploration and Analysis

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

Hoa T. Nguyen; Stone, Daithi; E. Wes Bethel

2016-01-01

An ongoing challenge in visual exploration and analysis of large, multi-dimensional datasets is how to present useful, concise information to a user for some specific visualization tasks. Typical approaches to this problem have proposed either reduced-resolution versions of data, or projections of data, or both. These approaches still have some limitations such as consuming high computation or suffering from errors. In this work, we explore the use of a statistical metric as the basis for both projections and reduced-resolution versions of data, with a particular focus on preserving one key trait in data, namely variation. We use two different casemore » studies to explore this idea, one that uses a synthetic dataset, and another that uses a large ensemble collection produced by an atmospheric modeling code to study long-term changes in global precipitation. The primary findings of our work are that in terms of preserving the variation signal inherent in data, that using a statistical measure more faithfully preserves this key characteristic across both multi-dimensional projections and multi-resolution representations than a methodology based upon averaging.« less

Discrete Cosine Transform Image Coding With Sliding Block Codes

NASA Astrophysics Data System (ADS)

Divakaran, Ajay; Pearlman, William A.

1989-11-01

A transform trellis coding scheme for images is presented. A two dimensional discrete cosine transform is applied to the image followed by a search on a trellis structured code. This code is a sliding block code that utilizes a constrained size reproduction alphabet. The image is divided into blocks by the transform coding. The non-stationarity of the image is counteracted by grouping these blocks in clusters through a clustering algorithm, and then encoding the clusters separately. Mandela ordered sequences are formed from each cluster i.e identically indexed coefficients from each block are grouped together to form one dimensional sequences. A separate search ensues on each of these Mandela ordered sequences. Padding sequences are used to improve the trellis search fidelity. The padding sequences absorb the error caused by the building up of the trellis to full size. The simulations were carried out on a 256x256 image ('LENA'). The results are comparable to any existing scheme. The visual quality of the image is enhanced considerably by the padding and clustering.

A modified adjoint-based grid adaptation and error correction method for unstructured grid

NASA Astrophysics Data System (ADS)

Cui, Pengcheng; Li, Bin; Tang, Jing; Chen, Jiangtao; Deng, Youqi

2018-05-01

Grid adaptation is an important strategy to improve the accuracy of output functions (e.g. drag, lift, etc.) in computational fluid dynamics (CFD) analysis and design applications. This paper presents a modified robust grid adaptation and error correction method for reducing simulation errors in integral outputs. The procedure is based on discrete adjoint optimization theory in which the estimated global error of output functions can be directly related to the local residual error. According to this relationship, local residual error contribution can be used as an indicator in a grid adaptation strategy designed to generate refined grids for accurately estimating the output functions. This grid adaptation and error correction method is applied to subsonic and supersonic simulations around three-dimensional configurations. Numerical results demonstrate that the sensitive grids to output functions are detected and refined after grid adaptation, and the accuracy of output functions is obviously improved after error correction. The proposed grid adaptation and error correction method is shown to compare very favorably in terms of output accuracy and computational efficiency relative to the traditional featured-based grid adaptation.

Multi-segmental movement patterns reflect juggling complexity and skill level.

PubMed

Zago, Matteo; Pacifici, Ilaria; Lovecchio, Nicola; Galli, Manuela; Federolf, Peter Andreas; Sforza, Chiarella

2017-08-01

The juggling action of six experts and six intermediates jugglers was recorded with a motion capture system and decomposed into its fundamental components through Principal Component Analysis. The aim was to quantify trends in movement dimensionality, multi-segmental patterns and rhythmicity as a function of proficiency level and task complexity. Dimensionality was quantified in terms of Residual Variance, while the Relative Amplitude was introduced to account for individual differences in movement components. We observed that: experience-related modifications in multi-segmental actions exist, such as the progressive reduction of error-correction movements, especially in complex task condition. The systematic identification of motor patterns sensitive to the acquisition of specific experience could accelerate the learning process. Copyright © 2017 Elsevier B.V. All rights reserved.

Numerical Analysis of an H 1-Galerkin Mixed Finite Element Method for Time Fractional Telegraph Equation

PubMed Central

Wang, Jinfeng; Zhao, Meng; Zhang, Min; Liu, Yang; Li, Hong

2014-01-01

We discuss and analyze an H 1-Galerkin mixed finite element (H 1-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H 1-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H 1-GMFE method. Based on the discussion on the theoretical error analysis in L 2-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H 1-norm. Moreover, we derive and analyze the stability of H 1-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure. PMID:25184148

The modified semi-discrete two-dimensional Toda lattice with self-consistent sources

NASA Astrophysics Data System (ADS)

Gegenhasi

2017-07-01

In this paper, we derive the Grammian determinant solutions to the modified semi-discrete two-dimensional Toda lattice equation, and then construct the semi-discrete two-dimensional Toda lattice equation with self-consistent sources via source generation procedure. The algebraic structure of the resulting coupled modified differential-difference equation is clarified by presenting its Grammian determinant solutions and Casorati determinant solutions. As an application of the Grammian determinant and Casorati determinant solution, the explicit one-soliton and two-soliton solution of the modified semi-discrete two-dimensional Toda lattice equation with self-consistent sources are given. We also construct another form of the modified semi-discrete two-dimensional Toda lattice equation with self-consistent sources which is the Bäcklund transformation for the semi-discrete two-dimensional Toda lattice equation with self-consistent sources.

On-line analysis of algae in water by discrete three-dimensional fluorescence spectroscopy.

PubMed

Zhao, Nanjing; Zhang, Xiaoling; Yin, Gaofang; Yang, Ruifang; Hu, Li; Chen, Shuang; Liu, Jianguo; Liu, Wenqing

2018-03-19

In view of the problem of the on-line measurement of algae classification, a method of algae classification and concentration determination based on the discrete three-dimensional fluorescence spectra was studied in this work. The discrete three-dimensional fluorescence spectra of twelve common species of algae belonging to five categories were analyzed, the discrete three-dimensional standard spectra of five categories were built, and the recognition, classification and concentration prediction of algae categories were realized by the discrete three-dimensional fluorescence spectra coupled with non-negative weighted least squares linear regression analysis. The results show that similarities between discrete three-dimensional standard spectra of different categories were reduced and the accuracies of recognition, classification and concentration prediction of the algae categories were significantly improved. By comparing with that of the chlorophyll a fluorescence excitation spectra method, the recognition accuracy rate in pure samples by discrete three-dimensional fluorescence spectra is improved 1.38%, and the recovery rate and classification accuracy in pure diatom samples 34.1% and 46.8%, respectively; the recognition accuracy rate of mixed samples by discrete-three dimensional fluorescence spectra is enhanced by 26.1%, the recovery rate of mixed samples with Chlorophyta 37.8%, and the classification accuracy of mixed samples with diatoms 54.6%.

Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

NASA Astrophysics Data System (ADS)

Bridges, Thomas J.; Reich, Sebastian

2001-06-01

The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

Numerical time-domain electromagnetics based on finite-difference and convolution

NASA Astrophysics Data System (ADS)

Lin, Yuanqu

Time-domain methods posses a number of advantages over their frequency-domain counterparts for the solution of wideband, nonlinear, and time varying electromagnetic scattering and radiation phenomenon. Time domain integral equation (TDIE)-based methods, which incorporate the beneficial properties of integral equation method, are thus well suited for solving broadband scattering problems for homogeneous scatterers. Widespread adoption of TDIE solvers has been retarded relative to other techniques by their inefficiency, inaccuracy and instability. Moreover, two-dimensional (2D) problems are especially problematic, because 2D Green's functions have infinite temporal support, exacerbating these difficulties. This thesis proposes a finite difference delay modeling (FDDM) scheme for the solution of the integral equations of 2D transient electromagnetic scattering problems. The method discretizes the integral equations temporally using first- and second-order finite differences to map Laplace-domain equations into the Z domain before transforming to the discrete time domain. The resulting procedure is unconditionally stable because of the nature of the Laplace- to Z-domain mapping. The first FDDM method developed in this thesis uses second-order Lagrange basis functions with Galerkin's method for spatial discretization. The second application of the FDDM method discretizes the space using a locally-corrected Nystrom method, which accelerates the precomputation phase and achieves high order accuracy. The Fast Fourier Transform (FFT) is applied to accelerate the marching-on-time process in both methods. While FDDM methods demonstrate impressive accuracy and stability in solving wideband scattering problems for homogeneous scatterers, they still have limitations in analyzing interactions between several inhomogenous scatterers. Therefore, this thesis devises a multi-region finite-difference time-domain (MR-FDTD) scheme based on domain-optimal Green's functions for solving sparsely-populated problems. The scheme uses a discrete Green's function (DGF) on the FDTD lattice to truncate the local subregions, and thus reduces reflection error on the local boundary. A continuous Green's function (CGF) is implemented to pass the influence of external fields into each FDTD region which mitigates the numerical dispersion and anisotropy of standard FDTD. Numerical results will illustrate the accuracy and stability of the proposed techniques.

Finite element solution for energy conservation using a highly stable explicit integration algorithm

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1972-01-01

Theoretical derivation of a finite element solution algorithm for the transient energy conservation equation in multidimensional, stationary multi-media continua with irregular solution domain closure is considered. The complete finite element matrix forms for arbitrarily irregular discretizations are established, using natural coordinate function representations. The algorithm is embodied into a user-oriented computer program (COMOC) which obtains transient temperature distributions at the node points of the finite element discretization using a highly stable explicit integration procedure with automatic error control features. The finite element algorithm is shown to posses convergence with discretization for a transient sample problem. The condensed form for the specific heat element matrix is shown to be preferable to the consistent form. Computed results for diverse problems illustrate the versatility of COMOC, and easily prepared output subroutines are shown to allow quick engineering assessment of solution behavior.

Fully decoupled monolithic projection method for natural convection problems

NASA Astrophysics Data System (ADS)

Pan, Xiaomin; Kim, Kyoungyoun; Lee, Changhoon; Choi, Jung-Il

2017-04-01

To solve time-dependent natural convection problems, we propose a fully decoupled monolithic projection method. The proposed method applies the Crank-Nicolson scheme in time and the second-order central finite difference in space. To obtain a non-iterative monolithic method from the fully discretized nonlinear system, we first adopt linearizations of the nonlinear convection terms and the general buoyancy term with incurring second-order errors in time. Approximate block lower-upper decompositions, along with an approximate factorization technique, are additionally employed to a global linearly coupled system, which leads to several decoupled subsystems, i.e., a fully decoupled monolithic procedure. We establish global error estimates to verify the second-order temporal accuracy of the proposed method for velocity, pressure, and temperature in terms of a discrete l2-norm. Moreover, according to the energy evolution, the proposed method is proved to be stable if the time step is less than or equal to a constant. In addition, we provide numerical simulations of two-dimensional Rayleigh-Bénard convection and periodic forced flow. The results demonstrate that the proposed method significantly mitigates the time step limitation, reduces the computational cost because only one Poisson equation is required to be solved, and preserves the second-order temporal accuracy for velocity, pressure, and temperature. Finally, the proposed method reasonably predicts a three-dimensional Rayleigh-Bénard convection for different Rayleigh numbers.

Multi-level Monte Carlo Methods for Efficient Simulation of Coulomb Collisions

NASA Astrophysics Data System (ADS)

Ricketson, Lee

2013-10-01

We discuss the use of multi-level Monte Carlo (MLMC) schemes--originally introduced by Giles for financial applications--for the efficient simulation of Coulomb collisions in the Fokker-Planck limit. The scheme is based on a Langevin treatment of collisions, and reduces the computational cost of achieving a RMS error scaling as ɛ from O (ɛ-3) --for standard Langevin methods and binary collision algorithms--to the theoretically optimal scaling O (ɛ-2) for the Milstein discretization, and to O (ɛ-2 (logɛ)2) with the simpler Euler-Maruyama discretization. In practice, this speeds up simulation by factors up to 100. We summarize standard MLMC schemes, describe some tricks for achieving the optimal scaling, present results from a test problem, and discuss the method's range of applicability. This work was performed under the auspices of the U.S. DOE by the University of California, Los Angeles, under grant DE-FG02-05ER25710, and by LLNL under contract DE-AC52-07NA27344.

The nonconforming virtual element method for eigenvalue problems

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

Gardini, Francesca; Manzini, Gianmarco; Vacca, Giuseppe

We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L 2-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problems. The proposed schemes provide a correct approximation of the spectrum and we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numericalmore » tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.« less

On Multi-Dimensional Unstructured Mesh Adaption

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1999-01-01

Anisotropic unstructured mesh adaption is developed for a truly multi-dimensional upwind fluctuation splitting scheme, as applied to scalar advection-diffusion. The adaption is performed locally using edge swapping, point insertion/deletion, and nodal displacements. Comparisons are made versus the current state of the art for aggressive anisotropic unstructured adaption, which is based on a posteriori error estimates. Demonstration of both schemes to model problems, with features representative of compressible gas dynamics, show the present method to be superior to the a posteriori adaption for linear advection. The performance of the two methods is more similar when applied to nonlinear advection, with a difference in the treatment of shocks. The a posteriori adaption can excessively cluster points to a shock, while the present multi-dimensional scheme tends to merely align with a shock, using fewer nodes. As a consequence of this alignment tendency, an implementation of eigenvalue limiting for the suppression of expansion shocks is developed for the multi-dimensional distribution scheme. The differences in the treatment of shocks by the adaption schemes, along with the inherently low levels of artificial dissipation in the fluctuation splitting solver, suggest the present method is a strong candidate for applications to compressible gas dynamics.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

Numerical solution of the Black-Scholes equation using cubic spline wavelets

NASA Astrophysics Data System (ADS)

Černá, Dana

2016-12-01

The Black-Scholes equation is used in financial mathematics for computation of market values of options at a given time. We use the θ-scheme for time discretization and an adaptive scheme based on wavelets for discretization on the given time level. Advantages of the proposed method are small number of degrees of freedom, high-order accuracy with respect to variables representing prices and relatively small number of iterations needed to resolve the problem with a desired accuracy. We use several cubic spline wavelet and multi-wavelet bases and discuss their advantages and disadvantages. We also compare an isotropic and anisotropic approach. Numerical experiments are presented for the two-dimensional Black-Scholes equation.

Multi-star processing and gyro filtering for the video inertial pointing system

NASA Technical Reports Server (NTRS)

Murphy, J. P.

1976-01-01

The video inertial pointing (VIP) system is being developed to satisfy the acquisition and pointing requirements of astronomical telescopes. The VIP system uses a single video sensor to provide star position information that can be used to generate three-axis pointing error signals (multi-star processing) and for input to a cathode ray tube (CRT) display of the star field. The pointing error signals are used to update the telescope's gyro stabilization system (gyro filtering). The CRT display facilitates target acquisition and positioning of the telescope by a remote operator. Linearized small angle equations are used for the multistar processing and a consideration of error performance and singularities lead to star pair location restrictions and equation selection criteria. A discrete steady-state Kalman filter which uses the integration of the gyros is developed and analyzed. The filter includes unit time delays representing asynchronous operations of the VIP microprocessor and video sensor. A digital simulation of a typical gyro stabilized gimbal is developed and used to validate the approach to the gyro filtering.

Finite Element A Posteriori Error Estimation for Heat Conduction. Degree awarded by George Washington Univ.

NASA Technical Reports Server (NTRS)

Lang, Christapher G.; Bey, Kim S. (Technical Monitor)

2002-01-01

This research investigates residual-based a posteriori error estimates for finite element approximations of heat conduction in single-layer and multi-layered materials. The finite element approximation, based upon hierarchical modelling combined with p-version finite elements, is described with specific application to a two-dimensional, steady state, heat-conduction problem. Element error indicators are determined by solving an element equation for the error with the element residual as a source, and a global error estimate in the energy norm is computed by collecting the element contributions. Numerical results of the performance of the error estimate are presented by comparisons to the actual error. Two methods are discussed and compared for approximating the element boundary flux. The equilibrated flux method provides more accurate results for estimating the error than the average flux method. The error estimation is applied to multi-layered materials with a modification to the equilibrated flux method to approximate the discontinuous flux along a boundary at the material interfaces. A directional error indicator is developed which distinguishes between the hierarchical modeling error and the finite element error. Numerical results are presented for single-layered materials which show that the directional indicators accurately determine which contribution to the total error dominates.

Multigrid for Staggered Lattice Fermions

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

Brower, Richard C.; Clark, M. A.; Strelchenko, Alexei

Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the K\\"ahler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model, however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.

A multi-band, multi-level, multi-electron model for efficient FDTD simulations of electromagnetic interactions with semiconductor quantum wells

NASA Astrophysics Data System (ADS)

Ravi, Koustuban; Wang, Qian; Ho, Seng-Tiong

2015-08-01

We report a new computational model for simulations of electromagnetic interactions with semiconductor quantum well(s) (SQW) in complex electromagnetic geometries using the finite-difference time-domain method. The presented model is based on an approach of spanning a large number of electron transverse momentum states in each SQW sub-band (multi-band) with a small number of discrete multi-electron states (multi-level, multi-electron). This enables accurate and efficient two-dimensional (2-D) and three-dimensional (3-D) simulations of nanophotonic devices with SQW active media. The model includes the following features: (1) Optically induced interband transitions between various SQW conduction and heavy-hole or light-hole sub-bands are considered. (2) Novel intra sub-band and inter sub-band transition terms are derived to thermalize the electron and hole occupational distributions to the correct Fermi-Dirac distributions. (3) The terms in (2) result in an explicit update scheme which circumvents numerically cumbersome iterative procedures. This significantly augments computational efficiency. (4) Explicit update terms to account for carrier leakage to unconfined states are derived, which thermalize the bulk and SQW populations to a common quasi-equilibrium Fermi-Dirac distribution. (5) Auger recombination and intervalence band absorption are included. The model is validated by comparisons to analytic band-filling calculations, simulations of SQW optical gain spectra, and photonic crystal lasers.

Are strategies in physics discrete? A remote controlled investigation

NASA Astrophysics Data System (ADS)

Heck, Robert; Sherson, Jacob F.; www. scienceathome. org Team; players Team

2017-04-01

In science, strategies are formulated based on observations, calculations, or physical insight. For any given physical process, often several distinct strategies are identified. Are these truly distinct or simply low dimensional representations of a high dimensional continuum of solutions? Our online citizen science platform www.scienceathome.org used by more than 150,000 people recently enabled finding solutions to fast, 1D single atom transport [Nature2016]. Surprisingly, player trajectories bunched into discrete solution strategies (clans) yielding clear, distinct physical insight. Introducing the multi-dimensional vector in the direction of other local maxima we locate narrow, high-yield ``bridges'' connecting the clans. This demonstrates for this problem that a continuum of solutions with no clear physical interpretation does in fact exist. Next, four distinct strategies for creating Bose-Einstein condensates were investigated experimentally: hybrid and crossed dipole trap configurations in combination with either large volume or dimple loading from a magnetic trap. We find that although each conventional strategy appears locally optimal, ``bridges'' can be identified. In a novel approach, the problem was gamified allowing 750 citizen scientists to contribute to the experimental optimization yielding nearly a factor two improvement in atom number.

A Lightning Channel Retrieval Algorithm for the North Alabama Lightning Mapping Array (LMA)

NASA Technical Reports Server (NTRS)

Koshak, William; Arnold, James E. (Technical Monitor)

2002-01-01

A new multi-station VHF time-of-arrival (TOA) antenna network is, at the time of this writing, coming on-line in Northern Alabama. The network, called the Lightning Mapping Array (LMA), employs GPS timing and detects VHF radiation from discrete segments (effectively point emitters) that comprise the channel of lightning strokes within cloud and ground flashes. The network will support on-going ground validation activities of the low Earth orbiting Lightning Imaging Sensor (LIS) satellite developed at NASA Marshall Space Flight Center (MSFC) in Huntsville, Alabama. It will also provide for many interesting and detailed studies of the distribution and evolution of thunderstorms and lightning in the Tennessee Valley, and will offer many interesting comparisons with other meteorological/geophysical wets associated with lightning and thunderstorms. In order to take full advantage of these benefits, it is essential that the LMA channel mapping accuracy (in both space and time) be fully characterized and optimized. In this study, a new revised channel mapping retrieval algorithm is introduced. The algorithm is an extension of earlier work provided in Koshak and Solakiewicz (1996) in the analysis of the NASA Kennedy Space Center (KSC) Lightning Detection and Ranging (LDAR) system. As in the 1996 study, direct algebraic solutions are obtained by inverting a simple linear system of equations, thereby making computer searches through a multi-dimensional parameter domain of a Chi-Squared function unnecessary. However, the new algorithm is developed completely in spherical Earth-centered coordinates (longitude, latitude, altitude), rather than in the (x, y, z) cartesian coordinates employed in the 1996 study. Hence, no mathematical transformations from (x, y, z) into spherical coordinates are required (such transformations involve more numerical error propagation, more computer program coding, and slightly more CPU computing time). The new algorithm also has a more realistic definition of source altitude that accounts for Earth oblateness (this can become important for sources that are hundreds of kilometers away from the network). In addition, the new algorithm is being applied to analyze computer simulated LMA datasets in order to obtain detailed location/time retrieval error maps for sources in and around the LMA network. These maps will provide a more comprehensive analysis of retrieval errors for LMA than the 1996 study did of LDAR retrieval errors. Finally, we note that the new algorithm can be applied to LDAR, and essentially any other multi-station TWA network that depends on direct line-of-site antenna excitation.

Stochastic Evolution Equations Driven by Fractional Noises

DTIC Science & Technology

2016-11-28

rate of convergence to zero or the error and the limit in distribution of the error fluctuations. We have studied time discrete numerical schemes...error fluctuations. We have studied time discrete numerical schemes based on Taylor expansions for rough differential equations and for stochastic...variations of the time discrete Taylor schemes for rough differential equations and for stochastic differential equations driven by fractional Brownian

The dimension split element-free Galerkin method for three-dimensional potential problems

NASA Astrophysics Data System (ADS)

Meng, Z. J.; Cheng, H.; Ma, L. D.; Cheng, Y. M.

2018-06-01

This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares (IMLS) approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method.

A Wavelet based Suboptimal Kalman Filter for Assimilation of Stratospheric Chemical Tracer Observations

NASA Technical Reports Server (NTRS)

Tangborn, Andrew; Auger, Ludovic

2003-01-01

A suboptimal Kalman filter system which evolves error covariances in terms of a truncated set of wavelet coefficients has been developed for the assimilation of chemical tracer observations of CH4. This scheme projects the discretized covariance propagation equations and covariance matrix onto an orthogonal set of compactly supported wavelets. Wavelet representation is localized in both location and scale, which allows for efficient representation of the inherently anisotropic structure of the error covariances. The truncation is carried out in such a way that the resolution of the error covariance is reduced only in the zonal direction, where gradients are smaller. Assimilation experiments which last 24 days, and used different degrees of truncation were carried out. These reduced the covariance size by 90, 97 and 99 % and the computational cost of covariance propagation by 80, 93 and 96 % respectively. The difference in both error covariance and the tracer field between the truncated and full systems over this period were found to be not growing in the first case, and growing relatively slowly in the later two cases. The largest errors in the tracer fields were found to occur in regions of largest zonal gradients in the constituent field. This results indicate that propagation of error covariances for a global two-dimensional data assimilation system are currently feasible. Recommendations for further reduction in computational cost are made with the goal of extending this technique to three-dimensional global assimilation systems.

The effectiveness of robotic training depends on motor task characteristics.

PubMed

Marchal-Crespo, Laura; Rappo, Nicole; Riener, Robert

2017-12-01

Previous research suggests that the effectiveness of robotic training depends on the motor task to be learned. However, it is still an open question which specific task's characteristics influence the efficacy of error-modulating training strategies. Motor tasks can be classified based on the time characteristics of the task, in particular the task's duration (discrete vs. continuous). Continuous tasks require movements without distinct beginning or end. Discrete tasks require fast movements that include well-defined postures at the beginning and the end. We developed two games, one that requires a continuous movement-a tracking task-and one that requires discrete movements-a fast reaching task. We conducted an experiment with thirty healthy subjects to evaluate the effectiveness of three error-modulating training strategies-no guidance, error amplification (i.e., repulsive forces proportional to errors) and haptic guidance-on self-reported motivation and learning of the continuous and discrete games. Training with error amplification resulted in better motor learning than haptic guidance, besides the fact that error amplification reduced subjects' interest/enjoyment and perceived competence during training. Only subjects trained with error amplification improved their performance after training the discrete game. In fact, subjects trained without guidance improved the performance in the continuous game significantly more than in the discrete game, probably because the continuous task required greater attentional levels. Error-amplifying training strategies have a great potential to provoke better motor learning in continuous and discrete tasks. However, their long-lasting negative effects on motivation might limit their applicability in intense neurorehabilitation programs.

Damageable contact between an elastic body and a rigid foundation

NASA Astrophysics Data System (ADS)

Campo, M.; Fernández, J. R.; Silva, A.

2009-02-01

In this work, the contact problem between an elastic body and a rigid obstacle is studied, including the development of material damage which results from internal compression or tension. The variational problem is formulated as a first-kind variational inequality for the displacements coupled with a parabolic partial differential equation for the damage field. The existence of a unique local weak solution is stated. Then, a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, three two-dimensional numerical simulations are performed to demonstrate the accuracy and the behaviour of the scheme.

Devaney chaos, Li-Yorke chaos, and multi-dimensional Li-Yorke chaos for topological dynamics

NASA Astrophysics Data System (ADS)

Dai, Xiongping; Tang, Xinjia

2017-11-01

Let π : T × X → X, written T↷π X, be a topological semiflow/flow on a uniform space X with T a multiplicative topological semigroup/group not necessarily discrete. We then prove: If T↷π X is non-minimal topologically transitive with dense almost periodic points, then it is sensitive to initial conditions. As a result of this, Devaney chaos ⇒ Sensitivity to initial conditions, for this very general setting. Let R+↷π X be a C0-semiflow on a Polish space; then we show: If R+↷π X is topologically transitive with at least one periodic point p and there is a dense orbit with no nonempty interior, then it is multi-dimensional Li-Yorke chaotic; that is, there is a uncountable set Θ ⊆ X such that for any k ≥ 2 and any distinct points x1 , … ,xk ∈ Θ, one can find two time sequences sn → ∞ ,tn → ∞ with Moreover, let X be a non-singleton Polish space; then we prove: Any weakly-mixing C0-semiflow R+↷π X is densely multi-dimensional Li-Yorke chaotic. Any minimal weakly-mixing topological flow T↷π X with T abelian is densely multi-dimensional Li-Yorke chaotic. Any weakly-mixing topological flow T↷π X is densely Li-Yorke chaotic. We in addition construct a completely Li-Yorke chaotic minimal SL (2 , R)-acting flow on the compact metric space R ∪ { ∞ }. Our various chaotic dynamics are sensitive to the choices of the topology of the phase semigroup/group T.

Large-scale hydropower system optimization using dynamic programming and object-oriented programming: the case of the Northeast China Power Grid.

PubMed

Li, Ji-Qing; Zhang, Yu-Shan; Ji, Chang-Ming; Wang, Ai-Jing; Lund, Jay R

2013-01-01

This paper examines long-term optimal operation using dynamic programming for a large hydropower system of 10 reservoirs in Northeast China. Besides considering flow and hydraulic head, the optimization explicitly includes time-varying electricity market prices to maximize benefit. Two techniques are used to reduce the 'curse of dimensionality' of dynamic programming with many reservoirs. Discrete differential dynamic programming (DDDP) reduces the search space and computer memory needed. Object-oriented programming (OOP) and the ability to dynamically allocate and release memory with the C++ language greatly reduces the cumulative effect of computer memory for solving multi-dimensional dynamic programming models. The case study shows that the model can reduce the 'curse of dimensionality' and achieve satisfactory results.

On the sub-model errors of a generalized one-way coupling scheme for linking models at different scales

NASA Astrophysics Data System (ADS)

Zeng, Jicai; Zha, Yuanyuan; Zhang, Yonggen; Shi, Liangsheng; Zhu, Yan; Yang, Jinzhong

2017-11-01

Multi-scale modeling of the localized groundwater flow problems in a large-scale aquifer has been extensively investigated under the context of cost-benefit controversy. An alternative is to couple the parent and child models with different spatial and temporal scales, which may result in non-trivial sub-model errors in the local areas of interest. Basically, such errors in the child models originate from the deficiency in the coupling methods, as well as from the inadequacy in the spatial and temporal discretizations of the parent and child models. In this study, we investigate the sub-model errors within a generalized one-way coupling scheme given its numerical stability and efficiency, which enables more flexibility in choosing sub-models. To couple the models at different scales, the head solution at parent scale is delivered downward onto the child boundary nodes by means of the spatial and temporal head interpolation approaches. The efficiency of the coupling model is improved either by refining the grid or time step size in the parent and child models, or by carefully locating the sub-model boundary nodes. The temporal truncation errors in the sub-models can be significantly reduced by the adaptive local time-stepping scheme. The generalized one-way coupling scheme is promising to handle the multi-scale groundwater flow problems with complex stresses and heterogeneity.

A submerged singularity method for calculating potential flow velocities at arbitrary near-field points

NASA Technical Reports Server (NTRS)

Maskew, B.

1976-01-01

A discrete singularity method has been developed for calculating the potential flow around two-dimensional airfoils. The objective was to calculate velocities at any arbitrary point in the flow field, including points that approach the airfoil surface. That objective was achieved and is demonstrated here on a Joukowski airfoil. The method used combined vortices and sources ''submerged'' a small distance below the airfoil surface and incorporated a near-field subvortex technique developed earlier. When a velocity calculation point approached the airfoil surface, the number of discrete singularities effectively increased (but only locally) to keep the point just outside the error region of the submerged singularity discretization. The method could be extended to three dimensions, and should improve nonlinear methods, which calculate interference effects between multiple wings, and which include the effects of force-free trailing vortex sheets. The capability demonstrated here would extend the scope of such calculations to allow the close approach of wings and vortex sheets (or vortices).

The Effects of Discrete-Trial Training Commission Errors on Learner Outcomes: An Extension

ERIC Educational Resources Information Center

Jenkins, Sarah R.; Hirst, Jason M.; DiGennaro Reed, Florence D.

2015-01-01

We conducted a parametric analysis of treatment integrity errors during discrete-trial training and investigated the effects of three integrity conditions (0, 50, or 100 % errors of commission) on performance in the presence and absence of programmed errors. The presence of commission errors impaired acquisition for three of four participants.…

A full-dimensional ab initio potential energy surface and rovibrational energies of the Ar–HF complex

NASA Astrophysics Data System (ADS)

Huang, Jing; Zhou, Yanzi; Xie, Daiqian

2018-04-01

We report a new full-dimensional ab initio potential energy surface for the Ar-HF van der Waals complex at the level of coupled-cluster singles and doubles with noniterative inclusion of connected triples levels [CCSD(T)] using augmented correlation-consistent quintuple-zeta basis set (aV5Z) plus bond functions. Full counterpoise correction was employed to correct the basis-set superposition error. The hypersurface was fitted using artificial neural network method with a root mean square error of 0.1085 cm-1 for more than 8000 ab initio points. The complex was found to prefer a linear Ar-H-F equilibrium structure. The three-dimensional discrete variable representation method and the Lanczos propagation algorithm were then employed to calculate the rovibrational states without separating inter- and intra- molecular nuclear motions. The calculated vibrational energies of Ar-HF differ from the experiment values within about 1 cm-1 on the first four HF vibrational states, and the predicted pure rotational energies on (0000) and (1000) vibrational states are deviated from the observed value by about 1%, which shows the accuracy of our new PES.

Simulation of DNAPL migration in heterogeneous translucent porous media based on estimation of representative elementary volume

NASA Astrophysics Data System (ADS)

Wu, Ming; Wu, Jianfeng; Wu, Jichun

2017-10-01

When the dense nonaqueous phase liquid (DNAPL) comes into the subsurface environment, its migration behavior is crucially affected by the permeability and entry pressure of subsurface porous media. A prerequisite for accurately simulating DNAPL migration in aquifers is then the determination of the permeability, entry pressure and corresponding representative elementary volumes (REV) of porous media. However, the permeability, entry pressure and corresponding representative elementary volumes (REV) are hard to determine clearly. This study utilizes the light transmission micro-tomography (LTM) method to determine the permeability and entry pressure of two dimensional (2D) translucent porous media and integrates the LTM with a criterion of relative gradient error to quantify the corresponding REV of porous media. As a result, the DNAPL migration in porous media might be accurately simulated by discretizing the model at the REV dimension. To validate the quantification methods, an experiment of perchloroethylene (PCE) migration is conducted in a two-dimensional heterogeneous bench-scale aquifer cell. Based on the quantifications of permeability, entry pressure and REV scales of 2D porous media determined by the LTM and relative gradient error, different models with different sizes of discretization grid are used to simulate the PCE migration. It is shown that the model based on REV size agrees well with the experimental results over the entire migration period including calibration, verification and validation processes. This helps to better understand the microstructures of porous media and achieve accurately simulating DNAPL migration in aquifers based on the REV estimation.

2.5D multi-view gait recognition based on point cloud registration.

PubMed

Tang, Jin; Luo, Jian; Tjahjadi, Tardi; Gao, Yan

2014-03-28

This paper presents a method for modeling a 2.5-dimensional (2.5D) human body and extracting the gait features for identifying the human subject. To achieve view-invariant gait recognition, a multi-view synthesizing method based on point cloud registration (MVSM) to generate multi-view training galleries is proposed. The concept of a density and curvature-based Color Gait Curvature Image is introduced to map 2.5D data onto a 2D space to enable data dimension reduction by discrete cosine transform and 2D principle component analysis. Gait recognition is achieved via a 2.5D view-invariant gait recognition method based on point cloud registration. Experimental results on the in-house database captured by a Microsoft Kinect camera show a significant performance gain when using MVSM.

Error control techniques for satellite and space communications

NASA Technical Reports Server (NTRS)

Costello, Daniel J., Jr.

1988-01-01

During the period December 1, 1987 through May 31, 1988, progress was made in the following areas: construction of Multi-Dimensional Bandwidth Efficient Trellis Codes with MPSK modulation; performance analysis of Bandwidth Efficient Trellis Coded Modulation schemes; and performance analysis of Bandwidth Efficient Trellis Codes on Fading Channels.

[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.

Visualizing histopathologic deep learning classification and anomaly detection using nonlinear feature space dimensionality reduction.

PubMed

Faust, Kevin; Xie, Quin; Han, Dominick; Goyle, Kartikay; Volynskaya, Zoya; Djuric, Ugljesa; Diamandis, Phedias

2018-05-16

There is growing interest in utilizing artificial intelligence, and particularly deep learning, for computer vision in histopathology. While accumulating studies highlight expert-level performance of convolutional neural networks (CNNs) on focused classification tasks, most studies rely on probability distribution scores with empirically defined cutoff values based on post-hoc analysis. More generalizable tools that allow humans to visualize histology-based deep learning inferences and decision making are scarce. Here, we leverage t-distributed Stochastic Neighbor Embedding (t-SNE) to reduce dimensionality and depict how CNNs organize histomorphologic information. Unique to our workflow, we develop a quantitative and transparent approach to visualizing classification decisions prior to softmax compression. By discretizing the relationships between classes on the t-SNE plot, we show we can super-impose randomly sampled regions of test images and use their distribution to render statistically-driven classifications. Therefore, in addition to providing intuitive outputs for human review, this visual approach can carry out automated and objective multi-class classifications similar to more traditional and less-transparent categorical probability distribution scores. Importantly, this novel classification approach is driven by a priori statistically defined cutoffs. It therefore serves as a generalizable classification and anomaly detection tool less reliant on post-hoc tuning. Routine incorporation of this convenient approach for quantitative visualization and error reduction in histopathology aims to accelerate early adoption of CNNs into generalized real-world applications where unanticipated and previously untrained classes are often encountered.

An adaptive discontinuous Galerkin solver for aerodynamic flows

NASA Astrophysics Data System (ADS)

Burgess, Nicholas K.

This work considers the accuracy, efficiency, and robustness of an unstructured high-order accurate discontinuous Galerkin (DG) solver for computational fluid dynamics (CFD). Recently, there has been a drive to reduce the discretization error of CFD simulations using high-order methods on unstructured grids. However, high-order methods are often criticized for lacking robustness and having high computational cost. The goal of this work is to investigate methods that enhance the robustness of high-order discontinuous Galerkin (DG) methods on unstructured meshes, while maintaining low computational cost and high accuracy of the numerical solutions. This work investigates robustness enhancement of high-order methods by examining effective non-linear solvers, shock capturing methods, turbulence model discretizations and adaptive refinement techniques. The goal is to develop an all encompassing solver that can simulate a large range of physical phenomena, where all aspects of the solver work together to achieve a robust, efficient and accurate solution strategy. The components and framework for a robust high-order accurate solver that is capable of solving viscous, Reynolds Averaged Navier-Stokes (RANS) and shocked flows is presented. In particular, this work discusses robust discretizations of the turbulence model equation used to close the RANS equations, as well as stable shock capturing strategies that are applicable across a wide range of discretization orders and applicable to very strong shock waves. Furthermore, refinement techniques are considered as both efficiency and robustness enhancement strategies. Additionally, efficient non-linear solvers based on multigrid and Krylov subspace methods are presented. The accuracy, efficiency, and robustness of the solver is demonstrated using a variety of challenging aerodynamic test problems, which include turbulent high-lift and viscous hypersonic flows. Adaptive mesh refinement was found to play a critical role in obtaining a robust and efficient high-order accurate flow solver. A goal-oriented error estimation technique has been developed to estimate the discretization error of simulation outputs. For high-order discretizations, it is shown that functional output error super-convergence can be obtained, provided the discretization satisfies a property known as dual consistency. The dual consistency of the DG methods developed in this work is shown via mathematical analysis and numerical experimentation. Goal-oriented error estimation is also used to drive an hp-adaptive mesh refinement strategy, where a combination of mesh or h-refinement, and order or p-enrichment, is employed based on the smoothness of the solution. The results demonstrate that the combination of goal-oriented error estimation and hp-adaptation yield superior accuracy, as well as enhanced robustness and efficiency for a variety of aerodynamic flows including flows with strong shock waves. This work demonstrates that DG discretizations can be the basis of an accurate, efficient, and robust CFD solver. Furthermore, enhancing the robustness of DG methods does not adversely impact the accuracy or efficiency of the solver for challenging and complex flow problems. In particular, when considering the computation of shocked flows, this work demonstrates that the available shock capturing techniques are sufficiently accurate and robust, particularly when used in conjunction with adaptive mesh refinement . This work also demonstrates that robust solutions of the Reynolds Averaged Navier-Stokes (RANS) and turbulence model equations can be obtained for complex and challenging aerodynamic flows. In this context, the most robust strategy was determined to be a low-order turbulence model discretization coupled to a high-order discretization of the RANS equations. Although RANS solutions using high-order accurate discretizations of the turbulence model were obtained, the behavior of current-day RANS turbulence models discretized to high-order was found to be problematic, leading to solver robustness issues. This suggests that future work is warranted in the area of turbulence model formulation for use with high-order discretizations. Alternately, the use of Large-Eddy Simulation (LES) subgrid scale models with high-order DG methods offers the potential to leverage the high accuracy of these methods for very high fidelity turbulent simulations. This thesis has developed the algorithmic improvements that will lay the foundation for the development of a three-dimensional high-order flow solution strategy that can be used as the basis for future LES simulations.

A GPU accelerated and error-controlled solver for the unbounded Poisson equation in three dimensions

NASA Astrophysics Data System (ADS)

Exl, Lukas

2017-12-01

An efficient solver for the three dimensional free-space Poisson equation is presented. The underlying numerical method is based on finite Fourier series approximation. While the error of all involved approximations can be fully controlled, the overall computation error is driven by the convergence of the finite Fourier series of the density. For smooth and fast-decaying densities the proposed method will be spectrally accurate. The method scales with O(N log N) operations, where N is the total number of discretization points in the Cartesian grid. The majority of the computational costs come from fast Fourier transforms (FFT), which makes it ideal for GPU computation. Several numerical computations on CPU and GPU validate the method and show efficiency and convergence behavior. Tests are performed using the Vienna Scientific Cluster 3 (VSC3). A free MATLAB implementation for CPU and GPU is provided to the interested community.

Hybrid Modeling for Testing Intelligent Software for Lunar-Mars Closed Life Support

NASA Technical Reports Server (NTRS)

Malin, Jane T.; Nicholson, Leonard S. (Technical Monitor)

1999-01-01

Intelligent software is being developed for closed life support systems with biological components, for human exploration of the Moon and Mars. The intelligent software functions include planning/scheduling, reactive discrete control and sequencing, management of continuous control, and fault detection, diagnosis, and management of failures and errors. Four types of modeling information have been essential to system modeling and simulation to develop and test the software and to provide operational model-based what-if analyses: discrete component operational and failure modes; continuous dynamic performance within component modes, modeled qualitatively or quantitatively; configuration of flows and power among components in the system; and operations activities and scenarios. CONFIG, a multi-purpose discrete event simulation tool that integrates all four types of models for use throughout the engineering and operations life cycle, has been used to model components and systems involved in the production and transfer of oxygen and carbon dioxide in a plant-growth chamber and between that chamber and a habitation chamber with physicochemical systems for gas processing.

Discrete-time online learning control for a class of unknown nonaffine nonlinear systems using reinforcement learning.

PubMed

Yang, Xiong; Liu, Derong; Wang, Ding; Wei, Qinglai

2014-07-01

In this paper, a reinforcement-learning-based direct adaptive control is developed to deliver a desired tracking performance for a class of discrete-time (DT) nonlinear systems with unknown bounded disturbances. We investigate multi-input-multi-output unknown nonaffine nonlinear DT systems and employ two neural networks (NNs). By using Implicit Function Theorem, an action NN is used to generate the control signal and it is also designed to cancel the nonlinearity of unknown DT systems, for purpose of utilizing feedback linearization methods. On the other hand, a critic NN is applied to estimate the cost function, which satisfies the recursive equations derived from heuristic dynamic programming. The weights of both the action NN and the critic NN are directly updated online instead of offline training. By utilizing Lyapunov's direct method, the closed-loop tracking errors and the NN estimated weights are demonstrated to be uniformly ultimately bounded. Two numerical examples are provided to show the effectiveness of the present approach. Copyright © 2014 Elsevier Ltd. All rights reserved.

A novel auto-tuning PID control mechanism for nonlinear systems.

PubMed

Cetin, Meric; Iplikci, Serdar

2015-09-01

In this paper, a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Comparing the Effectiveness of Error-Correction Strategies in Discrete Trial Training

ERIC Educational Resources Information Center

Turan, Michelle K.; Moroz, Lianne; Croteau, Natalie Paquet

2012-01-01

Error-correction strategies are essential considerations for behavior analysts implementing discrete trial training with children with autism. The research literature, however, is still lacking in the number of studies that compare and evaluate error-correction procedures. The purpose of this study was to compare two error-correction strategies:…

On the Importance of Both Dimensional and Discrete Models of Emotion.

PubMed

Harmon-Jones, Eddie; Harmon-Jones, Cindy; Summerell, Elizabeth

2017-09-29

We review research on the structure and functions of emotions that has benefitted from a serious consideration of both discrete and dimensional perspectives on emotion. To illustrate this point, we review research that demonstrates: (1) how affective valence within discrete emotions differs as a function of individuals and situations, and how these differences relate to various functions; (2) that anger (and other emotional states) should be considered as a discrete emotion but there are dimensions around and within anger; (3) that similarities exist between approach-related positive and negative discrete emotions and they have unique motivational functions; (4) that discrete emotions and broad dimensions of emotions both have unique functions; and (5) evidence that a "new" discrete emotion with discrete functions exists within a broader emotion family. We hope that this consideration of both discrete and dimensional perspectives on emotion will assist in understanding the functions of emotions.

On the Importance of Both Dimensional and Discrete Models of Emotion

PubMed Central

Harmon-Jones, Eddie

2017-01-01

We review research on the structure and functions of emotions that has benefitted from a serious consideration of both discrete and dimensional perspectives on emotion. To illustrate this point, we review research that demonstrates: (1) how affective valence within discrete emotions differs as a function of individuals and situations, and how these differences relate to various functions; (2) that anger (and other emotional states) should be considered as a discrete emotion but there are dimensions around and within anger; (3) that similarities exist between approach-related positive and negative discrete emotions and they have unique motivational functions; (4) that discrete emotions and broad dimensions of emotions both have unique functions; and (5) evidence that a “new” discrete emotion with discrete functions exists within a broader emotion family. We hope that this consideration of both discrete and dimensional perspectives on emotion will assist in understanding the functions of emotions. PMID:28961185

Semi-implicit integration factor methods on sparse grids for high-dimensional systems

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method.

A-posteriori error estimation for the finite point method with applications to compressible flow

NASA Astrophysics Data System (ADS)

Ortega, Enrique; Flores, Roberto; Oñate, Eugenio; Idelsohn, Sergio

2017-08-01

An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.

Robust iterative learning control for multi-phase batch processes: an average dwell-time method with 2D convergence indexes

NASA Astrophysics Data System (ADS)

Wang, Limin; Shen, Yiteng; Yu, Jingxian; Li, Ping; Zhang, Ridong; Gao, Furong

2018-01-01

In order to cope with system disturbances in multi-phase batch processes with different dimensions, a hybrid robust control scheme of iterative learning control combined with feedback control is proposed in this paper. First, with a hybrid iterative learning control law designed by introducing the state error, the tracking error and the extended information, the multi-phase batch process is converted into a two-dimensional Fornasini-Marchesini (2D-FM) switched system with different dimensions. Second, a switching signal is designed using the average dwell-time method integrated with the related switching conditions to give sufficient conditions ensuring stable running for the system. Finally, the minimum running time of the subsystems and the control law gains are calculated by solving the linear matrix inequalities. Meanwhile, a compound 2D controller with robust performance is obtained, which includes a robust extended feedback control for ensuring the steady-state tracking error to converge rapidly. The application on an injection molding process displays the effectiveness and superiority of the proposed strategy.

Space-time adaptive solution of inverse problems with the discrete adjoint method

NASA Astrophysics Data System (ADS)

Alexe, Mihai; Sandu, Adrian

2014-08-01

This paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent, adaptive grid, adaptive step models. Discrete adjoints are attractive in practice since they can be generated with low effort using automatic differentiation. However, this approach brings several important challenges. The space-time adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations. A reduction in accuracy of the discrete adjoint sensitivities may appear due to the inter-grid transfer operators. Moreover, the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations. This work shows that several of these potential issues can be avoided through a multi-level optimization strategy using discontinuous Galerkin (DG) hp-adaptive discretizations paired with Runge-Kutta (RK) time integration. We extend the concept of dual (adjoint) consistency to space-time RK-DG discretizations, which are then shown to be well suited for the adaptive solution of time-dependent inverse problems. Furthermore, we prove that DG mesh transfer operators on general meshes are also dual consistent. This allows the simultaneous derivation of the discrete adjoint for both the numerical solver and the mesh transfer logic with an automatic code generation mechanism such as algorithmic differentiation (AD), potentially speeding up development of large-scale simulation codes. The theoretical analysis is supported by numerical results reported for a two-dimensional non-stationary inverse problem.

Vertical discretization with finite elements for a global hydrostatic model on the cubed sphere

NASA Astrophysics Data System (ADS)

Yi, Tae-Hyeong; Park, Ja-Rin

2017-06-01

A formulation of Galerkin finite element with basis-spline functions on a hybrid sigma-pressure coordinate is presented to discretize the vertical terms of global Eulerian hydrostatic equations employed in a numerical weather prediction system, which is horizontally discretized with high-order spectral elements on a cubed sphere grid. This replaces the vertical discretization of conventional central finite difference that is first-order accurate in non-uniform grids and causes numerical instability in advection-dominant flows. Therefore, a model remains in the framework of Galerkin finite elements for both the horizontal and vertical spatial terms. The basis-spline functions, obtained from the de-Boor algorithm, are employed to derive both the vertical derivative and integral operators, since Eulerian advection terms are involved. These operators are used to discretize the vertical terms of the prognostic and diagnostic equations. To verify the vertical discretization schemes and compare their performance, various two- and three-dimensional idealized cases and a hindcast case with full physics are performed in terms of accuracy and stability. It was shown that the vertical finite element with the cubic basis-spline function is more accurate and stable than that of the vertical finite difference, as indicated by faster residual convergence, fewer statistical errors, and reduction in computational mode. This leads to the general conclusion that the overall performance of a global hydrostatic model might be significantly improved with the vertical finite element.

A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes

NASA Astrophysics Data System (ADS)

Raeli, Alice; Bergmann, Michel; Iollo, Angelo

2018-02-01

We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.

Multi-label classification of chronically ill patients with bag of words and supervised dimensionality reduction algorithms.

PubMed

Bromuri, Stefano; Zufferey, Damien; Hennebert, Jean; Schumacher, Michael

2014-10-01

This research is motivated by the issue of classifying illnesses of chronically ill patients for decision support in clinical settings. Our main objective is to propose multi-label classification of multivariate time series contained in medical records of chronically ill patients, by means of quantization methods, such as bag of words (BoW), and multi-label classification algorithms. Our second objective is to compare supervised dimensionality reduction techniques to state-of-the-art multi-label classification algorithms. The hypothesis is that kernel methods and locality preserving projections make such algorithms good candidates to study multi-label medical time series. We combine BoW and supervised dimensionality reduction algorithms to perform multi-label classification on health records of chronically ill patients. The considered algorithms are compared with state-of-the-art multi-label classifiers in two real world datasets. Portavita dataset contains 525 diabetes type 2 (DT2) patients, with co-morbidities of DT2 such as hypertension, dyslipidemia, and microvascular or macrovascular issues. MIMIC II dataset contains 2635 patients affected by thyroid disease, diabetes mellitus, lipoid metabolism disease, fluid electrolyte disease, hypertensive disease, thrombosis, hypotension, chronic obstructive pulmonary disease (COPD), liver disease and kidney disease. The algorithms are evaluated using multi-label evaluation metrics such as hamming loss, one error, coverage, ranking loss, and average precision. Non-linear dimensionality reduction approaches behave well on medical time series quantized using the BoW algorithm, with results comparable to state-of-the-art multi-label classification algorithms. Chaining the projected features has a positive impact on the performance of the algorithm with respect to pure binary relevance approaches. The evaluation highlights the feasibility of representing medical health records using the BoW for multi-label classification tasks. The study also highlights that dimensionality reduction algorithms based on kernel methods, locality preserving projections or both are good candidates to deal with multi-label classification tasks in medical time series with many missing values and high label density. Copyright © 2014 Elsevier Inc. All rights reserved.

Flyby Error Analysis Based on Contour Plots for the Cassini Tour

NASA Technical Reports Server (NTRS)

Stumpf, P. W.; Gist, E. M.; Goodson, T. D.; Hahn, Y.; Wagner, S. V.; Williams, P. N.

2008-01-01

The maneuver cancellation analysis consists of cost contour plots employed by the Cassini maneuver team. The plots are two-dimensional linear representations of a larger six-dimensional solution to a multi-maneuver, multi-encounter mission at Saturn. By using contours plotted with the dot product of vectors B and R and the dot product of vectors B and T components, it is possible to view the effects delta V on for various encounter positions in the B-plane. The plot is used in operations to help determine if the Approach Maneuver (ensuing encounter minus three days) and/or the Cleanup Maneuver (ensuing encounter plus three days) can be cancelled and also is a linear check of an integrated solution.

Data Visualization of Item-Total Correlation by Median Smoothing

ERIC Educational Resources Information Center

Yu, Chong Ho; Douglas, Samantha; Lee, Anna; An, Min

2016-01-01

This paper aims to illustrate how data visualization could be utilized to identify errors prior to modeling, using an example with multi-dimensional item response theory (MIRT). MIRT combines item response theory and factor analysis to identify a psychometric model that investigates two or more latent traits. While it may seem convenient to…

Assessment of Preconditioner for a USM3D Hierarchical Adaptive Nonlinear Method (HANIM) (Invited)

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frink, Neal T.

2016-01-01

Enhancements to the previously reported mixed-element USM3D Hierarchical Adaptive Nonlinear Iteration Method (HANIM) framework have been made to further improve robustness, efficiency, and accuracy of computational fluid dynamic simulations. The key enhancements include a multi-color line-implicit preconditioner, a discretely consistent symmetry boundary condition, and a line-mapping method for the turbulence source term discretization. The USM3D iterative convergence for the turbulent flows is assessed on four configurations. The configurations include a two-dimensional (2D) bump-in-channel, the 2D NACA 0012 airfoil, a three-dimensional (3D) bump-in-channel, and a 3D hemisphere cylinder. The Reynolds Averaged Navier Stokes (RANS) solutions have been obtained using a Spalart-Allmaras turbulence model and families of uniformly refined nested grids. Two types of HANIM solutions using line- and point-implicit preconditioners have been computed. Additional solutions using the point-implicit preconditioner alone (PA) method that broadly represents the baseline solver technology have also been computed. The line-implicit HANIM shows superior iterative convergence in most cases with progressively increasing benefits on finer grids.

ACCURATE CHEMICAL MASTER EQUATION SOLUTION USING MULTI-FINITE BUFFERS

PubMed Central

Cao, Youfang; Terebus, Anna; Liang, Jie

2016-01-01

The discrete chemical master equation (dCME) provides a fundamental framework for studying stochasticity in mesoscopic networks. Because of the multi-scale nature of many networks where reaction rates have large disparity, directly solving dCMEs is intractable due to the exploding size of the state space. It is important to truncate the state space effectively with quantified errors, so accurate solutions can be computed. It is also important to know if all major probabilistic peaks have been computed. Here we introduce the Accurate CME (ACME) algorithm for obtaining direct solutions to dCMEs. With multi-finite buffers for reducing the state space by O(n!), exact steady-state and time-evolving network probability landscapes can be computed. We further describe a theoretical framework of aggregating microstates into a smaller number of macrostates by decomposing a network into independent aggregated birth and death processes, and give an a priori method for rapidly determining steady-state truncation errors. The maximal sizes of the finite buffers for a given error tolerance can also be pre-computed without costly trial solutions of dCMEs. We show exactly computed probability landscapes of three multi-scale networks, namely, a 6-node toggle switch, 11-node phage-lambda epigenetic circuit, and 16-node MAPK cascade network, the latter two with no known solutions. We also show how probabilities of rare events can be computed from first-passage times, another class of unsolved problems challenging for simulation-based techniques due to large separations in time scales. Overall, the ACME method enables accurate and efficient solutions of the dCME for a large class of networks. PMID:27761104

Inference of multi-Gaussian property fields by probabilistic inversion of crosshole ground penetrating radar data using an improved dimensionality reduction

NASA Astrophysics Data System (ADS)

Hunziker, Jürg; Laloy, Eric; Linde, Niklas

2016-04-01

Deterministic inversion procedures can often explain field data, but they only deliver one final subsurface model that depends on the initial model and regularization constraints. This leads to poor insights about the uncertainties associated with the inferred model properties. In contrast, probabilistic inversions can provide an ensemble of model realizations that accurately span the range of possible models that honor the available calibration data and prior information allowing a quantitative description of model uncertainties. We reconsider the problem of inferring the dielectric permittivity (directly related to radar velocity) structure of the subsurface by inversion of first-arrival travel times from crosshole ground penetrating radar (GPR) measurements. We rely on the DREAM_(ZS) algorithm that is a state-of-the-art Markov chain Monte Carlo (MCMC) algorithm. Such algorithms need several orders of magnitude more forward simulations than deterministic algorithms and often become infeasible in high parameter dimensions. To enable high-resolution imaging with MCMC, we use a recently proposed dimensionality reduction approach that allows reproducing 2D multi-Gaussian fields with far fewer parameters than a classical grid discretization. We consider herein a dimensionality reduction from 5000 to 257 unknowns. The first 250 parameters correspond to a spectral representation of random and uncorrelated spatial fluctuations while the remaining seven geostatistical parameters are (1) the standard deviation of the data error, (2) the mean and (3) the variance of the relative electric permittivity, (4) the integral scale along the major axis of anisotropy, (5) the anisotropy angle, (6) the ratio of the integral scale along the minor axis of anisotropy to the integral scale along the major axis of anisotropy and (7) the shape parameter of the Matérn function. The latter essentially defines the type of covariance function (e.g., exponential, Whittle, Gaussian). We present an improved formulation of the dimensionality reduction, and numerically show how it reduces artifacts in the generated models and provides better posterior estimation of the subsurface geostatistical structure. We next show that the results of the method compare very favorably against previous deterministic and stochastic inversion results obtained at the South Oyster Bacterial Transport Site in Virginia, USA. The long-term goal of this work is to enable MCMC-based full waveform inversion of crosshole GPR data.

Parameterisation of multi-scale continuum perfusion models from discrete vascular networks.

PubMed

Hyde, Eoin R; Michler, Christian; Lee, Jack; Cookson, Andrew N; Chabiniok, Radek; Nordsletten, David A; Smith, Nicolas P

2013-05-01

Experimental data and advanced imaging techniques are increasingly enabling the extraction of detailed vascular anatomy from biological tissues. Incorporation of anatomical data within perfusion models is non-trivial, due to heterogeneous vessel density and disparate radii scales. Furthermore, previous idealised networks have assumed a spatially repeating motif or periodic canonical cell, thereby allowing for a flow solution via homogenisation. However, such periodicity is not observed throughout anatomical networks. In this study, we apply various spatial averaging methods to discrete vascular geometries in order to parameterise a continuum model of perfusion. Specifically, a multi-compartment Darcy model was used to provide vascular scale separation for the fluid flow. Permeability tensor fields were derived from both synthetic and anatomically realistic networks using (1) porosity-scaled isotropic, (2) Huyghe and Van Campen, and (3) projected-PCA methods. The Darcy pressure fields were compared via a root-mean-square error metric to an averaged Poiseuille pressure solution over the same domain. The method of Huyghe and Van Campen performed better than the other two methods in all simulations, even for relatively coarse networks. Furthermore, inter-compartment volumetric flux fields, determined using the spatially averaged discrete flux per unit pressure difference, were shown to be accurate across a range of pressure boundary conditions. This work justifies the application of continuum flow models to characterise perfusion resulting from flow in an underlying vascular network.

Free-space transmission with passive 2D beam steering for multi-gigabit-per-second per-beam indoor optical wireless networks.

PubMed

Oh, Chin Wan; Cao, Zizheng; Tangdiongga, Eduward; Koonen, Ton

2016-08-22

In order to circumvent radio spectrum congestion, we propose an innovative system which can provide multiple infrared optical wireless beams simultaneously where each beam supports multi-gigabit-per-second communication. Scalable two-dimensional beam steering by means of wavelength tuning is proposed. A passive beam-steering module constructed with cascaded reflection gratings is designed for simultaneous multi-user coverage. We experimentally characterized the beam-steered system and thoroughly evaluated the performance of steered channels using the spectrally efficient and robust discrete multitone modulation in a bandwidth-limited system deploying 10 GHz telecom transceivers. This study reports the achievement of at least 37 Gbps free-space transmission per beam over a distance of up to 2 m over 5.61° × 12.66° scanning angles.

2.5D Multi-View Gait Recognition Based on Point Cloud Registration

PubMed Central

Tang, Jin; Luo, Jian; Tjahjadi, Tardi; Gao, Yan

2014-01-01

This paper presents a method for modeling a 2.5-dimensional (2.5D) human body and extracting the gait features for identifying the human subject. To achieve view-invariant gait recognition, a multi-view synthesizing method based on point cloud registration (MVSM) to generate multi-view training galleries is proposed. The concept of a density and curvature-based Color Gait Curvature Image is introduced to map 2.5D data onto a 2D space to enable data dimension reduction by discrete cosine transform and 2D principle component analysis. Gait recognition is achieved via a 2.5D view-invariant gait recognition method based on point cloud registration. Experimental results on the in-house database captured by a Microsoft Kinect camera show a significant performance gain when using MVSM. PMID:24686727

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

Vincenti, H.; Vay, J. -L.

Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the result. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of themore » errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical discretization errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in each case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solver and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.« less

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

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

Jakeman, J.D., E-mail: jdjakem@sandia.gov; Wildey, T.

2015-01-01

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchicalmore » surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.« less

Integrated Aeromechanics with Three-Dimensional Solid-Multibody Structures

NASA Technical Reports Server (NTRS)

Datta, Anubhav; Johnson, Wayne

2014-01-01

A full three-dimensional finite element-multibody structural dynamic solver is coupled to a three-dimensional Reynolds-averaged Navier-Stokes solver for the prediction of integrated aeromechanical stresses and strains on a rotor blade in forward flight. The objective is to lay the foundations of all major pieces of an integrated three-dimensional rotor dynamic analysis - from model construction to aeromechanical solution to stress/strain calculation. The primary focus is on the aeromechanical solution. Two types of three-dimensional CFD/CSD interfaces are constructed for this purpose with an emphasis on resolving errors from geometry mis-match so that initial-stage approximate structural geometries can also be effectively analyzed. A three-dimensional structural model is constructed as an approximation to a UH-60A-like fully articulated rotor. The aerodynamic model is identical to the UH-60A rotor. For preliminary validation measurements from a UH-60A high speed flight is used where CFD coupling is essential to capture the advancing side tip transonic effects. The key conclusion is that an integrated aeromechanical analysis is indeed possible with three-dimensional structural dynamics but requires a careful description of its geometry and discretization of its parts.

A revision of the gamma-evaluation concept for the comparison of dose distributions.

PubMed

Bakai, Annemarie; Alber, Markus; Nüsslin, Fridtjof

2003-11-07

A method for the quantitative four-dimensional (4D) evaluation of discrete dose data based on gradient-dependent local acceptance thresholds is presented. The method takes into account the local dose gradients of a reference distribution for critical appraisal of misalignment and collimation errors. These contribute to the maximum tolerable dose error at each evaluation point to which the local dose differences between comparison and reference data are compared. As shown, the presented concept is analogous to the gamma-concept of Low et al (1998a Med. Phys. 25 656-61) if extended to (3+1) dimensions. The pointwise dose comparisons of the reformulated concept are easier to perform and speed up the evaluation process considerably, especially for fine-grid evaluations of 3D dose distributions. The occurrences of false negative indications due to the discrete nature of the data are reduced with the method. The presented method was applied to film-measured, clinical data and compared with gamma-evaluations. 4D and 3D evaluations were performed. Comparisons prove that 4D evaluations have to be given priority, especially if complex treatment situations are verified, e.g., non-coplanar beam configurations.

Upon Generating Discrete Expanding Integrable Models of the Toda Lattice Systems and Infinite Conservation Laws

NASA Astrophysics Data System (ADS)

Zhang, Yufeng; Zhang, Xiangzhi; Wang, Yan; Liu, Jiangen

2017-01-01

With the help of R-matrix approach, we present the Toda lattice systems that have extensive applications in statistical physics and quantum physics. By constructing a new discrete integrable formula by R-matrix, the discrete expanding integrable models of the Toda lattice systems and their Lax pairs are generated, respectively. By following the constructing formula again, we obtain the corresponding (2+1)-dimensional Toda lattice systems and their Lax pairs, as well as their (2+1)-dimensional discrete expanding integrable models. Finally, some conservation laws of a (1+1)-dimensional generalised Toda lattice system and a new (2+1)-dimensional lattice system are generated, respectively.

Multi-GPU Accelerated Admittance Method for High-Resolution Human Exposure Evaluation.

PubMed

Xiong, Zubiao; Feng, Shi; Kautz, Richard; Chandra, Sandeep; Altunyurt, Nevin; Chen, Ji

2015-12-01

A multi-graphics processing unit (GPU) accelerated admittance method solver is presented for solving the induced electric field in high-resolution anatomical models of human body when exposed to external low-frequency magnetic fields. In the solver, the anatomical model is discretized as a three-dimensional network of admittances. The conjugate orthogonal conjugate gradient (COCG) iterative algorithm is employed to take advantage of the symmetric property of the complex-valued linear system of equations. Compared against the widely used biconjugate gradient stabilized method, the COCG algorithm can reduce the solving time by 3.5 times and reduce the storage requirement by about 40%. The iterative algorithm is then accelerated further by using multiple NVIDIA GPUs. The computations and data transfers between GPUs are overlapped in time by using asynchronous concurrent execution design. The communication overhead is well hidden so that the acceleration is nearly linear with the number of GPU cards. Numerical examples show that our GPU implementation running on four NVIDIA Tesla K20c cards can reach 90 times faster than the CPU implementation running on eight CPU cores (two Intel Xeon E5-2603 processors). The implemented solver is able to solve large dimensional problems efficiently. A whole adult body discretized in 1-mm resolution can be solved in just several minutes. The high efficiency achieved makes it practical to investigate human exposure involving a large number of cases with a high resolution that meets the requirements of international dosimetry guidelines.

Errors due to the truncation of the computational domain in static three-dimensional electrical impedance tomography.

PubMed

Vauhkonen, P J; Vauhkonen, M; Kaipio, J P

2000-02-01

In electrical impedance tomography (EIT), an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. The currents spread out in three dimensions and therefore off-plane structures have a significant effect on the reconstructed images. A question arises: how far from the current carrying electrodes should the discretized model of the object be extended? If the model is truncated too near the electrodes, errors are produced in the reconstructed images. On the other hand if the model is extended very far from the electrodes the computational time may become too long in practice. In this paper the model truncation problem is studied with the extended finite element method. Forward solutions obtained using so-called infinite elements, long finite elements and separable long finite elements are compared to the correct solution. The effects of the truncation of the computational domain on the reconstructed images are also discussed and results from the three-dimensional (3D) sensitivity analysis are given. We show that if the finite element method with ordinary elements is used in static 3D EIT, the dimension of the problem can become fairly large if the errors associated with the domain truncation are to be avoided.

One-dimensional Lagrangian implicit hydrodynamic algorithm for Inertial Confinement Fusion applications

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

Ramis, Rafael, E-mail: rafael.ramis@upm.es

A new one-dimensional hydrodynamic algorithm, specifically developed for Inertial Confinement Fusion (ICF) applications, is presented. The scheme uses a fully conservative Lagrangian formulation in planar, cylindrical, and spherically symmetric geometries, and supports arbitrary equations of state with separate ion and electron components. Fluid equations are discretized on a staggered grid and stabilized by means of an artificial viscosity formulation. The space discretized equations are advanced in time using an implicit algorithm. The method includes several numerical parameters that can be adjusted locally. In regions with low Courant–Friedrichs–Lewy (CFL) number, where stability is not an issue, they can be adjusted tomore » optimize the accuracy. In typical problems, the truncation error can be reduced by a factor between 2 to 10 in comparison with conventional explicit algorithms. On the other hand, in regions with high CFL numbers, the parameters can be set to guarantee unconditional stability. The method can be integrated into complex ICF codes. This is demonstrated through several examples covering a wide range of situations: from thermonuclear ignition physics, where alpha particles are managed as an additional species, to low intensity laser–matter interaction, where liquid–vapor phase transitions occur.« less

Authenticating concealed private data while maintaining concealment

DOEpatents

Thomas, Edward V [Albuquerque, NM; Draelos, Timothy J [Albuquerque, NM

2007-06-26

A method of and system for authenticating concealed and statistically varying multi-dimensional data comprising: acquiring an initial measurement of an item, wherein the initial measurement is subject to measurement error; applying a transformation to the initial measurement to generate reference template data; acquiring a subsequent measurement of an item, wherein the subsequent measurement is subject to measurement error; applying the transformation to the subsequent measurement; and calculating a Euclidean distance metric between the transformed measurements; wherein the calculated Euclidean distance metric is identical to a Euclidean distance metric between the measurement prior to transformation.

Casing pipe damage detection with optical fiber sensors: a case study in oil well constructions

NASA Astrophysics Data System (ADS)

Zhou, Zhi; He, Jianping; Huang, Minghua; He, Jun; Ou, Jinping; Chen, Genda

2010-04-01

Casing pipes in oil well constructions may suddenly buckle inward as their inside and outside hydrostatic pressure difference increases. For the safety of construction workers and the steady development of oil industries, it is critically important to measure the stress state of a casing pipe. This study develops a rugged, real-time monitoring, and warning system that combines the distributed Brillouin Scattering Time Domain Reflectometry (BOTDR) and the discrete fiber Bragg grating (FBG) measurement. The BOTDR optical fiber sensors were embedded with no optical fiber splice joints in a fiber reinforced polymer (FRP) rebar and the FBG sensors were wrapped in epoxy resins and glass clothes, both installed during the segmental construction of casing pipes. In-situ tests indicate that the proposed sensing system and installation technique can survive the downhole driving process of casing pipes, withstand a harsh service environment, and remain in tact with the casing pipes for compatible strain measurements. The relative error of the measured strains between the distributed and discrete sensors is less than 12%. The FBG sensors successfully measured the maximum horizontal principal stress with a relative error of 6.7% in comparison with a cross multi-pole array acoustic instrument.

A Comparison of Error-Correction Procedures on Skill Acquisition during Discrete-Trial Instruction

ERIC Educational Resources Information Center

Carroll, Regina A.; Joachim, Brad T.; St. Peter, Claire C.; Robinson, Nicole

2015-01-01

Previous research supports the use of a variety of error-correction procedures to facilitate skill acquisition during discrete-trial instruction. We used an adapted alternating treatments design to compare the effects of 4 commonly used error-correction procedures on skill acquisition for 2 children with attention deficit hyperactivity disorder…

An Evaluation of Programmed Treatment-integrity Errors during Discrete-trial Instruction

ERIC Educational Resources Information Center

Carroll, Regina A.; Kodak, Tiffany; Fisher, Wayne W.

2013-01-01

This study evaluated the effects of programmed treatment-integrity errors on skill acquisition for children with an autism spectrum disorder (ASD) during discrete-trial instruction (DTI). In Study 1, we identified common treatment-integrity errors that occur during academic instruction in schools. In Study 2, we simultaneously manipulated 3…

A new PIC noise reduction technique

NASA Astrophysics Data System (ADS)

Barnes, D. C.

2014-10-01

Numerical solution of the Vlasov equation is considered in a general situation in which there is an underlying static solution (equilibrium). There are no further assumptions about dimensionality, smallenss of orbits, or disparate time scales. The semi-characteristic (SC) method for Vlasov solution is described. The usual characteristics of the equation, which are the single particle orbits, are modified in such a way that the equilibrium phase-space flow is removed. In this way, the shot noise introduced by the usual discrete particle representation of the equilibrium is static in time and can be removed completely by subtraction. An almost exact algorithm for this is based on the observation that a (infinitesimal or) discrete time step of any equilibrium MC realization is again a realization of the equilibrium, building up strings of associated simulation particles. In this way, the only added discretization error arises from the need to extrapolate backward in time the chain end points one dt using a canonical transformation. Previously developed energy-conserving time-implicit methods are applied without modification. 1D ES examples of Landau damping and velocity-space instability are given to illustrate the method.

Spectral collocation method with a flexible angular discretization scheme for radiative transfer in multi-layer graded index medium

NASA Astrophysics Data System (ADS)

Wei, Linyang; Qi, Hong; Sun, Jianping; Ren, Yatao; Ruan, Liming

2017-05-01

The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional SN discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.

Reduced discretization error in HZETRN

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

Slaba, Tony C., E-mail: Tony.C.Slaba@nasa.gov; Blattnig, Steve R., E-mail: Steve.R.Blattnig@nasa.gov; Tweed, John, E-mail: jtweed@odu.edu

2013-02-01

The deterministic particle transport code HZETRN is an efficient analysis tool for studying the effects of space radiation on humans, electronics, and shielding materials. In a previous work, numerical methods in the code were reviewed, and new methods were developed that further improved efficiency and reduced overall discretization error. It was also shown that the remaining discretization error could be attributed to low energy light ions (A < 4) with residual ranges smaller than the physical step-size taken by the code. Accurately resolving the spectrum of low energy light particles is important in assessing risk associated with astronaut radiation exposure.more » In this work, modifications to the light particle transport formalism are presented that accurately resolve the spectrum of low energy light ion target fragments. The modified formalism is shown to significantly reduce overall discretization error and allows a physical approximation to be removed. For typical step-sizes and energy grids used in HZETRN, discretization errors for the revised light particle transport algorithms are shown to be less than 4% for aluminum and water shielding thicknesses as large as 100 g/cm{sup 2} exposed to both solar particle event and galactic cosmic ray environments.« less

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

NASA Technical Reports Server (NTRS)

Cai, Z.; Manteuffel, T. A.; McCormick, S. F.

1996-01-01

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

Sampling-free Bayesian inversion with adaptive hierarchical tensor representations

NASA Astrophysics Data System (ADS)

Eigel, Martin; Marschall, Manuel; Schneider, Reinhold

2018-03-01

A sampling-free approach to Bayesian inversion with an explicit polynomial representation of the parameter densities is developed, based on an affine-parametric representation of a linear forward model. This becomes feasible due to the complete treatment in function spaces, which requires an efficient model reduction technique for numerical computations. The advocated perspective yields the crucial benefit that error bounds can be derived for all occuring approximations, leading to provable convergence subject to the discretization parameters. Moreover, it enables a fully adaptive a posteriori control with automatic problem-dependent adjustments of the employed discretizations. The method is discussed in the context of modern hierarchical tensor representations, which are used for the evaluation of a random PDE (the forward model) and the subsequent high-dimensional quadrature of the log-likelihood, alleviating the ‘curse of dimensionality’. Numerical experiments demonstrate the performance and confirm the theoretical results.

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio

1989-01-01

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

Image secure transmission for optical orthogonal frequency-division multiplexing visible light communication systems using chaotic discrete cosine transform

NASA Astrophysics Data System (ADS)

Wang, Zhongpeng; Zhang, Shaozhong; Chen, Fangni; Wu, Ming-Wei; Qiu, Weiwei

2017-11-01

A physical encryption scheme for orthogonal frequency-division multiplexing (OFDM) visible light communication (VLC) systems using chaotic discrete cosine transform (DCT) is proposed. In the scheme, the row of the DCT matrix is permutated by a scrambling sequence generated by a three-dimensional (3-D) Arnold chaos map. Furthermore, two scrambling sequences, which are also generated from a 3-D Arnold map, are employed to encrypt the real and imaginary parts of the transmitted OFDM signal before the chaotic DCT operation. The proposed scheme enhances the physical layer security and improves the bit error rate (BER) performance for OFDM-based VLC. The simulation results prove the efficiency of the proposed encryption method. The experimental results show that the proposed security scheme not only protects image data from eavesdroppers but also keeps the good BER and peak-to-average power ratio performances for image-based OFDM-VLC systems.

The Evolution and Discharge of Electric Fields within a Thunderstorm

NASA Astrophysics Data System (ADS)

Hager, William W.; Nisbet, John S.; Kasha, John R.

1989-05-01

A 3-dimensional electrical model for a thunderstorm is developed and finite difference approximations to the model are analyzed. If the spatial derivatives are approximated by a method akin to the ☐ scheme and if the temporal derivative is approximated by either a backward difference or the Crank-Nicholson scheme, we show that the resulting discretization is unconditionally stable. The forward difference approximation to the time derivative is stable when the time step is sufficiently small relative to the ratio between the permittivity and the conductivity. Max-norm error estimates for the discrete approximations are established. To handle the propagation of lightning, special numerical techniques are devised based on the Inverse Matrix Modification Formula and Cholesky updates. Numerical comparisons between the model and theoretical results of Wilson and Holzer-Saxon are presented. We also apply our model to a storm observed at the Kennedy Space Center on July 11, 1978.

An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Lu, James; Park, Michael A.; Darmofal, David L.

2003-01-01

An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.

Categorical dimensions of human odor descriptor space revealed by non-negative matrix factorization

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

Chennubhotla, Chakra; Castro, Jason

2013-01-01

In contrast to most other sensory modalities, the basic perceptual dimensions of olfaction remain un- clear. Here, we use non-negative matrix factorization (NMF) - a dimensionality reduction technique - to uncover structure in a panel of odor profiles, with each odor defined as a point in multi-dimensional descriptor space. The properties of NMF are favorable for the analysis of such lexical and perceptual data, and lead to a high-dimensional account of odor space. We further provide evidence that odor di- mensions apply categorically. That is, odor space is not occupied homogenously, but rather in a discrete and intrinsically clustered manner.more » We discuss the potential implications of these results for the neural coding of odors, as well as for developing classifiers on larger datasets that may be useful for predicting perceptual qualities from chemical structures.« less

Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature

NASA Technical Reports Server (NTRS)

Barth, Timothy; Abgrall, Remi; Biegel, Bryan (Technical Monitor)

2000-01-01

This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.

Six-component semi-discrete integrable nonlinear Schrödinger system

NASA Astrophysics Data System (ADS)

Vakhnenko, Oleksiy O.

2018-01-01

We suggest the six-component integrable nonlinear system on a quasi-one-dimensional lattice. Due to its symmetrical form, the general system permits a number of reductions; one of which treated as the semi-discrete integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell is considered in considerable details. Besides six truly independent basic field variables, the system is characterized by four concomitant fields whose background values produce three additional types of inter-site resonant interactions between the basic fields. As a result, the system dynamics becomes associated with the highly nonstandard form of Poisson structure. The elementary Poisson brackets between all field variables are calculated and presented explicitly. The richness of system dynamics is demonstrated on the multi-component soliton solution written in terms of properly parameterized soliton characteristics.

Numerical Error Estimation with UQ

NASA Astrophysics Data System (ADS)

Ackmann, Jan; Korn, Peter; Marotzke, Jochem

2014-05-01

Ocean models are still in need of means to quantify model errors, which are inevitably made when running numerical experiments. The total model error can formally be decomposed into two parts, the formulation error and the discretization error. The formulation error arises from the continuous formulation of the model not fully describing the studied physical process. The discretization error arises from having to solve a discretized model instead of the continuously formulated model. Our work on error estimation is concerned with the discretization error. Given a solution of a discretized model, our general problem statement is to find a way to quantify the uncertainties due to discretization in physical quantities of interest (diagnostics), which are frequently used in Geophysical Fluid Dynamics. The approach we use to tackle this problem is called the "Goal Error Ensemble method". The basic idea of the Goal Error Ensemble method is that errors in diagnostics can be translated into a weighted sum of local model errors, which makes it conceptually based on the Dual Weighted Residual method from Computational Fluid Dynamics. In contrast to the Dual Weighted Residual method these local model errors are not considered deterministically but interpreted as local model uncertainty and described stochastically by a random process. The parameters for the random process are tuned with high-resolution near-initial model information. However, the original Goal Error Ensemble method, introduced in [1], was successfully evaluated only in the case of inviscid flows without lateral boundaries in a shallow-water framework and is hence only of limited use in a numerical ocean model. Our work consists in extending the method to bounded, viscous flows in a shallow-water framework. As our numerical model, we use the ICON-Shallow-Water model. In viscous flows our high-resolution information is dependent on the viscosity parameter, making our uncertainty measures viscosity-dependent. We will show that we can choose a sensible parameter by using the Reynolds-number as a criteria. Another topic, we will discuss is the choice of the underlying distribution of the random process. This is especially of importance in the scope of lateral boundaries. We will present resulting error estimates for different height- and velocity-based diagnostics applied to the Munk gyre experiment. References [1] F. RAUSER: Error Estimation in Geophysical Fluid Dynamics through Learning; PhD Thesis, IMPRS-ESM, Hamburg, 2010 [2] F. RAUSER, J. MAROTZKE, P. KORN: Ensemble-type numerical uncertainty quantification from single model integrations; SIAM/ASA Journal on Uncertainty Quantification, submitted

Real-time correction of beamforming time delay errors in abdominal ultrasound imaging

NASA Astrophysics Data System (ADS)

Rigby, K. W.

2000-04-01

The speed of sound varies with tissue type, yet commercial ultrasound imagers assume a constant sound speed. Sound speed variation in abdominal fat and muscle layers is widely believed to be largely responsible for poor contrast and resolution in some patients. The simplest model of the abdominal wall assumes that it adds a spatially varying time delay to the ultrasound wavefront. The adequacy of this model is controversial. We describe an adaptive imaging system consisting of a GE LOGIQ 700 imager connected to a multi- processor computer. Arrival time errors for each beamforming channel, estimated by correlating each channel signal with the beamsummed signal, are used to correct the imager's beamforming time delays at the acoustic frame rate. A multi- row transducer provides two-dimensional sampling of arrival time errors. We observe significant improvement in abdominal images of healthy male volunteers: increased contrast of blood vessels, increased visibility of the renal capsule, and increased brightness of the liver.

Nonlinear Light Dynamics in Multi-Core Structures

DTIC Science & Technology

2017-02-27

be generated in continuous- discrete optical media such as multi-core optical fiber or waveguide arrays; localisation dynamics in a continuous... discrete nonlinear system. Detailed theoretical analysis is presented of the existence and stability of the discrete -continuous light bullets using a very...and pulse compression using wave collapse (self-focusing) energy localisation dynamics in a continuous- discrete nonlinear system, as implemented in a

Neural-Network-Based Robust Optimal Tracking Control for MIMO Discrete-Time Systems With Unknown Uncertainty Using Adaptive Critic Design.

PubMed

Liu, Lei; Wang, Zhanshan; Zhang, Huaguang

2018-04-01

This paper is concerned with the robust optimal tracking control strategy for a class of nonlinear multi-input multi-output discrete-time systems with unknown uncertainty via adaptive critic design (ACD) scheme. The main purpose is to establish an adaptive actor-critic control method, so that the cost function in the procedure of dealing with uncertainty is minimum and the closed-loop system is stable. Based on the neural network approximator, an action network is applied to generate the optimal control signal and a critic network is used to approximate the cost function, respectively. In contrast to the previous methods, the main features of this paper are: 1) the ACD scheme is integrated into the controllers to cope with the uncertainty and 2) a novel cost function, which is not in quadric form, is proposed so that the total cost in the design procedure is reduced. It is proved that the optimal control signals and the tracking errors are uniformly ultimately bounded even when the uncertainty exists. Finally, a numerical simulation is developed to show the effectiveness of the present approach.

The discrete-time compensated Kalman filter

NASA Technical Reports Server (NTRS)

Lee, W. H.; Athans, M.

1978-01-01

A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete time Kalman filter was derived. The resultant compensated Kalman Filter has the property that steady state bias estimation errors, resulting from modelling errors, were eliminated.

A fast numerical method for the valuation of American lookback put options

NASA Astrophysics Data System (ADS)

Song, Haiming; Zhang, Qi; Zhang, Ran

2015-10-01

A fast and efficient numerical method is proposed and analyzed for the valuation of American lookback options. American lookback option pricing problem is essentially a two-dimensional unbounded nonlinear parabolic problem. We reformulate it into a two-dimensional parabolic linear complementary problem (LCP) on an unbounded domain. The numeraire transformation and domain truncation technique are employed to convert the two-dimensional unbounded LCP into a one-dimensional bounded one. Furthermore, the variational inequality (VI) form corresponding to the one-dimensional bounded LCP is obtained skillfully by some discussions. The resulting bounded VI is discretized by a finite element method. Meanwhile, the stability of the semi-discrete solution and the symmetric positive definiteness of the full-discrete matrix are established for the bounded VI. The discretized VI related to options is solved by a projection and contraction method. Numerical experiments are conducted to test the performance of the proposed method.

Adaptive compressed sensing of multi-view videos based on the sparsity estimation

NASA Astrophysics Data System (ADS)

Yang, Senlin; Li, Xilong; Chong, Xin

2017-11-01

The conventional compressive sensing for videos based on the non-adaptive linear projections, and the measurement times is usually set empirically. As a result, the quality of videos reconstruction is always affected. Firstly, the block-based compressed sensing (BCS) with conventional selection for compressive measurements was described. Then an estimation method for the sparsity of multi-view videos was proposed based on the two dimensional discrete wavelet transform (2D DWT). With an energy threshold given beforehand, the DWT coefficients were processed with both energy normalization and sorting by descending order, and the sparsity of the multi-view video can be achieved by the proportion of dominant coefficients. And finally, the simulation result shows that, the method can estimate the sparsity of video frame effectively, and provides an active basis for the selection of compressive observation times. The result also shows that, since the selection of observation times is based on the sparsity estimated with the energy threshold provided, the proposed method can ensure the reconstruction quality of multi-view videos.

Hydrologic Model Development and Calibration: Contrasting a Single- and Multi-Objective Approach for Comparing Model Performance

NASA Astrophysics Data System (ADS)

Asadzadeh, M.; Maclean, A.; Tolson, B. A.; Burn, D. H.

2009-05-01

Hydrologic model calibration aims to find a set of parameters that adequately simulates observations of watershed behavior, such as streamflow, or a state variable, such as snow water equivalent (SWE). There are different metrics for evaluating calibration effectiveness that involve quantifying prediction errors, such as the Nash-Sutcliffe (NS) coefficient and bias evaluated for the entire calibration period, on a seasonal basis, for low flows, or for high flows. Many of these metrics are conflicting such that the set of parameters that maximizes the high flow NS differs from the set of parameters that maximizes the low flow NS. Conflicting objectives are very likely when different calibration objectives are based on different fluxes and/or state variables (e.g., NS based on streamflow versus SWE). One of the most popular ways to balance different metrics is to aggregate them based on their importance and find the set of parameters that optimizes a weighted sum of the efficiency metrics. Comparing alternative hydrologic models (e.g., assessing model improvement when a process or more detail is added to the model) based on the aggregated objective might be misleading since it represents one point on the tradeoff of desired error metrics. To derive a more comprehensive model comparison, we solved a bi-objective calibration problem to estimate the tradeoff between two error metrics for each model. Although this approach is computationally more expensive than the aggregation approach, it results in a better understanding of the effectiveness of selected models at each level of every error metric and therefore provides a better rationale for judging relative model quality. The two alternative models used in this study are two MESH hydrologic models (version 1.2) of the Wolf Creek Research basin that differ in their watershed spatial discretization (a single Grouped Response Unit, GRU, versus multiple GRUs). The MESH model, currently under development by Environment Canada, is a coupled land-surface and hydrologic model. Results will demonstrate the conclusions a modeller might make regarding the value of additional watershed spatial discretization under both an aggregated (single-objective) and multi-objective model comparison framework.

Effects of Mesh Irregularities on Accuracy of Finite-Volume Discretization Schemes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2012-01-01

The effects of mesh irregularities on accuracy of unstructured node-centered finite-volume discretizations are considered. The focus is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. For inviscid fluxes, the discretization is nominally third order accurate on general triangular meshes. For viscous fluxes, the scheme is an average-least-squares formulation that is nominally second order accurate and contrasted with a common Green-Gauss discretization scheme. Gradient errors, truncation errors, and discretization errors are separately studied according to a previously introduced comprehensive methodology. The methodology considers three classes of grids: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancing layer grids. The meshes within the classes range from regular to extremely irregular including meshes with random perturbation of nodes. Recommendations are made concerning the discretization schemes that are expected to be least sensitive to mesh irregularities in applications to turbulent flows in complex geometries.

An analytic-geometric model of the effect of spherically distributed injection errors for Galileo and Ulysses spacecraft - The multi-stage problem

NASA Technical Reports Server (NTRS)

Longuski, James M.; Mcronald, Angus D.

1988-01-01

In previous work the problem of injecting the Galileo and Ulysses spacecraft from low earth orbit into their respective interplanetary trajectories has been discussed for the single stage (Centaur) vehicle. The central issue, in the event of spherically distributed injection errors, is what happens to the vehicle? The difficulties addressed in this paper involve the multi-stage problem since both Galileo and Ulysses will be utilizing the two-stage IUS system. Ulysses will also include a third stage: the PAM-S. The solution is expressed in terms of probabilities for total percentage of escape, orbit decay and reentry trajectories. Analytic solutions are found for Hill's Equations of Relative Motion (more recently called Clohessy-Wiltshire Equations) for multi-stage injections. These solutions are interpreted geometrically on the injection sphere. The analytic-geometric models compare well with numerical solutions, provide insight into the behavior of trajectories mapped on the injection sphere and simplify the numerical two-dimensional search for trajectory families.

On the inversion of geodetic integrals defined over the sphere using 1-D FFT

NASA Astrophysics Data System (ADS)

García, R. V.; Alejo, C. A.

2005-08-01

An iterative method is presented which performs inversion of integrals defined over the sphere. The method is based on one-dimensional fast Fourier transform (1-D FFT) inversion and is implemented with the projected Landweber technique, which is used to solve constrained least-squares problems reducing the associated 1-D cyclic-convolution error. The results obtained are as precise as the direct matrix inversion approach, but with better computational efficiency. A case study uses the inversion of Hotine’s integral to obtain gravity disturbances from geoid undulations. Numerical convergence is also analyzed and comparisons with respect to the direct matrix inversion method using conjugate gradient (CG) iteration are presented. Like the CG method, the number of iterations needed to get the optimum (i.e., small) error decreases as the measurement noise increases. Nevertheless, for discrete data given over a whole parallel band, the method can be applied directly without implementing the projected Landweber method, since no cyclic convolution error exists.

A POSTERIORI ERROR ANALYSIS OF TWO STAGE COMPUTATION METHODS WITH APPLICATION TO EFFICIENT DISCRETIZATION AND THE PARAREAL ALGORITHM.

PubMed

Chaudhry, Jehanzeb Hameed; Estep, Don; Tavener, Simon; Carey, Varis; Sandelin, Jeff

2016-01-01

We consider numerical methods for initial value problems that employ a two stage approach consisting of solution on a relatively coarse discretization followed by solution on a relatively fine discretization. Examples include adaptive error control, parallel-in-time solution schemes, and efficient solution of adjoint problems for computing a posteriori error estimates. We describe a general formulation of two stage computations then perform a general a posteriori error analysis based on computable residuals and solution of an adjoint problem. The analysis accommodates various variations in the two stage computation and in formulation of the adjoint problems. We apply the analysis to compute "dual-weighted" a posteriori error estimates, to develop novel algorithms for efficient solution that take into account cancellation of error, and to the Parareal Algorithm. We test the various results using several numerical examples.

Discrete-Time Stable Generalized Self-Learning Optimal Control With Approximation Errors.

PubMed

Wei, Qinglai; Li, Benkai; Song, Ruizhuo

2018-04-01

In this paper, a generalized policy iteration (GPI) algorithm with approximation errors is developed for solving infinite horizon optimal control problems for nonlinear systems. The developed stable GPI algorithm provides a general structure of discrete-time iterative adaptive dynamic programming algorithms, by which most of the discrete-time reinforcement learning algorithms can be described using the GPI structure. It is for the first time that approximation errors are explicitly considered in the GPI algorithm. The properties of the stable GPI algorithm with approximation errors are analyzed. The admissibility of the approximate iterative control law can be guaranteed if the approximation errors satisfy the admissibility criteria. The convergence of the developed algorithm is established, which shows that the iterative value function is convergent to a finite neighborhood of the optimal performance index function, if the approximate errors satisfy the convergence criterion. Finally, numerical examples and comparisons are presented.

Method of grid generation

DOEpatents

Barnette, Daniel W.

2002-01-01

The present invention provides a method of grid generation that uses the geometry of the problem space and the governing relations to generate a grid. The method can generate a grid with minimized discretization errors, and with minimal user interaction. The method of the present invention comprises assigning grid cell locations so that, when the governing relations are discretized using the grid, at least some of the discretization errors are substantially zero. Conventional grid generation is driven by the problem space geometry; grid generation according to the present invention is driven by problem space geometry and by governing relations. The present invention accordingly can provide two significant benefits: more efficient and accurate modeling since discretization errors are minimized, and reduced cost grid generation since less human interaction is required.

Fractional Programming for Communication Systems—Part II: Uplink Scheduling via Matching

NASA Astrophysics Data System (ADS)

Shen, Kaiming; Yu, Wei

2018-05-01

This two-part paper develops novel methodologies for using fractional programming (FP) techniques to design and optimize communication systems. Part I of this paper proposes a new quadratic transform for FP and treats its application for continuous optimization problems. In this Part II of the paper, we study discrete problems, such as those involving user scheduling, which are considerably more difficult to solve. Unlike the continuous problems, discrete or mixed discrete-continuous problems normally cannot be recast as convex problems. In contrast to the common heuristic of relaxing the discrete variables, this work reformulates the original problem in an FP form amenable to distributed combinatorial optimization. The paper illustrates this methodology by tackling the important and challenging problem of uplink coordinated multi-cell user scheduling in wireless cellular systems. Uplink scheduling is more challenging than downlink scheduling, because uplink user scheduling decisions significantly affect the interference pattern in nearby cells. Further, the discrete scheduling variable needs to be optimized jointly with continuous variables such as transmit power levels and beamformers. The main idea of the proposed FP approach is to decouple the interaction among the interfering links, thereby permitting a distributed and joint optimization of the discrete and continuous variables with provable convergence. The paper shows that the well-known weighted minimum mean-square-error (WMMSE) algorithm can also be derived from a particular use of FP; but our proposed FP-based method significantly outperforms WMMSE when discrete user scheduling variables are involved, both in term of run-time efficiency and optimizing results.

The three-dimensional Multi-Block Advanced Grid Generation System (3DMAGGS)

NASA Technical Reports Server (NTRS)

Alter, Stephen J.; Weilmuenster, Kenneth J.

1993-01-01

As the size and complexity of three dimensional volume grids increases, there is a growing need for fast and efficient 3D volumetric elliptic grid solvers. Present day solvers are limited by computational speed and do not have all the capabilities such as interior volume grid clustering control, viscous grid clustering at the wall of a configuration, truncation error limiters, and convergence optimization residing in one code. A new volume grid generator, 3DMAGGS (Three-Dimensional Multi-Block Advanced Grid Generation System), which is based on the 3DGRAPE code, has evolved to meet these needs. This is a manual for the usage of 3DMAGGS and contains five sections, including the motivations and usage, a GRIDGEN interface, a grid quality analysis tool, a sample case for verifying correct operation of the code, and a comparison to both 3DGRAPE and GRIDGEN3D. Since it was derived from 3DGRAPE, this technical memorandum should be used in conjunction with the 3DGRAPE manual (NASA TM-102224).

Development of an Output-based Adaptive Method for Multi-Dimensional Euler and Navier-Stokes Simulations

NASA Technical Reports Server (NTRS)

Darmofal, David L.

2003-01-01

The use of computational simulations in the prediction of complex aerodynamic flows is becoming increasingly prevalent in the design process within the aerospace industry. Continuing advancements in both computing technology and algorithmic development are ultimately leading to attempts at simulating ever-larger, more complex problems. However, by increasing the reliance on computational simulations in the design cycle, we must also increase the accuracy of these simulations in order to maintain or improve the reliability arid safety of the resulting aircraft. At the same time, large-scale computational simulations must be made more affordable so that their potential benefits can be fully realized within the design cycle. Thus, a continuing need exists for increasing the accuracy and efficiency of computational algorithms such that computational fluid dynamics can become a viable tool in the design of more reliable, safer aircraft. The objective of this research was the development of an error estimation and grid adaptive strategy for reducing simulation errors in integral outputs (functionals) such as lift or drag from from multi-dimensional Euler and Navier-Stokes simulations. In this final report, we summarize our work during this grant.

New approach for simulating groundwater flow in discrete fracture network

NASA Astrophysics Data System (ADS)

Fang, H.; Zhu, J.

2017-12-01

In this study, we develop a new approach to calculate groundwater flowrate and hydraulic head distribution in two-dimensional discrete fracture network (DFN) where both laminar and turbulent flows co-exist in individual fractures. The cubic law is used to calculate hydraulic head distribution and flow behaviors in fractures where flow is laminar, while the Forchheimer's law is used to quantify turbulent flow behaviors. Reynolds number is used to distinguish flow characteristics in individual fractures. The combination of linear and non-linear equations is solved iteratively to determine flowrates in all fractures and hydraulic heads at all intersections. We examine potential errors in both flowrate and hydraulic head from the approach of uniform flow assumption. Applying the cubic law in all fractures regardless of actual flow conditions overestimates the flowrate when turbulent flow may exist while applying the Forchheimer's law indiscriminately underestimate the flowrate when laminar flows exist in the network. The contrast of apertures of large and small fractures in the DFN has significant impact on the potential errors of using only the cubic law or the Forchheimer's law. Both the cubic law and Forchheimer's law simulate similar hydraulic head distributions as the main difference between these two approaches lies in predicting different flowrates. Fracture irregularity does not significantly affect the potential errors from using only the cubic law or the Forchheimer's law if network configuration remains similar. Relative density of fractures does not significantly affect the relative performance of the cubic law and Forchheimer's law.

Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver

DOE PAGES

Vincenti, H.; Vay, J. -L.

2015-11-22

Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the result. Such modifications for instance occur when Perfectly Matched Layers (PMLs) are used at simulation domain boundaries to simulate open media. Another example is the use of arbitrary order Maxwell solver with domain decomposition technique that may under some condition involve stencil truncations at subdomain boundaries, resulting in small spurious errors that do eventually build up. In each case, a careful evaluation of the characteristics and magnitude of themore » errors resulting from these approximations, and their impact at any frequency and angle, requires detailed analytical and numerical studies. To this end, we present a general analytical approach that enables the evaluation of numerical discretization errors of fully three-dimensional arbitrary order finite-difference Maxwell solver, with arbitrary modification of the local stencil in the simulation domain. The analytical model is validated against simulations of domain decomposition technique and PMLs, when these are used with very high-order Maxwell solver, as well as in the infinite order limit of pseudo-spectral solvers. Results confirm that the new analytical approach enables exact predictions in each case. It also confirms that the domain decomposition technique can be used with very high-order Maxwell solver and a reasonably low number of guard cells with negligible effects on the whole accuracy of the simulation.« less

Simulation of 2D Kinetic Effects in Plasmas using the Grid Based Continuum Code LOKI

NASA Astrophysics Data System (ADS)

Banks, Jeffrey; Berger, Richard; Chapman, Tom; Brunner, Stephan

2016-10-01

Kinetic simulation of multi-dimensional plasma waves through direct discretization of the Vlasov equation is a useful tool to study many physical interactions and is particularly attractive for situations where minimal fluctuation levels are desired, for instance, when measuring growth rates of plasma wave instabilities. However, direct discretization of phase space can be computationally expensive, and as a result there are few examples of published results using Vlasov codes in more than a single configuration space dimension. In an effort to fill this gap we have developed the Eulerian-based kinetic code LOKI that evolves the Vlasov-Poisson system in 2+2-dimensional phase space. The code is designed to reduce the cost of phase-space computation by using fully 4th order accurate conservative finite differencing, while retaining excellent parallel scalability that efficiently uses large scale computing resources. In this poster I will discuss the algorithms used in the code as well as some aspects of their parallel implementation using MPI. I will also overview simulation results of basic plasma wave instabilities relevant to laser plasma interaction, which have been obtained using the code.

Reconfigurable WDM-PON empowered by a low-cost 8-channel directly modulated laser module

NASA Astrophysics Data System (ADS)

Zhang, Yi-ming; Liu, Yu; Zhang, Zhi-ke; Zhao, Ze-ping; Tian, Ye; Zhu, Ning-hua

2017-11-01

A 10 Gbit/s 16-km-long reconfigurable wavelength-division-multiplexing passive optical network (WDM-PON) is presented empowered by a low-cost multi-channel directly modulated laser (DML) module. Compared with the case using discrete devices in conventional scheme, the proposed DML module provides a cost-effective solution with reduced complexity. The clear eye diagram and the bit error rate ( BER) of less than 2×10-7 with a sensitivity of -7 dBm are obtained. Due to the special packaging design, the crosstalk between channels under condition of simultaneous operation can be negligible.

Effect of delayed reinforcement on skill acquisition during discrete-trial instruction: Implications for treatmen-integrity errors in academic settings.

PubMed

Carroll, Regina A; Kodak, Tiffany; Adolf, Kari J

2016-03-01

We used an adapted alternating treatments design to compare skill acquisition during discrete-trial instruction using immediate reinforcement, delayed reinforcement with immediate praise, and delayed reinforcement for 2 children with autism spectrum disorder. Participants acquired the skills taught with immediate reinforcement; however, delayed reinforcement decreased the efficiency and effectiveness of discrete-trial instruction. We discuss the importance of evaluating the influence of treatment-integrity errors on skill acquisition during discrete-trial instruction. © 2015 Society for the Experimental Analysis of Behavior.

Constitutive Behavior and Finite Element Analysis of FRP Composite and Concrete Members.

PubMed

Ann, Ki Yong; Cho, Chang-Geun

2013-09-10

The present study concerns compressive and flexural constitutive models incorporated into an isoparametric beam finite element scheme for fiber reinforced polymer (FRP) and concrete composites, using their multi-axial constitutive behavior. The constitutive behavior of concrete was treated in triaxial stress states as an orthotropic hypoelasticity-based formulation to determine the confinement effect of concrete from a three-dimensional failure surface in triaxial stress states. The constitutive behavior of the FRP composite was formulated from the two-dimensional classical lamination theory. To predict the flexural behavior of circular cross-section with FRP sheet and concrete composite, a layered discretization of cross-sections was incorporated into nonlinear isoparametric beam finite elements. The predicted constitutive behavior was validated by a comparison to available experimental results in the compressive and flexural beam loading test.

Exact Analytical Solutions for Elastodynamic Impact

DTIC Science & Technology

2015-11-30

corroborated by derivation of exact discrete solutions from recursive equations for the impact problems. 15. SUBJECT TERMS One-dimensional impact; Elastic...wave propagation; Laplace transform; Floor function; Discrete solutions 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18...impact Elastic wave propagation Laplace transform Floor function Discrete solutionsWe consider the one-dimensional impact problem in which a semi

Low-rank separated representation surrogates of high-dimensional stochastic functions: Application in Bayesian inference

NASA Astrophysics Data System (ADS)

Validi, AbdoulAhad

2014-03-01

This study introduces a non-intrusive approach in the context of low-rank separated representation to construct a surrogate of high-dimensional stochastic functions, e.g., PDEs/ODEs, in order to decrease the computational cost of Markov Chain Monte Carlo simulations in Bayesian inference. The surrogate model is constructed via a regularized alternative least-square regression with Tikhonov regularization using a roughening matrix computing the gradient of the solution, in conjunction with a perturbation-based error indicator to detect optimal model complexities. The model approximates a vector of a continuous solution at discrete values of a physical variable. The required number of random realizations to achieve a successful approximation linearly depends on the function dimensionality. The computational cost of the model construction is quadratic in the number of random inputs, which potentially tackles the curse of dimensionality in high-dimensional stochastic functions. Furthermore, this vector-valued separated representation-based model, in comparison to the available scalar-valued case, leads to a significant reduction in the cost of approximation by an order of magnitude equal to the vector size. The performance of the method is studied through its application to three numerical examples including a 41-dimensional elliptic PDE and a 21-dimensional cavity flow.

On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions

NASA Astrophysics Data System (ADS)

Talib, Imran; Belgacem, Fethi Bin Muhammad; Asif, Naseer Ahmad; Khalil, Hammad

2017-01-01

In this research article, we derive and analyze an efficient spectral method based on the operational matrices of three dimensional orthogonal Jacobi polynomials to solve numerically the mixed partial derivatives type multi-terms high dimensions generalized class of fractional order partial differential equations. We transform the considered fractional order problem to an easily solvable algebraic equations with the aid of the operational matrices. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some test problems are considered to confirm the accuracy and validity of the proposed numerical method. The convergence of the method is ensured by comparing our Matlab software simulations based obtained results with the exact solutions in the literature, yielding negligible errors. Moreover, comparative results discussed in the literature are extended and improved in this study.

Likelihood-based inference for discretely observed birth-death-shift processes, with applications to evolution of mobile genetic elements.

PubMed

Xu, Jason; Guttorp, Peter; Kato-Maeda, Midori; Minin, Vladimir N

2015-12-01

Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements-important genetic markers in molecular epidemiology. Estimation of the effects of individual covariates on the birth, death, and shift rates of the process can be accomplished by analyzing patient data, but inferring these rates in a discretely and unevenly observed setting presents computational challenges. We propose a multi-type branching process approximation to BDS processes and develop a corresponding expectation maximization algorithm, where we use spectral techniques to reduce calculation of expected sufficient statistics to low-dimensional integration. These techniques yield an efficient and robust optimization routine for inferring the rates of the BDS process, and apply broadly to multi-type branching processes whose rates can depend on many covariates. After rigorously testing our methodology in simulation studies, we apply our method to study intrapatient time evolution of IS6110 transposable element, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections. © 2015, The International Biometric Society.

Continuum approach for aerothermal flow through ablative porous material using discontinuous Galerkin discretization.

NASA Astrophysics Data System (ADS)

Schrooyen, Pierre; Chatelain, Philippe; Hillewaert, Koen; Magin, Thierry E.

2014-11-01

The atmospheric entry of spacecraft presents several challenges in simulating the aerothermal flow around the heat shield. Predicting an accurate heat-flux is a complex task, especially regarding the interaction between the flow in the free stream and the erosion of the thermal protection material. To capture this interaction, a continuum approach is developed to go progressively from the region fully occupied by fluid to a receding porous medium. The volume averaged Navier-Stokes equations are used to model both phases in the same computational domain considering a single set of conservation laws. The porosity is itself a variable of the computation, allowing to take volumetric ablation into account through adequate source terms. This approach is implemented within a computational tool based on a high-order discontinuous Galerkin discretization. The multi-dimensional tool has already been validated and has proven its efficient parallel implementation. Within this platform, a fully implicit method was developed to simulate multi-phase reacting flows. Numerical results to verify and validate the methodology are considered within this work. Interactions between the flow and the ablated geometry are also presented. Supported by Fund for Research Training in Industry and Agriculture.

Qualification of a multi-diagnostic detonator-output characterization procedure utilizing PMMA witness blocks

NASA Astrophysics Data System (ADS)

Biss, Matthew; Murphy, Michael; Lieber, Mark

2017-06-01

Experiments were conducted in an effort to qualify a multi-diagnostic characterization procedure for the performance output of a detonator when fired into a poly(methyl methacrylate) (PMMA) witness block. A suite of optical diagnostics were utilized in combination to both bound the shock wave interaction state at the detonator/PMMA interface and characterize the nature of the shock wave decay in PMMA. The diagnostics included the Shock Wave Image Framing Technique (SWIFT), a photocathode tube streak camera, and photonic Doppler velocimetry (PDV). High-precision, optically clear witness blocks permitted dynamic flow visualization of the shock wave in PMMA via focused shadowgraphy. SWIFT- and streak-imaging diagnostics captured the spatiotemporally evolving shock wave, providing a two-dimensional temporally discrete image set and a one-dimensional temporally continuous image, respectively. PDV provided the temporal velocity history of the detonator output along the detonator axis. Through combination of the results obtained, a bound was able to be placed on the interface condition and a more-physical profile representing the shock wave decay in PMMA for an exploding-bridgewire detonator was achieved.

Usefulness of biological fingerprint in magnetic resonance imaging for patient verification.

PubMed

Ueda, Yasuyuki; Morishita, Junji; Kudomi, Shohei; Ueda, Katsuhiko

2016-09-01

The purpose of our study is to investigate the feasibility of automated patient verification using multi-planar reconstruction (MPR) images generated from three-dimensional magnetic resonance (MR) imaging of the brain. Several anatomy-related MPR images generated from three-dimensional fast scout scan of each MR examination were used as biological fingerprint images in this study. The database of this study consisted of 730 temporal pairs of MR examination of the brain. We calculated the correlation value between current and prior biological fingerprint images of the same patient and also all combinations of two images for different patients to evaluate the effectiveness of our method for patient verification. The best performance of our system were as follows: a half-total error rate of 1.59 % with a false acceptance rate of 0.023 % and a false rejection rate of 3.15 %, an equal error rate of 1.37 %, and a rank-one identification rate of 98.6 %. Our method makes it possible to verify the identity of the patient using only some existing medical images without the addition of incidental equipment. Also, our method will contribute to patient misidentification error management caused by human errors.

Quantification of source impact to PM using three-dimensional weighted factor model analysis on multi-site data

NASA Astrophysics Data System (ADS)

Shi, Guoliang; Peng, Xing; Huangfu, Yanqi; Wang, Wei; Xu, Jiao; Tian, Yingze; Feng, Yinchang; Ivey, Cesunica E.; Russell, Armistead G.

2017-07-01

Source apportionment technologies are used to understand the impacts of important sources of particulate matter (PM) air quality, and are widely used for both scientific studies and air quality management. Generally, receptor models apportion speciated PM data from a single sampling site. With the development of large scale monitoring networks, PM speciation are observed at multiple sites in an urban area. For these situations, the models should account for three factors, or dimensions, of the PM, including the chemical species concentrations, sampling periods and sampling site information, suggesting the potential power of a three-dimensional source apportionment approach. However, the principle of three-dimensional Parallel Factor Analysis (Ordinary PARAFAC) model does not always work well in real environmental situations for multi-site receptor datasets. In this work, a new three-way receptor model, called "multi-site three way factor analysis" model is proposed to deal with the multi-site receptor datasets. Synthetic datasets were developed and introduced into the new model to test its performance. Average absolute error (AAE, between estimated and true contributions) for extracted sources were all less than 50%. Additionally, three-dimensional ambient datasets from a Chinese mega-city, Chengdu, were analyzed using this new model to assess the application. Four factors are extracted by the multi-site WFA3 model: secondary source have the highest contributions (64.73 and 56.24 μg/m3), followed by vehicular exhaust (30.13 and 33.60 μg/m3), crustal dust (26.12 and 29.99 μg/m3) and coal combustion (10.73 and 14.83 μg/m3). The model was also compared to PMF, with general agreement, though PMF suggested a lower crustal contribution.

An Adaptive Method of Lines with Error Control for Parabolic Equations of the Reaction-Diffusion Type.

DTIC Science & Technology

1984-06-01

space discretization error . 1. I 3 1. INTRODUCTION Reaction- diffusion processes occur in many branches of biology and physical chemistry. Examples...to model reaction- diffusion phenomena. The primary goal of this adaptive method is to keep a particular norm of the space discretization error less...AD-A142 253 AN ADAPTIVE MET6 OFD LNES WITH ERROR CONTROL FOR 1 INST FOR PHYSICAL SCIENCE AND TECH. I BABUSKAAAO C7 EA OH S UMR AN UNVC EEP R

Computer simulations of phase field drops on super-hydrophobic surfaces

NASA Astrophysics Data System (ADS)

Fedeli, Livio

2017-09-01

We present a novel quasi-Newton continuation procedure that efficiently solves the system of nonlinear equations arising from the discretization of a phase field model for wetting phenomena. We perform a comparative numerical analysis that shows the improved speed of convergence gained with respect to other numerical schemes. Moreover, we discuss the conditions that, on a theoretical level, guarantee the convergence of this method. At each iterative step, a suitable continuation procedure develops and passes to the nonlinear solver an accurate initial guess. Discretization performs through cell-centered finite differences. The resulting system of equations is solved on a composite grid that uses dynamic mesh refinement and multi-grid techniques. The final code achieves three-dimensional, realistic computer experiments comparable to those produced in laboratory settings. This code offers not only new insights into the phenomenology of super-hydrophobicity, but also serves as a reliable predictive tool for the study of hydrophobic surfaces.

Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations

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

Hepburn, I.; De Schutter, E., E-mail: erik@oist.jp; Theoretical Neurobiology & Neuroengineering, University of Antwerp, Antwerp 2610

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realisticmore » biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.« less

Research on the Factors Influencing the Measurement Errors of the Discrete Rogowski Coil †

PubMed Central

Xu, Mengyuan; Yan, Jing; Geng, Yingsan; Zhang, Kun; Sun, Chao

2018-01-01

An innovative array of magnetic coils (the discrete Rogowski coil—RC) with the advantages of flexible structure, miniaturization and mass producibility is investigated. First, the mutual inductance between the discrete RC and circular and rectangular conductors are calculated using the magnetic vector potential (MVP) method. The results are found to be consistent with those calculated using the finite element method, but the MVP method is simpler and more practical. Then, the influence of conductor section parameters, inclination, and eccentricity on the accuracy of the discrete RC is calculated to provide a reference. Studying the influence of an external current on the discrete RC’s interference error reveals optimal values for length, winding density, and position arrangement of the solenoids. It has also found that eccentricity and interference errors decreasing with increasing number of solenoids. Finally, a discrete RC prototype is devised and manufactured. The experimental results show consistent output characteristics, with the calculated sensitivity and mutual inductance of the discrete RC being very close to the experimental results. The influence of an external conductor on the measurement of the discrete RC is analyzed experimentally, and the results show that interference from an external current decreases with increasing distance between the external and measured conductors. PMID:29534006

Research on the Factors Influencing the Measurement Errors of the Discrete Rogowski Coil.

PubMed

Xu, Mengyuan; Yan, Jing; Geng, Yingsan; Zhang, Kun; Sun, Chao

2018-03-13

An innovative array of magnetic coils (the discrete Rogowski coil-RC) with the advantages of flexible structure, miniaturization and mass producibility is investigated. First, the mutual inductance between the discrete RC and circular and rectangular conductors are calculated using the magnetic vector potential (MVP) method. The results are found to be consistent with those calculated using the finite element method, but the MVP method is simpler and more practical. Then, the influence of conductor section parameters, inclination, and eccentricity on the accuracy of the discrete RC is calculated to provide a reference. Studying the influence of an external current on the discrete RC's interference error reveals optimal values for length, winding density, and position arrangement of the solenoids. It has also found that eccentricity and interference errors decreasing with increasing number of solenoids. Finally, a discrete RC prototype is devised and manufactured. The experimental results show consistent output characteristics, with the calculated sensitivity and mutual inductance of the discrete RC being very close to the experimental results. The influence of an external conductor on the measurement of the discrete RC is analyzed experimentally, and the results show that interference from an external current decreases with increasing distance between the external and measured conductors.

Geometric interpretations of the Discrete Fourier Transform (DFT)

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1984-01-01

One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.

Distinguishing discrete and gradient category structure in language: Insights from verb-particle constructions.

PubMed

Brehm, Laurel; Goldrick, Matthew

2017-10-01

The current work uses memory errors to examine the mental representation of verb-particle constructions (VPCs; e.g., make up the story, cut up the meat). Some evidence suggests that VPCs are represented by a cline in which the relationship between the VPC and its component elements ranges from highly transparent (cut up) to highly idiosyncratic (make up). Other evidence supports a multiple class representation, characterizing VPCs as belonging to discretely separated classes differing in semantic and syntactic structure. We outline a novel paradigm to investigate the representation of VPCs in which we elicit illusory conjunctions, or memory errors sensitive to syntactic structure. We then use a novel application of piecewise regression to demonstrate that the resulting error pattern follows a cline rather than discrete classes. A preregistered replication verifies these findings, and a final preregistered study verifies that these errors reflect syntactic structure. This provides evidence for gradient rather than discrete representations across levels of representation in language processing. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Robust and adaptive band-to-band image transform of UAS miniature multi-lens multispectral camera

NASA Astrophysics Data System (ADS)

Jhan, Jyun-Ping; Rau, Jiann-Yeou; Haala, Norbert

2018-03-01

Utilizing miniature multispectral (MS) or hyperspectral (HS) cameras by mounting them on an Unmanned Aerial System (UAS) has the benefits of convenience and flexibility to collect remote sensing imagery for precision agriculture, vegetation monitoring, and environment investigation applications. Most miniature MS cameras adopt a multi-lens structure to record discrete MS bands of visible and invisible information. The differences in lens distortion, mounting positions, and viewing angles among lenses mean that the acquired original MS images have significant band misregistration errors. We have developed a Robust and Adaptive Band-to-Band Image Transform (RABBIT) method for dealing with the band co-registration of various types of miniature multi-lens multispectral cameras (Mini-MSCs) to obtain band co-registered MS imagery for remote sensing applications. The RABBIT utilizes modified projective transformation (MPT) to transfer the multiple image geometry of a multi-lens imaging system to one sensor geometry, and combines this with a robust and adaptive correction (RAC) procedure to correct several systematic errors and to obtain sub-pixel accuracy. This study applies three state-of-the-art Mini-MSCs to evaluate the RABBIT method's performance, specifically the Tetracam Miniature Multiple Camera Array (MiniMCA), Micasense RedEdge, and Parrot Sequoia. Six MS datasets acquired at different target distances and dates, and locations are also applied to prove its reliability and applicability. Results prove that RABBIT is feasible for different types of Mini-MSCs with accurate, robust, and rapid image processing efficiency.

Upscaling permeability for three-dimensional fractured porous rocks with the multiple boundary method

NASA Astrophysics Data System (ADS)

Chen, Tao; Clauser, Christoph; Marquart, Gabriele; Willbrand, Karen; Hiller, Thomas

2018-02-01

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.

Meta-modelling, visualization and emulation of multi-dimensional data for virtual production intelligence

NASA Astrophysics Data System (ADS)

Schulz, Wolfgang; Hermanns, Torsten; Al Khawli, Toufik

2017-07-01

Decision making for competitive production in high-wage countries is a daily challenge where rational and irrational methods are used. The design of decision making processes is an intriguing, discipline spanning science. However, there are gaps in understanding the impact of the known mathematical and procedural methods on the usage of rational choice theory. Following Benjamin Franklin's rule for decision making formulated in London 1772, he called "Prudential Algebra" with the meaning of prudential reasons, one of the major ingredients of Meta-Modelling can be identified finally leading to one algebraic value labelling the results (criteria settings) of alternative decisions (parameter settings). This work describes the advances in Meta-Modelling techniques applied to multi-dimensional and multi-criterial optimization by identifying the persistence level of the corresponding Morse-Smale Complex. Implementations for laser cutting and laser drilling are presented, including the generation of fast and frugal Meta-Models with controlled error based on mathematical model reduction Reduced Models are derived to avoid any unnecessary complexity. Both, model reduction and analysis of multi-dimensional parameter space are used to enable interactive communication between Discovery Finders and Invention Makers. Emulators and visualizations of a metamodel are introduced as components of Virtual Production Intelligence making applicable the methods of Scientific Design Thinking and getting the developer as well as the operator more skilled.

Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research.

PubMed

Wu, Hulin; Xue, Hongqi; Kumar, Arun

2012-06-01

Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. © 2012, The International Biometric Society.

Design and Analysis of the Measurement Characteristics of a Bidirectional-Decoupling Over-Constrained Six-Dimensional Parallel-Mechanism Force Sensor

PubMed Central

Zhao, Tieshi; Zhao, Yanzhi; Hu, Qiangqiang; Ding, Shixing

2017-01-01

The measurement of large forces and the presence of errors due to dimensional coupling are significant challenges for multi-dimensional force sensors. To address these challenges, this paper proposes an over-constrained six-dimensional force sensor based on a parallel mechanism of steel ball structures as a measurement module. The steel ball structure can be subject to rolling friction instead of sliding friction, thus reducing the influence of friction. However, because the structure can only withstand unidirectional pressure, the application of steel balls in a six-dimensional force sensor is difficult. Accordingly, a new design of the sensor measurement structure was designed in this study. The static equilibrium and displacement compatibility equations of the sensor prototype’s over-constrained structure were established to obtain the transformation function, from which the forces in the measurement branches of the proposed sensor were then analytically derived. The sensor’s measurement characteristics were then analysed through numerical examples. Finally, these measurement characteristics were confirmed through calibration and application experiments. The measurement accuracy of the proposed sensor was determined to be 1.28%, with a maximum coupling error of 1.98%, indicating that the proposed sensor successfully overcomes the issues related to steel ball structures and provides sufficient accuracy. PMID:28867812

An evaluation of programmed treatment-integrity errors during discrete-trial instruction.

PubMed

Carroll, Regina A; Kodak, Tiffany; Fisher, Wayne W

2013-01-01

This study evaluated the effects of programmed treatment-integrity errors on skill acquisition for children with an autism spectrum disorder (ASD) during discrete-trial instruction (DTI). In Study 1, we identified common treatment-integrity errors that occur during academic instruction in schools. In Study 2, we simultaneously manipulated 3 integrity errors during DTI. In Study 3, we evaluated the effects of each of the 3 integrity errors separately on skill acquisition during DTI. Results showed that participants either demonstrated slower skill acquisition or did not acquire the target skills when instruction included treatment-integrity errors. © Society for the Experimental Analysis of Behavior.

Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Luo, Li-Shi

2007-01-01

In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

46 CFR 520.14 - Special permission.

Code of Federal Regulations, 2010 CFR

2010-10-01

... the Commission, in its discretion and for good cause shown, to permit increases or decreases in rates... its discretion and for good cause shown, permit departures from the requirements of this part. (b) Clerical errors. Typographical and/or clerical errors constitute good cause for the exercise of special...

46 CFR 520.14 - Special permission.

Code of Federal Regulations, 2011 CFR

2011-10-01

... the Commission, in its discretion and for good cause shown, to permit increases or decreases in rates... its discretion and for good cause shown, permit departures from the requirements of this part. (b) Clerical errors. Typographical and/or clerical errors constitute good cause for the exercise of special...

Dynamical error bounds for continuum discretisation via Gauss quadrature rules—A Lieb-Robinson bound approach

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

Woods, M. P.; Centre for Quantum Technologies, National University of Singapore; QuTech, Delft University of Technology, Lorentzweg 1, 2611 CJ Delft

2016-02-15

Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive error bounds on expectation values of system observables that have been time evolved under such discretised Hamiltonians. These bounds take on the form of a function of time and the number of discrete modes, where the discrete modes are chosen according to Gauss quadrature rules. The derivation makes use of tools from the field of Lieb-Robinson bounds and the theory of orthonormal polynomials.

Modeling error analysis of stationary linear discrete-time filters

NASA Technical Reports Server (NTRS)

Patel, R.; Toda, M.

1977-01-01

The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a design can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices is available.

Accounting for stimulus-specific variation in precision reveals a discrete capacity limit in visual working memory

PubMed Central

Pratte, Michael S.; Park, Young Eun; Rademaker, Rosanne L.; Tong, Frank

2016-01-01

If we view a visual scene that contains many objects, then momentarily close our eyes, some details persist while others seem to fade. Discrete models of visual working memory (VWM) assume that only a few items can be actively maintained in memory, beyond which pure guessing will emerge. Alternatively, continuous resource models assume that all items in a visual scene can be stored with some precision. Distinguishing between these competing models is challenging, however, as resource models that allow for stochastically variable precision (across items and trials) can produce error distributions that resemble random guessing behavior. Here, we evaluated the hypothesis that a major source of variability in VWM performance arises from systematic variation in precision across the stimuli themselves; such stimulus-specific variability can be incorporated into both discrete-capacity and variable-precision resource models. Participants viewed multiple oriented gratings, and then reported the orientation of a cued grating from memory. When modeling the overall distribution of VWM errors, we found that the variable-precision resource model outperformed the discrete model. However, VWM errors revealed a pronounced “oblique effect”, with larger errors for oblique than cardinal orientations. After this source of variability was incorporated into both models, we found that the discrete model provided a better account of VWM errors. Our results demonstrate that variable precision across the stimulus space can lead to an unwarranted advantage for resource models that assume stochastically variable precision. When these deterministic sources are adequately modeled, human working memory performance reveals evidence of a discrete capacity limit. PMID:28004957

Accounting for stimulus-specific variation in precision reveals a discrete capacity limit in visual working memory.

PubMed

Pratte, Michael S; Park, Young Eun; Rademaker, Rosanne L; Tong, Frank

2017-01-01

If we view a visual scene that contains many objects, then momentarily close our eyes, some details persist while others seem to fade. Discrete models of visual working memory (VWM) assume that only a few items can be actively maintained in memory, beyond which pure guessing will emerge. Alternatively, continuous resource models assume that all items in a visual scene can be stored with some precision. Distinguishing between these competing models is challenging, however, as resource models that allow for stochastically variable precision (across items and trials) can produce error distributions that resemble random guessing behavior. Here, we evaluated the hypothesis that a major source of variability in VWM performance arises from systematic variation in precision across the stimuli themselves; such stimulus-specific variability can be incorporated into both discrete-capacity and variable-precision resource models. Participants viewed multiple oriented gratings, and then reported the orientation of a cued grating from memory. When modeling the overall distribution of VWM errors, we found that the variable-precision resource model outperformed the discrete model. However, VWM errors revealed a pronounced "oblique effect," with larger errors for oblique than cardinal orientations. After this source of variability was incorporated into both models, we found that the discrete model provided a better account of VWM errors. Our results demonstrate that variable precision across the stimulus space can lead to an unwarranted advantage for resource models that assume stochastically variable precision. When these deterministic sources are adequately modeled, human working memory performance reveals evidence of a discrete capacity limit. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

A mass-energy preserving Galerkin FEM for the coupled nonlinear fractional Schrödinger equations

NASA Astrophysics Data System (ADS)

Zhang, Guoyu; Huang, Chengming; Li, Meng

2018-04-01

We consider the numerical simulation of the coupled nonlinear space fractional Schrödinger equations. Based on the Galerkin finite element method in space and the Crank-Nicolson (CN) difference method in time, a fully discrete scheme is constructed. Firstly, we focus on a rigorous analysis of conservation laws for the discrete system. The definitions of discrete mass and energy here correspond with the original ones in physics. Then, we prove that the fully discrete system is uniquely solvable. Moreover, we consider the unconditionally convergent properties (that is to say, we complete the error estimates without any mesh ratio restriction). We derive L2-norm error estimates for the nonlinear equations and L^{∞}-norm error estimates for the linear equations. Finally, some numerical experiments are included showing results in agreement with the theoretical predictions.

A Numerical Investigation of the Extinction of Low Strain Rate Diffusion Flames by an Agent in Microgravity

NASA Technical Reports Server (NTRS)

Puri, Ishwar K.

2004-01-01

Our goal has been to investigate the influence of both dilution and radiation on the extinction process of nonpremixed flames at low strain rates. Simulations have been performed by using a counterflow code and three radiation models have been included in it, namely, the optically thin, the narrowband, and discrete ordinate models. The counterflow flame code OPPDIFF was modified to account for heat transfer losses by radiation from the hot gases. The discrete ordinate method (DOM) approximation was first suggested by Chandrasekhar for solving problems in interstellar atmospheres. Carlson and Lathrop developed the method for solving multi-dimensional problem in neutron transport. Only recently has the method received attention in the field of heat transfer. Due to the applicability of the discrete ordinate method for thermal radiation problems involving flames, the narrowband code RADCAL was modified to calculate the radiative properties of the gases. A non-premixed counterflow flame was simulated with the discrete ordinate method for radiative emissions. In comparison with two other models, it was found that the heat losses were comparable with the optically thin and simple narrowband model. The optically thin model had the highest heat losses followed by the DOM model and the narrow-band model.

Dense image registration through MRFs and efficient linear programming.

PubMed

Glocker, Ben; Komodakis, Nikos; Tziritas, Georgios; Navab, Nassir; Paragios, Nikos

2008-12-01

In this paper, we introduce a novel and efficient approach to dense image registration, which does not require a derivative of the employed cost function. In such a context, the registration problem is formulated using a discrete Markov random field objective function. First, towards dimensionality reduction on the variables we assume that the dense deformation field can be expressed using a small number of control points (registration grid) and an interpolation strategy. Then, the registration cost is expressed using a discrete sum over image costs (using an arbitrary similarity measure) projected on the control points, and a smoothness term that penalizes local deviations on the deformation field according to a neighborhood system on the grid. Towards a discrete approach, the search space is quantized resulting in a fully discrete model. In order to account for large deformations and produce results on a high resolution level, a multi-scale incremental approach is considered where the optimal solution is iteratively updated. This is done through successive morphings of the source towards the target image. Efficient linear programming using the primal dual principles is considered to recover the lowest potential of the cost function. Very promising results using synthetic data with known deformations and real data demonstrate the potentials of our approach.

Accuracy Analysis for Finite-Volume Discretization Schemes on Irregular Grids

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2010-01-01

A new computational analysis tool, downscaling test, is introduced and applied for studying the convergence rates of truncation and discretization errors of nite-volume discretization schemes on general irregular (e.g., unstructured) grids. The study shows that the design-order convergence of discretization errors can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all. The downscaling test is a general, efficient, accurate, and practical tool, enabling straightforward extension of verification and validation to general unstructured grid formulations. It also allows separate analysis of the interior, boundaries, and singularities that could be useful even in structured-grid settings. There are several new findings arising from the use of the downscaling test analysis. It is shown that the discretization accuracy of a common node-centered nite-volume scheme, known to be second-order accurate for inviscid equations on triangular grids, degenerates to first order for mixed grids. Alternative node-centered schemes are presented and demonstrated to provide second and third order accuracies on general mixed grids. The local accuracy deterioration at intersections of tangency and in flow/outflow boundaries is demonstrated using the DS tests tailored to examining the local behavior of the boundary conditions. The discretization-error order reduction within inviscid stagnation regions is demonstrated. The accuracy deterioration is local, affecting mainly the velocity components, but applies to any order scheme.

New Statistical Techniques for Evaluating Longitudinal Models.

ERIC Educational Resources Information Center

Murray, James R.; Wiley, David E.

A basic methodological approach in developmental studies is the collection of longitudinal data. Behavioral data cen take at least two forms, qualitative (or discrete) and quantitative. Both types are fallible. Measurement errors can occur in quantitative data and measures of these are based on error variance. Qualitative or discrete data can…

Self-organizing neural networks--an alternative way of cluster analysis in clinical chemistry.

PubMed

Reibnegger, G; Wachter, H

1996-04-15

Supervised learning schemes have been employed by several workers for training neural networks designed to solve clinical problems. We demonstrate that unsupervised techniques can also produce interesting and meaningful results. Using a data set on the chemical composition of milk from 22 different mammals, we demonstrate that self-organizing feature maps (Kohonen networks) as well as a modified version of error backpropagation technique yield results mimicking conventional cluster analysis. Both techniques are able to project a potentially multi-dimensional input vector onto a two-dimensional space whereby neighborhood relationships remain conserved. Thus, these techniques can be used for reducing dimensionality of complicated data sets and for enhancing comprehensibility of features hidden in the data matrix.

Adaptive mixed finite element methods for Darcy flow in fractured porous media

NASA Astrophysics Data System (ADS)

Chen, Huangxin; Salama, Amgad; Sun, Shuyu

2016-10-01

In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.

New type of chaos synchronization in discrete-time systems: the F-M synchronization

NASA Astrophysics Data System (ADS)

Ouannas, Adel; Grassi, Giuseppe; Karouma, Abdulrahman; Ziar, Toufik; Wang, Xiong; Pham, Viet-Thanh

2018-04-01

In this paper, a new type of synchronization for chaotic (hyperchaotic) maps with different dimensions is proposed. The novel scheme is called F - M synchronization, since it combines the inverse generalized synchronization (based on a functional relationship F) with the matrix projective synchronization (based on a matrix M). In particular, the proposed approach enables F - M synchronization with index d to be achieved between n-dimensional drive system map and m-dimensional response system map, where the synchronization index d corresponds to the dimension of the synchronization error. The technique, which exploits nonlinear controllers and Lyapunov stability theory, proves to be effective in achieving the F - M synchronization not only when the synchronization index d equals n or m, but even if the synchronization index d is larger than the map dimensions n and m. Finally, simulation results are reported, with the aim to illustrate the capabilities of the novel scheme proposed herein.

An efficient nonlinear relaxation technique for the three-dimensional, Reynolds-averaged Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Edwards, Jack R.; Mcrae, D. S.

1993-01-01

An efficient implicit method for the computation of steady, three-dimensional, compressible Navier-Stokes flowfields is presented. A nonlinear iteration strategy based on planar Gauss-Seidel sweeps is used to drive the solution toward a steady state, with approximate factorization errors within a crossflow plane reduced by the application of a quasi-Newton technique. A hybrid discretization approach is employed, with flux-vector splitting utilized in the streamwise direction and central differences with artificial dissipation used for the transverse fluxes. Convergence histories and comparisons with experimental data are presented for several 3-D shock-boundary layer interactions. Both laminar and turbulent cases are considered, with turbulent closure provided by a modification of the Baldwin-Barth one-equation model. For the problems considered (175,000-325,000 mesh points), the algorithm provides steady-state convergence in 900-2000 CPU seconds on a single processor of a Cray Y-MP.

Uncertainty quantification for complex systems with very high dimensional response using Grassmann manifold variations

NASA Astrophysics Data System (ADS)

Giovanis, D. G.; Shields, M. D.

2018-07-01

This paper addresses uncertainty quantification (UQ) for problems where scalar (or low-dimensional vector) response quantities are insufficient and, instead, full-field (very high-dimensional) responses are of interest. To do so, an adaptive stochastic simulation-based methodology is introduced that refines the probability space based on Grassmann manifold variations. The proposed method has a multi-element character discretizing the probability space into simplex elements using a Delaunay triangulation. For every simplex, the high-dimensional solutions corresponding to its vertices (sample points) are projected onto the Grassmann manifold. The pairwise distances between these points are calculated using appropriately defined metrics and the elements with large total distance are sub-sampled and refined. As a result, regions of the probability space that produce significant changes in the full-field solution are accurately resolved. An added benefit is that an approximation of the solution within each element can be obtained by interpolation on the Grassmann manifold. The method is applied to study the probability of shear band formation in a bulk metallic glass using the shear transformation zone theory.

Constitutive Behavior and Finite Element Analysis of FRP Composite and Concrete Members

PubMed Central

Ann, Ki Yong; Cho, Chang-Geun

2013-01-01

The present study concerns compressive and flexural constitutive models incorporated into an isoparametric beam finite element scheme for fiber reinforced polymer (FRP) and concrete composites, using their multi-axial constitutive behavior. The constitutive behavior of concrete was treated in triaxial stress states as an orthotropic hypoelasticity-based formulation to determine the confinement effect of concrete from a three-dimensional failure surface in triaxial stress states. The constitutive behavior of the FRP composite was formulated from the two-dimensional classical lamination theory. To predict the flexural behavior of circular cross-section with FRP sheet and concrete composite, a layered discretization of cross-sections was incorporated into nonlinear isoparametric beam finite elements. The predicted constitutive behavior was validated by a comparison to available experimental results in the compressive and flexural beam loading test. PMID:28788312

{lambda} elements for singular problems in CFD: Viscoelastic fluids

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

Wong, K.K.; Surana, K.S.

1996-10-01

This paper presents two dimensional {lambda} element formulation for viscoelastic fluid flow containing point singularities in the flow field. The flow of viscoelastic fluid even without singularities are a difficult class of problems for increasing Deborah number or Weissenburg number due to increased dominance of convective terms and thus increased hyperbolicity. In the present work the equations of fluid motion and the constitutive laws are recast in the form of a first order system of coupled equations with the use of auxiliary variables. The velocity, pressure and stresses are interpolated using equal order C{sup 0} {lambda} element approximations. The Leastmore » Squares Finite Element Method (LSFEM) is used to construct the integral form (error functional I) corresponding to these equations. The error functional is constructed by taking the integrated sum of the squares of the errors or residuals (over the whole discretization) resulting when the element approximation is substituted into these equations. The conditions resulting from the minimization of the error functional are satisfied by using Newton`s method with line search. LSFEM has much superior performance when dealing with non-linear and convection dominated problems.« less

Enhancing Three-dimensional Movement Control System for Assemblies of Machine-Building Facilities

NASA Astrophysics Data System (ADS)

Kuzyakov, O. N.; Andreeva, M. A.

2018-01-01

Aspects of enhancing three-dimensional movement control system are given in the paper. Such system is to be used while controlling assemblies of machine-building facilities, which is a relevant issue. The base of the system known is three-dimensional movement control device with optical principle of action. The device consists of multi point light emitter and light receiver matrix. The processing of signals is enhanced to increase accuracy of measurements by switching from discrete to analog signals. Light receiver matrix is divided into four areas, and the output value of each light emitter in each matrix area is proportional to its luminance level. Thus, determing output electric signal value of each light emitter in corresponding area leads to determing position of multipoint light emitter and position of object tracked. This is done by using Case-based reasoning method, the precedent in which is described as integral signal value of each matrix area, coordinates of light receivers, which luminance level is high, and decision to be made in this situation.

Fast and Accurate Hybrid Stream PCRTMSOLAR Radiative Transfer Model for Reflected Solar Spectrum Simulation in the Cloudy Atmosphere

NASA Technical Reports Server (NTRS)

Yang, Qiguang; Liu, Xu; Wu, Wan; Kizer, Susan; Baize, Rosemary R.

2016-01-01

A hybrid stream PCRTM-SOLAR model has been proposed for fast and accurate radiative transfer simulation. It calculates the reflected solar (RS) radiances with a fast coarse way and then, with the help of a pre-saved matrix, transforms the results to obtain the desired high accurate RS spectrum. The methodology has been demonstrated with the hybrid stream discrete ordinate (HSDO) radiative transfer (RT) model. The HSDO method calculates the monochromatic radiances using a 4-stream discrete ordinate method, where only a small number of monochromatic radiances are simulated with both 4-stream and a larger N-stream (N = 16) discrete ordinate RT algorithm. The accuracy of the obtained channel radiance is comparable to the result from N-stream moderate resolution atmospheric transmission version 5 (MODTRAN5). The root-mean-square errors are usually less than 5x10(exp -4) mW/sq cm/sr/cm. The computational speed is three to four-orders of magnitude faster than the medium speed correlated-k option MODTRAN5. This method is very efficient to simulate thousands of RS spectra under multi-layer clouds/aerosols and solar radiation conditions for climate change study and numerical weather prediction applications.

Galerkin v. discrete-optimal projection in nonlinear model reduction

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

Carlberg, Kevin Thomas; Barone, Matthew Franklin; Antil, Harbir

Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes.more » We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.« less

Bayesian approach for three-dimensional aquifer characterization at the Hanford 300 Area

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

Murakami, Haruko; Chen, X.; Hahn, Melanie S.

2010-10-21

This study presents a stochastic, three-dimensional characterization of a heterogeneous hydraulic conductivity field within DOE's Hanford 300 Area site, Washington, by assimilating large-scale, constant-rate injection test data with small-scale, three-dimensional electromagnetic borehole flowmeter (EBF) measurement data. We first inverted the injection test data to estimate the transmissivity field, using zeroth-order temporal moments of pressure buildup curves. We applied a newly developed Bayesian geostatistical inversion framework, the method of anchored distributions (MAD), to obtain a joint posterior distribution of geostatistical parameters and local log-transmissivities at multiple locations. The unique aspects of MAD that make it suitable for this purpose are itsmore » ability to integrate multi-scale, multi-type data within a Bayesian framework and to compute a nonparametric posterior distribution. After we combined the distribution of transmissivities with depth-discrete relative-conductivity profile from EBF data, we inferred the three-dimensional geostatistical parameters of the log-conductivity field, using the Bayesian model-based geostatistics. Such consistent use of the Bayesian approach throughout the procedure enabled us to systematically incorporate data uncertainty into the final posterior distribution. The method was tested in a synthetic study and validated using the actual data that was not part of the estimation. Results showed broader and skewed posterior distributions of geostatistical parameters except for the mean, which suggests the importance of inferring the entire distribution to quantify the parameter uncertainty.« less

A hybrid demodulation method of fiber-optic Fabry-Perot pressure sensor

NASA Astrophysics Data System (ADS)

Yu, Le; Lang, Jianjun; Pan, Yong; Wu, Di; Zhang, Min

2013-12-01

The fiber-optic Fabry-Perot pressure sensors have been widely applied to measure pressure in oilfield. For multi-well it will take a long time (dozens of seconds) to demodulate downhole pressure values of all wells by using only one demodulation system and it will cost a lot when every well is equipped with one system, which heavily limits the sensor applied in oilfield. In present paper, a new hybrid demodulation method, combining the windowed nonequispaced discrete Fourier Transform (nDFT) method with segment search minimum mean square error estimation (MMSE) method, was developed, by which the demodulation time can be reduced to 200ms, i.e., measuring 10 channels/wells was less than 2s. Besides, experimental results showed the demodulation cavity length of the fiber-optic Fabry-Perot sensor has a maximum error of 0.5 nm and consequently pressure measurement accuracy can reach 0.4% F.S.

Urban air quality forecasting based on multi-dimensional collaborative Support Vector Regression (SVR): A case study of Beijing-Tianjin-Shijiazhuang

PubMed Central

Liu, Bing-Chun; Binaykia, Arihant; Chang, Pei-Chann; Tiwari, Manoj Kumar; Tsao, Cheng-Chin

2017-01-01

Today, China is facing a very serious issue of Air Pollution due to its dreadful impact on the human health as well as the environment. The urban cities in China are the most affected due to their rapid industrial and economic growth. Therefore, it is of extreme importance to come up with new, better and more reliable forecasting models to accurately predict the air quality. This paper selected Beijing, Tianjin and Shijiazhuang as three cities from the Jingjinji Region for the study to come up with a new model of collaborative forecasting using Support Vector Regression (SVR) for Urban Air Quality Index (AQI) prediction in China. The present study is aimed to improve the forecasting results by minimizing the prediction error of present machine learning algorithms by taking into account multiple city multi-dimensional air quality information and weather conditions as input. The results show that there is a decrease in MAPE in case of multiple city multi-dimensional regression when there is a strong interaction and correlation of the air quality characteristic attributes with AQI. Also, the geographical location is found to play a significant role in Beijing, Tianjin and Shijiazhuang AQI prediction. PMID:28708836

Study of the influence of the parameters of an experiment on the simulation of pole figures of polycrystalline materials using electron microscopy

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

Antonova, A. O., E-mail: aoantonova@mail.ru; Savyolova, T. I.

2016-05-15

A two-dimensional mathematical model of a polycrystalline sample and an experiment on electron backscattering diffraction (EBSD) is considered. The measurement parameters are taken to be the scanning step and threshold grain-boundary angle. Discrete pole figures for materials with hexagonal symmetry have been calculated based on the results of the model experiment. Discrete and smoothed (by the kernel method) pole figures of the model sample and the samples in the model experiment are compared using homogeneity criterion χ{sup 2}, an estimate of the pole figure maximum and its coordinate, a deviation of the pole figures of the model in the experimentmore » from the sample in the space of L{sub 1} measurable functions, and the RP-criterion for estimating the pole figure errors. Is is shown that the problem of calculating pole figures is ill-posed and their determination with respect to measurement parameters is not reliable.« less

Implicitly causality enforced solution of multidimensional transient photon transport equation.

PubMed

Handapangoda, Chintha C; Premaratne, Malin

2009-12-21

A novel method for solving the multidimensional transient photon transport equation for laser pulse propagation in biological tissue is presented. A Laguerre expansion is used to represent the time dependency of the incident short pulse. Owing to the intrinsic causal nature of Laguerre functions, our technique automatically always preserve the causality constrains of the transient signal. This expansion of the radiance using a Laguerre basis transforms the transient photon transport equation to the steady state version. The resulting equations are solved using the discrete ordinates method, using a finite volume approach. Therefore, our method enables one to handle general anisotropic, inhomogeneous media using a single formulation but with an added degree of flexibility owing to the ability to invoke higher-order approximations of discrete ordinate quadrature sets. Therefore, compared with existing strategies, this method offers the advantage of representing the intensity with a high accuracy thus minimizing numerical dispersion and false propagation errors. The application of the method to one, two and three dimensional geometries is provided.

A Novel Approach to Model the Air-Side Heat Transfer in Microchannel Condensers

NASA Astrophysics Data System (ADS)

Martínez-Ballester, S.; Corberán, José-M.; Gonzálvez-Maciá, J.

2012-11-01

The work presents a model (Fin1D×3) for microchannel condensers and gas coolers. The paper focusses on the description of the novel approach employed to model the air-side heat transfer. The model applies a segment-by-segment discretization to the heat exchanger adding, in each segment, a specific bi-dimensional grid to the air flow and fin wall. Given this discretization, the fin theory is applied by using a continuous piecewise function for the fin wall temperature. It allows taking into account implicitly the heat conduction between tubes along the fin, and the unmixed air influence on the heat capacity. The model has been validated against experimental data resulting in predicted capacity errors within ± 5%. Differences on prediction results and computational cost were studied and compared with the previous authors' model (Fin2D) and with other simplified model. Simulation time of the proposed model was reduced one order of magnitude respect the Fin2D's time retaining its same accuracy.

Exploiting sparsity and low-rank structure for the recovery of multi-slice breast MRIs with reduced sampling error.

PubMed

Yin, X X; Ng, B W-H; Ramamohanarao, K; Baghai-Wadji, A; Abbott, D

2012-09-01

It has been shown that, magnetic resonance images (MRIs) with sparsity representation in a transformed domain, e.g. spatial finite-differences (FD), or discrete cosine transform (DCT), can be restored from undersampled k-space via applying current compressive sampling theory. The paper presents a model-based method for the restoration of MRIs. The reduced-order model, in which a full-system-response is projected onto a subspace of lower dimensionality, has been used to accelerate image reconstruction by reducing the size of the involved linear system. In this paper, the singular value threshold (SVT) technique is applied as a denoising scheme to reduce and select the model order of the inverse Fourier transform image, and to restore multi-slice breast MRIs that have been compressively sampled in k-space. The restored MRIs with SVT for denoising show reduced sampling errors compared to the direct MRI restoration methods via spatial FD, or DCT. Compressive sampling is a technique for finding sparse solutions to underdetermined linear systems. The sparsity that is implicit in MRIs is to explore the solution to MRI reconstruction after transformation from significantly undersampled k-space. The challenge, however, is that, since some incoherent artifacts result from the random undersampling, noise-like interference is added to the image with sparse representation. These recovery algorithms in the literature are not capable of fully removing the artifacts. It is necessary to introduce a denoising procedure to improve the quality of image recovery. This paper applies a singular value threshold algorithm to reduce the model order of image basis functions, which allows further improvement of the quality of image reconstruction with removal of noise artifacts. The principle of the denoising scheme is to reconstruct the sparse MRI matrices optimally with a lower rank via selecting smaller number of dominant singular values. The singular value threshold algorithm is performed by minimizing the nuclear norm of difference between the sampled image and the recovered image. It has been illustrated that this algorithm improves the ability of previous image reconstruction algorithms to remove noise artifacts while significantly improving the quality of MRI recovery.

Inverse MDS: Inferring Dissimilarity Structure from Multiple Item Arrangements

PubMed Central

Kriegeskorte, Nikolaus; Mur, Marieke

2012-01-01

The pairwise dissimilarities of a set of items can be intuitively visualized by a 2D arrangement of the items, in which the distances reflect the dissimilarities. Such an arrangement can be obtained by multidimensional scaling (MDS). We propose a method for the inverse process: inferring the pairwise dissimilarities from multiple 2D arrangements of items. Perceptual dissimilarities are classically measured using pairwise dissimilarity judgments. However, alternative methods including free sorting and 2D arrangements have previously been proposed. The present proposal is novel (a) in that the dissimilarity matrix is estimated by “inverse MDS” based on multiple arrangements of item subsets, and (b) in that the subsets are designed by an adaptive algorithm that aims to provide optimal evidence for the dissimilarity estimates. The subject arranges the items (represented as icons on a computer screen) by means of mouse drag-and-drop operations. The multi-arrangement method can be construed as a generalization of simpler methods: It reduces to pairwise dissimilarity judgments if each arrangement contains only two items, and to free sorting if the items are categorically arranged into discrete piles. Multi-arrangement combines the advantages of these methods. It is efficient (because the subject communicates many dissimilarity judgments with each mouse drag), psychologically attractive (because dissimilarities are judged in context), and can characterize continuous high-dimensional dissimilarity structures. We present two procedures for estimating the dissimilarity matrix: a simple weighted-aligned-average of the partial dissimilarity matrices and a computationally intensive algorithm, which estimates the dissimilarity matrix by iteratively minimizing the error of MDS-predictions of the subject’s arrangements. The Matlab code for interactive arrangement and dissimilarity estimation is available from the authors upon request. PMID:22848204

Research on AHP decision algorithms based on BP algorithm

NASA Astrophysics Data System (ADS)

Ma, Ning; Guan, Jianhe

2017-10-01

Decision making is the thinking activity that people choose or judge, and scientific decision-making has always been a hot issue in the field of research. Analytic Hierarchy Process (AHP) is a simple and practical multi-criteria and multi-objective decision-making method that combines quantitative and qualitative and can show and calculate the subjective judgment in digital form. In the process of decision analysis using AHP method, the rationality of the two-dimensional judgment matrix has a great influence on the decision result. However, in dealing with the real problem, the judgment matrix produced by the two-dimensional comparison is often inconsistent, that is, it does not meet the consistency requirements. BP neural network algorithm is an adaptive nonlinear dynamic system. It has powerful collective computing ability and learning ability. It can perfect the data by constantly modifying the weights and thresholds of the network to achieve the goal of minimizing the mean square error. In this paper, the BP algorithm is used to deal with the consistency of the two-dimensional judgment matrix of the AHP.

Error due to unresolved scales in estimation problems for atmospheric data assimilation

NASA Astrophysics Data System (ADS)

Janjic, Tijana

The error arising due to unresolved scales in data assimilation procedures is examined. The problem of estimating the projection of the state of a passive scalar undergoing advection at a sequence of times is considered. The projection belongs to a finite- dimensional function space and is defined on the continuum. Using the continuum projection of the state of a passive scalar, a mathematical definition is obtained for the error arising due to the presence, in the continuum system, of scales unresolved by the discrete dynamical model. This error affects the estimation procedure through point observations that include the unresolved scales. In this work, two approximate methods for taking into account the error due to unresolved scales and the resulting correlations are developed and employed in the estimation procedure. The resulting formulas resemble the Schmidt-Kalman filter and the usual discrete Kalman filter, respectively. For this reason, the newly developed filters are called the Schmidt-Kalman filter and the traditional filter. In order to test the assimilation methods, a two- dimensional advection model with nonstationary spectrum was developed for passive scalar transport in the atmosphere. An analytical solution on the sphere was found depicting the model dynamics evolution. Using this analytical solution the model error is avoided, and the error due to unresolved scales is the only error left in the estimation problem. It is demonstrated that the traditional and the Schmidt- Kalman filter work well provided the exact covariance function of the unresolved scales is known. However, this requirement is not satisfied in practice, and the covariance function must be modeled. The Schmidt-Kalman filter cannot be computed in practice without further approximations. Therefore, the traditional filter is better suited for practical use. Also, the traditional filter does not require modeling of the full covariance function of the unresolved scales, but only modeling of the covariance matrix obtained by evaluating the covariance function at the observation points. We first assumed that this covariance matrix is stationary and that the unresolved scales are not correlated between the observation points, i.e., the matrix is diagonal, and that the values along the diagonal are constant. Tests with these assumptions were unsuccessful, indicating that a more sophisticated model of the covariance is needed for assimilation of data with nonstationary spectrum. A new method for modeling the covariance matrix based on an extended set of modeling assumptions is proposed. First, it is assumed that the covariance matrix is diagonal, that is, that the unresolved scales are not correlated between the observation points. It is postulated that the values on the diagonal depend on a wavenumber that is characteristic for the unresolved part of the spectrum. It is further postulated that this characteristic wavenumber can be diagnosed from the observations and from the estimate of the projection of the state that is being estimated. It is demonstrated that the new method successfully overcomes previously encountered difficulties.

Factor structure and longitudinal measurement invariance of the demand control support model: an evidence from the Swedish Longitudinal Occupational Survey of Health (SLOSH).

PubMed

Chungkham, Holendro Singh; Ingre, Michael; Karasek, Robert; Westerlund, Hugo; Theorell, Töres

2013-01-01

To examine the factor structure and to evaluate the longitudinal measurement invariance of the demand-control-support questionnaire (DCSQ), using the Swedish Longitudinal Occupational Survey of Health (SLOSH). A confirmatory factor analysis (CFA) and multi-group confirmatory factor analysis (MGCFA) models within the framework of structural equation modeling (SEM) have been used to examine the factor structure and invariance across time. Four factors: psychological demand, skill discretion, decision authority and social support, were confirmed by CFA at baseline, with the best fit obtained by removing the item repetitive work of skill discretion. A measurement error correlation (0.42) between work fast and work intensively for psychological demands was also detected. Acceptable composite reliability measures were obtained except for skill discretion (0.68). The invariance of the same factor structure was established, but caution in comparing mean levels of factors over time is warranted as lack of intercept invariance was evident. However, partial intercept invariance was established for work intensively. Our findings indicate that skill discretion and decision authority represent two distinct constructs in the retained model. However removing the item repetitive work along with either work fast or work intensively would improve model fit. Care should also be taken while making comparisons in the constructs across time. Further research should investigate invariance across occupations or socio-economic classes.

Factor Structure and Longitudinal Measurement Invariance of the Demand Control Support Model: An Evidence from the Swedish Longitudinal Occupational Survey of Health (SLOSH)

PubMed Central

Chungkham, Holendro Singh; Ingre, Michael; Karasek, Robert; Westerlund, Hugo; Theorell, Töres

2013-01-01

Objectives To examine the factor structure and to evaluate the longitudinal measurement invariance of the demand-control-support questionnaire (DCSQ), using the Swedish Longitudinal Occupational Survey of Health (SLOSH). Methods A confirmatory factor analysis (CFA) and multi-group confirmatory factor analysis (MGCFA) models within the framework of structural equation modeling (SEM) have been used to examine the factor structure and invariance across time. Results Four factors: psychological demand, skill discretion, decision authority and social support, were confirmed by CFA at baseline, with the best fit obtained by removing the item repetitive work of skill discretion. A measurement error correlation (0.42) between work fast and work intensively for psychological demands was also detected. Acceptable composite reliability measures were obtained except for skill discretion (0.68). The invariance of the same factor structure was established, but caution in comparing mean levels of factors over time is warranted as lack of intercept invariance was evident. However, partial intercept invariance was established for work intensively. Conclusion Our findings indicate that skill discretion and decision authority represent two distinct constructs in the retained model. However removing the item repetitive work along with either work fast or work intensively would improve model fit. Care should also be taken while making comparisons in the constructs across time. Further research should investigate invariance across occupations or socio-economic classes. PMID:23950957

A discrete Fourier-encoded, diagonal-free experiment to simplify homonuclear 2D NMR correlations.

PubMed

Huang, Zebin; Guan, Quanshuai; Chen, Zhong; Frydman, Lucio; Lin, Yulan

2017-07-21

Nuclear magnetic resonance (NMR) spectroscopy has long served as an irreplaceable, versatile tool in physics, chemistry, biology, and materials sciences, owing to its ability to study molecular structure and dynamics in detail. In particular, the connectivity of chemical sites within molecules, and thereby molecular structure, becomes visible by multi-dimensional NMR. Homonuclear correlation experiments are a powerful tool for identifying coupled spins. Generally, diagonal peaks in these correlation spectra display the strongest intensities and do not offer any new information beyond the standard one-dimensional spectrum, whereas weaker, symmetrically placed cross peaks contain most of the coupling information. The cross peaks near the diagonal are often affected by the tails of strong diagonal peaks or even obscured entirely by the diagonal. In this paper, we demonstrate a homonuclear encoding approach based on imparting a discrete phase modulation of the targeted cross peaks and combine it with a site-selective sculpting scheme, capable of simplifying the patterns arising in these 2D correlation spectra. The theoretical principles of the new methods are laid out, and experimental observations are rationalized on the basis of theoretical analyses. The ensuing techniques provide a new way to retrieve 2D coupling information within homonuclear spin systems, with enhanced sensitivity, speed, and clarity.

A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION.

PubMed

Mang, Andreas; Biros, George

2017-01-01

We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20 × speedup for a two dimensional, real world multi-subject medical image registration problem.

A discrete Fourier-encoded, diagonal-free experiment to simplify homonuclear 2D NMR correlations

NASA Astrophysics Data System (ADS)

Huang, Zebin; Guan, Quanshuai; Chen, Zhong; Frydman, Lucio; Lin, Yulan

2017-07-01

Nuclear magnetic resonance (NMR) spectroscopy has long served as an irreplaceable, versatile tool in physics, chemistry, biology, and materials sciences, owing to its ability to study molecular structure and dynamics in detail. In particular, the connectivity of chemical sites within molecules, and thereby molecular structure, becomes visible by multi-dimensional NMR. Homonuclear correlation experiments are a powerful tool for identifying coupled spins. Generally, diagonal peaks in these correlation spectra display the strongest intensities and do not offer any new information beyond the standard one-dimensional spectrum, whereas weaker, symmetrically placed cross peaks contain most of the coupling information. The cross peaks near the diagonal are often affected by the tails of strong diagonal peaks or even obscured entirely by the diagonal. In this paper, we demonstrate a homonuclear encoding approach based on imparting a discrete phase modulation of the targeted cross peaks and combine it with a site-selective sculpting scheme, capable of simplifying the patterns arising in these 2D correlation spectra. The theoretical principles of the new methods are laid out, and experimental observations are rationalized on the basis of theoretical analyses. The ensuing techniques provide a new way to retrieve 2D coupling information within homonuclear spin systems, with enhanced sensitivity, speed, and clarity.

Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices.

PubMed

Español, Malena I; Golovaty, Dmitry; Wilber, J Patrick

2018-01-01

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

Solving Upwind-Biased Discretizations. 2; Multigrid Solver Using Semicoarsening

NASA Technical Reports Server (NTRS)

Diskin, Boris

1999-01-01

This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation obtained by AMA is always better than the required accuracy; the computational complexity of the AMA algorithm is (nearly) optimal (comparable with the complexity of the FMG algorithm applied to solve the problem on the optimally spaced target grid).

Multi-Level Reduced Order Modeling Equipped with Probabilistic Error Bounds

NASA Astrophysics Data System (ADS)

Abdo, Mohammad Gamal Mohammad Mostafa

This thesis develops robust reduced order modeling (ROM) techniques to achieve the needed efficiency to render feasible the use of high fidelity tools for routine engineering analyses. Markedly different from the state-of-the-art ROM techniques, our work focuses only on techniques which can quantify the credibility of the reduction which can be measured with the reduction errors upper-bounded for the envisaged range of ROM model application. Our objective is two-fold. First, further developments of ROM techniques are proposed when conventional ROM techniques are too taxing to be computationally practical. This is achieved via a multi-level ROM methodology designed to take advantage of the multi-scale modeling strategy typically employed for computationally taxing models such as those associated with the modeling of nuclear reactor behavior. Second, the discrepancies between the original model and ROM model predictions over the full range of model application conditions are upper-bounded in a probabilistic sense with high probability. ROM techniques may be classified into two broad categories: surrogate construction techniques and dimensionality reduction techniques, with the latter being the primary focus of this work. We focus on dimensionality reduction, because it offers a rigorous approach by which reduction errors can be quantified via upper-bounds that are met in a probabilistic sense. Surrogate techniques typically rely on fitting a parametric model form to the original model at a number of training points, with the residual of the fit taken as a measure of the prediction accuracy of the surrogate. This approach, however, does not generally guarantee that the surrogate model predictions at points not included in the training process will be bound by the error estimated from the fitting residual. Dimensionality reduction techniques however employ a different philosophy to render the reduction, wherein randomized snapshots of the model variables, such as the model parameters, responses, or state variables, are projected onto lower dimensional subspaces, referred to as the "active subspaces", which are selected to capture a user-defined portion of the snapshots variations. Once determined, the ROM model application involves constraining the variables to the active subspaces. In doing so, the contribution from the variables discarded components can be estimated using a fundamental theorem from random matrix theory which has its roots in Dixon's theory, developed in 1983. This theory was initially presented for linear matrix operators. The thesis extends this theorem's results to allow reduction of general smooth nonlinear operators. The result is an approach by which the adequacy of a given active subspace determined using a given set of snapshots, generated either using the full high fidelity model, or other models with lower fidelity, can be assessed, which provides insight to the analyst on the type of snapshots required to reach a reduction that can satisfy user-defined preset tolerance limits on the reduction errors. Reactor physics calculations are employed as a test bed for the proposed developments. The focus will be on reducing the effective dimensionality of the various data streams such as the cross-section data and the neutron flux. The developed methods will be applied to representative assembly level calculations, where the size of the cross-section and flux spaces are typically large, as required by downstream core calculations, in order to capture the broad range of conditions expected during reactor operation. (Abstract shortened by ProQuest.).

Fast maximum likelihood estimation using continuous-time neural point process models.

PubMed

Lepage, Kyle Q; MacDonald, Christopher J

2015-06-01

A recent report estimates that the number of simultaneously recorded neurons is growing exponentially. A commonly employed statistical paradigm using discrete-time point process models of neural activity involves the computation of a maximum-likelihood estimate. The time to computate this estimate, per neuron, is proportional to the number of bins in a finely spaced discretization of time. By using continuous-time models of neural activity and the optimally efficient Gaussian quadrature, memory requirements and computation times are dramatically decreased in the commonly encountered situation where the number of parameters p is much less than the number of time-bins n. In this regime, with q equal to the quadrature order, memory requirements are decreased from O(np) to O(qp), and the number of floating-point operations are decreased from O(np(2)) to O(qp(2)). Accuracy of the proposed estimates is assessed based upon physiological consideration, error bounds, and mathematical results describing the relation between numerical integration error and numerical error affecting both parameter estimates and the observed Fisher information. A check is provided which is used to adapt the order of numerical integration. The procedure is verified in simulation and for hippocampal recordings. It is found that in 95 % of hippocampal recordings a q of 60 yields numerical error negligible with respect to parameter estimate standard error. Statistical inference using the proposed methodology is a fast and convenient alternative to statistical inference performed using a discrete-time point process model of neural activity. It enables the employment of the statistical methodology available with discrete-time inference, but is faster, uses less memory, and avoids any error due to discretization.

Extension-torsion coupling behavior of advanced composite tilt-rotor blades

NASA Technical Reports Server (NTRS)

Kosmatka, J. B.

1989-01-01

An analytic model was developed to study the extension-bend-twist coupling behavior of an advanced composite helicopter or tilt-rotor blade. The outer surface of the blade is defined by rotating an arbitrary cross section about an initial twist axis. The cross section can be nonhomogeneous and composed of generally anisotropic materials. The model is developed based upon a three dimensional elasticity approach that is recast as a coupled two-dimensional boundary value problem defined in a curvilinear coordinate system. Displacement solutions are written in terms of known functions that represent extension, bending, and twisting and unknown functions for local cross section deformations. The unknown local deformation functions are determined by applying the principle of minimum potential energy to the discretized two-dimensional cross section. This is an application of the Ritz method, where the trial function family is the displacement field associated with a finite element (8-node isoparametric quadrilaterals) representation of the section. A computer program was written where the cross section is discretized into 8-node quadrilateral subregions. Initially the program was verified using previously published results (both three-dimensional elasticity and technical beam theory) for pretwisted isotropic bars with an elliptical cross section. In addition, solid and thin-wall multi-cell NACA-0012 airfoil sections were analyzed to illustrate the pronounced effects that pretwist, initial twist axis location, and spar location has on coupled behavior. Currently, a series of advanced composite airfoils are being modeled in order to assess how the use of laminated composite materials interacts with pretwist to alter the coupling behavior of the blade. These studies will investigate the use of different ply angle orientations and the use of symmetric versus unsymmetric laminates.

Three-dimensional discrete-time Lotka-Volterra models with an application to industrial clusters

NASA Astrophysics Data System (ADS)

Bischi, G. I.; Tramontana, F.

2010-10-01

We consider a three-dimensional discrete dynamical system that describes an application to economics of a generalization of the Lotka-Volterra prey-predator model. The dynamic model proposed is used to describe the interactions among industrial clusters (or districts), following a suggestion given by [23]. After studying some local and global properties and bifurcations in bidimensional Lotka-Volterra maps, by numerical explorations we show how some of them can be extended to their three-dimensional counterparts, even if their analytic and geometric characterization becomes much more difficult and challenging. We also show a global bifurcation of the three-dimensional system that has no two-dimensional analogue. Besides the particular economic application considered, the study of the discrete version of Lotka-Volterra dynamical systems turns out to be a quite rich and interesting topic by itself, i.e. from a purely mathematical point of view.

Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates

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

Cheng, Juan, E-mail: cheng_juan@iapcm.ac.cn; Shu, Chi-Wang, E-mail: shu@dam.brown.edu

In applications such as astrophysics and inertial confinement fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simulated by Lagrangian schemes in the two-dimensional cylindrical coordinates. For this type of simulation, a critical issue for the schemes is to keep spherical symmetry in the cylindrical coordinate system if the original physical problem has this symmetry. In the past decades, several Lagrangian schemes with such symmetry property have been developed, but all of them are only first order accurate. In this paper, we develop a second order cell-centered Lagrangian scheme for solving compressible Euler equations in cylindrical coordinates, basedmore » on the control volume discretizations, which is designed to have uniformly second order accuracy and capability to preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid. The scheme maintains several good properties such as conservation for mass, momentum and total energy, and the geometric conservation law. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of accuracy, symmetry, non-oscillation and robustness. The advantage of higher order accuracy is demonstrated in these examples.« less

Discrete Emotion Effects on Lexical Decision Response Times

PubMed Central

Briesemeister, Benny B.; Kuchinke, Lars; Jacobs, Arthur M.

2011-01-01

Our knowledge about affective processes, especially concerning effects on cognitive demands like word processing, is increasing steadily. Several studies consistently document valence and arousal effects, and although there is some debate on possible interactions and different notions of valence, broad agreement on a two dimensional model of affective space has been achieved. Alternative models like the discrete emotion theory have received little interest in word recognition research so far. Using backward elimination and multiple regression analyses, we show that five discrete emotions (i.e., happiness, disgust, fear, anger and sadness) explain as much variance as two published dimensional models assuming continuous or categorical valence, with the variables happiness, disgust and fear significantly contributing to this account. Moreover, these effects even persist in an experiment with discrete emotion conditions when the stimuli are controlled for emotional valence and arousal levels. We interpret this result as evidence for discrete emotion effects in visual word recognition that cannot be explained by the two dimensional affective space account. PMID:21887307

Discrete emotion effects on lexical decision response times.

PubMed

Briesemeister, Benny B; Kuchinke, Lars; Jacobs, Arthur M

2011-01-01

Our knowledge about affective processes, especially concerning effects on cognitive demands like word processing, is increasing steadily. Several studies consistently document valence and arousal effects, and although there is some debate on possible interactions and different notions of valence, broad agreement on a two dimensional model of affective space has been achieved. Alternative models like the discrete emotion theory have received little interest in word recognition research so far. Using backward elimination and multiple regression analyses, we show that five discrete emotions (i.e., happiness, disgust, fear, anger and sadness) explain as much variance as two published dimensional models assuming continuous or categorical valence, with the variables happiness, disgust and fear significantly contributing to this account. Moreover, these effects even persist in an experiment with discrete emotion conditions when the stimuli are controlled for emotional valence and arousal levels. We interpret this result as evidence for discrete emotion effects in visual word recognition that cannot be explained by the two dimensional affective space account.

Quantum trilogy: discrete Toda, Y-system and chaos

NASA Astrophysics Data System (ADS)

Yamazaki, Masahito

2018-02-01

We discuss a discretization of the quantum Toda field theory associated with a semisimple finite-dimensional Lie algebra or a tamely-laced infinite-dimensional Kac-Moody algebra G, generalizing the previous construction of discrete quantum Liouville theory for the case G  =  A 1. The model is defined on a discrete two-dimensional lattice, whose spatial direction is of length L. In addition we also find a ‘discretized extra dimension’ whose width is given by the rank r of G, which decompactifies in the large r limit. For the case of G  =  A N or AN-1(1) , we find a symmetry exchanging L and N under appropriate spatial boundary conditions. The dynamical time evolution rule of the model is quantizations of the so-called Y-system, and the theory can be well described by the quantum cluster algebra. We discuss possible implications for recent discussions of quantum chaos, and comment on the relation with the quantum higher Teichmüller theory of type A N .

Ice Shape Characterization Using Self-Organizing Maps

NASA Technical Reports Server (NTRS)

McClain, Stephen T.; Tino, Peter; Kreeger, Richard E.

2011-01-01

A method for characterizing ice shapes using a self-organizing map (SOM) technique is presented. Self-organizing maps are neural-network techniques for representing noisy, multi-dimensional data aligned along a lower-dimensional and possibly nonlinear manifold. For a large set of noisy data, each element of a finite set of codebook vectors is iteratively moved in the direction of the data closest to the winner codebook vector. Through successive iterations, the codebook vectors begin to align with the trends of the higher-dimensional data. In information processing, the intent of SOM methods is to transmit the codebook vectors, which contains far fewer elements and requires much less memory or bandwidth, than the original noisy data set. When applied to airfoil ice accretion shapes, the properties of the codebook vectors and the statistical nature of the SOM methods allows for a quantitative comparison of experimentally measured mean or average ice shapes to ice shapes predicted using computer codes such as LEWICE. The nature of the codebook vectors also enables grid generation and surface roughness descriptions for use with the discrete-element roughness approach. In the present study, SOM characterizations are applied to a rime ice shape, a glaze ice shape at an angle of attack, a bi-modal glaze ice shape, and a multi-horn glaze ice shape. Improvements and future explorations will be discussed.

A scalable method to improve gray matter segmentation at ultra high field MRI.

PubMed

Gulban, Omer Faruk; Schneider, Marian; Marquardt, Ingo; Haast, Roy A M; De Martino, Federico

2018-01-01

High-resolution (functional) magnetic resonance imaging (MRI) at ultra high magnetic fields (7 Tesla and above) enables researchers to study how anatomical and functional properties change within the cortical ribbon, along surfaces and across cortical depths. These studies require an accurate delineation of the gray matter ribbon, which often suffers from inclusion of blood vessels, dura mater and other non-brain tissue. Residual segmentation errors are commonly corrected by browsing the data slice-by-slice and manually changing labels. This task becomes increasingly laborious and prone to error at higher resolutions since both work and error scale with the number of voxels. Here we show that many mislabeled, non-brain voxels can be corrected more efficiently and semi-automatically by representing three-dimensional anatomical images using two-dimensional histograms. We propose both a uni-modal (based on first spatial derivative) and multi-modal (based on compositional data analysis) approach to this representation and quantify the benefits in 7 Tesla MRI data of nine volunteers. We present an openly accessible Python implementation of these approaches and demonstrate that editing cortical segmentations using two-dimensional histogram representations as an additional post-processing step aids existing algorithms and yields improved gray matter borders. By making our data and corresponding expert (ground truth) segmentations openly available, we facilitate future efforts to develop and test segmentation algorithms on this challenging type of data.

A scalable method to improve gray matter segmentation at ultra high field MRI

PubMed Central

De Martino, Federico

2018-01-01

High-resolution (functional) magnetic resonance imaging (MRI) at ultra high magnetic fields (7 Tesla and above) enables researchers to study how anatomical and functional properties change within the cortical ribbon, along surfaces and across cortical depths. These studies require an accurate delineation of the gray matter ribbon, which often suffers from inclusion of blood vessels, dura mater and other non-brain tissue. Residual segmentation errors are commonly corrected by browsing the data slice-by-slice and manually changing labels. This task becomes increasingly laborious and prone to error at higher resolutions since both work and error scale with the number of voxels. Here we show that many mislabeled, non-brain voxels can be corrected more efficiently and semi-automatically by representing three-dimensional anatomical images using two-dimensional histograms. We propose both a uni-modal (based on first spatial derivative) and multi-modal (based on compositional data analysis) approach to this representation and quantify the benefits in 7 Tesla MRI data of nine volunteers. We present an openly accessible Python implementation of these approaches and demonstrate that editing cortical segmentations using two-dimensional histogram representations as an additional post-processing step aids existing algorithms and yields improved gray matter borders. By making our data and corresponding expert (ground truth) segmentations openly available, we facilitate future efforts to develop and test segmentation algorithms on this challenging type of data. PMID:29874295

Empirical parameterization of setup, swash, and runup

USGS Publications Warehouse

Stockdon, H.F.; Holman, R.A.; Howd, P.A.; Sallenger, A.H.

2006-01-01

Using shoreline water-level time series collected during 10 dynamically diverse field experiments, an empirical parameterization for extreme runup, defined by the 2% exceedence value, has been developed for use on natural beaches over a wide range of conditions. Runup, the height of discrete water-level maxima, depends on two dynamically different processes; time-averaged wave setup and total swash excursion, each of which is parameterized separately. Setup at the shoreline was best parameterized using a dimensional form of the more common Iribarren-based setup expression that includes foreshore beach slope, offshore wave height, and deep-water wavelength. Significant swash can be decomposed into the incident and infragravity frequency bands. Incident swash is also best parameterized using a dimensional form of the Iribarren-based expression. Infragravity swash is best modeled dimensionally using offshore wave height and wavelength and shows no statistically significant linear dependence on either foreshore or surf-zone slope. On infragravity-dominated dissipative beaches, the magnitudes of both setup and swash, modeling both incident and infragravity frequency components together, are dependent only on offshore wave height and wavelength. Statistics of predicted runup averaged over all sites indicate a - 17 cm bias and an rms error of 38 cm: the mean observed runup elevation for all experiments was 144 cm. On intermediate and reflective beaches with complex foreshore topography, the use of an alongshore-averaged beach slope in practical applications of the runup parameterization may result in a relative runup error equal to 51% of the fractional variability between the measured and the averaged slope.

A new systematic calibration method of ring laser gyroscope inertial navigation system

NASA Astrophysics Data System (ADS)

Wei, Guo; Gao, Chunfeng; Wang, Qi; Wang, Qun; Xiong, Zhenyu; Long, Xingwu

2016-10-01

Inertial navigation system has been the core component of both military and civil navigation systems. Before the INS is put into application, it is supposed to be calibrated in the laboratory in order to compensate repeatability error caused by manufacturing. Discrete calibration method cannot fulfill requirements of high-accurate calibration of the mechanically dithered ring laser gyroscope navigation system with shock absorbers. This paper has analyzed theories of error inspiration and separation in detail and presented a new systematic calibration method for ring laser gyroscope inertial navigation system. Error models and equations of calibrated Inertial Measurement Unit are given. Then proper rotation arrangement orders are depicted in order to establish the linear relationships between the change of velocity errors and calibrated parameter errors. Experiments have been set up to compare the systematic errors calculated by filtering calibration result with those obtained by discrete calibration result. The largest position error and velocity error of filtering calibration result are only 0.18 miles and 0.26m/s compared with 2 miles and 1.46m/s of discrete calibration result. These results have validated the new systematic calibration method and proved its importance for optimal design and accuracy improvement of calibration of mechanically dithered ring laser gyroscope inertial navigation system.

CRASH: A BLOCK-ADAPTIVE-MESH CODE FOR RADIATIVE SHOCK HYDRODYNAMICS-IMPLEMENTATION AND VERIFICATION

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

Van der Holst, B.; Toth, G.; Sokolov, I. V.

We describe the Center for Radiative Shock Hydrodynamics (CRASH) code, a block-adaptive-mesh code for multi-material radiation hydrodynamics. The implementation solves the radiation diffusion model with a gray or multi-group method and uses a flux-limited diffusion approximation to recover the free-streaming limit. Electrons and ions are allowed to have different temperatures and we include flux-limited electron heat conduction. The radiation hydrodynamic equations are solved in the Eulerian frame by means of a conservative finite-volume discretization in either one-, two-, or three-dimensional slab geometry or in two-dimensional cylindrical symmetry. An operator-split method is used to solve these equations in three substeps: (1)more » an explicit step of a shock-capturing hydrodynamic solver; (2) a linear advection of the radiation in frequency-logarithm space; and (3) an implicit solution of the stiff radiation diffusion, heat conduction, and energy exchange. We present a suite of verification test problems to demonstrate the accuracy and performance of the algorithms. The applications are for astrophysics and laboratory astrophysics. The CRASH code is an extension of the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATS-R-US) code with a new radiation transfer and heat conduction library and equation-of-state and multi-group opacity solvers. Both CRASH and BATS-R-US are part of the publicly available Space Weather Modeling Framework.« less

Multi-particle three-dimensional coordinate estimation in real-time optical manipulation

NASA Astrophysics Data System (ADS)

Dam, J. S.; Perch-Nielsen, I.; Palima, D.; Gluckstad, J.

2009-11-01

We have previously shown how stereoscopic images can be obtained in our three-dimensional optical micromanipulation system [J. S. Dam et al, Opt. Express 16, 7244 (2008)]. Here, we present an extension and application of this principle to automatically gather the three-dimensional coordinates for all trapped particles with high tracking range and high reliability without requiring user calibration. Through deconvolving of the red, green, and blue colour planes to correct for bleeding between colour planes, we show that we can extend the system to also utilize green illumination, in addition to the blue and red. Applying the green colour as on-axis illumination yields redundant information for enhanced error correction, which is used to verify the gathered data, resulting in reliable coordinates as well as producing visually attractive images.

Nonparametric probability density estimation by optimization theoretic techniques

NASA Technical Reports Server (NTRS)

Scott, D. W.

1976-01-01

Two nonparametric probability density estimators are considered. The first is the kernel estimator. The problem of choosing the kernel scaling factor based solely on a random sample is addressed. An interactive mode is discussed and an algorithm proposed to choose the scaling factor automatically. The second nonparametric probability estimate uses penalty function techniques with the maximum likelihood criterion. A discrete maximum penalized likelihood estimator is proposed and is shown to be consistent in the mean square error. A numerical implementation technique for the discrete solution is discussed and examples displayed. An extensive simulation study compares the integrated mean square error of the discrete and kernel estimators. The robustness of the discrete estimator is demonstrated graphically.

High-fidelity gates towards a scalable superconducting quantum processor

NASA Astrophysics Data System (ADS)

Chow, Jerry M.; Corcoles, Antonio D.; Gambetta, Jay M.; Rigetti, Chad; Johnson, Blake R.; Smolin, John A.; Merkel, Seth; Poletto, Stefano; Rozen, Jim; Rothwell, Mary Beth; Keefe, George A.; Ketchen, Mark B.; Steffen, Matthias

2012-02-01

We experimentally explore the implementation of high-fidelity gates on multiple superconducting qubits coupled to multiple resonators. Having demonstrated all-microwave single and two qubit gates with fidelities > 90% on multi-qubit single-resonator systems, we expand the application to qubits across two resonators and investigate qubit coupling in this circuit. The coupled qubit-resonators are building blocks towards two-dimensional lattice networks for the application of surface code quantum error correction algorithms.

SU-E-T-22: A Deterministic Solver of the Boltzmann-Fokker-Planck Equation for Dose Calculation

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

Hong, X; Gao, H; Paganetti, H

2015-06-15

Purpose: The Boltzmann-Fokker-Planck equation (BFPE) accurately models the migration of photons/charged particles in tissues. While the Monte Carlo (MC) method is popular for solving BFPE in a statistical manner, we aim to develop a deterministic BFPE solver based on various state-of-art numerical acceleration techniques for rapid and accurate dose calculation. Methods: Our BFPE solver is based on the structured grid that is maximally parallelizable, with the discretization in energy, angle and space, and its cross section coefficients are derived or directly imported from the Geant4 database. The physical processes that are taken into account are Compton scattering, photoelectric effect, pairmore » production for photons, and elastic scattering, ionization and bremsstrahlung for charged particles.While the spatial discretization is based on the diamond scheme, the angular discretization synergizes finite element method (FEM) and spherical harmonics (SH). Thus, SH is used to globally expand the scattering kernel and FFM is used to locally discretize the angular sphere. As a Result, this hybrid method (FEM-SH) is both accurate in dealing with forward-peaking scattering via FEM, and efficient for multi-energy-group computation via SH. In addition, FEM-SH enables the analytical integration in energy variable of delta scattering kernel for elastic scattering with reduced truncation error from the numerical integration based on the classic SH-based multi-energy-group method. Results: The accuracy of the proposed BFPE solver was benchmarked against Geant4 for photon dose calculation. In particular, FEM-SH had improved accuracy compared to FEM, while both were within 2% of the results obtained with Geant4. Conclusion: A deterministic solver of the Boltzmann-Fokker-Planck equation is developed for dose calculation, and benchmarked against Geant4. Xiang Hong and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500)« less

Discrete elliptic solitons in two-dimensional waveguide arrays

NASA Astrophysics Data System (ADS)

Ye, Fangwei; Dong, Liangwei; Wang, Jiandong; Cai, Tian; Li, Yong-Ping

2005-04-01

The fundamental properties of discrete elliptic solitons (DESs) in the two-dimensional waveguide arrays were studied. The DESs show nontrivial spatial structures in their parameters space due to the introduction of the new freedom of ellipticity, and their stability is closely linked to their propagation directions in the transverse plane.

Compact single mode tunable laser using a digital micromirror device.

PubMed

Havermeyer, Frank; Ho, Lawrence; Moser, Christophe

2011-07-18

The wavelength tuning properties of a tunable external cavity laser based on multiplexed volume holographic gratings and a commercial micromirror device are reported. The 3x3x3 cm(3) laser exhibits single mode operation in single or multi colors between 776 nm and 783 nm with less than 7.5 MHz linewidth, 37 mW output power, 50 μs rise/fall time constant and a maximum switching rate of 0.66 KHz per wavelength. The unique discrete-wavelength-switching features of this laser are also well suited as a source for continuous wave Terahertz generation and three-dimensional metrology.

Metriplectic integrators for the Landau collision operator

DOE PAGES

Kraus, Michael; Hirvijoki, Eero

2017-10-02

Here, we present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and, using a Galerkin discretization for the velocity space, we transform the infinite-dimensional system into a finite-dimensional, time-continuous metriplectic system. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of energy, momentum, and particle densities, as well as the production of entropy is demonstrated algebraically for the fully discrete system. Due to the generality of our approach, the conservation properties and the monotonicmore » behavior of entropy are guaranteed for finite element discretizations, in general, independently of the mesh configuration.« less

Omics-Based Strategies in Precision Medicine: Toward a Paradigm Shift in Inborn Errors of Metabolism Investigations

PubMed Central

Tebani, Abdellah; Afonso, Carlos; Marret, Stéphane; Bekri, Soumeya

2016-01-01

The rise of technologies that simultaneously measure thousands of data points represents the heart of systems biology. These technologies have had a huge impact on the discovery of next-generation diagnostics, biomarkers, and drugs in the precision medicine era. Systems biology aims to achieve systemic exploration of complex interactions in biological systems. Driven by high-throughput omics technologies and the computational surge, it enables multi-scale and insightful overviews of cells, organisms, and populations. Precision medicine capitalizes on these conceptual and technological advancements and stands on two main pillars: data generation and data modeling. High-throughput omics technologies allow the retrieval of comprehensive and holistic biological information, whereas computational capabilities enable high-dimensional data modeling and, therefore, accessible and user-friendly visualization. Furthermore, bioinformatics has enabled comprehensive multi-omics and clinical data integration for insightful interpretation. Despite their promise, the translation of these technologies into clinically actionable tools has been slow. In this review, we present state-of-the-art multi-omics data analysis strategies in a clinical context. The challenges of omics-based biomarker translation are discussed. Perspectives regarding the use of multi-omics approaches for inborn errors of metabolism (IEM) are presented by introducing a new paradigm shift in addressing IEM investigations in the post-genomic era. PMID:27649151

Omics-Based Strategies in Precision Medicine: Toward a Paradigm Shift in Inborn Errors of Metabolism Investigations.

PubMed

Tebani, Abdellah; Afonso, Carlos; Marret, Stéphane; Bekri, Soumeya

2016-09-14

The rise of technologies that simultaneously measure thousands of data points represents the heart of systems biology. These technologies have had a huge impact on the discovery of next-generation diagnostics, biomarkers, and drugs in the precision medicine era. Systems biology aims to achieve systemic exploration of complex interactions in biological systems. Driven by high-throughput omics technologies and the computational surge, it enables multi-scale and insightful overviews of cells, organisms, and populations. Precision medicine capitalizes on these conceptual and technological advancements and stands on two main pillars: data generation and data modeling. High-throughput omics technologies allow the retrieval of comprehensive and holistic biological information, whereas computational capabilities enable high-dimensional data modeling and, therefore, accessible and user-friendly visualization. Furthermore, bioinformatics has enabled comprehensive multi-omics and clinical data integration for insightful interpretation. Despite their promise, the translation of these technologies into clinically actionable tools has been slow. In this review, we present state-of-the-art multi-omics data analysis strategies in a clinical context. The challenges of omics-based biomarker translation are discussed. Perspectives regarding the use of multi-omics approaches for inborn errors of metabolism (IEM) are presented by introducing a new paradigm shift in addressing IEM investigations in the post-genomic era.

Multi-Aperture Digital Coherent Combining for Free-Space Optical Communication Receivers

DTIC Science & Technology

2016-04-21

Distribution A: Public Release; unlimited distribution 2016 Optical Society of America OCIS codes: (060.1660) Coherent communications; (070.2025) Discrete ...Coherent combining algorithm Multi-aperture coherent combining enables using many discrete apertures together to create a large effective aperture. A

Enhancing adaptive sparse grid approximations and improving refinement strategies using adjoint-based a posteriori error estimates

DOE PAGES

Jakeman, J. D.; Wildey, T.

2015-01-01

In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity. We show that utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this papermore » we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.« less

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

Flory, John Andrew; Padilla, Denise D.; Gauthier, John H.

Upcoming weapon programs require an aggressive increase in Application Specific Integrated Circuit (ASIC) production at Sandia National Laboratories (SNL). SNL has developed unique modeling and optimization tools that have been instrumental in improving ASIC production productivity and efficiency, identifying optimal operational and tactical execution plans under resource constraints, and providing confidence in successful mission execution. With ten products and unprecedented levels of demand, a single set of shared resources, highly variable processes, and the need for external supplier task synchronization, scheduling is an integral part of successful manufacturing. The scheduler uses an iterative multi-objective genetic algorithm and a multi-dimensional performancemore » evaluator. Schedule feasibility is assessed using a discrete event simulation (DES) that incorporates operational uncertainty, variability, and resource availability. The tools provide rapid scenario assessments and responses to variances in the operational environment, and have been used to inform major equipment investments and workforce planning decisions in multiple SNL facilities.« less

Multi-scale modeling of irradiation effects in spallation neutron source materials

NASA Astrophysics Data System (ADS)

Yoshiie, T.; Ito, T.; Iwase, H.; Kaneko, Y.; Kawai, M.; Kishida, I.; Kunieda, S.; Sato, K.; Shimakawa, S.; Shimizu, F.; Hashimoto, S.; Hashimoto, N.; Fukahori, T.; Watanabe, Y.; Xu, Q.; Ishino, S.

2011-07-01

Changes in mechanical property of Ni under irradiation by 3 GeV protons were estimated by multi-scale modeling. The code consisted of four parts. The first part was based on the Particle and Heavy-Ion Transport code System (PHITS) code for nuclear reactions, and modeled the interactions between high energy protons and nuclei in the target. The second part covered atomic collisions by particles without nuclear reactions. Because the energy of the particles was high, subcascade analysis was employed. The direct formation of clusters and the number of mobile defects were estimated using molecular dynamics (MD) and kinetic Monte-Carlo (kMC) methods in each subcascade. The third part considered damage structural evolutions estimated by reaction kinetic analysis. The fourth part involved the estimation of mechanical property change using three-dimensional discrete dislocation dynamics (DDD). Using the above four part code, stress-strain curves for high energy proton irradiated Ni were obtained.

Multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) approach to the correlated exciton-vibrational dynamics in the FMO complex

NASA Astrophysics Data System (ADS)

Schulze, Jan; Shibl, Mohamed F.; Al-Marri, Mohammed J.; Kühn, Oliver

2016-05-01

The coupled quantum dynamics of excitonic and vibrational degrees of freedom is investigated for high-dimensional models of the Fenna-Matthews-Olson complex. This includes a seven- and an eight-site model with 518 and 592 harmonic vibrational modes, respectively. The coupling between local electronic transitions and vibrations is described within the Huang-Rhys model using parameters that are obtained by discretization of an experimental spectral density. Different pathways of excitation energy flow are analyzed in terms of the reduced one-exciton density matrix, focussing on the role of vibrational and vibronic excitations. Distinct features due to both competing time scales of vibrational and exciton motion and vibronically assisted transfer are observed. The question of the effect of initial state preparation is addressed by comparing the case of an instantaneous Franck-Condon excitation at a single site with that of a laser field excitation.

Two-dimensional optoelectronic interconnect-processor and its operational bit error rate

NASA Astrophysics Data System (ADS)

Liu, J. Jiang; Gollsneider, Brian; Chang, Wayne H.; Carhart, Gary W.; Vorontsov, Mikhail A.; Simonis, George J.; Shoop, Barry L.

2004-10-01

Two-dimensional (2-D) multi-channel 8x8 optical interconnect and processor system were designed and developed using complementary metal-oxide-semiconductor (CMOS) driven 850-nm vertical-cavity surface-emitting laser (VCSEL) arrays and the photodetector (PD) arrays with corresponding wavelengths. We performed operation and bit-error-rate (BER) analysis on this free-space integrated 8x8 VCSEL optical interconnects driven by silicon-on-sapphire (SOS) circuits. Pseudo-random bit stream (PRBS) data sequence was used in operation of the interconnects. Eye diagrams were measured from individual channels and analyzed using a digital oscilloscope at data rates from 155 Mb/s to 1.5 Gb/s. Using a statistical model of Gaussian distribution for the random noise in the transmission, we developed a method to compute the BER instantaneously with the digital eye-diagrams. Direct measurements on this interconnects were also taken on a standard BER tester for verification. We found that the results of two methods were in the same order and within 50% accuracy. The integrated interconnects were investigated in an optoelectronic processing architecture of digital halftoning image processor. Error diffusion networks implemented by the inherently parallel nature of photonics promise to provide high quality digital halftoned images.

A mathematical theory of learning control for linear discrete multivariable systems

NASA Technical Reports Server (NTRS)

Phan, Minh; Longman, Richard W.

1988-01-01

When tracking control systems are used in repetitive operations such as robots in various manufacturing processes, the controller will make the same errors repeatedly. Here consideration is given to learning controllers that look at the tracking errors in each repetition of the process and adjust the control to decrease these errors in the next repetition. A general formalism is developed for learning control of discrete-time (time-varying or time-invariant) linear multivariable systems. Methods of specifying a desired trajectory (such that the trajectory can actually be performed by the discrete system) are discussed, and learning controllers are developed. Stability criteria are obtained which are relatively easy to use to insure convergence of the learning process, and proper gain settings are discussed in light of measurement noise and system uncertainties.

Distributed-observer-based cooperative control for synchronization of linear discrete-time multi-agent systems.

PubMed

Liang, Hongjing; Zhang, Huaguang; Wang, Zhanshan

2015-11-01

This paper considers output synchronization of discrete-time multi-agent systems with directed communication topologies. The directed communication graph contains a spanning tree and the exosystem as its root. Distributed observer-based consensus protocols are proposed, based on the relative outputs of neighboring agents. A multi-step algorithm is presented to construct the observer-based protocols. In light of the discrete-time algebraic Riccati equation and internal model principle, synchronization problem is completed. At last, numerical simulation is provided to verify the effectiveness of the theoretical results. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Multi-object model-based multi-atlas segmentation for rodent brains using dense discrete correspondences

NASA Astrophysics Data System (ADS)

Lee, Joohwi; Kim, Sun Hyung; Styner, Martin

2016-03-01

The delineation of rodent brain structures is challenging due to low-contrast multiple cortical and subcortical organs that are closely interfacing to each other. Atlas-based segmentation has been widely employed due to its ability to delineate multiple organs at the same time via image registration. The use of multiple atlases and subsequent label fusion techniques has further improved the robustness and accuracy of atlas-based segmentation. However, the accuracy of atlas-based segmentation is still prone to registration errors; for example, the segmentation of in vivo MR images can be less accurate and robust against image artifacts than the segmentation of post mortem images. In order to improve the accuracy and robustness of atlas-based segmentation, we propose a multi-object, model-based, multi-atlas segmentation method. We first establish spatial correspondences across atlases using a set of dense pseudo-landmark particles. We build a multi-object point distribution model using those particles in order to capture inter- and intra- subject variation among brain structures. The segmentation is obtained by fitting the model into a subject image, followed by label fusion process. Our result shows that the proposed method resulted in greater accuracy than comparable segmentation methods, including a widely used ANTs registration tool.

A Kronecker product splitting preconditioner for two-dimensional space-fractional diffusion equations

NASA Astrophysics Data System (ADS)

Chen, Hao; Lv, Wen; Zhang, Tongtong

2018-05-01

We study preconditioned iterative methods for the linear system arising in the numerical discretization of a two-dimensional space-fractional diffusion equation. Our approach is based on a formulation of the discrete problem that is shown to be the sum of two Kronecker products. By making use of an alternating Kronecker product splitting iteration technique we establish a class of fixed-point iteration methods. Theoretical analysis shows that the new method converges to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real. The basic iteration is accelerated by a Krylov subspace method like GMRES. The corresponding preconditioner is in a form of a Kronecker product structure and requires at each iteration the solution of a set of discrete one-dimensional fractional diffusion equations. We use structure preserving approximations to the discrete one-dimensional fractional diffusion operators in the action of the preconditioning matrix. Numerical examples are presented to illustrate the effectiveness of this approach.

Nonlocal continuous models for forced vibration analysis of two- and three-dimensional ensembles of single-walled carbon nanotubes

NASA Astrophysics Data System (ADS)

Kiani, Keivan

2014-06-01

Novel nonlocal discrete and continuous models are proposed for dynamic analysis of two- and three-dimensional ensembles of single-walled carbon nanotubes (SWCNTs). The generated extra van der Waals forces between adjacent SWCNTs due to their lateral motions are evaluated via Lennard-Jones potential function. Using a nonlocal Rayleigh beam model, the discrete and continuous models are developed for both two- and three-dimensional ensembles of SWCNTs acted upon by transverse dynamic loads. The capabilities of the proposed continuous models in capturing the vibration behavior of SWCNTs ensembles are then examined through various numerical simulations. A reasonably good agreement between the results of the continuous models and those of the discrete ones is also reported. The effects of the applied load frequency, intertube spaces, and small-scale parameter on the transverse dynamic responses of both two- and three-dimensional ensembles of SWCNTs are explained. The proposed continuous models would be very useful for dynamic analyses of large populated ensembles of SWCNTs whose discrete models suffer from both computational efforts and labor costs.

A mathematical model of the structure and evolution of small scale discrete auroral arcs

NASA Technical Reports Server (NTRS)

Seyler, C. E.

1990-01-01

A three dimensional fluid model which includes the dispersive effect of electron inertia is used to study the nonlinear macroscopic plasma dynamics of small scale discrete auroral arcs within the auroral acceleration zone and ionosphere. The motion of the Alfven wave source relative to the magnetospheric and ionospheric plasma forms an oblique Alfven wave which is reflected from the topside ionosphere by the negative density gradient. The superposition of the incident and reflected wave can be described by a steady state analytical solution of the model equations with the appropriate boundary conditions. This two dimensional discrete auroral arc equilibrium provides a simple explanation of auroral acceleration associated with the parallel electric field. Three dimensional fully nonlinear numerical simulations indicate that the equilibrium arc configuration evolves three dimensionally through collisionless tearing and reconnection of the current layer. The interaction of the perturbed flow and the transverse magnetic field produces complex transverse structure that may be the origin of the folds and curls observed to be associated with small scale discrete arcs.

An optimization-based framework for anisotropic simplex mesh adaptation

NASA Astrophysics Data System (ADS)

Yano, Masayuki; Darmofal, David L.

2012-09-01

We present a general framework for anisotropic h-adaptation of simplex meshes. Given a discretization and any element-wise, localizable error estimate, our adaptive method iterates toward a mesh that minimizes error for a given degrees of freedom. Utilizing mesh-metric duality, we consider a continuous optimization problem of the Riemannian metric tensor field that provides an anisotropic description of element sizes. First, our method performs a series of local solves to survey the behavior of the local error function. This information is then synthesized using an affine-invariant tensor manipulation framework to reconstruct an approximate gradient of the error function with respect to the metric tensor field. Finally, we perform gradient descent in the metric space to drive the mesh toward optimality. The method is first demonstrated to produce optimal anisotropic meshes minimizing the L2 projection error for a pair of canonical problems containing a singularity and a singular perturbation. The effectiveness of the framework is then demonstrated in the context of output-based adaptation for the advection-diffusion equation using a high-order discontinuous Galerkin discretization and the dual-weighted residual (DWR) error estimate. The method presented provides a unified framework for optimizing both the element size and anisotropy distribution using an a posteriori error estimate and enables efficient adaptation of anisotropic simplex meshes for high-order discretizations.

Three-Dimensional Registration for Handheld Profiling Systems Based on Multiple Shot Structured Light

PubMed Central

Ayaz, Shirazi Muhammad; Kim, Min Young

2018-01-01

In this article, a multi-view registration approach for the 3D handheld profiling system based on the multiple shot structured light technique is proposed. The multi-view registration approach is categorized into coarse registration and point cloud refinement using the iterative closest point (ICP) algorithm. Coarse registration of multiple point clouds was performed using relative orientation and translation parameters estimated via homography-based visual navigation. The proposed system was evaluated using an artificial human skull and a paper box object. For the quantitative evaluation of the accuracy of a single 3D scan, a paper box was reconstructed, and the mean errors in its height and breadth were found to be 9.4 μm and 23 μm, respectively. A comprehensive quantitative evaluation and comparison of proposed algorithm was performed with other variants of ICP. The root mean square error for the ICP algorithm to register a pair of point clouds of the skull object was also found to be less than 1 mm. PMID:29642552

Analysis of the Hessian for Inverse Scattering Problems. Part 3. Inverse Medium Scattering of Electromagnetic Waves in Three Dimensions

DTIC Science & Technology

2012-08-01

small data noise and model error, the discrete Hessian can be approximated by a low-rank matrix. This in turn enables fast solution of an appropriately...implication of the compactness of the Hessian is that for small data noise and model error, the discrete Hessian can be approximated by a low-rank matrix. This...probability distribution is given by the inverse of the Hessian of the negative log likelihood function. For Gaussian data noise and model error, this

An error bound for a discrete reduced order model of a linear multivariable system

NASA Technical Reports Server (NTRS)

Al-Saggaf, Ubaid M.; Franklin, Gene F.

1987-01-01

The design of feasible controllers for high dimension multivariable systems can be greatly aided by a method of model reduction. In order for the design based on the order reduction to include a guarantee of stability, it is sufficient to have a bound on the model error. Previous work has provided such a bound for continuous-time systems for algorithms based on balancing. In this note an L-infinity bound is derived for model error for a method of order reduction of discrete linear multivariable systems based on balancing.

Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation

NASA Astrophysics Data System (ADS)

Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji

2017-01-01

We introduce a so-called coprimeness-preserving non-integrable extension to the two-dimensional Toda lattice equation. We believe that this equation is the first example of such discrete equations defined over a three-dimensional lattice. We prove that all the iterates of the equation are irreducible Laurent polynomials of the initial data and that every pair of two iterates is co-prime, which indicate confined singularities of the equation. By reducing the equation to two- or one-dimensional lattices, we obtain coprimeness-preserving non-integrable extensions to the one-dimensional Toda lattice equation and the Somos-4 recurrence.

Error reduction in three-dimensional metrology combining optical and touch probe data

NASA Astrophysics Data System (ADS)

Gerde, Janice R.; Christens-Barry, William A.

2010-08-01

Analysis of footwear under the Harmonized Tariff Schedule of the United States (HTSUS) is partly based on identifying the boundary ("parting line") between the "external surface area upper" (ESAU) and the sample's sole. Often, that boundary is obscured. We establish the parting line as the curved intersection between the sample outer surface and its insole surface. The outer surface is determined by discrete point cloud coordinates obtained using a laser scanner. The insole surface is defined by point cloud data, obtained using a touch probe device-a coordinate measuring machine (CMM). Because these point cloud data sets do not overlap spatially, a polynomial surface is fitted to the insole data and extended to intersect a mesh fitted to the outer surface point cloud. This line of intersection defines the ESAU boundary, permitting further fractional area calculations to proceed. The defined parting line location is sensitive to the polynomial used to fit experimental data. Extrapolation to the intersection with the ESAU can heighten this sensitivity. We discuss a methodology for transforming these data into a common reference frame. Three scenarios are considered: measurement error in point cloud coordinates, from fitting a polynomial surface to a point cloud then extrapolating beyond the data set, and error from reference frame transformation. These error sources can influence calculated surface areas. We describe experiments to assess error magnitude, the sensitivity of calculated results on these errors, and minimizing error impact on calculated quantities. Ultimately, we must ensure that statistical error from these procedures is minimized and within acceptance criteria.

2d affine XY-spin model/4d gauge theory duality and deconfinement

NASA Astrophysics Data System (ADS)

Anber, Mohamed M.; Poppitz, Erich; Ünsal, Mithat

2012-04-01

We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2) and SU(2)/ {{Z}_2} gauge theories, compactified on a small spatial circle {{R}^{{^{{{1},{2}}}}}} × {{S}^{{^{{1}}}}} , and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on {{R}^{{^{{2}}}}} × {{T}^{{^{{2}}}}} . Similarly, thermal gauge theories of higher rank are dual to new families of "affine" XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multi-component electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopole-instantons or magnetic bions, and the vortices in the spin system map to the electrically charged W-bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU( N c ) gauge theories with n f ≥1 adjoint Weyl fermions.

Towards a consistent framework to oversample multi-sensors, multi-species satellite data into a common grid

NASA Astrophysics Data System (ADS)

Sun, K.; Zhu, L.; Gonzalez Abad, G.; Nowlan, C. R.; Miller, C. E.; Huang, G.; Liu, X.; Chance, K.; Yang, K.

2017-12-01

It has been well demonstrated that regridding Level 2 products (satellite observations from individual footprints, or pixels) from multiple sensors/species onto regular spatial and temporal grids makes the data more accessible for scientific studies and can even lead to additional discoveries. However, synergizing multiple species retrieved from multiple satellite sensors faces many challenges, including differences in spatial coverage, viewing geometry, and data filtering criteria. These differences will lead to errors and biases if not treated carefully. Operational gridded products are often at 0.25°×0.25° resolution with a global scale, which is too coarse for local heterogeneous emission sources (e.g., urban areas), and at fixed temporal intervals (e.g., daily or monthly). We propose a consistent framework to fully use and properly weight the information of all possible individual satellite observations. A key aspect of this work is an accurate knowledge of the spatial response function (SRF) of the satellite Level 2 pixels. We found that the conventional overlap-area-weighting method (tessellation) is accurate only when the SRF is homogeneous within the parameterized pixel boundary and zero outside the boundary. There will be a tessellation error if the SRF is a smooth distribution, and if this distribution is not properly considered. On the other hand, discretizing the SRF at the destination grid will also induce errors. By balancing these error sources, we found that the SRF should be used in gridding OMI data to 0.2° for fine resolutions. Case studies by merging multiple species and wind data into 0.01° grid will be shown in the presentation.

On the Probability of Error and Stochastic Resonance in Discrete Memoryless Channels

DTIC Science & Technology

2013-12-01

Information - Driven Doppler Shift Estimation and Compensation Methods for Underwater Wireless Sensor Networks ”, which is to analyze and develop... underwater wireless sensor networks . We formulated an analytic relationship that relates the average probability of error to the systems parameters, the...thesis, we studied the performance of Discrete Memoryless Channels (DMC), arising in the context of cooperative underwater wireless sensor networks

Parallel Cartesian grid refinement for 3D complex flow simulations

NASA Astrophysics Data System (ADS)

Angelidis, Dionysios; Sotiropoulos, Fotis

2013-11-01

A second order accurate method for discretizing the Navier-Stokes equations on 3D unstructured Cartesian grids is presented. Although the grid generator is based on the oct-tree hierarchical method, fully unstructured data-structure is adopted enabling robust calculations for incompressible flows, avoiding both the need of synchronization of the solution between different levels of refinement and usage of prolongation/restriction operators. The current solver implements a hybrid staggered/non-staggered grid layout, employing the implicit fractional step method to satisfy the continuity equation. The pressure-Poisson equation is discretized by using a novel second order fully implicit scheme for unstructured Cartesian grids and solved using an efficient Krylov subspace solver. The momentum equation is also discretized with second order accuracy and the high performance Newton-Krylov method is used for integrating them in time. Neumann and Dirichlet conditions are used to validate the Poisson solver against analytical functions and grid refinement results to a significant reduction of the solution error. The effectiveness of the fractional step method results in the stability of the overall algorithm and enables the performance of accurate multi-resolution real life simulations. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482.

Periodic solutions of second-order nonlinear difference equations containing a small parameter. IV - Multi-discrete time method

NASA Technical Reports Server (NTRS)

Mickens, Ronald E.

1987-01-01

It is shown that a discrete multi-time method can be constructed to obtain approximations to the periodic solutions of a special class of second-order nonlinear difference equations containing a small parameter. Three examples illustrating the method are presented.

Multi-beam and single-chip LIDAR with discrete beam steering by digital micromirror device

NASA Astrophysics Data System (ADS)

Rodriguez, Joshua; Smith, Braden; Hellman, Brandon; Gin, Adley; Espinoza, Alonzo; Takashima, Yuzuru

2018-02-01

A novel Digital Micromirror Device (DMD) based beam steering enables a single chip Light Detection and Ranging (LIDAR) system for discrete scanning points. We present increasing number of scanning point by using multiple laser diodes for Multi-beam and Single-chip DMD-based LIDAR.

Visually Lossless Data Compression for Real-Time Frame/Pushbroom Space Science Imagers

NASA Technical Reports Server (NTRS)

Yeh, Pen-Shu; Venbrux, Jack; Bhatia, Prakash; Miller, Warner H.

2000-01-01

A visually lossless data compression technique is currently being developed for space science applications under the requirement of high-speed push-broom scanning. The technique is also applicable to frame based imaging and is error-resilient in that error propagation is contained within a few scan lines. The algorithm is based on a block transform of a hybrid of modulated lapped transform (MLT) and discrete cosine transform (DCT), or a 2-dimensional lapped transform, followed by bit-plane encoding; this combination results in an embedded bit string with exactly the desirable compression rate as desired by the user. The approach requires no unique table to maximize its performance. The compression scheme performs well on a suite of test images typical of images from spacecraft instruments. Flight qualified hardware implementations are in development; a functional chip set is expected by the end of 2001. The chip set is being designed to compress data in excess of 20 Msamples/sec and support quantizations from 2 to 16 bits.

Discrete distributed strain sensing of intelligent structures

NASA Technical Reports Server (NTRS)

Anderson, Mark S.; Crawley, Edward F.

1992-01-01

Techniques are developed for the design of discrete highly distributed sensor systems for use in intelligent structures. First the functional requirements for such a system are presented. Discrete spatially averaging strain sensors are then identified as satisfying the functional requirements. A variety of spatial weightings for spatially averaging sensors are examined, and their wave number characteristics are determined. Preferable spatial weightings are identified. Several numerical integration rules used to integrate such sensors in order to determine the global deflection of the structure are discussed. A numerical simulation is conducted using point and rectangular sensors mounted on a cantilevered beam under static loading. Gage factor and sensor position uncertainties are incorporated to assess the absolute error and standard deviation of the error in the estimated tip displacement found by numerically integrating the sensor outputs. An experiment is carried out using a statically loaded cantilevered beam with five point sensors. It is found that in most cases the actual experimental error is within one standard deviation of the absolute error as found in the numerical simulation.

Multi-petascale highly efficient parallel supercomputer

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

Asaad, Sameh; Bellofatto, Ralph E.; Blocksome, Michael A.

A Multi-Petascale Highly Efficient Parallel Supercomputer of 100 petaflop-scale includes node architectures based upon System-On-a-Chip technology, where each processing node comprises a single Application Specific Integrated Circuit (ASIC). The ASIC nodes are interconnected by a five dimensional torus network that optimally maximize the throughput of packet communications between nodes and minimize latency. The network implements collective network and a global asynchronous network that provides global barrier and notification functions. Integrated in the node design include a list-based prefetcher. The memory system implements transaction memory, thread level speculation, and multiversioning cache that improves soft error rate at the same time andmore » supports DMA functionality allowing for parallel processing message-passing.« less

Digital fabrication of multi-material biomedical objects.

PubMed

Cheung, H H; Choi, S H

2009-12-01

This paper describes a multi-material virtual prototyping (MMVP) system for modelling and digital fabrication of discrete and functionally graded multi-material objects for biomedical applications. The MMVP system consists of a DMMVP module, an FGMVP module and a virtual reality (VR) simulation module. The DMMVP module is used to model discrete multi-material (DMM) objects, while the FGMVP module is for functionally graded multi-material (FGM) objects. The VR simulation module integrates these two modules to perform digital fabrication of multi-material objects, which can be subsequently visualized and analysed in a virtual environment to optimize MMLM processes for fabrication of product prototypes. Using the MMVP system, two biomedical objects, including a DMM human spine and an FGM intervertebral disc spacer are modelled and digitally fabricated for visualization and analysis in a VR environment. These studies show that the MMVP system is a practical tool for modelling, visualization, and subsequent fabrication of biomedical objects of discrete and functionally graded multi-materials for biomedical applications. The system may be adapted to control MMLM machines with appropriate hardware for physical fabrication of biomedical objects.

Comparison of algorithms for computing the two-dimensional discrete Hartley transform

NASA Technical Reports Server (NTRS)

Reichenbach, Stephen E.; Burton, John C.; Miller, Keith W.

1989-01-01

Three methods have been described for computing the two-dimensional discrete Hartley transform. Two of these employ a separable transform, the third method, the vector-radix algorithm, does not require separability. In-place computation of the vector-radix method is described. Operation counts and execution times indicate that the vector-radix method is fastest.

Infinite Conservation Laws, Continuous Symmetries and Invariant Solutions of Some Discrete Integrable Equations

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Zhang, Xiang-Zhi; Dong, Huan-He

2017-12-01

Two new shift operators are introduced for which a few differential-difference equations are generated by applying the R-matrix method. These equations can be reduced to the standard Toda lattice equation and (1+1)-dimensional and (2+1)-dimensional Toda-type equations which have important applications in hydrodynamics, plasma physics, and so on. Based on these consequences, we deduce the Hamiltonian structures of two discrete systems. Finally, we obtain some new infinite conservation laws of two discrete equations and employ Lie-point transformation group to obtain some continuous symmetries and part of invariant solutions for the (1+1) and (2+1)-dimensional Toda-type equations. Supported by the Fundamental Research Funds for the Central University under Grant No. 2017XKZD11

Real-time and accurate rail wear measurement method and experimental analysis.

PubMed

Liu, Zhen; Li, Fengjiao; Huang, Bangkui; Zhang, Guangjun

2014-08-01

When a train is running on uneven or curved rails, it generates violent vibrations on the rails. As a result, the light plane of the single-line structured light vision sensor is not vertical, causing errors in rail wear measurements (referred to as vibration errors in this paper). To avoid vibration errors, a novel rail wear measurement method is introduced in this paper, which involves three main steps. First, a multi-line structured light vision sensor (which has at least two linear laser projectors) projects a stripe-shaped light onto the inside of the rail. Second, the central points of the light stripes in the image are extracted quickly, and the three-dimensional profile of the rail is obtained based on the mathematical model of the structured light vision sensor. Then, the obtained rail profile is transformed from the measurement coordinate frame (MCF) to the standard rail coordinate frame (RCF) by taking the three-dimensional profile of the measured rail waist as the datum. Finally, rail wear constraint points are adopted to simplify the location of the rail wear points, and the profile composed of the rail wear points are compared with the standard rail profile in RCF to determine the rail wear. Both real data experiments and simulation experiments show that the vibration errors can be eliminated when the proposed method is used.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

One-dimensional collision carts computer model and its design ideas for productive experiential learning

NASA Astrophysics Data System (ADS)

Wee, Loo Kang

2012-05-01

We develop an Easy Java Simulation (EJS) model for students to experience the physics of idealized one-dimensional collision carts. The physics model is described and simulated by both continuous dynamics and discrete transition during collision. In designing the simulations, we discuss briefly three pedagogical considerations namely (1) a consistent simulation world view with a pen and paper representation, (2) a data table, scientific graphs and symbolic mathematical representations for ease of data collection and multiple representational visualizations and (3) a game for simple concept testing that can further support learning. We also suggest using a physical world setup augmented by simulation by highlighting three advantages of real collision carts equipment such as a tacit 3D experience, random errors in measurement and the conceptual significance of conservation of momentum applied to just before and after collision. General feedback from the students has been relatively positive, and we hope teachers will find the simulation useful in their own classes.

On the number of eigenvalues of the discrete one-dimensional Dirac operator with a complex potential

NASA Astrophysics Data System (ADS)

Hulko, Artem

2018-03-01

In this paper we define a one-dimensional discrete Dirac operator on Z . We study the eigenvalues of the Dirac operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity. We also estimate the number of eigenvalues for the discrete Schrödinger operator with complex potential on Z . That is we extend the result obtained by Hulko (Bull Math Sci, to appear) to the whole Z.

Periodic measure for the stochastic equation of the barotropic viscous gas in a discretized one-dimensional domain

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

Benseghir, Rym, E-mail: benseghirrym@ymail.com, E-mail: benseghirrym@ymail.com; Benchettah, Azzedine, E-mail: abenchettah@hotmail.com; Raynaud de Fitte, Paul, E-mail: prf@univ-rouen.fr

2015-11-30

A stochastic equation system corresponding to the description of the motion of a barotropic viscous gas in a discretized one-dimensional domain with a weight regularizing the density is considered. In [2], the existence of an invariant measure was established for this discretized problem in the stationary case. In this paper, applying a slightly modified version of Khas’minskii’s theorem [5], we generalize this result in the periodic case by proving the existence of a periodic measure for this problem.

Computations of Complex Three-Dimensional Turbulent Free Jets

NASA Technical Reports Server (NTRS)

Wilson, Robert V.; Demuren, Ayodeji O.

1997-01-01

Three-dimensional, incompressible turbulent jets with rectangular and elliptical cross-sections are simulated with a finite-difference numerical method. The full Navier- Stokes equations are solved at low Reynolds numbers, whereas at high Reynolds numbers filtered forms of the equations are solved along with a sub-grid scale model to approximate the effects of the unresolved scales. A 2-N storage, third-order Runge-Kutta scheme is used for temporary discretization and a fourth-order compact scheme is used for spatial discretization. Although such methods are widely used in the simulation of compressible flows, the lack of an evolution equation for pressure or density presents particular difficulty in incompressible flows. The pressure-velocity coupling must be established indirectly. It is achieved, in this study, through a Poisson equation which is solved by a compact scheme of the same order of accuracy. The numerical formulation is validated and the dispersion and dissipation errors are documented by the solution of a wide range of benchmark problems. Three-dimensional computations are performed for different inlet conditions which model the naturally developing and forced jets. The experimentally observed phenomenon of axis-switching is captured in the numerical simulation, and it is confirmed through flow visualization that this is based on self-induction of the vorticity field. Statistical quantities such as mean velocity, mean pressure, two-point velocity spatial correlations and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stress equations are presented to aid in the turbulence modeling of complex jets. Simulations of circular jets are used to quantify the effect of the non-uniform curvature of the non-circular jets.

Dynamics and elastic interactions of the discrete multi-dark soliton solutions for the Kaup-Newell lattice equation

NASA Astrophysics Data System (ADS)

Liu, Nan; Wen, Xiao-Yong

2018-03-01

Under consideration in this paper is the Kaup-Newell (KN) lattice equation which is an integrable discretization of the KN equation. Infinitely, many conservation laws and discrete N-fold Darboux transformation (DT) for this system are constructed and established based on its Lax representation. Via the resulting N-fold DT, the discrete multi-dark soliton solutions in terms of determinants are derived from non-vanishing background. Propagation and elastic interaction structures of such solitons are shown graphically. Overtaking interaction phenomena between/among the two, three and four solitons are discussed. Numerical simulations are used to explore their dynamical behaviors of such multi-dark solitons. Numerical results show that their evolutions are stable against a small noise. Results in this paper might be helpful for understanding the propagation of nonlinear Alfvén waves in plasmas.

Simultaneous Estimation of Model State Variables and Observation and Forecast Biases Using a Two-Stage Hybrid Kalman Filter

NASA Technical Reports Server (NTRS)

Pauwels, V. R. N.; DeLannoy, G. J. M.; Hendricks Franssen, H.-J.; Vereecken, H.

2013-01-01

In this paper, we present a two-stage hybrid Kalman filter to estimate both observation and forecast bias in hydrologic models, in addition to state variables. The biases are estimated using the discrete Kalman filter, and the state variables using the ensemble Kalman filter. A key issue in this multi-component assimilation scheme is the exact partitioning of the difference between observation and forecasts into state, forecast bias and observation bias updates. Here, the error covariances of the forecast bias and the unbiased states are calculated as constant fractions of the biased state error covariance, and the observation bias error covariance is a function of the observation prediction error covariance. In a series of synthetic experiments, focusing on the assimilation of discharge into a rainfall-runoff model, it is shown that both static and dynamic observation and forecast biases can be successfully estimated. The results indicate a strong improvement in the estimation of the state variables and resulting discharge as opposed to the use of a bias-unaware ensemble Kalman filter. Furthermore, minimal code modification in existing data assimilation software is needed to implement the method. The results suggest that a better performance of data assimilation methods should be possible if both forecast and observation biases are taken into account.

Application Of Multi-grid Method On China Seas' Temperature Forecast

NASA Astrophysics Data System (ADS)

Li, W.; Xie, Y.; He, Z.; Liu, K.; Han, G.; Ma, J.; Li, D.

2006-12-01

Correlation scales have been used in traditional scheme of 3-dimensional variational (3D-Var) data assimilation to estimate the background error covariance for the numerical forecast and reanalysis of atmosphere and ocean for decades. However there are still some drawbacks of this scheme. First, the correlation scales are difficult to be determined accurately. Second, the positive definition of the first-guess error covariance matrix cannot be guaranteed unless the correlation scales are sufficiently small. Xie et al. (2005) indicated that a traditional 3D-Var only corrects some certain wavelength errors and its accuracy depends on the accuracy of the first-guess covariance. And in general, short wavelength error can not be well corrected until long one is corrected and then inaccurate first-guess covariance may mistakenly take long wave error as short wave ones and result in erroneous analysis. For the purpose of quickly minimizing the errors of long and short waves successively, a new 3D-Var data assimilation scheme, called multi-grid data assimilation scheme, is proposed in this paper. By assimilating the shipboard SST and temperature profiles data into a numerical model of China Seas, we applied this scheme in two-month data assimilation and forecast experiment which ended in a favorable result. Comparing with the traditional scheme of 3D-Var, the new scheme has higher forecast accuracy and a lower forecast Root-Mean-Square (RMS) error. Furthermore, this scheme was applied to assimilate the SST of shipboard, AVHRR Pathfinder Version 5.0 SST and temperature profiles at the same time, and a ten-month forecast experiment on sea temperature of China Seas was carried out, in which a successful forecast result was obtained. Particularly, the new scheme is demonstrated a great numerical efficiency in these analyses.

Accuracy improvement of laser line scanning for feature measurements on CMM

NASA Astrophysics Data System (ADS)

Bešić, Igor; Van Gestel, Nick; Kruth, Jean-Pierre; Bleys, Philip; Hodolič, Janko

2011-11-01

Because of its high speed and high detail output, laser line scanning is increasingly included in coordinate metrology applications where its performance can satisfy specified tolerances. Increasing its accuracy will open the possibility to use it in other areas where contact methods are still dominant. Multi-sensor systems allow to select discrete probing or scanning methods to measure part elements. Decision is often based on the principle that tight toleranced elements should be measured by contact methods, while other more loose toleranced elements can be laser scanned. This paper aims to introduce a method for improving the output of a CMM mounted laser line scanner for metrology applications. This improvement is achieved by filtering of the scanner's random error and by combination with widely spread and reliable but slow touch trigger probing. The filtered point cloud is used to estimate the form deviation of the inspected element while few tactile obtained points were used to effectively compensate for errors in the point cloud position.

A high order cell-centered semi-Lagrangian scheme for multi-dimensional kinetic simulations of neutral gas flows

NASA Astrophysics Data System (ADS)

Güçlü, Y.; Hitchon, W. N. G.

2012-04-01

The term 'Convected Scheme' (CS) refers to a family of algorithms, most usually applied to the solution of Boltzmann's equation, which uses a method of characteristics in an integral form to project an initial cell forward to a group of final cells. As such the CS is a 'forward-trajectory' semi-Lagrangian scheme. For multi-dimensional simulations of neutral gas flows, the cell-centered version of this semi-Lagrangian (CCSL) scheme has advantages over other options due to its implementation simplicity, low memory requirements, and easier treatment of boundary conditions. The main drawback of the CCSL-CS to date has been its high numerical diffusion in physical space, because of the 2nd order remapping that takes place at the end of each time step. By means of a modified equation analysis, it is shown that a high order estimate of the remapping error can be obtained a priori, and a small correction to the final position of the cells can be applied upon remapping, in order to achieve full compensation of this error. The resulting scheme is 4th order accurate in space while retaining the desirable properties of the CS: it is conservative and positivity-preserving, and the overall algorithm complexity is not appreciably increased. Two monotone (i.e. non-oscillating) versions of the fourth order CCSL-CS are also presented: one uses a common flux-limiter approach; the other uses a non-polynomial reconstruction to evaluate the derivatives of the density function. The method is illustrated in simple one- and two-dimensional examples, and a fully 3D solution of the Boltzmann equation describing expansion of a gas into vacuum through a cylindrical tube.

40 CFR 73.37 - Account error.

Code of Federal Regulations, 2010 CFR

2010-07-01

... ALLOWANCE SYSTEM Allowance Tracking System § 73.37 Account error. The Administrator may, at his or her sole discretion and on his or her own motion, correct any error in any Allowance Tracking System account. Within...

40 CFR 60.4156 - Account error.

Code of Federal Regulations, 2011 CFR

2011-07-01

... Generating Units Hg Allowance Tracking System § 60.4156 Account error. The Administrator may, at his or her sole discretion and on his or her own motion, correct any error in any Hg Allowance Tracking System...

40 CFR 73.37 - Account error.

Code of Federal Regulations, 2011 CFR

2011-07-01

... ALLOWANCE SYSTEM Allowance Tracking System § 73.37 Account error. The Administrator may, at his or her sole discretion and on his or her own motion, correct any error in any Allowance Tracking System account. Within...

Cirrus Cloud Optical Thickness and Effective Diameter Retrieved by MODIS: Impacts of Single Habit Assumption, 3-D Radiative Effects, and Cloud Inhomogeneity

NASA Astrophysics Data System (ADS)

Zhou, Yongbo; Sun, Xuejin; Mielonen, Tero; Li, Haoran; Zhang, Riwei; Li, Yan; Zhang, Chuanliang

2018-01-01

For inhomogeneous cirrus clouds, cloud optical thickness (COT) and effective diameter (De) provided by the Moderate Resolution Imaging Spectrometer (MODIS) Collection 6 cloud products are associated with errors due to the single habit assumption (SHA), independent pixel assumption (IPA), photon absorption effect (PAE), and plane-parallel assumption (PPA). SHA means that every cirrus cloud is assumed to have the same shape habit of ice crystals. IPA errors are caused by three-dimensional (3D) radiative effects. PPA and PAE errors are caused by cloud inhomogeneity. We proposed a method to single out these different errors. These errors were examined using the Spherical Harmonics Discrete Ordinate Method simulations done for the MODIS 0.86 μm and 2.13 μm bands. Four midlatitude and tropical cirrus cases were studied. For the COT retrieval, the impacts of SHA and IPA were especially large for optically thick cirrus cases. SHA errors in COT varied distinctly with scattering angles. For the De retrieval, SHA decreased De under most circumstances. PAE decreased De for optically thick cirrus cases. For the COT and De retrievals, the dominant error source was SHA for overhead sun whereas for oblique sun, it could be any of SHA, IPA, and PAE, varying with cirrus cases and sun-satellite viewing geometries. On the domain average, the SHA errors in COT (De) were within -16.1%-42.6% (-38.7%-2.0%), whereas the 3-D radiative effects- and cloud inhomogeneity-induced errors in COT (De) were within -5.6%-19.6% (-2.9%-8.0%) and -2.6%-0% (-3.7%-9.8%), respectively.

Determination of secondary flow morphologies by wavelet analysis in a curved artery model with physiological inflow

NASA Astrophysics Data System (ADS)

Bulusu, Kartik V.; Hussain, Shadman; Plesniak, Michael W.

2014-11-01

Secondary flow vortical patterns in arterial curvatures have the potential to affect several cardiovascular phenomena, e.g., progression of atherosclerosis by altering wall shear stresses, carotid atheromatous disease, thoracic aortic aneurysms and Marfan's syndrome. Temporal characteristics of secondary flow structures vis-à-vis physiological (pulsatile) inflow waveform were explored by continuous wavelet transform (CWT) analysis of phase-locked, two-component, two-dimensional particle image velocimeter data. Measurements were made in a 180° curved artery test section upstream of the curvature and at the 90° cross-sectional plane. Streamwise, upstream flow rate measurements were analyzed using a one-dimensional antisymmetric wavelet. Cross-stream measurements at the 90° location of the curved artery revealed interesting multi-scale, multi-strength coherent secondary flow structures. An automated process for coherent structure detection and vortical feature quantification was applied to large ensembles of PIV data. Metrics such as the number of secondary flow structures, their sizes and strengths were generated at every discrete time instance of the physiological inflow waveform. An autonomous data post-processing method incorporating two-dimensional CWT for coherent structure detection was implemented. Loss of coherence in secondary flow structures during the systolic deceleration phase is observed in accordance with previous research. The algorithmic approach presented herein further elucidated the sensitivity and dependence of morphological changes in secondary flow structures on quasiperiodicity and magnitude of temporal gradients in physiological inflow conditions.

Application of Exactly Linearized Error Transport Equations to AIAA CFD Prediction Workshops

NASA Technical Reports Server (NTRS)

Derlaga, Joseph M.; Park, Michael A.; Rallabhandi, Sriram

2017-01-01

The computational fluid dynamics (CFD) prediction workshops sponsored by the AIAA have created invaluable opportunities in which to discuss the predictive capabilities of CFD in areas in which it has struggled, e.g., cruise drag, high-lift, and sonic boom pre diction. While there are many factors that contribute to disagreement between simulated and experimental results, such as modeling or discretization error, quantifying the errors contained in a simulation is important for those who make decisions based on the computational results. The linearized error transport equations (ETE) combined with a truncation error estimate is a method to quantify one source of errors. The ETE are implemented with a complex-step method to provide an exact linearization with minimal source code modifications to CFD and multidisciplinary analysis methods. The equivalency of adjoint and linearized ETE functional error correction is demonstrated. Uniformly refined grids from a series of AIAA prediction workshops demonstrate the utility of ETE for multidisciplinary analysis with a connection between estimated discretization error and (resolved or under-resolved) flow features.

The nonlinear modified equation approach to analyzing finite difference schemes

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1981-01-01

The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.

Construction of a cardiac conduction system subject to extracellular stimulation.

PubMed

Clements, Clyde; Vigmond, Edward

2005-01-01

Proper electrical excitation of the heart is dependent on the specialized conduction system that coordinates the electrical activity from the atria to the ventricles. This paper describes the construction of a conduction system as a branching network of Purkinje fibers on the endocardial surface. Endocardial surfaces were extracted from an FEM model of the ventricles and transformed to 2D. A Purkinje network was drawn on top and the inverse transform performed. The underlying mathematics utilized one dimensional cubic Hermite finite elements. Compared to linear elements, the cubic Hermite solution was found to have a much smaller RMS error. Furthermore, this method has the advantage of enforcing current conservation at bifurcation and unification points, and allows for discrete coupling resistances.

Optimization of control gain by operator adjustment

NASA Technical Reports Server (NTRS)

Kruse, W.; Rothbauer, G.

1973-01-01

An optimal gain was established by measuring errors at 5 discrete control gain settings in an experimental set-up consisting of a 2-dimensional, first-order pursuit tracking task performed by subjects (S's). No significant experience effect on optimum gain setting was found in the first experiment. During the second experiment, in which control gain was continuously adjustable, high experienced S's tended to reach the previously determined optimum gain quite accurately and quickly. Less experienced S's tended to select a marginally optimum gain either below or above the experimentally determined optimum depending on initial control gain setting, although mean settings of both groups were equal. This quick and simple method is recommended for selecting control gains for different control systems and forcing functions.

Shielding analyses: the rabbit vs the turtle?

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

Broadhead, B.L.

1996-12-31

This paper compares solutions using Monte Carlo and discrete- ordinates methods applied to two actual shielding situations in order to make some general observations concerning the efficiency and advantages/disadvantages of the two approaches. The discrete- ordinates solutions are performed using two-dimensional geometries, while the Monte Carlo approaches utilize three-dimensional geometries with both multigroup and point cross-section data.

Spectral analysis of a two-species competition model: Determining the effects of extreme conditions on the color of noise generated from simulated time series

NASA Astrophysics Data System (ADS)

Golinski, M. R.

2006-07-01

Ecologists have observed that environmental noise affects population variance in the logistic equation for one-species growth. Interactions between deterministic and stochastic dynamics in a one-dimensional system result in increased variance in species population density over time. Since natural populations do not live in isolation, the present paper simulates a discrete-time two-species competition model with environmental noise to determine the type of colored population noise generated by extreme conditions in the long-term population dynamics of competing populations. Discrete Fourier analysis is applied to the simulation results and the calculated Hurst exponent ( H) is used to determine how the color of population noise for the two species corresponds to extreme conditions in population dynamics. To interpret the biological meaning of the color of noise generated by the two-species model, the paper determines the color of noise generated by three reference models: (1) A two-dimensional discrete-time white noise model (0⩽ H<1/2); (2) A two-dimensional fractional Brownian motion model (H=1/2); and (3) A two-dimensional discrete-time model with noise for unbounded growth of two uncoupled species (1/2< H⩽1).

Joint sparsity based heterogeneous data-level fusion for target detection and estimation

NASA Astrophysics Data System (ADS)

Niu, Ruixin; Zulch, Peter; Distasio, Marcello; Blasch, Erik; Shen, Dan; Chen, Genshe

2017-05-01

Typical surveillance systems employ decision- or feature-level fusion approaches to integrate heterogeneous sensor data, which are sub-optimal and incur information loss. In this paper, we investigate data-level heterogeneous sensor fusion. Since the sensors monitor the common targets of interest, whose states can be determined by only a few parameters, it is reasonable to assume that the measurement domain has a low intrinsic dimensionality. For heterogeneous sensor data, we develop a joint-sparse data-level fusion (JSDLF) approach based on the emerging joint sparse signal recovery techniques by discretizing the target state space. This approach is applied to fuse signals from multiple distributed radio frequency (RF) signal sensors and a video camera for joint target detection and state estimation. The JSDLF approach is data-driven and requires minimum prior information, since there is no need to know the time-varying RF signal amplitudes, or the image intensity of the targets. It can handle non-linearity in the sensor data due to state space discretization and the use of frequency/pixel selection matrices. Furthermore, for a multi-target case with J targets, the JSDLF approach only requires discretization in a single-target state space, instead of discretization in a J-target state space, as in the case of the generalized likelihood ratio test (GLRT) or the maximum likelihood estimator (MLE). Numerical examples are provided to demonstrate that the proposed JSDLF approach achieves excellent performance with near real-time accurate target position and velocity estimates.

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes.

PubMed

Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon

2017-12-01

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.

Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method

NASA Astrophysics Data System (ADS)

Chen, Hui; Deng, Ju-Zhi; Yin, Min; Yin, Chang-Chun; Tang, Wen-Wu

2017-03-01

To speed up three-dimensional (3D) DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method (AGMG). We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner (AGMG-CG) to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling (3DDCXH). In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.

Conceptual structure and the procedural affordances of rational numbers: relational reasoning with fractions and decimals.

PubMed

DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J

2015-02-01

The standard number system includes several distinct types of notations, which differ conceptually and afford different procedures. Among notations for rational numbers, the bipartite format of fractions (a/b) enables them to represent 2-dimensional relations between sets of discrete (i.e., countable) elements (e.g., red marbles/all marbles). In contrast, the format of decimals is inherently 1-dimensional, expressing a continuous-valued magnitude (i.e., proportion) but not a 2-dimensional relation between sets of countable elements. Experiment 1 showed that college students indeed view these 2-number notations as conceptually distinct. In a task that did not involve mathematical calculations, participants showed a strong preference to represent partitioned displays of discrete objects with fractions and partitioned displays of continuous masses with decimals. Experiment 2 provided evidence that people are better able to identify and evaluate ratio relationships using fractions than decimals, especially for discrete (or discretized) quantities. Experiments 3 and 4 found a similar pattern of performance for a more complex analogical reasoning task. When solving relational reasoning problems based on discrete or discretized quantities, fractions yielded greater accuracy than decimals; in contrast, when quantities were continuous, accuracy was lower for both symbolic notations. Whereas previous research has established that decimals are more effective than fractions in supporting magnitude comparisons, the present study reveals that fractions are relatively advantageous in supporting relational reasoning with discrete (or discretized) concepts. These findings provide an explanation for the effectiveness of natural frequency formats in supporting some types of reasoning, and have implications for teaching of rational numbers.

Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization

NASA Astrophysics Data System (ADS)

Burman, Erik; Hansbo, Peter; Larson, Mats G.

2018-03-01

Tikhonov regularization is one of the most commonly used methods for the regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to adding suitably weighted least squares terms of the control variable, or derivatives thereof, to the Lagrangian determining the optimality system. In this note we show that the stabilization methods for discretely ill-posed problems developed in the setting of convection-dominated convection-diffusion problems, can be highly suitable for stabilizing optimal control problems, and that Tikhonov regularization will lead to less accurate discrete solutions. We consider some inverse problems for Poisson’s equation as an illustration and derive new error estimates both for the reconstruction of the solution from the measured data and reconstruction of the source term from the measured data. These estimates include both the effect of the discretization error and error in the measurements.

Design of an optimal preview controller for linear discrete-time descriptor systems with state delay

NASA Astrophysics Data System (ADS)

Cao, Mengjuan; Liao, Fucheng

2015-04-01

In this paper, the linear discrete-time descriptor system with state delay is studied, and a design method for an optimal preview controller is proposed. First, by using the discrete lifting technique, the original system is transformed into a general descriptor system without state delay in form. Then, taking advantage of the first-order forward difference operator, we construct a descriptor augmented error system, including the state vectors of the lifted system, error vectors, and desired target signals. Rigorous mathematical proofs are given for the regularity, stabilisability, causal controllability, and causal observability of the descriptor augmented error system. Based on these, the optimal preview controller with preview feedforward compensation for the original system is obtained by using the standard optimal regulator theory of the descriptor system. The effectiveness of the proposed method is shown by numerical simulation.

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1987-01-01

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes–Vanstone elliptic curve cryptosystem

NASA Astrophysics Data System (ADS)

Liu, Zeyu; Xia, Tiecheng; Wang, Jinbo

2018-03-01

We propose a new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference. Moreover, the chaos behaviors of the proposed map are observed and the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits are derived, respectively. Finally, with the secret keys generated by Menezes–Vanstone elliptic curve cryptosystem, we apply the discrete fractional map into color image encryption. After that, the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms. Project supported by the National Natural Science Foundation of China (Grant Nos. 61072147 and 11271008).

Reliability study of tibialis posterior and selected leg muscle EMG and multi-segment foot kinematics in rheumatoid arthritis associated pes planovalgus

PubMed Central

Barn, Ruth; Rafferty, Daniel; Turner, Deborah E.; Woodburn, James

2012-01-01

Objective To determine within- and between-day reliability characteristics of electromyographic (EMG) activity patterns of selected lower leg muscles and kinematic variables in patients with rheumatoid arthritis (RA) and pes planovalgus. Methods Five patients with RA underwent gait analysis barefoot and shod on two occasions 1 week apart. Fine-wire (tibialis posterior [TP]) and surface EMG for selected muscles and 3D kinematics using a multi-segmented foot model was undertaken barefoot and shod. Reliability of pre-determined variables including EMG activity patterns and inter-segment kinematics were analysed using coefficients of multiple correlation, intraclass correlation coefficients (ICC) and the standard error of the measurement (SEM). Results Muscle activation patterns within- and between-day ranged from fair-to-good to excellent in both conditions. Discrete temporal and amplitude variables were highly variable across all muscle groups in both conditions but particularly poor for TP and peroneus longus. SEMs ranged from 1% to 9% of stance and 4% to 27% of maximum voluntary contraction; in most cases the 95% confidence interval crossed zero. Excellent within-day reliability was found for the inter-segment kinematics in both conditions. Between-day reliability ranged from fair-to-good to excellent for kinematic variables and all ICCs were excellent; the SEM ranged from 0.60° to 1.99°. Conclusion Multi-segmented foot kinematics can be reliably measured in RA patients with pes planovalgus. Serial measurement of discrete variables for TP and other selected leg muscles via EMG is not supported from the findings in this cohort of RA patients. Caution should be exercised when EMG measurements are considered to study disease progression or intervention effects. PMID:22721819

Inversion of geophysical potential field data using the finite element method

NASA Astrophysics Data System (ADS)

Lamichhane, Bishnu P.; Gross, Lutz

2017-12-01

The inversion of geophysical potential field data can be formulated as an optimization problem with a constraint in the form of a partial differential equation (PDE). It is common practice, if possible, to provide an analytical solution for the forward problem and to reduce the problem to a finite dimensional optimization problem. In an alternative approach the optimization is applied to the problem and the resulting continuous problem which is defined by a set of coupled PDEs is subsequently solved using a standard PDE discretization method, such as the finite element method (FEM). In this paper, we show that under very mild conditions on the data misfit functional and the forward problem in the three-dimensional space, the continuous optimization problem and its FEM discretization are well-posed including the existence and uniqueness of respective solutions. We provide error estimates for the FEM solution. A main result of the paper is that the FEM spaces used for the forward problem and the Lagrange multiplier need to be identical but can be chosen independently from the FEM space used to represent the unknown physical property. We will demonstrate the convergence of the solution approximations in a numerical example. The second numerical example which investigates the selection of FEM spaces, shows that from the perspective of computational efficiency one should use 2 to 4 times finer mesh for the forward problem in comparison to the mesh of the physical property.

Matter-wave solitons supported by quadrupole-quadrupole interactions and anisotropic discrete lattices

NASA Astrophysics Data System (ADS)

Zhong, Rong-Xuan; Huang, Nan; Li, Huang-Wu; He, He-Xiang; Lü, Jian-Tao; Huang, Chun-Qing; Chen, Zhao-Pin

2018-04-01

We numerically and analytically investigate the formations and features of two-dimensional discrete Bose-Einstein condensate solitons, which are constructed by quadrupole-quadrupole interactional particles trapped in the tunable anisotropic discrete optical lattices. The square optical lattices in the model can be formed by two pairs of interfering plane waves with different intensities. Two hopping rates of the particles in the orthogonal directions are different, which gives rise to a linear anisotropic system. We find that if all of the pairs of dipole and anti-dipole are perpendicular to the lattice panel and the line connecting the dipole and anti-dipole which compose the quadrupole is parallel to horizontal direction, both the linear anisotropy and the nonlocal nonlinear one can strongly influence the formations of the solitons. There exist three patterns of stable solitons, namely horizontal elongation quasi-one-dimensional discrete solitons, disk-shape isotropic pattern solitons and vertical elongation quasi-continuous solitons. We systematically demonstrate the relationships of chemical potential, size and shape of the soliton with its total norm and vertical hopping rate and analytically reveal the linear dispersion relation for quasi-one-dimensional discrete solitons.

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2010-01-01

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence.

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Error analysis and correction of discrete solutions from finite element codes

NASA Technical Reports Server (NTRS)

Thurston, G. A.; Stein, P. A.; Knight, N. F., Jr.; Reissner, J. E.

1984-01-01

Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of finite element results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.

Multi-indexed (q-)Racah polynomials

NASA Astrophysics Data System (ADS)

Odake, Satoru; Sasaki, Ryu

2012-09-01

As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of ‘discrete quantum mechanics’ with real shifts in one dimension, the multi-indexed (q-)Racah polynomials. They are obtained from the (q-)Racah polynomials by the multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of ‘virtual state’ vectors, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier. The virtual state vectors are the ‘solutions’ of the matrix Schrödinger equation with negative ‘eigenvalues’, except for one of the two boundary points.

Adjoint-Based Algorithms for Adaptation and Design Optimizations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.

2006-01-01

Schemes based on discrete adjoint algorithms present several exciting opportunities for significantly advancing the current state of the art in computational fluid dynamics. Such methods provide an extremely efficient means for obtaining discretely consistent sensitivity information for hundreds of design variables, opening the door to rigorous, automated design optimization of complex aerospace configuration using the Navier-Stokes equation. Moreover, the discrete adjoint formulation provides a mathematically rigorous foundation for mesh adaptation and systematic reduction of spatial discretization error. Error estimates are also an inherent by-product of an adjoint-based approach, valuable information that is virtually non-existent in today's large-scale CFD simulations. An overview of the adjoint-based algorithm work at NASA Langley Research Center is presented, with examples demonstrating the potential impact on complex computational problems related to design optimization as well as mesh adaptation.

Multi-scale and multi-physics simulations using the multi-fluid plasma model

DTIC Science & Technology

2017-04-25

small The simulation uses 512 second-order elements Bz = 1.0, Te = Ti = 0.01, ui = ue = 0 ne = ni = 1.0 + e−10(x−6) 2 Baboolal, Math . and Comp. Sim. 55...DISTRIBUTION Clearance No. 17211 23 / 31 SUMMARY The blended finite element method (BFEM) is presented DG spatial discretization with explicit Runge...Kutta (i+, n) CG spatial discretization with implicit Crank-Nicolson (e−, fileds) DG captures shocks and discontinuities CG is efficient and robust for

Aerodynamics of Engine-Airframe Interaction

NASA Technical Reports Server (NTRS)

Caughey, D. A.

1986-01-01

The report describes progress in research directed towards the efficient solution of the inviscid Euler and Reynolds-averaged Navier-Stokes equations for transonic flows through engine inlets, and past complete aircraft configurations, with emphasis on the flowfields in the vicinity of engine inlets. The research focusses upon the development of solution-adaptive grid procedures for these problems, and the development of multi-grid algorithms in conjunction with both, implicit and explicit time-stepping schemes for the solution of three-dimensional problems. The work includes further development of mesh systems suitable for inlet and wing-fuselage-inlet geometries using a variational approach. Work during this reporting period concentrated upon two-dimensional problems, and has been in two general areas: (1) the development of solution-adaptive procedures to cluster the grid cells in regions of high (truncation) error;and (2) the development of a multigrid scheme for solution of the two-dimensional Euler equations using a diagonalized alternating direction implicit (ADI) smoothing algorithm.

Minimizing finite-volume discretization errors on polyhedral meshes

NASA Astrophysics Data System (ADS)

Mouly, Quentin; Evrard, Fabien; van Wachem, Berend; Denner, Fabian

2017-11-01

Tetrahedral meshes are widely used in CFD to simulate flows in and around complex geometries, as automatic generation tools now allow tetrahedral meshes to represent arbitrary domains in a relatively accessible manner. Polyhedral meshes, however, are an increasingly popular alternative. While tetrahedron have at most four neighbours, the higher number of neighbours per polyhedral cell leads to a more accurate evaluation of gradients, essential for the numerical resolution of PDEs. The use of polyhedral meshes, nonetheless, introduces discretization errors for finite-volume methods: skewness and non-orthogonality, which occur with all sorts of unstructured meshes, as well as errors due to non-planar faces, specific to polygonal faces with more than three vertices. Indeed, polyhedral mesh generation algorithms cannot, in general, guarantee to produce meshes free of non-planar faces. The presented work focuses on the quantification and optimization of discretization errors on polyhedral meshes in the context of finite-volume methods. A quasi-Newton method is employed to optimize the relevant mesh quality measures. Various meshes are optimized and CFD results of cases with known solutions are presented to assess the improvements the optimization approach can provide.

Thermal breakage of a discrete one-dimensional string.

PubMed

Lee, Chiu Fan

2009-09-01

We study the thermal breakage of a discrete one-dimensional string, with open and fixed ends, in the heavily damped regime. Basing our analysis on the multidimensional Kramers escape theory, we are able to make analytical predictions on the mean breakage rate and on the breakage propensity with respect to the breakage location on the string. We then support our predictions with numerical simulations.

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

PubMed

Fu, Wei; Nijhoff, Frank W

2017-07-01

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

Three-Class Mammogram Classification Based on Descriptive CNN Features

PubMed Central

Zhang, Qianni; Jadoon, Adeel

2017-01-01

In this paper, a novel classification technique for large data set of mammograms using a deep learning method is proposed. The proposed model targets a three-class classification study (normal, malignant, and benign cases). In our model we have presented two methods, namely, convolutional neural network-discrete wavelet (CNN-DW) and convolutional neural network-curvelet transform (CNN-CT). An augmented data set is generated by using mammogram patches. To enhance the contrast of mammogram images, the data set is filtered by contrast limited adaptive histogram equalization (CLAHE). In the CNN-DW method, enhanced mammogram images are decomposed as its four subbands by means of two-dimensional discrete wavelet transform (2D-DWT), while in the second method discrete curvelet transform (DCT) is used. In both methods, dense scale invariant feature (DSIFT) for all subbands is extracted. Input data matrix containing these subband features of all the mammogram patches is created that is processed as input to convolutional neural network (CNN). Softmax layer and support vector machine (SVM) layer are used to train CNN for classification. Proposed methods have been compared with existing methods in terms of accuracy rate, error rate, and various validation assessment measures. CNN-DW and CNN-CT have achieved accuracy rate of 81.83% and 83.74%, respectively. Simulation results clearly validate the significance and impact of our proposed model as compared to other well-known existing techniques. PMID:28191461

Three-Class Mammogram Classification Based on Descriptive CNN Features.

PubMed

Jadoon, M Mohsin; Zhang, Qianni; Haq, Ihsan Ul; Butt, Sharjeel; Jadoon, Adeel

2017-01-01

In this paper, a novel classification technique for large data set of mammograms using a deep learning method is proposed. The proposed model targets a three-class classification study (normal, malignant, and benign cases). In our model we have presented two methods, namely, convolutional neural network-discrete wavelet (CNN-DW) and convolutional neural network-curvelet transform (CNN-CT). An augmented data set is generated by using mammogram patches. To enhance the contrast of mammogram images, the data set is filtered by contrast limited adaptive histogram equalization (CLAHE). In the CNN-DW method, enhanced mammogram images are decomposed as its four subbands by means of two-dimensional discrete wavelet transform (2D-DWT), while in the second method discrete curvelet transform (DCT) is used. In both methods, dense scale invariant feature (DSIFT) for all subbands is extracted. Input data matrix containing these subband features of all the mammogram patches is created that is processed as input to convolutional neural network (CNN). Softmax layer and support vector machine (SVM) layer are used to train CNN for classification. Proposed methods have been compared with existing methods in terms of accuracy rate, error rate, and various validation assessment measures. CNN-DW and CNN-CT have achieved accuracy rate of 81.83% and 83.74%, respectively. Simulation results clearly validate the significance and impact of our proposed model as compared to other well-known existing techniques.

A prefiltering version of the Kalman filter with new numerical integration formulas for Riccati equations

NASA Technical Reports Server (NTRS)

Womble, M. E.; Potter, J. E.

1975-01-01

A prefiltering version of the Kalman filter is derived for both discrete and continuous measurements. The derivation consists of determining a single discrete measurement that is equivalent to either a time segment of continuous measurements or a set of discrete measurements. This prefiltering version of the Kalman filter easily handles numerical problems associated with rapid transients and ill-conditioned Riccati matrices. Therefore, the derived technique for extrapolating the Riccati matrix from one time to the next constitutes a new set of integration formulas which alleviate ill-conditioning problems associated with continuous Riccati equations. Furthermore, since a time segment of continuous measurements is converted into a single discrete measurement, Potter's square root formulas can be used to update the state estimate and its error covariance matrix. Therefore, if having the state estimate and its error covariance matrix at discrete times is acceptable, the prefilter extends square root filtering with all its advantages, to continuous measurement problems.

Numerical study of supersonic combustors by multi-block grids with mismatched interfaces

NASA Technical Reports Server (NTRS)

Moon, Young J.

1990-01-01

A three dimensional, finite rate chemistry, Navier-Stokes code was extended to a multi-block code with mismatched interface for practical calculations of supersonic combustors. To ensure global conservation, a conservative algorithm was used for the treatment of mismatched interfaces. The extended code was checked against one test case, i.e., a generic supersonic combustor with transverse fuel injection, examining solution accuracy, convergence, and local mass flux error. After testing, the code was used to simulate the chemically reacting flow fields in a scramjet combustor with parallel fuel injectors (unswept and swept ramps). Computational results were compared with experimental shadowgraph and pressure measurements. Fuel-air mixing characteristics of the unswept and swept ramps were compared and investigated.

Pollutant source identification model for water pollution incidents in small straight rivers based on genetic algorithm

NASA Astrophysics Data System (ADS)

Zhang, Shou-ping; Xin, Xiao-kang

2017-07-01

Identification of pollutant sources for river pollution incidents is an important and difficult task in the emergency rescue, and an intelligent optimization method can effectively compensate for the weakness of traditional methods. An intelligent model for pollutant source identification has been established using the basic genetic algorithm (BGA) as an optimization search tool and applying an analytic solution formula of one-dimensional unsteady water quality equation to construct the objective function. Experimental tests show that the identification model is effective and efficient: the model can accurately figure out the pollutant amounts or positions no matter single pollution source or multiple sources. Especially when the population size of BGA is set as 10, the computing results are sound agree with analytic results for a single source amount and position identification, the relative errors are no more than 5 %. For cases of multi-point sources and multi-variable, there are some errors in computing results for the reasons that there exist many possible combinations of the pollution sources. But, with the help of previous experience to narrow the search scope, the relative errors of the identification results are less than 5 %, which proves the established source identification model can be used to direct emergency responses.

Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods.

Decision-Level Fusion of Spatially Scattered Multi-Modal Data for Nondestructive Inspection of Surface Defects

PubMed Central

Heideklang, René; Shokouhi, Parisa

2016-01-01

This article focuses on the fusion of flaw indications from multi-sensor nondestructive materials testing. Because each testing method makes use of a different physical principle, a multi-method approach has the potential of effectively differentiating actual defect indications from the many false alarms, thus enhancing detection reliability. In this study, we propose a new technique for aggregating scattered two- or three-dimensional sensory data. Using a density-based approach, the proposed method explicitly addresses localization uncertainties such as registration errors. This feature marks one of the major of advantages of this approach over pixel-based image fusion techniques. We provide guidelines on how to set all the key parameters and demonstrate the technique’s robustness. Finally, we apply our fusion approach to experimental data and demonstrate its capability to locate small defects by substantially reducing false alarms under conditions where no single-sensor method is adequate. PMID:26784200

A Noncontact FMCW Radar Sensor for Displacement Measurement in Structural Health Monitoring

PubMed Central

Li, Cunlong; Chen, Weimin; Liu, Gang; Yan, Rong; Xu, Hengyi; Qi, Yi

2015-01-01

This paper investigates the Frequency Modulation Continuous Wave (FMCW) radar sensor for multi-target displacement measurement in Structural Health Monitoring (SHM). The principle of three-dimensional (3-D) displacement measurement of civil infrastructures is analyzed. The requirements of high-accuracy displacement and multi-target identification for the measuring sensors are discussed. The fundamental measuring principle of FMCW radar is presented with rigorous mathematical formulas, and further the multiple-target displacement measurement is analyzed and simulated. In addition, a FMCW radar prototype is designed and fabricated based on an off-the-shelf radar frontend and data acquisition (DAQ) card, and the displacement error induced by phase asynchronism is analyzed. The conducted outdoor experiments verify the feasibility of this sensing method applied to multi-target displacement measurement, and experimental results show that three targets located at different distances can be distinguished simultaneously with millimeter level accuracy. PMID:25822139

A noncontact FMCW radar sensor for displacement measurement in structural health monitoring.

PubMed

Li, Cunlong; Chen, Weimin; Liu, Gang; Yan, Rong; Xu, Hengyi; Qi, Yi

2015-03-26

This paper investigates the Frequency Modulation Continuous Wave (FMCW) radar sensor for multi-target displacement measurement in Structural Health Monitoring (SHM). The principle of three-dimensional (3-D) displacement measurement of civil infrastructures is analyzed. The requirements of high-accuracy displacement and multi-target identification for the measuring sensors are discussed. The fundamental measuring principle of FMCW radar is presented with rigorous mathematical formulas, and further the multiple-target displacement measurement is analyzed and simulated. In addition, a FMCW radar prototype is designed and fabricated based on an off-the-shelf radar frontend and data acquisition (DAQ) card, and the displacement error induced by phase asynchronism is analyzed. The conducted outdoor experiments verify the feasibility of this sensing method applied to multi-target displacement measurement, and experimental results show that three targets located at different distances can be distinguished simultaneously with millimeter level accuracy.

Solution of elastic-plastic stress analysis problems by the p-version of the finite element method

NASA Technical Reports Server (NTRS)

Szabo, Barna A.; Actis, Ricardo L.; Holzer, Stefan M.

1993-01-01

The solution of small strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus. Numerical examples which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors are presented.

Self-adaptive difference method for the effective solution of computationally complex problems of boundary layer theory

NASA Technical Reports Server (NTRS)

Schoenauer, W.; Daeubler, H. G.; Glotz, G.; Gruening, J.

1986-01-01

An implicit difference procedure for the solution of equations for a chemically reacting hypersonic boundary layer is described. Difference forms of arbitrary error order in the x and y coordinate plane were used to derive estimates for discretization error. Computational complexity and time were minimized by the use of this difference method and the iteration of the nonlinear boundary layer equations was regulated by discretization error. Velocity and temperature profiles are presented for Mach 20.14 and Mach 18.5; variables are velocity profiles, temperature profiles, mass flow factor, Stanton number, and friction drag coefficient; three figures include numeric data.

Temporal rainfall estimation using input data reduction and model inversion

NASA Astrophysics Data System (ADS)

Wright, A. J.; Vrugt, J. A.; Walker, J. P.; Pauwels, V. R. N.

2016-12-01

Floods are devastating natural hazards. To provide accurate, precise and timely flood forecasts there is a need to understand the uncertainties associated with temporal rainfall and model parameters. The estimation of temporal rainfall and model parameter distributions from streamflow observations in complex dynamic catchments adds skill to current areal rainfall estimation methods, allows for the uncertainty of rainfall input to be considered when estimating model parameters and provides the ability to estimate rainfall from poorly gauged catchments. Current methods to estimate temporal rainfall distributions from streamflow are unable to adequately explain and invert complex non-linear hydrologic systems. This study uses the Discrete Wavelet Transform (DWT) to reduce rainfall dimensionality for the catchment of Warwick, Queensland, Australia. The reduction of rainfall to DWT coefficients allows the input rainfall time series to be simultaneously estimated along with model parameters. The estimation process is conducted using multi-chain Markov chain Monte Carlo simulation with the DREAMZS algorithm. The use of a likelihood function that considers both rainfall and streamflow error allows for model parameter and temporal rainfall distributions to be estimated. Estimation of the wavelet approximation coefficients of lower order decomposition structures was able to estimate the most realistic temporal rainfall distributions. These rainfall estimates were all able to simulate streamflow that was superior to the results of a traditional calibration approach. It is shown that the choice of wavelet has a considerable impact on the robustness of the inversion. The results demonstrate that streamflow data contains sufficient information to estimate temporal rainfall and model parameter distributions. The extent and variance of rainfall time series that are able to simulate streamflow that is superior to that simulated by a traditional calibration approach is a demonstration of equifinality. The use of a likelihood function that considers both rainfall and streamflow error combined with the use of the DWT as a model data reduction technique allows the joint inference of hydrologic model parameters along with rainfall.

Scattering in discrete random media with implications to propagation through rain. Ph.D. Thesis George Washingtion Univ., Washington, D.C.

NASA Technical Reports Server (NTRS)

Ippolito, L. J., Jr.

1977-01-01

The multiple scattering effects on wave propagation through a volume of discrete scatterers were investigated. The mean field and intensity for a distribution of scatterers was developed using a discrete random media formulation, and second order series expansions for the mean field and total intensity derived for one-dimensional and three-dimensional configurations. The volume distribution results were shown to proceed directly from the one-dimensional results. The multiple scattering intensity expansion was compared to the classical single scattering intensity and the classical result was found to represent only the first three terms in the total intensity expansion. The Foldy approximation to the mean field was applied to develop the coherent intensity, and was found to exactly represent all coherent terms of the total intensity.

Numerical study of multi-point forming of thick sheet using remeshing procedure

NASA Astrophysics Data System (ADS)

Cherouat, A.; Ma, X.; Borouchaki, H.; Zhang, Q.

2018-05-01

Multi-point forming MPF is an innovative technology of manufacturing complex thick sheet metal products without the need for solid tools. The central component of this system is a pair of the desired discrete matrices of punches, and die surface constructed by changing the positions of the tools though CAD and a control system. Because reconfigurable discrete tools are used, part-manufacturing costs are reduced and manufacturing time is shorten substantially. Firstly, in this work we develop constitutive equations which couples isotropic ductile damage into various flow stress based on the Continuum Damage Mechanic theory. The modified Johnson-Cook flow model fully coupled with an isotropic ductile damage is established using the quasi-unilateral damage evolution for considering both the open and the close of micro-cracks. During the forming processes severe mesh distortion of elements occur after a few incremental forming steps. Secondly, we introduce 3D adaptive remeshing procedure based on linear tetrahedral element and geometrical/physical errors estimation to optimize the element quality, to refine the mesh size in the whole model and to adapt the deformed mesh to the tools geometry. Simulation of the MPF process (see Fig. 1) and the unloading spring-back are carried out using adaptive remeshing scheme using the commercial finite element package ABAQUS and OPTIFORM mesher. Subsequently, influencing factors of MPF spring-back are researched to investigate the MPF spring-back tendency with the proposed remeshing procedure.

Evaluation and optimization of footwear comfort parameters using finite element analysis and a discrete optimization algorithm

NASA Astrophysics Data System (ADS)

Papagiannis, P.; Azariadis, P.; Papanikos, P.

2017-10-01

Footwear is subject to bending and torsion deformations that affect comfort perception. Following review of Finite Element Analysis studies of sole rigidity and comfort, a three-dimensional, linear multi-material finite element sole model for quasi-static bending and torsion simulation, overcoming boundary and optimisation limitations, is described. Common footwear materials properties and boundary conditions from gait biomechanics are used. The use of normalised strain energy for product benchmarking is demonstrated along with comfort level determination through strain energy density stratification. Sensitivity of strain energy against material thickness is greater for bending than for torsion, with results of both deformations showing positive correlation. Optimization for a targeted performance level and given layer thickness is demonstrated with bending simulations sufficing for overall comfort assessment. An algorithm for comfort optimization w.r.t. bending is presented, based on a discrete approach with thickness values set in line with practical manufacturing accuracy. This work illustrates the potential of the developed finite element analysis applications to offer viable and proven aids to modern footwear sole design assessment and optimization.

An Assessment of Five Modeling Approaches for Thermo-Mechanical Stress Analysis of Laminated Composite Panels

NASA Technical Reports Server (NTRS)

Noor, A. K.; Malik, M.

2000-01-01

A study is made of the effects of variation in the lamination and geometric parameters, and boundary conditions of multi-layered composite panels on the accuracy of the detailed response characteristics obtained by five different modeling approaches. The modeling approaches considered include four two-dimensional models, each with five parameters to characterize the deformation in the thickness direction, and a predictor-corrector approach with twelve displacement parameters. The two-dimensional models are first-order shear deformation theory, third-order theory; a theory based on trigonometric variation of the transverse shear stresses through the thickness, and a discrete layer theory. The combination of the following four key elements distinguishes the present study from previous studies reported in the literature: (1) the standard of comparison is taken to be the solutions obtained by using three-dimensional continuum models for each of the individual layers; (2) both mechanical and thermal loadings are considered; (3) boundary conditions other than simply supported edges are considered; and (4) quantities compared include detailed through-the-thickness distributions of transverse shear and transverse normal stresses. Based on the numerical studies conducted, the predictor-corrector approach appears to be the most effective technique for obtaining accurate transverse stresses, and for thermal loading, none of the two-dimensional models is adequate for calculating transverse normal stresses, even when used in conjunction with three-dimensional equilibrium equations.

Stable multi-domain spectral penalty methods for fractional partial differential equations

NASA Astrophysics Data System (ADS)

Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

Dynamic dielectrophoresis model of multi-phase ionic fluids.

PubMed

Yan, Ying; Luo, Jing; Guo, Dan; Wen, Shizhu

2015-01-01

Ionic-based dielectrophoretic microchips have attracted significant attention due to their wide-ranging applications in electro kinetic and biological experiments. In this work, a numerical method is used to simulate the dynamic behaviors of ionic droplets in a microchannel under the effect of dielectrophoresis. When a discrete liquid dielectric is encompassed within a continuous fluid dielectric placed in an electric field, an electric force is produced due to the dielectrophoresis effect. If either or both of the fluids are ionic liquids, the magnitude and even the direction of the force will be changed because the net ionic charge induced by an electric field can affect the polarization degree of the dielectrics. However, using a dielectrophoresis model, assuming ideal dielectrics, results in significant errors. To avoid the inaccuracy caused by the model, this work incorporates the electrode kinetic equation and defines a relationship between the polarization charge and the net ionic charge. According to the simulation conditions presented herein, the electric force obtained in this work has an error exceeding 70% of the actual value if the false effect of net ionic charge is not accounted for, which would result in significant issues in the design and optimization of experimental parameters. Therefore, there is a clear motivation for developing a model adapted to ionic liquids to provide precise control for the dielectrophoresis of multi-phase ionic liquids.

Remarks on a New Possible Discretization Scheme for Gauge Theories

NASA Astrophysics Data System (ADS)

Magnot, Jean-Pierre

2018-03-01

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.

Remarks on a New Possible Discretization Scheme for Gauge Theories

NASA Astrophysics Data System (ADS)

Magnot, Jean-Pierre

2018-07-01

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.

Multi-Interval Discretization of Continuous-Valued Attributes for Classification Learning

NASA Technical Reports Server (NTRS)

Fayyad, U.; Irani, K.

1993-01-01

Since most real-world applications of classification learning involve continuous-valued attributes, properly addressing the discretization process is an important problem. This paper addresses the use of the entropy minimization heuristic for discretizing the range of a continuous-valued attribute into multiple intervals.

Error correcting coding-theory for structured light illumination systems

NASA Astrophysics Data System (ADS)

Porras-Aguilar, Rosario; Falaggis, Konstantinos; Ramos-Garcia, Ruben

2017-06-01

Intensity discrete structured light illumination systems project a series of projection patterns for the estimation of the absolute fringe order using only the temporal grey-level sequence at each pixel. This work proposes the use of error-correcting codes for pixel-wise correction of measurement errors. The use of an error correcting code is advantageous in many ways: it allows reducing the effect of random intensity noise, it corrects outliners near the border of the fringe commonly present when using intensity discrete patterns, and it provides a robustness in case of severe measurement errors (even for burst errors where whole frames are lost). The latter aspect is particular interesting in environments with varying ambient light as well as in critical safety applications as e.g. monitoring of deformations of components in nuclear power plants, where a high reliability is ensured even in case of short measurement disruptions. A special form of burst errors is the so-called salt and pepper noise, which can largely be removed with error correcting codes using only the information of a given pixel. The performance of this technique is evaluated using both simulations and experiments.

Aliasing errors in measurements of beam position and ellipticity

NASA Astrophysics Data System (ADS)

Ekdahl, Carl

2005-09-01

Beam position monitors (BPMs) are used in accelerators and ion experiments to measure currents, position, and azimuthal asymmetry. These usually consist of discrete arrays of electromagnetic field detectors, with detectors located at several equally spaced azimuthal positions at the beam tube wall. The discrete nature of these arrays introduces systematic errors into the data, independent of uncertainties resulting from signal noise, lack of recording dynamic range, etc. Computer simulations were used to understand and quantify these aliasing errors. If required, aliasing errors can be significantly reduced by employing more than the usual four detectors in the BPMs. These simulations show that the error in measurements of the centroid position of a large beam is indistinguishable from the error in the position of a filament. The simulations also show that aliasing errors in the measurement of beam ellipticity are very large unless the beam is accurately centered. The simulations were used to quantify the aliasing errors in beam parameter measurements during early experiments on the DARHT-II accelerator, demonstrating that they affected the measurements only slightly, if at all.

Correlation between discrete probability and reaction front propagation rate in heterogeneous mixtures

NASA Astrophysics Data System (ADS)

Naine, Tarun Bharath; Gundawar, Manoj Kumar

2017-09-01

We demonstrate a very powerful correlation between the discrete probability of distances of neighboring cells and thermal wave propagation rate, for a system of cells spread on a one-dimensional chain. A gamma distribution is employed to model the distances of neighboring cells. In the absence of an analytical solution and the differences in ignition times of adjacent reaction cells following non-Markovian statistics, invariably the solution for thermal wave propagation rate for a one-dimensional system with randomly distributed cells is obtained by numerical simulations. However, such simulations which are based on Monte-Carlo methods require several iterations of calculations for different realizations of distribution of adjacent cells. For several one-dimensional systems, differing in the value of shaping parameter of the gamma distribution, we show that the average reaction front propagation rates obtained by a discrete probability between two limits, shows excellent agreement with those obtained numerically. With the upper limit at 1.3, the lower limit depends on the non-dimensional ignition temperature. Additionally, this approach also facilitates the prediction of burning limits of heterogeneous thermal mixtures. The proposed method completely eliminates the need for laborious, time intensive numerical calculations where the thermal wave propagation rates can now be calculated based only on macroscopic entity of discrete probability.

Quantum error-correcting code for ternary logic

NASA Astrophysics Data System (ADS)

Majumdar, Ritajit; Basu, Saikat; Ghosh, Shibashis; Sur-Kolay, Susmita

2018-05-01

Ternary quantum systems are being studied because they provide more computational state space per unit of information, known as qutrit. A qutrit has three basis states, thus a qubit may be considered as a special case of a qutrit where the coefficient of one of the basis states is zero. Hence both (2 ×2 ) -dimensional and (3 ×3 ) -dimensional Pauli errors can occur on qutrits. In this paper, we (i) explore the possible (2 ×2 ) -dimensional as well as (3 ×3 ) -dimensional Pauli errors in qutrits and show that any pairwise bit swap error can be expressed as a linear combination of shift errors and phase errors, (ii) propose a special type of error called a quantum superposition error and show its equivalence to arbitrary rotation, (iii) formulate a nine-qutrit code which can correct a single error in a qutrit, and (iv) provide its stabilizer and circuit realization.

A method of boundary equations for unsteady hyperbolic problems in 3D

NASA Astrophysics Data System (ADS)

Petropavlovsky, S.; Tsynkov, S.; Turkel, E.

2018-07-01

We consider interior and exterior initial boundary value problems for the three-dimensional wave (d'Alembert) equation. First, we reduce a given problem to an equivalent operator equation with respect to unknown sources defined only at the boundary of the original domain. In doing so, the Huygens' principle enables us to obtain the operator equation in a form that involves only finite and non-increasing pre-history of the solution in time. Next, we discretize the resulting boundary equation and solve it efficiently by the method of difference potentials (MDP). The overall numerical algorithm handles boundaries of general shape using regular structured grids with no deterioration of accuracy. For long simulation times it offers sub-linear complexity with respect to the grid dimension, i.e., is asymptotically cheaper than the cost of a typical explicit scheme. In addition, our algorithm allows one to share the computational cost between multiple similar problems. On multi-processor (multi-core) platforms, it benefits from what can be considered an effective parallelization in time.

Multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) approach to the correlated exciton-vibrational dynamics in the FMO complex

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

Schulze, Jan; Kühn, Oliver, E-mail: oliver.kuehn@uni-rostock.de; Shibl, Mohamed F., E-mail: mfshibl@qu.edu.qa

2016-05-14

The coupled quantum dynamics of excitonic and vibrational degrees of freedom is investigated for high-dimensional models of the Fenna-Matthews-Olson complex. This includes a seven- and an eight-site model with 518 and 592 harmonic vibrational modes, respectively. The coupling between local electronic transitions and vibrations is described within the Huang-Rhys model using parameters that are obtained by discretization of an experimental spectral density. Different pathways of excitation energy flow are analyzed in terms of the reduced one-exciton density matrix, focussing on the role of vibrational and vibronic excitations. Distinct features due to both competing time scales of vibrational and exciton motionmore » and vibronically assisted transfer are observed. The question of the effect of initial state preparation is addressed by comparing the case of an instantaneous Franck-Condon excitation at a single site with that of a laser field excitation.« less

A Generic multi-dimensional feature extraction method using multiobjective genetic programming.

PubMed

Zhang, Yang; Rockett, Peter I

2009-01-01

In this paper, we present a generic feature extraction method for pattern classification using multiobjective genetic programming. This not only evolves the (near-)optimal set of mappings from a pattern space to a multi-dimensional decision space, but also simultaneously optimizes the dimensionality of that decision space. The presented framework evolves vector-to-vector feature extractors that maximize class separability. We demonstrate the efficacy of our approach by making statistically-founded comparisons with a wide variety of established classifier paradigms over a range of datasets and find that for most of the pairwise comparisons, our evolutionary method delivers statistically smaller misclassification errors. At very worst, our method displays no statistical difference in a few pairwise comparisons with established classifier/dataset combinations; crucially, none of the misclassification results produced by our method is worse than any comparator classifier. Although principally focused on feature extraction, feature selection is also performed as an implicit side effect; we show that both feature extraction and selection are important to the success of our technique. The presented method has the practical consequence of obviating the need to exhaustively evaluate a large family of conventional classifiers when faced with a new pattern recognition problem in order to attain a good classification accuracy.

CVD-MPFA full pressure support, coupled unstructured discrete fracture-matrix Darcy-flux approximations

NASA Astrophysics Data System (ADS)

Ahmed, Raheel; Edwards, Michael G.; Lamine, Sadok; Huisman, Bastiaan A. H.; Pal, Mayur

2017-11-01

Two novel control-volume methods are presented for flow in fractured media, and involve coupling the control-volume distributed multi-point flux approximation (CVD-MPFA) constructed with full pressure support (FPS), to two types of discrete fracture-matrix approximation for simulation on unstructured grids; (i) involving hybrid grids and (ii) a lower dimensional fracture model. Flow is governed by Darcy's law together with mass conservation both in the matrix and the fractures, where large discontinuities in permeability tensors can occur. Finite-volume FPS schemes are more robust than the earlier CVD-MPFA triangular pressure support (TPS) schemes for problems involving highly anisotropic homogeneous and heterogeneous full-tensor permeability fields. We use a cell-centred hybrid-grid method, where fractures are modelled by lower-dimensional interfaces between matrix cells in the physical mesh but expanded to equi-dimensional cells in the computational domain. We present a simple procedure to form a consistent hybrid-grid locally for a dual-cell. We also propose a novel hybrid-grid for intersecting fractures, for the FPS method, which reduces the condition number of the global linear system and leads to larger time steps for tracer transport. The transport equation for tracer flow is coupled with the pressure equation and provides flow parameter assessment of the fracture models. Transport results obtained via TPS and FPS hybrid-grid formulations are compared with the corresponding results of fine-scale explicit equi-dimensional formulations. The results show that the hybrid-grid FPS method applies to general full-tensor fields and provides improved robust approximations compared to the hybrid-grid TPS method for fractured domains, for both weakly anisotropic permeability fields and very strong anisotropic full-tensor permeability fields where the TPS scheme exhibits spurious oscillations. The hybrid-grid FPS formulation is extended to compressible flow and the results demonstrate the method is also robust for transient flow. Furthermore, we present FPS coupled with a lower-dimensional fracture model, where fractures are strictly lower-dimensional in the physical mesh as well as in the computational domain. We present a comparison of the hybrid-grid FPS method and the lower-dimensional fracture model for several cases of isotropic and anisotropic fractured media which illustrate the benefits of the respective methods.

Magnetospheric Multiscale (MMS) Mission Commissioning Phase Orbit Determination Error Analysis

NASA Technical Reports Server (NTRS)

Chung, Lauren R.; Novak, Stefan; Long, Anne; Gramling, Cheryl

2009-01-01

The Magnetospheric MultiScale (MMS) mission commissioning phase starts in a 185 km altitude x 12 Earth radii (RE) injection orbit and lasts until the Phase 1 mission orbits and orientation to the Earth-Sun li ne are achieved. During a limited time period in the early part of co mmissioning, five maneuvers are performed to raise the perigee radius to 1.2 R E, with a maneuver every other apogee. The current baseline is for the Goddard Space Flight Center Flight Dynamics Facility to p rovide MMS orbit determination support during the early commissioning phase using all available two-way range and Doppler tracking from bo th the Deep Space Network and Space Network. This paper summarizes th e results from a linear covariance analysis to determine the type and amount of tracking data required to accurately estimate the spacecraf t state, plan each perigee raising maneuver, and support thruster cal ibration during this phase. The primary focus of this study is the na vigation accuracy required to plan the first and the final perigee ra ising maneuvers. Absolute and relative position and velocity error hi stories are generated for all cases and summarized in terms of the ma ximum root-sum-square consider and measurement noise error contributi ons over the definitive and predictive arcs and at discrete times inc luding the maneuver planning and execution times. Details of the meth odology, orbital characteristics, maneuver timeline, error models, and error sensitivities are provided.

Discrete ordinates-Monte Carlo coupling: A comparison of techniques in NERVA radiation analysis

NASA Technical Reports Server (NTRS)

Lindstrom, D. G.; Normand, E.; Wilcox, A. D.

1972-01-01

In the radiation analysis of the NERVA nuclear rocket system, two-dimensional discrete ordinates calculations are sufficient to provide detail in the pressure vessel and reactor assembly. Other parts of the system, however, require three-dimensional Monte Carlo analyses. To use these two methods in a single analysis, a means of coupling was developed whereby the results of a discrete ordinates calculation can be used to produce source data for a Monte Carlo calculation. Several techniques for producing source detail were investigated. Results of calculations on the NERVA system are compared and limitations and advantages of the coupling techniques discussed.

On higher order discrete phase-locked loops.

NASA Technical Reports Server (NTRS)

Gill, G. S.; Gupta, S. C.

1972-01-01

An exact mathematical model is developed for a discrete loop of a general order particularly suitable for digital computation. The deterministic response of the loop to the phase step and the frequency step is investigated. The design of the digital filter for the second-order loop is considered. Use is made of the incremental phase plane to study the phase error behavior of the loop. The model of the noisy loop is derived and the optimization of the loop filter for minimum mean-square error is considered.

Vapor-liquid equilibrium and equation of state of two-dimensional fluids from a discrete perturbation theory

NASA Astrophysics Data System (ADS)

Trejos, Víctor M.; Santos, Andrés; Gámez, Francisco

2018-05-01

The interest in the description of the properties of fluids of restricted dimensionality is growing for theoretical and practical reasons. In this work, we have firstly developed an analytical expression for the Helmholtz free energy of the two-dimensional square-well fluid in the Barker-Henderson framework. This equation of state is based on an approximate analytical radial distribution function for d-dimensional hard-sphere fluids (1 ≤ d ≤ 3) and is validated against existing and new simulation results. The so-obtained equation of state is implemented in a discrete perturbation theory able to account for general potential shapes. The prototypical Lennard-Jones and Yukawa fluids are tested in its two-dimensional version against available and new simulation data with semiquantitative agreement.

A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates

NASA Astrophysics Data System (ADS)

Läuter, Matthias; Giraldo, Francis X.; Handorf, Dörthe; Dethloff, Klaus

2008-12-01

A global model of the atmosphere is presented governed by the shallow water equations and discretized by a Runge-Kutta discontinuous Galerkin method on an unstructured triangular grid. The shallow water equations on the sphere, a two-dimensional surface in R3, are locally represented in terms of spherical triangular coordinates, the appropriate local coordinate mappings on triangles. On every triangular grid element, this leads to a two-dimensional representation of tangential momentum and therefore only two discrete momentum equations. The discontinuous Galerkin method consists of an integral formulation which requires both area (elements) and line (element faces) integrals. Here, we use a Rusanov numerical flux to resolve the discontinuous fluxes at the element faces. A strong stability-preserving third-order Runge-Kutta method is applied for the time discretization. The polynomial space of order k on each curved triangle of the grid is characterized by a Lagrange basis and requires high-order quadature rules for the integration over elements and element faces. For the presented method no mass matrix inversion is necessary, except in a preprocessing step. The validation of the atmospheric model has been done considering standard tests from Williamson et al. [D.L. Williamson, J.B. Drake, J.J. Hack, R. Jakob, P.N. Swarztrauber, A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys. 102 (1992) 211-224], unsteady analytical solutions of the nonlinear shallow water equations and a barotropic instability caused by an initial perturbation of a jet stream. A convergence rate of O(Δx) was observed in the model experiments. Furthermore, a numerical experiment is presented, for which the third-order time-integration method limits the model error. Thus, the time step Δt is restricted by both the CFL-condition and accuracy demands. Conservation of mass was shown up to machine precision and energy conservation converges for both increasing grid resolution and increasing polynomial order k.

AUV Underwater Positioning Algorithm Based on Interactive Assistance of SINS and LBL.

PubMed

Zhang, Tao; Chen, Liping; Li, Yao

2015-12-30

This paper studies an underwater positioning algorithm based on the interactive assistance of a strapdown inertial navigation system (SINS) and LBL, and this algorithm mainly includes an optimal correlation algorithm with aided tracking of an SINS/Doppler velocity log (DVL)/magnetic compass pilot (MCP), a three-dimensional TDOA positioning algorithm of Taylor series expansion and a multi-sensor information fusion algorithm. The final simulation results show that compared to traditional underwater positioning algorithms, this scheme can not only directly correct accumulative errors caused by a dead reckoning algorithm, but also solves the problem of ambiguous correlation peaks caused by multipath transmission of underwater acoustic signals. The proposed method can calibrate the accumulative error of the AUV position more directly and effectively, which prolongs the underwater operating duration of the AUV.

SAGE: The Self-Adaptive Grid Code. 3

NASA Technical Reports Server (NTRS)

Davies, Carol B.; Venkatapathy, Ethiraj

1999-01-01

The multi-dimensional self-adaptive grid code, SAGE, is an important tool in the field of computational fluid dynamics (CFD). It provides an efficient method to improve the accuracy of flow solutions while simultaneously reducing computer processing time. Briefly, SAGE enhances an initial computational grid by redistributing the mesh points into more appropriate locations. The movement of these points is driven by an equal-error-distribution algorithm that utilizes the relationship between high flow gradients and excessive solution errors. The method also provides a balance between clustering points in the high gradient regions and maintaining the smoothness and continuity of the adapted grid, The latest version, Version 3, includes the ability to change the boundaries of a given grid to more efficiently enclose flow structures and provides alternative redistribution algorithms.

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

A deterministic particle method for one-dimensional reaction-diffusion equations

NASA Technical Reports Server (NTRS)

Mascagni, Michael

1995-01-01

We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.

Long Range Debye-Hückel Correction for Computation of Grid-based Electrostatic Forces Between Biomacromolecules

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

Mereghetti, Paolo; Martinez, M.; Wade, Rebecca C.

Brownian dynamics (BD) simulations can be used to study very large molecular systems, such as models of the intracellular environment, using atomic-detail structures. Such simulations require strategies to contain the computational costs, especially for the computation of interaction forces and energies. A common approach is to compute interaction forces between macromolecules by precomputing their interaction potentials on three-dimensional discretized grids. For long-range interactions, such as electrostatics, grid-based methods are subject to finite size errors. We describe here the implementation of a Debye-Hückel correction to the grid-based electrostatic potential used in the SDA BD simulation software that was applied to simulatemore » solutions of bovine serum albumin and of hen egg white lysozyme.« less

On Some Parabolic Type Problems from Thin Film Theory and Chemical Reaction-Diffusion Networks

NASA Astrophysics Data System (ADS)

Mohamed, Fatma Naser Ali

This dissertation considers some parabolic type problems from thin film theory and chemical reaction-diffusion networks. The dissertation consists of two parts: In the first part, we study the evolution of a thin film of fluid modeled by the lubrication approximation for thin viscous films. We prove an existence of (dissipative) strong solutions for the Cauchy problem when the sub-diffusive exponent ranges between 3/8 and 2; then we show that these solutions tend to zero at rates matching the decay of the source-type self-similar solutions with zero contact angle. We introduce the weaker concept of dissipative mild solutions and we show that, in this case, the surface-tension energy dissipation is the mechanism responsible for the H1-norm decay to zero of the thickness of the film at an explicit rate. Relaxed problems, with second-order nonlinear terms of porous media type, are also successfully treated by the same means. [special characters omitted]. In the second part, we are concerned with the convergence of a certain space-discretization scheme -the so-called method of lines- for mass-action reaction-diffusion systems. First, we start with a toy model, namely. [special characters omitted]. and prove convergence of method of lines for this linear case. Here weak convergence in L2(0,1) is enough to prove convergence of the method of lines. Then we adopt the framework for convergence analysis introduced in [23] and concentrate on the proof-of-concept reaction. within 1D space, while at the same time noting that our techniques are readily generalizable to other reaction-diffusion networks and to more than one space dimension. Indeed, it will be obvious how to extend our proofs to the multi-dimensional case; we only note that the proof of the comparison principle (the continuous and the discrete versions; see chapter 6) imposes a limitation on the spatial dimension (should be at most five; see [24] for details). The Method of Lines (MOL) is not a mainstream numerical tool and the specialized literature is rather scarce. The method amounts to discretizing evolutionary PDE's in space only, so it produces a semi-discrete numerical scheme which consists of a system of ODE's (in the time variable). To prove convergence of the semi-discrete MOL scheme to the original PDE one needs to perform some more or less traditional analysis: it is necessary to show that the scheme is consistent with the continuous problem and that the discretized version of the spatial differential operator retains sufficient dissipative properties in order to allow an application of Gronwall's Lemma to the error term. As shown in [23], a uniform (in time) consistency estimate is sufficient to obtain convergence; however, the consistency estimate we proved is not uniform for a small time, so we cannot directly employ the results in [23] to prove convergence in our case. Instead, we prove all the required estimates "from the scratch", then we use their exact quantitative form in order to conclude convergence.

Multigrid Method for Modeling Multi-Dimensional Combustion with Detailed Chemistry

NASA Technical Reports Server (NTRS)

Zheng, Xiaoqing; Liu, Chaoqun; Liao, Changming; Liu, Zhining; McCormick, Steve

1996-01-01

A highly accurate and efficient numerical method is developed for modeling 3-D reacting flows with detailed chemistry. A contravariant velocity-based governing system is developed for general curvilinear coordinates to maintain simplicity of the continuity equation and compactness of the discretization stencil. A fully-implicit backward Euler technique and a third-order monotone upwind-biased scheme on a staggered grid are used for the respective temporal and spatial terms. An efficient semi-coarsening multigrid method based on line-distributive relaxation is used as the flow solver. The species equations are solved in a fully coupled way and the chemical reaction source terms are treated implicitly. Example results are shown for a 3-D gas turbine combustor with strong swirling inflows.

Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals.

PubMed

Theocharis, G; Boechler, N; Kevrekidis, P G; Job, S; Porter, Mason A; Daraio, C

2010-11-01

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic Fermi-Pasta-Ulam (FPU)-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and note that the asymmetric nature of the tensionless interaction potential can lead to hybrid bulk-surface localized solutions.

Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals

NASA Astrophysics Data System (ADS)

Theocharis, G.; Boechler, N.; Kevrekidis, P. G.; Job, S.; Porter, Mason A.; Daraio, C.

2010-11-01

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic Fermi-Pasta-Ulam (FPU)-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and note that the asymmetric nature of the tensionless interaction potential can lead to hybrid bulk-surface localized solutions.

Optimal block cosine transform image coding for noisy channels

NASA Technical Reports Server (NTRS)

Vaishampayan, V.; Farvardin, N.

1986-01-01

The two dimensional block transform coding scheme based on the discrete cosine transform was studied extensively for image coding applications. While this scheme has proven to be efficient in the absence of channel errors, its performance degrades rapidly over noisy channels. A method is presented for the joint source channel coding optimization of a scheme based on the 2-D block cosine transform when the output of the encoder is to be transmitted via a memoryless design of the quantizers used for encoding the transform coefficients. This algorithm produces a set of locally optimum quantizers and the corresponding binary code assignment for the assumed transform coefficient statistics. To determine the optimum bit assignment among the transform coefficients, an algorithm was used based on the steepest descent method, which under certain convexity conditions on the performance of the channel optimized quantizers, yields the optimal bit allocation. Comprehensive simulation results for the performance of this locally optimum system over noisy channels were obtained and appropriate comparisons against a reference system designed for no channel error were rendered.

42 CFR 412.278 - Administrator's review.

Code of Federal Regulations, 2014 CFR

2014-10-01

... or computational errors, or to correct the decision if the evidence that was considered in making the... discretion, may amend the decision to correct mathematical or computational errors, or to correct the...

42 CFR 412.278 - Administrator's review.

Code of Federal Regulations, 2011 CFR

2011-10-01

... or computational errors, or to correct the decision if the evidence that was considered in making the... discretion, may amend the decision to correct mathematical or computational errors, or to correct the...

42 CFR 412.278 - Administrator's review.

Code of Federal Regulations, 2012 CFR

2012-10-01

... or computational errors, or to correct the decision if the evidence that was considered in making the... discretion, may amend the decision to correct mathematical or computational errors, or to correct the...

42 CFR 412.278 - Administrator's review.

Code of Federal Regulations, 2013 CFR

2013-10-01

... or computational errors, or to correct the decision if the evidence that was considered in making the... discretion, may amend the decision to correct mathematical or computational errors, or to correct the...

Sampling trace organic compounds in water: a comparison of a continuous active sampler to continuous passive and discrete sampling methods

USGS Publications Warehouse

Coes, Alissa L.; Paretti, Nicholas V.; Foreman, William T.; Iverson, Jana L.; Alvarez, David A.

2014-01-01

A continuous active sampling method was compared to continuous passive and discrete sampling methods for the sampling of trace organic compounds (TOCs) in water. Results from each method are compared and contrasted in order to provide information for future investigators to use while selecting appropriate sampling methods for their research. The continuous low-level aquatic monitoring (CLAM) sampler (C.I.Agent® Storm-Water Solutions) is a submersible, low flow-rate sampler, that continuously draws water through solid-phase extraction media. CLAM samplers were deployed at two wastewater-dominated stream field sites in conjunction with the deployment of polar organic chemical integrative samplers (POCIS) and the collection of discrete (grab) water samples. All samples were analyzed for a suite of 69 TOCs. The CLAM and POCIS samples represent time-integrated samples that accumulate the TOCs present in the water over the deployment period (19–23 h for CLAM and 29 days for POCIS); the discrete samples represent only the TOCs present in the water at the time and place of sampling. Non-metric multi-dimensional scaling and cluster analysis were used to examine patterns in both TOC detections and relative concentrations between the three sampling methods. A greater number of TOCs were detected in the CLAM samples than in corresponding discrete and POCIS samples, but TOC concentrations in the CLAM samples were significantly lower than in the discrete and (or) POCIS samples. Thirteen TOCs of varying polarity were detected by all of the three methods. TOC detections and concentrations obtained by the three sampling methods, however, are dependent on multiple factors. This study found that stream discharge, constituent loading, and compound type all affected TOC concentrations detected by each method. In addition, TOC detections and concentrations were affected by the reporting limits, bias, recovery, and performance of each method.

Sampling trace organic compounds in water: a comparison of a continuous active sampler to continuous passive and discrete sampling methods.

PubMed

Coes, Alissa L; Paretti, Nicholas V; Foreman, William T; Iverson, Jana L; Alvarez, David A

2014-03-01

A continuous active sampling method was compared to continuous passive and discrete sampling methods for the sampling of trace organic compounds (TOCs) in water. Results from each method are compared and contrasted in order to provide information for future investigators to use while selecting appropriate sampling methods for their research. The continuous low-level aquatic monitoring (CLAM) sampler (C.I.Agent® Storm-Water Solutions) is a submersible, low flow-rate sampler, that continuously draws water through solid-phase extraction media. CLAM samplers were deployed at two wastewater-dominated stream field sites in conjunction with the deployment of polar organic chemical integrative samplers (POCIS) and the collection of discrete (grab) water samples. All samples were analyzed for a suite of 69 TOCs. The CLAM and POCIS samples represent time-integrated samples that accumulate the TOCs present in the water over the deployment period (19-23 h for CLAM and 29 days for POCIS); the discrete samples represent only the TOCs present in the water at the time and place of sampling. Non-metric multi-dimensional scaling and cluster analysis were used to examine patterns in both TOC detections and relative concentrations between the three sampling methods. A greater number of TOCs were detected in the CLAM samples than in corresponding discrete and POCIS samples, but TOC concentrations in the CLAM samples were significantly lower than in the discrete and (or) POCIS samples. Thirteen TOCs of varying polarity were detected by all of the three methods. TOC detections and concentrations obtained by the three sampling methods, however, are dependent on multiple factors. This study found that stream discharge, constituent loading, and compound type all affected TOC concentrations detected by each method. In addition, TOC detections and concentrations were affected by the reporting limits, bias, recovery, and performance of each method. Published by Elsevier B.V.

Robust preview control for a class of uncertain discrete-time systems with time-varying delay.

PubMed

Li, Li; Liao, Fucheng

2018-02-01

This paper proposes a concept of robust preview tracking control for uncertain discrete-time systems with time-varying delay. Firstly, a model transformation is employed for an uncertain discrete system with time-varying delay. Then, the auxiliary variables related to the system state and input are introduced to derive an augmented error system that includes future information on the reference signal. This leads to the tracking problem being transformed into a regulator problem. Finally, for the augmented error system, a sufficient condition of asymptotic stability is derived and the preview controller design method is proposed based on the scaled small gain theorem and linear matrix inequality (LMI) technique. The method proposed in this paper not only solves the difficulty problem of applying the difference operator to the time-varying matrices but also simplifies the structure of the augmented error system. The numerical simulation example also illustrates the effectiveness of the results presented in the paper. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Prevention 0f Unwanted Free-Declaration of Static Obstacles in Probability Occupancy Grids

NASA Astrophysics Data System (ADS)

Krause, Stefan; Scholz, M.; Hohmann, R.

2017-10-01

Obstacle detection and avoidance are major research fields in unmanned aviation. Map based obstacle detection approaches often use discrete world representations such as probabilistic grid maps to fuse incremental environment data from different views or sensors to build a comprehensive representation. The integration of continuous measurements into a discrete representation can result in rounding errors which, in turn, leads to differences between the artificial model and real environment. The cause of these deviations is a low spatial resolution of the world representation comparison to the used sensor data. Differences between artificial representations which are used for path planning or obstacle avoidance and the real world can lead to unexpected behavior up to collisions with unmapped obstacles. This paper presents three approaches to the treatment of errors that can occur during the integration of continuous laser measurement in the discrete probabilistic grid. Further, the quality of the error prevention and the processing performance are compared with real sensor data.

Trans-dimensional matched-field geoacoustic inversion with hierarchical error models and interacting Markov chains.

PubMed

Dettmer, Jan; Dosso, Stan E

2012-10-01

This paper develops a trans-dimensional approach to matched-field geoacoustic inversion, including interacting Markov chains to improve efficiency and an autoregressive model to account for correlated errors. The trans-dimensional approach and hierarchical seabed model allows inversion without assuming any particular parametrization by relaxing model specification to a range of plausible seabed models (e.g., in this case, the number of sediment layers is an unknown parameter). Data errors are addressed by sampling statistical error-distribution parameters, including correlated errors (covariance), by applying a hierarchical autoregressive error model. The well-known difficulty of low acceptance rates for trans-dimensional jumps is addressed with interacting Markov chains, resulting in a substantial increase in efficiency. The trans-dimensional seabed model and the hierarchical error model relax the degree of prior assumptions required in the inversion, resulting in substantially improved (more realistic) uncertainty estimates and a more automated algorithm. In particular, the approach gives seabed parameter uncertainty estimates that account for uncertainty due to prior model choice (layering and data error statistics). The approach is applied to data measured on a vertical array in the Mediterranean Sea.

Accessing Multi-Dimensional Images and Data Cubes in the Virtual Observatory

NASA Astrophysics Data System (ADS)

Tody, Douglas; Plante, R. L.; Berriman, G. B.; Cresitello-Dittmar, M.; Good, J.; Graham, M.; Greene, G.; Hanisch, R. J.; Jenness, T.; Lazio, J.; Norris, P.; Pevunova, O.; Rots, A. H.

2014-01-01

Telescopes across the spectrum are routinely producing multi-dimensional images and datasets, such as Doppler velocity cubes, polarization datasets, and time-resolved “movies.” Examples of current telescopes producing such multi-dimensional images include the JVLA, ALMA, and the IFU instruments on large optical and near-infrared wavelength telescopes. In the near future, both the LSST and JWST will also produce such multi-dimensional images routinely. High-energy instruments such as Chandra produce event datasets that are also a form of multi-dimensional data, in effect being a very sparse multi-dimensional image. Ensuring that the data sets produced by these telescopes can be both discovered and accessed by the community is essential and is part of the mission of the Virtual Observatory (VO). The Virtual Astronomical Observatory (VAO, http://www.usvao.org/), in conjunction with its international partners in the International Virtual Observatory Alliance (IVOA), has developed a protocol and an initial demonstration service designed for the publication, discovery, and access of arbitrarily large multi-dimensional images. The protocol describing multi-dimensional images is the Simple Image Access Protocol, version 2, which provides the minimal set of metadata required to characterize a multi-dimensional image for its discovery and access. A companion Image Data Model formally defines the semantics and structure of multi-dimensional images independently of how they are serialized, while providing capabilities such as support for sparse data that are essential to deal effectively with large cubes. A prototype data access service has been deployed and tested, using a suite of multi-dimensional images from a variety of telescopes. The prototype has demonstrated the capability to discover and remotely access multi-dimensional data via standard VO protocols. The prototype informs the specification of a protocol that will be submitted to the IVOA for approval, with an operational data cube service to be delivered in mid-2014. An associated user-installable VO data service framework will provide the capabilities required to publish VO-compatible multi-dimensional images or data cubes.

Minimization of three-dimensional beam emittance growth in rare-isotope accelerator

NASA Astrophysics Data System (ADS)

Oh, B. H.; Yoon, M.

2016-12-01

In this paper, we describe a research to minimize the three-dimensional (3D) emittance growth (EG) in the RAON accelerator, a heavy ion accelerator currently being developed in Korea to produce various rare isotopes. The emittance minimization is performed using the multi-objective genetic algorithm and the simplex method. We use them to analyze the driver linac for the in-flight fragmentation separator of the RAON facility and show that redesign of the 90-degree bending section of the RAON accelerator together with adjustment of optics in the upstream and downstream superconducting linacs can limit the 3D EG to 20 % in the entire region of the driver linac. Effects of various magnet and rf accelerating cavity errors on the beam-EG are also discussed.

Sampling Versus Filtering in Large-Eddy Simulations

NASA Technical Reports Server (NTRS)

Debliquy, O.; Knaepen, B.; Carati, D.; Wray, A. A.

2004-01-01

A LES formalism in which the filter operator is replaced by a sampling operator is proposed. The unknown quantities that appear in the LES equations originate only from inadequate resolution (Discretization errors). The resulting viewpoint seems to make a link between finite difference approaches and finite element methods. Sampling operators are shown to commute with nonlinearities and to be purely projective. Moreover, their use allows an unambiguous definition of the LES numerical grid. The price to pay is that sampling never commutes with spatial derivatives and the commutation errors must be modeled. It is shown that models for the discretization errors may be treated using the dynamic procedure. Preliminary results, using the Smagorinsky model, are very encouraging.

Volume error analysis for lung nodules attached to pulmonary vessels in an anthropomorphic thoracic phantom

NASA Astrophysics Data System (ADS)

Kinnard, Lisa M.; Gavrielides, Marios A.; Myers, Kyle J.; Zeng, Rongping; Peregoy, Jennifer; Pritchard, William; Karanian, John W.; Petrick, Nicholas

2008-03-01

High-resolution CT, three-dimensional (3D) methods for nodule volumetry have been introduced, with the hope that such methods will be more accurate and consistent than currently used planar measures of size. However, the error associated with volume estimation methods still needs to be quantified. Volume estimation error is multi-faceted in the sense that it is impacted by characteristics of the patient, the software tool and the CT system. The overall goal of this research is to quantify the various sources of measurement error and, when possible, minimize their effects. In the current study, we estimated nodule volume from ten repeat scans of an anthropomorphic phantom containing two synthetic spherical lung nodules (diameters: 5 and 10 mm; density: -630 HU), using a 16-slice Philips CT with 20, 50, 100 and 200 mAs exposures and 0.8 and 3.0 mm slice thicknesses. True volume was estimated from an average of diameter measurements, made using digital calipers. We report variance and bias results for volume measurements as a function of slice thickness, nodule diameter, and X-ray exposure.

Superfast algorithms of multidimensional discrete k-wave transforms and Volterra filtering based on superfast radon transform

NASA Astrophysics Data System (ADS)

Labunets, Valeri G.; Labunets-Rundblad, Ekaterina V.; Astola, Jaakko T.

2001-12-01

Fast algorithms for a wide class of non-separable n-dimensional (nD) discrete unitary K-transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix-2 FFT-type approach. The method utilizes a decomposition of the nD K-transform into the product of a new nD discrete Radon transform and of a set of parallel/independ 1D K-transforms. If the nD K-transform has a separable kernel (e.g., the case of the discrete Fourier transform) our approach leads to decrease of multiplicative complexity by the factor of n comparing to the classical row/column separable approach. It is well known that an n-th order Volterra filter of one dimensional signal can be evaluated by an appropriate nD linear convolution. This work describes new superfast algorithm for Volterra filtering. New approach is based on the superfast discrete Radon and Nussbaumer polynomial transforms.

Bifacial DNA origami-directed discrete, three-dimensional, anisotropic plasmonic nanoarchitectures with tailored optical chirality.

PubMed

Lan, Xiang; Chen, Zhong; Dai, Gaole; Lu, Xuxing; Ni, Weihai; Wang, Qiangbin

2013-08-07

Discrete three-dimensional (3D) plasmonic nanoarchitectures with well-defined spatial configuration and geometry have aroused increasing interest, as new optical properties may originate from plasmon resonance coupling within the nanoarchitectures. Although spherical building blocks have been successfully employed in constructing 3D plasmonic nanoarchitectures because their isotropic nature facilitates unoriented localization, it still remains challenging to assemble anisotropic building blocks into discrete and rationally tailored 3D plasmonic nanoarchitectures. Here we report the first example of discrete 3D anisotropic gold nanorod (AuNR) dimer nanoarchitectures formed using bifacial DNA origami as a template, in which the 3D spatial configuration is precisely tuned by rationally shifting the location of AuNRs on the origami template. A distinct plasmonic chiral response was experimentally observed from the discrete 3D AuNR dimer nanoarchitectures and appeared in a spatial-configuration-dependent manner. This study represents great progress in the fabrication of 3D plasmonic nanoarchitectures with tailored optical chirality.

A new flux-conserving numerical scheme for the steady, incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.

1994-01-01

This paper is concerned with the continued development of a new numerical method, the space-time solution element (STS) method, for solving conservation laws. The present work focuses on the two-dimensional, steady, incompressible Navier-Stokes equations. Using first an integral approach, and then a differential approach, the discrete flux conservation equations presented in a recent paper are rederived. Here a simpler method for determining the flux expressions at cell interfaces is given; a systematic and rigorous derivation of the conditions used to simulate the differential form of the governing conservation law(s) is provided; necessary and sufficient conditions for a discrete approximation to satisfy a conservation law in E2 are derived; and an estimate of the local truncation error is given. A specific scheme is then constructed for the solution of the thin airfoil boundary layer problem. Numerical results are presented which demonstrate the ability of the scheme to accurately resolve the developing boundary layer and wake regions using grids which are much coarser than those employed by other numerical methods. It is shown that ten cells in the cross-stream direction are sufficient to accurately resolve the developing airfoil boundary layer.

Discrete Wavelet Transform-Based Whole-Spectral and Subspectral Analysis for Improved Brain Tumor Clustering Using Single Voxel MR Spectroscopy.

PubMed

Yang, Guang; Nawaz, Tahir; Barrick, Thomas R; Howe, Franklyn A; Slabaugh, Greg

2015-12-01

Many approaches have been considered for automatic grading of brain tumors by means of pattern recognition with magnetic resonance spectroscopy (MRS). Providing an improved technique which can assist clinicians in accurately identifying brain tumor grades is our main objective. The proposed technique, which is based on the discrete wavelet transform (DWT) of whole-spectral or subspectral information of key metabolites, combined with unsupervised learning, inspects the separability of the extracted wavelet features from the MRS signal to aid the clustering. In total, we included 134 short echo time single voxel MRS spectra (SV MRS) in our study that cover normal controls, low grade and high grade tumors. The combination of DWT-based whole-spectral or subspectral analysis and unsupervised clustering achieved an overall clustering accuracy of 94.8% and a balanced error rate of 7.8%. To the best of our knowledge, it is the first study using DWT combined with unsupervised learning to cluster brain SV MRS. Instead of dimensionality reduction on SV MRS or feature selection using model fitting, our study provides an alternative method of extracting features to obtain promising clustering results.

Virtual gap element approach for the treatment of non-matching interface using three-dimensional solid elements

NASA Astrophysics Data System (ADS)

Song, Yeo-Ul; Youn, Sung-Kie; Park, K. C.

2017-10-01

A method for three-dimensional non-matching interface treatment with a virtual gap element is developed. When partitioned structures contain curved interfaces and have different brick meshes, the discretized models have gaps along the interfaces. As these gaps bring unexpected errors, special treatments are required to handle the gaps. In the present work, a virtual gap element is introduced to link the frame and surface domain nodes in the frame work of the mortar method. Since the surface of the hexahedron element is quadrilateral, the gap element is pyramidal. The pyramidal gap element consists of four domain nodes and one frame node. Zero-strain condition in the gap element is utilized for the interpolation of frame nodes in terms of the domain nodes. This approach is taken to satisfy the momentum and energy conservation. The present method is applicable not only to curved interfaces with gaps, but also to flat interfaces in three dimensions. Several numerical examples are given to describe the effectiveness and accuracy of the proposed method.

On Channel Sharing in Discrete-Time, Multi-Access Broadcast Communications,

DTIC Science & Technology

1980-09-01

towards a physical intepretation . of the solutions. 1.4.3 THE PROBLEM OF CAPACITY Our discussion of capacity has two objectives. First, to explore...8021 (DARPA). Yemnii, Y., "On Channel Sharing in Discrete-Time, Multi-Access Broadcast Communication," Sep- tember 1980, UCLA-ENG-8061. (DARPA). 280 FILMED 9-83 DTIC 𔃾’W 9111 ’K4VFClMlP-- Om mFoca 1,00,

Some applications of the multi-dimensional fractional order for the Riemann-Liouville derivative

NASA Astrophysics Data System (ADS)

Ahmood, Wasan Ajeel; Kiliçman, Adem

2017-01-01

In this paper, the aim of this work is to study theorem for the one-dimensional space-time fractional deriative, generalize some function for the one-dimensional fractional by table represents the fractional Laplace transforms of some elementary functions to be valid for the multi-dimensional fractional Laplace transform and give the definition of the multi-dimensional fractional Laplace transform. This study includes that, dedicate the one-dimensional fractional Laplace transform for functions of only one independent variable and develop of the one-dimensional fractional Laplace transform to multi-dimensional fractional Laplace transform based on the modified Riemann-Liouville derivative.

A GPU-based symmetric non-rigid image registration method in human lung.

PubMed

Haghighi, Babak; D Ellingwood, Nathan; Yin, Youbing; Hoffman, Eric A; Lin, Ching-Long

2018-03-01

Quantitative computed tomography (QCT) of the lungs plays an increasing role in identifying sub-phenotypes of pathologies previously lumped into broad categories such as chronic obstructive pulmonary disease and asthma. Methods for image matching and linking multiple lung volumes have proven useful in linking structure to function and in the identification of regional longitudinal changes. Here, we seek to improve the accuracy of image matching via the use of a symmetric multi-level non-rigid registration employing an inverse consistent (IC) transformation whereby images are registered both in the forward and reverse directions. To develop the symmetric method, two similarity measures, the sum of squared intensity difference (SSD) and the sum of squared tissue volume difference (SSTVD), were used. The method is based on a novel generic mathematical framework to include forward and backward transformations, simultaneously, eliminating the need to compute the inverse transformation. Two implementations were used to assess the proposed method: a two-dimensional (2-D) implementation using synthetic examples with SSD, and a multi-core CPU and graphics processing unit (GPU) implementation with SSTVD for three-dimensional (3-D) human lung datasets (six normal adults studied at total lung capacity (TLC) and functional residual capacity (FRC)). Success was evaluated in terms of the IC transformation consistency serving to link TLC to FRC. 2-D registration on synthetic images, using both symmetric and non-symmetric SSD methods, and comparison of displacement fields showed that the symmetric method gave a symmetrical grid shape and reduced IC errors, with the mean values of IC errors decreased by 37%. Results for both symmetric and non-symmetric transformations of human datasets showed that the symmetric method gave better results for IC errors in all cases, with mean values of IC errors for the symmetric method lower than the non-symmetric methods using both SSD and SSTVD. The GPU version demonstrated an average of 43 times speedup and ~5.2 times speedup over the single-threaded and 12-threaded CPU versions, respectively. Run times with the GPU were as fast as 2 min. The symmetric method improved the inverse consistency, aiding the use of image registration in the QCT-based evaluation of the lung.

Accuracy Improvement of Multi-Axis Systems Based on Laser Correction of Volumetric Geometric Errors

NASA Astrophysics Data System (ADS)

Teleshevsky, V. I.; Sokolov, V. A.; Pimushkin, Ya I.

2018-04-01

The article describes a volumetric geometric errors correction method for CNC- controlled multi-axis systems (machine-tools, CMMs etc.). The Kalman’s concept of “Control and Observation” is used. A versatile multi-function laser interferometer is used as Observer in order to measure machine’s error functions. A systematic error map of machine’s workspace is produced based on error functions measurements. The error map results into error correction strategy. The article proposes a new method of error correction strategy forming. The method is based on error distribution within machine’s workspace and a CNC-program postprocessor. The postprocessor provides minimal error values within maximal workspace zone. The results are confirmed by error correction of precision CNC machine-tools.

Models of multidimensional discrete distribution of probabilities of random variables in information systems

NASA Astrophysics Data System (ADS)

Gromov, Yu Yu; Minin, Yu V.; Ivanova, O. G.; Morozova, O. N.

2018-03-01

Multidimensional discrete distributions of probabilities of independent random values were received. Their one-dimensional distribution is widely used in probability theory. Producing functions of those multidimensional distributions were also received.

Space-time least-squares Petrov-Galerkin projection in nonlinear model reduction.

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

Choi, Youngsoo; Carlberg, Kevin Thomas

Our work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply Petrov-Galerkin projection in the spatial dimension and subsequently apply time integration to numerically resolve the resulting low-dimensional dynamical system, the proposed method applies projection in space and time simultaneously. To accomplish this, the method first introduces a low-dimensional space-time trial subspace, which can be obtained by computing tensor decompositions of state-snapshot data. The method then computes discrete-optimal approximations in this space-time trial subspace by minimizing the residual arising after time discretization over allmore » space and time in a weighted ℓ 2-norm. This norm can be de ned to enable complexity reduction (i.e., hyper-reduction) in time, which leads to space-time collocation and space-time GNAT variants of the ST-LSPG method. Advantages of the approach relative to typical spatial-projection-based nonlinear model reduction methods such as Galerkin projection and least-squares Petrov-Galerkin projection include: (1) a reduction of both the spatial and temporal dimensions of the dynamical system, (2) the removal of spurious temporal modes (e.g., unstable growth) from the state space, and (3) error bounds that exhibit slower growth in time. Numerical examples performed on model problems in fluid dynamics demonstrate the ability of the method to generate orders-of-magnitude computational savings relative to spatial-projection-based reduced-order models without sacrificing accuracy.« less

Smooth empirical Bayes estimation of observation error variances in linear systems

NASA Technical Reports Server (NTRS)

Martz, H. F., Jr.; Lian, M. W.

1972-01-01

A smooth empirical Bayes estimator was developed for estimating the unknown random scale component of each of a set of observation error variances. It is shown that the estimator possesses a smaller average squared error loss than other estimators for a discrete time linear system.

The Extraction of One-Dimensional Flow Properties from Multi-Dimensional Data Sets

NASA Technical Reports Server (NTRS)

Baurle, Robert A.; Gaffney, Richard L., Jr.

2007-01-01

The engineering design and analysis of air-breathing propulsion systems relies heavily on zero- or one-dimensional properties (e.g. thrust, total pressure recovery, mixing and combustion efficiency, etc.) for figures of merit. The extraction of these parameters from experimental data sets and/or multi-dimensional computational data sets is therefore an important aspect of the design process. A variety of methods exist for extracting performance measures from multi-dimensional data sets. Some of the information contained in the multi-dimensional flow is inevitably lost when any one-dimensionalization technique is applied. Hence, the unique assumptions associated with a given approach may result in one-dimensional properties that are significantly different than those extracted using alternative approaches. The purpose of this effort is to examine some of the more popular methods used for the extraction of performance measures from multi-dimensional data sets, reveal the strengths and weaknesses of each approach, and highlight various numerical issues that result when mapping data from a multi-dimensional space to a space of one dimension.

The Art of Extracting One-Dimensional Flow Properties from Multi-Dimensional Data Sets

NASA Technical Reports Server (NTRS)

Baurle, R. A.; Gaffney, R. L.

2007-01-01

The engineering design and analysis of air-breathing propulsion systems relies heavily on zero- or one-dimensional properties (e:g: thrust, total pressure recovery, mixing and combustion efficiency, etc.) for figures of merit. The extraction of these parameters from experimental data sets and/or multi-dimensional computational data sets is therefore an important aspect of the design process. A variety of methods exist for extracting performance measures from multi-dimensional data sets. Some of the information contained in the multi-dimensional flow is inevitably lost when any one-dimensionalization technique is applied. Hence, the unique assumptions associated with a given approach may result in one-dimensional properties that are significantly different than those extracted using alternative approaches. The purpose of this effort is to examine some of the more popular methods used for the extraction of performance measures from multi-dimensional data sets, reveal the strengths and weaknesses of each approach, and highlight various numerical issues that result when mapping data from a multi-dimensional space to a space of one dimension.

Lie Symmetry Analysis of the Inhomogeneous Toda Lattice Equation via Semi-Discrete Exterior Calculus

NASA Astrophysics Data System (ADS)

Liu, Jiang; Wang, Deng-Shan; Yin, Yan-Bin

2017-06-01

In this work, the Lie point symmetries of the inhomogeneous Toda lattice equation are obtained by semi-discrete exterior calculus, which is a semi-discrete version of Harrison and Estabrook’s geometric approach. A four-dimensional Lie algebra and its one-, two- and three-dimensional subalgebras are given. Two similarity reductions of the inhomogeneous Toda lattice equation are obtained by using the symmetry vectors. Supported by National Natural Science Foundation of China under Grant Nos. 11375030, 11472315, and Department of Science and Technology of Henan Province under Grant No. 162300410223 and Beijing Finance Funds of Natural Science Program for Excellent Talents under Grant No. 2014000026833ZK19

Nonlinear initial-boundary value solutions by the finite element method. [for Navier-Stokes equations of two dimensional flow

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.

Isogeometric Divergence-conforming B-splines for the Darcy-Stokes-Brinkman Equations

DTIC Science & Technology

2012-01-01

dimensionality ofQ0,h using T-splines [5]. However, a proof of mesh-independent discrete stability remains absent with this choice of pressure space ... the boundary ∂K +/− of element K+/−. With the above notation established, let us define the following bilinear form: a ∗h(w,v) = np∑ i=1 ( (2ν∇sw,∇sv...8.3 Two- Dimensional Problem with a Singular Solution To examine how our discretization performs in

Three-dimensional simulation of vortex breakdown

NASA Technical Reports Server (NTRS)

Kuruvila, G.; Salas, M. D.

1990-01-01

The integral form of the complete, unsteady, compressible, three-dimensional Navier-Stokes equations in the conservation form, cast in generalized coordinate system, are solved, numerically, to simulate the vortex breakdown phenomenon. The inviscid fluxes are discretized using Roe's upwind-biased flux-difference splitting scheme and the viscous fluxes are discretized using central differencing. Time integration is performed using a backward Euler ADI (alternating direction implicit) scheme. A full approximation multigrid is used to accelerate the convergence to steady state.

A Fourier dimensionality reduction model for big data interferometric imaging

NASA Astrophysics Data System (ADS)

Vijay Kartik, S.; Carrillo, Rafael E.; Thiran, Jean-Philippe; Wiaux, Yves

2017-06-01

Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability of imaging methods to the big data setting of the next-generation telescopes. This article sheds new light on dimensionality reduction from the perspective of the compressed sensing theory and studies its interplay with imaging algorithms designed in the context of convex optimization. We propose a post-gridding linear data embedding to the space spanned by the left singular vectors of the measurement operator, providing a dimensionality reduction below image size. This embedding preserves the null space of the measurement operator and hence its sampling properties are also preserved in light of the compressed sensing theory. We show that this can be approximated by first computing the dirty image and then applying a weighted subsampled discrete Fourier transform to obtain the final reduced data vector. This Fourier dimensionality reduction model ensures a fast implementation of the full measurement operator, essential for any iterative image reconstruction method. The proposed reduction also preserves the independent and identically distributed Gaussian properties of the original measurement noise. For convex optimization-based imaging algorithms, this is key to justify the use of the standard ℓ2-norm as the data fidelity term. Our simulations confirm that this dimensionality reduction approach can be leveraged by convex optimization algorithms with no loss in imaging quality relative to reconstructing the image from the complete visibility data set. Reconstruction results in simulation settings with no direction dependent effects or calibration errors show promising performance of the proposed dimensionality reduction. Further tests on real data are planned as an extension of the current work. matlab code implementing the proposed reduction method is available on GitHub.

Comparison of genetic algorithm and imperialist competitive algorithms in predicting bed load transport in clean pipe.

PubMed

Ebtehaj, Isa; Bonakdari, Hossein

2014-01-01

The existence of sediments in wastewater greatly affects the performance of the sewer and wastewater transmission systems. Increased sedimentation in wastewater collection systems causes problems such as reduced transmission capacity and early combined sewer overflow. The article reviews the performance of the genetic algorithm (GA) and imperialist competitive algorithm (ICA) in minimizing the target function (mean square error of observed and predicted Froude number). To study the impact of bed load transport parameters, using four non-dimensional groups, six different models have been presented. Moreover, the roulette wheel selection method is used to select the parents. The ICA with root mean square error (RMSE) = 0.007, mean absolute percentage error (MAPE) = 3.5% show better results than GA (RMSE = 0.007, MAPE = 5.6%) for the selected model. All six models return better results than the GA. Also, the results of these two algorithms were compared with multi-layer perceptron and existing equations.

Multi-exponential analysis of magnitude MR images using a quantitative multispectral edge-preserving filter.

PubMed

Bonny, Jean Marie; Boespflug-Tanguly, Odile; Zanca, Michel; Renou, Jean Pierre

2003-03-01

A solution for discrete multi-exponential analysis of T(2) relaxation decay curves obtained in current multi-echo imaging protocol conditions is described. We propose a preprocessing step to improve the signal-to-noise ratio and thus lower the signal-to-noise ratio threshold from which a high percentage of true multi-exponential detection is detected. It consists of a multispectral nonlinear edge-preserving filter that takes into account the signal-dependent Rician distribution of noise affecting magnitude MR images. Discrete multi-exponential decomposition, which requires no a priori knowledge, is performed by a non-linear least-squares procedure initialized with estimates obtained from a total least-squares linear prediction algorithm. This approach was validated and optimized experimentally on simulated data sets of normal human brains.

GoPhast: a graphical user interface for PHAST

USGS Publications Warehouse

Winston, Richard B.

2006-01-01

GoPhast is a graphical user interface (GUI) for the USGS model PHAST. PHAST simulates multicomponent, reactive solute transport in three-dimensional, saturated, ground-water flow systems. PHAST can model both equilibrium and kinetic geochemical reactions. PHAST is derived from HST3D (flow and transport) and PHREEQC (geochemical calculations). The flow and transport calculations are restricted to constant fluid density and constant temperature. The complexity of the input required by PHAST makes manual construction of its input files tedious and error-prone. GoPhast streamlines the creation of the input file and helps reduce errors. GoPhast allows the user to define the spatial input for the PHAST flow and transport data file by drawing points, lines, or polygons on top, front, and side views of the model domain. These objects can have up to two associated formulas that define their extent perpendicular to the view plane, allowing the objects to be three-dimensional. Formulas are also used to specify the values of spatial data (data sets) both globally and for individual objects. Objects can be used to specify the values of data sets independent of the spatial and temporal discretization of the model. Thus, the grid and simulation periods for the model can be changed without respecifying spatial data pertaining to the hydrogeologic framework and boundary conditions. This report describes the operation of GoPhast and demonstrates its use with examples. GoPhast runs on Windows 2000, Windows XP, and Linux operating systems.

Using field inversion to quantify functional errors in turbulence closures

NASA Astrophysics Data System (ADS)

Singh, Anand Pratap; Duraisamy, Karthik

2016-04-01

A data-informed approach is presented with the objective of quantifying errors and uncertainties in the functional forms of turbulence closure models. The approach creates modeling information from higher-fidelity simulations and experimental data. Specifically, a Bayesian formalism is adopted to infer discrepancies in the source terms of transport equations. A key enabling idea is the transformation of the functional inversion procedure (which is inherently infinite-dimensional) into a finite-dimensional problem in which the distribution of the unknown function is estimated at discrete mesh locations in the computational domain. This allows for the use of an efficient adjoint-driven inversion procedure. The output of the inversion is a full-field of discrepancy that provides hitherto inaccessible modeling information. The utility of the approach is demonstrated by applying it to a number of problems including channel flow, shock-boundary layer interactions, and flows with curvature and separation. In all these cases, the posterior model correlates well with the data. Furthermore, it is shown that even if limited data (such as surface pressures) are used, the accuracy of the inferred solution is improved over the entire computational domain. The results suggest that, by directly addressing the connection between physical data and model discrepancies, the field inversion approach materially enhances the value of computational and experimental data for model improvement. The resulting information can be used by the modeler as a guiding tool to design more accurate model forms, or serve as input to machine learning algorithms to directly replace deficient modeling terms.

Feature extraction using extrema sampling of discrete derivatives for spike sorting in implantable upper-limb neural prostheses.

PubMed

Zamani, Majid; Demosthenous, Andreas

2014-07-01

Next generation neural interfaces for upper-limb (and other) prostheses aim to develop implantable interfaces for one or more nerves, each interface having many neural signal channels that work reliably in the stump without harming the nerves. To achieve real-time multi-channel processing it is important to integrate spike sorting on-chip to overcome limitations in transmission bandwidth. This requires computationally efficient algorithms for feature extraction and clustering suitable for low-power hardware implementation. This paper describes a new feature extraction method for real-time spike sorting based on extrema analysis (namely positive peaks and negative peaks) of spike shapes and their discrete derivatives at different frequency bands. Employing simulation across different datasets, the accuracy and computational complexity of the proposed method are assessed and compared with other methods. The average classification accuracy of the proposed method in conjunction with online sorting (O-Sort) is 91.6%, outperforming all the other methods tested with the O-Sort clustering algorithm. The proposed method offers a better tradeoff between classification error and computational complexity, making it a particularly strong choice for on-chip spike sorting.

Comparative Study of Advanced Turbulence Models for Turbomachinery

NASA Technical Reports Server (NTRS)

Hadid, Ali H.; Sindir, Munir M.

1996-01-01

A computational study has been undertaken to study the performance of advanced phenomenological turbulence models coded in a modular form to describe incompressible turbulent flow behavior in two dimensional/axisymmetric and three dimensional complex geometry. The models include a variety of two equation models (single and multi-scale k-epsilon models with different near wall treatments) and second moment algebraic and full Reynolds stress closure models. These models were systematically assessed to evaluate their performance in complex flows with rotation, curvature and separation. The models are coded as self contained modules that can be interfaced with a number of flow solvers. These modules are stand alone satellite programs that come with their own formulation, finite-volume discretization scheme, solver and boundary condition implementation. They will take as input (from any generic Navier-Stokes solver) the velocity field, grid (structured H-type grid) and computational domain specification (boundary conditions), and will deliver, depending on the model used, turbulent viscosity, or the components of the Reynolds stress tensor. There are separate 2D/axisymmetric and/or 3D decks for each module considered. The modules are tested using Rocketdyn's proprietary code REACT. The code utilizes an efficient solution procedure to solve Navier-Stokes equations in a non-orthogonal body-fitted coordinate system. The differential equations are discretized over a finite-volume grid using a non-staggered variable arrangement and an efficient solution procedure based on the SIMPLE algorithm for the velocity-pressure coupling is used. The modules developed have been interfaced and tested using finite-volume, pressure-correction CFD solvers which are widely used in the CFD community. Other solvers can also be used to test these modules since they are independently structured with their own discretization scheme and solver methodology. Many of these modules have been independently tested by Professor C.P. Chen and his group at the University of Alabama at Huntsville (UAH) by interfacing them with own flow solver (MAST).

Discrete Time Crystals: Rigidity, Criticality, and Realizations.

PubMed

Yao, N Y; Potter, A C; Potirniche, I-D; Vishwanath, A

2017-01-20

Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.

Theory of relativistic Brownian motion: the (1+3) -dimensional case.

PubMed

Dunkel, Jörn; Hänggi, Peter

2005-09-01

A theory for (1+3) -dimensional relativistic Brownian motion under the influence of external force fields is put forward. Starting out from a set of relativistically covariant, but multiplicative Langevin equations we describe the relativistic stochastic dynamics of a forced Brownian particle. The corresponding Fokker-Planck equations are studied in the laboratory frame coordinates. In particular, the stochastic integration prescription--i.e., the discretization rule dilemma--is elucidated (prepoint discretization rule versus midpoint discretization rule versus postpoint discretization rule). Remarkably, within our relativistic scheme we find that the postpoint rule (or the transport form) yields the only Fokker-Planck dynamics from which the relativistic Maxwell-Boltzmann statistics is recovered as the stationary solution. The relativistic velocity effects become distinctly more pronounced by going from one to three spatial dimensions. Moreover, we present numerical results for the asymptotic mean-square displacement of a free relativistic Brownian particle moving in 1+3 dimensions.

Some theorems and properties of multi-dimensional fractional Laplace transforms

NASA Astrophysics Data System (ADS)

Ahmood, Wasan Ajeel; Kiliçman, Adem

2016-06-01

The aim of this work is to study theorems and properties for the one-dimensional fractional Laplace transform, generalize some properties for the one-dimensional fractional Lapalce transform to be valid for the multi-dimensional fractional Lapalce transform and is to give the definition of the multi-dimensional fractional Lapalce transform. This study includes: dedicate the one-dimensional fractional Laplace transform for functions of only one independent variable with some of important theorems and properties and develop of some properties for the one-dimensional fractional Laplace transform to multi-dimensional fractional Laplace transform. Also, we obtain a fractional Laplace inversion theorem after a short survey on fractional analysis based on the modified Riemann-Liouville derivative.

Video compression of coronary angiograms based on discrete wavelet transform with block classification.

PubMed

Ho, B T; Tsai, M J; Wei, J; Ma, M; Saipetch, P

1996-01-01

A new method of video compression for angiographic images has been developed to achieve high compression ratio (~20:1) while eliminating block artifacts which leads to loss of diagnostic accuracy. This method adopts motion picture experts group's (MPEGs) motion compensated prediction to takes advantage of frame to frame correlation. However, in contrast to MPEG, the error images arising from mismatches in the motion estimation are encoded by discrete wavelet transform (DWT) rather than block discrete cosine transform (DCT). Furthermore, the authors developed a classification scheme which label each block in an image as intra, error, or background type and encode it accordingly. This hybrid coding can significantly improve the compression efficiency in certain eases. This method can be generalized for any dynamic image sequences applications sensitive to block artifacts.

The Faceted Discrete Growth and Phase Differentiation During the Directional Solidification of 20SiMnMo5 Steel

NASA Astrophysics Data System (ADS)

Ma, Xiaoping; Li, Dianzhong

2018-07-01

The microstructures, segregation and cooling curve were investigated in the directional solidification of 20SiMnMo5 steel. The typical characteristic of faceted growth is identified. The microstructures within the single cellular and within the single dendritic arm, together with the contradictive segregation distribution against the cooling curve, verify the discrete crystal growth in multi-scales. Not only the single cellular/dendritic arm but also the single martensite zone within the single cellular/dendritic arm is produced by the discrete growth. In the viewpoint of segregation, the basic domain following continuous growth has not been revealed. Along with the multi-scale faceted discrete growth, the phase differentiation happens for both the solid and liquid. The differentiated liquid phases appear and evolve with different sizes, positions, compositions and durations. The physical mechanism for the faceted discrete growth is qualitatively established based on the nucleation of new faceted steps induced by the composition gradient and temperature gradient.

The Faceted Discrete Growth and Phase Differentiation During the Directional Solidification of 20SiMnMo5 Steel

NASA Astrophysics Data System (ADS)

Ma, Xiaoping; Li, Dianzhong

2018-03-01

The microstructures, segregation and cooling curve were investigated in the directional solidification of 20SiMnMo5 steel. The typical characteristic of faceted growth is identified. The microstructures within the single cellular and within the single dendritic arm, together with the contradictive segregation distribution against the cooling curve, verify the discrete crystal growth in multi-scales. Not only the single cellular/dendritic arm but also the single martensite zone within the single cellular/dendritic arm is produced by the discrete growth. In the viewpoint of segregation, the basic domain following continuous growth has not been revealed. Along with the multi-scale faceted discrete growth, the phase differentiation happens for both the solid and liquid. The differentiated liquid phases appear and evolve with different sizes, positions, compositions and durations. The physical mechanism for the faceted discrete growth is qualitatively established based on the nucleation of new faceted steps induced by the composition gradient and temperature gradient.

Application of time series discretization using evolutionary programming for classification of precancerous cervical lesions.

PubMed

Acosta-Mesa, Héctor-Gabriel; Rechy-Ramírez, Fernando; Mezura-Montes, Efrén; Cruz-Ramírez, Nicandro; Hernández Jiménez, Rodolfo

2014-06-01

In this work, we present a novel application of time series discretization using evolutionary programming for the classification of precancerous cervical lesions. The approach optimizes the number of intervals in which the length and amplitude of the time series should be compressed, preserving the important information for classification purposes. Using evolutionary programming, the search for a good discretization scheme is guided by a cost function which considers three criteria: the entropy regarding the classification, the complexity measured as the number of different strings needed to represent the complete data set, and the compression rate assessed as the length of the discrete representation. This discretization approach is evaluated using a time series data based on temporal patterns observed during a classical test used in cervical cancer detection; the classification accuracy reached by our method is compared with the well-known times series discretization algorithm SAX and the dimensionality reduction method PCA. Statistical analysis of the classification accuracy shows that the discrete representation is as efficient as the complete raw representation for the present application, reducing the dimensionality of the time series length by 97%. This representation is also very competitive in terms of classification accuracy when compared with similar approaches. Copyright © 2014 Elsevier Inc. All rights reserved.

RELAP-7 Development Updates

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

Zhang, Hongbin; Zhao, Haihua; Gleicher, Frederick Nathan

RELAP-7 is a nuclear systems safety analysis code being developed at the Idaho National Laboratory, and is the next generation tool in the RELAP reactor safety/systems analysis application series. RELAP-7 development began in 2011 to support the Risk Informed Safety Margins Characterization (RISMC) Pathway of the Light Water Reactor Sustainability (LWRS) program. The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical methods, and physical models in order to provide capabilities needed for the RISMC methodology and to support nuclear power safety analysis. The code is beingmore » developed based on Idaho National Laboratory’s modern scientific software development framework – MOOSE (the Multi-Physics Object-Oriented Simulation Environment). The initial development goal of the RELAP-7 approach focused primarily on the development of an implicit algorithm capable of strong (nonlinear) coupling of the dependent hydrodynamic variables contained in the 1-D/2-D flow models with the various 0-D system reactor components that compose various boiling water reactor (BWR) and pressurized water reactor nuclear power plants (NPPs). During Fiscal Year (FY) 2015, the RELAP-7 code has been further improved with expanded capability to support boiling water reactor (BWR) and pressurized water reactor NPPs analysis. The accumulator model has been developed. The code has also been coupled with other MOOSE-based applications such as neutronics code RattleSnake and fuel performance code BISON to perform multiphysics analysis. A major design requirement for the implicit algorithm in RELAP-7 is that it is capable of second-order discretization accuracy in both space and time, which eliminates the traditional first-order approximation errors. The second-order temporal is achieved by a second-order backward temporal difference, and the one-dimensional second-order accurate spatial discretization is achieved with the Galerkin approximation of Lagrange finite elements. During FY-2015, we have done numerical verification work to verify that the RELAP-7 code indeed achieves 2nd-order accuracy in both time and space for single phase models at the system level.« less

Quantifying the uncertainty introduced by discretization and time-averaging in two-fluid model predictions

DOE PAGES

Syamlal, Madhava; Celik, Ismail B.; Benyahia, Sofiane

2017-07-12

The two-fluid model (TFM) has become a tool for the design and troubleshooting of industrial fluidized bed reactors. To use TFM for scale up with confidence, the uncertainty in its predictions must be quantified. Here, we study two sources of uncertainty: discretization and time-averaging. First, we show that successive grid refinement may not yield grid-independent transient quantities, including cross-section–averaged quantities. Successive grid refinement would yield grid-independent time-averaged quantities on sufficiently fine grids. A Richardson extrapolation can then be used to estimate the discretization error, and the grid convergence index gives an estimate of the uncertainty. Richardson extrapolation may not workmore » for industrial-scale simulations that use coarse grids. We present an alternative method for coarse grids and assess its ability to estimate the discretization error. Second, we assess two methods (autocorrelation and binning) and find that the autocorrelation method is more reliable for estimating the uncertainty introduced by time-averaging TFM data.« less

A three-dimensional image processing program for accurate, rapid, and semi-automated segmentation of neuronal somata with dense neurite outgrowth

PubMed Central

Ross, James D.; Cullen, D. Kacy; Harris, James P.; LaPlaca, Michelle C.; DeWeerth, Stephen P.

2015-01-01

Three-dimensional (3-D) image analysis techniques provide a powerful means to rapidly and accurately assess complex morphological and functional interactions between neural cells. Current software-based identification methods of neural cells generally fall into two applications: (1) segmentation of cell nuclei in high-density constructs or (2) tracing of cell neurites in single cell investigations. We have developed novel methodologies to permit the systematic identification of populations of neuronal somata possessing rich morphological detail and dense neurite arborization throughout thick tissue or 3-D in vitro constructs. The image analysis incorporates several novel automated features for the discrimination of neurites and somata by initially classifying features in 2-D and merging these classifications into 3-D objects; the 3-D reconstructions automatically identify and adjust for over and under segmentation errors. Additionally, the platform provides for software-assisted error corrections to further minimize error. These features attain very accurate cell boundary identifications to handle a wide range of morphological complexities. We validated these tools using confocal z-stacks from thick 3-D neural constructs where neuronal somata had varying degrees of neurite arborization and complexity, achieving an accuracy of ≥95%. We demonstrated the robustness of these algorithms in a more complex arena through the automated segmentation of neural cells in ex vivo brain slices. These novel methods surpass previous techniques by improving the robustness and accuracy by: (1) the ability to process neurites and somata, (2) bidirectional segmentation correction, and (3) validation via software-assisted user input. This 3-D image analysis platform provides valuable tools for the unbiased analysis of neural tissue or tissue surrogates within a 3-D context, appropriate for the study of multi-dimensional cell-cell and cell-extracellular matrix interactions. PMID:26257609

Simulation of Fluid Flow and Collection Efficiency for an SEA Multi-element Probe

NASA Technical Reports Server (NTRS)

Rigby, David L.; Struk, Peter M.; Bidwell, Colin

2014-01-01

Numerical simulations of fluid flow and collection efficiency for a Science Engineering Associates (SEA) multi-element probe are presented. Simulation of the flow field was produced using the Glenn-HT Navier-Stokes solver. Three-dimensional unsteady results were produced and then time averaged for the heat transfer and collection efficiency results. Three grid densities were investigated to enable an assessment of grid dependence. Simulations were completed for free stream velocities ranging from 85-135 meters per second, and free stream total pressure of 44.8 and 93.1 kilopascals (6.5 and 13.5 pounds per square inch absolute). In addition, the effect of angle of attack and yaw were investigated by including 5 degree deviations from straight for one of the flow conditions. All but one of the cases simulated a probe in isolation (i.e. in a very large domain without any support strut). One case is included which represents a probe mounted on a support strut within a finite sized wind tunnel. Collection efficiencies were generated, using the LEWICE3D code, for four spherical particle sizes, 100, 50, 20, and 5 micron in diameter. It was observed that a reduction in velocity of about 20% occurred, for all cases, as the flow entered the shroud of the probe. The reduction in velocity within the shroud is not indicative of any error in the probe measurement accuracy. Heat transfer results are presented which agree quite well with a correlation for the circular cross section heated elements. Collection efficiency results indicate a reduction in collection efficiency as particle size is reduced. The reduction with particle size is expected, however, the results tended to be lower than the previous results generated for isolated two-dimensional elements. The deviation from the two-dimensional results is more pronounced for the smaller particles and is likely due to the reduced flow within the protective shroud. As particle size increases differences between the two-dimensional and three dimensional results become negligible. Taken as a group, the total collection efficiency of the elements including the effects of the shroud has been shown to be in the range of 0.93 to 0.99 for particles above 20 microns. The 3D model has improved the estimated collection efficiency for smaller particles where errors in previous estimates were more significant.

AUV Underwater Positioning Algorithm Based on Interactive Assistance of SINS and LBL

PubMed Central

Zhang, Tao; Chen, Liping; Li, Yao

2015-01-01

This paper studies an underwater positioning algorithm based on the interactive assistance of a strapdown inertial navigation system (SINS) and LBL, and this algorithm mainly includes an optimal correlation algorithm with aided tracking of an SINS/Doppler velocity log (DVL)/magnetic compass pilot (MCP), a three-dimensional TDOA positioning algorithm of Taylor series expansion and a multi-sensor information fusion algorithm. The final simulation results show that compared to traditional underwater positioning algorithms, this scheme can not only directly correct accumulative errors caused by a dead reckoning algorithm, but also solves the problem of ambiguous correlation peaks caused by multipath transmission of underwater acoustic signals. The proposed method can calibrate the accumulative error of the AUV position more directly and effectively, which prolongs the underwater operating duration of the AUV. PMID:26729120

A new discrete dipole kernel for quantitative susceptibility mapping.

PubMed

Milovic, Carlos; Acosta-Cabronero, Julio; Pinto, José Miguel; Mattern, Hendrik; Andia, Marcelo; Uribe, Sergio; Tejos, Cristian

2018-09-01

Most approaches for quantitative susceptibility mapping (QSM) are based on a forward model approximation that employs a continuous Fourier transform operator to solve a differential equation system. Such formulation, however, is prone to high-frequency aliasing. The aim of this study was to reduce such errors using an alternative dipole kernel formulation based on the discrete Fourier transform and discrete operators. The impact of such an approach on forward model calculation and susceptibility inversion was evaluated in contrast to the continuous formulation both with synthetic phantoms and in vivo MRI data. The discrete kernel demonstrated systematically better fits to analytic field solutions, and showed less over-oscillations and aliasing artifacts while preserving low- and medium-frequency responses relative to those obtained with the continuous kernel. In the context of QSM estimation, the use of the proposed discrete kernel resulted in error reduction and increased sharpness. This proof-of-concept study demonstrated that discretizing the dipole kernel is advantageous for QSM. The impact on small or narrow structures such as the venous vasculature might by particularly relevant to high-resolution QSM applications with ultra-high field MRI - a topic for future investigations. The proposed dipole kernel has a straightforward implementation to existing QSM routines. Copyright © 2018 Elsevier Inc. All rights reserved.

Iterative spectral methods and spectral solutions to compressible flows

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Zang, T. A.

1982-01-01

A spectral multigrid scheme is described which can solve pseudospectral discretizations of self-adjoint elliptic problems in O(N log N) operations. An iterative technique for efficiently implementing semi-implicit time-stepping for pseudospectral discretizations of Navier-Stokes equations is discussed. This approach can handle variable coefficient terms in an effective manner. Pseudospectral solutions of compressible flow problems are presented. These include one dimensional problems and two dimensional Euler solutions. Results are given both for shock-capturing approaches and for shock-fitting ones.

An integrative and functional framework for the study of animal emotion and mood

PubMed Central

Mendl, Michael; Burman, Oliver H. P.; Paul, Elizabeth S.

2010-01-01

A better understanding of animal emotion is an important goal in disciplines ranging from neuroscience to animal welfare science. The conscious experience of emotion cannot be assessed directly, but neural, behavioural and physiological indicators of emotion can be measured. Researchers have used these measures to characterize how animals respond to situations assumed to induce discrete emotional states (e.g. fear). While advancing our understanding of specific emotions, this discrete emotion approach lacks an overarching framework that can incorporate and integrate the wide range of possible emotional states. Dimensional approaches that conceptualize emotions in terms of universal core affective characteristics (e.g. valence (positivity versus negativity) and arousal) can provide such a framework. Here, we bring together discrete and dimensional approaches to: (i) offer a structure for integrating different discrete emotions that provides a functional perspective on the adaptive value of emotional states, (ii) suggest how long-term mood states arise from short-term discrete emotions, how they also influence these discrete emotions through a bi-directional relationship and how they may function to guide decision-making, and (iii) generate novel hypothesis-driven measures of animal emotion and mood. PMID:20685706

An integrative and functional framework for the study of animal emotion and mood.

PubMed

Mendl, Michael; Burman, Oliver H P; Paul, Elizabeth S

2010-10-07

A better understanding of animal emotion is an important goal in disciplines ranging from neuroscience to animal welfare science. The conscious experience of emotion cannot be assessed directly, but neural, behavioural and physiological indicators of emotion can be measured. Researchers have used these measures to characterize how animals respond to situations assumed to induce discrete emotional states (e.g. fear). While advancing our understanding of specific emotions, this discrete emotion approach lacks an overarching framework that can incorporate and integrate the wide range of possible emotional states. Dimensional approaches that conceptualize emotions in terms of universal core affective characteristics (e.g. valence (positivity versus negativity) and arousal) can provide such a framework. Here, we bring together discrete and dimensional approaches to: (i) offer a structure for integrating different discrete emotions that provides a functional perspective on the adaptive value of emotional states, (ii) suggest how long-term mood states arise from short-term discrete emotions, how they also influence these discrete emotions through a bi-directional relationship and how they may function to guide decision-making, and (iii) generate novel hypothesis-driven measures of animal emotion and mood.

The Neural Correlates of Deficient Error Awareness in Attention-Deficit Hyperactivity Disorder (ADHD)

ERIC Educational Resources Information Center

O'Connell, Redmond G.; Bellgrove, Mark A.; Dockree, Paul M.; Lau, Adam; Hester, Robert; Garavan, Hugh; Fitzgerald, Michael; Foxe, John J.; Robertson, Ian H.

2009-01-01

The ability to detect and correct errors is critical to adaptive control of behaviour and represents a discrete neuropsychological function. A number of studies have highlighted that attention-deficit hyperactivity disorder (ADHD) is associated with abnormalities in behavioural and neural responsiveness to performance errors. One limitation of…

Goal-based h-adaptivity of the 1-D diamond difference discrete ordinate method

NASA Astrophysics Data System (ADS)

Jeffers, R. S.; Kópházi, J.; Eaton, M. D.; Févotte, F.; Hülsemann, F.; Ragusa, J.

2017-04-01

The quantity of interest (QoI) associated with a solution of a partial differential equation (PDE) is not, in general, the solution itself, but a functional of the solution. Dual weighted residual (DWR) error estimators are one way of providing an estimate of the error in the QoI resulting from the discretisation of the PDE. This paper aims to provide an estimate of the error in the QoI due to the spatial discretisation, where the discretisation scheme being used is the diamond difference (DD) method in space and discrete ordinate (SN) method in angle. The QoI are reaction rates in detectors and the value of the eigenvalue (Keff) for 1-D fixed source and eigenvalue (Keff criticality) neutron transport problems respectively. Local values of the DWR over individual cells are used as error indicators for goal-based mesh refinement, which aims to give an optimal mesh for a given QoI.

Sparsity enabled cluster reduced-order models for control

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J. Nathan; Brunton, Bingni W.; Brunton, Steven L.

2018-01-01

Characterizing and controlling nonlinear, multi-scale phenomena are central goals in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron-Frobenius operator, resulting in a probabilistic model for ensembles of trajectories. A key advantage of CROM is that it embeds nonlinear dynamics in a linear framework, which enables the application of standard linear techniques to the nonlinear system. CROM is typically computed on high-dimensional data; however, access to and computations on this full-state data limit the online implementation of CROM for prediction and control. Here, we address this key challenge by identifying a small subset of critical measurements to learn an efficient CROM, referred to as sparsity-enabled CROM. In particular, we leverage compressive measurements to faithfully embed the cluster geometry and preserve the probabilistic dynamics. Further, we show how to identify fewer optimized sensor locations tailored to a specific problem that outperform random measurements. Both of these sparsity-enabled sensing strategies significantly reduce the burden of data acquisition and processing for low-latency in-time estimation and control. We illustrate this unsupervised learning approach on three different high-dimensional nonlinear dynamical systems from fluids with increasing complexity, with one application in flow control. Sparsity-enabled CROM is a critical facilitator for real-time implementation on high-dimensional systems where full-state information may be inaccessible.

Progress in multi-dimensional upwind differencing

NASA Technical Reports Server (NTRS)

Vanleer, Bram

1992-01-01

Multi-dimensional upwind-differencing schemes for the Euler equations are reviewed. On the basis of the first-order upwind scheme for a one-dimensional convection equation, the two approaches to upwind differencing are discussed: the fluctuation approach and the finite-volume approach. The usual extension of the finite-volume method to the multi-dimensional Euler equations is not entirely satisfactory, because the direction of wave propagation is always assumed to be normal to the cell faces. This leads to smearing of shock and shear waves when these are not grid-aligned. Multi-directional methods, in which upwind-biased fluxes are computed in a frame aligned with a dominant wave, overcome this problem, but at the expense of robustness. The same is true for the schemes incorporating a multi-dimensional wave model not based on multi-dimensional data but on an 'educated guess' of what they could be. The fluctuation approach offers the best possibilities for the development of genuinely multi-dimensional upwind schemes. Three building blocks are needed for such schemes: a wave model, a way to achieve conservation, and a compact convection scheme. Recent advances in each of these components are discussed; putting them all together is the present focus of a worldwide research effort. Some numerical results are presented, illustrating the potential of the new multi-dimensional schemes.

Temperature-dependent errors in nuclear lattice simulations

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

Lee, Dean; Thomson, Richard

2007-06-15

We study the temperature dependence of discretization errors in nuclear lattice simulations. We find that for systems with strong attractive interactions the predominant error arises from the breaking of Galilean invariance. We propose a local 'well-tempered' lattice action which eliminates much of this error. The well-tempered action can be readily implemented in lattice simulations for nuclear systems as well as cold atomic Fermi systems.

A high precision dual feedback discrete control system designed for satellite trajectory simulator

NASA Astrophysics Data System (ADS)

Liu, Ximin; Liu, Liren; Sun, Jianfeng; Xu, Nan

2005-08-01

Cooperating with the free-space laser communication terminals, the satellite trajectory simulator is used to test the acquisition, pointing, tracking and communicating performances of the terminals. So the satellite trajectory simulator plays an important role in terminal ground test and verification. Using the double-prism, Sun etc in our group designed a satellite trajectory simulator. In this paper, a high precision dual feedback discrete control system designed for the simulator is given and a digital fabrication of the simulator is made correspondingly. In the dual feedback discrete control system, Proportional- Integral controller is used in velocity feedback loop and Proportional- Integral- Derivative controller is used in position feedback loop. In the controller design, simplex method is introduced and an improvement to the method is made. According to the transfer function of the control system in Z domain, the digital fabrication of the simulator is given when it is exposed to mechanism error and moment disturbance. Typically, when the mechanism error is 100urad, the residual standard error of pitching angle, azimuth angle, x-coordinate position and y-coordinate position are 0.49urad, 6.12urad, 4.56urad, 4.09urad respectively. When the moment disturbance is 0.1rad, the residual standard error of pitching angle, azimuth angle, x-coordinate position and y-coordinate position are 0.26urad, 0.22urad, 0.16urad, 0.15urad respectively. The digital fabrication results demonstrate that the dual feedback discrete control system designed for the simulator can achieve the anticipated high precision performance.

Accurate position estimation methods based on electrical impedance tomography measurements

NASA Astrophysics Data System (ADS)

Vergara, Samuel; Sbarbaro, Daniel; Johansen, T. A.

2017-08-01

Electrical impedance tomography (EIT) is a technology that estimates the electrical properties of a body or a cross section. Its main advantages are its non-invasiveness, low cost and operation free of radiation. The estimation of the conductivity field leads to low resolution images compared with other technologies, and high computational cost. However, in many applications the target information lies in a low intrinsic dimensionality of the conductivity field. The estimation of this low-dimensional information is addressed in this work. It proposes optimization-based and data-driven approaches for estimating this low-dimensional information. The accuracy of the results obtained with these approaches depends on modelling and experimental conditions. Optimization approaches are sensitive to model discretization, type of cost function and searching algorithms. Data-driven methods are sensitive to the assumed model structure and the data set used for parameter estimation. The system configuration and experimental conditions, such as number of electrodes and signal-to-noise ratio (SNR), also have an impact on the results. In order to illustrate the effects of all these factors, the position estimation of a circular anomaly is addressed. Optimization methods based on weighted error cost functions and derivate-free optimization algorithms provided the best results. Data-driven approaches based on linear models provided, in this case, good estimates, but the use of nonlinear models enhanced the estimation accuracy. The results obtained by optimization-based algorithms were less sensitive to experimental conditions, such as number of electrodes and SNR, than data-driven approaches. Position estimation mean squared errors for simulation and experimental conditions were more than twice for the optimization-based approaches compared with the data-driven ones. The experimental position estimation mean squared error of the data-driven models using a 16-electrode setup was less than 0.05% of the tomograph radius value. These results demonstrate that the proposed approaches can estimate an object’s position accurately based on EIT measurements if enough process information is available for training or modelling. Since they do not require complex calculations it is possible to use them in real-time applications without requiring high-performance computers.

Sinc-Galerkin estimation of diffusivity in parabolic problems

NASA Technical Reports Server (NTRS)

Smith, Ralph C.; Bowers, Kenneth L.

1991-01-01

A fully Sinc-Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newton/trust region algorithm. The L-curve technique for determining an approximate value of the regularization parameter is briefly discussed, and numerical examples are given which show the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.

A framework for discrete stochastic simulation on 3D moving boundary domains

DOE PAGES

Drawert, Brian; Hellander, Stefan; Trogdon, Michael; ...

2016-11-14

We have developed a method for modeling spatial stochastic biochemical reactions in complex, three-dimensional, and time-dependent domains using the reaction-diffusion master equation formalism. In particular, we look to address the fully coupled problems that arise in systems biology where the shape and mechanical properties of a cell are determined by the state of the biochemistry and vice versa. To validate our method and characterize the error involved, we compare our results for a carefully constructed test problem to those of a microscale implementation. Finally, we demonstrate the effectiveness of our method by simulating a model of polarization and shmoo formationmore » during the mating of yeast. The method is generally applicable to problems in systems biology where biochemistry and mechanics are coupled, and spatial stochastic effects are critical.« less

Measured and calculated fast neutron spectra in a depleted uranium and lithium hydride shielded reactor

NASA Technical Reports Server (NTRS)

Lahti, G. P.; Mueller, R. A.

1973-01-01

Measurements of MeV neutron were made at the surface of a lithium hydride and depleted uranium shielded reactor. Four shield configurations were considered: these were assembled progressively with cylindrical shells of 5-centimeter-thick depleted uranium, 13-centimeter-thick lithium hydride, 5-centimeter-thick depleted uranium, 13-centimeter-thick lithium hydride, 5-centimeter-thick depleted uranium, and 3-centimeter-thick depleted uranium. Measurements were made with a NE-218 scintillation spectrometer; proton pulse height distributions were differentiated to obtain neutron spectra. Calculations were made using the two-dimensional discrete ordinates code DOT and ENDF/B (version 3) cross sections. Good agreement between measured and calculated spectral shape was observed. Absolute measured and calculated fluxes were within 50 percent of one another; observed discrepancies in absolute flux may be due to cross section errors.

An assessment of some non-gray global radiation models in enclosures

NASA Astrophysics Data System (ADS)

Meulemans, J.

2016-01-01

The accuracy of several non-gray global gas/soot radiation models, namely the Wide-Band Correlated-K (WBCK) model, the Spectral Line Weighted-sum-of-gray-gases model with one optimized gray gas (SLW-1), the (non-gray) Weighted-Sum-of-Gray-Gases (WSGG) model with different sets of coefficients (Smith et al., Soufiani and Djavdan, Taylor and Foster) was assessed on several test cases from the literature. Non-isothermal (or isothermal) participating media containing non-homogeneous (or homogeneous) mixtures of water vapor, carbon dioxide and soot in one-dimensional planar enclosures and multi-dimensional rectangular enclosures were investigated. For all the considered test cases, a benchmark solution (LBL or SNB) was used in order to compute the relative error of each model on the predicted radiative source term and the wall net radiative heat flux.

An upwind multigrid method for solving viscous flows on unstructured triangular meshes. M.S. Thesis

NASA Technical Reports Server (NTRS)

Bonhaus, Daryl Lawrence

1993-01-01

A multigrid algorithm is combined with an upwind scheme for solving the two dimensional Reynolds averaged Navier-Stokes equations on triangular meshes resulting in an efficient, accurate code for solving complex flows around multiple bodies. The relaxation scheme uses a backward-Euler time difference and relaxes the resulting linear system using a red-black procedure. Roe's flux-splitting scheme is used to discretize convective and pressure terms, while a central difference is used for the diffusive terms. The multigrid scheme is demonstrated for several flows around single and multi-element airfoils, including inviscid, laminar, and turbulent flows. The results show an appreciable speed up of the scheme for inviscid and laminar flows, and dramatic increases in efficiency for turbulent cases, especially those on increasingly refined grids.

Multi-dimensional roles of ketone bodies in fuel metabolism, signaling, and therapeutics

PubMed Central

Puchalska, Patrycja; Crawford, Peter A.

2017-01-01

Ketone body metabolism is a central node in physiological homeostasis. In this review, we discuss how ketones serve discrete fine-tuning metabolic roles that optimize organ and organism performance in varying nutrient states, and protect from inflammation and injury in multiple organ systems. Traditionally viewed as metabolic substrates enlisted only in carbohydrate restriction, recent observations underscore the importance of ketone bodies as vital metabolic and signaling mediators when carbohydrates are abundant. Complementing a repertoire of known therapeutic options for diseases of the nervous system, prospective roles for ketone bodies in cancer have arisen, as have intriguing protective roles in heart and liver, opening therapeutic options in obesity-related and cardiovascular disease. Controversies in ketone metabolism and signaling are discussed to reconcile classical dogma with contemporary observations. PMID:28178565

A chaotic modified-DFT encryption scheme for physical layer security and PAPR reduction in OFDM-PON

NASA Astrophysics Data System (ADS)

Fu, Xiaosong; Bi, Meihua; Zhou, Xuefang; Yang, Guowei; Li, Qiliang; Zhou, Zhao; Yang, Xuelin

2018-05-01

This letter proposes a modified discrete Fourier transform (DFT) encryption scheme with multi-dimensional chaos for the physical layer security and peak-to-average power ratio (PAPR) reduction in orthogonal frequency division multiplexing passive optical network (OFDM-PON) system. This multiple-fold encryption algorithm is mainly composed by using the column vectors permutation and the random phase encryption in the standard DFT matrix, which can create ∼10551 key space. The transmission of ∼10 Gb/s encrypted OFDM signal is verified over 20-km standard single mode fiber (SMF). Moreover, experimental results show that, the proposed scheme can achieve ∼2.6-dB PAPR reduction and ∼1-dB improvement of receiver sensitivity if compared with the common OFDM-PON.

Non-polynomial extensions of solvable potentials à la Abraham-Moses

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

Odake, Satoru; Sasaki, Ryu; Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan

2013-10-15

Abraham-Moses transformations, besides Darboux transformations, are well-known procedures to generate extensions of solvable potentials in one-dimensional quantum mechanics. Here we present the explicit forms of infinitely many seed solutions for adding eigenstates at arbitrary real energy through the Abraham-Moses transformations for typical solvable potentials, e.g., the radial oscillator, the Darboux-Pöschl-Teller, and some others. These seed solutions are simple generalisations of the virtual state wavefunctions, which are obtained from the eigenfunctions by discrete symmetries of the potentials. The virtual state wavefunctions have been an essential ingredient for constructing multi-indexed Laguerre and Jacobi polynomials through multiple Darboux-Crum transformations. In contrast to themore » Darboux transformations, the virtual state wavefunctions generate non-polynomial extensions of solvable potentials through the Abraham-Moses transformations.« less

Quasi two-dimensional astigmatic solitons in soft chiral metastructures

NASA Astrophysics Data System (ADS)

Laudyn, Urszula A.; Jung, Paweł S.; Karpierz, Mirosław A.; Assanto, Gaetano

2016-03-01

We investigate a non-homogeneous layered structure encompassing dual spatial dispersion: continuous diffraction in one transverse dimension and discrete diffraction in the orthogonal one. Such dual diffraction can be balanced out by one and the same nonlinear response, giving rise to light self-confinement into astigmatic spatial solitons: self-focusing can compensate for the spreading of a bell-shaped beam, leading to quasi-2D solitary wavepackets which result from 1D transverse self-localization combined with a discrete soliton. We demonstrate such intensity-dependent beam trapping in chiral soft matter, exhibiting one-dimensional discrete diffraction along the helical axis and one-dimensional continuous diffraction in the orthogonal plane. In nematic liquid crystals with suitable birefringence and chiral arrangement, the reorientational nonlinearity is shown to support bell-shaped solitary waves with simple astigmatism dependent on the medium birefringence as well as on the dual diffraction of the input wavepacket. The observations are in agreement with a nonlinear nonlocal model for the all-optical response.

Study of discrete-particle effects in a one-dimensional plasma simulation with the Krook type collision model

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

Lai, Po-Yen; Chen, Liu; Institute for Fusion Theory and Simulation, Zhejiang University, 310027 Hangzhou

2015-09-15

The thermal relaxation time of a one-dimensional plasma has been demonstrated to scale with N{sub D}{sup 2} due to discrete particle effects by collisionless particle-in-cell (PIC) simulations, where N{sub D} is the particle number in a Debye length. The N{sub D}{sup 2} scaling is consistent with the theoretical analysis based on the Balescu-Lenard-Landau kinetic equation. However, it was found that the thermal relaxation time is anomalously shortened to scale with N{sub D} while externally introducing the Krook type collision model in the one-dimensional electrostatic PIC simulation. In order to understand the discrete particle effects enhanced by the Krook type collisionmore » model, the superposition principle of dressed test particles was applied to derive the modified Balescu-Lenard-Landau kinetic equation. The theoretical results are shown to be in good agreement with the simulation results when the collisional effects dominate the plasma system.« less

Cursor Control Device Test Battery

NASA Technical Reports Server (NTRS)

Holden, Kritina; Sandor, Aniko; Pace, John; Thompson, Shelby

2013-01-01

The test battery was developed to provide a standard procedure for cursor control device evaluation. The software was built in Visual Basic and consists of nine tasks and a main menu that integrates the set-up of the tasks. The tasks can be used individually, or in a series defined in the main menu. Task 1, the Unidirectional Pointing Task, tests the speed and accuracy of clicking on targets. Two rectangles with an adjustable width and adjustable center- to-center distance are presented. The task is to click back and forth between the two rectangles. Clicks outside of the rectangles are recorded as errors. Task 2, Multidirectional Pointing Task, measures speed and accuracy of clicking on targets approached from different angles. Twenty-five numbered squares of adjustable width are arranged around an adjustable diameter circle. The task is to point and click on the numbered squares (placed on opposite sides of the circle) in consecutive order. Clicks outside of the squares are recorded as errors. Task 3, Unidirectional (horizontal) Dragging Task, is similar to dragging a file into a folder on a computer desktop. Task 3 requires dragging a square of adjustable width from one rectangle and dropping it into another. The width of each rectangle is adjustable, as well as the distance between the two rectangles. Dropping the square outside of the rectangles is recorded as an error. Task 4, Unidirectional Path Following, is similar to Task 3. The task is to drag a square through a tunnel consisting of two lines. The size of the square and the width of the tunnel are adjustable. If the square touches any of the lines, it is counted as an error and the task is restarted. Task 5, Text Selection, involves clicking on a Start button, and then moving directly to the underlined portion of the displayed text and highlighting it. The pointing distance to the text is adjustable, as well as the to-be-selected font size and the underlined character length. If the selection does not include all of the underlined characters, or includes non-underlined characters, it is recorded as an error. Task 6, Multi-size and Multi-distance Pointing, presents the participant with 24 consecutively numbered buttons of different sizes (63 to 163 pixels), and at different distances (60 to 80 pixels) from the Start button. The task is to click on the Start button, and then move directly to, and click on, each numbered target button in consecutive order. Clicks outside of the target area are errors. Task 7, Standard Interface Elements Task, involves interacting with standard interface elements as instructed in written procedures, including: drop-down menus, sliders, text boxes, radio buttons, and check boxes. Task completion time is recorded. In Task 8, a circular track is presented with a disc in it at the top. Track width and disc size are adjustable. The task is to move the disc with circular motion within the path without touching the boundaries of the track. Time and errors are recorded. Task 9 is a discrete task that allows evaluation of discrete cursor control devices that tab from target to target, such as a castle switch. The task is to follow a predefined path and to click on the yellow targets along the path.

Empirical Bayes Approaches to Multivariate Fuzzy Partitions.

ERIC Educational Resources Information Center

Woodbury, Max A.; Manton, Kenneth G.

1991-01-01

An empirical Bayes-maximum likelihood estimation procedure is presented for the application of fuzzy partition models in describing high dimensional discrete response data. The model describes individuals in terms of partial membership in multiple latent categories that represent bounded discrete spaces. (SLD)

A comparison of medication administration errors from original medication packaging and multi-compartment compliance aids in care homes: A prospective observational study.

PubMed

Gilmartin-Thomas, Julia Fiona-Maree; Smith, Felicity; Wolfe, Rory; Jani, Yogini

2017-07-01

No published study has been specifically designed to compare medication administration errors between original medication packaging and multi-compartment compliance aids in care homes, using direct observation. Compare the effect of original medication packaging and multi-compartment compliance aids on medication administration accuracy. Prospective observational. Ten Greater London care homes. Nurses and carers administering medications. Between October 2014 and June 2015, a pharmacist researcher directly observed solid, orally administered medications in tablet or capsule form at ten purposively sampled care homes (five only used original medication packaging and five used both multi-compartment compliance aids and original medication packaging). The medication administration error rate was calculated as the number of observed doses administered (or omitted) in error according to medication administration records, compared to the opportunities for error (total number of observed doses plus omitted doses). Over 108.4h, 41 different staff (35 nurses, 6 carers) were observed to administer medications to 823 residents during 90 medication administration rounds. A total of 2452 medication doses were observed (1385 from original medication packaging, 1067 from multi-compartment compliance aids). One hundred and seventy eight medication administration errors were identified from 2493 opportunities for error (7.1% overall medication administration error rate). A greater medication administration error rate was seen for original medication packaging than multi-compartment compliance aids (9.3% and 3.1% respectively, risk ratio (RR)=3.9, 95% confidence interval (CI) 2.4 to 6.1, p<0.001). Similar differences existed when comparing medication administration error rates between original medication packaging (from original medication packaging-only care homes) and multi-compartment compliance aids (RR=2.3, 95%CI 1.1 to 4.9, p=0.03), and between original medication packaging and multi-compartment compliance aids within care homes that used a combination of both medication administration systems (RR=4.3, 95%CI 2.7 to 6.8, p<0.001). A significant difference in error rate was not observed between use of a single or combination medication administration system (p=0.44). The significant difference in, and high overall, medication administration error rate between original medication packaging and multi-compartment compliance aids supports the use of the latter in care homes, as well as local investigation of tablet and capsule impact on medication administration errors and staff training to prevent errors occurring. As a significant difference in error rate was not observed between use of a single or combination medication administration system, common practice of using both multi-compartment compliance aids (for most medications) and original packaging (for medications with stability issues) is supported. Copyright © 2017 Elsevier Ltd. All rights reserved.

Process for producing dispersed particulate composite materials

DOEpatents

Henager, Jr., Charles H.; Hirth, John P.

1995-01-01

This invention is directed to a process for forming noninterwoven dispersed particulate composite products. In one case a composite multi-layer film product comprises a substantially noninterwoven multi-layer film having a plurality of discrete layers. This noninterwoven film comprises at least one discrete layer of a first material and at least one discrete layer of a second material. In another case the first and second materials are blended together with each other. In either case, the first material comprises a metalloid and the second material a metal compound. At least one component of a first material in one discrete layer undergoes a solid state displacement reaction with at least one component of a second material thereby producing the requisite noninterwoven composite film product. Preferably, the first material comprises silicon, the second material comprises Mo.sub.2 C, the third material comprises SiC and the fourth material comprises MoSi.sub.2.

Noise Propagation and Uncertainty Quantification in Hybrid Multiphysics Models: Initiation and Reaction Propagation in Energetic Materials

DTIC Science & Technology

2016-05-23

general model for heterogeneous granular media under compaction and (ii) the lack of a reliable multiscale discrete -to-continuum framework for...dynamics. These include a continuum- discrete model of heat dissipation/diffusion and a continuum- discrete model of compaction of a granular material with...the lack of a general model for het- erogeneous granular media under compac- tion and (ii) the lack of a reliable multi- scale discrete -to-continuum

Optimal generalized multistep integration formulae for real-time digital simulation

NASA Technical Reports Server (NTRS)

Moerder, D. D.; Halyo, N.

1985-01-01

The problem of discretizing a dynamical system for real-time digital simulation is considered. Treating the system and its simulation as stochastic processes leads to a statistical characterization of simulator fidelity. A plant discretization procedure based on an efficient matrix generalization of explicit linear multistep discrete integration formulae is introduced, which minimizes a weighted sum of the mean squared steady-state and transient error between the system and simulator outputs.

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1997-01-01

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1997-01-01

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Tbeodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modem three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Results of the Simulation of the HTR-Proteus Core 4.2 Using PEBBED-COMBINE: FY10 Report

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

Hans Gougar

2010-07-01

ABSTRACT The Idaho National Laboratory’s deterministic neutronics analysis codes and methods were applied to the computation of the core multiplication factor of the HTR-Proteus pebble bed reactor critical facility. This report is a follow-on to INL/EXT-09-16620 in which the same calculation was performed but using earlier versions of the codes and less developed methods. In that report, results indicated that the cross sections generated using COMBINE-7.0 did not yield satisfactory estimates of keff. It was concluded in the report that the modeling of control rods was not satisfactory. In the past year, improvements to the homogenization capability in COMBINE havemore » enabled the explicit modeling of TRIS particles, pebbles, and heterogeneous core zones including control rod regions using a new multi-scale version of COMBINE in which the 1-dimensional discrete ordinate transport code ANISN has been integrated. The new COMBINE is shown to yield benchmark quality results for pebble unit cell models, the first step in preparing few-group diffusion parameters for core simulations. In this report, the full critical core is modeled once again but with cross sections generated using the capabilities and physics of the improved COMBINE code. The new PEBBED-COMBINE model enables the exact modeling of the pebbles and control rod region along with better approximation to structures in the reflector. Initial results for the core multiplication factor indicate significant improvement in the INL’s tools for modeling the neutronic properties of a pebble bed reactor. Errors on the order of 1.6-2.5% in keff are obtained; a significant improvement over the 5-6% error observed in the earlier This is acceptable for a code system and model in the early stages of development but still too high for a production code. Analysis of a simpler core model indicates an over-prediction of the flux in the low end of the thermal spectrum. Causes of this discrepancy are under investigation. New homogenization techniques and assumptions were used in this analysis and as such, they require further confirmation and validation. Further refinement and review of the complex Proteus core model are likely to reduce the errors even further.« less

Surfactant 1-Hexadecyl-3-methylimidazolium Chloride Can Convert One-Dimensional Viologen Bromoplumbate into Zero-Dimensional.

PubMed

Liu, Guangfeng; Liu, Jie; Nie, Lina; Ban, Rui; Armatas, Gerasimos S; Tao, Xutang; Zhang, Qichun

2017-05-15

A zero-dimensional N,N'-dibutyl-4,4'-dipyridinium bromoplumbate, [BV] 6 [Pb 9 Br 30 ], with unusual discrete [Pb 9 Br 30 ] 12- anionic clusters was prepared via a facile surfactant-mediated solvothermal process. This bromoplumbate exhibits a narrower optical band gap relative to the congeneric one-dimensional viologen bromoplumbates.

5 CFR 1605.22 - Claims for correction of Board or TSP record keeper errors; time limitations.

Code of Federal Regulations, 2010 CFR

2010-01-01

... record keeper errors; time limitations. 1605.22 Section 1605.22 Administrative Personnel FEDERAL... § 1605.22 Claims for correction of Board or TSP record keeper errors; time limitations. (a) Filing claims... after that time, the Board or TSP record keeper may use its sound discretion in deciding whether to...