CT-derived Biomechanical Metrics Improve Agreement Between Spirometry and Emphysema

PubMed Central

Bhatt, Surya P.; Bodduluri, Sandeep; Newell, John D.; Hoffman, Eric A.; Sieren, Jessica C.; Han, Meilan K.; Dransfield, Mark T.; Reinhardt, Joseph M.

2016-01-01

Rationale and Objectives Many COPD patients have marked discordance between FEV1 and degree of emphysema on CT. Biomechanical differences between these patients have not been studied. We aimed to identify reasons for the discordance between CT and spirometry in some patients with COPD. Materials and Methods Subjects with GOLD stage I–IV from a large multicenter study (COPDGene) were arranged by percentiles of %predicted FEV1 and emphysema on CT. Three categories were created using differences in percentiles: Catspir with predominant airflow obstruction/minimal emphysema, CatCT with predominant emphysema/minimal airflow obstruction, and Catmatched with matched FEV1 and emphysema. Image registration was used to derive Jacobian determinants, a measure of lung elasticity, anisotropy and strain tensors, to assess biomechanical differences between groups. Regression models were created with the above categories as outcome variable, adjusting for demographics, scanner type, quantitative CT-derived emphysema, gas trapping, and airway thickness (Model 1), and after adding biomechanical CT metrics (Model 2). Results Jacobian determinants, anisotropy and strain tensors were strongly associated with FEV1. With Catmatched as control, Model 2 predicted Catspir and CatCT better than Model 1 (Akaike Information Criterion, AIC 255.8 vs. 320.8). In addition to demographics, the strongest independent predictors of FEV1 were Jacobian mean (β= 1.60,95%CI = 1.16 to 1.98; p<0.001), coefficient of variation (CV) of Jacobian (β= 1.45,95%CI = 0.86 to 2.03; p<0.001) and CV strain (β= 1.82,95%CI = 0.68 to 2.95; p = 0.001). CVs of Jacobian and strain are both potential markers of biomechanical lung heterogeneity. Conclusions CT-derived measures of lung mechanics improve the link between quantitative CT and spirometry, offering the potential for new insights into the linkage between regional parenchymal destruction and global decrement in lung function in COPD patients. PMID:27055745

Algorithmic vs. finite difference Jacobians for infrared atmospheric radiative transfer

NASA Astrophysics Data System (ADS)

Schreier, Franz; Gimeno García, Sebastián; Vasquez, Mayte; Xu, Jian

2015-10-01

Jacobians, i.e. partial derivatives of the radiance and transmission spectrum with respect to the atmospheric state parameters to be retrieved from remote sensing observations, are important for the iterative solution of the nonlinear inverse problem. Finite difference Jacobians are easy to implement, but computationally expensive and possibly of dubious quality; on the other hand, analytical Jacobians are accurate and efficient, but the implementation can be quite demanding. GARLIC, our "Generic Atmospheric Radiation Line-by-line Infrared Code", utilizes algorithmic differentiation (AD) techniques to implement derivatives w.r.t. atmospheric temperature and molecular concentrations. In this paper, we describe our approach for differentiation of the high resolution infrared and microwave spectra and provide an in-depth assessment of finite difference approximations using "exact" AD Jacobians as a reference. The results indicate that the "standard" two-point finite differences with 1 K and 1% perturbation for temperature and volume mixing ratio, respectively, can exhibit substantial errors, and central differences are significantly better. However, these deviations do not transfer into the truncated singular value decomposition solution of a least squares problem. Nevertheless, AD Jacobians are clearly recommended because of the superior speed and accuracy.

pyJac: Analytical Jacobian generator for chemical kinetics

NASA Astrophysics Data System (ADS)

Niemeyer, Kyle E.; Curtis, Nicholas J.; Sung, Chih-Jen

2017-06-01

Accurate simulations of combustion phenomena require the use of detailed chemical kinetics in order to capture limit phenomena such as ignition and extinction as well as predict pollutant formation. However, the chemical kinetic models for hydrocarbon fuels of practical interest typically have large numbers of species and reactions and exhibit high levels of mathematical stiffness in the governing differential equations, particularly for larger fuel molecules. In order to integrate the stiff equations governing chemical kinetics, generally reactive-flow simulations rely on implicit algorithms that require frequent Jacobian matrix evaluations. Some in situ and a posteriori computational diagnostics methods also require accurate Jacobian matrices, including computational singular perturbation and chemical explosive mode analysis. Typically, finite differences numerically approximate these, but for larger chemical kinetic models this poses significant computational demands since the number of chemical source term evaluations scales with the square of species count. Furthermore, existing analytical Jacobian tools do not optimize evaluations or support emerging SIMD processors such as GPUs. Here we introduce pyJac, a Python-based open-source program that generates analytical Jacobian matrices for use in chemical kinetics modeling and analysis. In addition to producing the necessary customized source code for evaluating reaction rates (including all modern reaction rate formulations), the chemical source terms, and the Jacobian matrix, pyJac uses an optimized evaluation order to minimize computational and memory operations. As a demonstration, we first establish the correctness of the Jacobian matrices for kinetic models of hydrogen, methane, ethylene, and isopentanol oxidation (number of species ranging 13-360) by showing agreement within 0.001% of matrices obtained via automatic differentiation. We then demonstrate the performance achievable on CPUs and GPUs using pyJac via matrix evaluation timing comparisons; the routines produced by pyJac outperformed first-order finite differences by 3-7.5 times and the existing analytical Jacobian software TChem by 1.1-2.2 times on a single-threaded basis. It is noted that TChem is not thread-safe, while pyJac is easily parallelized, and hence can greatly outperform TChem on multicore CPUs. The Jacobian matrix generator we describe here will be useful for reducing the cost of integrating chemical source terms with implicit algorithms in particular and algorithms that require an accurate Jacobian matrix in general. Furthermore, the open-source release of the program and Python-based implementation will enable wide adoption.

A systematic study of finite BRST-BFV transformations in generalized Hamiltonian formalism

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2014-09-01

We study systematically finite BRST-BFV transformations in the generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate an arbitrary finite change of gauge-fixing functions in the path integral.

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries.

PubMed

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-15

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 - 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

A Newton–Krylov method with an approximate analytical Jacobian for implicit solution of Navier–Stokes equations on staggered overset-curvilinear grids with immersed boundaries

PubMed Central

Asgharzadeh, Hafez; Borazjani, Iman

2016-01-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 – 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80–90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future. PMID:28042172

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries

NASA Astrophysics Data System (ADS)

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for non-linear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form a preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42-74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal and full Jacobian, respectivley, when the stretching factor was increased. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

Principal Component Geostatistical Approach for large-dimensional inverse problems

PubMed Central

Kitanidis, P K; Lee, J

2014-01-01

The quasi-linear geostatistical approach is for weakly nonlinear underdetermined inverse problems, such as Hydraulic Tomography and Electrical Resistivity Tomography. It provides best estimates as well as measures for uncertainty quantification. However, for its textbook implementation, the approach involves iterations, to reach an optimum, and requires the determination of the Jacobian matrix, i.e., the derivative of the observation function with respect to the unknown. Although there are elegant methods for the determination of the Jacobian, the cost is high when the number of unknowns, m, and the number of observations, n, is high. It is also wasteful to compute the Jacobian for points away from the optimum. Irrespective of the issue of computing derivatives, the computational cost of implementing the method is generally of the order of m2n, though there are methods to reduce the computational cost. In this work, we present an implementation that utilizes a matrix free in terms of the Jacobian matrix Gauss-Newton method and improves the scalability of the geostatistical inverse problem. For each iteration, it is required to perform K runs of the forward problem, where K is not just much smaller than m but can be smaller that n. The computational and storage cost of implementation of the inverse procedure scales roughly linearly with m instead of m2 as in the textbook approach. For problems of very large m, this implementation constitutes a dramatic reduction in computational cost compared to the textbook approach. Results illustrate the validity of the approach and provide insight in the conditions under which this method perform best. PMID:25558113

Principal Component Geostatistical Approach for large-dimensional inverse problems.

PubMed

Kitanidis, P K; Lee, J

2014-07-01

The quasi-linear geostatistical approach is for weakly nonlinear underdetermined inverse problems, such as Hydraulic Tomography and Electrical Resistivity Tomography. It provides best estimates as well as measures for uncertainty quantification. However, for its textbook implementation, the approach involves iterations, to reach an optimum, and requires the determination of the Jacobian matrix, i.e., the derivative of the observation function with respect to the unknown. Although there are elegant methods for the determination of the Jacobian, the cost is high when the number of unknowns, m , and the number of observations, n , is high. It is also wasteful to compute the Jacobian for points away from the optimum. Irrespective of the issue of computing derivatives, the computational cost of implementing the method is generally of the order of m 2 n , though there are methods to reduce the computational cost. In this work, we present an implementation that utilizes a matrix free in terms of the Jacobian matrix Gauss-Newton method and improves the scalability of the geostatistical inverse problem. For each iteration, it is required to perform K runs of the forward problem, where K is not just much smaller than m but can be smaller that n . The computational and storage cost of implementation of the inverse procedure scales roughly linearly with m instead of m 2 as in the textbook approach. For problems of very large m , this implementation constitutes a dramatic reduction in computational cost compared to the textbook approach. Results illustrate the validity of the approach and provide insight in the conditions under which this method perform best.

A systematic study of finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2014-09-01

We study systematically finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.

Generating log-normal mock catalog of galaxies in redshift space

NASA Astrophysics Data System (ADS)

Agrawal, Aniket; Makiya, Ryu; Chiang, Chi-Ting; Jeong, Donghui; Saito, Shun; Komatsu, Eiichiro

2017-10-01

We present a public code to generate a mock galaxy catalog in redshift space assuming a log-normal probability density function (PDF) of galaxy and matter density fields. We draw galaxies by Poisson-sampling the log-normal field, and calculate the velocity field from the linearised continuity equation of matter fields, assuming zero vorticity. This procedure yields a PDF of the pairwise velocity fields that is qualitatively similar to that of N-body simulations. We check fidelity of the catalog, showing that the measured two-point correlation function and power spectrum in real space agree with the input precisely. We find that a linear bias relation in the power spectrum does not guarantee a linear bias relation in the density contrasts, leading to a cross-correlation coefficient of matter and galaxies deviating from unity on small scales. We also find that linearising the Jacobian of the real-to-redshift space mapping provides a poor model for the two-point statistics in redshift space. That is, non-linear redshift-space distortion is dominated by non-linearity in the Jacobian. The power spectrum in redshift space shows a damping on small scales that is qualitatively similar to that of the well-known Fingers-of-God (FoG) effect due to random velocities, except that the log-normal mock does not include random velocities. This damping is a consequence of non-linearity in the Jacobian, and thus attributing the damping of the power spectrum solely to FoG, as commonly done in the literature, is misleading.

Modular Expression Language for Ordinary Differential Equation Editing

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

Blake, Robert C.

MELODEEis a system for describing systems of initial value problem ordinary differential equations, and a compiler for the language that produces optimized code to integrate the differential equations. Features include rational polynomial approximation for expensive functions and automatic differentiation for symbolic jacobians

Implicit solution of Navier-Stokes equations on staggered curvilinear grids using a Newton-Krylov method with a novel analytical Jacobian.

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Asgharzadeh, Hafez

2015-11-01

Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.

Generating log-normal mock catalog of galaxies in redshift space

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

Agrawal, Aniket; Makiya, Ryu; Saito, Shun

We present a public code to generate a mock galaxy catalog in redshift space assuming a log-normal probability density function (PDF) of galaxy and matter density fields. We draw galaxies by Poisson-sampling the log-normal field, and calculate the velocity field from the linearised continuity equation of matter fields, assuming zero vorticity. This procedure yields a PDF of the pairwise velocity fields that is qualitatively similar to that of N-body simulations. We check fidelity of the catalog, showing that the measured two-point correlation function and power spectrum in real space agree with the input precisely. We find that a linear biasmore » relation in the power spectrum does not guarantee a linear bias relation in the density contrasts, leading to a cross-correlation coefficient of matter and galaxies deviating from unity on small scales. We also find that linearising the Jacobian of the real-to-redshift space mapping provides a poor model for the two-point statistics in redshift space. That is, non-linear redshift-space distortion is dominated by non-linearity in the Jacobian. The power spectrum in redshift space shows a damping on small scales that is qualitatively similar to that of the well-known Fingers-of-God (FoG) effect due to random velocities, except that the log-normal mock does not include random velocities. This damping is a consequence of non-linearity in the Jacobian, and thus attributing the damping of the power spectrum solely to FoG, as commonly done in the literature, is misleading.« less

Reducing computational costs in large scale 3D EIT by using a sparse Jacobian matrix with block-wise CGLS reconstruction.

PubMed

Yang, C L; Wei, H Y; Adler, A; Soleimani, M

2013-06-01

Electrical impedance tomography (EIT) is a fast and cost-effective technique to provide a tomographic conductivity image of a subject from boundary current-voltage data. This paper proposes a time and memory efficient method for solving a large scale 3D EIT inverse problem using a parallel conjugate gradient (CG) algorithm. The 3D EIT system with a large number of measurement data can produce a large size of Jacobian matrix; this could cause difficulties in computer storage and the inversion process. One of challenges in 3D EIT is to decrease the reconstruction time and memory usage, at the same time retaining the image quality. Firstly, a sparse matrix reduction technique is proposed using thresholding to set very small values of the Jacobian matrix to zero. By adjusting the Jacobian matrix into a sparse format, the element with zeros would be eliminated, which results in a saving of memory requirement. Secondly, a block-wise CG method for parallel reconstruction has been developed. The proposed method has been tested using simulated data as well as experimental test samples. Sparse Jacobian with a block-wise CG enables the large scale EIT problem to be solved efficiently. Image quality measures are presented to quantify the effect of sparse matrix reduction in reconstruction results.

Finite BRST-BFV transformations for dynamical systems with second-class constraints

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2015-06-01

We study finite field-dependent BRST-BFV transformations for dynamical systems with first- and second-class constraints within the generalized Hamiltonian formalism. We find explicitly their Jacobians and the form of a solution to the compensation equation necessary for generating an arbitrary finite change of gauge-fixing functionals in the path integral.

Derivative matrices of a skew ray for spherical boundary surfaces and their applications in system analysis and design.

PubMed

Lin, Psang Dain

2014-05-10

In a previous paper [Appl. Opt.52, 4151 (2013)], we presented the first- and second-order derivatives of a ray for a flat boundary surface to design prisms. In this paper, that scheme is extended to determine the Jacobian and Hessian matrices of a skew ray as it is reflected/refracted at a spherical boundary surface. The validity of the proposed approach as an analysis and design tool is demonstrated using an axis-symmetrical system for illustration purpose. It is found that these two matrices can provide the search direction used by existing gradient-based schemes to minimize the merit function during the optimization stage of the optical system design process. It is also possible to make the optical system designs more automatic, if the image defects can be extracted from the Jacobian and Hessian matrices of a skew ray.

Efficient Jacobian inversion for the control of simple robot manipulators

NASA Technical Reports Server (NTRS)

Fijany, Amir; Bejczy, Antal K.

1988-01-01

Symbolic inversion of the Jacobian matrix for spherical wrist arms is investigated. It is shown that, taking advantage of the simple geometry of these arms, the closed-form solution of the system Q = J-1X, representing a transformation from task space to joint space, can be obtained very efficiently. The solutions for PUMA, Stanford, and a six-revolute-joint coplanar arm, along with all singular points, are presented. The solution for each joint variable is found as an explicit function of the singular points which provides a better insight into the effect of different singular points on the motion and force exertion of each individual joint. For the above arms, the computation cost of the solution is on the same order as the cost of forward kinematic solution and it is significantly reduced if forward kinematic solution is already obtained. A comparison with previous methods shows that this method is the most efficient to date.

A generalized chemistry version of SPARK

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.

1988-01-01

An extension of the reacting H2-air computer code SPARK is presented, which enables the code to be used on any reacting flow problem. Routines are developed calculating in a general fashion, the reaction rates, and chemical Jacobians of any reacting system. In addition, an equilibrium routine is added so that the code will have frozen, finite rate, and equilibrium capabilities. The reaction rate for the species is determined from the law of mass action using Arrhenius expressions for the rate constants. The Jacobian routines are determined by numerically or analytically differentiating the law of mass action for each species. The equilibrium routine is based on a Gibbs free energy minimization routine. The routines are written in FORTRAN 77, with special consideration given to vectorization. Run times for the generalized routines are generally 20 percent slower than reaction specific routines. The numerical efficiency of the generalized analytical Jacobian, however, is nearly 300 percent better than the reaction specific numerical Jacobian used in SPARK.

Methods for calculating the electrode position Jacobian for impedance imaging.

PubMed

Boyle, A; Crabb, M G; Jehl, M; Lionheart, W R B; Adler, A

2017-03-01

Electrical impedance tomography (EIT) or electrical resistivity tomography (ERT) current and measure voltages at the boundary of a domain through electrodes. The movement or incorrect placement of electrodes may lead to modelling errors that result in significant reconstructed image artifacts. These errors may be accounted for by allowing for electrode position estimates in the model. Movement may be reconstructed through a first-order approximation, the electrode position Jacobian. A reconstruction that incorporates electrode position estimates and conductivity can significantly reduce image artifacts. Conversely, if electrode position is ignored it can be difficult to distinguish true conductivity changes from reconstruction artifacts which may increase the risk of a flawed interpretation. In this work, we aim to determine the fastest, most accurate approach for estimating the electrode position Jacobian. Four methods of calculating the electrode position Jacobian were evaluated on a homogeneous halfspace. Results show that Fréchet derivative and rank-one update methods are competitive in computational efficiency but achieve different solutions for certain values of contact impedance and mesh density.

A formula for the entropy of the convolution of Gibbs probabilities on the circle

NASA Astrophysics Data System (ADS)

Lopes, Artur O.

2018-07-01

Consider the transformation , such that (mod 1), and where S 1 is the unitary circle. Suppose is Hölder continuous and positive, and moreover that, for any , we have that We say that ρ is a Gibbs probability for the Hölder continuous potential , if where is the Ruelle operator for . We call J the Jacobian of ρ. Suppose is the convolution of two Gibbs probabilities and associated, respectively, to and . We show that ν is also Gibbs and its Jacobian is given by . In this case, the entropy is given by the expression For a fixed we consider differentiable variations , , of on the Banach manifold of Gibbs probabilities, where , and we estimate the derivative of the entropy at t  =  0. We also present an expression for the Jacobian of the convolution of a Gibbs probability ρ with the invariant probability with support on a periodic orbit of period two. This expression is based on the Jacobian of ρ and two Radon–Nidodym derivatives.

Neural network uncertainty assessment using Bayesian statistics: a remote sensing application

NASA Technical Reports Server (NTRS)

Aires, F.; Prigent, C.; Rossow, W. B.

2004-01-01

Neural network (NN) techniques have proved successful for many regression problems, in particular for remote sensing; however, uncertainty estimates are rarely provided. In this article, a Bayesian technique to evaluate uncertainties of the NN parameters (i.e., synaptic weights) is first presented. In contrast to more traditional approaches based on point estimation of the NN weights, we assess uncertainties on such estimates to monitor the robustness of the NN model. These theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature, microwave surface emissivities, and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land. The weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs (i.e., error bars and correlation structure of these errors). Such quantities are very important for evaluating any application of an NN model. The uncertainties on the NN Jacobians are then considered in the third part of this article. Used for regression fitting, NN models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis is put on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the regression model. The complex structure of dependency inside the NN is the essence of the model, and assessing its quality, coherency, and physical character makes all the difference between a blackbox model with small output errors and a reliable, robust, and physically coherent model. Such dependency structures are described to the first order by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model for given input data. We use a Monte Carlo integration procedure to estimate the robustness of the NN Jacobians. A regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these Jacobians robust and physically meaningful.

Evaluation of Jacobian determinants by Monte Carlo methods: Application to the quasiclassical approximation in molecular scattering

NASA Technical Reports Server (NTRS)

Labudde, R. A.

1971-01-01

A technique is described which can be used to evaluate Jacobian determinants which occur in classical mechanical and quasiclassical approximation descriptions of molecular scattering. The method may be valuable in the study of reactive scattering using the quasiclassical approximation.

Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton–Krylov method

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-08-24

This study presents a numerical investigation on using the Jacobian-free Newton–Krylov (JFNK) method to solve the two-phase flow four-equation drift flux model with realistic constitutive correlations (‘closure models’). The drift flux model is based on Isshi and his collaborators’ work. Additional constitutive correlations for vertical channel flow, such as two-phase flow pressure drop, flow regime map, wall boiling and interfacial heat transfer models, were taken from the RELAP5-3D Code Manual and included to complete the model. The staggered grid finite volume method and fully implicit backward Euler method was used for the spatial discretization and time integration schemes, respectively. Themore » Jacobian-free Newton–Krylov method shows no difficulty in solving the two-phase flow drift flux model with a discrete flow regime map. In addition to the Jacobian-free approach, the preconditioning matrix is obtained by using the default finite differencing method provided in the PETSc package, and consequently the labor-intensive implementation of complex analytical Jacobian matrix is avoided. Extensive and successful numerical verification and validation have been performed to prove the correct implementation of the models and methods. Code-to-code comparison with RELAP5-3D has further demonstrated the successful implementation of the drift flux model.« less

Inversion Of Jacobian Matrix For Robot Manipulators

NASA Technical Reports Server (NTRS)

Fijany, Amir; Bejczy, Antal K.

1989-01-01

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

Flux Jacobian matrices and generaled Roe average for an equilibrium real gas

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1988-01-01

Inviscid flux Jacobian matrices and their properties used in numerical solutions of conservation laws are extended to general, equilibrium gas laws. Exact and approximate generalizations of the Roe average are presented. Results are given for one-dimensional flow, and then extended to three-dimensional flow with time-varying grids.

New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

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

Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil

2016-04-29

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less

Adaptive Jacobian Fuzzy Attitude Control for Flexible Spacecraft Combined Attitude and Sun Tracking System

NASA Astrophysics Data System (ADS)

Chak, Yew-Chung; Varatharajoo, Renuganth

2016-07-01

Many spacecraft attitude control systems today use reaction wheels to deliver precise torques to achieve three-axis attitude stabilization. However, irrecoverable mechanical failure of reaction wheels could potentially lead to mission interruption or total loss. The electrically-powered Solar Array Drive Assemblies (SADA) are usually installed in the pitch axis which rotate the solar arrays to track the Sun, can produce torques to compensate for the pitch-axis wheel failure. In addition, the attitude control of a flexible spacecraft poses a difficult problem. These difficulties include the strong nonlinear coupled dynamics between the rigid hub and flexible solar arrays, and the imprecisely known system parameters, such as inertia matrix, damping ratios, and flexible mode frequencies. In order to overcome these drawbacks, the adaptive Jacobian tracking fuzzy control is proposed for the combined attitude and sun-tracking control problem of a flexible spacecraft during attitude maneuvers in this work. For the adaptation of kinematic and dynamic uncertainties, the proposed scheme uses an adaptive sliding vector based on estimated attitude velocity via approximate Jacobian matrix. The unknown nonlinearities are approximated by deriving the fuzzy models with a set of linguistic If-Then rules using the idea of sector nonlinearity and local approximation in fuzzy partition spaces. The uncertain parameters of the estimated nonlinearities and the Jacobian matrix are being adjusted online by an adaptive law to realize feedback control. The attitude of the spacecraft can be directly controlled with the Jacobian feedback control when the attitude pointing trajectory is designed with respect to the spacecraft coordinate frame itself. A significant feature of this work is that the proposed adaptive Jacobian tracking scheme will result in not only the convergence of angular position and angular velocity tracking errors, but also the convergence of estimated angular velocity to the actual angular velocity. Numerical results are presented to demonstrate the effectiveness of the proposed scheme in tracking the desired attitude, as well as suppressing the elastic deflection effects of solar arrays during maneuver.

Implicit Plasma Kinetic Simulation Using The Jacobian-Free Newton-Krylov Method

NASA Astrophysics Data System (ADS)

Taitano, William; Knoll, Dana; Chacon, Luis

2009-11-01

The use of fully implicit time integration methods in kinetic simulation is still area of algorithmic research. A brute-force approach to simultaneously including the field equations and the particle distribution function would result in an intractable linear algebra problem. A number of algorithms have been put forward which rely on an extrapolation in time. They can be thought of as linearly implicit methods or one-step Newton methods. However, issues related to time accuracy of these methods still remain. We are pursuing a route to implicit plasma kinetic simulation which eliminates extrapolation, eliminates phase-space from the linear algebra problem, and converges the entire nonlinear system within a time step. We accomplish all this using the Jacobian-Free Newton-Krylov algorithm. The original research along these lines considered particle methods to advance the distribution function [1]. In the current research we are advancing the Vlasov equations on a grid. Results will be presented which highlight algorithmic details for single species electrostatic problems and coupled ion-electron electrostatic problems. [4pt] [1] H. J. Kim, L. Chac'on, G. Lapenta, ``Fully implicit particle in cell algorithm,'' 47th Annual Meeting of the Division of Plasma Physics, Oct. 24-28, 2005, Denver, CO

On linearization and preconditioning for radiation diffusion coupled to material thermal conduction equations

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

Feng, Tao, E-mail: fengtao2@mail.ustc.edu.cn; Graduate School of China Academy Engineering Physics, Beijing 100083; An, Hengbin, E-mail: an_hengbin@iapcm.ac.cn

2013-03-01

Jacobian-free Newton–Krylov (JFNK) method is an effective algorithm for solving large scale nonlinear equations. One of the most important advantages of JFNK method is that there is no necessity to form and store the Jacobian matrix of the nonlinear system when JFNK method is employed. However, an approximation of the Jacobian is needed for the purpose of preconditioning. In this paper, JFNK method is employed to solve a class of non-equilibrium radiation diffusion coupled to material thermal conduction equations, and two preconditioners are designed by linearizing the equations in two methods. Numerical results show that the two preconditioning methods canmore » improve the convergence behavior and efficiency of JFNK method.« less

Differential Kinematics Of Contemporary Industrial Robots

NASA Astrophysics Data System (ADS)

Szkodny, T.

2014-08-01

The paper presents a simple method of avoiding singular configurations of contemporary industrial robot manipulators of such renowned companies as ABB, Fanuc, Mitsubishi, Adept, Kawasaki, COMAU and KUKA. To determine the singular configurations of these manipulators a global form of description of the end-effector kinematics was prepared, relative to the other links. On the basis of this description , the formula for the Jacobian was defined in the end-effector coordinates. Next, a closed form of the determinant of the Jacobian was derived. From the formula, singular configurations, where the determinant's value equals zero, were determined. Additionally, geometric interpretations of these configurations were given and they were illustrated. For the exemplary manipulator, small corrections of joint variables preventing the reduction of the Jacobian order were suggested. An analysis of positional errors, caused by these corrections, was presented

Flux Jacobian Matrices For Equilibrium Real Gases

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1990-01-01

Improved formulation includes generalized Roe average and extension to three dimensions. Flux Jacobian matrices derived for use in numerical solutions of conservation-law differential equations of inviscid flows of ideal gases extended to real gases. Real-gas formulation of these matrices retains simplifying assumptions of thermodynamic and chemical equilibrium, but adds effects of vibrational excitation, dissociation, and ionization of gas molecules via general equation of state.

A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

NASA Technical Reports Server (NTRS)

Hanson, R. J.; Krogh, Fred T.

1992-01-01

A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

Linearized blade row compression component model. Stability and frequency response analysis of a J85-3 compressor

NASA Technical Reports Server (NTRS)

Tesch, W. A.; Moszee, R. H.; Steenken, W. G.

1976-01-01

NASA developed stability and frequency response analysis techniques were applied to a dynamic blade row compression component stability model to provide a more economic approach to surge line and frequency response determination than that provided by time-dependent methods. This blade row model was linearized and the Jacobian matrix was formed. The clean-inlet-flow stability characteristics of the compressors of two J85-13 engines were predicted by applying the alternate Routh-Hurwitz stability criterion to the Jacobian matrix. The predicted surge line agreed with the clean-inlet-flow surge line predicted by the time-dependent method to a high degree except for one engine at 94% corrected speed. No satisfactory explanation of this discrepancy was found. The frequency response of the linearized system was determined by evaluating its Laplace transfer function. The results of the linearized-frequency-response analysis agree with the time-dependent results when the time-dependent inlet total-pressure and exit-flow function amplitude boundary conditions are less than 1 percent and 3 percent, respectively. The stability analysis technique was extended to a two-sector parallel compressor model with and without interstage crossflow and predictions were carried out for total-pressure distortion extents of 180 deg, 90 deg, 60 deg, and 30 deg.

Integration of Mesh Optimization with 3D All-Hex Mesh Generation, LDRD Subcase 3504340000, Final Report

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

KNUPP,PATRICK; MITCHELL,SCOTT A.

1999-11-01

In an attempt to automatically produce high-quality all-hex meshes, we investigated a mesh improvement strategy: given an initial poor-quality all-hex mesh, we iteratively changed the element connectivity, adding and deleting elements and nodes, and optimized the node positions. We found a set of hex reconnection primitives. We improved the optimization algorithms so they can untangle a negative-Jacobian mesh, even considering Jacobians on the boundary, and subsequently optimize the condition number of elements in an untangled mesh. However, even after applying both the primitives and optimization we were unable to produce high-quality meshes in certain regions. Our experiences suggest that manymore » boundary configurations of quadrilaterals admit no hexahedral mesh with positive Jacobians, although we have no proof of this.« less

Algorithms for Nonlinear Least-Squares Problems

DTIC Science & Technology

1988-09-01

O -,i(x) 2 , where each -,(x) is a smooth function mapping Rn to R. J - The m x n Jacobian matrix of f. ... x g - The gradient of the nonlinear least...V211f(X*)I112~ l~ l) J(xk)T J(xk) 2 + O(k - X*) For more convergence results and detailed convergence analysis for the Gauss-Newton method, see, e. g ...for a class of nonlinear least-squares problems that includes zero-residual prob- lems. The function Jt is the pseudo-inverse of Jk (see, e. g

Kinematic functions for the 7 DOF robotics research arm

NASA Technical Reports Server (NTRS)

Kreutz, K.; Long, M.; Seraji, Homayoun

1989-01-01

The Robotics Research Model K-1207 manipulator is a redundant 7R serial link arm with offsets at all joints. To uniquely determine joint angles for a given end-effector configuration, the redundancy is parameterized by a scalar variable which corresponds to the angle between the manipulator elbow plane and the vertical plane. The forward kinematic mappings from joint-space to end-effector configuration and elbow angle, and the augmented Jacobian matrix which gives end-effector and elbow angle rates as a function of joint rates, are also derived.

On Some Separated Algorithms for Separable Nonlinear Least Squares Problems.

PubMed

Gan, Min; Chen, C L Philip; Chen, Guang-Yong; Chen, Long

2017-10-03

For a class of nonlinear least squares problems, it is usually very beneficial to separate the variables into a linear and a nonlinear part and take full advantage of reliable linear least squares techniques. Consequently, the original problem is turned into a reduced problem which involves only nonlinear parameters. We consider in this paper four separated algorithms for such problems. The first one is the variable projection (VP) algorithm with full Jacobian matrix of Golub and Pereyra. The second and third ones are VP algorithms with simplified Jacobian matrices proposed by Kaufman and Ruano et al. respectively. The fourth one only uses the gradient of the reduced problem. Monte Carlo experiments are conducted to compare the performance of these four algorithms. From the results of the experiments, we find that: 1) the simplified Jacobian proposed by Ruano et al. is not a good choice for the VP algorithm; moreover, it may render the algorithm hard to converge; 2) the fourth algorithm perform moderately among these four algorithms; 3) the VP algorithm with the full Jacobian matrix perform more stable than that of the VP algorithm with Kuafman's simplified one; and 4) the combination of VP algorithm and Levenberg-Marquardt method is more effective than the combination of VP algorithm and Gauss-Newton method.

Inversion of high frequency surface waves with fundamental and higher modes

USGS Publications Warehouse

Xia, J.; Miller, R.D.; Park, C.B.; Tian, G.

2003-01-01

The phase velocity of Rayleigh-waves of a layered earth model is a function of frequency and four groups of earth parameters: compressional (P)-wave velocity, shear (S)-wave velocity, density, and thickness of layers. For the fundamental mode of Rayleigh waves, analysis of the Jacobian matrix for high frequencies (2-40 Hz) provides a measure of dispersion curve sensitivity to earth model parameters. S-wave velocities are the dominant influence of the four earth model parameters. This thesis is true for higher modes of high frequency Rayleigh waves as well. Our numerical modeling by analysis of the Jacobian matrix supports at least two quite exciting higher mode properties. First, for fundamental and higher mode Rayleigh wave data with the same wavelength, higher modes can "see" deeper than the fundamental mode. Second, higher mode data can increase the resolution of the inverted S-wave velocities. Real world examples show that the inversion process can be stabilized and resolution of the S-wave velocity model can be improved when simultaneously inverting the fundamental and higher mode data. ?? 2002 Elsevier Science B.V. All rights reserved.

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

Loef, P.A.; Smed, T.; Andersson, G.

The minimum singular value of the power flow Jacobian matrix has been used as a static voltage stability index, indicating the distance between the studied operating point and the steady state voltage stability limit. In this paper a fast method to calculate the minimum singular value and the corresponding (left and right) singular vectors is presented. The main advantages of the developed algorithm are the small amount of computation time needed, and that it only requires information available from an ordinary program for power flow calculations. Furthermore, the proposed method fully utilizes the sparsity of the power flow Jacobian matrixmore » and hence the memory requirements for the computation are low. These advantages are preserved when applied to various submatrices of the Jacobian matrix, which can be useful in constructing special voltage stability indices. The developed algorithm was applied to small test systems as well as to a large (real size) system with over 1000 nodes, with satisfactory results.« less

Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) non-commutative motives

NASA Astrophysics Data System (ADS)

Bernardara, M.; Tabuada, G.

2016-06-01

Conjectures of Beilinson-Bloch type predict that the low-degree rational Chow groups of intersections of quadrics are one-dimensional. This conjecture was proved by Otwinowska in [20]. By making use of homological projective duality and the recent theory of (Jacobians of) non-commutative motives, we give an alternative proof of this conjecture in the case of a complete intersection of either two quadrics or three odd-dimensional quadrics. Moreover, we prove that in these cases the unique non-trivial algebraic Jacobian is the middle one. As an application, we make use of Vial's work [26], [27] to describe the rational Chow motives of these complete intersections and show that smooth fibrations into such complete intersections over bases S of small dimension satisfy Murre's conjecture (when \\dim (S)≤ 1), Grothendieck's standard conjecture of Lefschetz type (when \\dim (S)≤ 2), and Hodge's conjecture (when \\dim(S)≤ 3).

Advanced control schemes and kinematic analysis for a kinematically redundant 7 DOF manipulator

NASA Technical Reports Server (NTRS)

Nguyen, Charles C.; Zhou, Zhen-Lei

1990-01-01

The kinematic analysis and control of a kinematically redundant manipulator is addressed. The manipulator is the slave arm of a telerobot system recently built at Goddard Space Flight Center (GSFC) to serve as a testbed for investigating research issues in telerobotics. A forward kinematic transformation is developed in its most simplified form, suitable for real-time control applications, and the manipulator Jacobian is derived using the vector cross product method. Using the developed forward kinematic transformation and quaternion representation of orientation matrices, we perform computer simulation to evaluate the efficiency of the Jacobian in converting joint velocities into Cartesian velocities and to investigate the accuracy of Jacobian pseudo-inverse for various sampling times. The equivalence between Cartesian velocities and quaternion is also verified using computer simulation. Three control schemes are proposed and discussed for controlling the motion of the slave arm end-effector.

Methods of computing steady-state voltage stability margins of power systems

DOEpatents

Chow, Joe Hong; Ghiocel, Scott Gordon

2018-03-20

In steady-state voltage stability analysis, as load increases toward a maximum, conventional Newton-Raphson power flow Jacobian matrix becomes increasingly ill-conditioned so power flow fails to converge before reaching maximum loading. A method to directly eliminate this singularity reformulates the power flow problem by introducing an AQ bus with specified bus angle and reactive power consumption of a load bus. For steady-state voltage stability analysis, the angle separation between the swing bus and AQ bus can be varied to control power transfer to the load, rather than specifying the load power itself. For an AQ bus, the power flow formulation is only made up of a reactive power equation, thus reducing the size of the Jacobian matrix by one. This reduced Jacobian matrix is nonsingular at the critical voltage point, eliminating a major difficulty in voltage stability analysis for power system operations.

Parallel Computation of the Jacobian Matrix for Nonlinear Equation Solvers Using MATLAB

NASA Technical Reports Server (NTRS)

Rose, Geoffrey K.; Nguyen, Duc T.; Newman, Brett A.

2017-01-01

Demonstrating speedup for parallel code on a multicore shared memory PC can be challenging in MATLAB due to underlying parallel operations that are often opaque to the user. This can limit potential for improvement of serial code even for the so-called embarrassingly parallel applications. One such application is the computation of the Jacobian matrix inherent to most nonlinear equation solvers. Computation of this matrix represents the primary bottleneck in nonlinear solver speed such that commercial finite element (FE) and multi-body-dynamic (MBD) codes attempt to minimize computations. A timing study using MATLAB's Parallel Computing Toolbox was performed for numerical computation of the Jacobian. Several approaches for implementing parallel code were investigated while only the single program multiple data (spmd) method using composite objects provided positive results. Parallel code speedup is demonstrated but the goal of linear speedup through the addition of processors was not achieved due to PC architecture.

3-D Magnetotelluric Forward Modeling And Inversion Incorporating Topography By Using Vector Finite-Element Method Combined With Divergence Corrections Based On The Magnetic Field (VFEH++)

NASA Astrophysics Data System (ADS)

Shi, X.; Utada, H.; Jiaying, W.

2009-12-01

The vector finite-element method combined with divergence corrections based on the magnetic field H, referred to as VFEH++ method, is developed to simulate the magnetotelluric (MT) responses of 3-D conductivity models. The advantages of the new VFEH++ method are the use of edge-elements to eliminate the vector parasites and the divergence corrections to explicitly guarantee the divergence-free conditions in the whole modeling domain. 3-D MT topographic responses are modeling using the new VFEH++ method, and are compared with those calculated by other numerical methods. The results show that MT responses can be modeled highly accurate using the VFEH+ +method. The VFEH++ algorithm is also employed for the 3-D MT data inversion incorporating topography. The 3-D MT inverse problem is formulated as a minimization problem of the regularized misfit function. In order to avoid the huge memory requirement and very long time for computing the Jacobian sensitivity matrix for Gauss-Newton method, we employ the conjugate gradient (CG) approach to solve the inversion equation. In each iteration of CG algorithm, the cost computation is the product of the Jacobian sensitivity matrix with a model vector x or its transpose with a data vector y, which can be transformed into two pseudo-forwarding modeling. This avoids the full explicitly Jacobian matrix calculation and storage which leads to considerable savings in the memory required by the inversion program in PC computer. The performance of CG algorithm will be illustrated by several typical 3-D models with horizontal earth surface and topographic surfaces. The results show that the VFEH++ and CG algorithms can be effectively employed to 3-D MT field data inversion.

Modular Bundle Adjustment for Photogrammetric Computations

NASA Astrophysics Data System (ADS)

Börlin, N.; Murtiyoso, A.; Grussenmeyer, P.; Menna, F.; Nocerino, E.

2018-05-01

In this paper we investigate how the residuals in bundle adjustment can be split into a composition of simple functions. According to the chain rule, the Jacobian (linearisation) of the residual can be formed as a product of the Jacobians of the individual steps. When implemented, this enables a modularisation of the computation of the bundle adjustment residuals and Jacobians where each component has limited responsibility. This enables simple replacement of components to e.g. implement different projection or rotation models by exchanging a module. The technique has previously been used to implement bundle adjustment in the open-source package DBAT (Börlin and Grussenmeyer, 2013) based on the Photogrammetric and Computer Vision interpretations of Brown (1971) lens distortion model. In this paper, we applied the technique to investigate how affine distortions can be used to model the projection of a tilt-shift lens. Two extended distortion models were implemented to test the hypothesis that the ordering of the affine and lens distortion steps can be changed to reduce the size of the residuals of a tilt-shift lens calibration. Results on synthetic data confirm that the ordering of the affine and lens distortion steps matter and is detectable by DBAT. However, when applied to a real camera calibration data set of a tilt-shift lens, no difference between the extended models was seen. This suggests that the tested hypothesis is false and that other effects need to be modelled to better explain the projection. The relatively low implementation effort that was needed to generate the models suggest that the technique can be used to investigate other novel projection models in photogrammetry, including modelling changes in the 3D geometry to better understand the tilt-shift lens.

Quasi-periodic solutions of the Belov-Chaltikian lattice hierarchy

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Zeng, Xin

Utilizing the characteristic polynomial of Lax matrix for the Belov-Chaltikian (BC) lattice hierarchy associated with a 3 × 3 discrete matrix spectral problem, we introduce a trigonal curve with three infinite points, from which we establish the associated Dubrovin-type equations. The essential properties of the Baker-Akhiezer function and the meromorphic function are discussed, that include their asymptotic behavior near three infinite points on the trigonal curve and the divisor of the meromorphic function. The Abel map is introduced to straighten out the continuous flow and the discrete flow in the Jacobian variety, from which the quasi-periodic solutions of the entire BC lattice hierarchy are obtained in terms of the Riemann theta function.

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

DOE PAGES

Woodward, Carol S.; Gardner, David J.; Evans, Katherine J.

2015-01-01

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but thismore » Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.« less

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

Watkins, W.T.; Siebers, J.V.; Bzdusek, K.

Purpose: To introduce methods to analyze Deformable Image Registration (DIR) and identify regions of potential DIR errors. Methods: DIR Deformable Vector Fields (DVFs) quantifying patient anatomic changes were evaluated using the Jacobian determinant and the magnitude of DVF curl as functions of tissue density and tissue type. These quantities represent local relative deformation and rotation, respectively. Large values in dense tissues can potentially identify non-physical DVF errors. For multiple DVFs per patient, histograms and visualization of DVF differences were also considered. To demonstrate the capabilities of methods, we computed multiple DVFs for each of five Head and Neck (H'N) patientsmore » (P1–P5) via a Fast-symmetric Demons (FSD) algorithm and via a Diffeomorphic Demons (DFD) algorithm, and show the potential to identify DVF errors. Results: Quantitative comparisons of the FSD and DFD registrations revealed <0.3 cm DVF differences in >99% of all voxels for P1, >96% for P2, and >90% of voxels for P3. While the FSD and DFD registrations were very similar for these patients, the Jacobian determinant was >50% in 9–15% of soft tissue and in 3–17% of bony tissue in each of these cases. The volumes of large soft tissue deformation were consistent for all five patients using the FSD algorithm (mean 15%±4% volume), whereas DFD reduced regions of large deformation by 10% volume (785 cm{sup 3}) for P4 and by 14% volume (1775 cm{sup 3}) for P5. The DFD registrations resulted in fewer regions of large DVF-curl; 50% rotations in FSD registrations averaged 209±136 cm{sup 3} in soft tissue and 10±11 cm{sup 3} in bony tissue, but using DFD these values were reduced to 42±53 cm{sup 3} and 1.1±1.5 cm{sup 3}, respectively. Conclusion: Analysis of Jacobian determinant and curl as functions of tissue density can identify regions of potential DVF errors by identifying non-physical deformations and rotations. Collaboration with Phillips Healthcare, as indicated in authorship.« less

WE-AB-202-05: Validation of Lung Stress Maps for CT-Ventilation Imaging

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

Cazoulat, G; Jolly, S; Matuszak, M

Purpose: To date, lung CT-ventilation imaging has been based on quantification of local breathing-induced changes in Hounsfield Units (HU) or volume. This work investigates the use of a stress map resulting from a biomechanical deformable image registration (DIR) algorithm as a metric of the ventilation function. Method: Eight lung cancer patients presenting different kinds of ventilation defects were retrospectively analyzed. Additionally, to the 4DCT acquired for radiotherapy planning, five of them had PET and three had SPECT imaging following inhalation of Ga-68 and Tc-99m, respectively. For each patient, the inhale phase of the 4DCT was registered to the exhale phasemore » using Morfeus, a biomechanical DIR algorithm based on the determination of boundary conditions on the lung surfaces and vessel tree. To take into account the heterogeneity of the tissue stiffness in the stress map estimation, each tetrahedral element of the finite-element model was assigned a Young’s modulus ranging from 60kPa to 12MPa, as a function of the HU in the inhale CT. The node displacements and element stresses resulting from the numerical simulation were used to generate three CT-ventilation maps based on: (i) volume changes (Jacobian determinant), (ii) changes in HU, (iii) the maximum principal stress. The voxel-wise correlation between each CT-ventilation map and the PET or SPECT V image was computed in a lung mask. Results: For patients with PET, the mean (min-max) Spearman correlation coefficients r were: 0.33 (0.19–0.45), 0.36 (0.16–0.51) and 0.42 (0.21–0.59) considering the Jacobian, changes in HU and maximum principal stress, respectively. For patients with SPECT V, the mean r were: 0.12 (−0.12–0.43), 0.29 (0.22–0.45) and 0.33 (0.25–0.39). Conclusion: The maximum principal stress maps showed a stronger correlation with the ventilation images than the previously proposed Jacobian or change in HU maps. This metric thus appears promising for CT-ventilation imaging. This work was funded in part by NIH P01CA059827.« less

Toric Networks, Geometric R-Matrices and Generalized Discrete Toda Lattices

NASA Astrophysics Data System (ADS)

Inoue, Rei; Lam, Thomas; Pylyavskyy, Pavlo

2016-11-01

We use the combinatorics of toric networks and the double affine geometric R-matrix to define a three-parameter family of generalizations of the discrete Toda lattice. We construct the integrals of motion and a spectral map for this system. The family of commuting time evolutions arising from the action of the R-matrix is explicitly linearized on the Jacobian of the spectral curve. The solution to the initial value problem is constructed using Riemann theta functions.

A Framework for Hierarchical Perception-Action Learning Utilizing Fuzzy Reasoning.

PubMed

Windridge, David; Felsberg, Michael; Shaukat, Affan

2013-02-01

Perception-action (P-A) learning is an approach to cognitive system building that seeks to reduce the complexity associated with conventional environment-representation/action-planning approaches. Instead, actions are directly mapped onto the perceptual transitions that they bring about, eliminating the need for intermediate representation and significantly reducing training requirements. We here set out a very general learning framework for cognitive systems in which online learning of the P-A mapping may be conducted within a symbolic processing context, so that complex contextual reasoning can influence the P-A mapping. In utilizing a variational calculus approach to define a suitable objective function, the P-A mapping can be treated as an online learning problem via gradient descent using partial derivatives. Our central theoretical result is to demonstrate top-down modulation of low-level perceptual confidences via the Jacobian of the higher levels of a subsumptive P-A hierarchy. Thus, the separation of the Jacobian as a multiplying factor between levels within the objective function naturally enables the integration of abstract symbolic manipulation in the form of fuzzy deductive logic into the P-A mapping learning. We experimentally demonstrate that the resulting framework achieves significantly better accuracy than using P-A learning without top-down modulation. We also demonstrate that it permits novel forms of context-dependent multilevel P-A mapping, applying the mechanism in the context of an intelligent driver assistance system.

Parallel processing architecture for computing inverse differential kinematic equations of the PUMA arm

NASA Technical Reports Server (NTRS)

Hsia, T. C.; Lu, G. Z.; Han, W. H.

1987-01-01

In advanced robot control problems, on-line computation of inverse Jacobian solution is frequently required. Parallel processing architecture is an effective way to reduce computation time. A parallel processing architecture is developed for the inverse Jacobian (inverse differential kinematic equation) of the PUMA arm. The proposed pipeline/parallel algorithm can be inplemented on an IC chip using systolic linear arrays. This implementation requires 27 processing cells and 25 time units. Computation time is thus significantly reduced.

Tracking lung tissue motion and expansion/compression with inverse consistent image registration and spirometry

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

Christensen, Gary E.; Song, Joo Hyun; Lu, Wei

2007-06-15

Breathing motion is one of the major limiting factors for reducing dose and irradiation of normal tissue for conventional conformal radiotherapy. This paper describes a relationship between tracking lung motion using spirometry data and image registration of consecutive CT image volumes collected from a multislice CT scanner over multiple breathing periods. Temporal CT sequences from 5 individuals were analyzed in this study. The couch was moved from 11 to 14 different positions to image the entire lung. At each couch position, 15 image volumes were collected over approximately 3 breathing periods. It is assumed that the expansion and contraction ofmore » lung tissue can be modeled as an elastic material. Furthermore, it is assumed that the deformation of the lung is small over one-fifth of a breathing period and therefore the motion of the lung can be adequately modeled using a small deformation linear elastic model. The small deformation inverse consistent linear elastic image registration algorithm is therefore well suited for this problem and was used to register consecutive image scans. The pointwise expansion and compression of lung tissue was measured by computing the Jacobian of the transformations used to register the images. The logarithm of the Jacobian was computed so that expansion and compression of the lung were scaled equally. The log-Jacobian was computed at each voxel in the volume to produce a map of the local expansion and compression of the lung during the breathing period. These log-Jacobian images demonstrate that the lung does not expand uniformly during the breathing period, but rather expands and contracts locally at different rates during inhalation and exhalation. The log-Jacobian numbers were averaged over a cross section of the lung to produce an estimate of the average expansion or compression from one time point to the next and compared to the air flow rate measured by spirometry. In four out of five individuals, the average log-Jacobian value and the air flow rate correlated well (R{sup 2}=0.858 on average for the entire lung). The correlation for the fifth individual was not as good (R{sup 2}=0.377 on average for the entire lung) and can be explained by the small variation in tidal volume for this individual. The correlation of the average log-Jacobian value and the air flow rate for images near the diaphragm correlated well in all five individuals (R{sup 2}=0.943 on average). These preliminary results indicate a strong correlation between the expansion/compression of the lung measured by image registration and the air flow rate measured by spirometry. Predicting the location, motion, and compression/expansion of the tumor and normal tissue using image registration and spirometry could have many important benefits for radiotherapy treatment. These benefits include reducing radiation dose to normal tissue, maximizing dose to the tumor, improving patient care, reducing treatment cost, and increasing patient throughput.« less

Tracking lung tissue motion and expansion/compression with inverse consistent image registration and spirometry.

PubMed

Christensen, Gary E; Song, Joo Hyun; Lu, Wei; El Naqa, Issam; Low, Daniel A

2007-06-01

Breathing motion is one of the major limiting factors for reducing dose and irradiation of normal tissue for conventional conformal radiotherapy. This paper describes a relationship between tracking lung motion using spirometry data and image registration of consecutive CT image volumes collected from a multislice CT scanner over multiple breathing periods. Temporal CT sequences from 5 individuals were analyzed in this study. The couch was moved from 11 to 14 different positions to image the entire lung. At each couch position, 15 image volumes were collected over approximately 3 breathing periods. It is assumed that the expansion and contraction of lung tissue can be modeled as an elastic material. Furthermore, it is assumed that the deformation of the lung is small over one-fifth of a breathing period and therefore the motion of the lung can be adequately modeled using a small deformation linear elastic model. The small deformation inverse consistent linear elastic image registration algorithm is therefore well suited for this problem and was used to register consecutive image scans. The pointwise expansion and compression of lung tissue was measured by computing the Jacobian of the transformations used to register the images. The logarithm of the Jacobian was computed so that expansion and compression of the lung were scaled equally. The log-Jacobian was computed at each voxel in the volume to produce a map of the local expansion and compression of the lung during the breathing period. These log-Jacobian images demonstrate that the lung does not expand uniformly during the breathing period, but rather expands and contracts locally at different rates during inhalation and exhalation. The log-Jacobian numbers were averaged over a cross section of the lung to produce an estimate of the average expansion or compression from one time point to the next and compared to the air flow rate measured by spirometry. In four out of five individuals, the average log-Jacobian value and the air flow rate correlated well (R2 = 0.858 on average for the entire lung). The correlation for the fifth individual was not as good (R2 = 0.377 on average for the entire lung) and can be explained by the small variation in tidal volume for this individual. The correlation of the average log-Jacobian value and the air flow rate for images near the diaphragm correlated well in all five individuals (R2 = 0.943 on average). These preliminary results indicate a strong correlation between the expansion/compression of the lung measured by image registration and the air flow rate measured by spirometry. Predicting the location, motion, and compression/expansion of the tumor and normal tissue using image registration and spirometry could have many important benefits for radiotherapy treatment. These benefits include reducing radiation dose to normal tissue, maximizing dose to the tumor, improving patient care, reducing treatment cost, and increasing patient throughput.

An entropy-variables-based formulation of residual distribution schemes for non-equilibrium flows

NASA Astrophysics Data System (ADS)

Garicano-Mena, Jesús; Lani, Andrea; Degrez, Gérard

2018-06-01

In this paper we present an extension of Residual Distribution techniques for the simulation of compressible flows in non-equilibrium conditions. The latter are modeled by means of a state-of-the-art multi-species and two-temperature model. An entropy-based variable transformation that symmetrizes the projected advective Jacobian for such a thermophysical model is introduced. Moreover, the transformed advection Jacobian matrix presents a block diagonal structure, with mass-species and electronic-vibrational energy being completely decoupled from the momentum and total energy sub-system. The advantageous structure of the transformed advective Jacobian can be exploited by contour-integration-based Residual Distribution techniques: established schemes that operate on dense matrices can be substituted by the same scheme operating on the momentum-energy subsystem matrix and repeated application of scalar scheme to the mass-species and electronic-vibrational energy terms. Finally, the performance gain of the symmetrizing-variables formulation is quantified on a selection of representative testcases, ranging from subsonic to hypersonic, in inviscid or viscous conditions.

Experiments with conjugate gradient algorithms for homotopy curve tracking

NASA Technical Reports Server (NTRS)

Irani, Kashmira M.; Ribbens, Calvin J.; Watson, Layne T.; Kamat, Manohar P.; Walker, Homer F.

1991-01-01

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.

Indirect iterative learning control for a discrete visual servo without a camera-robot model.

PubMed

Jiang, Ping; Bamforth, Leon C A; Feng, Zuren; Baruch, John E F; Chen, YangQuan

2007-08-01

This paper presents a discrete learning controller for vision-guided robot trajectory imitation with no prior knowledge of the camera-robot model. A teacher demonstrates a desired movement in front of a camera, and then, the robot is tasked to replay it by repetitive tracking. The imitation procedure is considered as a discrete tracking control problem in the image plane, with an unknown and time-varying image Jacobian matrix. Instead of updating the control signal directly, as is usually done in iterative learning control (ILC), a series of neural networks are used to approximate the unknown Jacobian matrix around every sample point in the demonstrated trajectory, and the time-varying weights of local neural networks are identified through repetitive tracking, i.e., indirect ILC. This makes repetitive segmented training possible, and a segmented training strategy is presented to retain the training trajectories solely within the effective region for neural network approximation. However, a singularity problem may occur if an unmodified neural-network-based Jacobian estimation is used to calculate the robot end-effector velocity. A new weight modification algorithm is proposed which ensures invertibility of the estimation, thus circumventing the problem. Stability is further discussed, and the relationship between the approximation capability of the neural network and the tracking accuracy is obtained. Simulations and experiments are carried out to illustrate the validity of the proposed controller for trajectory imitation of robot manipulators with unknown time-varying Jacobian matrices.

Robust large-scale parallel nonlinear solvers for simulations.

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

Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson

2005-11-01

This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their usemore » in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any existing linear solver, which makes it simple to write and easily portable. However, the method usually takes twice as long to solve as Newton-GMRES on general problems because it solves two linear systems at each iteration. In this paper, we discuss modifications to Bouaricha's method for a practical implementation, including a special globalization technique and other modifications for greater efficiency. We present numerical results showing computational advantages over Newton-GMRES on some realistic problems. We further discuss a new approach for dealing with singular (or ill-conditioned) matrices. In particular, we modify an algorithm for identifying a turning point so that an increasingly ill-conditioned Jacobian does not prevent convergence.« less

Finite element solution of optimal control problems with state-control inequality constraints

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.

1992-01-01

It is demonstrated that the weak Hamiltonian finite-element formulation is amenable to the solution of optimal control problems with inequality constraints which are functions of both state and control variables. Difficult problems can be treated on account of the ease with which algebraic equations can be generated before having to specify the problem. These equations yield very accurate solutions. Owing to the sparse structure of the resulting Jacobian, computer solutions can be obtained quickly when the sparsity is exploited.

On differential transformations between Cartesian and curvilinear (geodetic) coordinates

NASA Technical Reports Server (NTRS)

Soler, T.

1976-01-01

Differential transformations are developed between Cartesian and curvilinear orthogonal coordinates. Only matrix algebra is used for the presentation of the basic concepts. After defining the reference systems used the rotation (R), metric (H), and Jacobian (J) matrices of the transformations between cartesian and curvilinear coordinate systems are introduced. A value of R as a function of H and J is presented. Likewise an analytical expression for J(-1) as a function of H(-2) and R is obtained. Emphasis is placed on showing that differential equations are equivalent to conventional similarity transformations. Scaling methods are discussed along with ellipsoidal coordinates. Differential transformations between elipsoidal and geodetic coordinates are established.

Conservative-variable average states for equilibrium gas multi-dimensional fluxes

NASA Technical Reports Server (NTRS)

Iannelli, G. S.

1992-01-01

Modern split component evaluations of the flux vector Jacobians are thoroughly analyzed for equilibrium-gas average-state determinations. It is shown that all such derivations satisfy a fundamental eigenvalue consistency theorem. A conservative-variable average state is then developed for arbitrary equilibrium-gas equations of state and curvilinear-coordinate fluxes. Original expressions for eigenvalues, sound speed, Mach number, and eigenvectors are then determined for a general average Jacobian, and it is shown that the average eigenvalues, Mach number, and eigenvectors may not coincide with their classical pointwise counterparts. A general equilibrium-gas equation of state is then discussed for conservative-variable computational fluid dynamics (CFD) Euler formulations. The associated derivations lead to unique compatibility relations that constrain the pressure Jacobian derivatives. Thereafter, alternative forms for the pressure variation and average sound speed are developed in terms of two average pressure Jacobian derivatives. Significantly, no additional degree of freedom exists in the determination of these two average partial derivatives of pressure. Therefore, they are simultaneously computed exactly without any auxiliary relation, hence without any geometric solution projection or arbitrary scale factors. Several alternative formulations are then compared and key differences highlighted with emphasis on the determination of the pressure variation and average sound speed. The relevant underlying assumptions are identified, including some subtle approximations that are inherently employed in published average-state procedures. Finally, a representative test case is discussed for which an intrinsically exact average state is determined. This exact state is then compared with the predictions of recent methods, and their inherent approximations are appropriately quantified.

Weighted augmented Jacobian matrix with a variable coefficient method for kinematics mapping of space teleoperation based on human-robot motion similarity

NASA Astrophysics Data System (ADS)

Shi, Zhong; Huang, Xuexiang; Hu, Tianjian; Tan, Qian; Hou, Yuzhuo

2016-10-01

Space teleoperation is an important space technology, and human-robot motion similarity can improve the flexibility and intuition of space teleoperation. This paper aims to obtain an appropriate kinematics mapping method of coupled Cartesian-joint space for space teleoperation. First, the coupled Cartesian-joint similarity principles concerning kinematics differences are defined. Then, a novel weighted augmented Jacobian matrix with a variable coefficient (WAJM-VC) method for kinematics mapping is proposed. The Jacobian matrix is augmented to achieve a global similarity of human-robot motion. A clamping weighted least norm scheme is introduced to achieve local optimizations, and the operating ratio coefficient is variable to pursue similarity in the elbow joint. Similarity in Cartesian space and the property of joint constraint satisfaction is analysed to determine the damping factor and clamping velocity. Finally, a teleoperation system based on human motion capture is established, and the experimental results indicate that the proposed WAJM-VC method can improve the flexibility and intuition of space teleoperation to complete complex space tasks.

Overdetermined shooting methods for computing standing water waves with spectral accuracy

NASA Astrophysics Data System (ADS)

Wilkening, Jon; Yu, Jia

2012-01-01

A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on standing water waves. We identify new nucleation mechanisms in which isolated large-amplitude solutions, and closed loops of such solutions, suddenly exist for depths below a critical threshold. We also study degenerate and secondary bifurcations related to Wilton's ripples in the traveling case, and explore the breakdown of self-similarity at the crests of extreme standing waves. In shallow water, we find that standing waves take the form of counter-propagating solitary waves that repeatedly collide quasi-elastically. In deep water with surface tension, we find that standing waves resemble counter-propagating depression waves. We also discuss the existence and non-uniqueness of solutions, and smooth versus erratic dependence of Fourier modes on wave amplitude and fluid depth. In the numerical method, robustness is achieved by posing the problem as an overdetermined nonlinear system and using either adjoint-based minimization techniques or a quadratically convergent trust-region method to minimize the objective function. Efficiency is achieved in the trust-region approach by parallelizing the Jacobian computation, so the setup cost of computing the Dirichlet-to-Neumann operator in the variational equation is not repeated for each column. Updates of the Jacobian are also delayed until the previous Jacobian ceases to be useful. Accuracy is maintained using spectral collocation with optional mesh refinement in space, a high-order Runge-Kutta or spectral deferred correction method in time and quadruple precision for improved navigation of delicate regions of parameter space as well as validation of double-precision results. Implementation issues for transferring much of the computation to a graphic processing units are briefly discussed, and the performance of the algorithm is tested for a number of hardware configurations.

TH-CD-202-06: A Method for Characterizing and Validating Dynamic Lung Density Change During Quiet Respiration

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

Dou, T; Ruan, D; Heinrich, M

2016-06-15

Purpose: To obtain a functional relationship that calibrates the lung tissue density change under free breathing conditions through correlating Jacobian values to the Hounsfield units. Methods: Free-breathing lung computed tomography images were acquired using a fast helical CT protocol, where 25 scans were acquired per patient. Using a state-of-the-art deformable registration algorithm, a set of the deformation vector fields (DVF) was generated to provide spatial mapping from the reference image geometry to the other free-breathing scans. These DVFs were used to generate Jacobian maps, which estimate voxelwise volume change. Subsequently, the set of 25 corresponding Jacobian and voxel intensity inmore » Hounsfield units (HU) were collected and linear regression was performed based on the mass conservation relationship to correlate the volume change to density change. Based on the resulting fitting coefficients, the tissues were classified into parenchymal (Type I), vascular (Type II), and soft tissue (Type III) types. These coefficients modeled the voxelwise density variation during quiet breathing. The accuracy of the proposed method was assessed using mean absolute difference in HU between the CT scan intensities and the model predicted values. In addition, validation experiments employing a leave-five-out method were performed to evaluate the model accuracy. Results: The computed mean model errors were 23.30±9.54 HU, 29.31±10.67 HU, and 35.56±20.56 HU, respectively, for regions I, II, and III, respectively. The cross validation experiments averaged over 100 trials had mean errors of 30.02 ± 1.67 HU over the entire lung. These mean values were comparable with the estimated CT image background noise. Conclusion: The reported validation experiment statistics confirmed the lung density modeling during free breathing. The proposed technique was general and could be applied to a wide range of problem scenarios where accurate dynamic lung density information is needed. This work was supported in part by NIH R01 CA0096679.« less

mrpy: Renormalized generalized gamma distribution for HMF and galaxy ensemble properties comparisons

NASA Astrophysics Data System (ADS)

Murray, Steven G.; Robotham, Aaron S. G.; Power, Chris

2018-02-01

mrpy calculates the MRP parameterization of the Halo Mass Function. It calculates basic statistics of the truncated generalized gamma distribution (TGGD) with the TGGD class, including mean, mode, variance, skewness, pdf, and cdf. It generates MRP quantities with the MRP class, such as differential number counts and cumulative number counts, and offers various methods for generating normalizations. It can generate the MRP-based halo mass function as a function of physical parameters via the mrp_b13 function, and fit MRP parameters to data in the form of arbitrary curves and in the form of a sample of variates with the SimFit class. mrpy also calculates analytic hessians and jacobians at any point, and allows the user to alternate parameterizations of the same form via the reparameterize module.

Computation and analysis for a constrained entropy optimization problem in finance

NASA Astrophysics Data System (ADS)

He, Changhong; Coleman, Thomas F.; Li, Yuying

2008-12-01

In [T. Coleman, C. He, Y. Li, Calibrating volatility function bounds for an uncertain volatility model, Journal of Computational Finance (2006) (submitted for publication)], an entropy minimization formulation has been proposed to calibrate an uncertain volatility option pricing model (UVM) from market bid and ask prices. To avoid potential infeasibility due to numerical error, a quadratic penalty function approach is applied. In this paper, we show that the solution to the quadratic penalty problem can be obtained by minimizing an objective function which can be evaluated via solving a Hamilton-Jacobian-Bellman (HJB) equation. We prove that the implicit finite difference solution of this HJB equation converges to its viscosity solution. In addition, we provide computational examples illustrating accuracy of calibration.

Computing sparse derivatives and consecutive zeros problem

NASA Astrophysics Data System (ADS)

Chandra, B. V. Ravi; Hossain, Shahadat

2013-02-01

We describe a substitution based sparse Jacobian matrix determination method using algorithmic differentiation. Utilizing the a priori known sparsity pattern, a compression scheme is determined using graph coloring. The "compressed pattern" of the Jacobian matrix is then reordered into a form suitable for computation by substitution. We show that the column reordering of the compressed pattern matrix (so as to align the zero entries into consecutive locations in each row) can be viewed as a variant of traveling salesman problem. Preliminary computational results show that on the test problems the performance of nearest-neighbor type heuristic algorithms is highly encouraging.

Covariance expressions for eigenvalue and eigenvector problems

NASA Astrophysics Data System (ADS)

Liounis, Andrew J.

There are a number of important scientific and engineering problems whose solutions take the form of an eigenvalue--eigenvector problem. Some notable examples include solutions to linear systems of ordinary differential equations, controllability of linear systems, finite element analysis, chemical kinetics, fitting ellipses to noisy data, and optimal estimation of attitude from unit vectors. In many of these problems, having knowledge of the eigenvalue and eigenvector Jacobians is either necessary or is nearly as important as having the solution itself. For instance, Jacobians are necessary to find the uncertainty in a computed eigenvalue or eigenvector estimate. This uncertainty, which is usually represented as a covariance matrix, has been well studied for problems similar to the eigenvalue and eigenvector problem, such as singular value decomposition. There has been substantially less research on the covariance of an optimal estimate originating from an eigenvalue-eigenvector problem. In this thesis we develop two general expressions for the Jacobians of eigenvalues and eigenvectors with respect to the elements of their parent matrix. The expressions developed make use of only the parent matrix and the eigenvalue and eigenvector pair under consideration. In addition, they are applicable to any general matrix (including complex valued matrices, eigenvalues, and eigenvectors) as long as the eigenvalues are simple. Alongside this, we develop expressions that determine the uncertainty in a vector estimate obtained from an eigenvalue-eigenvector problem given the uncertainty of the terms of the matrix. The Jacobian expressions developed are numerically validated with forward finite, differencing and the covariance expressions are validated using Monte Carlo analysis. Finally, the results from this work are used to determine covariance expressions for a variety of estimation problem examples and are also applied to the design of a dynamical system.

Semi-implicit iterative methods for low Mach number turbulent reacting flows: Operator splitting versus approximate factorization

NASA Astrophysics Data System (ADS)

MacArt, Jonathan F.; Mueller, Michael E.

2016-12-01

Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport-reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.

Optimal trace inequality constants for interior penalty discontinuous Galerkin discretisations of elliptic operators using arbitrary elements with non-constant Jacobians

NASA Astrophysics Data System (ADS)

Owens, A. R.; Kópházi, J.; Eaton, M. D.

2017-12-01

In this paper, a new method to numerically calculate the trace inequality constants, which arise in the calculation of penalty parameters for interior penalty discretisations of elliptic operators, is presented. These constants are provably optimal for the inequality of interest. As their calculation is based on the solution of a generalised eigenvalue problem involving the volumetric and face stiffness matrices, the method is applicable to any element type for which these matrices can be calculated, including standard finite elements and the non-uniform rational B-splines of isogeometric analysis. In particular, the presented method does not require the Jacobian of the element to be constant, and so can be applied to a much wider variety of element shapes than are currently available in the literature. Numerical results are presented for a variety of finite element and isogeometric cases. When the Jacobian is constant, it is demonstrated that the new method produces lower penalty parameters than existing methods in the literature in all cases, which translates directly into savings in the solution time of the resulting linear system. When the Jacobian is not constant, it is shown that the naive application of existing approaches can result in penalty parameters that do not guarantee coercivity of the bilinear form, and by extension, the stability of the solution. The method of manufactured solutions is applied to a model reaction-diffusion equation with a range of parameters, and it is found that using penalty parameters based on the new trace inequality constants result in better conditioned linear systems, which can be solved approximately 11% faster than those produced by the methods from the literature.

Closing the contrast gap between testbed and model prediction with WFIRST-CGI shaped pupil coronagraph

NASA Astrophysics Data System (ADS)

Zhou, Hanying; Nemati, Bijan; Krist, John; Cady, Eric; Prada, Camilo M.; Kern, Brian; Poberezhskiy, Ilya

2016-07-01

JPL has recently passed an important milestone in its technology development for a proposed NASA WFIRST mission coronagraph: demonstration of better than 1x10-8 contrast over broad bandwidth (10%) on both shaped pupil coronagraph (SPC) and hybrid Lyot coronagraph (HLC) testbeds with the WFIRST obscuration pattern. Challenges remain, however, in the technology readiness for the proposed mission. One is the discrepancies between the achieved contrasts on the testbeds and their corresponding model predictions. A series of testbed diagnoses and modeling activities were planned and carried out on the SPC testbed in order to close the gap. A very useful tool we developed was a derived "measured" testbed wavefront control Jacobian matrix that could be compared with the model-predicted "control" version that was used to generate the high contrast dark hole region in the image plane. The difference between these two is an estimate of the error in the control Jacobian. When the control matrix, which includes both amplitude and phase, was modified to reproduce the error, the simulated performance closely matched the SPC testbed behavior in both contrast floor and contrast convergence speed. This is a step closer toward model validation for high contrast coronagraphs. Further Jacobian analysis and modeling provided clues to the possible sources for the mismatch: DM misregistration and testbed optical wavefront error (WFE) and the deformable mirror (DM) setting for correcting this WFE. These analyses suggested that a high contrast coronagraph has a tight tolerance in the accuracy of its control Jacobian. Modifications to both testbed control model as well as prediction model are being implemented, and future works are discussed.

Numerical solution of Euler's equation by perturbed functionals

NASA Technical Reports Server (NTRS)

Dey, S. K.

1985-01-01

A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows

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

HyeongKae Park; Robert Nourgaliev; Vincent Mousseau

2008-07-01

A novel numerical algorithm (rDG-JFNK) for all-speed fluid flows with heat conduction and viscosity is introduced. The rDG-JFNK combines the Discontinuous Galerkin spatial discretization with the implicit Runge-Kutta time integration under the Jacobian-free Newton-Krylov framework. We solve fully-compressible Navier-Stokes equations without operator-splitting of hyperbolic, diffusion and reaction terms, which enables fully-coupled high-order temporal discretization. The stability constraint is removed due to the L-stable Explicit, Singly Diagonal Implicit Runge-Kutta (ESDIRK) scheme. The governing equations are solved in the conservative form, which allows one to accurately compute shock dynamics, as well as low-speed flows. For spatial discretization, we develop a “recovery” familymore » of DG, exhibiting nearly-spectral accuracy. To precondition the Krylov-based linear solver (GMRES), we developed an “Operator-Split”-(OS) Physics Based Preconditioner (PBP), in which we transform/simplify the fully-coupled system to a sequence of segregated scalar problems, each can be solved efficiently with Multigrid method. Each scalar problem is designed to target/cluster eigenvalues of the Jacobian matrix associated with a specific physics.« less

Acceleration methods for multi-physics compressible flow

NASA Astrophysics Data System (ADS)

Peles, Oren; Turkel, Eli

2018-04-01

In this work we investigate the Runge-Kutta (RK)/Implicit smoother scheme as a convergence accelerator for complex multi-physics flow problems including turbulent, reactive and also two-phase flows. The flows considered are subsonic, transonic and supersonic flows in complex geometries, and also can be either steady or unsteady flows. All of these problems are considered to be a very stiff. We then introduce an acceleration method for the compressible Navier-Stokes equations. We start with the multigrid method for pure subsonic flow, including reactive flows. We then add the Rossow-Swanson-Turkel RK/Implicit smoother that enables performing all these complex flow simulations with a reasonable CFL number. We next discuss the RK/Implicit smoother for time dependent problem and also for low Mach numbers. The preconditioner includes an intrinsic low Mach number treatment inside the smoother operator. We also develop a modified Roe scheme with a corresponding flux Jacobian matrix. We then give the extension of the method for real gas and reactive flow. Reactive flows are governed by a system of inhomogeneous Navier-Stokes equations with very stiff source terms. The extension of the RK/Implicit smoother requires an approximation of the source term Jacobian. The properties of the Jacobian are very important for the stability of the method. We discuss what the chemical physics theory of chemical kinetics tells about the mathematical properties of the Jacobian matrix. We focus on the implication of the Le-Chatelier's principle on the sign of the diagonal entries of the Jacobian. We present the implementation of the method for turbulent flow. We use a two RANS turbulent model - one equation model - Spalart-Allmaras and a two-equation model - k-ω SST model. The last extension is for two-phase flows with a gas as a main phase and Eulerian representation of a dispersed particles phase (EDP). We present some examples for such flow computations inside a ballistic evaluation rocket motor. The numerical examples in this work include transonic flow about a RAE2822 airfoil, about a M6 Onera wing, NACA0012 airfoil at very low Mach number, two-phase flow inside a Ballistic evaluation motor (BEM), a turbulent reactive shear layer and a time dependent Sod's tube problem.

Bifurcation Analysis of a Predator-Prey System with Ratio-Dependent Functional Response

NASA Astrophysics Data System (ADS)

Jiang, Xin; She, Zhikun; Feng, Zhaosheng; Zheng, Xiuliang

2017-12-01

In this paper, we are concerned with the structural stability of a density dependent predator-prey system with ratio-dependent functional response. Starting with the geometrical analysis of hyperbolic curves, we obtain that the system has one or two positive equilibria under various conditions. Inspired by the S-procedure and semi-definite programming, we use the sum of squares decomposition based method to ensure the global asymptotic stability of the positive equilibrium through the associated polynomial Lyapunov functions. By exploring the monotonic property of the trace of the Jacobian matrix with respect to r under the given different conditions, we analytically verify that there is a corresponding unique r∗ such that the trace is equal to zero and prove the existence of Hopf bifurcation, respectively.

Application of a Modal Approach in Solving the Static Stability Problem for Electric Power Systems

NASA Astrophysics Data System (ADS)

Sharov, J. V.

2017-12-01

Application of a modal approach in solving the static stability problem for power systems is examined. It is proposed to use the matrix exponent norm as a generalized transition function of the power system disturbed motion. Based on the concept of a stability radius and the pseudospectrum of Jacobian matrix, the necessary and sufficient conditions for existence of the static margins were determined. The capabilities and advantages of the modal approach in designing centralized or distributed control and the prospects for the analysis of nonlinear oscillations and rendering the dynamic stability are demonstrated.

Rogue periodic waves of the focusing nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Chen, Jinbing; Pelinovsky, Dmitry E.

2018-02-01

Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn. Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

Rogue periodic waves of the focusing nonlinear Schrödinger equation.

PubMed

Chen, Jinbing; Pelinovsky, Dmitry E

2018-02-01

Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn . Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

A Method to Solve Interior and Exterior Camera Calibration Parameters for Image Resection

NASA Technical Reports Server (NTRS)

Samtaney, Ravi

1999-01-01

An iterative method is presented to solve the internal and external camera calibration parameters, given model target points and their images from one or more camera locations. The direct linear transform formulation was used to obtain a guess for the iterative method, and herein lies one of the strengths of the present method. In all test cases, the method converged to the correct solution. In general, an overdetermined system of nonlinear equations is solved in the least-squares sense. The iterative method presented is based on Newton-Raphson for solving systems of nonlinear algebraic equations. The Jacobian is analytically derived and the pseudo-inverse of the Jacobian is obtained by singular value decomposition.

Magnetotelluric inversion via reverse time migration algorithm of seismic data

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

Ha, Taeyoung; Shin, Changsoo

2007-07-01

We propose a new algorithm for two-dimensional magnetotelluric (MT) inversion. Our algorithm is an MT inversion based on the steepest descent method, borrowed from the backpropagation technique of seismic inversion or reverse time migration, introduced in the middle 1980s by Lailly and Tarantola. The steepest descent direction can be calculated efficiently by using the symmetry of numerical Green's function derived from a mixed finite element method proposed by Nedelec for Maxwell's equation, without calculating the Jacobian matrix explicitly. We construct three different objective functions by taking the logarithm of the complex apparent resistivity as introduced in the recent waveform inversionmore » algorithm by Shin and Min. These objective functions can be naturally separated into amplitude inversion, phase inversion and simultaneous inversion. We demonstrate our algorithm by showing three inversion results for synthetic data.« less

Accelerated gradient based diffuse optical tomographic image reconstruction.

PubMed

Biswas, Samir Kumar; Rajan, K; Vasu, R M

2011-01-01

Fast reconstruction of interior optical parameter distribution using a new approach called Broyden-based model iterative image reconstruction (BMOBIIR) and adjoint Broyden-based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT). DOT is a nonlinear and ill-posed inverse problem. Newton-based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach-based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low-rank updates. Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton-based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction. We have shown through experimental and simulation studies that Broyden-based MOBIIR and adjoint Broyden-based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue-mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton-based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data.

Multi-GPU Jacobian accelerated computing for soft-field tomography.

PubMed

Borsic, A; Attardo, E A; Halter, R J

2012-10-01

Image reconstruction in soft-field tomography is based on an inverse problem formulation, where a forward model is fitted to the data. In medical applications, where the anatomy presents complex shapes, it is common to use finite element models (FEMs) to represent the volume of interest and solve a partial differential equation that models the physics of the system. Over the last decade, there has been a shifting interest from 2D modeling to 3D modeling, as the underlying physics of most problems are 3D. Although the increased computational power of modern computers allows working with much larger FEM models, the computational time required to reconstruct 3D images on a fine 3D FEM model can be significant, on the order of hours. For example, in electrical impedance tomography (EIT) applications using a dense 3D FEM mesh with half a million elements, a single reconstruction iteration takes approximately 15-20 min with optimized routines running on a modern multi-core PC. It is desirable to accelerate image reconstruction to enable researchers to more easily and rapidly explore data and reconstruction parameters. Furthermore, providing high-speed reconstructions is essential for some promising clinical application of EIT. For 3D problems, 70% of the computing time is spent building the Jacobian matrix, and 25% of the time in forward solving. In this work, we focus on accelerating the Jacobian computation by using single and multiple GPUs. First, we discuss an optimized implementation on a modern multi-core PC architecture and show how computing time is bounded by the CPU-to-memory bandwidth; this factor limits the rate at which data can be fetched by the CPU. Gains associated with the use of multiple CPU cores are minimal, since data operands cannot be fetched fast enough to saturate the processing power of even a single CPU core. GPUs have much faster memory bandwidths compared to CPUs and better parallelism. We are able to obtain acceleration factors of 20 times on a single NVIDIA S1070 GPU, and of 50 times on four GPUs, bringing the Jacobian computing time for a fine 3D mesh from 12 min to 14 s. We regard this as an important step toward gaining interactive reconstruction times in 3D imaging, particularly when coupled in the future with acceleration of the forward problem. While we demonstrate results for EIT, these results apply to any soft-field imaging modality where the Jacobian matrix is computed with the adjoint method.

Multi-GPU Jacobian Accelerated Computing for Soft Field Tomography

PubMed Central

Borsic, A.; Attardo, E. A.; Halter, R. J.

2012-01-01

Image reconstruction in soft-field tomography is based on an inverse problem formulation, where a forward model is fitted to the data. In medical applications, where the anatomy presents complex shapes, it is common to use Finite Element Models to represent the volume of interest and to solve a partial differential equation that models the physics of the system. Over the last decade, there has been a shifting interest from 2D modeling to 3D modeling, as the underlying physics of most problems are three-dimensional. Though the increased computational power of modern computers allows working with much larger FEM models, the computational time required to reconstruct 3D images on a fine 3D FEM model can be significant, on the order of hours. For example, in Electrical Impedance Tomography applications using a dense 3D FEM mesh with half a million elements, a single reconstruction iteration takes approximately 15 to 20 minutes with optimized routines running on a modern multi-core PC. It is desirable to accelerate image reconstruction to enable researchers to more easily and rapidly explore data and reconstruction parameters. Further, providing high-speed reconstructions are essential for some promising clinical application of EIT. For 3D problems 70% of the computing time is spent building the Jacobian matrix, and 25% of the time in forward solving. In the present work, we focus on accelerating the Jacobian computation by using single and multiple GPUs. First, we discuss an optimized implementation on a modern multi-core PC architecture and show how computing time is bounded by the CPU-to-memory bandwidth; this factor limits the rate at which data can be fetched by the CPU. Gains associated with use of multiple CPU cores are minimal, since data operands cannot be fetched fast enough to saturate the processing power of even a single CPU core. GPUs have a much faster memory bandwidths compared to CPUs and better parallelism. We are able to obtain acceleration factors of 20 times on a single NVIDIA S1070 GPU, and of 50 times on 4 GPUs, bringing the Jacobian computing time for a fine 3D mesh from 12 minutes to 14 seconds. We regard this as an important step towards gaining interactive reconstruction times in 3D imaging, particularly when coupled in the future with acceleration of the forward problem. While we demonstrate results for Electrical Impedance Tomography, these results apply to any soft-field imaging modality where the Jacobian matrix is computed with the Adjoint Method. PMID:23010857

A Nonlinear Dynamics-Based Estimator for Functional Electrical Stimulation: Preliminary Results From Lower-Leg Extension Experiments.

PubMed

Allen, Marcus; Zhong, Qiang; Kirsch, Nicholas; Dani, Ashwin; Clark, William W; Sharma, Nitin

2017-12-01

Miniature inertial measurement units (IMUs) are wearable sensors that measure limb segment or joint angles during dynamic movements. However, IMUs are generally prone to drift, external magnetic interference, and measurement noise. This paper presents a new class of nonlinear state estimation technique called state-dependent coefficient (SDC) estimation to accurately predict joint angles from IMU measurements. The SDC estimation method uses limb dynamics, instead of limb kinematics, to estimate the limb state. Importantly, the nonlinear limb dynamic model is formulated into state-dependent matrices that facilitate the estimator design without performing a Jacobian linearization. The estimation method is experimentally demonstrated to predict knee joint angle measurements during functional electrical stimulation of the quadriceps muscle. The nonlinear knee musculoskeletal model was identified through a series of experiments. The SDC estimator was then compared with an extended kalman filter (EKF), which uses a Jacobian linearization and a rotation matrix method, which uses a kinematic model instead of the dynamic model. Each estimator's performance was evaluated against the true value of the joint angle, which was measured through a rotary encoder. The experimental results showed that the SDC estimator, the rotation matrix method, and EKF had root mean square errors of 2.70°, 2.86°, and 4.42°, respectively. Our preliminary experimental results show the new estimator's advantage over the EKF method but a slight advantage over the rotation matrix method. However, the information from the dynamic model allows the SDC method to use only one IMU to measure the knee angle compared with the rotation matrix method that uses two IMUs to estimate the angle.

The cometary and asteroidal origins of meteors

NASA Technical Reports Server (NTRS)

Kresak, L.

1973-01-01

A quantitative examination of the gravitational and nongravitational changes of orbits shows that for larger interplanetary bodies the perturbations by Jupiter strongly predominate over all other effects, which include perturbations by other planets, splitting of comet nuclei and jet effects of cometary ejections. The structure of meteor streams, indicates that the mutual compensation of the changes in individual elements entering the Jacobian integral, which is characteristic for the comets, does not work among the meteoroids. It appears that additional forces of a different kind must exert appreciable influence on the motion of interplanetary particles of meteoroid size. Nevertheless, the distribution of the Jacobian constant in various samples of meteor orbits furnishes some information on the type of their parent bodies and on the relative contribution of individual sources.

TU-A-12A-01: Consistency of Lung Expansion and Contraction During Respiration: Implications for Quantitative Imaging

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

Patton, T; Du, K; Bayouth, J

Purpose: Four-dimensional computed tomography (4DCT) can be used to evaluate longitudinal changes in pulmonary function. The sensitivity of such measurements to identify function change may be improved with reproducible breathing patterns. The purpose of this study was to determine if inhale was more consistent than exhale, i.e., lung expansion during inhalation compared to lung contraction during exhalation. Methods: Repeat 4DCT image data acquired within a short time interval from 8 patients. Using a tissue volume preserving deformable image registration algorithm, Jacobian ventilation maps in two scanning sessions were computed and compared on the same coordinate for reproducibility analysis. Equivalent lungmore » volumes (ELV) were used for 5 subjects and equivalent title volumes (ETV) for the 3 subjects who experienced a baseline shift between scans. In addition, gamma pass rate was calculated from a modified gamma index evaluation between two ventilation maps, using acceptance criterions of 2mm distance-to-agreement and 5% ventilation difference. The gamma pass rates were then compared using paired t-test to determine if there was a significant difference. Results: Inhalation was more reproducible than exhalation. In the 5 ELV subjects 78.5% of the lung voxels met the gamma criteria for expansion during inhalation when comparing the two scans, while significantly fewer (70.9% of the lung voxels) met the gamma criteria for contraction during exhalation (p = .027). In the 8 total subjects analyzed the average gamma pass rate for expansion during inhalation was 75.2% while for contraction during exhalation it was 70.3%; which trended towards significant (p = .064). Conclusion: This work implies inhalation is more reproducible than exhalation, when equivalent respiratory volumes are considered. The reason for this difference is unknown. Longitudinal investigation of pulmonary function change based on inhalation images appears appropriate for Jacobian-based measure of lung tissue expansion. NIH Grant: R01 CA166703.« less

Robust Inversion and Data Compression in Control Allocation

NASA Technical Reports Server (NTRS)

Hodel, A. Scottedward

2000-01-01

We present an off-line computational method for control allocation design. The control allocation function delta = F(z)tau = delta (sub 0) (z) mapping commanded body-frame torques to actuator commands is implicitly specified by trim condition delta (sub 0) (z) and by a robust pseudo-inverse problem double vertical line I - G(z) F(z) double vertical line less than epsilon (z) where G(z) is a system Jacobian evaluated at operating point z, z circumflex is an estimate of z, and epsilon (z) less than 1 is a specified error tolerance. The allocation function F(z) = sigma (sub i) psi (z) F (sub i) is computed using a heuristic technique for selecting wavelet basis functions psi and a constrained least-squares criterion for selecting the allocation matrices F (sub i). The method is applied to entry trajectory control allocation for a reusable launch vehicle (X-33).

Nonlinear study of the parallel velocity/tearing instability using an implicit, nonlinear resistive MHD solver

NASA Astrophysics Data System (ADS)

Chacon, L.; Finn, J. M.; Knoll, D. A.

2000-10-01

Recently, a new parallel velocity instability has been found.(J. M. Finn, Phys. Plasmas), 2, 12 (1995) This mode is a tearing mode driven unstable by curvature effects and sound wave coupling in the presence of parallel velocity shear. Under such conditions, linear theory predicts that tearing instabilities will grow even in situations in which the classical tearing mode is stable. This could then be a viable seed mechanism for the neoclassical tearing mode, and hence a non-linear study is of interest. Here, the linear and non-linear stages of this instability are explored using a fully implicit, fully nonlinear 2D reduced resistive MHD code,(L. Chacon et al), ``Implicit, Jacobian-free Newton-Krylov 2D reduced resistive MHD nonlinear solver,'' submitted to J. Comput. Phys. (2000) including viscosity and particle transport effects. The nonlinear implicit time integration is performed using the Newton-Raphson iterative algorithm. Krylov iterative techniques are employed for the required algebraic matrix inversions, implemented Jacobian-free (i.e., without ever forming and storing the Jacobian matrix), and preconditioned with a ``physics-based'' preconditioner. Nonlinear results indicate that, for large total plasma beta and large parallel velocity shear, the instability results in the generation of large poloidal shear flows and large magnetic islands even in regimes when the classical tearing mode is absolutely stable. For small viscosity, the time asymptotic state can be turbulent.

Development of advanced control schemes for telerobot manipulators

NASA Technical Reports Server (NTRS)

Nguyen, Charles C.; Zhou, Zhen-Lei

1991-01-01

To study space applications of telerobotics, Goddard Space Flight Center (NASA) has recently built a testbed composed mainly of a pair of redundant slave arms having seven degrees of freedom and a master hand controller system. The mathematical developments required for the computerized simulation study and motion control of the slave arms are presented. The slave arm forward kinematic transformation is presented which is derived using the D-H notation and is then reduced to its most simplified form suitable for real-time control applications. The vector cross product method is then applied to obtain the slave arm Jacobian matrix. Using the developed forward kinematic transformation and quaternions representation of the slave arm end-effector orientation, computer simulation is conducted to evaluate the efficiency of the Jacobian in converting joint velocities into Cartesian velocities and to investigate the accuracy of the Jacobian pseudo-inverse for various sampling times. In addition, the equivalence between Cartesian velocities and quaternion is also verified using computer simulation. The motion control of the slave arm is examined. Three control schemes, the joint-space adaptive control scheme, the Cartesian adaptive control scheme, and the hybrid position/force control scheme are proposed for controlling the motion of the slave arm end-effector. Development of the Cartesian adaptive control scheme is presented and some preliminary results of the remaining control schemes are presented and discussed.

Jacobian-Based Iterative Method for Magnetic Localization in Robotic Capsule Endoscopy

PubMed Central

Di Natali, Christian; Beccani, Marco; Simaan, Nabil; Valdastri, Pietro

2016-01-01

The purpose of this study is to validate a Jacobian-based iterative method for real-time localization of magnetically controlled endoscopic capsules. The proposed approach applies finite-element solutions to the magnetic field problem and least-squares interpolations to obtain closed-form and fast estimates of the magnetic field. By defining a closed-form expression for the Jacobian of the magnetic field relative to changes in the capsule pose, we are able to obtain an iterative localization at a faster computational time when compared with prior works, without suffering from the inaccuracies stemming from dipole assumptions. This new algorithm can be used in conjunction with an absolute localization technique that provides initialization values at a slower refresh rate. The proposed approach was assessed via simulation and experimental trials, adopting a wireless capsule equipped with a permanent magnet, six magnetic field sensors, and an inertial measurement unit. The overall refresh rate, including sensor data acquisition and wireless communication was 7 ms, thus enabling closed-loop control strategies for magnetic manipulation running faster than 100 Hz. The average localization error, expressed in cylindrical coordinates was below 7 mm in both the radial and axial components and 5° in the azimuthal component. The average error for the capsule orientation angles, obtained by fusing gyroscope and inclinometer measurements, was below 5°. PMID:27087799

A new div-curl result. Applications to the homogenization of elliptic systems and to the weak continuity of the Jacobian

NASA Astrophysics Data System (ADS)

Briane, M.; Casado Díaz, J.

2016-04-01

In this paper a new div-curl result is established in an open set Ω of RN, N ≥ 2, for the product σn ṡηn of two sequences of vector-valued functions σn, ηn such that σn is bounded in Lp(Ω)N, ηn is bounded in Lq(Ω)N, with 1 / p + 1 / q = 1 + 1 / (N - 1), and such that divσn, curlηn are compact in suitable spaces. The new assumption is that the product converges weakly in W - 1 , 1 (Ω). The approach is also new in the topic, and is based on a compactness result for bounded sequences in W 1 , q (Ω) through a suitable selection of annuli on which the gradients are not too high, in the spirit of [26,32] and using the imbedding of W 1 , q into Lp‧ for the unit sphere of RN. The div-curl result is applied to the homogenization of equi-coercive systems whose coefficients are equi-bounded in Lρ (Ω) for some ρ >N-1/2 if N > 2, or in L1 (Ω) if N = 2. It also allows us to prove a weak continuity result for the Jacobian for bounded sequences in W 1 , N - 1 (Ω) satisfying an alternative assumption to the L∞-strong estimate of [8]. Two examples show the sharpness of the results.

Three-dimensional magnetotelluric inversion including topography using deformed hexahedral edge finite elements, direct solvers and data space Gauss-Newton, parallelized on SMP computers

NASA Astrophysics Data System (ADS)

Kordy, M. A.; Wannamaker, P. E.; Maris, V.; Cherkaev, E.; Hill, G. J.

2014-12-01

We have developed an algorithm for 3D simulation and inversion of magnetotelluric (MT) responses using deformable hexahedral finite elements that permits incorporation of topography. Direct solvers parallelized on symmetric multiprocessor (SMP), single-chassis workstations with large RAM are used for the forward solution, parameter jacobians, and model update. The forward simulator, jacobians calculations, as well as synthetic and real data inversion are presented. We use first-order edge elements to represent the secondary electric field (E), yielding accuracy O(h) for E and its curl (magnetic field). For very low frequency or small material admittivity, the E-field requires divergence correction. Using Hodge decomposition, correction may be applied after the forward solution is calculated. It allows accurate E-field solutions in dielectric air. The system matrix factorization is computed using the MUMPS library, which shows moderately good scalability through 12 processor cores but limited gains beyond that. The factored matrix is used to calculate the forward response as well as the jacobians of field and MT responses using the reciprocity theorem. Comparison with other codes demonstrates accuracy of our forward calculations. We consider a popular conductive/resistive double brick structure and several topographic models. In particular, the ability of finite elements to represent smooth topographic slopes permits accurate simulation of refraction of electromagnetic waves normal to the slopes at high frequencies. Run time tests indicate that for meshes as large as 150x150x60 elements, MT forward response and jacobians can be calculated in ~2.5 hours per frequency. For inversion, we implemented data space Gauss-Newton method, which offers reduction in memory requirement and a significant speedup of the parameter step versus model space approach. For dense matrix operations we use tiling approach of PLASMA library, which shows very good scalability. In synthetic inversions we examine the importance of including the topography in the inversion and we test different regularization schemes using weighted second norm of model gradient as well as inverting for a static distortion matrix following Miensopust/Avdeeva approach. We also apply our algorithm to invert MT data collected at Mt St Helens.

A new family Jacobian solver for global three-dimensional modeling of atmospheric chemistry

NASA Astrophysics Data System (ADS)

Zhao, Xuepeng; Turco, Richard P.; Shen, Mei

1999-01-01

We present a new technique to solve complex sets of photochemical rate equations that is applicable to global modeling of the troposphere and stratosphere. The approach is based on the concept of "families" of species, whose chemical rate equations are tightly coupled. Variations of species concentrations within a family can be determined by inverting a linearized Jacobian matrix representing the family group. Since this group consists of a relatively small number of species the corresponding Jacobian has a low order (a minimatrix) compared to the Jacobian of the entire system. However, we go further and define a super-family that is the set of all families. The super-family is also solved by linearization and matrix inversion. The resulting Super-Family Matrix Inversion (SFMI) scheme is more stable and accurate than common family approaches. We discuss the numerical structure of the SFMI scheme and apply our algorithms to a comprehensive set of photochemical reactions. To evaluate performance, the SFMI scheme is compared with an optimized Gear solver. We find that the SFMI technique can be at least an order of magnitude more efficient than existing chemical solvers while maintaining relative errors in the calculations of 15% or less over a diurnal cycle. The largest SFMI errors arise at sunrise and sunset and during the evening when species concentrations may be very low. We show that sunrise/sunset errors can be minimized through a careful treatment of photodissociation during these periods; the nighttime deviations are negligible from the point of view of acceptable computational accuracy. The stability and flexibility of the SFMI algorithm should be sufficient for most modeling applications until major improvements in other modeling factors are achieved. In addition, because of its balanced computational design, SFMI can easily be adapted to parallel computing architectures. SFMI thus should allow practical long-term integrations of global chemistry coupled to general circulation and climate models, studies of interannual and interdecadal variability in atmospheric composition, simulations of past multidecadal trends owing to anthropogenic emissions, long-term forecasting associated with projected emissions, and sensitivity analyses for a wide range of physical and chemical parameters.

Non-classical continuum theory for solids incorporating internal rotations and rotations of Cosserat theories

NASA Astrophysics Data System (ADS)

Surana, K. S.; Joy, A. D.; Reddy, J. N.

2017-03-01

This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory, we have (i) the usual displacements ( ±b \\varvec{u}) and (ii) three internal rotations ({}_i ±b \\varvec{Θ}) about the axes of a triad whose axes are parallel to the x-frame arising from the Jacobian of deformation (which are completely defined by the skew-symmetric part of the Jacobian of deformation), and (iii) three additional rotations ({}_e ±b \\varvec{Θ}) about the axes of the same triad located at each material point as additional three degrees of freedom referred to as Cosserat rotations. This gives rise to ±b \\varvec{u} and {}_e ±b \\varvec{{Θ} as six degrees of freedom at a material point. The internal rotations ({}_i ±b \\varvec{Θ}), often neglected in classical continuum mechanics, exist in all deforming solid continua as these are due to Jacobian of deformation. When the internal rotations {}_i ±b \\varvec{Θ} are resisted by the deforming matter, conjugate moment tensor arises that together with {}_i ±b \\varvec{Θ} may result in energy storage and/or dissipation, which must be accounted for in the conservation and the balance laws. The Cosserat rotations {}_e ±b \\varvec{Θ} also result in conjugate moment tensor which, together with {}_e ±b \\varvec{Θ}, may also result in energy storage and/or dissipation. The main focus of the paper is a consistent derivation of conservation and balance laws that incorporate aforementioned physics and associated constitutive theories for thermoelastic solids. The mathematical model derived here has closure, and the constitutive theories derived using two alternate approaches are in agreement with each other as well as with the condition resulting from the entropy inequality. Material coefficients introduced in the constitutive theories are clearly defined and discussed.

Nonparaxial rogue waves in optical Kerr media.

PubMed

Temgoua, D D Estelle; Kofane, T C

2015-06-01

We consider the inhomogeneous nonparaxial nonlinear Schrödinger (NLS) equation with varying dispersion, nonlinearity, and nonparaxiality coefficients, which governs the nonlinear wave propagation in an inhomogeneous optical fiber system. We present the similarity and Darboux transformations and for the chosen specific set of parameters and free functions, the first- and second-order rational solutions of the nonparaxial NLS equation are generated. In particular, the features of rogue waves throughout polynomial and Jacobian elliptic functions are analyzed, showing the nonparaxial effects. It is shown that the nonparaxiality increases the intensity of rogue waves by increasing the length and reducing the width simultaneously, by the way it increases their speed and penalizes interactions between them. These properties and the characteristic controllability of the nonparaxial rogue waves may give another opportunity to perform experimental realizations and potential applications in optical fibers.

Improved Quasi-Newton method via PSB update for solving systems of nonlinear equations

NASA Astrophysics Data System (ADS)

Mamat, Mustafa; Dauda, M. K.; Waziri, M. Y.; Ahmad, Fadhilah; Mohamad, Fatma Susilawati

2016-10-01

The Newton method has some shortcomings which includes computation of the Jacobian matrix which may be difficult or even impossible to compute and solving the Newton system in every iteration. Also, the common setback with some quasi-Newton methods is that they need to compute and store an n × n matrix at each iteration, this is computationally costly for large scale problems. To overcome such drawbacks, an improved Method for solving systems of nonlinear equations via PSB (Powell-Symmetric-Broyden) update is proposed. In the proposed method, the approximate Jacobian inverse Hk of PSB is updated and its efficiency has improved thereby require low memory storage, hence the main aim of this paper. The preliminary numerical results show that the proposed method is practically efficient when applied on some benchmark problems.

Multivariate statistics of the Jacobian matrices in tensor based morphometry and their application to HIV/AIDS.

PubMed

Lepore, Natasha; Brun, Caroline A; Chiang, Ming-Chang; Chou, Yi-Yu; Dutton, Rebecca A; Hayashi, Kiralee M; Lopez, Oscar L; Aizenstein, Howard J; Toga, Arthur W; Becker, James T; Thompson, Paul M

2006-01-01

Tensor-based morphometry (TBM) is widely used in computational anatomy as a means to understand shape variation between structural brain images. A 3D nonlinear registration technique is typically used to align all brain images to a common neuroanatomical template, and the deformation fields are analyzed statistically to identify group differences in anatomy. However, the differences are usually computed solely from the determinants of the Jacobian matrices that are associated with the deformation fields computed by the registration procedure. Thus, much of the information contained within those matrices gets thrown out in the process. Only the magnitude of the expansions or contractions is examined, while the anisotropy and directional components of the changes are ignored. Here we remedy this problem by computing multivariate shape change statistics using the strain matrices. As the latter do not form a vector space, means and covariances are computed on the manifold of positive-definite matrices to which they belong. We study the brain morphology of 26 HIV/AIDS patients and 14 matched healthy control subjects using our method. The images are registered using a high-dimensional 3D fluid registration algorithm, which optimizes the Jensen-Rényi divergence, an information-theoretic measure of image correspondence. The anisotropy of the deformation is then computed. We apply a manifold version of Hotelling's T2 test to the strain matrices. Our results complement those found from the determinants of the Jacobians alone and provide greater power in detecting group differences in brain structure.

A cut-&-paste strategy for the 3-D inversion of helicopter-borne electromagnetic data - I. 3-D inversion using the explicit Jacobian and a tensor-based formulation

NASA Astrophysics Data System (ADS)

Scheunert, M.; Ullmann, A.; Afanasjew, M.; Börner, R.-U.; Siemon, B.; Spitzer, K.

2016-06-01

We present an inversion concept for helicopter-borne frequency-domain electromagnetic (HEM) data capable of reconstructing 3-D conductivity structures in the subsurface. Standard interpretation procedures often involve laterally constrained stitched 1-D inversion techniques to create pseudo-3-D models that are largely representative for smoothly varying conductivity distributions in the subsurface. Pronounced lateral conductivity changes may, however, produce significant artifacts that can lead to serious misinterpretation. Still, 3-D inversions of entire survey data sets are numerically very expensive. Our approach is therefore based on a cut-&-paste strategy whereupon the full 3-D inversion needs to be applied only to those parts of the survey where the 1-D inversion actually fails. The introduced 3-D Gauss-Newton inversion scheme exploits information given by a state-of-the-art (laterally constrained) 1-D inversion. For a typical HEM measurement, an explicit representation of the Jacobian matrix is inevitable which is caused by the unique transmitter-receiver relation. We introduce tensor quantities which facilitate the matrix assembly of the forward operator as well as the efficient calculation of the Jacobian. The finite difference forward operator incorporates the displacement currents because they may seriously affect the electromagnetic response at frequencies above 100. Finally, we deliver the proof of concept for the inversion using a synthetic data set with a noise level of up to 5%.

Correlation of spacecraft thermal mathematical models to reference data

NASA Astrophysics Data System (ADS)

Torralbo, Ignacio; Perez-Grande, Isabel; Sanz-Andres, Angel; Piqueras, Javier

2018-03-01

Model-to-test correlation is a frequent problem in spacecraft-thermal control design. The idea is to determine the values of the parameters of the thermal mathematical model (TMM) that allows reaching a good fit between the TMM results and test data, in order to reduce the uncertainty of the mathematical model. Quite often, this task is performed manually, mainly because a good engineering knowledge and experience is needed to reach a successful compromise, but the use of a mathematical tool could facilitate this work. The correlation process can be considered as the minimization of the error of the model results with regard to the reference data. In this paper, a simple method is presented suitable to solve the TMM-to-test correlation problem, using Jacobian matrix formulation and Moore-Penrose pseudo-inverse, generalized to include several load cases. Aside, in simple cases, this method also allows for analytical solutions to be obtained, which helps to analyze some problems that appear when the Jacobian matrix is singular. To show the implementation of the method, two problems have been considered, one more academic, and the other one the TMM of an electronic box of PHI instrument of ESA Solar Orbiter mission, to be flown in 2019. The use of singular value decomposition of the Jacobian matrix to analyze and reduce these models is also shown. The error in parameter space is used to assess the quality of the correlation results in both models.

Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method

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

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-04-01

The phase appearance/disappearance issue presents serious numerical challenges in two-phase flow simulations. Many existing reactor safety analysis codes use different kinds of treatments for the phase appearance/disappearance problem. However, to our best knowledge, there are no fully satisfactory solutions. Additionally, the majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many situations, it is desirable to use high-resolution spatial discretization and fully implicit time integration schemes to reduce numerical errors. In this work, we adapted a high-resolution spatial discretization scheme on staggered grid mesh and fully implicit time integrationmore » methods (such as BDF1 and BDF2) to solve the two-phase flow problems. The discretized nonlinear system was solved by the Jacobian-free Newton Krylov (JFNK) method, which does not require the derivation and implementation of analytical Jacobian matrix. These methods were tested with a few two-phase flow problems with phase appearance/disappearance phenomena considered, such as a linear advection problem, an oscillating manometer problem, and a sedimentation problem. The JFNK method demonstrated extremely robust and stable behaviors in solving the two-phase flow problems with phase appearance/disappearance. No special treatments such as water level tracking or void fraction limiting were used. High-resolution spatial discretization and second- order fully implicit method also demonstrated their capabilities in significantly reducing numerical errors.« less

Application of sensitivity-analysis techniques to the calculation of topological quantities

NASA Astrophysics Data System (ADS)

Gilchrist, Stuart

2017-08-01

Magnetic reconnection in the corona occurs preferentially at sites where the magnetic connectivity is either discontinuous or has a large spatial gradient. Hence there is a general interest in computing quantities (like the squashing factor) that characterize the gradient in the field-line mapping function. Here we present an algorithm for calculating certain (quasi)topological quantities using mathematical techniques from the field of ``sensitivity-analysis''. The method is based on the calculation of a three dimensional field-line mapping Jacobian from which all the present topological quantities of interest can be derived. We will present the algorithm and the details of a publicly available set of libraries that implement the algorithm.

Surface and Atmospheric Contributions to Passive Microwave Brightness Temperatures for Falling Snow Events

NASA Technical Reports Server (NTRS)

Skofronick-Jackson, Gail; Johnson, Benjamin T.

2011-01-01

Physically based passive microwave precipitation retrieval algorithms require a set of relationships between satellite -observed brightness temperatures (TBs) and the physical state of the underlying atmosphere and surface. These relationships are nonlinear, such that inversions are ill ]posed especially over variable land surfaces. In order to elucidate these relationships, this work presents a theoretical analysis using TB weighting functions to quantify the percentage influence of the TB resulting from absorption, emission, and/or reflection from the surface, as well as from frozen hydrometeors in clouds, from atmospheric water vapor, and from other contributors. The percentage analysis was also compared to Jacobians. The results are presented for frequencies from 10 to 874 GHz, for individual snow profiles, and for averages over three cloud-resolving model simulations of falling snow. The bulk structure (e.g., ice water path and cloud depth) of the underlying cloud scene was found to affect the resultant TB and percentages, producing different values for blizzard, lake effect, and synoptic snow events. The slant path at a 53 viewing angle increases the hydrometeor contributions relative to nadir viewing channels. Jacobians provide the magnitude and direction of change in the TB values due to a change in the underlying scene; however, the percentage analysis provides detailed information on how that change affected contributions to the TB from the surface, hydrometeors, and water vapor. The TB percentage information presented in this paper provides information about the relative contributions to the TB and supplies key pieces of information required to develop and improve precipitation retrievals over land surfaces.

Chemistry-split techniques for viscous reactive blunt body flow computations

NASA Technical Reports Server (NTRS)

Li, C. P.

1987-01-01

The weak-coupling structure between the fluid and species equations has been exploited and resulted in three, closely related, time-iterative implicit techniques. While the primitive variables are solved in two separated groups and each by an Alternating Direction Implicit (ADI) factorization scheme, the rate-species Jacobian can be treated in either full or diagonal matrix form, or simply ignored. The latter two versions render the split technique to solving for species as scalar rather than vector variables. The solution is completed at the end of each iteration after determining temperature and pressure from the flow density, energy and species concentrations. Numerical experimentation has shown that the split scalar technique, using partial rate Jacobian, yields the best overall stability and consistency. Satisfactory viscous solutions were obtained for an ellipsoidal body of axis ratio 3:1 at Mach 35 and an angle of attack of 20 degrees.

An assessment of coupling algorithms for nuclear reactor core physics simulations

DOE PAGES

Hamilton, Steven; Berrill, Mark; Clarno, Kevin; ...

2016-04-01

This paper evaluates the performance of multiphysics coupling algorithms applied to a light water nuclear reactor core simulation. The simulation couples the k-eigenvalue form of the neutron transport equation with heat conduction and subchannel flow equations. We compare Picard iteration (block Gauss–Seidel) to Anderson acceleration and multiple variants of preconditioned Jacobian-free Newton–Krylov (JFNK). The performance of the methods are evaluated over a range of energy group structures and core power levels. A novel physics-based approximation to a Jacobian-vector product has been developed to mitigate the impact of expensive on-line cross section processing steps. Furthermore, numerical simulations demonstrating the efficiency ofmore » JFNK and Anderson acceleration relative to standard Picard iteration are performed on a 3D model of a nuclear fuel assembly. Both criticality (k-eigenvalue) and critical boron search problems are considered.« less

Symmetric and Asymmetric Tendencies in Stable Complex Systems

PubMed Central

Tan, James P. L.

2016-01-01

A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by obtaining eigenvalue bounds of the Jacobian, we show that stable complex systems will favor mutualistic and competitive relationships that are asymmetrical (non-reciprocative) and trophic relationships that are symmetrical (reciprocative). Additionally, we define a measure called the interdependence diversity that quantifies how distributed the dependencies are between the dynamical variables in the system. We find that increasing interdependence diversity has a destabilizing effect on the equilibrium point, and the effect is greater for trophic relationships than for mutualistic and competitive relationships. These predictions are consistent with empirical observations in ecology. More importantly, our findings suggest stabilization algorithms that can apply very generally to a variety of complex systems. PMID:27545722

Symmetric and Asymmetric Tendencies in Stable Complex Systems.

PubMed

Tan, James P L

2016-08-22

A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by obtaining eigenvalue bounds of the Jacobian, we show that stable complex systems will favor mutualistic and competitive relationships that are asymmetrical (non-reciprocative) and trophic relationships that are symmetrical (reciprocative). Additionally, we define a measure called the interdependence diversity that quantifies how distributed the dependencies are between the dynamical variables in the system. We find that increasing interdependence diversity has a destabilizing effect on the equilibrium point, and the effect is greater for trophic relationships than for mutualistic and competitive relationships. These predictions are consistent with empirical observations in ecology. More importantly, our findings suggest stabilization algorithms that can apply very generally to a variety of complex systems.

An assessment of coupling algorithms for nuclear reactor core physics simulations

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

Hamilton, Steven; Berrill, Mark; Clarno, Kevin

This paper evaluates the performance of multiphysics coupling algorithms applied to a light water nuclear reactor core simulation. The simulation couples the k-eigenvalue form of the neutron transport equation with heat conduction and subchannel flow equations. We compare Picard iteration (block Gauss–Seidel) to Anderson acceleration and multiple variants of preconditioned Jacobian-free Newton–Krylov (JFNK). The performance of the methods are evaluated over a range of energy group structures and core power levels. A novel physics-based approximation to a Jacobian-vector product has been developed to mitigate the impact of expensive on-line cross section processing steps. Furthermore, numerical simulations demonstrating the efficiency ofmore » JFNK and Anderson acceleration relative to standard Picard iteration are performed on a 3D model of a nuclear fuel assembly. Both criticality (k-eigenvalue) and critical boron search problems are considered.« less

An assessment of coupling algorithms for nuclear reactor core physics simulations

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

Hamilton, Steven, E-mail: hamiltonsp@ornl.gov; Berrill, Mark, E-mail: berrillma@ornl.gov; Clarno, Kevin, E-mail: clarnokt@ornl.gov

This paper evaluates the performance of multiphysics coupling algorithms applied to a light water nuclear reactor core simulation. The simulation couples the k-eigenvalue form of the neutron transport equation with heat conduction and subchannel flow equations. We compare Picard iteration (block Gauss–Seidel) to Anderson acceleration and multiple variants of preconditioned Jacobian-free Newton–Krylov (JFNK). The performance of the methods are evaluated over a range of energy group structures and core power levels. A novel physics-based approximation to a Jacobian-vector product has been developed to mitigate the impact of expensive on-line cross section processing steps. Numerical simulations demonstrating the efficiency of JFNKmore » and Anderson acceleration relative to standard Picard iteration are performed on a 3D model of a nuclear fuel assembly. Both criticality (k-eigenvalue) and critical boron search problems are considered.« less

Correction of electrode modelling errors in multi-frequency EIT imaging.

PubMed

Jehl, Markus; Holder, David

2016-06-01

The differentiation of haemorrhagic from ischaemic stroke using electrical impedance tomography (EIT) requires measurements at multiple frequencies, since the general lack of healthy measurements on the same patient excludes time-difference imaging methods. It has previously been shown that the inaccurate modelling of electrodes constitutes one of the largest sources of image artefacts in non-linear multi-frequency EIT applications. To address this issue, we augmented the conductivity Jacobian matrix with a Jacobian matrix with respect to electrode movement. Using this new algorithm, simulated ischaemic and haemorrhagic strokes in a realistic head model were reconstructed for varying degrees of electrode position errors. The simultaneous recovery of conductivity spectra and electrode positions removed most artefacts caused by inaccurately modelled electrodes. Reconstructions were stable for electrode position errors of up to 1.5 mm standard deviation along both surface dimensions. We conclude that this method can be used for electrode model correction in multi-frequency EIT.

Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate.

PubMed

Liu, Haofei; Sun, Wei

2017-08-01

Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.

Tall sections from non-minimal transformations

DOE PAGES

Morrison, David R.; Park, Daniel S.

2016-10-10

In previous study, we have shown that elliptic fibrations with two sections, or Mordell-Weil rank one, can always be mapped birationally to a Weierstrass model of a certain form, namely, the Jacobian of a P 112 model. Most constructions of elliptically fibered Calabi-Yau manifolds with two sections have been carried out assuming that the image of this birational map was a “minimal” Weierstrass model. In this paper, we show that for some elliptically fibered Calabi-Yau manifolds with Mordell-Weil rank-one, the Jacobian of the P 112 model is not minimal. Said another way, starting from a Calabi-Yau Weierstrass model, the totalmore » space must be blown up (thereby destroying the “Calabi-Yau” property) in order to embed the model into P 112. In particular, we show that the elliptic fibrations studied recently by Klevers and Taylor fall into this class of models.« less

Efficient numerical calculation of MHD equilibria with magnetic islands, with particular application to saturated neoclassical tearing modes

NASA Astrophysics Data System (ADS)

Raburn, Daniel Louis

We have developed a preconditioned, globalized Jacobian-free Newton-Krylov (JFNK) solver for calculating equilibria with magnetic islands. The solver has been developed in conjunction with the Princeton Iterative Equilibrium Solver (PIES) and includes two notable enhancements over a traditional JFNK scheme: (1) globalization of the algorithm by a sophisticated backtracking scheme, which optimizes between the Newton and steepest-descent directions; and, (2) adaptive preconditioning, wherein information regarding the system Jacobian is reused between Newton iterations to form a preconditioner for our GMRES-like linear solver. We have developed a formulation for calculating saturated neoclassical tearing modes (NTMs) which accounts for the incomplete loss of a bootstrap current due to gradients of multiple physical quantities. We have applied the coupled PIES-JFNK solver to calculate saturated island widths on several shots from the Tokamak Fusion Test Reactor (TFTR) and have found reasonable agreement with experimental measurement.

Radiance and Jacobian Intercomparison of Radiative Transfer Models Applied to HIRS and AMSU Channels

NASA Technical Reports Server (NTRS)

Garand, L.; Turner, D. S.; Larocque, M.; Bates, J.; Boukabara, S.; Brunel, P.; Chevallier, F.; Deblonde, G.; Engelen, R.; Hollingshead, M.;

Radiance and Jacobian Intercomparison of Radiative Transfer Models Applied to HIRS and AMSU Channels

NASA Technical Reports Server (NTRS)

Garand, L.; Turner, D. S.; Larocque, M.; Bates, J.; Boukabara, S.; Brunel, P.; Chevallier, F.; Deblonde, G.; Engelen, R.; Atlas, Robert (Technical Monitor)

2000-01-01

The goals of this study are the evaluation of current fast radiative transfer models (RTMs) and line-by-line (LBL) models. The intercomparison focuses on the modeling of 11 representative sounding channels routinely used at numerical weather prediction centers: seven HIRS (High-resolution Infrared Sounder) and four AMSU (Advanced Microwave Sounding Unit) channels. Interest in this topic was evidenced by the participation of 24 scientists from 16 institutions. An ensemble of 42 diverse atmospheres was used and results compiled for 19 infrared models and 10 microwave models, including several LBL RTMs. For the first time, not only radiances, but also Jacobians (of temperature, water vapor, and ozone) were compared to various LBL models for many channels. In the infrared, LBL models typically agree to within 0.05-0.15 K (standard deviation) in terms of top-of-the-atmosphere brightness temperature (BT). Individual differences up to 0.5 K still exist, systematic in some channels, and linked to the type of atmosphere in others. The best fast models emulate LBL BTs to within 0.25 K, but no model achieves this desirable level of success for all channels. The ozone modeling is particularly challenging. In the microwave, fast models generally do quite well against the LBL model to which they were tuned. However significant differences were noted among LBL models. Extending the intercomparison to the Jacobians proved very useful in detecting subtle and more obvious modeling errors. In addition, total and single gas optical depths were calculated, which provided additional insight on the nature of differences. Recommendations for future intercomparisons are suggested.

Lung deformations and radiation-induced regional lung collapse in patients treated with stereotactic body radiation therapy

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

Diot, Quentin, E-mail: quentin.diot@ucdenver.edu; Kavanagh, Brian; Vinogradskiy, Yevgeniy

2015-11-15

Purpose: To differentiate radiation-induced fibrosis from regional lung collapse outside of the high dose region in patients treated with stereotactic body radiation therapy (SBRT) for lung tumors. Methods: Lung deformation maps were computed from pre-treatment and post-treatment computed tomography (CT) scans using a point-to-point translation method. Fifty anatomical landmarks inside the lung (vessel or airway branches) were matched on planning and follow-up scans for the computation process. Two methods using the deformation maps were developed to differentiate regional lung collapse from fibrosis: vector field and Jacobian methods. A total of 40 planning and follow-ups CT scans were analyzed for 20more » lung SBRT patients. Results: Regional lung collapse was detected in 15 patients (75%) using the vector field method, in ten patients (50%) using the Jacobian method, and in 12 patients (60%) by radiologists. In terms of sensitivity and specificity the Jacobian method performed better. Only weak correlations were observed between the dose to the proximal airways and the occurrence of regional lung collapse. Conclusions: The authors presented and evaluated two novel methods using anatomical lung deformations to investigate lung collapse and fibrosis caused by SBRT treatment. Differentiation of these distinct physiological mechanisms beyond what is usually labeled “fibrosis” is necessary for accurate modeling of lung SBRT-induced injuries. With the help of better models, it becomes possible to expand the therapeutic benefits of SBRT to a larger population of lung patients with large or centrally located tumors that were previously considered ineligible.« less

Regularization Parameter Selection for Nonlinear Iterative Image Restoration and MRI Reconstruction Using GCV and SURE-Based Methods

PubMed Central

Ramani, Sathish; Liu, Zhihao; Rosen, Jeffrey; Nielsen, Jon-Fredrik; Fessler, Jeffrey A.

2012-01-01

Regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values. We focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive (possibly complex) Gaussian noise. Generalized cross-validation (GCV) and (weighted) mean-squared error (MSE) approaches (based on Stein's Unbiased Risk Estimate— SURE) need the Jacobian matrix of the nonlinear reconstruction operator (representative of the iterative algorithm) with respect to the data. We derive the desired Jacobian matrix for two types of nonlinear iterative algorithms: a fast variant of the standard iterative reweighted least-squares method and the contemporary split-Bregman algorithm, both of which can accommodate a wide variety of analysis- and synthesis-type regularizers. The proposed approach iteratively computes two weighted SURE-type measures: Predicted-SURE and Projected-SURE (that require knowledge of noise variance σ2), and GCV (that does not need σ2) for these algorithms. We apply the methods to image restoration and to magnetic resonance image (MRI) reconstruction using total variation (TV) and an analysis-type ℓ1-regularization. We demonstrate through simulations and experiments with real data that minimizing Predicted-SURE and Projected-SURE consistently lead to near-MSE-optimal reconstructions. We also observed that minimizing GCV yields reconstruction results that are near-MSE-optimal for image restoration and slightly sub-optimal for MRI. Theoretical derivations in this work related to Jacobian matrix evaluations can be extended, in principle, to other types of regularizers and reconstruction algorithms. PMID:22531764

Aerosol Polarimetry Sensor (APS): Design Summary, Performance and Potential Modifications

NASA Technical Reports Server (NTRS)

Cairns, Brian

2014-01-01

APS is a mature design that has already been built and has a TRL of 7. Algorithmic and retrieval capabilities continue to improve and make better and more sophisticated used of the data. Adjoint solutions, both in one dimensional and three dimensional are computationally efficient and should be the preferred implementation for the calculation of Jacobians (one dimensional), or cost-function gradients (three dimensional). Adjoint solutions necessarily provide resolution of internal fields and simplify incorporation of active measurements in retrievals, which will be necessary for a future ACE mission. Its best to test these capabilities when you know the answer: OSSEs that are well constrained observationally provide the best place to test future multi-instrument platform capabilities and ensure capabilities will meet scientific needs.

Mapped grid methods for long-range molecules and cold collisions

NASA Astrophysics Data System (ADS)

Willner, K.; Dulieu, O.; Masnou-Seeuws, F.

2004-01-01

The paper discusses ways of improving the accuracy of numerical calculations for vibrational levels of diatomic molecules close to the dissociation limit or for ultracold collisions, in the framework of a grid representation. In order to avoid the implementation of very large grids, Kokoouline et al. [J. Chem. Phys. 110, 9865 (1999)] have proposed a mapping procedure through introduction of an adaptive coordinate x subjected to the variation of the local de Broglie wavelength as a function of the internuclear distance R. Some unphysical levels ("ghosts") then appear in the vibrational series computed via a mapped Fourier grid representation. In the present work the choice of the basis set is reexamined, and two alternative expansions are discussed: Sine functions and Hardy functions. It is shown that use of a basis set with fixed nodes at both grid ends is efficient to eliminate "ghost" solutions. It is further shown that the Hamiltonian matrix in the sine basis can be calculated very accurately by using an auxiliary basis of cosine functions, overcoming the problems arising from numerical calculation of the Jacobian J(x) of the R→x coordinate transformation.

Analysis of Hypersonic Vehicle Wakes

DTIC Science & Technology

2015-09-17

factor used with viscous Jacobian matrix of left eigenvectors for A R specific gas constant Re Reynolds number Recell cell Reynolds number......focus was shifted to characterizing other wake phenomena. The aerothermal phenomena of interest in the wake include: gas properties, chemical species

Strategies to Enhance the Model Update in Regions of Weak Sensitivities for Use in Full Waveform Inversion

NASA Astrophysics Data System (ADS)

Nuber, André; Manukyan, Edgar; Maurer, Hansruedi

2014-05-01

Conventional methods of interpreting seismic data rely on filtering and processing limited portions of the recorded wavefield. Typically, either reflections, refractions or surface waves are considered in isolation. Particularly in near-surface engineering and environmental investigations (depths less than, say 100 m), these wave types often overlap in time and are difficult to separate. Full waveform inversion is a technique that seeks to exploit and interpret the full information content of the seismic records without the need for separating events first; it yields models of the subsurface at sub-wavelength resolution. We use a finite element modelling code to solve the 2D elastic isotropic wave equation in the frequency domain. This code is part of a Gauss-Newton inversion scheme which we employ to invert for the P- and S-wave velocities as well as for density in the subsurface. For shallow surface data the use of an elastic forward solver is essential because surface waves often dominate the seismograms. This leads to high sensitivities (partial derivatives contained in the Jacobian matrix of the Gauss-Newton inversion scheme) and thus large model updates close to the surface. Reflections from deeper structures may also include useful information, but the large sensitivities of the surface waves often preclude this information from being fully exploited. We have developed two methods that balance the sensitivity distributions and thus may help resolve the deeper structures. The first method includes equilibrating the columns of the Jacobian matrix prior to every inversion step by multiplying them with individual scaling factors. This is expected to also balance the model updates throughout the entire subsurface model. It can be shown that this procedure is mathematically equivalent to balancing the regularization weights of the individual model parameters. A proper choice of the scaling factors required to balance the Jacobian matrix is critical. We decided to normalise the columns of the Jacobian based on their absolute column sum, but defining an upper threshold for the scaling factors. This avoids particularly small and therefore insignificant sensitivities being over-boosted, which would produce unstable results. The second method proposed includes adjusting the inversion cell size with depth. Multiple cells of the forward modelling grid are merged to form larger inversion cells (typical ratios between forward and inversion cells are in the order of 1:100). The irregular inversion grid is adapted to the expected resolution power of full waveform inversion. Besides stabilizing the inversion, this approach also reduces the number of model parameters to be recovered. Consequently, the computational costs and the memory consumption are reduced significantly. This is particularly critical when Gauss-Newton type inversion schemes are employed. Extensive tests with synthetic data demonstrated that both methods stabilise the inversion and improve the inversion results. The two methods have some redundancy, which can be seen when both are applied simultaneously, that is, when scaling of the Jacobian matrix is applied to an irregular inversion grid. The calculated scaling factors are quite balanced and span a much smaller range than in the case of a regular inversion grid.

Sensitivity analysis of dynamic biological systems with time-delays.

PubMed

Wu, Wu Hsiung; Wang, Feng Sheng; Chang, Maw Shang

2010-10-15

Mathematical modeling has been applied to the study and analysis of complex biological systems for a long time. Some processes in biological systems, such as the gene expression and feedback control in signal transduction networks, involve a time delay. These systems are represented as delay differential equation (DDE) models. Numerical sensitivity analysis of a DDE model by the direct method requires the solutions of model and sensitivity equations with time-delays. The major effort is the computation of Jacobian matrix when computing the solution of sensitivity equations. The computation of partial derivatives of complex equations either by the analytic method or by symbolic manipulation is time consuming, inconvenient, and prone to introduce human errors. To address this problem, an automatic approach to obtain the derivatives of complex functions efficiently and accurately is necessary. We have proposed an efficient algorithm with an adaptive step size control to compute the solution and dynamic sensitivities of biological systems described by ordinal differential equations (ODEs). The adaptive direct-decoupled algorithm is extended to solve the solution and dynamic sensitivities of time-delay systems describing by DDEs. To save the human effort and avoid the human errors in the computation of partial derivatives, an automatic differentiation technique is embedded in the extended algorithm to evaluate the Jacobian matrix. The extended algorithm is implemented and applied to two realistic models with time-delays: the cardiovascular control system and the TNF-α signal transduction network. The results show that the extended algorithm is a good tool for dynamic sensitivity analysis on DDE models with less user intervention. By comparing with direct-coupled methods in theory, the extended algorithm is efficient, accurate, and easy to use for end users without programming background to do dynamic sensitivity analysis on complex biological systems with time-delays.

Entropy-stable summation-by-parts discretization of the Euler equations on general curved elements

NASA Astrophysics Data System (ADS)

Crean, Jared; Hicken, Jason E.; Del Rey Fernández, David C.; Zingg, David W.; Carpenter, Mark H.

2018-03-01

We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we consider general multidimensional SBP elements, building on and generalizing previous work with tensor-product discretizations. In the absence of dissipation, we prove that the semi-discrete scheme conserves entropy; significantly, this proof of nonlinear L2 stability does not rely on integral exactness. Furthermore, interior penalties can be incorporated into the discretization to ensure that the total (mathematical) entropy decreases monotonically, producing an entropy-stable scheme. SBP discretizations with curved elements remain accurate, conservative, and entropy stable provided the mapping Jacobian satisfies the discrete metric invariants; polynomial mappings at most one degree higher than the SBP operators automatically satisfy the metric invariants in two dimensions. In three-dimensions, we describe an elementwise optimization that leads to suitable Jacobians in the case of polynomial mappings. The properties of the semi-discrete scheme are verified and investigated using numerical experiments.

Jointly reconstructing ground motion and resistivity for ERT-based slope stability monitoring

NASA Astrophysics Data System (ADS)

Boyle, Alistair; Wilkinson, Paul B.; Chambers, Jonathan E.; Meldrum, Philip I.; Uhlemann, Sebastian; Adler, Andy

2018-02-01

Electrical resistivity tomography (ERT) is increasingly being used to investigate unstable slopes and monitor the hydrogeological processes within. But movement of electrodes or incorrect placement of electrodes with respect to an assumed model can introduce significant resistivity artefacts into the reconstruction. In this work, we demonstrate a joint resistivity and electrode movement reconstruction algorithm within an iterative Gauss-Newton framework. We apply this to ERT monitoring data from an active slow-moving landslide in the UK. Results show fewer resistivity artefacts and suggest that electrode movement and resistivity can be reconstructed at the same time under certain conditions. A new 2.5-D formulation for the electrode position Jacobian is developed and is shown to give accurate numerical solutions when compared to the adjoint method on 3-D models. On large finite element meshes, the calculation time of the newly developed approach was also proven to be orders of magnitude faster than the 3-D adjoint method and addressed modelling errors in the 2-D perturbation and adjoint electrode position Jacobian.

Robust adaptive kinematic control of redundant robots

NASA Technical Reports Server (NTRS)

Tarokh, M.; Zuck, D. D.

1992-01-01

The paper presents a general method for the resolution of redundancy that combines the Jacobian pseudoinverse and augmentation approaches. A direct adaptive control scheme is developed to generate joint angle trajectories for achieving desired end-effector motion as well as additional user defined tasks. The scheme ensures arbitrarily small errors between the desired and the actual motion of the manipulator. Explicit bounds on the errors are established that are directly related to the mismatch between actual and estimated pseudoinverse Jacobian matrix, motion velocity and the controller gain. It is shown that the scheme is tolerant of the mismatch and consequently only infrequent pseudoinverse computations are needed during a typical robot motion. As a result, the scheme is computationally fast, and can be implemented for real-time control of redundant robots. A method is incorporated to cope with the robot singularities allowing the manipulator to get very close or even pass through a singularity while maintaining a good tracking performance and acceptable joint velocities. Computer simulations and experimental results are provided in support of the theoretical developments.

A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids

DOE PAGES

Xia, Yidong; Luo, Hong; Frisbey, Megan; ...

2014-07-01

A set of implicit methods are proposed for a third-order hierarchical WENO reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. An attractive feature in these methods are the application of the Jacobian matrix based on the P1 element approximation, resulting in a huge reduction of memory requirement compared with DG (P2). Also, three approaches -- analytical derivation, divided differencing, and automatic differentiation (AD) are presented to construct the Jacobian matrix respectively, where the AD approach shows the best robustness. A variety of compressible flow problems are computed to demonstrate the fast convergence property of the implemented flowmore » solver. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results on complex geometries indicate that this low-storage implicit method can provide a viable and attractive DG solution for complicated flows of practical importance.« less

Analysis and design of a six-degree-of-freedom Stewart platform-based robotic wrist

NASA Technical Reports Server (NTRS)

Nguyen, Charles C.; Antrazi, Sami; Zhou, Zhen-Lei

1991-01-01

The kinematic analysis and implementation of a six degree of freedom robotic wrist which is mounted to a general open-kinetic chain manipulator to serve as a restbed for studying precision robotic assembly in space is discussed. The wrist design is based on the Stewart Platform mechanism and consists mainly of two platforms and six linear actuators driven by DC motors. Position feedback is achieved by linear displacement transducers mounted along the actuators and force feedback is obtained by a 6 degree of freedom force sensor mounted between the gripper and the payload platform. The robot wrist inverse kinematics which computes the required actuator lengths corresponding to Cartesian variables has a closed-form solution. The forward kinematics is solved iteratively using the Newton-Ralphson method which simultaneously provides a modified Jacobian Matrix which relates length velocities to Cartesian translational velocities and time rates of change of roll-pitch-yaw angles. Results of computer simulation conducted to evaluate the efficiency of the forward kinematics and Modified Jacobian Matrix are discussed.

Coordinated Control of a Planar Dual-Crane Non-Fully Restrained System

DTIC Science & Technology

2008-12-01

Support Over-The-Shore (HSOTS) 2007 in Puerto Quetzal , Guatemala. . . . . . . . . . . . . . 30 Figure 27. Reference frame and coordinate definitions...2007 in Puerto Quetzal , Guatemala. 30 require the construction an inverse of the Jacobian, but rather the transpose only. It is noted that the effector

Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change

DOE PAGES

Nourgaliev, R.; Luo, H.; Weston, B.; ...

2015-11-11

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method’s capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing (AM). We focus on the method’s accuracy (in both space and time), as wellmore » as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver.« less

Generalized spherical and simplicial coordinates

NASA Astrophysics Data System (ADS)

Richter, Wolf-Dieter

2007-12-01

Elementary trigonometric quantities are defined in l2,p analogously to that in l2,2, the sine and cosine functions are generalized for each p>0 as functions sinp and cosp such that they satisfy the basic equation cosp([phi])p+sinp([phi])p=1. The p-generalized radius coordinate of a point [xi][set membership, variant]Rn is defined for each p>0 as . On combining these quantities, ln,p-spherical coordinates are defined. It is shown that these coordinates are nearly related to ln,p-simplicial coordinates. The Jacobians of these generalized coordinate transformations are derived. Applications and interpretations from analysis deal especially with the definition of a generalized surface content on ln,p-spheres which is nearly related to a modified co-area formula and an extension of Cavalieri's and Torricelli's indivisibeln method, and with differential equations. Applications from probability theory deal especially with a geometric interpretation of the uniform probability distribution on the ln,p-sphere and with the derivation of certain generalized statistical distributions.

A constrained registration problem based on Ciarlet-Geymonat stored energy

NASA Astrophysics Data System (ADS)

Derfoul, Ratiba; Le Guyader, Carole

2014-03-01

In this paper, we address the issue of designing a theoretically well-motivated registration model capable of handling large deformations and including geometrical constraints, namely landmark points to be matched, in a variational framework. The theory of linear elasticity being unsuitable in this case, since assuming small strains and the validity of Hooke's law, the introduced functional is based on nonlinear elasticity principles. More precisely, the shapes to be matched are viewed as Ciarlet-Geymonat materials. We demonstrate the existence of minimizers of the related functional minimization problem and prove a convergence result when the number of geometric constraints increases. We then describe and analyze a numerical method of resolution based on the introduction of an associated decoupled problem under inequality constraint in which an auxiliary variable simulates the Jacobian matrix of the deformation field. A theoretical result of 􀀀-convergence is established. We then provide preliminary 2D results of the proposed matching model for the registration of mouse brain gene expression data to a neuroanatomical mouse atlas.

TU-G-BRA-04: Changes in Regional Lung Function Measured by 4D-CT Ventilation Imaging for Thoracic Radiotherapy

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

Nakajima, Y; Kadoya, N; Kabus, S

Purpose: To test the hypothesis: 4D-CT ventilation imaging can show the known effects of radiotherapy on lung function: (1) radiation-induced ventilation reductions, and (2) ventilation increases caused by tumor regression. Methods: Repeat 4D-CT scans (pre-, mid- and/or post-treatment) were acquired prospectively for 11 thoracic cancer patients in an IRB-approved clinical trial. A ventilation image for each time point was created using deformable image registration and the Hounsfield unit (HU)-based or Jacobian-based metric. The 11 patients were divided into two subgroups based on tumor volume reduction using a threshold of 5 cm{sup 3}. To quantify radiation-induced ventilation reduction, six patients whomore » showed a small tumor volume reduction (<5 cm{sup 3}) were analyzed for dose-response relationships. To investigate ventilation increase caused by tumor regression, two of the other five patients were analyzed to compare ventilation changes in the lung lobes affected and unaffected by the tumor. The remaining three patients were excluded because there were no unaffected lobes. Results: Dose-dependent reductions of HU-based ventilation were observed in a majority of the patient-specific dose-response curves and in the population-based dose-response curve, whereas no clear relationship was seen for Jacobian-based ventilation. The post-treatment population-based dose-response curve of HU-based ventilation demonstrated the average ventilation reductions of 20.9±7.0% at 35–40 Gy (equivalent dose in 2-Gy fractions, EQD2), and 40.6±22.9% at 75–80 Gy EQD2. Remarkable ventilation increases in the affected lobes were observed for the two patients who showed an average tumor volume reduction of 37.1 cm{sup 3} and re-opening airways. The mid-treatment increase in HU-based ventilation of patient 3 was 100.4% in the affected lobes, which was considerably greater than 7.8% in the unaffected lobes. Conclusion: This study has demonstrated that 4D-CT ventilation imaging shows the known effects of radiotherapy on lung function: radiation-induced ventilation reduction and ventilation increase caused by tumor regression, providing validation for 4D-CT ventilation imaging. This study was supported in part by a National Lung Cancer Partnership Young Investigator Research grant.« less

Recent Developments Related To An Optically Controlled Microwave Phased Array Antenna.

NASA Astrophysics Data System (ADS)

Kittel, A.; Peinke, J.; Klein, M.; Baier, G.; Parisi, J.; Rössler, O. E.

1990-12-01

A generic 3-dimensional diffeomorphic map, with constant Jacobian determinant, is proposed and looked at numerically. It contains a lower-dimensional basin boundary along which a chaotic motion takes place. This boundary is nowhere differentiable in one direction. Therefore, nowhere differentiable limit sets exist generically in nature.

3-D orbital evolution model of outer asteroid belt

NASA Technical Reports Server (NTRS)

Solovaya, Nina A.; Gerasimov, Igor A.; Pittich, Eduard M.

1992-01-01

The evolution of minor planets in the outer part of the asteroid belt is considered. In the framework of the semi-averaged elliptic restricted three-dimensional three-body model, the boundary of regions of the Hill's stability is found. As was shown in our work, the Jacobian integral exists.

A General Pressure Gradient Formulation for Ocean Models, Part 1: Scheme Design and Diagnostic Analysis, Part II: Energy, Momentum, and Bottom Torque Consistency

NASA Technical Reports Server (NTRS)

Song, Y. T.

1998-01-01

A Jacobian formulation of the pressure gradient force for use in models with topography following coordinates is proposed. It can be used in conjunction with any vertical coordinate system and is easily implemented.

AQUASOL: An efficient solver for the dipolar Poisson–Boltzmann–Langevin equation

PubMed Central

Koehl, Patrice; Delarue, Marc

2010-01-01

The Poisson–Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson–Boltzmann–Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available. PMID:20151727

AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.

PubMed

Koehl, Patrice; Delarue, Marc

2010-02-14

The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available.

Solution des systemes de controle de grandes dimensions basee sur les boucles de retroaction dans la simulation des reseaux electriques

NASA Astrophysics Data System (ADS)

Mugombozi, Chuma Francis

The generation of electrical energy, as well as its transportation and consumption, requires complex control systems for the regulation of power and frequency. These control systems must take into account, among others, new energy sources such as wind energy and new technologies for interconnection by high voltage DC link. These control systems must be able to monitor and achieve such regulation in accordance with the dynamics of the energy source, faults and other events which may induce transients phenomena into the power network. Such transients conditions have to be analyzed using the most accurate and detailed hence, complex models of control system. In addition, in the feasibility study phase, the calibration or the setup of equipment as well as in the operation of the power network, one may require decision aid tools for engineers. This includes, for instance, knowledge of energy dissipated into the arresters in transient analysis. These tools use simulation programs data as inputs and may require that complex functions be solved with numerical methods. These functions are part of control system in computer simulator. Moreover, the simulation evolves in a broader context of the development of digital controller, distributed and parallel high performance computing and rapid evolutions in computer (multiprocessor) technology. In such context, a continuing improvement of the control equations solver is welcomed. Control systems are modelled using ax=b simultaneous system of equations. These equations are sometimes non-linear with feedback loops and thus require iterative Newton methods, including the formation of a Jacobian matrix and ordering as well as processing by graph theory tools. The proposed approach is based on the formulation of a reduced rank Jacobian matrix. The dimension is reduced up to the count of feedback loops. With this new approach, gains in computation speed are expected without compromising its accuracy when compared to classical full rank Jacobian matrix representation. A directed graph representation is adopted and a proper approach for detecting and removing cycles within the graph is introduced. A condition of all zero eigenvalues of adjacency matrix of the graph is adopted. The transformation of the graph of controls with no cycle permits a formulation of control equations for only feedback points. This yields a general feedback interconnection (GFBI) representation of control, which is the main contribution of this thesis. Methods for solving (non-linear) equations of control systems were deployed into the new GFBI approach. Five variants of the new approach were illustrated including firstly, a basic Newton method (1), a more robust one, the Dogleg method (2) and a fixed-point iterations method (3). I. The presented approach is implemented in Electromagnetic Transient program EMTP-RV and tested on practical systems of various types and levels of complexity: the PLL, an asynchronous machine with 87 blocks reduced to 23 feedback equations by GFBI, and 12 wind power plants integrated to the IEEE-39 buses system. Further analysis, which opens up avenues for future research includes comparison of the proposed approach against existing ones. With respect to the sole representation, it is shown that the proposed approach is equivalent to full classic representation of system of equations through a proper substitution process which complies with topological sequence and by skipping feedback variable identified by GFBI. Moreover, a second comparison with state space based approach, such as that in MATLAB/Simulink, shows that output evaluation step in state-space approach with algebraic constraints is similar to the GFBI. The algebraic constraints are similar to feedback variables. A difference may arise, however, when the number of algebraic constraints is not the optimal number of cuts for the GFBI method: for the PLL, for example, MATLAB/Simulink generated 3 constraints while the GFBI generated only 2. The GFBI method may offer some advantages in this case. A last analysis axis prompted further work in initialization. It is shown that GFBI method may modifies the convergence properties of iterations of the Newton method. The Newton- Kantorovich theorem, using bounds on the norms of the Jacobian, has been applied to the proposed GFBI and classic full representation of control equations. The expressions of the Jacobian norms have been established for generic cases using Coates graph. It appears from the analysis of a simple case, for the same initial conditions, the behaviour of the Newton- Kantorovich theorem differs in both cases. These differences may also be more pronounced in the non-linear case. Further work would be useful to investigate this aspect and, eventually, pave the way to new initialization approaches. Despite these limitations, not to mention areas for improvement in further work, one notes the contribution of this thesis to improve the gain of time on simulation for the solution of control systems. (Abstract shortened by UMI.).

Respiratory effort correction strategies to improve the reproducibility of lung expansion measurements

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

Du, Kaifang; Reinhardt, Joseph M.; Christensen, Gary E.

2013-12-15

Purpose: Four-dimensional computed tomography (4DCT) can be used to make measurements of pulmonary function longitudinally. The sensitivity of such measurements to identify change depends on measurement uncertainty. Previously, intrasubject reproducibility of Jacobian-based measures of lung tissue expansion was studied in two repeat prior-RT 4DCT human acquisitions. Difference in respiratory effort such as breathing amplitude and frequency may affect longitudinal function assessment. In this study, the authors present normalization schemes that correct ventilation images for variations in respiratory effort and assess the reproducibility improvement after effort correction.Methods: Repeat 4DCT image data acquired within a short time interval from 24 patients priormore » to radiation therapy (RT) were used for this analysis. Using a tissue volume preserving deformable image registration algorithm, Jacobian ventilation maps in two scanning sessions were computed and compared on the same coordinate for reproducibility analysis. In addition to computing the ventilation maps from end expiration to end inspiration, the authors investigated the effort normalization strategies using other intermediated inspiration phases upon the principles of equivalent tidal volume (ETV) and equivalent lung volume (ELV). Scatter plots and mean square error of the repeat ventilation maps and the Jacobian ratio map were generated for four conditions: no effort correction, global normalization, ETV, and ELV. In addition, gamma pass rate was calculated from a modified gamma index evaluation between two ventilation maps, using acceptance criterions of 2 mm distance-to-agreement and 5% ventilation difference.Results: The pattern of regional pulmonary ventilation changes as lung volume changes. All effort correction strategies improved reproducibility when changes in respiratory effort were greater than 150 cc (p < 0.005 with regard to the gamma pass rate). Improvement of reproducibility was correlated with respiratory effort difference (R = 0.744 for ELV in the cohort with tidal volume difference greater than 100 cc). In general for all subjects, global normalization, ETV and ELV significantly improved reproducibility compared to no effort correction (p = 0.009, 0.002, 0.005 respectively). When tidal volume difference was small (less than 100 cc), none of the three effort correction strategies improved reproducibility significantly (p = 0.52, 0.46, 0.46 respectively). For the cohort (N = 13) with tidal volume difference greater than 100 cc, the average gamma pass rate improves from 57.3% before correction to 66.3% after global normalization, and 76.3% after ELV. ELV was found to be significantly better than global normalization (p = 0.04 for all subjects, and p = 0.003 for the cohort with tidal volume difference greater than 100 cc).Conclusions: All effort correction strategies improve the reproducibility of the authors' pulmonary ventilation measures, and the improvement of reproducibility is highly correlated with the changes in respiratory effort. ELV gives better results as effort difference increase, followed by ETV, then global. However, based on the spatial and temporal heterogeneity in the lung expansion rate, a single scaling factor (e.g., global normalization) appears to be less accurate to correct the ventilation map when changes in respiratory effort are large.« less

On the period of the periodic orbits of the restricted three body problem

NASA Astrophysics Data System (ADS)

Perdomo, Oscar

2017-09-01

We will show that the period T of a closed orbit of the planar circular restricted three body problem (viewed on rotating coordinates) depends on the region it encloses. Roughly speaking, we show that, 2 T=kπ +\\int _Ω g where k is an integer, Ω is the region enclosed by the periodic orbit and g:R^2→ R is a function that only depends on the constant C known as the Jacobian constant; it does not depend on Ω . This theorem has a Keplerian flavor in the sense that it relates the period with the space "swept" by the orbit. As an application we prove that there is a neighborhood around L_4 such that every periodic solution contained in this neighborhood must move clockwise. The same result holds true for L_5.

Neural network-based systems for handprint OCR applications.

PubMed

Ganis, M D; Wilson, C L; Blue, J L

1998-01-01

Over the last five years or so, neural network (NN)-based approaches have been steadily gaining performance and popularity for a wide range of optical character recognition (OCR) problems, from isolated digit recognition to handprint recognition. We present an NN classification scheme based on an enhanced multilayer perceptron (MLP) and describe an end-to-end system for form-based handprint OCR applications designed by the National Institute of Standards and Technology (NIST) Visual Image Processing Group. The enhancements to the MLP are based on (i) neuron activations functions that reduce the occurrences of singular Jacobians; (ii) successive regularization to constrain the volume of the weight space; and (iii) Boltzmann pruning to constrain the dimension of the weight space. Performance characterization studies of NN systems evaluated at the first OCR systems conference and the NIST form-based handprint recognition system are also summarized.

Advanced classical thermodynamics

NASA Astrophysics Data System (ADS)

Emanuel, George

The theoretical and mathematical foundations of thermodynamics are presented in an advanced text intended for graduate engineering students. Chapters are devoted to definitions and postulates, the fundamental equation, equilibrium, the application of Jacobian theory to thermodynamics, the Maxwell equations, stability, the theory of real gases, critical-point theory, and chemical thermodynamics. Diagrams, graphs, tables, and sample problems are provided.

A Continuum Description of Nonlinear Elasticity, Slip and Twinning, With Application to Sapphire

DTIC Science & Technology

2009-03-01

Twinning is modelled via the isochoric term FI, and residual volume changes associated with defects are captured by the Jacobian determinant J . The...BF00126994) Farber, Y. A., Yoon, S. Y., Lagerlof, K. P. D. & Heuer, A. H. 1993 Microplasticity during high temperature indentation and the Peierls

GRIZZLY

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

2012-12-17

Grizzly is a simulation tool for assessing the effects of age-related degradation on systems, structures, and components of nuclear power plants. Grizzly is built on the MOOSE framework, and uses a Jacobian-free Newton Krylov method to obtain solutions to tightly coupled thermo-mechanical simulations. Grizzly runs on a wide range of hardware, from a single processor to massively parallel machines.

Unifying dynamical and structural stability of equilibria

NASA Astrophysics Data System (ADS)

Arnoldi, Jean-François; Haegeman, Bart

2016-09-01

We exhibit a fundamental relationship between measures of dynamical and structural stability of linear dynamical systems-e.g. linearized models in the vicinity of equilibria. We show that dynamical stability, quantified via the response to external perturbations (i.e. perturbation of dynamical variables), coincides with the minimal internal perturbation (i.e. perturbations of interactions between variables) able to render the system unstable. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian's coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a linear system's response to white-noise perturbations directly reflects the intensity of internal white-noise disturbance that it can accommodate before becoming stochastically unstable.

Joint three-dimensional inversion of coupled groundwater flow and heat transfer based on automatic differentiation: sensitivity calculation, verification, and synthetic examples

NASA Astrophysics Data System (ADS)

Rath, V.; Wolf, A.; Bücker, H. M.

2006-10-01

Inverse methods are useful tools not only for deriving estimates of unknown parameters of the subsurface, but also for appraisal of the thus obtained models. While not being neither the most general nor the most efficient methods, Bayesian inversion based on the calculation of the Jacobian of a given forward model can be used to evaluate many quantities useful in this process. The calculation of the Jacobian, however, is computationally expensive and, if done by divided differences, prone to truncation error. Here, automatic differentiation can be used to produce derivative code by source transformation of an existing forward model. We describe this process for a coupled fluid flow and heat transport finite difference code, which is used in a Bayesian inverse scheme to estimate thermal and hydraulic properties and boundary conditions form measured hydraulic potentials and temperatures. The resulting derivative code was validated by comparison to simple analytical solutions and divided differences. Synthetic examples from different flow regimes demonstrate the use of the inverse scheme, and its behaviour in different configurations.

Topology preserving non-rigid image registration using time-varying elasticity model for MRI brain volumes.

PubMed

Ahmad, Sahar; Khan, Muhammad Faisal

2015-12-01

In this paper, we present a new non-rigid image registration method that imposes a topology preservation constraint on the deformation. We propose to incorporate the time varying elasticity model into the deformable image matching procedure and constrain the Jacobian determinant of the transformation over the entire image domain. The motion of elastic bodies is governed by a hyperbolic partial differential equation, generally termed as elastodynamics wave equation, which we propose to use as a deformation model. We carried out clinical image registration experiments on 3D magnetic resonance brain scans from IBSR database. The results of the proposed registration approach in terms of Kappa index and relative overlap computed over the subcortical structures were compared against the existing topology preserving non-rigid image registration methods and non topology preserving variant of our proposed registration scheme. The Jacobian determinant maps obtained with our proposed registration method were qualitatively and quantitatively analyzed. The results demonstrated that the proposed scheme provides good registration accuracy with smooth transformations, thereby guaranteeing the preservation of topology. Copyright © 2015 Elsevier Ltd. All rights reserved.

Robust Kalman filtering cooperated Elman neural network learning for vision-sensing-based robotic manipulation with global stability.

PubMed

Zhong, Xungao; Zhong, Xunyu; Peng, Xiafu

2013-10-08

In this paper, a global-state-space visual servoing scheme is proposed for uncalibrated model-independent robotic manipulation. The scheme is based on robust Kalman filtering (KF), in conjunction with Elman neural network (ENN) learning techniques. The global map relationship between the vision space and the robotic workspace is learned using an ENN. This learned mapping is shown to be an approximate estimate of the Jacobian in global space. In the testing phase, the desired Jacobian is arrived at using a robust KF to improve the ENN learning result so as to achieve robotic precise convergence of the desired pose. Meanwhile, the ENN weights are updated (re-trained) using a new input-output data pair vector (obtained from the KF cycle) to ensure robot global stability manipulation. Thus, our method, without requiring either camera or model parameters, avoids the corrupted performances caused by camera calibration and modeling errors. To demonstrate the proposed scheme's performance, various simulation and experimental results have been presented using a six-degree-of-freedom robotic manipulator with eye-in-hand configurations.

Learning the inverse kinetics of an octopus-like manipulator in three-dimensional space.

PubMed

Giorelli, M; Renda, F; Calisti, M; Arienti, A; Ferri, G; Laschi, C

2015-05-13

This work addresses the inverse kinematics problem of a bioinspired octopus-like manipulator moving in three-dimensional space. The bioinspired manipulator has a conical soft structure that confers the ability of twirling around objects as a real octopus arm does. Despite the simple design, the soft conical shape manipulator driven by cables is described by nonlinear differential equations, which are difficult to solve analytically. Since exact solutions of the equations are not available, the Jacobian matrix cannot be calculated analytically and the classical iterative methods cannot be used. To overcome the intrinsic problems of methods based on the Jacobian matrix, this paper proposes a neural network learning the inverse kinematics of a soft octopus-like manipulator driven by cables. After the learning phase, a feed-forward neural network is able to represent the relation between manipulator tip positions and forces applied to the cables. Experimental results show that a desired tip position can be achieved in a short time, since heavy computations are avoided, with a degree of accuracy of 8% relative average error with respect to the total arm length.

Kinematic equations for control of the redundant eight-degree-of-freedom advanced research manipulator 2

NASA Technical Reports Server (NTRS)

Williams, Robert L., II

1992-01-01

The forward position and velocity kinematics for the redundant eight-degree-of-freedom Advanced Research Manipulator 2 (ARM2) are presented. Inverse position and velocity kinematic solutions are also presented. The approach in this paper is to specify two of the unknowns and solve for the remaining six unknowns. Two unknowns can be specified with two restrictions. First, the elbow joint angle and rate cannot be specified because they are known from the end-effector position and velocity. Second, one unknown must be specified from the four-jointed wrist, and the second from joints that translate the wrist, elbow joint excluded. There are eight solutions to the inverse position problem. The inverse velocity solution is unique, assuming the Jacobian matrix is not singular. A discussion of singularities is based on specifying two joint rates and analyzing the reduced Jacobian matrix. When this matrix is singular, the generalized inverse may be used as an alternate solution. Computer simulations were developed to verify the equations. Examples demonstrate agreement between forward and inverse solutions.

Unifying dynamical and structural stability of equilibria.

PubMed

Arnoldi, Jean-François; Haegeman, Bart

2016-09-01

We exhibit a fundamental relationship between measures of dynamical and structural stability of linear dynamical systems-e.g. linearized models in the vicinity of equilibria. We show that dynamical stability, quantified via the response to external perturbations (i.e. perturbation of dynamical variables), coincides with the minimal internal perturbation (i.e. perturbations of interactions between variables) able to render the system unstable. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian's coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a linear system's response to white-noise perturbations directly reflects the intensity of internal white-noise disturbance that it can accommodate before becoming stochastically unstable.

Kinematics of an in-parallel actuated manipulator based on the Stewart platform mechanism

NASA Technical Reports Server (NTRS)

Williams, Robert L., II

1992-01-01

This paper presents kinematic equations and solutions for an in-parallel actuated robotic mechanism based on Stewart's platform. These equations are required for inverse position and resolved rate (inverse velocity) platform control. NASA LaRC has a Vehicle Emulator System (VES) platform designed by MIT which is based on Stewart's platform. The inverse position solution is straight-forward and computationally inexpensive. Given the desired position and orientation of the moving platform with respect to the base, the lengths of the prismatic leg actuators are calculated. The forward position solution is more complicated and theoretically has 16 solutions. The position and orientation of the moving platform with respect to the base is calculated given the leg actuator lengths. Two methods are pursued in this paper to solve this problem. The resolved rate (inverse velocity) solution is derived. Given the desired Cartesian velocity of the end-effector, the required leg actuator rates are calculated. The Newton-Raphson Jacobian matrix resulting from the second forward position kinematics solution is a modified inverse Jacobian matrix. Examples and simulations are given for the VES.

TH-E-BRF-06: Kinetic Modeling of Tumor Response to Fractionated Radiotherapy

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

Zhong, H; Gordon, J; Chetty, I

2014-06-15

Purpose: Accurate calibration of radiobiological parameters is crucial to predicting radiation treatment response. Modeling differences may have a significant impact on calibrated parameters. In this study, we have integrated two existing models with kinetic differential equations to formulate a new tumor regression model for calibrating radiobiological parameters for individual patients. Methods: A system of differential equations that characterizes the birth-and-death process of tumor cells in radiation treatment was analytically solved. The solution of this system was used to construct an iterative model (Z-model). The model consists of three parameters: tumor doubling time Td, half-life of dying cells Tr and cellmore » survival fraction SFD under dose D. The Jacobian determinant of this model was proposed as a constraint to optimize the three parameters for six head and neck cancer patients. The derived parameters were compared with those generated from the two existing models, Chvetsov model (C-model) and Lim model (L-model). The C-model and L-model were optimized with the parameter Td fixed. Results: With the Jacobian-constrained Z-model, the mean of the optimized cell survival fractions is 0.43±0.08, and the half-life of dying cells averaged over the six patients is 17.5±3.2 days. The parameters Tr and SFD optimized with the Z-model differ by 1.2% and 20.3% from those optimized with the Td-fixed C-model, and by 32.1% and 112.3% from those optimized with the Td-fixed L-model, respectively. Conclusion: The Z-model was analytically constructed from the cellpopulation differential equations to describe changes in the number of different tumor cells during the course of fractionated radiation treatment. The Jacobian constraints were proposed to optimize the three radiobiological parameters. The developed modeling and optimization methods may help develop high-quality treatment regimens for individual patients.« less

Objectively Quantifying Radiation Esophagitis With Novel Computed Tomography–Based Metrics

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

Niedzielski, Joshua S., E-mail: jsniedzielski@mdanderson.org; University of Texas Houston Graduate School of Biomedical Science, Houston, Texas; Yang, Jinzhong

Purpose: To study radiation-induced esophageal expansion as an objective measure of radiation esophagitis in patients with non-small cell lung cancer (NSCLC) treated with intensity modulated radiation therapy. Methods and Materials: Eighty-five patients had weekly intra-treatment CT imaging and esophagitis scoring according to Common Terminlogy Criteria for Adverse Events 4.0, (24 Grade 0, 45 Grade 2, and 16 Grade 3). Nineteen esophageal expansion metrics based on mean, maximum, spatial length, and volume of expansion were calculated as voxel-based relative volume change, using the Jacobian determinant from deformable image registration between the planning and weekly CTs. An anatomic variability correction method wasmore » validated and applied to these metrics to reduce uncertainty. An analysis of expansion metrics and radiation esophagitis grade was conducted using normal tissue complication probability from univariate logistic regression and Spearman rank for grade 2 and grade 3 esophagitis endpoints, as well as the timing of expansion and esophagitis grade. Metrics' performance in classifying esophagitis was tested with receiver operating characteristic analysis. Results: Expansion increased with esophagitis grade. Thirteen of 19 expansion metrics had receiver operating characteristic area under the curve values >0.80 for both grade 2 and grade 3 esophagitis endpoints, with the highest performance from maximum axial expansion (MaxExp1) and esophageal length with axial expansion ≥30% (LenExp30%) with area under the curve values of 0.93 and 0.91 for grade 2, 0.90 and 0.90 for grade 3 esophagitis, respectively. Conclusions: Esophageal expansion may be a suitable objective measure of esophagitis, particularly maximum axial esophageal expansion and esophageal length with axial expansion ≥30%, with 2.1 Jacobian value and 98.6 mm as the metric value for 50% probability of grade 3 esophagitis. The uncertainty in esophageal Jacobian calculations can be reduced with anatomic correction methods.« less

Spatial patterns of progressive brain volume loss after moderate-severe traumatic brain injury

PubMed Central

Jolly, Amy; de Simoni, Sara; Bourke, Niall; Patel, Maneesh C; Scott, Gregory; Sharp, David J

2018-01-01

Abstract Traumatic brain injury leads to significant loss of brain volume, which continues into the chronic stage. This can be sensitively measured using volumetric analysis of MRI. Here we: (i) investigated longitudinal patterns of brain atrophy; (ii) tested whether atrophy is greatest in sulcal cortical regions; and (iii) showed how atrophy could be used to power intervention trials aimed at slowing neurodegeneration. In 61 patients with moderate-severe traumatic brain injury (mean age = 41.55 years ± 12.77) and 32 healthy controls (mean age = 34.22 years ± 10.29), cross-sectional and longitudinal (1-year follow-up) brain structure was assessed using voxel-based morphometry on T1-weighted scans. Longitudinal brain volume changes were characterized using a novel neuroimaging analysis pipeline that generates a Jacobian determinant metric, reflecting spatial warping between baseline and follow-up scans. Jacobian determinant values were summarized regionally and compared with clinical and neuropsychological measures. Patients with traumatic brain injury showed lower grey and white matter volume in multiple brain regions compared to controls at baseline. Atrophy over 1 year was pronounced following traumatic brain injury. Patients with traumatic brain injury lost a mean (± standard deviation) of 1.55% ± 2.19 of grey matter volume per year, 1.49% ± 2.20 of white matter volume or 1.51% ± 1.60 of whole brain volume. Healthy controls lost 0.55% ± 1.13 of grey matter volume and gained 0.26% ± 1.11 of white matter volume; equating to a 0.22% ± 0.83 reduction in whole brain volume. Atrophy was greatest in white matter, where the majority (84%) of regions were affected. This effect was independent of and substantially greater than that of ageing. Increased atrophy was also seen in cortical sulci compared to gyri. There was no relationship between atrophy and time since injury or age at baseline. Atrophy rates were related to memory performance at the end of the follow-up period, as well as to changes in memory performance, prior to multiple comparison correction. In conclusion, traumatic brain injury results in progressive loss of brain tissue volume, which continues for many years post-injury. Atrophy is most prominent in the white matter, but is also more pronounced in cortical sulci compared to gyri. These findings suggest the Jacobian determinant provides a method of quantifying brain atrophy following a traumatic brain injury and is informative in determining the long-term neurodegenerative effects after injury. Power calculations indicate that Jacobian determinant images are an efficient surrogate marker in clinical trials of neuroprotective therapeutics. PMID:29309542

A note on large gauge transformations in double field theory

DOE PAGES

Naseer, Usman

2015-06-03

Here, we give a detailed proof of the conjecture by Hohm and Zwiebach in double field theory. Our result implies that their proposal for large gauge transformations in terms of the Jacobian matrix for coordinate transformations is, as required, equivalent to the standard exponential map associated with the generalized Lie derivative along a suitable parameter.

Tensor Calculus: Unlearning Vector Calculus

ERIC Educational Resources Information Center

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-01-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

Equidistant map projections of a triaxial ellipsoid with the use of reduced coordinates

NASA Astrophysics Data System (ADS)

Pędzich, Paweł

2017-12-01

The paper presents a new method of constructing equidistant map projections of a triaxial ellipsoid as a function of reduced coordinates. Equations for x and y coordinates are expressed with the use of the normal elliptic integral of the second kind and Jacobian elliptic functions. This solution allows to use common known and widely described in literature methods of solving such integrals and functions. The main advantage of this method is the fact that the calculations of x and y coordinates are practically based on a single algorithm that is required to solve the elliptic integral of the second kind. Equations are provided for three types of map projections: cylindrical, azimuthal and pseudocylindrical. These types of projections are often used in planetary cartography for presentation of entire and polar regions of extraterrestrial objects. The paper also contains equations for the calculation of the length of a meridian and a parallel of a triaxial ellipsoid in reduced coordinates. Moreover, graticules of three coordinates systems (planetographic, planetocentric and reduced) in developed map projections are presented. The basic properties of developed map projections are also described. The obtained map projections may be applied in planetary cartography in order to create maps of extraterrestrial objects.

Lung Motion Model Validation Experiments, Free-Breathing Tissue Densitometry, and Ventilation Mapping using Fast Helical CT Imaging

NASA Astrophysics Data System (ADS)

Dou, Hsiang-Tai

The uncertainties due to respiratory motion present significant challenges to accurate characterization of cancerous tissues both in terms of imaging and treatment. Currently available clinical lung imaging techniques are subject to inferior image quality and incorrect motion estimation, with consequences that can systematically impact the downstream treatment delivery and outcome. The main objective of this thesis is the development of the techniques of fast helical computed tomography (CT) imaging and deformable image registration for the radiotherapy applications in accurate breathing motion modeling, lung tissue density modeling and ventilation imaging. Fast helical CT scanning was performed on 64-slice CT scanner using the shortest available gantry rotation time and largest pitch value such that scanning of the thorax region amounts to just two seconds, which is less than typical breathing cycle in humans. The scanning was conducted under free breathing condition. Any portion of the lung anatomy undergoing such scanning protocol would be irradiated for only a quarter second, effectively removing any motion induced image artifacts. The resulting CT data were pristine volumetric images that record the lung tissue position and density in a fraction of the breathing cycle. Following our developed protocol, multiple fast helical CT scans were acquired to sample the tissue positions in different breathing states. To measure the tissue displacement, deformable image registration was performed that registers the non-reference images to the reference one. In modeling breathing motion, external breathing surrogate signal was recorded synchronously with the CT image slices. This allowed for the tissue-specific displacement to be modeled as parametrization of the recorded breathing signal using the 5D lung motion model. To assess the accuracy of the motion model in describing tissue position change, the model was used to simulate the original high-pitch helical CT scan geometries, employed as ground truth data. Image similarity between the simulated and ground truth scans was evaluated. The model validation experiments were conducted in a patient cohort of seventeen patients to assess the model robustness and inter-patient variation. The model error averaged over multiple tracked positions from several breathing cycles was found to be on the order of one millimeter. In modeling the density change under free breathing condition, the determinant of Jacobian matrix from the registration-derived deformation vector field yielded volume change information of the lung tissues. Correlation of the Jacobian values to the corresponding voxel Housfield units (HU) reveals that the density variation for the majority of lung tissues can be very well described by mass conservation relationship. Different tissue types were identified and separately modeled. Large trials of validation experiments were performed. The averaged deviation between the modeled and the reference lung density was 30 HU, which was estimated to be the background CT noise level. In characterizing the lung ventilation function, a novel method was developed to determine the extent of lung tissue volume change. Information on volume change was derived from the deformable image registration of the fast helical CT images in terms of Jacobian values with respect to a reference image. Assuming the multiple volume change measurements are independently and identically distributed, statistical formulation was derived to model ventilation distribution of each lung voxels and empirical minimum and maximum probability distribution of the Jacobian values was computed. Ventilation characteristic was evaluated as the difference of the expectation value from these extremal distributions. The resulting ventilation map was compared with an independently obtained ventilation image derived directly from the lung intensities and good correlation was found using statistical test. In addition, dynamic ventilation characterization was investigated by estimating the voxel-specific ventilation distribution. Ventilation maps were generated at different percentile levels using the tissue volume expansion metrics.

3-dimensional magnetotelluric inversion including topography using deformed hexahedral edge finite elements and direct solvers parallelized on symmetric multiprocessor computers - Part II: direct data-space inverse solution

NASA Astrophysics Data System (ADS)

Kordy, M.; Wannamaker, P.; Maris, V.; Cherkaev, E.; Hill, G.

2016-01-01

Following the creation described in Part I of a deformable edge finite-element simulator for 3-D magnetotelluric (MT) responses using direct solvers, in Part II we develop an algorithm named HexMT for 3-D regularized inversion of MT data including topography. Direct solvers parallelized on large-RAM, symmetric multiprocessor (SMP) workstations are used also for the Gauss-Newton model update. By exploiting the data-space approach, the computational cost of the model update becomes much less in both time and computer memory than the cost of the forward simulation. In order to regularize using the second norm of the gradient, we factor the matrix related to the regularization term and apply its inverse to the Jacobian, which is done using the MKL PARDISO library. For dense matrix multiplication and factorization related to the model update, we use the PLASMA library which shows very good scalability across processor cores. A synthetic test inversion using a simple hill model shows that including topography can be important; in this case depression of the electric field by the hill can cause false conductors at depth or mask the presence of resistive structure. With a simple model of two buried bricks, a uniform spatial weighting for the norm of model smoothing recovered more accurate locations for the tomographic images compared to weightings which were a function of parameter Jacobians. We implement joint inversion for static distortion matrices tested using the Dublin secret model 2, for which we are able to reduce nRMS to ˜1.1 while avoiding oscillatory convergence. Finally we test the code on field data by inverting full impedance and tipper MT responses collected around Mount St Helens in the Cascade volcanic chain. Among several prominent structures, the north-south trending, eruption-controlling shear zone is clearly imaged in the inversion.

Inverse optimal self-tuning PID control design for an autonomous underwater vehicle

NASA Astrophysics Data System (ADS)

Rout, Raja; Subudhi, Bidyadhar

2017-01-01

This paper presents a new approach to path following control design for an autonomous underwater vehicle (AUV). A NARMAX model of the AUV is derived first and then its parameters are adapted online using the recursive extended least square algorithm. An adaptive Propotional-Integral-Derivative (PID) controller is developed using the derived parameters to accomplish the path following task of an AUV. The gain parameters of the PID controller are tuned using an inverse optimal control technique, which alleviates the problem of solving Hamilton-Jacobian equation and also satisfies an error cost function. Simulation studies were pursued to verify the efficacy of the proposed control algorithm. From the obtained results, it is envisaged that the proposed NARMAX model-based self-tuning adaptive PID control provides good path following performance even in the presence of uncertainty arising due to ocean current or hydrodynamic parameter.

A mathematical analysis of the effects of Hebbian learning rules on the dynamics and structure of discrete-time random recurrent neural networks.

PubMed

Siri, Benoît; Berry, Hugues; Cessac, Bruno; Delord, Bruno; Quoy, Mathias

2008-12-01

We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule, including passive forgetting and different timescales, for neuronal activity and learning dynamics. Previous numerical work has reported that Hebbian learning drives the system from chaos to a steady state through a sequence of bifurcations. Here, we interpret these results mathematically and show that these effects, involving a complex coupling between neuronal dynamics and synaptic graph structure, can be analyzed using Jacobian matrices, which introduce both a structural and a dynamical point of view on neural network evolution. Furthermore, we show that sensitivity to a learned pattern is maximal when the largest Lyapunov exponent is close to 0. We discuss how neural networks may take advantage of this regime of high functional interest.

Universal moduli spaces of Riemann surfaces

NASA Astrophysics Data System (ADS)

Ji, Lizhen; Jost, Jürgen

2017-04-01

We construct a moduli space for Riemann surfaces that is universal in the sense that it represents compact Riemann surfaces of any finite genus. This moduli space is a connected complex subspace of an infinite dimensional complex space, and is stratified according to genus such that each stratum has a compact closure, and it carries a metric and a measure that induce a Riemannian metric and a finite volume measure on each stratum. Applications to the Plateau-Douglas problem for minimal surfaces of varying genus and to the partition function of Bosonic string theory are outlined. The construction starts with a universal moduli space of Abelian varieties. This space carries a structure of an infinite dimensional locally symmetric space which is of interest in its own right. The key to our construction of the universal moduli space then is the Torelli map that assigns to every Riemann surface its Jacobian and its extension to the Satake-Baily-Borel compactifications.

The application of nonlinear programming and collocation to optimal aeroassisted orbital transfers

NASA Astrophysics Data System (ADS)

Shi, Y. Y.; Nelson, R. L.; Young, D. H.; Gill, P. E.; Murray, W.; Saunders, M. A.

1992-01-01

Sequential quadratic programming (SQP) and collocation of the differential equations of motion were applied to optimal aeroassisted orbital transfers. The Optimal Trajectory by Implicit Simulation (OTIS) computer program codes with updated nonlinear programming code (NZSOL) were used as a testbed for the SQP nonlinear programming (NLP) algorithms. The state-of-the-art sparse SQP method is considered to be effective for solving large problems with a sparse matrix. Sparse optimizers are characterized in terms of memory requirements and computational efficiency. For the OTIS problems, less than 10 percent of the Jacobian matrix elements are nonzero. The SQP method encompasses two phases: finding an initial feasible point by minimizing the sum of infeasibilities and minimizing the quadratic objective function within the feasible region. The orbital transfer problem under consideration involves the transfer from a high energy orbit to a low energy orbit.

Two-boundary grid generation for the solution of the three dimensional compressible Navier-Stokes equations. Ph.D. Thesis - Old Dominion Univ.

NASA Technical Reports Server (NTRS)

Smith, R. E.

1981-01-01

A grid generation technique called the two boundary technique is developed and applied for the solution of the three dimensional Navier-Stokes equations. The Navier-Stokes equations are transformed from a cartesian coordinate system to a computational coordinate system, and the grid generation technique provides the Jacobian matrix describing the transformation. The two boundary technique is based on algebraically defining two distinct boundaries of a flow domain and the distribution of the grid is achieved by applying functions to the uniform computational grid which redistribute the computational independent variables and consequently concentrate or disperse the grid points in the physical domain. The Navier-Stokes equations are solved using a MacCormack time-split technique. Grids and supersonic laminar flow solutions are obtained for a family of three dimensional corners and two spike-nosed bodies.

On functional determinants of matrix differential operators with multiple zero modes

NASA Astrophysics Data System (ADS)

Falco, G. M.; Fedorenko, Andrei A.; Gruzberg, Ilya A.

2017-12-01

We generalize the method of computing functional determinants with a single excluded zero eigenvalue developed by McKane and Tarlie to differential operators with multiple zero eigenvalues. We derive general formulas for such functional determinants of r× r matrix second order differential operators O with 0 < n ≤slant 2r linearly independent zero modes. We separately discuss the cases of the homogeneous Dirichlet boundary conditions, when the number of zero modes cannot exceed r, and the case of twisted boundary conditions, including the periodic and anti-periodic ones, when the number of zero modes is bounded above by 2r. In all cases the determinants with excluded zero eigenvalues can be expressed only in terms of the n zero modes and other r-n or 2r-n (depending on the boundary conditions) solutions of the homogeneous equation O h=0 , in the spirit of Gel’fand-Yaglom approach. In instanton calculations, the contribution of the zero modes is taken into account by introducing the so-called collective coordinates. We show that there is a remarkable cancellation of a factor (involving scalar products of zero modes) between the Jacobian of the transformation to the collective coordinates and the functional fluctuation determinant with excluded zero eigenvalues. This cancellation drastically simplifies instanton calculations when one uses our formulas.

Calculation of low-Z impurity pellet induced fluxes of charge exchange neutral particles escaping from magnetically confined toroidal plasmas.

PubMed

Goncharov, P R; Ozaki, T; Sudo, S; Tamura, N; Tolstikhina, I Yu; Sergeev, V Yu

2008-10-01

Measurements of energy- and time-resolved neutral hydrogen and helium fluxes from an impurity pellet ablation cloud, referred to as pellet charge exchange or PCX experiments, can be used to study local fast ion energy distributions in fusion plasmas. The estimation of the local distribution function f(i)(E) of fast ions entering the cloud requires knowledge of both the fraction F(0)(E) of incident ions exiting the cloud as neutral atoms and the attenuation factor A(E,rho) describing the loss of fast atoms in the plasma. Determination of A(E,rho), in turn, requires the total stopping cross section sigma(loss) of neutral atoms in the plasma and the Jacobian reflecting the measurement geometry and the magnetic surface shape. The obtained functions F(0)(E) and A(E,rho) enter multiplicatively into the probability density for escaping neutral particle kinetic energy. A general calculation scheme has been developed and realized as a FORTRAN code, which is to be applied for the calculation of f(i)(E) from PCX experimental results obtained with low-Z impurity pellets.

Algebraic grid generation using tensor product B-splines. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Saunders, B. V.

1985-01-01

Finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. The development of an algorithm which produces such a grid when given the boundary description. Topological considerations in structuring the grid generation mapping are discussed. The concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid is examined. The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the splines produce Schoenberg's variation diminishing spline approximation to the boundary. Interior coefficients are initially chosen to give a variation diminishing approximation to the transfinite bilinear interpolant of the function mapping the boundary of the unit square onto the boundary grid. The practicality of optimizing the grid by minimizing a functional involving the Jacobian of the grid generation mapping at each interior grid point and the dot product of vectors tangent to the grid lines is investigated. Grids generated by using the algorithm are presented.

Coupling a Reactive Transport Code with a Global Land Surface Model for Mechanistic Biogeochemistry Representation: 1. Addressing the Challenge of Nonnegativity

DOE PAGES

Tang, Guoping; Yuan, Fengming; Bisht, Gautam; ...

2016-01-01

Reactive transport codes (e.g., PFLOTRAN) are increasingly used to improve the representation of biogeochemical processes in terrestrial ecosystem models (e.g., the Community Land Model, CLM). As CLM and PFLOTRAN use explicit and implicit time stepping, implementation of CLM biogeochemical reactions in PFLOTRAN can result in negative concentration, which is not physical and can cause numerical instability and errors. The objective of this work is to address the nonnegativity challenge to obtain accurate, efficient, and robust solutions. We illustrate the implementation of a reaction network with the CLM-CN decomposition, nitrification, denitrification, and plant nitrogen uptake reactions and test the implementation atmore » arctic, temperate, and tropical sites. We examine use of scaling back the update during each iteration (SU), log transformation (LT), and downregulating the reaction rate to account for reactant availability limitation to enforce nonnegativity. Both SU and LT guarantee nonnegativity but with implications. When a very small scaling factor occurs due to either consumption or numerical overshoot, and the iterations are deemed converged because of too small an update, SU can introduce excessive numerical error. LT involves multiplication of the Jacobian matrix by the concentration vector, which increases the condition number, decreases the time step size, and increases the computational cost. Neither SU nor SE prevents zero concentration. When the concentration is close to machine precision or 0, a small positive update stops all reactions for SU, and LT can fail due to a singular Jacobian matrix. The consumption rate has to be downregulated such that the solution to the mathematical representation is positive. A first-order rate downregulates consumption and is nonnegative, and adding a residual concentration makes it positive. For zero-order rate or when the reaction rate is not a function of a reactant, representing the availability limitation of each reactant with a Monod substrate limiting function provides a smooth transition between a zero-order rate when the reactant is abundant and first-order rate when the reactant becomes limiting. When the half saturation is small, marching through the transition may require small time step sizes to resolve the sharp change within a small range of concentration values. Our results from simple tests and CLM-PFLOTRAN simulations caution against use of SU and indicate that accurate, stable, and relatively efficient solutions can be achieved with LT and downregulation with Monod substrate limiting function and residual concentration.« less

Multiphase wavetrains, singular wave interactions and the emergence of the Korteweg–de Vries equation

PubMed Central

Bridges, Thomas J.

2016-01-01

Multiphase wavetrains are multiperiodic travelling waves with a set of distinct wavenumbers and distinct frequencies. In conservative systems, such families are associated with the conservation of wave action or other conservation law. At generic points (where the Jacobian of the wave action flux is non-degenerate), modulation of the wavetrain leads to the dispersionless multiphase conservation of wave action. The main result of this paper is that modulation of the multiphase wavetrain, when the Jacobian of the wave action flux vector is singular, morphs the vector-valued conservation law into the scalar Korteweg–de Vries (KdV) equation. The coefficients in the emergent KdV equation have a geometrical interpretation in terms of projection of the vector components of the conservation law. The theory herein is restricted to two phases to simplify presentation, with extensions to any finite dimension discussed in the concluding remarks. Two applications of the theory are presented: a coupled nonlinear Schrödinger equation and two-layer shallow-water hydrodynamics with a free surface. Both have two-phase solutions where criticality and the properties of the emergent KdV equation can be determined analytically. PMID:28119546

A simplified method for power-law modelling of metabolic pathways from time-course data and steady-state flux profiles.

PubMed

Kitayama, Tomoya; Kinoshita, Ayako; Sugimoto, Masahiro; Nakayama, Yoichi; Tomita, Masaru

2006-07-17

In order to improve understanding of metabolic systems there have been attempts to construct S-system models from time courses. Conventionally, non-linear curve-fitting algorithms have been used for modelling, because of the non-linear properties of parameter estimation from time series. However, the huge iterative calculations required have hindered the development of large-scale metabolic pathway models. To solve this problem we propose a novel method involving power-law modelling of metabolic pathways from the Jacobian of the targeted system and the steady-state flux profiles by linearization of S-systems. The results of two case studies modelling a straight and a branched pathway, respectively, showed that our method reduced the number of unknown parameters needing to be estimated. The time-courses simulated by conventional kinetic models and those described by our method behaved similarly under a wide range of perturbations of metabolite concentrations. The proposed method reduces calculation complexity and facilitates the construction of large-scale S-system models of metabolic pathways, realizing a practical application of reverse engineering of dynamic simulation models from the Jacobian of the targeted system and steady-state flux profiles.

Comparison of image registration based measures of regional lung ventilation from dynamic spiral CT with Xe-CT

PubMed Central

Ding, Kai; Cao, Kunlin; Fuld, Matthew K.; Du, Kaifang; Christensen, Gary E.; Hoffman, Eric A.; Reinhardt, Joseph M.

2012-01-01

Purpose: Regional lung volume change as a function of lung inflation serves as an index of parenchymal and airway status as well as an index of regional ventilation and can be used to detect pathologic changes over time. In this paper, the authors propose a new regional measure of lung mechanics—the specific air volume change by corrected Jacobian. The authors compare this new measure, along with two existing registration based measures of lung ventilation, to a regional ventilation measurement derived from xenon-CT (Xe-CT) imaging. Methods: 4DCT and Xe-CT datasets from four adult sheep are used in this study. Nonlinear, 3D image registration is applied to register an image acquired near end inspiration to an image acquired near end expiration. Approximately 200 annotated anatomical points are used as landmarks to evaluate registration accuracy. Three different registration based measures of regional lung mechanics are derived and compared: the specific air volume change calculated from the Jacobian (SAJ); the specific air volume change calculated by the corrected Jacobian (SACJ); and the specific air volume change by intensity change (SAI). The authors show that the commonly used SAI measure can be derived from the direct SAJ measure by using the air-tissue mixture model and assuming there is no tissue volume change between the end inspiration and end expiration datasets. All three ventilation measures are evaluated by comparing to Xe-CT estimates of regional ventilation. Results: After registration, the mean registration error is on the order of 1 mm. For cubical regions of interest (ROIs) in cubes with size 20 mm × 20 mm × 20 mm, the SAJ and SACJ measures show significantly higher correlation (linear regression, average r2 = 0.75 and r2 = 0.82) with the Xe-CT based measure of specific ventilation (sV) than the SAI measure. For ROIs in slabs along the ventral-dorsal vertical direction with size of 150 mm × 8 mm × 40 mm, the SAJ, SACJ, and SAI all show high correlation (linear regression, average r2 = 0.88, r2 = 0.92, and r2 = 0.87) with the Xe-CT based sV without significant differences when comparing between the three methods. The authors demonstrate a linear relationship between the difference of specific air volume change and difference of tissue volume in all four animals (linear regression, average r2 = 0.86). Conclusions: Given a deformation field by an image registration algorithm, significant differences between the SAJ, SACJ, and SAI measures were found at a regional level compared to the Xe-CT sV in four sheep that were studied. The SACJ introduced here, provides better correlations with Xe-CT based sV than the SAJ and SAI measures, thus providing an improved surrogate for regional ventilation. PMID:22894434

Validation of a Node-Centered Wall Function Model for the Unstructured Flow Code FUN3D

NASA Technical Reports Server (NTRS)

Carlson, Jan-Renee; Vasta, Veer N.; White, Jeffery

2015-01-01

In this paper, the implementation of two wall function models in the Reynolds averaged Navier-Stokes (RANS) computational uid dynamics (CFD) code FUN3D is described. FUN3D is a node centered method for solving the three-dimensional Navier-Stokes equations on unstructured computational grids. The first wall function model, based on the work of Knopp et al., is used in conjunction with the one-equation turbulence model of Spalart-Allmaras. The second wall function model, also based on the work of Knopp, is used in conjunction with the two-equation k-! turbulence model of Menter. The wall function models compute the wall momentum and energy flux, which are used to weakly enforce the wall velocity and pressure flux boundary conditions in the mean flow momentum and energy equations. These wall conditions are implemented in an implicit form where the contribution of the wall function model to the Jacobian are also included. The boundary conditions of the turbulence transport equations are enforced explicitly (strongly) on all solid boundaries. The use of the wall function models is demonstrated on four test cases: a at plate boundary layer, a subsonic di user, a 2D airfoil, and a 3D semi-span wing. Where possible, different near-wall viscous spacing tactics are examined. Iterative residual convergence was obtained in most cases. Solution results are compared with theoretical and experimental data for several variations of grid spacing. In general, very good comparisons with data were achieved.

Tensor calculus: unlearning vector calculus

NASA Astrophysics Data System (ADS)

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-02-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can serve as a bridge for vector calculus into tensor calculus.

Chaotic dynamics of Heisenberg ferromagnetic spin chain with bilinear and biquadratic interactions

NASA Astrophysics Data System (ADS)

Blessy, B. S. Gnana; Latha, M. M.

2017-10-01

We investigate the chaotic dynamics of one dimensional Heisenberg ferromagnetic spin chain by constructing the Hamiltonian equations of motion. We present the trajectory and phase plots of the system with bilinear and also biquadratic interactions. The stability of the system is analysed in both cases by constructing the Jacobian matrix and by measuring the Lyapunov exponents. The results are illustrated graphically.

Systolic Algorithms for Imaging from Space

DTIC Science & Technology

1989-07-31

on a keystone or trapezoidal grid [ Arikan & Munson, 1987]. The image reconstruction algorithm then simply applies an inverse 2-D FFT to the stored...rithm composed of groups of point targets, and we determined the effects of windowing and incor- poration of a Jacobian weighting factor [ Arikan ...the impulse response of the desired filter [ Arikan & Munson, 1989]. The necessary filtering is then accomplished through the physical mechanism of the

SU-F-I-51: CT/MR Image Deformation: The Clinical Assessment QA in Target Delineation

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

Yang, C; Chen, Y

Purpose: To study the deformation effects in CT/MR image registration of head and neck (HN) cancers. We present a clinical indication in guiding and simplifying registration procedures of this process while CT images possessed artifacts. Methods: CT/MR image fusion provides better soft tissue contrast in intracranial GTV definition with artifacts. However, whether the fusion process should include the deformation process is questionable and not recommended. We performed CT/MR image registration of a HN patient with tonsil GTV and nodes delineation on Varian Velocity™ system. Both rigid transformation and deformable registration of the same CT/MR imaging data were processed separately. Physician’smore » selection of target delineation was implemented to identify the variations. Transformation matrix was shown with visual identification, as well as the deformation QA numbers and figures were assessed. Results: The deformable CT/MR images were traced with the calculated matrix, both translation and rotational parameters were summarized. In deformable quality QA, the calculated Jacobian matrix was analyzed, which the min/mean/max of 0.73/0/99/1.37, respectively. Jacobian matrix of right neck node was 0.84/1.13/1.41, which present dis-similarity of the nodal area. If Jacobian = 1, the deformation is at the optimum situation. In this case, the deformation results have shown better target delineation for CT/MR deformation than rigid transformation. Though the root-mean-square vector difference is 1.48 mm, with similar rotational components, the cord and vertebrae position were aligned much better in the deformable MR images than the rigid transformation. Conclusion: CT/MR with/without image deformation presents similar image registration matrix; there were significant differentiate the anatomical structures in the region of interest by deformable process. Though vendor suggested only rigid transformation between CT/MR assuming the geometry remain similar, our findings indicated with patient positional variations, deformation registration is needed to generate proper GTV coverage, which will be irradiated more accurately in the following boost phase.« less

Dosimetric feasibility of 4DCT-ventilation imaging guided proton therapy for locally advanced non-small-cell lung cancer.

PubMed

Huang, Qijie; Jabbour, Salma K; Xiao, Zhiyan; Yue, Ning; Wang, Xiao; Cao, Hongbin; Kuang, Yu; Zhang, Yin; Nie, Ke

2018-04-25

The principle aim of this study is to incorporate 4DCT ventilation imaging into functional treatment planning that preserves high-functioning lung with both double scattering and scanning beam techniques in proton therapy. Eight patients with locally advanced non-small-cell lung cancer were included in this study. Deformable image registration was performed for each patient on their planning 4DCTs and the resultant displacement vector field with Jacobian analysis was used to identify the high-, medium- and low-functional lung regions. Five plans were designed for each patient: a regular photon IMRT vs. anatomic proton plans without consideration of functional ventilation information using double scattering proton therapy (DSPT) and intensity modulated proton therapy (IMPT) vs. functional proton plans with avoidance of high-functional lung using both DSPT and IMPT. Dosimetric parameters were compared in terms of tumor coverage, plan heterogeneity, and avoidance of normal tissues. Our results showed that both DSPT and IMPT plans gave superior dose advantage to photon IMRTs in sparing low dose regions of the total lung in terms of V5 (volume receiving 5Gy). The functional DSPT only showed marginal benefit in sparing high-functioning lung in terms of V5 or V20 (volume receiving 20Gy) compared to anatomical plans. Yet, the functional planning in IMPT delivery, can further reduce the low dose in high-functioning lung without degrading the PTV dosimetric coverages, compared to anatomical proton planning. Although the doses to some critical organs might increase during functional planning, the necessary constraints were all met. Incorporating 4DCT ventilation imaging into functional proton therapy is feasible. The functional proton plans, in intensity modulated proton delivery, are effective to further preserve high-functioning lung regions without degrading the PTV coverage.

Minimization for conditional simulation: Relationship to optimal transport

NASA Astrophysics Data System (ADS)

Oliver, Dean S.

2014-05-01

In this paper, we consider the problem of generating independent samples from a conditional distribution when independent samples from the prior distribution are available. Although there are exact methods for sampling from the posterior (e.g. Markov chain Monte Carlo or acceptance/rejection), these methods tend to be computationally demanding when evaluation of the likelihood function is expensive, as it is for most geoscience applications. As an alternative, in this paper we discuss deterministic mappings of variables distributed according to the prior to variables distributed according to the posterior. Although any deterministic mappings might be equally useful, we will focus our discussion on a class of algorithms that obtain implicit mappings by minimization of a cost function that includes measures of data mismatch and model variable mismatch. Algorithms of this type include quasi-linear estimation, randomized maximum likelihood, perturbed observation ensemble Kalman filter, and ensemble of perturbed analyses (4D-Var). When the prior pdf is Gaussian and the observation operators are linear, we show that these minimization-based simulation methods solve an optimal transport problem with a nonstandard cost function. When the observation operators are nonlinear, however, the mapping of variables from the prior to the posterior obtained from those methods is only approximate. Errors arise from neglect of the Jacobian determinant of the transformation and from the possibility of discontinuous mappings.

Fully-Implicit Reconstructed Discontinuous Galerkin Method for Stiff Multiphysics Problems

NASA Astrophysics Data System (ADS)

Nourgaliev, Robert

2015-11-01

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method's capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing. We focus on the method's accuracy (in both space and time), as well as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, and funded by the LDRD at LLNL under project tracking code 13-SI-002.

Streamline integration as a method for two-dimensional elliptic grid generation

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

Wiesenberger, M., E-mail: Matthias.Wiesenberger@uibk.ac.at; Held, M.; Einkemmer, L.

We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. Furthermore, we can adapt any analytically given boundary aligned structured grid, which specifically includes polar and Cartesian grids. The resulting coordinate lines are orthogonal to the boundary. Grid points as well as the elements of the Jacobian matrix can be computed efficiently and up to machine precision. In the simplest case we construct conformal grids, yet with the help of weight functions and monitor metricsmore » we can control the distribution of cells across the domain. Our algorithm is parallelizable and easy to implement with elementary numerical methods. We assess the quality of grids by considering both the distribution of cell sizes and the accuracy of the solution to elliptic problems. Among the tested grids these key properties are best fulfilled by the grid constructed with the monitor metric approach. - Graphical abstract: - Highlights: • Construct structured, elliptic numerical grids with elementary numerical methods. • Align coordinate lines with or make them orthogonal to the domain boundary. • Compute grid points and metric elements up to machine precision. • Control cell distribution by adaption functions or monitor metrics.« less

A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes

DOE PAGES

Svyatsky, Daniil; Lipnikov, Konstantin

2017-03-18

Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less

Comparison of time-series registration methods in breast dynamic infrared imaging

NASA Astrophysics Data System (ADS)

Riyahi-Alam, S.; Agostini, V.; Molinari, F.; Knaflitz, M.

2015-03-01

Automated motion reduction in dynamic infrared imaging is on demand in clinical applications, since movement disarranges time-temperature series of each pixel, thus originating thermal artifacts that might bias the clinical decision. All previously proposed registration methods are feature based algorithms requiring manual intervention. The aim of this work is to optimize the registration strategy specifically for Breast Dynamic Infrared Imaging and to make it user-independent. We implemented and evaluated 3 different 3D time-series registration methods: 1. Linear affine, 2. Non-linear Bspline, 3. Demons applied to 12 datasets of healthy breast thermal images. The results are evaluated through normalized mutual information with average values of 0.70 ±0.03, 0.74 ±0.03 and 0.81 ±0.09 (out of 1) for Affine, Bspline and Demons registration, respectively, as well as breast boundary overlap and Jacobian determinant of the deformation field. The statistical analysis of the results showed that symmetric diffeomorphic Demons' registration method outperforms also with the best breast alignment and non-negative Jacobian values which guarantee image similarity and anatomical consistency of the transformation, due to homologous forces enforcing the pixel geometric disparities to be shortened on all the frames. We propose Demons' registration as an effective technique for time-series dynamic infrared registration, to stabilize the local temperature oscillation.

Fully Implicit, Nonlinear 3D Extended Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Chacon, Luis; Knoll, Dana

2003-10-01

Extended magnetohydrodynamics (XMHD) includes nonideal effects such as nonlinear, anisotropic transport and two-fluid (Hall) effects. XMHD supports multiple, separate time scales that make explicit time differencing approaches extremely inefficient. While a fully implicit implementation promises efficiency without sacrificing numerical accuracy,(D. A. Knoll et al., phJ. Comput. Phys.) 185 (2), 583-611 (2003) the nonlinear nature of the XMHD system and the numerical stiffness associated with the fast waves make this endeavor difficult. Newton-Krylov methods are, however, ideally suited for such a task. These synergistically combine Newton's method for nonlinear convergence, and Krylov techniques to solve the associated Jacobian (linear) systems. Krylov methods can be implemented Jacobian-free and can be preconditioned for efficiency. Successful preconditioning strategies have been developed for 2D incompressible resistive(L. Chacón et al., phJ. Comput. Phys). 178 (1), 15- 36 (2002) and Hall(L. Chacón and D. A. Knoll, phJ. Comput. Phys.), 188 (2), 573-592 (2003) MHD models. These are based on ``physics-based'' ideas, in which knowledge of the physics is exploited to derive well-conditioned (diagonally-dominant) approximations to the original system that are amenable to optimal solver technologies (multigrid). In this work, we will describe the status of the extension of the 2D preconditioning ideas for a 3D compressible, single-fluid XMHD model.

Implementation of the Jacobian-free Newton-Krylov method for solving the for solving the first-order ice sheet momentum balance

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

Salinger, Andy; Evans, Katherine J; Lemieux, Jean-Francois

2011-01-01

We have implemented the Jacobian-free Newton-Krylov (JFNK) method for solving the rst-order ice sheet momentum equation in order to improve the numerical performance of the Community Ice Sheet Model (CISM), the land ice component of the Community Earth System Model (CESM). Our JFNK implementation is based on signicant re-use of existing code. For example, our physics-based preconditioner uses the original Picard linear solver in CISM. For several test cases spanning a range of geometries and boundary conditions, our JFNK implementation is 1.84-3.62 times more efficient than the standard Picard solver in CISM. Importantly, this computational gain of JFNK over themore » Picard solver increases when rening the grid. Global convergence of the JFNK solver has been signicantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact Newton method. While a diverse set of test cases show that our JFNK implementation is usually robust, for some problems it may fail to converge with increasing resolution (as does the Picard solver). Globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of Picard and JFNK and the use of homotopy methods.« less

A Matlab toolkit for three-dimensional electrical impedance tomography: a contribution to the Electrical Impedance and Diffuse Optical Reconstruction Software project

NASA Astrophysics Data System (ADS)

Polydorides, Nick; Lionheart, William R. B.

2002-12-01

The objective of the Electrical Impedance and Diffuse Optical Reconstruction Software project is to develop freely available software that can be used to reconstruct electrical or optical material properties from boundary measurements. Nonlinear and ill posed problems such as electrical impedance and optical tomography are typically approached using a finite element model for the forward calculations and a regularized nonlinear solver for obtaining a unique and stable inverse solution. Most of the commercially available finite element programs are unsuitable for solving these problems because of their conventional inefficient way of calculating the Jacobian, and their lack of accurate electrode modelling. A complete package for the two-dimensional EIT problem was officially released by Vauhkonen et al at the second half of 2000. However most industrial and medical electrical imaging problems are fundamentally three-dimensional. To assist the development we have developed and released a free toolkit of Matlab routines which can be employed to solve the forward and inverse EIT problems in three dimensions based on the complete electrode model along with some basic visualization utilities, in the hope that it will stimulate further development. We also include a derivation of the formula for the Jacobian (or sensitivity) matrix based on the complete electrode model.

Jacobian projection reduced-order models for dynamic systems with contact nonlinearities

NASA Astrophysics Data System (ADS)

Gastaldi, Chiara; Zucca, Stefano; Epureanu, Bogdan I.

2018-02-01

In structural dynamics, the prediction of the response of systems with localized nonlinearities, such as friction dampers, is of particular interest. This task becomes especially cumbersome when high-resolution finite element models are used. While state-of-the-art techniques such as Craig-Bampton component mode synthesis are employed to generate reduced order models, the interface (nonlinear) degrees of freedom must still be solved in-full. For this reason, a new generation of specialized techniques capable of reducing linear and nonlinear degrees of freedom alike is emerging. This paper proposes a new technique that exploits spatial correlations in the dynamics to compute a reduction basis. The basis is composed of a set of vectors obtained using the Jacobian of partial derivatives of the contact forces with respect to nodal displacements. These basis vectors correspond to specifically chosen boundary conditions at the contacts over one cycle of vibration. The technique is shown to be effective in the reduction of several models studied using multiple harmonics with a coupled static solution. In addition, this paper addresses another challenge common to all reduction techniques: it presents and validates a novel a posteriori error estimate capable of evaluating the quality of the reduced-order solution without involving a comparison with the full-order solution.

Optimization of computations for adjoint field and Jacobian needed in 3D CSEM inversion

NASA Astrophysics Data System (ADS)

Dehiya, Rahul; Singh, Arun; Gupta, Pravin K.; Israil, M.

2017-01-01

We present the features and results of a newly developed code, based on Gauss-Newton optimization technique, for solving three-dimensional Controlled-Source Electromagnetic inverse problem. In this code a special emphasis has been put on representing the operations by block matrices for conjugate gradient iteration. We show how in the computation of Jacobian, the matrix formed by differentiation of system matrix can be made independent of frequency to optimize the operations at conjugate gradient step. The coarse level parallel computing, using OpenMP framework, is used primarily due to its simplicity in implementation and accessibility of shared memory multi-core computing machine to almost anyone. We demonstrate how the coarseness of modeling grid in comparison to source (comp`utational receivers) spacing can be exploited for efficient computing, without compromising the quality of the inverted model, by reducing the number of adjoint calls. It is also demonstrated that the adjoint field can even be computed on a grid coarser than the modeling grid without affecting the inversion outcome. These observations were reconfirmed using an experiment design where the deviation of source from straight tow line is considered. Finally, a real field data inversion experiment is presented to demonstrate robustness of the code.

An efficient strongly coupled immersed boundary method for deforming bodies

NASA Astrophysics Data System (ADS)

Goza, Andres; Colonius, Tim

2016-11-01

Immersed boundary methods treat the fluid and immersed solid with separate domains. As a result, a nonlinear interface constraint must be satisfied when these methods are applied to flow-structure interaction problems. This typically results in a large nonlinear system of equations that is difficult to solve efficiently. Often, this system is solved with a block Gauss-Seidel procedure, which is easy to implement but can require many iterations to converge for small solid-to-fluid mass ratios. Alternatively, a Newton-Raphson procedure can be used to solve the nonlinear system. This typically leads to convergence in a small number of iterations for arbitrary mass ratios, but involves the use of large Jacobian matrices. We present an immersed boundary formulation that, like the Newton-Raphson approach, uses a linearization of the system to perform iterations. It therefore inherits the same favorable convergence behavior. However, we avoid large Jacobian matrices by using a block LU factorization of the linearized system. We derive our method for general deforming surfaces and perform verification on 2D test problems of flow past beams. These test problems involve large amplitude flapping and a wide range of mass ratios. This work was partially supported by the Jet Propulsion Laboratory and Air Force Office of Scientific Research.

Toward GPGPU accelerated human electromechanical cardiac simulations

PubMed Central

Vigueras, Guillermo; Roy, Ishani; Cookson, Andrew; Lee, Jack; Smith, Nicolas; Nordsletten, David

2014-01-01

In this paper, we look at the acceleration of weakly coupled electromechanics using the graphics processing unit (GPU). Specifically, we port to the GPU a number of components of Heart—a CPU-based finite element code developed for simulating multi-physics problems. On the basis of a criterion of computational cost, we implemented on the GPU the ODE and PDE solution steps for the electrophysiology problem and the Jacobian and residual evaluation for the mechanics problem. Performance of the GPU implementation is then compared with single core CPU (SC) execution as well as multi-core CPU (MC) computations with equivalent theoretical performance. Results show that for a human scale left ventricle mesh, GPU acceleration of the electrophysiology problem provided speedups of 164 × compared with SC and 5.5 times compared with MC for the solution of the ODE model. Speedup of up to 72 × compared with SC and 2.6 × compared with MC was also observed for the PDE solve. Using the same human geometry, the GPU implementation of mechanics residual/Jacobian computation provided speedups of up to 44 × compared with SC and 2.0 × compared with MC. © 2013 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons, Ltd. PMID:24115492

Application of Jacobian-free Newton–Krylov method in implicitly solving two-fluid six-equation two-phase flow problems: Implementation, validation and benchmark

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-03-09

This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3Dmore » code further verifies the correct code implementation. The combined methods employed in this work exhibit strong robustness in solving two-phase flow problems even when phase appearance (boiling) and realistic discrete flow regimes are considered. Transitional flow regimes used in existing system analysis codes, normally introduced to overcome numerical difficulty, were completely removed in this work. As a result, this in turn provides the possibility to utilize more sophisticated flow regime maps in the future to further improve simulation accuracy.« less

A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes

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

Svyatsky, Daniil; Lipnikov, Konstantin

Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less

Efficient Coupling of Fluid-Plasma and Monte-Carlo-Neutrals Models for Edge Plasma Transport

NASA Astrophysics Data System (ADS)

Dimits, A. M.; Cohen, B. I.; Friedman, A.; Joseph, I.; Lodestro, L. L.; Rensink, M. E.; Rognlien, T. D.; Sjogreen, B.; Stotler, D. P.; Umansky, M. V.

2017-10-01

UEDGE has been valuable for modeling transport in the tokamak edge and scrape-off layer due in part to its efficient fully implicit solution of coupled fluid neutrals and plasma models. We are developing an implicit coupling of the kinetic Monte-Carlo (MC) code DEGAS-2, as the neutrals model component, to the UEDGE plasma component, based on an extension of the Jacobian-free Newton-Krylov (JFNK) method to MC residuals. The coupling components build on the methods and coding already present in UEDGE. For the linear Krylov iterations, a procedure has been developed to ``extract'' a good preconditioner from that of UEDGE. This preconditioner may also be used to greatly accelerate the convergence rate of a relaxed fixed-point iteration, which may provide a useful ``intermediate'' algorithm. The JFNK method also requires calculation of Jacobian-vector products, for which any finite-difference procedure is inaccurate when a MC component is present. A semi-analytical procedure that retains the standard MC accuracy and fully kinetic neutrals physics is therefore being developed. Prepared for US DOE by LLNL under Contract DE-AC52-07NA27344 and LDRD project 15-ERD-059, by PPPL under Contract DE-AC02-09CH11466, and supported in part by the U.S. DOE, OFES.

Monte Carlo-based fluorescence molecular tomography reconstruction method accelerated by a cluster of graphic processing units.

PubMed

Quan, Guotao; Gong, Hui; Deng, Yong; Fu, Jianwei; Luo, Qingming

2011-02-01

High-speed fluorescence molecular tomography (FMT) reconstruction for 3-D heterogeneous media is still one of the most challenging problems in diffusive optical fluorescence imaging. In this paper, we propose a fast FMT reconstruction method that is based on Monte Carlo (MC) simulation and accelerated by a cluster of graphics processing units (GPUs). Based on the Message Passing Interface standard, we modified the MC code for fast FMT reconstruction, and different Green's functions representing the flux distribution in media are calculated simultaneously by different GPUs in the cluster. A load-balancing method was also developed to increase the computational efficiency. By applying the Fréchet derivative, a Jacobian matrix is formed to reconstruct the distribution of the fluorochromes using the calculated Green's functions. Phantom experiments have shown that only 10 min are required to get reconstruction results with a cluster of 6 GPUs, rather than 6 h with a cluster of multiple dual opteron CPU nodes. Because of the advantages of high accuracy and suitability for 3-D heterogeneity media with refractive-index-unmatched boundaries from the MC simulation, the GPU cluster-accelerated method provides a reliable approach to high-speed reconstruction for FMT imaging.

A fully-implicit Particle-In-Cell Monte Carlo Collision code for the simulation of inductively coupled plasmas

NASA Astrophysics Data System (ADS)

Mattei, S.; Nishida, K.; Onai, M.; Lettry, J.; Tran, M. Q.; Hatayama, A.

2017-12-01

We present a fully-implicit electromagnetic Particle-In-Cell Monte Carlo collision code, called NINJA, written for the simulation of inductively coupled plasmas. NINJA employs a kinetic enslaved Jacobian-Free Newton Krylov method to solve self-consistently the interaction between the electromagnetic field generated by the radio-frequency coil and the plasma response. The simulated plasma includes a kinetic description of charged and neutral species as well as the collision processes between them. The algorithm allows simulations with cell sizes much larger than the Debye length and time steps in excess of the Courant-Friedrichs-Lewy condition whilst preserving the conservation of the total energy. The code is applied to the simulation of the plasma discharge of the Linac4 H- ion source at CERN. Simulation results of plasma density, temperature and EEDF are discussed and compared with optical emission spectroscopy measurements. A systematic study of the energy conservation as a function of the numerical parameters is presented.

A complete analytical solution for the inverse instantaneous kinematics of a spherical-revolute-spherical (7R) redundant manipulator

NASA Technical Reports Server (NTRS)

Podhorodeski, R. P.; Fenton, R. G.; Goldenberg, A. A.

1989-01-01

Using a method based upon resolving joint velocities using reciprocal screw quantities, compact analytical expressions are generated for the inverse solution of the joint rates of a seven revolute (spherical-revolute-spherical) manipulator. The method uses a sequential decomposition of screw coordinates to identify reciprocal screw quantities used in the resolution of a particular joint rate solution, and also to identify a Jacobian null-space basis used for the direct solution of optimal joint rates. The results of the screw decomposition are used to study special configurations of the manipulator, generating expressions for the inverse velocity solution for all non-singular configurations of the manipulator, and identifying singular configurations and their characteristics. Two functions are therefore served: a new general method for the solution of the inverse velocity problem is presented; and complete analytical expressions are derived for the resolution of the joint rates of a seven degree of freedom manipulator useful for telerobotic and industrial robotic application.

Dynamic Analysis and Control of Lightweight Manipulators with Flexible Parallel Link Mechanisms. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Lee, Jeh Won

1990-01-01

The objective is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. The resulting equation of motion have a structure which is useful to reduce the number of terms calculated, to check correctness, or to extend the model to higher order. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. Elastic motion is expressed by the assumed mode method. Mode shape functions of each link are chosen using the load interfaced component mode synthesis. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model.

A high order accurate finite element algorithm for high Reynolds number flow prediction

NASA Technical Reports Server (NTRS)

Baker, A. J.

1978-01-01

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

Kinematically redundant robot manipulators

NASA Technical Reports Server (NTRS)

Baillieul, J.; Hollerbach, J.; Brockett, R.; Martin, D.; Percy, R.; Thomas, R.

1987-01-01

Research on control, design and programming of kinematically redundant robot manipulators (KRRM) is discussed. These are devices in which there are more joint space degrees of freedom than are required to achieve every position and orientation of the end-effector necessary for a given task in a given workspace. The technological developments described here deal with: kinematic programming techniques for automatically generating joint-space trajectories to execute prescribed tasks; control of redundant manipulators to optimize dynamic criteria (e.g., applications of forces and moments at the end-effector that optimally distribute the loading of actuators); and design of KRRMs to optimize functionality in congested work environments or to achieve other goals unattainable with non-redundant manipulators. Kinematic programming techniques are discussed, which show that some pseudo-inverse techniques that have been proposed for redundant manipulator control fail to achieve the goals of avoiding kinematic singularities and also generating closed joint-space paths corresponding to close paths of the end effector in the workspace. The extended Jacobian is proposed as an alternative to pseudo-inverse techniques.

Electrical impedance tomography in anisotropic media with known eigenvectors

NASA Astrophysics Data System (ADS)

Abascal, Juan-Felipe P. J.; Lionheart, William R. B.; Arridge, Simon R.; Schweiger, Martin; Atkinson, David; Holder, David S.

2011-06-01

Electrical impedance tomography is an imaging method, with which volumetric images of conductivity are produced by injecting electrical current and measuring boundary voltages. It has the potential to become a portable non-invasive medical imaging technique. Until now, most implementations have neglected anisotropy even though human tissues like bone, muscle and brain white matter are markedly anisotropic. The recovery of an anisotropic conductivity tensor is uniquely determined by boundary measurements only up to a diffeomorphism that fixes the boundary. Nevertheless, uniqueness can be restored by providing information about the diffeomorphism. There are uniqueness results for two constraints: one eigenvalue and a multiple scalar of a general tensor. A useable constraint for medical applications is when the eigenvectors of the underlying tissue are known, which can be approximated from MRI or estimated from DT-MRI, although the eigenvalues are unknown. However there is no known theoretical result guaranteeing uniqueness for this constraint. In fact, only a few previous inversion studies have attempted to recover one or more eigenvalues assuming certain symmetries while ignoring nonuniqueness. In this work, the aim was to undertake a numerical study of the feasibility of the recovery of a piecewise linear finite element conductivity tensor in anisotropic media with known eigenvectors from the complete boundary data. The work suggests that uniqueness holds for this constraint, in addition to proposing a methodology for the incorporation of this prior for general conductivity tensors. This was carried out by performing an analysis of the Jacobian rank and by reconstructing four conductivity distributions: two diagonal tensors whose eigenvalues were linear and sinusoidal functions, and two general tensors whose eigenvectors resembled physiological tissue, one with eigenvectors spherically orientated like a spherical layered structure, and a sample of DT-MRI data of brain white matter. The Jacobian with respect to three eigenvalues was full-rank and it was possible to recover three eigenvalues for the four simulated distributions. This encourages further theoretical study of the uniqueness for this constraint and supports the use of this as a relevant usable method for medical applications.

Nonequilibrium flow computations. 1: An analysis of numerical formulations of conservation laws

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel

1988-01-01

Modern numerical techniques employing properties of flux Jacobian matrices are extended to general, nonequilibrium flows. Generalizations of the Beam-Warming scheme, Steger-Warming and van Leer Flux-vector splittings, and Roe's approximate Riemann solver are presented for 3-D, time-varying grids. The analysis is based on a thermodynamic model that includes the most general thermal and chemical nonequilibrium flow of an arbitrary gas. Various special cases are also discussed.

Neonatal MRI is associated with future cognition and academic achievement in preterm children

PubMed Central

Spencer-Smith, Megan; Thompson, Deanne K.; Doyle, Lex W.; Inder, Terrie E.; Anderson, Peter J.; Klingberg, Torkel

2015-01-01

School-age children born preterm are particularly at risk for low mathematical achievement, associated with reduced working memory and number skills. Early identification of preterm children at risk for future impairments using brain markers might assist in referral for early intervention. This study aimed to examine the use of neonatal magnetic resonance imaging measures derived from automated methods (Jacobian maps from deformation-based morphometry; fractional anisotropy maps from diffusion tensor images) to predict skills important for mathematical achievement (working memory, early mathematical skills) at 5 and 7 years in a cohort of preterm children using both univariable (general linear model) and multivariable models (support vector regression). Participants were preterm children born <30 weeks’ gestational age and healthy control children born ≥37 weeks’ gestational age at the Royal Women’s Hospital in Melbourne, Australia between July 2001 and December 2003 and recruited into a prospective longitudinal cohort study. At term-equivalent age ( ±2 weeks) 224 preterm and 46 control infants were recruited for magnetic resonance imaging. Working memory and early mathematics skills were assessed at 5 years (n = 195 preterm; n = 40 controls) and 7 years (n = 197 preterm; n = 43 controls). In the preterm group, results identified localized regions around the insula and putamen in the neonatal Jacobian map that were positively associated with early mathematics at 5 and 7 years (both P < 0.05), even after covarying for important perinatal clinical factors using general linear model but not support vector regression. The neonatal Jacobian map showed the same trend for association with working memory at 7 years (models ranging from P = 0.07 to P = 0.05). Neonatal fractional anisotropy was positively associated with working memory and early mathematics at 5 years (both P < 0.001) even after covarying for clinical factors using support vector regression but not general linear model. These significant relationships were not observed in the control group. In summary, we identified, in the preterm brain, regions around the insula and putamen using neonatal deformation-based morphometry, and brain microstructural organization using neonatal diffusion tensor imaging, associated with skills important for childhood mathematical achievement. Results contribute to the growing evidence for the clinical utility of neonatal magnetic resonance imaging for early identification of preterm infants at risk for childhood cognitive and academic impairment. PMID:26329284

Three dimensional PNS solutions of hypersonic internal flows with equilibrium chemistry

NASA Technical Reports Server (NTRS)

Liou, May-Fun

1989-01-01

An implicit procedure for solving parabolized Navier-Stokes equations under the assumption of a general equation of state for a gas in chemical equilibrium is given. A general and consistent approach for the evaluation of Jacobian matrices in the implicit operator avoids the use of unnecessary auxiliary quantities and approximations, and leads to a simple expression. Applications to two- and three-dimensional flow problems show efficiency in computer time and economy in storage.

A Scientific Analysis of Galaxy Tangential Speed of Revolution Curves III

NASA Astrophysics Data System (ADS)

Taff, Laurence

2015-04-01

I last reported on my preliminary analysis of 350 + spiral, lenticular, irregular, polar ring, ring, and dwarf elliptical galaxies' tangential speed of revolution curves [TSRCs; and not rotation (sic) curves]. I now know that the consensus opinion in the literature--for which I can find no geometrical, numerical, statistical, nor scientific testing in 2,500 + publications--that the TSRC, vB(r), in the central bulges of these galaxies, is a linear function of the radial distance from the minor axis of symmetry r--is false. For the majority (>98%) vB(r) is rarely well represented by vB(r) = ωB r (for which the unique material model is an homogeneous, oblate, spheroid). Discovered via a scientific analysis of the gravitational potential energy computed directly from the observational data, vB(r) is almost exactly given by vB2(r) = (ωB r)2(1 + η r2) with | η | < 10-2 and frequently orders of magnitude less. The corresponding mass model is the simplest generalization: a two component homoeoid. The set of possible periodic orbits, based on circular trigonometric functions, becomes a set of periodic orbits based on the Jacobian elliptic functions. Once again it is possible to prove that the mass-to-light ratio can neither be a constant nor follow the de Vaucouleurs R1/4 rule.

Refined elasticity sampling for Monte Carlo-based identification of stabilizing network patterns.

PubMed

Childs, Dorothee; Grimbs, Sergio; Selbig, Joachim

2015-06-15

Structural kinetic modelling (SKM) is a framework to analyse whether a metabolic steady state remains stable under perturbation, without requiring detailed knowledge about individual rate equations. It provides a representation of the system's Jacobian matrix that depends solely on the network structure, steady state measurements, and the elasticities at the steady state. For a measured steady state, stability criteria can be derived by generating a large number of SKMs with randomly sampled elasticities and evaluating the resulting Jacobian matrices. The elasticity space can be analysed statistically in order to detect network positions that contribute significantly to the perturbation response. Here, we extend this approach by examining the kinetic feasibility of the elasticity combinations created during Monte Carlo sampling. Using a set of small example systems, we show that the majority of sampled SKMs would yield negative kinetic parameters if they were translated back into kinetic models. To overcome this problem, a simple criterion is formulated that mitigates such infeasible models. After evaluating the small example pathways, the methodology was used to study two steady states of the neuronal TCA cycle and the intrinsic mechanisms responsible for their stability or instability. The findings of the statistical elasticity analysis confirm that several elasticities are jointly coordinated to control stability and that the main source for potential instabilities are mutations in the enzyme alpha-ketoglutarate dehydrogenase. © The Author 2015. Published by Oxford University Press.

Linearized image reconstruction method for ultrasound modulated electrical impedance tomography based on power density distribution

NASA Astrophysics Data System (ADS)

Song, Xizi; Xu, Yanbin; Dong, Feng

2017-04-01

Electrical resistance tomography (ERT) is a promising measurement technique with important industrial and clinical applications. However, with limited effective measurements, it suffers from poor spatial resolution due to the ill-posedness of the inverse problem. Recently, there has been an increasing research interest in hybrid imaging techniques, utilizing couplings of physical modalities, because these techniques obtain much more effective measurement information and promise high resolution. Ultrasound modulated electrical impedance tomography (UMEIT) is one of the newly developed hybrid imaging techniques, which combines electric and acoustic modalities. A linearized image reconstruction method based on power density is proposed for UMEIT. The interior data, power density distribution, is adopted to reconstruct the conductivity distribution with the proposed image reconstruction method. At the same time, relating the power density change to the change in conductivity, the Jacobian matrix is employed to make the nonlinear problem into a linear one. The analytic formulation of this Jacobian matrix is derived and its effectiveness is also verified. In addition, different excitation patterns are tested and analyzed, and opposite excitation provides the best performance with the proposed method. Also, multiple power density distributions are combined to implement image reconstruction. Finally, image reconstruction is implemented with the linear back-projection (LBP) algorithm. Compared with ERT, with the proposed image reconstruction method, UMEIT can produce reconstructed images with higher quality and better quantitative evaluation results.

Optical control of the Advanced Technology Solar Telescope.

PubMed

Upton, Robert

2006-08-10

The Advanced Technology Solar Telescope (ATST) is an off-axis Gregorian astronomical telescope design. The ATST is expected to be subject to thermal and gravitational effects that result in misalignments of its mirrors and warping of its primary mirror. These effects require active, closed-loop correction to maintain its as-designed diffraction-limited optical performance. The simulation and modeling of the ATST with a closed-loop correction strategy are presented. The correction strategy is derived from the linear mathematical properties of two Jacobian, or influence, matrices that map the ATST rigid-body (RB) misalignments and primary mirror figure errors to wavefront sensor (WFS) measurements. The two Jacobian matrices also quantify the sensitivities of the ATST to RB and primary mirror figure perturbations. The modeled active correction strategy results in a decrease of the rms wavefront error averaged over the field of view (FOV) from 500 to 19 nm, subject to 10 nm rms WFS noise. This result is obtained utilizing nine WFSs distributed in the FOV with a 300 nm rms astigmatism figure error on the primary mirror. Correction of the ATST RB perturbations is demonstrated for an optimum subset of three WFSs with corrections improving the ATST rms wavefront error from 340 to 17.8 nm. In addition to the active correction of the ATST, an analytically robust sensitivity analysis that can be generally extended to a wider class of optical systems is presented.

Multivariate Tensor-based Morphometry on Surfaces: Application to Mapping Ventricular Abnormalities in HIV/AIDS

PubMed Central

Wang, Yalin; Zhang, Jie; Gutman, Boris; Chan, Tony F.; Becker, James T.; Aizenstein, Howard J.; Lopez, Oscar L.; Tamburo, Robert J.; Toga, Arthur W.; Thompson, Paul M.

2010-01-01

Here we developed a new method, called multivariate tensor-based surface morphometry (TBM), and applied it to study lateral ventricular surface differences associated with HIV/AIDS. Using concepts from differential geometry and the theory of differential forms, we created mathematical structures known as holomorphic one-forms, to obtain an efficient and accurate conformal parameterization of the lateral ventricular surfaces in the brain. The new meshing approach also provides a natural way to register anatomical surfaces across subjects, and improves on prior methods as it handles surfaces that branch and join at complex 3D junctions. To analyze anatomical differences, we computed new statistics from the Riemannian surface metrics - these retain multivariate information on local surface geometry. We applied this framework to analyze lateral ventricular surface morphometry in 3D MRI data from 11 subjects with HIV/AIDS and 8 healthy controls. Our method detected a 3D profile of surface abnormalities even in this small sample. Multivariate statistics on the local tensors gave better effect sizes for detecting group differences, relative to other TBM-based methods including analysis of the Jacobian determinant, the largest and smallest eigenvalues of the surface metric, and the pair of eigenvalues of the Jacobian matrix. The resulting analysis pipeline may improve the power of surface-based morphometry studies of the brain. PMID:19900560

Effects of high-frequency damping on iterative convergence of implicit viscous solver

NASA Astrophysics Data System (ADS)

Nishikawa, Hiroaki; Nakashima, Yoshitaka; Watanabe, Norihiko

2017-11-01

This paper discusses effects of high-frequency damping on iterative convergence of an implicit defect-correction solver for viscous problems. The study targets a finite-volume discretization with a one parameter family of damped viscous schemes. The parameter α controls high-frequency damping: zero damping with α = 0, and larger damping for larger α (> 0). Convergence rates are predicted for a model diffusion equation by a Fourier analysis over a practical range of α. It is shown that the convergence rate attains its minimum at α = 1 on regular quadrilateral grids, and deteriorates for larger values of α. A similar behavior is observed for regular triangular grids. In both quadrilateral and triangular grids, the solver is predicted to diverge for α smaller than approximately 0.5. Numerical results are shown for the diffusion equation and the Navier-Stokes equations on regular and irregular grids. The study suggests that α = 1 and 4/3 are suitable values for robust and efficient computations, and α = 4 / 3 is recommended for the diffusion equation, which achieves higher-order accuracy on regular quadrilateral grids. Finally, a Jacobian-Free Newton-Krylov solver with the implicit solver (a low-order Jacobian approximately inverted by a multi-color Gauss-Seidel relaxation scheme) used as a variable preconditioner is recommended for practical computations, which provides robust and efficient convergence for a wide range of α.

Anderson acceleration and application to the three-temperature energy equations

NASA Astrophysics Data System (ADS)

An, Hengbin; Jia, Xiaowei; Walker, Homer F.

2017-10-01

The Anderson acceleration method is an algorithm for accelerating the convergence of fixed-point iterations, including the Picard method. Anderson acceleration was first proposed in 1965 and, for some years, has been used successfully to accelerate the convergence of self-consistent field iterations in electronic-structure computations. Recently, the method has attracted growing attention in other application areas and among numerical analysts. Compared with a Newton-like method, an advantage of Anderson acceleration is that there is no need to form the Jacobian matrix. Thus the method is easy to implement. In this paper, an Anderson-accelerated Picard method is employed to solve the three-temperature energy equations, which are a type of strong nonlinear radiation-diffusion equations. Two strategies are used to improve the robustness of the Anderson acceleration method. One strategy is to adjust the iterates when necessary to satisfy the physical constraint. Another strategy is to monitor and, if necessary, reduce the matrix condition number of the least-squares problem in the Anderson-acceleration implementation so that numerical stability can be guaranteed. Numerical results show that the Anderson-accelerated Picard method can solve the three-temperature energy equations efficiently. Compared with the Picard method without acceleration, Anderson acceleration can reduce the number of iterations by at least half. A comparison between a Jacobian-free Newton-Krylov method, the Picard method, and the Anderson-accelerated Picard method is conducted in this paper.

A Linearized Prognostic Cloud Scheme in NASAs Goddard Earth Observing System Data Assimilation Tools

NASA Technical Reports Server (NTRS)

Holdaway, Daniel; Errico, Ronald M.; Gelaro, Ronald; Kim, Jong G.; Mahajan, Rahul

2015-01-01

A linearized prognostic cloud scheme has been developed to accompany the linearized convection scheme recently implemented in NASA's Goddard Earth Observing System data assimilation tools. The linearization, developed from the nonlinear cloud scheme, treats cloud variables prognostically so they are subject to linearized advection, diffusion, generation, and evaporation. Four linearized cloud variables are modeled, the ice and water phases of clouds generated by large-scale condensation and, separately, by detraining convection. For each species the scheme models their sources, sublimation, evaporation, and autoconversion. Large-scale, anvil and convective species of precipitation are modeled and evaporated. The cloud scheme exhibits linearity and realistic perturbation growth, except around the generation of clouds through large-scale condensation. Discontinuities and steep gradients are widely used here and severe problems occur in the calculation of cloud fraction. For data assimilation applications this poor behavior is controlled by replacing this part of the scheme with a perturbation model. For observation impacts, where efficiency is less of a concern, a filtering is developed that examines the Jacobian. The replacement scheme is only invoked if Jacobian elements or eigenvalues violate a series of tuned constants. The linearized prognostic cloud scheme is tested by comparing the linear and nonlinear perturbation trajectories for 6-, 12-, and 24-h forecast times. The tangent linear model performs well and perturbations of clouds are well captured for the lead times of interest.

WE-AB-202-04: Statistical Evaluation of Lung Function Using 4DCT Ventilation Imaging: Proton Therapy VS IMRT

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

Huang, Q; Zhang, M; Chen, T

Purpose: Variation in function of different lung regions has been ignored so far for conventional lung cancer treatment planning, which may lead to higher risk of radiation induced lung disease. 4DCT based lung ventilation imaging provides a novel yet convenient approach for lung functional imaging as 4DCT is taken as routine for lung cancer treatment. Our work aims to evaluate the impact of accounting for spatial heterogeneity in lung function using 4DCT based lung ventilation imaging for proton and IMRT plans. Methods: Six patients with advanced stage lung cancer of various tumor locations were retrospectively evaluated for the study. Protonmore » and IMRT plans were designed following identical planning objective and constrains for each patient. Ventilation images were calculated from patients’ 4DCT using deformable image registration implemented by Velocity AI software based on Jacobian-metrics. Lung was delineated into two function level regions based on ventilation (low and high functional area). High functional region was defined as lung ventilation greater than 30%. Dose distribution and statistics in different lung function area was calculated for patients. Results: Variation in dosimetric statistics of different function lung region was observed between proton and IMRT plans. In all proton plans, high function lung regions receive lower maximum dose (100.2%–108.9%), compared with IMRT plans (106.4%–119.7%). Interestingly, three out of six proton plans gave higher mean dose by up to 2.2% than IMRT to high function lung region. Lower mean dose (lower by up to 14.1%) and maximum dose (lower by up to 9%) were observed in low function lung for proton plans. Conclusion: A systematic approach was developed to generate function lung ventilation imaging and use it to evaluate plans. This method hold great promise in function analysis of lung during planning. We are currently studying more subjects to evaluate this tool.« less

Effects of radiation pressure on the equipotential surfaces in X-ray binaries

NASA Technical Reports Server (NTRS)

Kondo, Y.; Mccluskey, G. E., Jr.; Gulden, S. L.

1976-01-01

Equipotential surfaces incorporating the effect of radiation pressure were computed for the X-ray binaries Cen X-3, Cyg X-1 = HDE 226868, Vela XR-1 = 3U 0900-40 = HD 77581, and 3U 1700-37 = HD 153919. The topology of the equipotential surfaces is significantly affected by radiation pressure. In particular, the so-called critical Roche (Jacobian) lobes, the traditional figure 8's, do not exist. The effects of these results on modeling X-ray binaries are discussed.

A new Newton-like method for solving nonlinear equations.

PubMed

Saheya, B; Chen, Guo-Qing; Sui, Yun-Kang; Wu, Cai-Ying

2016-01-01

This paper presents an iterative scheme for solving nonline ar equations. We establish a new rational approximation model with linear numerator and denominator which has generalizes the local linear model. We then employ the new approximation for nonlinear equations and propose an improved Newton's method to solve it. The new method revises the Jacobian matrix by a rank one matrix each iteration and obtains the quadratic convergence property. The numerical performance and comparison show that the proposed method is efficient.

Automatic computation and solution of generalized harmonic balance equations

NASA Astrophysics Data System (ADS)

Peyton Jones, J. C.; Yaser, K. S. A.; Stevenson, J.

2018-02-01

Generalized methods are presented for generating and solving the harmonic balance equations for a broad class of nonlinear differential or difference equations and for a general set of harmonics chosen by the user. In particular, a new algorithm for automatically generating the Jacobian of the balance equations enables efficient solution of these equations using continuation methods. Efficient numeric validation techniques are also presented, and the combined algorithm is applied to the analysis of dc, fundamental, second and third harmonic response of a nonlinear automotive damper.

Arc-Length Continuation and Multi-Grid Techniques for Nonlinear Elliptic Eigenvalue Problems,

DTIC Science & Technology

1981-03-19

size of the finest grid. We use the (AM) adaptive version of the Cycle C algorithm , unless otherwise stated. The first modified algorithm is the...by computing the derivative, uk, at a known solution and use it to get a better initial guess for the next value of X in a predictor - corrector fashion...factorization of the Jacobian Gu computed already in the Newton step. Using such a predictor - corrector method will often allow us to take a much bigger step

Adaptive Implicit Non-Equilibrium Radiation Diffusion

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

Philip, Bobby; Wang, Zhen; Berrill, Mark A

2013-01-01

We describe methods for accurate and efficient long term time integra- tion of non-equilibrium radiation diffusion systems: implicit time integration for effi- cient long term time integration of stiff multiphysics systems, local control theory based step size control to minimize the required global number of time steps while control- ling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

Concurrent MR-NIR Imaging for Breast Cancer Diagnosis

DTIC Science & Technology

2008-06-01

the extended Kalman filtering (EKF) framework. Note that both the fluorophore concentrations in different compartments, C(rj , k), and the system...r1 − r2)δ(k1 − k2)Z1. 10) Estimation of Pharmacokinetic-Rate Images by Extended Kalman Filtering: Our objective is to estimate the fluorophore...covariance update at time k. Hk is the recursive Kalman gain matrix at time k and I is the identity matrix. Jk−1 is the Jacobian matrix due to iterative

Configuration Synthesis and Efficient Motion Programming of Robot Manipulators

DTIC Science & Technology

1991-03-15

Gupta and Ma 90- Robotica 8:81-84]. When a set of discrete stations are specified along a robot task path, it becomes necessary to find a related...velocity Jacobian relations for the manipulator [Singh 87-MS Thesis][Gupta and Singh 89- Robotica 7:159-1641 and [Cheng 89-PhD Thesis][Cheng and Gupta...1987; Robotica 7:159-164, 1989 (revised). K. C. Gupta, "Kinematics of a Robot with Continuous Roll Wrist," IEEE J. Robotics and Automation 4(4):440-443

Grasp planning under uncertainty

NASA Technical Reports Server (NTRS)

Erkmen, A. M.; Stephanou, H. E.

1989-01-01

The planning of dexterous grasps for multifingered robot hands operating in uncertain environments is covered. A sensor-based approach to the planning of a reach path prior to grasping is first described. An on-line, joint space finger path planning algorithm for the enclose phase of grasping was then developed. The algorithm minimizes the impact momentum of the hand. It uses a Preshape Jacobian matrix to map task-level hand preshape requirements into kinematic constraints. A master slave scheme avoids inter-finger collisions and reduces the dimensionality of the planning problem.

CFD in the 1980's from one point of view

NASA Technical Reports Server (NTRS)

Lomax, Harvard

1991-01-01

The present interpretive treatment of the development history of CFD in the 1980s gives attention to advancements in such algorithmic techniques as flux Jacobian-based upwind differencing, total variation-diminishing and essentially nonoscillatory schemes, multigrid methods, unstructured grids, and nonrectangular structured grids. At the same time, computational turbulence research gave attention to turbulence modeling on the bases of increasingly powerful supercomputers and meticulously constructed databases. The major future developments in CFD will encompass such capabilities as structured and unstructured three-dimensional grids.

A comparison between different finite elements for elastic and aero-elastic analyses.

PubMed

Mahran, Mohamed; ELsabbagh, Adel; Negm, Hani

2017-11-01

In the present paper, a comparison between five different shell finite elements, including the Linear Triangular Element, Linear Quadrilateral Element, Linear Quadrilateral Element based on deformation modes, 8-node Quadrilateral Element, and 9-Node Quadrilateral Element was presented. The shape functions and the element equations related to each element were presented through a detailed mathematical formulation. Additionally, the Jacobian matrix for the second order derivatives was simplified and used to derive each element's strain-displacement matrix in bending. The elements were compared using carefully selected elastic and aero-elastic bench mark problems, regarding the number of elements needed to reach convergence, the resulting accuracy, and the needed computation time. The best suitable element for elastic free vibration analysis was found to be the Linear Quadrilateral Element with deformation-based shape functions, whereas the most suitable element for stress analysis was the 8-Node Quadrilateral Element, and the most suitable element for aero-elastic analysis was the 9-Node Quadrilateral Element. Although the linear triangular element was the last choice for modal and stress analyses, it establishes more accurate results in aero-elastic analyses, however, with much longer computation time. Additionally, the nine-node quadrilateral element was found to be the best choice for laminated composite plates analysis.

Neural Networks for Signal Processing and Control

NASA Astrophysics Data System (ADS)

Hesselroth, Ted Daniel

Neural networks are developed for controlling a robot-arm and camera system and for processing images. The networks are based upon computational schemes that may be found in the brain. In the first network, a neural map algorithm is employed to control a five-joint pneumatic robot arm and gripper through feedback from two video cameras. The pneumatically driven robot arm employed shares essential mechanical characteristics with skeletal muscle systems. To control the position of the arm, 200 neurons formed a network representing the three-dimensional workspace embedded in a four-dimensional system of coordinates from the two cameras, and learned a set of pressures corresponding to the end effector positions, as well as a set of Jacobian matrices for interpolating between these positions. Because of the properties of the rubber-tube actuators of the arm, the position as a function of supplied pressure is nonlinear, nonseparable, and exhibits hysteresis. Nevertheless, through the neural network learning algorithm the position could be controlled to an accuracy of about one pixel (~3 mm) after two hundred learning steps. Applications of repeated corrections in each step via the Jacobian matrices leads to a very robust control algorithm since the Jacobians learned by the network have to satisfy the weak requirement that they yield a reduction of the distance between gripper and target. The second network is proposed as a model for the mammalian vision system in which backward connections from the primary visual cortex (V1) to the lateral geniculate nucleus play a key role. The application of hebbian learning to the forward and backward connections causes the formation of receptive fields which are sensitive to edges, bars, and spatial frequencies of preferred orientations. The receptive fields are learned in such a way as to maximize the rate of transfer of information from the LGN to V1. Orientational preferences are organized into a feature map in the primary visual cortex by the application of lateral interactions during the learning phase. The organization of the mature network is compared to that found in the macaque monkey by several analytical tests. The capacity of the network to process images is investigated. By a method of reconstructing the input images in terms of V1 activities, the simulations show that images can be faithfully represented in V1 by the proposed network. The signal-to-noise ratio of the image is improved by the representation, and compression ratios of well over two-hundred are possible. Lateral interactions between V1 neurons sharpen their orientational tuning. We further study the dynamics of the processing, showing that the rate of decrease of the error of the reconstruction is maximized for the receptive fields used. Lastly, we employ a Fokker-Planck equation for a more detailed prediction of the error value vs. time. The Fokker-Planck equation for an underdamped system with a driving force is derived, yielding an energy-dependent diffusion coefficient which is the integral of the spectral densities of the force and the velocity of the system. The theory is applied to correlated noise activation and resonant activation. Simulation results for the error of the network vs time are compared to the solution of the Fokker-Planck equation.

CLFs-based optimization control for a class of constrained visual servoing systems.

PubMed

Song, Xiulan; Miaomiao, Fu

2017-03-01

In this paper, we use the control Lyapunov function (CLF) technique to present an optimized visual servo control method for constrained eye-in-hand robot visual servoing systems. With the knowledge of camera intrinsic parameters and depth of target changes, visual servo control laws (i.e. translation speed) with adjustable parameters are derived by image point features and some known CLF of the visual servoing system. The Fibonacci method is employed to online compute the optimal value of those adjustable parameters, which yields an optimized control law to satisfy constraints of the visual servoing system. The Lyapunov's theorem and the properties of CLF are used to establish stability of the constrained visual servoing system in the closed-loop with the optimized control law. One merit of the presented method is that there is no requirement of online calculating the pseudo-inverse of the image Jacobian's matrix and the homography matrix. Simulation and experimental results illustrated the effectiveness of the method proposed here. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Electromagnetic imaging with an arbitrarily oriented magnetic dipole

NASA Astrophysics Data System (ADS)

Guillemoteau, Julien; Sailhac, Pascal; Behaegel, Mickael

2013-04-01

We present the theoretical background for the geophysical EM analysis with arbitrarily oriented magnetic dipoles. The first application of such a development is that we would now be able to correct the data when they are not acquired in accordance to the actual interpretation methods. In order to illustrate this case, we study the case of airborne TEM measurements over an inclined ground. This context can be encountered if the measurements are made in mountain area. We show in particular that transient central loop helicopter borne magnetic data should be corrected by a factor proportional to the angle of the slope under the system. In addition, we studied the sensitivity function of a grounded multi-angle frequency domain system. Our development leads to a general Jacobian kernel that could be used for all the induction number and all the position/orientation of both transmitter and receiver in the air layer. Indeed, if one could design a system controlling the angles of Tx and Rx, the present development would allow to interpret such a data set and enhance the ground analysis, especially in order to constrain the 3D anisotropic inverse problem.

Gene Expression Data to Mouse Atlas Registration Using a Nonlinear Elasticity Smoother and Landmark Points Constraints

PubMed Central

Lin, Tungyou; Guyader, Carole Le; Dinov, Ivo; Thompson, Paul; Toga, Arthur; Vese, Luminita

2013-01-01

This paper proposes a numerical algorithm for image registration using energy minimization and nonlinear elasticity regularization. Application to the registration of gene expression data to a neuroanatomical mouse atlas in two dimensions is shown. We apply a nonlinear elasticity regularization to allow larger and smoother deformations, and further enforce optimality constraints on the landmark points distance for better feature matching. To overcome the difficulty of minimizing the nonlinear elasticity functional due to the nonlinearity in the derivatives of the displacement vector field, we introduce a matrix variable to approximate the Jacobian matrix and solve for the simplified Euler-Lagrange equations. By comparison with image registration using linear regularization, experimental results show that the proposed nonlinear elasticity model also needs fewer numerical corrections such as regridding steps for binary image registration, it renders better ground truth, and produces larger mutual information; most importantly, the landmark points distance and L2 dissimilarity measure between the gene expression data and corresponding mouse atlas are smaller compared with the registration model with biharmonic regularization. PMID:24273381

Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review

NASA Technical Reports Server (NTRS)

Kennedy, Christopher A.; Carpenter, Mark H.

2016-01-01

A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di erential equations (ODEs) is undertaken. The goal of this review is to summarize the characteristics, assess the potential, and then design several nearly optimal, general purpose, DIRK-type methods. Over 20 important aspects of DIRKtype methods are reviewed. A design study is then conducted on DIRK-type methods having from two to seven implicit stages. From this, 15 schemes are selected for general purpose application. Testing of the 15 chosen methods is done on three singular perturbation problems. Based on the review of method characteristics, these methods focus on having a stage order of two, sti accuracy, L-stability, high quality embedded and dense-output methods, small magnitudes of the algebraic stability matrix eigenvalues, small values of aii, and small or vanishing values of the internal stability function for large eigenvalues of the Jacobian. Among the 15 new methods, ESDIRK4(3)6L[2]SA is recommended as a good default method for solving sti problems at moderate error tolerances.

Modeling mantle convection in the spherical annulus

NASA Astrophysics Data System (ADS)

Hernlund, John W.; Tackley, Paul J.

2008-12-01

Most methods for modeling mantle convection in a two-dimensional (2D) circular annular domain suffer from innate shortcomings in their ability to capture several characteristics of the spherical shell geometry of planetary mantles. While methods such as rescaling the inner and outer radius to reduce anomalous effects in a 2D polar cylindrical coordinate system have been introduced and widely implemented, such fixes may have other drawbacks that adversely affect the outcome of some kinds of mantle convection studies. Here we propose a new approach that we term the "spherical annulus," which is a 2D slice that bisects the spherical shell and is quantitatively formulated at the equator of a spherical polar coordinate system after neglecting terms in the governing equations related to variations in latitude. Spherical scaling is retained in this approximation since the Jacobian function remains proportional to the square of the radius. We present example calculations to show that the behavior of convection in the spherical annulus compares favorably against calculations performed in other 2D annular domains when measured relative to those in a fully three-dimensional (3D) spherical shell.

A Second Order Semi-Discrete Cosserat Rod Model Suitable for Dynamic Simulations in Real Time

NASA Astrophysics Data System (ADS)

Lang, Holger; Linn, Joachim

2009-09-01

We present an alternative approach for a semi-discrete viscoelastic Cosserat rod model that allows both fast dynamic computations within milliseconds and accurate results compared to detailed finite element solutions. The model is able to represent extension, shearing, bending and torsion. For inner dissipation, a consistent damping potential from Antman is chosen. The continuous equations of motion, which consist a system of nonlinear hyperbolic partial differential algebraic equations, are derived from a two dimensional variational principle. The semi-discrete balance equations are obtained by spatial finite difference schemes on a staggered grid and standard index reduction techniques. The right-hand side of the model and its Jacobian can be chosen free of higher algebraic (e.g. root) or transcendent (e.g. trigonometric or exponential) functions and is therefore extremely cheap to evaluate numerically. For the time integration of the system, we use well established stiff solvers. As our model yields computational times within milliseconds, it is suitable for interactive manipulation. It reflects structural mechanics solutions sufficiently correct, as comparison with detailed finite element results shows.

A global approach for using kinematic redundancy to minimize base reactions of manipulators

NASA Technical Reports Server (NTRS)

Chung, C. L.; Desa, S.

1989-01-01

An important consideration in the use of manipulators in microgravity environments is the minimization of the base reactions, i.e. the magnitude of the force and the moment exerted by the manipulator on its base as it performs its tasks. One approach which was proposed and implemented is to use the redundant degree of freedom in a kinematically redundant manipulator to plan manipulator trajectories to minimize base reactions. A global approach was developed for minimizing the magnitude of the base reactions for kinematically redundant manipulators which integrates the Partitioned Jacobian method of redundancy resolution, a 4-3-4 joint-trajectory representation and the minimization of a cost function which is the time-integral of the magnitude of the base reactions. The global approach was also compared with a local approach developed earlier for the case of point-to-point motion of a three degree-of-freedom planar manipulator with one redundant degree-of-freedom. The results show that the global approach is more effective in reducing and smoothing the base force while the local approach is superior in reducing the base moment.

Performance of mixed formulations for the particle finite element method in soil mechanics problems

NASA Astrophysics Data System (ADS)

Monforte, Lluís; Carbonell, Josep Maria; Arroyo, Marcos; Gens, Antonio

2017-07-01

This paper presents a computational framework for the numerical analysis of fluid-saturated porous media at large strains. The proposal relies, on one hand, on the particle finite element method (PFEM), known for its capability to tackle large deformations and rapid changing boundaries, and, on the other hand, on constitutive descriptions well established in current geotechnical analyses (Darcy's law; Modified Cam Clay; Houlsby hyperelasticity). An important feature of this kind of problem is that incompressibility may arise either from undrained conditions or as a consequence of material behaviour; incompressibility may lead to volumetric locking of the low-order elements that are typically used in PFEM. In this work, two different three-field mixed formulations for the coupled hydromechanical problem are presented, in which either the effective pressure or the Jacobian are considered as nodal variables, in addition to the solid skeleton displacement and water pressure. Additionally, several mixed formulations are described for the simplified single-phase problem due to its formal similitude to the poromechanical case and its relevance in geotechnics, since it may approximate the saturated soil behaviour under undrained conditions. In order to use equal-order interpolants in displacements and scalar fields, stabilization techniques are used in the mass conservation equation of the biphasic medium and in the rest of scalar equations. Finally, all mixed formulations are assessed in some benchmark problems and their performances are compared. It is found that mixed formulations that have the Jacobian as a nodal variable perform better.

A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems

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

Hansen, Glen, E-mail: Glen.Hansen@inl.gov

2011-07-20

Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear fuel rod, which consists of cylindrical pellets of uranium dioxide (UO{sub 2}) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. Themore » accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces. The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.« less

A Jacobian-Free Newton Krylov Method for Mortar-Discretized Thermomechanical Contact Problems

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

Glen Hansen

2011-07-01

Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear reactor fuel rod, which consists of cylindrical pellets of uranium dioxide (UO2) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. Themore » accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces. The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.« less

Inverse consistent non-rigid image registration based on robust point set matching

PubMed Central

2014-01-01

Background Robust point matching (RPM) has been extensively used in non-rigid registration of images to robustly register two sets of image points. However, except for the location at control points, RPM cannot estimate the consistent correspondence between two images because RPM is a unidirectional image matching approach. Therefore, it is an important issue to make an improvement in image registration based on RPM. Methods In our work, a consistent image registration approach based on the point sets matching is proposed to incorporate the property of inverse consistency and improve registration accuracy. Instead of only estimating the forward transformation between the source point sets and the target point sets in state-of-the-art RPM algorithms, the forward and backward transformations between two point sets are estimated concurrently in our algorithm. The inverse consistency constraints are introduced to the cost function of RPM and the fuzzy correspondences between two point sets are estimated based on both the forward and backward transformations simultaneously. A modified consistent landmark thin-plate spline registration is discussed in detail to find the forward and backward transformations during the optimization of RPM. The similarity of image content is also incorporated into point matching in order to improve image matching. Results Synthetic data sets, medical images are employed to demonstrate and validate the performance of our approach. The inverse consistent errors of our algorithm are smaller than RPM. Especially, the topology of transformations is preserved well for our algorithm for the large deformation between point sets. Moreover, the distance errors of our algorithm are similar to that of RPM, and they maintain a downward trend as whole, which demonstrates the convergence of our algorithm. The registration errors for image registrations are evaluated also. Again, our algorithm achieves the lower registration errors in same iteration number. The determinant of the Jacobian matrix of the deformation field is used to analyse the smoothness of the forward and backward transformations. The forward and backward transformations estimated by our algorithm are smooth for small deformation. For registration of lung slices and individual brain slices, large or small determinant of the Jacobian matrix of the deformation fields are observed. Conclusions Results indicate the improvement of the proposed algorithm in bi-directional image registration and the decrease of the inverse consistent errors of the forward and the reverse transformations between two images. PMID:25559889

A Parallel Implicit Reconstructed Discontinuous Galerkin Method for Compressible Flows on Hybrid Grids

NASA Astrophysics Data System (ADS)

Xia, Yidong

The objective this work is to develop a parallel, implicit reconstructed discontinuous Galerkin (RDG) method using Taylor basis for the solution of the compressible Navier-Stokes equations on 3D hybrid grids. This third-order accurate RDG method is based on a hierarchical weighed essentially non- oscillatory reconstruction scheme, termed as HWENO(P1P 2) to indicate that a quadratic polynomial solution is obtained from the underlying linear polynomial DG solution via a hierarchical WENO reconstruction. The HWENO(P1P2) is designed not only to enhance the accuracy of the underlying DG(P1) method but also to ensure non-linear stability of the RDG method. In this reconstruction scheme, a quadratic polynomial (P2) solution is first reconstructed using a least-squares approach from the underlying linear (P1) discontinuous Galerkin solution. The final quadratic solution is then obtained using a Hermite WENO reconstruction, which is necessary to ensure the linear stability of the RDG method on 3D unstructured grids. The first derivatives of the quadratic polynomial solution are then reconstructed using a WENO reconstruction in order to eliminate spurious oscillations in the vicinity of strong discontinuities, thus ensuring the non-linear stability of the RDG method. The parallelization in the RDG method is based on a message passing interface (MPI) programming paradigm, where the METIS library is used for the partitioning of a mesh into subdomain meshes of approximately the same size. Both multi-stage explicit Runge-Kutta and simple implicit backward Euler methods are implemented for time advancement in the RDG method. In the implicit method, three approaches: analytical differentiation, divided differencing (DD), and automatic differentiation (AD) are developed and implemented to obtain the resulting flux Jacobian matrices. The automatic differentiation is a set of techniques based on the mechanical application of the chain rule to obtain derivatives of a function given as a computer program. By using an AD tool, the manpower can be significantly reduced for deriving the flux Jacobians, which can be quite complicated, tedious, and error-prone if done by hand or symbolic arithmetic software, depending on the complexity of the numerical flux scheme. In addition, the workload for code maintenance can also be largely reduced in case the underlying flux scheme is updated. The approximate system of linear equations arising from the Newton linearization is solved by the general minimum residual (GMRES) algorithm with lower-upper symmetric gauss-seidel (LUSGS) preconditioning. This GMRES+LU-SGS linear solver is the most robust and efficient for implicit time integration of the discretized Navier-Stokes equations when the AD-based flux Jacobians are provided other than the other two approaches. The developed HWENO(P1P2) method is used to compute a variety of well-documented compressible inviscid and viscous flow test cases on 3D hybrid grids, including some standard benchmark test cases such as the Sod shock tube, flow past a circular cylinder, and laminar flow past a at plate. The computed solutions are compared with either analytical solutions or experimental data, if available to assess the accuracy of the HWENO(P 1P2) method. Numerical results demonstrate that the HWENO(P 1P2) method is able to not only enhance the accuracy of the underlying HWENO(P1) method, but also ensure the linear and non-linear stability at the presence of strong discontinuities. An extensive study of grid convergence analysis on various types of elements: tetrahedron, prism, hexahedron, and hybrid prism/hexahedron, for a number of test cases indicates that the developed HWENO(P1P2) method is able to achieve the designed third-order accuracy of spatial convergence for smooth inviscid flows: one order higher than the underlying second-order DG(P1) method without significant increase in computing costs and storage requirements. The performance of the the developed GMRES+LU-SGS implicit method is compared with the multi-stage Runge-Kutta time stepping scheme for a number of test cases in terms of the timestep and CPU time. Numerical results indicate that the overall performance of the implicit method with AD-based Jacobians is order of magnitude better than the its explicit counterpart. Finally, a set of parallel scaling tests for both explicit and implicit methods is conducted on North Carolina State University's ARC cluster, demonstrating almost an ideal scalability of the RDG method. (Abstract shortened by UMI.)

Input-output-controlled nonlinear equation solvers

NASA Technical Reports Server (NTRS)

Padovan, Joseph

1988-01-01

To upgrade the efficiency and stability of the successive substitution (SS) and Newton-Raphson (NR) schemes, the concept of input-output-controlled solvers (IOCS) is introduced. By employing the formal properties of the constrained version of the SS and NR schemes, the IOCS algorithm can handle indefiniteness of the system Jacobian, can maintain iterate monotonicity, and provide for separate control of load incrementation and iterate excursions, as well as having other features. To illustrate the algorithmic properties, the results for several benchmark examples are presented. These define the associated numerical efficiency and stability of the IOCS.

A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1992-01-01

The present treatment of elliptic regions via hyperbolic flux-splitting and high order methods proposes a flux splitting in which the corresponding Jacobians have real and positive/negative eigenvalues. While resembling the flux splitting used in hyperbolic systems, the present generalization of such splitting to elliptic regions allows the handling of mixed-type systems in a unified and heuristically stable fashion. The van der Waals fluid-dynamics equation is used. Convergence with good resolution to weak solutions for various Riemann problems are observed.

Biomechanical stability analysis of the lambda-model controlling one joint.

PubMed

Lan, L; Zhu, K Y

2007-06-01

Computer modeling and control of the human motor system might be helpful for understanding the mechanism of human motor system and for the diagnosis and treatment of neuromuscular disorders. In this paper, a brief view of the equilibrium point hypothesis for human motor system modeling is given, and the lambda-model derived from this hypothesis is studied. The stability of the lambda-model based on equilibrium and Jacobian matrix is investigated. The results obtained in this paper suggest that the lambda-model is stable and has a unique equilibrium point under certain conditions.

Towards local estimation of emphysema progression using image registration

NASA Astrophysics Data System (ADS)

Staring, M.; Bakker, M. E.; Shamonin, D. P.; Stolk, J.; Reiber, J. H. C.; Stoel, B. C.

2009-02-01

Progression measurement of emphysema is required to evaluate the health condition of a patient and the effect of drugs. To locally estimate progression we use image registration, which allows for volume correction using the determinant of the Jacobian of the transformation. We introduce an adaptation of the so-called sponge model that circumvents its constant-mass assumption. Preliminary results from CT scans of a lung phantom and from CT data sets of three patients suggest that image registration may be a suitable method to locally estimate emphysema progression.

A coherent discrete variable representation method on a sphere

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

Yu, Hua -Gen

Here, the coherent discrete variable representation (ZDVR) has been extended for construct- ing a multidimensional potential-optimized DVR basis on a sphere. In order to deal with the non-constant Jacobian in spherical angles, two direct product primitive basis methods are proposed so that the original ZDVR technique can be properly implemented. The method has been demonstrated by computing the lowest states of a two dimensional (2D) vibrational model. Results show that the extended ZDVR method gives accurate eigenval- ues and exponential convergence with increasing ZDVR basis size.

A coherent discrete variable representation method on a sphere

DOE PAGES

Yu, Hua -Gen

2017-09-05

Here, the coherent discrete variable representation (ZDVR) has been extended for construct- ing a multidimensional potential-optimized DVR basis on a sphere. In order to deal with the non-constant Jacobian in spherical angles, two direct product primitive basis methods are proposed so that the original ZDVR technique can be properly implemented. The method has been demonstrated by computing the lowest states of a two dimensional (2D) vibrational model. Results show that the extended ZDVR method gives accurate eigenval- ues and exponential convergence with increasing ZDVR basis size.

Lunar Flight Study Series: Volume 6. A Study of Geometrical and Terminal Characteristics of Earth-Moon Transits Embedded in the Earth-Moon Plane

NASA Technical Reports Server (NTRS)

Lisle, B. J.

1963-01-01

This report represents the results of a study of coplanar earth-moon transits. The study was initiated to provide information concerning coplanar geometrical characteristics of earth-moon trnasits. The geometrical aspects of transit behavior are related to variations injection conditions. The model of the earth-moon system used in this investigation is the Jacobian model of the restricted three body problem. All transits considered in this study are restricted to the moon-earth plane (MEP).

An implicit flux-split algorithm to calculate hypersonic flowfields in chemical equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1987-01-01

An implicit, finite-difference, shock-capturing algorithm that calculates inviscid, hypersonic flows in chemical equilibrium is presented. The flux vectors and flux Jacobians are differenced using a first-order, flux-split technique. The equilibrium composition of the gas is determined by minimizing the Gibbs free energy at every node point. The code is validated by comparing results over an axisymmetric hemisphere against previously published results. The algorithm is also applied to more practical configurations. The accuracy, stability, and versatility of the algorithm have been promising.

Probing light nonthermal dark matter at the LHC

NASA Astrophysics Data System (ADS)

Dutta, Bhaskar; Gao, Yu; Kamon, Teruki

2014-05-01

This paper investigates the collider phenomenology of a minimal nonthermal dark matter model with a 1-GeV dark matter candidate, which naturally explains baryogenesis. Since the light dark matter is not parity protected, it can be singly produced at the LHC. This leads to large missing energy associated with an energetic jet whose transverse momentum distribution is featured by a Jacobian-like shape. The monojet, dijet, paired dijet, and two jets + missing energy channels are studied. Currently existing data at the Tevatron and LHC offer significant bounds on our model.

An iterative ensemble quasi-linear data assimilation approach for integrated reservoir monitoring

NASA Astrophysics Data System (ADS)

Li, J. Y.; Kitanidis, P. K.

2013-12-01

Reservoir forecasting and management are increasingly relying on an integrated reservoir monitoring approach, which involves data assimilation to calibrate the complex process of multi-phase flow and transport in the porous medium. The numbers of unknowns and measurements arising in such joint inversion problems are usually very large. The ensemble Kalman filter and other ensemble-based techniques are popular because they circumvent the computational barriers of computing Jacobian matrices and covariance matrices explicitly and allow nonlinear error propagation. These algorithms are very useful but their performance is not well understood and it is not clear how many realizations are needed for satisfactory results. In this presentation we introduce an iterative ensemble quasi-linear data assimilation approach for integrated reservoir monitoring. It is intended for problems for which the posterior or conditional probability density function is not too different from a Gaussian, despite nonlinearity in the state transition and observation equations. The algorithm generates realizations that have the potential to adequately represent the conditional probability density function (pdf). Theoretical analysis sheds light on the conditions under which this algorithm should work well and explains why some applications require very few realizations while others require many. This algorithm is compared with the classical ensemble Kalman filter (Evensen, 2003) and with Gu and Oliver's (2007) iterative ensemble Kalman filter on a synthetic problem of monitoring a reservoir using wellbore pressure and flux data.

On the Magnetic Squashing Factor and the Lie Transport of Tangents

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

Scott, Roger B.; Pontin, David I.; Hornig, Gunnar

The squashing factor (or squashing degree) of a vector field is a quantitative measure of the deformation of the field line mapping between two surfaces. In the context of solar magnetic fields, it is often used to identify gradients in the mapping of elementary magnetic flux tubes between various flux domains. Regions where these gradients in the mapping are large are referred to as quasi-separatrix layers (QSLs), and are a continuous extension of separators and separatrix surfaces. These QSLs are observed to be potential sites for the formation of strong electric currents, and are therefore important for the study ofmore » magnetic reconnection in three dimensions. Since the squashing factor, Q , is defined in terms of the Jacobian of the field line mapping, it is most often calculated by first determining the mapping between two surfaces (or some approximation of it) and then numerically differentiating. Tassev and Savcheva have introduced an alternative method, in which they parameterize the change in separation between adjacent field lines, and then integrate along individual field lines to get an estimate of the Jacobian without the need to numerically differentiate the mapping itself. But while their method offers certain computational advantages, it is formulated on a perturbative description of the field line trajectory, and the accuracy of this method is not entirely clear. Here we show, through an alternative derivation, that this integral formulation is, in principle, exact. We then demonstrate the result in the case of a linear, 3D magnetic null, which allows for an exact analytical description and direct comparison to numerical estimates.« less

The features of the Cosmic Web unveiled by the flip-flop field

NASA Astrophysics Data System (ADS)

Shandarin, Sergei F.; Medvedev, Mikhail V.

2017-07-01

Currently the dark matter environment is widely accepted as a framework for understanding of the observed structure in the universe. N-body simulations are indispensable for the analysis of the formation and evolution of the dark matter web. Two primary fields - density and velocity fields - are used in most of studies. Dark matter provides two additional fields that are unique for collisionless media only. They are the multistream field in Eulerian space and flip-flop field in Lagrangian space. The flip-flop field represents the number of sign reversals of an elementary volume of each collisionless fluid element. This field can be estimated by counting the sign reversals of the Jacobian at each particle at every time step of the simulation. The Jacobian is evaluated by numerical differentiation of the Lagrangian submanifold, I.e. the three-dimensional dark matter sheet in the six-dimensional space formed by three Lagrangian and three Eulerian coordinates. We present the results of the statistical study of the evolution of the flip-flop field from z = 50 to the present time z = 0. A number of statistical characteristics show that the pattern of the flip-flop field remains remarkably stable from z ≈ 30 to the present time. As a result the flip-flop field evaluated at z = 0 stores a wealth of information about the dynamical history of the dark matter web. In particular one of the most intriguing properties of the flip-flop is a unique capability to preserve the information about the merging history of haloes.

Validating and improving CT ventilation imaging by correlating with ventilation 4D-PET/CT using {sup 68}Ga-labeled nanoparticles

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

Kipritidis, John, E-mail: john.kipritidis@sydney.edu.au; Keall, Paul J.; Siva, Shankar

Purpose: CT ventilation imaging is a novel functional lung imaging modality based on deformable image registration. The authors present the first validation study of CT ventilation using positron emission tomography with{sup 68}Ga-labeled nanoparticles (PET-Galligas). The authors quantify this agreement for different CT ventilation metrics and PET reconstruction parameters. Methods: PET-Galligas ventilation scans were acquired for 12 lung cancer patients using a four-dimensional (4D) PET/CT scanner. CT ventilation images were then produced by applying B-spline deformable image registration between the respiratory correlated phases of the 4D-CT. The authors test four ventilation metrics, two existing and two modified. The two existing metricsmore » model mechanical ventilation (alveolar air-flow) based on Hounsfield unit (HU) change (V{sub HU}) or Jacobian determinant of deformation (V{sub Jac}). The two modified metrics incorporate a voxel-wise tissue-density scaling (ρV{sub HU} and ρV{sub Jac}) and were hypothesized to better model the physiological ventilation. In order to assess the impact of PET image quality, comparisons were performed using both standard and respiratory-gated PET images with the former exhibiting better signal. Different median filtering kernels (σ{sub m} = 0 or 3 mm) were also applied to all images. As in previous studies, similarity metrics included the Spearman correlation coefficient r within the segmented lung volumes, and Dice coefficient d{sub 20} for the (0 − 20)th functional percentile volumes. Results: The best agreement between CT and PET ventilation was obtained comparing standard PET images to the density-scaled HU metric (ρV{sub HU}) with σ{sub m} = 3 mm. This leads to correlation values in the ranges 0.22 ⩽ r ⩽ 0.76 and 0.38 ⩽ d{sub 20} ⩽ 0.68, with r{sup ¯}=0.42±0.16 and d{sup ¯}{sub 20}=0.52±0.09 averaged over the 12 patients. Compared to Jacobian-based metrics, HU-based metrics lead to statistically significant improvements in r{sup ¯} and d{sup ¯}{sub 20} (p < 0.05), with density scaled metrics also showing higher r{sup ¯} than for unscaled versions (p < 0.02). r{sup ¯} and d{sup ¯}{sub 20} were also sensitive to image quality, with statistically significant improvements using standard (as opposed to gated) PET images and with application of median filtering. Conclusions: The use of modified CT ventilation metrics, in conjunction with PET-Galligas and careful application of image filtering has resulted in improved correlation compared to earlier studies using nuclear medicine ventilation. However, CT ventilation and PET-Galligas do not always provide the same functional information. The authors have demonstrated that the agreement can improve for CT ventilation metrics incorporating a tissue density scaling, and also with increasing PET image quality. CT ventilation imaging has clear potential for imaging regional air volume change in the lung, and further development is warranted.« less

Adjoint Methods for Adjusting Three-Dimensional Atmosphere and Surface Properties to Fit Multi-Angle Multi-Pixel Polarimetric Measurements

NASA Technical Reports Server (NTRS)

Martin, William G.; Cairns, Brian; Bal, Guillaume

2014-01-01

This paper derives an efficient procedure for using the three-dimensional (3D) vector radiative transfer equation (VRTE) to adjust atmosphere and surface properties and improve their fit with multi-angle/multi-pixel radiometric and polarimetric measurements of scattered sunlight. The proposed adjoint method uses the 3D VRTE to compute the measurement misfit function and the adjoint 3D VRTE to compute its gradient with respect to all unknown parameters. In the remote sensing problems of interest, the scalar-valued misfit function quantifies agreement with data as a function of atmosphere and surface properties, and its gradient guides the search through this parameter space. Remote sensing of the atmosphere and surface in a three-dimensional region may require thousands of unknown parameters and millions of data points. Many approaches would require calls to the 3D VRTE solver in proportion to the number of unknown parameters or measurements. To avoid this issue of scale, we focus on computing the gradient of the misfit function as an alternative to the Jacobian of the measurement operator. The resulting adjoint method provides a way to adjust 3D atmosphere and surface properties with only two calls to the 3D VRTE solver for each spectral channel, regardless of the number of retrieval parameters, measurement view angles or pixels. This gives a procedure for adjusting atmosphere and surface parameters that will scale to the large problems of 3D remote sensing. For certain types of multi-angle/multi-pixel polarimetric measurements, this encourages the development of a new class of three-dimensional retrieval algorithms with more flexible parametrizations of spatial heterogeneity, less reliance on data screening procedures, and improved coverage in terms of the resolved physical processes in the Earth?s atmosphere.

Inexact adaptive Newton methods

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

Bertiger, W.I.; Kelsey, F.J.

1985-02-01

The Inexact Adaptive Newton method (IAN) is a modification of the Adaptive Implicit Method/sup 1/ (AIM) with improved Newton convergence. Both methods simplify the Jacobian at each time step by zeroing coefficients in regions where saturations are changing slowly. The methods differ in how the diagonal block terms are treated. On test problems with up to 3,000 cells, IAN consistently saves approximately 30% of the CPU time when compared to the fully implicit method. AIM shows similar savings on some problems, but takes as much CPU time as fully implicit on other test problems due to poor Newton convergence.

Telerobotic control of the seven-degree-of-freedom CESAR manipulator

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

Babcock, S.M.; Dubey, R.V.; Euler, J.A.

1988-01-01

The application of a computationally efficient kinematic control scheme for manipulators with redundant degrees of freedom to the unilateral telerobotic control of seven-degree-of-freedom manipulator (CESARM) at the Oak Ridge National Laboratory Center for Engineering Systems Advanced Research is presented. The kinematic control scheme uses a gradient projection optimization method, which eliminates that need to determine the generalized inverse of the Jacobian when solving for joint velocities, given Cartesian end-effector velocities. A six-degree-of-freedom (nonreplica) master controller is used. Performance indices for redundancy resolution are discussed. 5 ref., 6 figs.

Robust inverse kinematics using damped least squares with dynamic weighting

NASA Technical Reports Server (NTRS)

Schinstock, D. E.; Faddis, T. N.; Greenway, R. B.

1994-01-01

This paper presents a general method for calculating the inverse kinematics with singularity and joint limit robustness for both redundant and non-redundant serial-link manipulators. Damped least squares inverse of the Jacobian is used with dynamic weighting matrices in approximating the solution. This reduces specific joint differential vectors. The algorithm gives an exact solution away from the singularities and joint limits, and an approximate solution at or near the singularities and/or joint limits. The procedure is here implemented for a six d.o.f. teleoperator and a well behaved slave manipulator resulted under teleoperational control.

A Riemann solver for RANS

NASA Astrophysics Data System (ADS)

Chuvakhov, P. V.

2014-01-01

An exact expression for a system of both eigenvalues and right/left eigenvectors of a Jacobian matrix for a convective two-equation differential closure RANS operator split along a curvilinear coordinate is derived. It is shown by examples of numerical modeling of supersonic flows over a flat plate and a compression corner with separation that application of the exact system of eigenvalues and eigenvectors to the Roe approach for approximate solution of the Riemann problem gives rise to an increase in the convergence rate, better stability and higher accuracy of a steady-state solution in comparison with those in the case of an approximate system.

RMS massless arm dynamics capability in the SVDS. [equations of motion

NASA Technical Reports Server (NTRS)

Flanders, H. A.

1977-01-01

The equations of motion for the remote manipulator system, assuming that the masses and inertias of the arm can be neglected, are developed for implementation into the space vehicle dynamics simulation (SVDS) program for the Orbiter payload system. The arm flexibility is incorporated into the equations by the computation of flexibility terms for use in the joint servo model. The approach developed in this report is based on using the Jacobian transformation matrix to transform force and velocity terms between the configuration space and the task space to simplify the form of the equations.

Globally convergent techniques in nonlinear Newton-Krylov

NASA Technical Reports Server (NTRS)

Brown, Peter N.; Saad, Youcef

1989-01-01

Some convergence theory is presented for nonlinear Krylov subspace methods. The basic idea of these methods is to use variants of Newton's iteration in conjunction with a Krylov subspace method for solving the Jacobian linear systems. These methods are variants of inexact Newton methods where the approximate Newton direction is taken from a subspace of small dimensions. The main focus is to analyze these methods when they are combined with global strategies such as linesearch techniques and model trust region algorithms. Most of the convergence results are formulated for projection onto general subspaces rather than just Krylov subspaces.

Description of a computer program and numerical techniques for developing linear perturbation models from nonlinear systems simulations

NASA Technical Reports Server (NTRS)

Dieudonne, J. E.

1978-01-01

A numerical technique was developed which generates linear perturbation models from nonlinear aircraft vehicle simulations. The technique is very general and can be applied to simulations of any system that is described by nonlinear differential equations. The computer program used to generate these models is discussed, with emphasis placed on generation of the Jacobian matrices, calculation of the coefficients needed for solving the perturbation model, and generation of the solution of the linear differential equations. An example application of the technique to a nonlinear model of the NASA terminal configured vehicle is included.

Congruence Approximations for Entrophy Endowed Hyperbolic Systems

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Saini, Subhash (Technical Monitor)

1998-01-01

Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.

A diagonal implicit scheme for computing flows with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Eberhardt, Scott; Imlay, Scott

1990-01-01

A new algorithm for solving steady, finite-rate chemistry, flow problems is presented. The new scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The source Jacobian matrix is replaced by a diagonal matrix which is tailored to account for the fastest reactions in the chemical system. A point-implicit procedure is discussed and then the algorithm is included into the LU-SGS scheme. Solutions are presented for hypervelocity reentry and Hydrogen-Oxygen combustion. For the LU-SGS scheme a CFL number in excess of 10,000 has been achieved.

Comparison between a model-based and a conventional pyramid sensor reconstructor.

PubMed

Korkiakoski, Visa; Vérinaud, Christophe; Le Louarn, Miska; Conan, Rodolphe

2007-08-20

A model of a non-modulated pyramid wavefront sensor (P-WFS) based on Fourier optics has been presented. Linearizations of the model represented as Jacobian matrices are used to improve the P-WFS phase estimates. It has been shown in simulations that a linear approximation of the P-WFS is sufficient in closed-loop adaptive optics. Also a method to compute model-based synthetic P-WFS command matrices is shown, and its performance is compared to the conventional calibration. It was observed that in poor visibility the new calibration is better than the conventional.

Harmonic analysis of spacecraft power systems using a personal computer

NASA Technical Reports Server (NTRS)

Williamson, Frank; Sheble, Gerald B.

1989-01-01

The effects that nonlinear devices such as ac/dc converters, HVDC transmission links, and motor drives have on spacecraft power systems are discussed. The nonsinusoidal currents, along with the corresponding voltages, are calculated by a harmonic power flow which decouples and solves for each harmonic component individually using an iterative Newton-Raphson algorithm. The sparsity of the harmonic equations and the overall Jacobian matrix is used to an advantage in terms of saving computer memory space and in terms of reducing computation time. The algorithm could also be modified to analyze each harmonic separately instead of all at the same time.

A method for exponential propagation of large systems of stiff nonlinear differential equations

NASA Technical Reports Server (NTRS)

Friesner, Richard A.; Tuckerman, Laurette S.; Dornblaser, Bright C.; Russo, Thomas V.

1989-01-01

A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.

Bearing-only Cooperative Localization: Simulation and Experimental Results

DTIC Science & Technology

2013-01-01

matrix Fi and Bi are the system jacobian with respect to state Xi and control ui, which are given below Fi = I3 + Ts ∂fi ∂Xi |Xi=Xi(k) =  1 0 − ViTs ...sinψ(k)0 1 ViTs cosψ(k) 0 0 1  , (8) Bi = Ts ∂fi ∂ui |ui=ui(k) Ts cosψk 0Ts sinψk 0 0 Ts  , (9) and Qi(k) = ( σ2vi 0 0 σ2ωi ) , where σvi and σωi

The effect of satellite-derived surface soil moisture and leaf area index land data assimilation on streamflow simulations over France

NASA Astrophysics Data System (ADS)

Fairbairn, David; Lavinia Barbu, Alina; Napoly, Adrien; Albergel, Clément; Mahfouf, Jean-François; Calvet, Jean-Christophe

2017-04-01

This study evaluates the impact of assimilating surface soil moisture (SSM) and leaf area index (LAI) observations into a land surface model using the SAFRAN-ISBA-MODCOU (SIM) hydrological suite. SIM consists of three stages: (1) an atmospheric reanalysis (SAFRAN) over France, which forces (2) the three-layer ISBA land surface model, which then provides drainage and runoff inputs to (3) the MODCOU hydro-geological model. The drainage and runoff outputs from ISBA are validated by comparing the simulated river discharge from MODCOU with over 500 river-gauge observations over France and with a subset of stations with low-anthropogenic influence, over several years. This study makes use of the A-gs version of ISBA that allows for physiological processes. The atmospheric forcing for the ISBA-A-gs model underestimates direct shortwave and long-wave radiation by approximately 5 % averaged over France. The ISBA-A-gs model also substantially underestimates the grassland LAI compared with satellite retrievals during winter dormancy. These differences result in an underestimation (overestimation) of evapotranspiration (drainage and runoff). The excess runoff flowing into the rivers and aquifers contributes to an overestimation of the SIM river discharge. Two experiments attempted to resolve these problems: (i) a correction of the minimum LAI model parameter for grasslands and (ii) a bias-correction of the model radiative forcing. Two data assimilation experiments were also performed, which are designed to correct random errors in the initial conditions: (iii) the assimilation of LAI observations and (iv) the assimilation of SSM and LAI observations. The data assimilation for (iii) and (iv) was done with a simplified extended Kalman filter (SEKF), which uses finite differences in the observation operator Jacobians to relate the observations to the model variables. Experiments (i) and (ii) improved the median SIM Nash scores by about 9 % and 18 % respectively. Experiment (iii) reduced the LAI phase errors in ISBA-A-gs but had little impact on the discharge Nash efficiency of SIM. In contrast, experiment (iv) resulted in spurious increases in drainage and runoff, which degraded the median discharge Nash efficiency by about 7 %. The poor performance of the SEKF originates from the observation operator Jacobians. These Jacobians are dampened when the soil is saturated and when the vegetation is dormant, which leads to positive biases in drainage and/or runoff and to insufficient corrections during winter, respectively. Possible ways to improve the model are discussed, including a new multi-layer diffusion model and a more realistic response of photosynthesis to temperature in mountainous regions. The data assimilation should be advanced by accounting for model and forcing uncertainties.

Radiofrequency pulse design using nonlinear gradient magnetic fields.

PubMed

Kopanoglu, Emre; Constable, R Todd

2015-09-01

An iterative k-space trajectory and radiofrequency (RF) pulse design method is proposed for excitation using nonlinear gradient magnetic fields. The spatial encoding functions (SEFs) generated by nonlinear gradient fields are linearly dependent in Cartesian coordinates. Left uncorrected, this may lead to flip angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a matching pursuit algorithm, and the RF pulse is designed using a conjugate gradient algorithm. Three variants of the proposed approach are given: the full algorithm, a computationally cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments. The method is compared with other iterative (matching pursuit and conjugate gradient) and noniterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity. An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest. © 2014 Wiley Periodicals, Inc.

A contracting-interval program for the Danilewski method. Ph.D. Thesis - Va. Univ.

NASA Technical Reports Server (NTRS)

Harris, J. D.

1971-01-01

The concept of contracting-interval programs is applied to finding the eigenvalues of a matrix. The development is a three-step process in which (1) a program is developed for the reduction of a matrix to Hessenberg form, (2) a program is developed for the reduction of a Hessenberg matrix to colleague form, and (3) the characteristic polynomial with interval coefficients is readily obtained from the interval of colleague matrices. This interval polynomial is then factored into quadratic factors so that the eigenvalues may be obtained. To develop a contracting-interval program for factoring this polynomial with interval coefficients it is necessary to have an iteration method which converges even in the presence of controlled rounding errors. A theorem is stated giving sufficient conditions for the convergence of Newton's method when both the function and its Jacobian cannot be evaluated exactly but errors can be made proportional to the square of the norm of the difference between the previous two iterates. This theorem is applied to prove the convergence of the generalization of the Newton-Bairstow method that is used to obtain quadratic factors of the characteristic polynomial.

Optimizing Cubature for Efficient Integration of Subspace Deformations

PubMed Central

An, Steven S.; Kim, Theodore; James, Doug L.

2009-01-01

We propose an efficient scheme for evaluating nonlinear subspace forces (and Jacobians) associated with subspace deformations. The core problem we address is efficient integration of the subspace force density over the 3D spatial domain. Similar to Gaussian quadrature schemes that efficiently integrate functions that lie in particular polynomial subspaces, we propose cubature schemes (multi-dimensional quadrature) optimized for efficient integration of force densities associated with particular subspace deformations, particular materials, and particular geometric domains. We support generic subspace deformation kinematics, and nonlinear hyperelastic materials. For an r-dimensional deformation subspace with O(r) cubature points, our method is able to evaluate subspace forces at O(r2) cost. We also describe composite cubature rules for runtime error estimation. Results are provided for various subspace deformation models, several hyperelastic materials (St.Venant-Kirchhoff, Mooney-Rivlin, Arruda-Boyce), and multimodal (graphics, haptics, sound) applications. We show dramatically better efficiency than traditional Monte Carlo integration. CR Categories: I.6.8 [Simulation and Modeling]: Types of Simulation—Animation, I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Physically based modeling G.1.4 [Mathematics of Computing]: Numerical Analysis—Quadrature and Numerical Differentiation PMID:19956777

Neural Networks Technique for Filling Gaps in Satellite Measurements: Application to Ocean Color Observations.

PubMed

Krasnopolsky, Vladimir; Nadiga, Sudhir; Mehra, Avichal; Bayler, Eric; Behringer, David

2016-01-01

A neural network (NN) technique to fill gaps in satellite data is introduced, linking satellite-derived fields of interest with other satellites and in situ physical observations. Satellite-derived "ocean color" (OC) data are used in this study because OC variability is primarily driven by biological processes related and correlated in complex, nonlinear relationships with the physical processes of the upper ocean. Specifically, ocean color chlorophyll-a fields from NOAA's operational Visible Imaging Infrared Radiometer Suite (VIIRS) are used, as well as NOAA and NASA ocean surface and upper-ocean observations employed--signatures of upper-ocean dynamics. An NN transfer function is trained, using global data for two years (2012 and 2013), and tested on independent data for 2014. To reduce the impact of noise in the data and to calculate a stable NN Jacobian for sensitivity studies, an ensemble of NNs with different weights is constructed and compared with a single NN. The impact of the NN training period on the NN's generalization ability is evaluated. The NN technique provides an accurate and computationally cheap method for filling in gaps in satellite ocean color observation fields and time series.

Neural Networks Technique for Filling Gaps in Satellite Measurements: Application to Ocean Color Observations

PubMed Central

Nadiga, Sudhir; Mehra, Avichal; Bayler, Eric; Behringer, David

2016-01-01

A neural network (NN) technique to fill gaps in satellite data is introduced, linking satellite-derived fields of interest with other satellites and in situ physical observations. Satellite-derived “ocean color” (OC) data are used in this study because OC variability is primarily driven by biological processes related and correlated in complex, nonlinear relationships with the physical processes of the upper ocean. Specifically, ocean color chlorophyll-a fields from NOAA's operational Visible Imaging Infrared Radiometer Suite (VIIRS) are used, as well as NOAA and NASA ocean surface and upper-ocean observations employed—signatures of upper-ocean dynamics. An NN transfer function is trained, using global data for two years (2012 and 2013), and tested on independent data for 2014. To reduce the impact of noise in the data and to calculate a stable NN Jacobian for sensitivity studies, an ensemble of NNs with different weights is constructed and compared with a single NN. The impact of the NN training period on the NN's generalization ability is evaluated. The NN technique provides an accurate and computationally cheap method for filling in gaps in satellite ocean color observation fields and time series. PMID:26819586

Gradient-based model calibration with proxy-model assistance

NASA Astrophysics Data System (ADS)

Burrows, Wesley; Doherty, John

2016-02-01

Use of a proxy model in gradient-based calibration and uncertainty analysis of a complex groundwater model with large run times and problematic numerical behaviour is described. The methodology is general, and can be used with models of all types. The proxy model is based on a series of analytical functions that link all model outputs used in the calibration process to all parameters requiring estimation. In enforcing history-matching constraints during the calibration and post-calibration uncertainty analysis processes, the proxy model is run for the purposes of populating the Jacobian matrix, while the original model is run when testing parameter upgrades; the latter process is readily parallelized. Use of a proxy model in this fashion dramatically reduces the computational burden of complex model calibration and uncertainty analysis. At the same time, the effect of model numerical misbehaviour on calculation of local gradients is mitigated, this allowing access to the benefits of gradient-based analysis where lack of integrity in finite-difference derivatives calculation would otherwise have impeded such access. Construction of a proxy model, and its subsequent use in calibration of a complex model, and in analysing the uncertainties of predictions made by that model, is implemented in the PEST suite.

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

Zhong, H; Li, H; Gordon, J

Purpose: To investigate radiotherapy outcomes by incorporating 4DCT-based physiological and tumor elasticity functions for lung cancer patients. Methods: 4DCT images were acquired from 28 lung SBRT patients before radiation treatment. Deformable image registration (DIR) was performed from the end-inhale to the end-exhale using a B-Spline-based algorithm (Elastix, an open source software package). The resultant displacement vector fields (DVFs) were used to calculate a relative Jacobian function (RV) for each patient. The computed functions in the lung and tumor regions represent lung ventilation and tumor elasticity properties, respectively. The 28 patients were divided into two groups: 16 with two-year tumor localmore » control (LC) and 12 with local failure (LF). The ventilation and elasticity related RV functions were calculated for each of these patients. Results: The LF patients have larger RV values than the LC patients. The mean RV value in the lung region was 1.15 (±0.67) for the LF patients, higher than 1.06 (±0.59) for the LC patients. In the tumor region, the elasticity-related RV values are 1.2 (±0.97) and 0.86 (±0.64) for the LF and LC patients, respectively. Among the 16 LC patients, 3 have the mean RV values greater than 1.0 in the tumors. These tumors were located near the diaphragm, where the displacements are relatively large.. RV functions calculated in the tumor were better correlated with treatment outcomes than those calculated in the lung. Conclusion: The ventilation and elasticity-related RV functions in the lung and tumor regions were calculated from 4DCT image and the resultant values showed differences between the LC and LF patients. Further investigation of the impact of the displacements on the computed RV is warranted. Results suggest that the RV images might be useful for evaluation of treatment outcome for lung cancer patients.« less

Clinical Validation of 4-Dimensional Computed Tomography Ventilation With Pulmonary Function Test Data

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

Brennan, Douglas; Schubert, Leah; Diot, Quentin

Purpose: A new form of functional imaging has been proposed in the form of 4-dimensional computed tomography (4DCT) ventilation. Because 4DCTs are acquired as part of routine care for lung cancer patients, calculating ventilation maps from 4DCTs provides spatial lung function information without added dosimetric or monetary cost to the patient. Before 4DCT-ventilation is implemented it needs to be clinically validated. Pulmonary function tests (PFTs) provide a clinically established way of evaluating lung function. The purpose of our work was to perform a clinical validation by comparing 4DCT-ventilation metrics with PFT data. Methods and Materials: Ninety-eight lung cancer patients withmore » pretreatment 4DCT and PFT data were included in the study. Pulmonary function test metrics used to diagnose obstructive lung disease were recorded: forced expiratory volume in 1 second (FEV1) and FEV1/forced vital capacity. Four-dimensional CT data sets and spatial registration were used to compute 4DCT-ventilation images using a density change–based and a Jacobian-based model. The ventilation maps were reduced to single metrics intended to reflect the degree of ventilation obstruction. Specifically, we computed the coefficient of variation (SD/mean), ventilation V20 (volume of lung ≤20% ventilation), and correlated the ventilation metrics with PFT data. Regression analysis was used to determine whether 4DCT ventilation data could predict for normal versus abnormal lung function using PFT thresholds. Results: Correlation coefficients comparing 4DCT-ventilation with PFT data ranged from 0.63 to 0.72, with the best agreement between FEV1 and coefficient of variation. Four-dimensional CT ventilation metrics were able to significantly delineate between clinically normal versus abnormal PFT results. Conclusions: Validation of 4DCT ventilation with clinically relevant metrics is essential. We demonstrate good global agreement between PFTs and 4DCT-ventilation, indicating that 4DCT-ventilation provides a reliable assessment of lung function. Four-dimensional CT ventilation enables exciting opportunities to assess lung function and create functional avoidance radiation therapy plans. The present work provides supporting evidence for the integration of 4DCT-ventilation into clinical trials.« less

SU-C-BRA-03: An Automated and Quick Contour Errordetection for Auto Segmentation in Online Adaptive Radiotherapy

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

Zhang, J; Ates, O; Li, X

Purpose: To develop a tool that can quickly and automatically assess contour quality generated from auto segmentation during online adaptive replanning. Methods: Due to the strict time requirement of online replanning and lack of ‘ground truth’ contours in daily images, our method starts with assessing image registration accuracy focusing on the surface of the organ in question. Several metrics tightly related to registration accuracy including Jacobian maps, contours shell deformation, and voxel-based root mean square (RMS) analysis were computed. To identify correct contours, additional metrics and an adaptive decision tree are introduced. To approve in principle, tests were performed withmore » CT sets, planned and daily CTs acquired using a CT-on-rails during routine CT-guided RT delivery for 20 prostate cancer patients. The contours generated on daily CTs using an auto-segmentation tool (ADMIRE, Elekta, MIM) based on deformable image registration of the planning CT and daily CT were tested. Results: The deformed contours of 20 patients with total of 60 structures were manually checked as baselines. The incorrect rate of total contours is 49%. To evaluate the quality of local deformation, the Jacobian determinant (1.047±0.045) on contours has been analyzed. In an analysis of rectum contour shell deformed, the higher rate (0.41) of error contours detection was obtained compared to 0.32 with manual check. All automated detections took less than 5 seconds. Conclusion: The proposed method can effectively detect contour errors in micro and macro scope by evaluating multiple deformable registration metrics in a parallel computing process. Future work will focus on improving practicability and optimizing calculation algorithms and metric selection.« less

3-D Inhomogeous Radiative Transfer Model using a Planar-stratified Forward RT Model and Horizontal Perturbation Series

NASA Astrophysics Data System (ADS)

Zhang, K.; Gasiewski, A. J.

2017-12-01

A horizontally inhomogeneous unified microwave radiative transfer (HI-UMRT) model based upon a nonspherical hydrometeor scattering model is being developed at the University of Colorado at Boulder to facilitate forward radiative simulations for 3-dimensionally inhomogeneous clouds in severe weather. The HI-UMRT 3-D analytical solution is based on incorporating a planar-stratified 1-D UMRT algorithm within a horizontally inhomogeneous iterative perturbation scheme. Single-scattering parameters are computed using the Discrete Dipole Scattering (DDSCAT v7.3) program for hundreds of carefully selected nonspherical complex frozen hydrometeors from the NASA/GSFC DDSCAT database. The required analytic factorization symmetry of transition matrix in a normalized RT equation was analytically proved and validated numerically using the DDSCAT-based full Stokes matrix of randomly oriented hydrometeors. The HI-UMRT model thus inherits the properties of unconditional numerical stability, efficiency, and accuracy from the UMRT algorithm and provides a practical 3-D two-Stokes parameter radiance solution with Jacobian to be used within microwave retrievals and data assimilation schemes. In addition, a fast forward radar reflectivity operator with Jacobian based on DDSCAT backscatter efficiency computed for large hydrometeors is incorporated into the HI-UMRT model to provide applicability to active radar sensors. The HI-UMRT will be validated strategically at two levels: 1) intercomparison of brightness temperature (Tb) results with those of several 1-D and 3-D RT models, including UMRT, CRTM and Monte Carlo models, 2) intercomparison of Tb with observed data from combined passive and active spaceborne sensors (e.g. GPM GMI and DPR). The precise expression for determining the required number of 3-D iterations to achieve an error bound on the perturbation solution will be developed to facilitate the numerical verification of the HI-UMRT code complexity and computation performance.

Laterally constrained inversion for CSAMT data interpretation

NASA Astrophysics Data System (ADS)

Wang, Ruo; Yin, Changchun; Wang, Miaoyue; Di, Qingyun

2015-10-01

Laterally constrained inversion (LCI) has been successfully applied to the inversion of dc resistivity, TEM and airborne EM data. However, it hasn't been yet applied to the interpretation of controlled-source audio-frequency magnetotelluric (CSAMT) data. In this paper, we apply the LCI method for CSAMT data inversion by preconditioning the Jacobian matrix. We apply a weighting matrix to Jacobian to balance the sensitivity of model parameters, so that the resolution with respect to different model parameters becomes more uniform. Numerical experiments confirm that this can improve the convergence of the inversion. We first invert a synthetic dataset with and without noise to investigate the effect of LCI applications to CSAMT data, for the noise free data, the results show that the LCI method can recover the true model better compared to the traditional single-station inversion; and for the noisy data, the true model is recovered even with a noise level of 8%, indicating that LCI inversions are to some extent noise insensitive. Then, we re-invert two CSAMT datasets collected respectively in a watershed and a coal mine area in Northern China and compare our results with those from previous inversions. The comparison with the previous inversion in a coal mine shows that LCI method delivers smoother layer interfaces that well correlate to seismic data, while comparison with a global searching algorithm of simulated annealing (SA) in a watershed shows that though both methods deliver very similar good results, however, LCI algorithm presented in this paper runs much faster. The inversion results for the coal mine CSAMT survey show that a conductive water-bearing zone that was not revealed by the previous inversions has been identified by the LCI. This further demonstrates that the method presented in this paper works for CSAMT data inversion.

Sensitivity analysis of eigenvalues for an electro-hydraulic servomechanism

NASA Astrophysics Data System (ADS)

Stoia-Djeska, M.; Safta, C. A.; Halanay, A.; Petrescu, C.

2012-11-01

Electro-hydraulic servomechanisms (EHSM) are important components of flight control systems and their role is to control the movement of the flying control surfaces in response to the movement of the cockpit controls. As flight-control systems, the EHSMs have a fast dynamic response, a high power to inertia ratio and high control accuracy. The paper is devoted to the study of the sensitivity for an electro-hydraulic servomechanism used for an aircraft aileron action. The mathematical model of the EHSM used in this paper includes a large number of parameters whose actual values may vary within some ranges of uncertainty. It consists in a nonlinear ordinary differential equation system composed by the mass and energy conservation equations, the actuator movement equations and the controller equation. In this work the focus is on the sensitivities of the eigenvalues of the linearized homogeneous system, which are the partial derivatives of the eigenvalues of the state-space system with respect the parameters. These are obtained using a modal approach based on the eigenvectors of the state-space direct and adjoint systems. To calculate the eigenvalues and their sensitivity the system's Jacobian and its partial derivatives with respect the parameters are determined. The calculation of the derivative of the Jacobian matrix with respect to the parameters is not a simple task and for many situations it must be done numerically. The system stability is studied in relation with three parameters: m, the equivalent inertial load of primary control surface reduced to the actuator rod; B, the bulk modulus of oil and p a pressure supply proportionality coefficient. All the sensitivities calculated in this work are in good agreement with those obtained through recalculations.

Analysis of coined quantum walks with renormalization

NASA Astrophysics Data System (ADS)

Boettcher, Stefan; Li, Shanshan

2018-01-01

We introduce a framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights into the analytic structure as well as generic results about the long-time behavior can be extracted. The RG flow for such a walk on a dual Sierpinski gasket and a Migdal-Kadanoff hierarchical network is obtained explicitly from elementary algebraic manipulations, after transforming the unitary evolution equation into Laplace space. Unlike for classical random walks, we find that the long-time asymptotics for the quantum walk requires consideration of a diverging number of Laplace poles, which we demonstrate exactly for the closed-form solution available for the walk on a one-dimensional loop. In particular, we calculate the probability of the walk to overlap with its starting position, which oscillates with a period that scales as NdwQ/df with system size N . While the largest Jacobian eigenvalue λ1 of the RG flow merely reproduces the fractal dimension, df=log2λ1 , the asymptotic analysis shows that the second Jacobian eigenvalue λ2 becomes essential to determine the dimension of the quantum walk via dwQ=log2√{λ1λ2 } . We trace this fact to delicate cancellations caused by unitarity. We obtain identical relations for other networks, although the details of the RG analysis may exhibit surprisingly distinct features. Thus, our conclusions—which trivially reproduce those for regular lattices with translational invariance with df=d and dwQ=1 —appear to be quite general and likely apply to networks beyond those studied here.

Feedforward-Feedback Hybrid Control for Magnetic Shape Memory Alloy Actuators Based on the Krasnosel'skii-Pokrovskii Model

PubMed Central

Zhou, Miaolei; Zhang, Qi; Wang, Jingyuan

2014-01-01

As a new type of smart material, magnetic shape memory alloy has the advantages of a fast response frequency and outstanding strain capability in the field of microdrive and microposition actuators. The hysteresis nonlinearity in magnetic shape memory alloy actuators, however, limits system performance and further application. Here we propose a feedforward-feedback hybrid control method to improve control precision and mitigate the effects of the hysteresis nonlinearity of magnetic shape memory alloy actuators. First, hysteresis nonlinearity compensation for the magnetic shape memory alloy actuator is implemented by establishing a feedforward controller which is an inverse hysteresis model based on Krasnosel'skii-Pokrovskii operator. Secondly, the paper employs the classical Proportion Integration Differentiation feedback control with feedforward control to comprise the hybrid control system, and for further enhancing the adaptive performance of the system and improving the control accuracy, the Radial Basis Function neural network self-tuning Proportion Integration Differentiation feedback control replaces the classical Proportion Integration Differentiation feedback control. Utilizing self-learning ability of the Radial Basis Function neural network obtains Jacobian information of magnetic shape memory alloy actuator for the on-line adjustment of parameters in Proportion Integration Differentiation controller. Finally, simulation results show that the hybrid control method proposed in this paper can greatly improve the control precision of magnetic shape memory alloy actuator and the maximum tracking error is reduced from 1.1% in the open-loop system to 0.43% in the hybrid control system. PMID:24828010

Feedforward-feedback hybrid control for magnetic shape memory alloy actuators based on the Krasnosel'skii-Pokrovskii model.

PubMed

Zhou, Miaolei; Zhang, Qi; Wang, Jingyuan

2014-01-01

As a new type of smart material, magnetic shape memory alloy has the advantages of a fast response frequency and outstanding strain capability in the field of microdrive and microposition actuators. The hysteresis nonlinearity in magnetic shape memory alloy actuators, however, limits system performance and further application. Here we propose a feedforward-feedback hybrid control method to improve control precision and mitigate the effects of the hysteresis nonlinearity of magnetic shape memory alloy actuators. First, hysteresis nonlinearity compensation for the magnetic shape memory alloy actuator is implemented by establishing a feedforward controller which is an inverse hysteresis model based on Krasnosel'skii-Pokrovskii operator. Secondly, the paper employs the classical Proportion Integration Differentiation feedback control with feedforward control to comprise the hybrid control system, and for further enhancing the adaptive performance of the system and improving the control accuracy, the Radial Basis Function neural network self-tuning Proportion Integration Differentiation feedback control replaces the classical Proportion Integration Differentiation feedback control. Utilizing self-learning ability of the Radial Basis Function neural network obtains Jacobian information of magnetic shape memory alloy actuator for the on-line adjustment of parameters in Proportion Integration Differentiation controller. Finally, simulation results show that the hybrid control method proposed in this paper can greatly improve the control precision of magnetic shape memory alloy actuator and the maximum tracking error is reduced from 1.1% in the open-loop system to 0.43% in the hybrid control system.

SU-E-J-86: Functional Conformal Planning for Stereotactic Body Radiation Therapy with CT-Pulmonary Ventilation Imaging

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

Kurosawa, T; Moriya, S; Sato, M

2015-06-15

Purpose: To evaluate the functional planning using CT-pulmonary ventilation imaging for conformal SBRT. Methods: The CT-pulmonary ventilation image was generated using the Jacobian metric in the in-house program with the NiftyReg software package. Using the ventilation image, the normal lung was split into three lung regions for functionality (high, moderate and low). The anatomical plan (AP) and functional plan (FP) were made for ten lung SBRT patients. For the AP, the beam angles were optimized with the dose-volume constraints for the normal lung sparing and the PTV coverage. For the FP, the gantry angles were also optimized with the additionalmore » constraint for high functional lung. The MLC aperture shapes were adjusted to the PTV with the additional 5 mm margin. The dosimetric parameters for PTV, the functional volumes, spinal cord and so on were compared in both plans. Results: Compared to the AP, the FP showed better dose sparing for high- and moderate-functional lungs with similar PTV coverage while not taking care of the low functional lung (High:−12.9±9.26% Moderate: −2.0±7.09%, Low: +4.1±12.2%). For the other normal organs, the FP and AP showed similar dose sparing in the eight patients. However, the FP showed that the maximum doses for spinal cord were increased with the significant increment of 16.4Gy and 21.0Gy in other two patients, respectively. Because the beam direction optimizer chose the unexpected directions passing through the spinal cord. Conclusion: Even the functional conformal SBRT can selectively reduce high- and moderatefunctional lung while keeping the PTV coverage. However, it would be careful that the optimizer would choose unexpected beam angles and the dose sparing for the other normal organs can be worse. Therefore, the planner needs to control the dose-volume constraints and also limit the beam angles in order to achieve the expected dose sparing and coverage.« less

A computer model for one-dimensional mass and energy transport in and around chemically reacting particles, including complex gas-phase chemistry, multicomponent molecular diffusion, surface evaporation, and heterogeneous reaction

NASA Technical Reports Server (NTRS)

Cho, S. Y.; Yetter, R. A.; Dryer, F. L.

1992-01-01

Various chemically reacting flow problems highlighting chemical and physical fundamentals rather than flow geometry are presently investigated by means of a comprehensive mathematical model that incorporates multicomponent molecular diffusion, complex chemistry, and heterogeneous processes, in the interest of obtaining sensitivity-related information. The sensitivity equations were decoupled from those of the model, and then integrated one time-step behind the integration of the model equations, and analytical Jacobian matrices were applied to improve the accuracy of sensitivity coefficients that are calculated together with model solutions.

Two Dimensional Finite Element Based Magnetotelluric Inversion using Singular Value Decomposition Method on Transverse Electric Mode

NASA Astrophysics Data System (ADS)

Tjong, Tiffany; Yihaa’ Roodhiyah, Lisa; Nurhasan; Sutarno, Doddy

2018-04-01

In this work, an inversion scheme was performed using a vector finite element (VFE) based 2-D magnetotelluric (MT) forward modelling. We use an inversion scheme with Singular value decomposition (SVD) method toimprove the accuracy of MT inversion.The inversion scheme was applied to transverse electric (TE) mode of MT. SVD method was used in this inversion to decompose the Jacobian matrices. Singular values which obtained from the decomposition process were analyzed. This enabled us to determine the importance of data and therefore to define a threshold for truncation process. The truncation of singular value in inversion processcould improve the resulted model.

Aerothermodynamic shape optimization of hypersonic blunt bodies

NASA Astrophysics Data System (ADS)

Eyi, Sinan; Yumuşak, Mine

2015-07-01

The aim of this study is to develop a reliable and efficient design tool that can be used in hypersonic flows. The flow analysis is based on the axisymmetric Euler/Navier-Stokes and finite-rate chemical reaction equations. The equations are coupled simultaneously and solved implicitly using Newton's method. The Jacobian matrix is evaluated analytically. A gradient-based numerical optimization is used. The adjoint method is utilized for sensitivity calculations. The objective of the design is to generate a hypersonic blunt geometry that produces the minimum drag with low aerodynamic heating. Bezier curves are used for geometry parameterization. The performances of the design optimization method are demonstrated for different hypersonic flow conditions.

Proceedings of the International Conference on Stiff Computation, April 12-14, 1982, Park City, Utah. Volume III.

DTIC Science & Technology

1982-01-01

The symbolic generation of the Jacobian fy would then be Scomparatively trivial, if a full mode updating scheme were applied (where each entry of f... scheme in LARKIN are on one - hand rather concise and on the other hand general enough to -n permit the use of any of the presently ava2.lable sparse sol...sufficiently small, I W(z)-a(z)I< ch In (X-X )I with u=xh. When X i o, W(s (u)) is the diagonal Padd approximation tsf1 8e he general first-order (Wl1 : first

Real-time photo-magnetic imaging.

PubMed

Nouizi, Farouk; Erkol, Hakan; Luk, Alex; Unlu, Mehmet B; Gulsen, Gultekin

2016-10-01

We previously introduced a new high resolution diffuse optical imaging modality termed, photo-magnetic imaging (PMI). PMI irradiates the object under investigation with near-infrared light and monitors the variations of temperature using magnetic resonance thermometry (MRT). In this paper, we present a real-time PMI image reconstruction algorithm that uses analytic methods to solve the forward problem and assemble the Jacobian matrix much faster. The new algorithm is validated using real MRT measured temperature maps. In fact, it accelerates the reconstruction process by more than 250 times compared to a single iteration of the FEM-based algorithm, which opens the possibility for the real-time PMI.

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

Jones, J E; Vassilevski, P S; Woodward, C S

This paper provides extensions of an element agglomeration AMG method to nonlinear elliptic problems discretized by the finite element method on general unstructured meshes. The method constructs coarse discretization spaces and corresponding coarse nonlinear operators as well as their Jacobians. We introduce both standard (fairly quasi-uniformly coarsened) and non-standard (coarsened away) coarse meshes and respective finite element spaces. We use both kind of spaces in FAS type coarse subspace correction (or Schwarz) algorithms. Their performance is illustrated on a number of model problems. The coarsened away spaces seem to perform better than the standard spaces for problems with nonlinearities inmore » the principal part of the elliptic operator.« less

Accurate quantification of fluorescent targets within turbid media based on a decoupled fluorescence Monte Carlo model.

PubMed

Deng, Yong; Luo, Zhaoyang; Jiang, Xu; Xie, Wenhao; Luo, Qingming

2015-07-01

We propose a method based on a decoupled fluorescence Monte Carlo model for constructing fluorescence Jacobians to enable accurate quantification of fluorescence targets within turbid media. The effectiveness of the proposed method is validated using two cylindrical phantoms enclosing fluorescent targets within homogeneous and heterogeneous background media. The results demonstrate that our method can recover relative concentrations of the fluorescent targets with higher accuracy than the perturbation fluorescence Monte Carlo method. This suggests that our method is suitable for quantitative fluorescence diffuse optical tomography, especially for in vivo imaging of fluorophore targets for diagnosis of different diseases and abnormalities.

Coupling Schemes for Multiphysics Reactor Simulation

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

Vijay Mahadeven; Jean Ragusa

2007-11-01

This report documents the progress of the student Vijay S. Mahadevan from the Nuclear Engineering Department of Texas A&M University over the summer of 2007 during his visit to the INL. The purpose of his visit was to investigate the physics-based preconditioned Jacobian-free Newton-Krylov method applied to physics relevant to nuclear reactor simulation. To this end he studied two test problems that represented reaction-diffusion and advection-reaction. These two test problems will provide the basis for future work in which neutron diffusion, nonlinear heat conduction, and a twophase flow model will be tightly coupled to provide an accurate model of amore » BWR core.« less

Nonlinear Transient Problems Using Structure Compatible Heat Transfer Code

NASA Technical Reports Server (NTRS)

Hou, Gene

2000-01-01

The report documents the recent effort to enhance a transient linear heat transfer code so as to solve nonlinear problems. The linear heat transfer code was originally developed by Dr. Kim Bey of NASA Largely and called the Structure-Compatible Heat Transfer (SCHT) code. The report includes four parts. The first part outlines the formulation of the heat transfer problem of concern. The second and the third parts give detailed procedures to construct the nonlinear finite element equations and the required Jacobian matrices for the nonlinear iterative method, Newton-Raphson method. The final part summarizes the results of the numerical experiments on the newly enhanced SCHT code.

Manipulator control by exact linearization

NASA Technical Reports Server (NTRS)

Kruetz, K.

1987-01-01

Comments on the application to rigid link manipulators of geometric control theory, resolved acceleration control, operational space control, and nonlinear decoupling theory are given, and the essential unity of these techniques for externally linearizing and decoupling end effector dynamics is discussed. Exploiting the fact that the mass matrix of a rigid link manipulator is positive definite, a consequence of rigid link manipulators belonging to the class of natural physical systems, it is shown that a necessary and sufficient condition for a locally externally linearizing and output decoupling feedback law to exist is that the end effector Jacobian matrix be nonsingular. Furthermore, this linearizing feedback is easy to produce.

Maximally Informative Statistics for Localization and Mapping

NASA Technical Reports Server (NTRS)

Deans, Matthew C.

2001-01-01

This paper presents an algorithm for localization and mapping for a mobile robot using monocular vision and odometry as its means of sensing. The approach uses the Variable State Dimension filtering (VSDF) framework to combine aspects of Extended Kalman filtering and nonlinear batch optimization. This paper describes two primary improvements to the VSDF. The first is to use an interpolation scheme based on Gaussian quadrature to linearize measurements rather than relying on analytic Jacobians. The second is to replace the inverse covariance matrix in the VSDF with its Cholesky factor to improve the computational complexity. Results of applying the filter to the problem of localization and mapping with omnidirectional vision are presented.

Simple and Efficient Numerical Evaluation of Near-Hypersingular Integrals

NASA Technical Reports Server (NTRS)

Fink, Patrick W.; Wilton, Donald R.; Khayat, Michael A.

2007-01-01

Recently, significant progress has been made in the handling of singular and nearly-singular potential integrals that commonly arise in the Boundary Element Method (BEM). To facilitate object-oriented programming and handling of higher order basis functions, cancellation techniques are favored over techniques involving singularity subtraction. However, gradients of the Newton-type potentials, which produce hypersingular kernels, are also frequently required in BEM formulations. As is the case with the potentials, treatment of the near-hypersingular integrals has proven more challenging than treating the limiting case in which the observation point approaches the surface. Historically, numerical evaluation of these near-hypersingularities has often involved a two-step procedure: a singularity subtraction to reduce the order of the singularity, followed by a boundary contour integral evaluation of the extracted part. Since this evaluation necessarily links basis function, Green s function, and the integration domain (element shape), the approach ill fits object-oriented programming concepts. Thus, there is a need for cancellation-type techniques for efficient numerical evaluation of the gradient of the potential. Progress in the development of efficient cancellation-type procedures for the gradient potentials was recently presented. To the extent possible, a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. However, since the gradient kernel involves singularities of different orders, we also require that the transformation leaves remaining terms that are analytic. The terms "normal" and "tangential" are used herein with reference to the source element. Also, since computational formulations often involve the numerical evaluation of both potentials and their gradients, it is highly desirable that a single integration procedure efficiently handles both.

Implicit Formulation of Muscle Dynamics in OpenSim

NASA Technical Reports Server (NTRS)

Humphreys, Brad; Dembia, Chris; Lewandowski, Beth; Van Den Bogert, Antonie

2017-01-01

Astronauts lose bone and muscle mass during spaceflight. Exercise countermeasure is the primary method for counteracting bone and muscle mass loss in space. New spacecraft exercise device concepts are currently being developed for the NASAs new crew exploration vehicle. The NASA Digital Astronaut Project (DAP) uses computational modeling to help determine if the new exercise devices will be effective as countermeasures. The NASA Digital Astronaut Project is developing the ability to utilize predictive simulation to provide insight into the change in kinematics and kinetics with a change in device and gravitational environment (1-g versus 0-g). For example, in space exercise the subject's body weight is applied in addition to the loads prescribed for musculoskeletal maintenance. How and where these loads are applied obviously directly impacts bone and tissue loads. Additionally, due to space vehicle structural requirements, exercise devices are often placed on vibration isolation systems. This changes the apparent impedance or stiffness of the device as seen by the user. Data collection under these conditions is often impractical and limited. Predictive modeling provides a means to have a virtual subject to test hypotheses. Predictive simulation provides a virtual subject for which we are able to perform studies such as sensitivity to device loading and vibration isolation without the need for laboratory kinematic or kinetic test data.Direct Collocation optimization provides an efficient means to perform task based optimization and predictive modeling. It is relatively straight forward to structure a physical exercise task in a Direct Collocation mathematical formulation: perform a motion such that you start at an initial pose, achieve a given amount of deflection i.e a squat, return to the initial pose, and minimize muscle activation cost. Direct Collocation is advantageous in that it does not require numerical integration to evaluate the objective function. Instead, the system dynamics are transformed to discrete time and the optimizer is constrained such that the solution is not considered to be a valid unless the dynamic equations are satisfied at all time points. The simulation and optimization are effectively done simultaneously. Due to the implicit integration, time steps can be more coarse than in a differential equation solver. In a gait scenario this means that that the model constraints and cost function are evaluated at 100 nodes in the gait cycle versus 10,000 integration steps in a variable-step forward dynamic simulation. Furthermore, no time is wasted on accurate simulations of movements that are far from the optimum. Constrained optimization algorithms require a Jacobian matrix that contains the partial derivatives of each of the dynamic constraints with respect to of each of the state and control variables at all time points. This is a large but sparse matrix. An implicit dynamics formulation requires computation of the dynamic residuals f as a function of the states x and their derivatives, and controls u:f(x, dxdt, u) 0If the dynamics of musculoskeletal system are formulated implicitly, the Jacobian elements are often available analytically, eliminating the need for numerical differentiation; this is obviously computationally advantageous. Additionally, implicit formulation of musculoskeletal dynamics do not suffer from singularities from low mass bodies, zero muscle activation, or other stiff system or

RF Pulse Design using Nonlinear Gradient Magnetic Fields

PubMed Central

Kopanoglu, Emre; Constable, R. Todd

2014-01-01

Purpose An iterative k-space trajectory and radio-frequency (RF) pulse design method is proposed for Excitation using Nonlinear Gradient Magnetic fields (ENiGMa). Theory and Methods The spatial encoding functions (SEFs) generated by nonlinear gradient fields (NLGFs) are linearly dependent in Cartesian-coordinates. Left uncorrected, this may lead to flip-angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a Matching-Pursuit algorithm, and the RF pulse is designed using a Conjugate-Gradient algorithm. Three variants of the proposed approach are given: the full-algorithm, a computationally-cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments. Results The method is compared to other iterative (Matching-Pursuit and Conjugate Gradient) and non-iterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity significantly. Conclusion An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest. PMID:25203286

Astrochem: Abundances of chemical species in the interstellar medium

NASA Astrophysics Data System (ADS)

Maret, Sébastien; Bergin, Edwin A.

2015-07-01

Astrochem computes the abundances of chemical species in the interstellar medium, as function of time. It studies the chemistry in a variety of astronomical objects, including diffuse clouds, dense clouds, photodissociation regions, prestellar cores, protostars, and protostellar disks. Astrochem reads a network of chemical reactions from a text file, builds up a system of kinetic rates equations, and solves it using a state-of-the-art stiff ordinary differential equation (ODE) solver. The Jacobian matrix of the system is computed implicitly, so the resolution of the system is extremely fast: large networks containing several thousands of reactions are usually solved in a few seconds. A variety of gas phase process are considered, as well as simple gas-grain interactions, such as the freeze-out and the desorption via several mechanisms (thermal desorption, cosmic-ray desorption and photo-desorption). The computed abundances are written in a HDF5 file, and can be plotted in different ways with the tools provided with Astrochem. Chemical reactions and their rates are written in a format which is meant to be easy to read and to edit. A tool to convert the chemical networks from the OSU and KIDA databases into this format is also provided. Astrochem is written in C, and its source code is distributed under the terms of the GNU General Public License (GPL).

Limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method for the parameter estimation on geographically weighted ordinal logistic regression model (GWOLR)

NASA Astrophysics Data System (ADS)

Saputro, Dewi Retno Sari; Widyaningsih, Purnami

2017-08-01

In general, the parameter estimation of GWOLR model uses maximum likelihood method, but it constructs a system of nonlinear equations, making it difficult to find the solution. Therefore, an approximate solution is needed. There are two popular numerical methods: the methods of Newton and Quasi-Newton (QN). Newton's method requires large-scale time in executing the computation program since it contains Jacobian matrix (derivative). QN method overcomes the drawback of Newton's method by substituting derivative computation into a function of direct computation. The QN method uses Hessian matrix approach which contains Davidon-Fletcher-Powell (DFP) formula. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is categorized as the QN method which has the DFP formula attribute of having positive definite Hessian matrix. The BFGS method requires large memory in executing the program so another algorithm to decrease memory usage is needed, namely Low Memory BFGS (LBFGS). The purpose of this research is to compute the efficiency of the LBFGS method in the iterative and recursive computation of Hessian matrix and its inverse for the GWOLR parameter estimation. In reference to the research findings, we found out that the BFGS and LBFGS methods have arithmetic operation schemes, including O(n2) and O(nm).

Biomechanical Analysis of Normal Brain Development during the First Year of Life Using Finite Strain Theory.

PubMed

Kim, Jeong Chul; Wang, Li; Shen, Dinggang; Lin, Weili

2016-12-02

The first year of life is the most critical time period for structural and functional development of the human brain. Combining longitudinal MR imaging and finite strain theory, this study aimed to provide new insights into normal brain development through a biomechanical framework. Thirty-three normal infants were longitudinally imaged using MRI from 2 weeks to 1 year of age. Voxel-wise Jacobian determinant was estimated to elucidate volumetric changes while Lagrange strains (both normal and shear strains) were measured to reveal directional growth information every 3 months during the first year of life. Directional normal strain maps revealed that, during the first 6 months, the growth pattern of gray matter is anisotropic and spatially inhomogeneous with higher left-right stretch around the temporal lobe and interhemispheric fissure, anterior-posterior stretch in the frontal and occipital lobes, and superior-inferior stretch in right inferior occipital and right inferior temporal gyri. In contrast, anterior lateral ventricles and insula showed an isotropic stretch pattern. Volumetric and directional growth rates were linearly decreased with age for most of the cortical regions. Our results revealed anisotropic and inhomogeneous brain growth patterns of the human brain during the first year of life using longitudinal MRI and a biomechanical framework.

Rogue periodic waves of the modified KdV equation

NASA Astrophysics Data System (ADS)

Chen, Jinbing; Pelinovsky, Dmitry E.

2018-05-01

Rogue periodic waves stand for rogue waves on a periodic background. Two families of travelling periodic waves of the modified Korteweg–de Vries (mKdV) equation in the focusing case are expressed by the Jacobian elliptic functions dn and cn. By using one-fold and two-fold Darboux transformations of the travelling periodic waves, we construct new explicit solutions for the mKdV equation. Since the dn-periodic wave is modulationally stable with respect to long-wave perturbations, the new solution constructed from the dn-periodic wave is a nonlinear superposition of an algebraically decaying soliton and the dn-periodic wave. On the other hand, since the cn-periodic wave is modulationally unstable with respect to long-wave perturbations, the new solution constructed from the cn-periodic wave is a rogue wave on the cn-periodic background, which generalizes the classical rogue wave (the so-called Peregrine’s breather) of the nonlinear Schrödinger equation. We compute the magnification factor for the rogue cn-periodic wave of the mKdV equation and show that it remains constant for all amplitudes. As a by-product of our work, we find explicit expressions for the periodic eigenfunctions of the spectral problem associated with the dn and cn periodic waves of the mKdV equation.

Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves

USGS Publications Warehouse

Xia, J.; Miller, R.D.; Park, C.B.

1999-01-01

The shear-wave (S-wave) velocity of near-surface materials (soil, rocks, pavement) and its effect on seismic-wave propagation are of fundamental interest in many groundwater, engineering, and environmental studies. Rayleigh-wave phase velocity of a layered-earth model is a function of frequency and four groups of earth properties: P-wave velocity, S-wave velocity, density, and thickness of layers. Analysis of the Jacobian matrix provides a measure of dispersion-curve sensitivity to earth properties. S-wave velocities are the dominant influence on a dispersion curve in a high-frequency range (>5 Hz) followed by layer thickness. An iterative solution technique to the weighted equation proved very effective in the high-frequency range when using the Levenberg-Marquardt and singular-value decomposition techniques. Convergence of the weighted solution is guaranteed through selection of the damping factor using the Levenberg-Marquardt method. Synthetic examples demonstrated calculation efficiency and stability of inverse procedures. We verify our method using borehole S-wave velocity measurements.Iterative solutions to the weighted equation by the Levenberg-Marquardt and singular-value decomposition techniques are derived to estimate near-surface shear-wave velocity. Synthetic and real examples demonstrate the calculation efficiency and stability of the inverse procedure. The inverse results of the real example are verified by borehole S-wave velocity measurements.

Regularized solution of a nonlinear problem in electromagnetic sounding

NASA Astrophysics Data System (ADS)

Piero Deidda, Gian; Fenu, Caterina; Rodriguez, Giuseppe

2014-12-01

Non destructive investigation of soil properties is crucial when trying to identify inhomogeneities in the ground or the presence of conductive substances. This kind of survey can be addressed with the aid of electromagnetic induction measurements taken with a ground conductivity meter. In this paper, starting from electromagnetic data collected by this device, we reconstruct the electrical conductivity of the soil with respect to depth, with the aid of a regularized damped Gauss-Newton method. We propose an inversion method based on the low-rank approximation of the Jacobian of the function to be inverted, for which we develop exact analytical formulae. The algorithm chooses a relaxation parameter in order to ensure the positivity of the solution and implements various methods for the automatic estimation of the regularization parameter. This leads to a fast and reliable algorithm, which is tested on numerical experiments both on synthetic data sets and on field data. The results show that the algorithm produces reasonable solutions in the case of synthetic data sets, even in the presence of a noise level consistent with real applications, and yields results that are compatible with those obtained by electrical resistivity tomography in the case of field data. Research supported in part by Regione Sardegna grant CRP2_686.

Diffusion-model analysis of pPb and PbPb collisions at LHC energies

NASA Astrophysics Data System (ADS)

Schulz, P.; Wolschin, G.

2018-06-01

We present an analysis of centrality-dependent pseudorapidity distributions of produced charged hadrons in pPb and PbPb collisions at the Large Hadron Collider (LHC) energy of s NN = 5.02 TeV, and of minimum-bias pPb collisions at 8.16 TeV within the non-equilibrium-statistical relativistic diffusion model (RDM). In a three-source approach, the role of the fragmentation sources is emphasized. Together with the Jacobian transformation from rapidity to pseudorapidity and the limiting fragmentation conjecture, these are essential for modeling the centrality dependence. For central PbPb collisions, a prediction at the projected FCC energy of s NN = 39 TeV is made.

Progress on a generalized coordinates tensor product finite element 3DPNS algorithm for subsonic

NASA Technical Reports Server (NTRS)

Baker, A. J.; Orzechowski, J. A.

1983-01-01

A generalized coordinates form of the penalty finite element algorithm for the 3-dimensional parabolic Navier-Stokes equations for turbulent subsonic flows was derived. This algorithm formulation requires only three distinct hypermatrices and is applicable using any boundary fitted coordinate transformation procedure. The tensor matrix product approximation to the Jacobian of the Newton linear algebra matrix statement was also derived. Tne Newton algorithm was restructured to replace large sparse matrix solution procedures with grid sweeping using alpha-block tridiagonal matrices, where alpha equals the number of dependent variables. Numerical experiments were conducted and the resultant data gives guidance on potentially preferred tensor product constructions for the penalty finite element 3DPNS algorithm.

The Copenhagen problem with a quasi-homogeneous potential

NASA Astrophysics Data System (ADS)

Fakis, Demetrios; Kalvouridis, Tilemahos

2017-05-01

The Copenhagen problem is a well-known case of the famous restricted three-body problem. In this work instead of considering Newtonian potentials and forces we assume that the two primaries create a quasi-homogeneous potential, which means that we insert to the inverse square law of gravitation an inverse cube corrective term in order to approximate various phenomena as the radiation pressure of the primaries or the non-sphericity of them. Based on this new consideration we investigate the equilibrium locations of the small body and their parametric dependence, as well as the zero-velocity curves and surfaces for the planar motion, and the evolution of the regions where this motion is permitted when the Jacobian constant varies.

Optimal Stabilization of Social Welfare under Small Variation of Operating Condition with Bifurcation Analysis

NASA Astrophysics Data System (ADS)

Chanda, Sandip; De, Abhinandan

2016-12-01

A social welfare optimization technique has been proposed in this paper with a developed state space based model and bifurcation analysis to offer substantial stability margin even in most inadvertent states of power system networks. The restoration of the power market dynamic price equilibrium has been negotiated in this paper, by forming Jacobian of the sensitivity matrix to regulate the state variables for the standardization of the quality of solution in worst possible contingencies of the network and even with co-option of intermittent renewable energy sources. The model has been tested in IEEE 30 bus system and illustrious particle swarm optimization has assisted the fusion of the proposed model and methodology.

Non-parametric diffeomorphic image registration with the demons algorithm.

PubMed

Vercauteren, Tom; Pennec, Xavier; Perchant, Aymeric; Ayache, Nicholas

2007-01-01

We propose a non-parametric diffeomorphic image registration algorithm based on Thirion's demons algorithm. The demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. The main idea of our algorithm is to adapt this procedure to a space of diffeomorphic transformations. In contrast to many diffeomorphic registration algorithms, our solution is computationally efficient since in practice it only replaces an addition of free form deformations by a few compositions. Our experiments show that in addition to being diffeomorphic, our algorithm provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the true ones in terms of Jacobians.

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Highly dissipative Hénon map behavior in the four-level model of the CO 2 laser with modulated losses

NASA Astrophysics Data System (ADS)

Pando L., C. L.; Acosta, G. A. Luna; Meucci, R.; Ciofini, M.

1995-02-01

We show that the four-level model for the CO 2 laser with modulated losses behaves in a qualitatively similar way as the highly dissipative Hénon map. The ubiquity of elements of the universal sequence, their related symbolic dynamics, and the presence of reverse bifurcations of chaotic bands in the model are reminiscent of the logistic map which is the limit of the Hénon map when the Jacobian equals zero. The coexistence of attractors, its dynamics related to contraction of volumes in phase space and the associated return maps can be correlated with those of the highly dissipative Hénon map.

On the mathematical analysis of Ebola hemorrhagic fever: deathly infection disease in West African countries.

PubMed

Atangana, Abdon; Goufo, Emile Franc Doungmo

2014-01-01

For a given West African country, we constructed a model describing the spread of the deathly disease called Ebola hemorrhagic fever. The model was first constructed using the classical derivative and then converted to the generalized version using the beta-derivative. We studied in detail the endemic equilibrium points and provided the Eigen values associated using the Jacobian method. We furthered our investigation by solving the model numerically using an iteration method. The simulations were done in terms of time and beta. The study showed that, for small portion of infected individuals, the whole country could die out in a very short period of time in case there is not good prevention.

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

Wollaber, Allan Benton; Park, HyeongKae; Lowrie, Robert Byron

Moment-based acceleration via the development of “high-order, low-order” (HO-LO) algorithms has provided substantial accuracy and efficiency enhancements for solutions of the nonlinear, thermal radiative transfer equations by CCS-2 and T-3 staff members. Accuracy enhancements over traditional, linearized methods are obtained by solving a nonlinear, timeimplicit HO-LO system via a Jacobian-free Newton Krylov procedure. This also prevents the appearance of non-physical maximum principle violations (“temperature spikes”) associated with linearization. Efficiency enhancements are obtained in part by removing “effective scattering” from the linearized system. In this highlight, we summarize recent work in which we formally extended the HO-LO radiation algorithm to includemore » operator-split radiation-hydrodynamics.« less

Asynchronous, macrotasked relaxation strategies for the solution of viscous, hypersonic flows

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

1991-01-01

A point-implicit, asynchronous macrotasked relaxation of the steady, thin-layer, Navier-Stokes equations is presented. The method employs multidirectional, single-level storage Gauss-Seidel relaxation sweeps, which effectively communicate perturbations across the entire domain in 2n sweeps, where n is the dimension of the domain. In order to enhance convergence the application of relaxation factors to specific components of the Jacobian is examined using a stability analysis of the advection and diffusion equations. Attention is also given to the complications associated with asynchronous multitasking. Solutions are generated for hypersonic flows over blunt bodies in two and three dimensions with chemical reactions, utilizing single-tasked and multitasked relaxation strategies.

A template-based approach for parallel hexahedral two-refinement

DOE PAGES

Owen, Steven J.; Shih, Ryan M.; Ernst, Corey D.

2016-10-17

Here, we provide a template-based approach for generating locally refined all-hex meshes. We focus specifically on refinement of initially structured grids utilizing a 2-refinement approach where uniformly refined hexes are subdivided into eight child elements. The refinement algorithm consists of identifying marked nodes that are used as the basis for a set of four simple refinement templates. The target application for 2-refinement is a parallel grid-based all-hex meshing tool for high performance computing in a distributed environment. The result is a parallel consistent locally refined mesh requiring minimal communication and where minimum mesh quality is greater than scaled Jacobian 0.3more » prior to smoothing.« less

A template-based approach for parallel hexahedral two-refinement

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

Owen, Steven J.; Shih, Ryan M.; Ernst, Corey D.

Here, we provide a template-based approach for generating locally refined all-hex meshes. We focus specifically on refinement of initially structured grids utilizing a 2-refinement approach where uniformly refined hexes are subdivided into eight child elements. The refinement algorithm consists of identifying marked nodes that are used as the basis for a set of four simple refinement templates. The target application for 2-refinement is a parallel grid-based all-hex meshing tool for high performance computing in a distributed environment. The result is a parallel consistent locally refined mesh requiring minimal communication and where minimum mesh quality is greater than scaled Jacobian 0.3more » prior to smoothing.« less

Use of symbolic computation in robotics education

NASA Technical Reports Server (NTRS)

Vira, Naren; Tunstel, Edward

1992-01-01

An application of symbolic computation in robotics education is described. A software package is presented which combines generality, user interaction, and user-friendliness with the systematic usage of symbolic computation and artificial intelligence techniques. The software utilizes MACSYMA, a LISP-based symbolic algebra language, to automatically generate closed-form expressions representing forward and inverse kinematics solutions, the Jacobian transformation matrices, robot pose error-compensation models equations, and Lagrange dynamics formulation for N degree-of-freedom, open chain robotic manipulators. The goal of such a package is to aid faculty and students in the robotics course by removing burdensome tasks of mathematical manipulations. The software package has been successfully tested for its accuracy using commercially available robots.

MIND Demons: Symmetric Diffeomorphic Deformable Registration of MR and CT for Image-Guided Spine Surgery.

PubMed

Reaungamornrat, Sureerat; De Silva, Tharindu; Uneri, Ali; Vogt, Sebastian; Kleinszig, Gerhard; Khanna, Akhil J; Wolinsky, Jean-Paul; Prince, Jerry L; Siewerdsen, Jeffrey H

2016-11-01

Intraoperative localization of target anatomy and critical structures defined in preoperative MR/CT images can be achieved through the use of multimodality deformable registration. We propose a symmetric diffeomorphic deformable registration algorithm incorporating a modality-independent neighborhood descriptor (MIND) and a robust Huber metric for MR-to-CT registration. The method, called MIND Demons, finds a deformation field between two images by optimizing an energy functional that incorporates both the forward and inverse deformations, smoothness on the integrated velocity fields, a modality-insensitive similarity function suitable to multimodality images, and smoothness on the diffeomorphisms themselves. Direct optimization without relying on the exponential map and stationary velocity field approximation used in conventional diffeomorphic Demons is carried out using a Gauss-Newton method for fast convergence. Registration performance and sensitivity to registration parameters were analyzed in simulation, phantom experiments, and clinical studies emulating application in image-guided spine surgery, and results were compared to mutual information (MI) free-form deformation (FFD), local MI (LMI) FFD, normalized MI (NMI) Demons, and MIND with a diffusion-based registration method (MIND-elastic). The method yielded sub-voxel invertibility (0.008 mm) and nonzero-positive Jacobian determinants. It also showed improved registration accuracy in comparison to the reference methods, with mean target registration error (TRE) of 1.7 mm compared to 11.3, 3.1, 5.6, and 2.4 mm for MI FFD, LMI FFD, NMI Demons, and MIND-elastic methods, respectively. Validation in clinical studies demonstrated realistic deformations with sub-voxel TRE in cases of cervical, thoracic, and lumbar spine.

MIND Demons: Symmetric Diffeomorphic Deformable Registration of MR and CT for Image-Guided Spine Surgery

PubMed Central

Reaungamornrat, Sureerat; De Silva, Tharindu; Uneri, Ali; Vogt, Sebastian; Kleinszig, Gerhard; Khanna, Akhil J; Wolinsky, Jean-Paul; Prince, Jerry L.

2016-01-01

Intraoperative localization of target anatomy and critical structures defined in preoperative MR/CT images can be achieved through the use of multimodality deformable registration. We propose a symmetric diffeomorphic deformable registration algorithm incorporating a modality-independent neighborhood descriptor (MIND) and a robust Huber metric for MR-to-CT registration. The method, called MIND Demons, finds a deformation field between two images by optimizing an energy functional that incorporates both the forward and inverse deformations, smoothness on the integrated velocity fields, a modality-insensitive similarity function suitable to multimodality images, and smoothness on the diffeomorphisms themselves. Direct optimization without relying on the exponential map and stationary velocity field approximation used in conventional diffeomorphic Demons is carried out using a Gauss-Newton method for fast convergence. Registration performance and sensitivity to registration parameters were analyzed in simulation, phantom experiments, and clinical studies emulating application in image-guided spine surgery, and results were compared to mutual information (MI) free-form deformation (FFD), local MI (LMI) FFD, normalized MI (NMI) Demons, and MIND with a diffusion-based registration method (MIND-elastic). The method yielded sub-voxel invertibility (0.008 mm) and nonzero-positive Jacobian determinants. It also showed improved registration accuracy in comparison to the reference methods, with mean target registration error (TRE) of 1.7 mm compared to 11.3, 3.1, 5.6, and 2.4 mm for MI FFD, LMI FFD, NMI Demons, and MIND-elastic methods, respectively. Validation in clinical studies demonstrated realistic deformations with sub-voxel TRE in cases of cervical, thoracic, and lumbar spine. PMID:27295656

Control of the seven-degree-of-freedom upper limb exoskeleton for an improved human-robot interface

NASA Astrophysics Data System (ADS)

Kim, Hyunchul; Kim, Jungsuk

2017-04-01

This study analyzes a practical scheme for controlling an exoskeleton robot with seven degrees of freedom (DOFs) that supports natural movements of the human arm. A redundant upper limb exoskeleton robot with seven DOFs is mechanically coupled to the human body such that it becomes a natural extension of the body. If the exoskeleton robot follows the movement of the human body synchronously, the energy exchange between the human and the robot will be reduced significantly. In order to achieve this, the redundancy of the human arm, which is represented by the swivel angle, should be resolved using appropriate constraints and applied to the robot. In a redundant 7-DOF upper limb exoskeleton, the pseudoinverse of the Jacobian with secondary objective functions is widely used to resolve the redundancy that defines the desired joint angles. A secondary objective function requires the desired joint angles for the movement of the human arm, and the angles are estimated by maximizing the projection of the longest principle axis of the manipulability ellipsoid for the human arm onto the virtual destination toward the head region. Then, they are fed into the muscle model with a relative damping to achieve more realistic robot-arm movements. Various natural arm movements are recorded using a motion capture system, and the actual swivel-angle is compared to that estimated using the proposed swivel angle estimation algorithm. The results indicate that the proposed algorithm provides a precise reference for estimating the desired joint angle with an error less than 5°.

Keeping it Together: Advanced algorithms and software for magma dynamics (and other coupled multi-physics problems)

NASA Astrophysics Data System (ADS)

Spiegelman, M.; Wilson, C. R.

2011-12-01

A quantitative theory of magma production and transport is essential for understanding the dynamics of magmatic plate boundaries, intra-plate volcanism and the geochemical evolution of the planet. It also provides one of the most challenging computational problems in solid Earth science, as it requires consistent coupling of fluid and solid mechanics together with the thermodynamics of melting and reactive flows. Considerable work on these problems over the past two decades shows that small changes in assumptions of coupling (e.g. the relationship between melt fraction and solid rheology), can have profound changes on the behavior of these systems which in turn affects critical computational choices such as discretizations, solvers and preconditioners. To make progress in exploring and understanding this physically rich system requires a computational framework that allows more flexible, high-level description of multi-physics problems as well as increased flexibility in composing efficient algorithms for solution of the full non-linear coupled system. Fortunately, recent advances in available computational libraries and algorithms provide a platform for implementing such a framework. We present results from a new model building system that leverages functionality from both the FEniCS project (www.fenicsproject.org) and PETSc libraries (www.mcs.anl.gov/petsc) along with a model independent options system and gui, Spud (amcg.ese.ic.ac.uk/Spud). Key features from FEniCS include fully unstructured FEM with a wide range of elements; a high-level language (ufl) and code generation compiler (FFC) for describing the weak forms of residuals and automatic differentiation for calculation of exact and approximate jacobians. The overall strategy is to monitor/calculate residuals and jacobians for the entire non-linear system of equations within a global non-linear solve based on PETSc's SNES routines. PETSc already provides a wide range of solvers and preconditioners, from parallel sparse direct to algebraic multigrid, that can be chosen at runtime. In particular, we make extensive use of PETSc's FieldSplit block preconditioners that allow us to use optimal solvers for subproblems (such as Stokes, or advection/diffusion of temperature) as preconditioners for the full problem. Thus these routines let us reuse effective solving recipes/splittings from previous experience while monitoring the convergence of the global problem. These techniques often yield quadratic (Newton like) convergence for the work of standard Picard schemes. We will illustrate this new framework with examples from the Magma Dynamic Demonstration suite (MADDs) of well understood magma dynamics benchmark problems including stokes flow in ridge geometries, magmatic solitary waves and shear-driven melt bands. While development of this system has been driven by magma dynamics, this framework is much more general and can be used for a wide range of PDE based multi-physics models.

Efficient Inversion of Mult-frequency and Multi-Source Electromagnetic Data

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

Gary D. Egbert

2007-03-22

The project covered by this report focused on development of efficient but robust non-linear inversion algorithms for electromagnetic induction data, in particular for data collected with multiple receivers, and multiple transmitters, a situation extremely common in eophysical EM subsurface imaging methods. A key observation is that for such multi-transmitter problems each step in commonly used linearized iterative limited memory search schemes such as conjugate gradients (CG) requires solution of forward and adjoint EM problems for each of the N frequencies or sources, essentially generating data sensitivities for an N dimensional data-subspace. These multiple sensitivities allow a good approximation to themore » full Jacobian of the data mapping to be built up in many fewer search steps than would be required by application of textbook optimization methods, which take no account of the multiplicity of forward problems that must be solved for each search step. We have applied this idea to a develop a hybrid inversion scheme that combines features of the iterative limited memory type methods with a Newton-type approach using a partial calculation of the Jacobian. Initial tests on 2D problems show that the new approach produces results essentially identical to a Newton type Occam minimum structure inversion, while running more rapidly than an iterative (fixed regularization parameter) CG style inversion. Memory requirements, while greater than for something like CG, are modest enough that even in 3D the scheme should allow 3D inverse problems to be solved on a common desktop PC, at least for modest (~ 100 sites, 15-20 frequencies) data sets. A secondary focus of the research has been development of a modular system for EM inversion, using an object oriented approach. This system has proven useful for more rapid prototyping of inversion algorithms, in particular allowing initial development and testing to be conducted with two-dimensional example problems, before approaching more computationally cumbersome three-dimensional problems.« less

Joint retrieval of aerosol and water-leaving radiance from multispectral, multiangular and polarimetric measurements over ocean

NASA Astrophysics Data System (ADS)

Xu, Feng; Dubovik, Oleg; Zhai, Peng-Wang; Diner, David J.; Kalashnikova, Olga V.; Seidel, Felix C.; Litvinov, Pavel; Bovchaliuk, Andrii; Garay, Michael J.; van Harten, Gerard; Davis, Anthony B.

2016-07-01

An optimization approach has been developed for simultaneous retrieval of aerosol properties and normalized water-leaving radiance (nLw) from multispectral, multiangular, and polarimetric observations over ocean. The main features of the method are (1) use of a simplified bio-optical model to estimate nLw, followed by an empirical refinement within a specified range to improve its accuracy; (2) improved algorithm convergence and stability by applying constraints on the spatial smoothness of aerosol loading and Chlorophyll a (Chl a) concentration across neighboring image patches and spectral constraints on aerosol optical properties and nLw across relevant bands; and (3) enhanced Jacobian calculation by modeling and storing the radiative transfer (RT) in aerosol/Rayleigh mixed layer, pure Rayleigh-scattering layers, and ocean medium separately, then coupling them to calculate the field at the sensor. This approach avoids unnecessary and time-consuming recalculations of RT in unperturbed layers in Jacobian evaluations. The Markov chain method is used to model RT in the aerosol/Rayleigh mixed layer and the doubling method is used for the uniform layers of the atmosphere-ocean system. Our optimization approach has been tested using radiance and polarization measurements acquired by the Airborne Multiangle SpectroPolarimetric Imager (AirMSPI) over the AERONET USC_SeaPRISM ocean site (6 February 2013) and near the AERONET La Jolla site (14 January 2013), which, respectively, reported relatively high and low aerosol loadings. Validation of the results is achieved through comparisons to AERONET aerosol and ocean color products. For comparison, the USC_SeaPRISM retrieval is also performed by use of the Generalized Retrieval of Aerosol and Surface Properties algorithm (Dubovik et al., 2011). Uncertainties of aerosol and nLw retrievals due to random and systematic instrument errors are analyzed by truth-in/truth-out tests with three Chl a concentrations, five aerosol loadings, three different types of aerosols, and nine combinations of solar incidence and viewing geometries.

Using computer algebra and SMT-solvers to analyze a mathematical model of cholera propagation

NASA Astrophysics Data System (ADS)

Trujillo Arredondo, Mariana

2014-06-01

We analyze a mathematical model for the transmission of cholera. The model is already defined and involves variables such as the pathogen agent, which in this case is the bacterium Vibrio cholera, and the human population. The human population is divided into three classes: susceptible, infectious and removed. Using Computer Algebra, specifically Maple we obtain two equilibrium states: the disease free state and the endemic state. Using Maple it is possible to prove that the disease free state is locally asymptotically stable if and only if R0 < 1. Using Maple it is possible to prove that the endemic equilibrium state is locally stable when it exists, it is to say when R0 > 1. Using the package Red-Log of the Computer algebra system Reduce and the SMT-Solver Z3Py it is possible to obtain numerical conditions for the model. The formula for the basic reproductive number makes a synthesis with all epidemic parameters in the model. Also it is possible to make numerical simulations which are very illustrative about the epidemic patters that are expected to be observed in real situations. We claim that these kinds of software are very useful in the analysis of epidemic models given that the symbolic computation provides algebraic formulas for the basic reproductive number and such algebraic formulas are very useful to derive control measures. For other side, computer algebra software is a powerful tool to make the stability analysis for epidemic models given that the all steps in the stability analysis can be made automatically: finding the equilibrium points, computing the jacobian, computing the characteristic polynomial for the jacobian, and applying the Routh-Hurwitz theorem to the characteristic polynomial. Finally, using SMT-Solvers is possible to make automatically checks of satisfiability, validity and quantifiers elimination being these computations very useful to analyse complicated epidemic models.

F-theory on all toric hypersurface fibrations and its Higgs branches

DOE PAGES

Klevers, Denis; Mayorga Pena, Damian Kaloni; Oehlmann, Paul-Konstantin; ...

2015-01-27

We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the codimension one, two and three singularities of these fibrations. We use these geometric results to determine the gauge groups, matter representations, 6D matter multiplicities and 4D Yukawa couplings of the corresponding effective theories. All these theories have a non-trivial gauge group and matter content. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blow-ups in the 2D toric varieties. We recover the 6D effective theories of all 16 toric hypersurface fibrations by repeatedly Higgsing the theories that exhibit Mordell-Weil torsion. We find that the three Calabi-Yau manifolds without section, whose fibers are given by the toric hypersurfaces inmore » $$\\mathbb P^{2}$$, $$\\mathbb P^{1}$$ × $$\\mathbb P^{1}$$ and the recently studied $$\\mathbb P^{2}$$ (1,1, 2) , yield F-theory realizations of SUGRA theories with discrete gauge groups $$\\mathbb Z$$ 3, $$\\mathbb Z$$ 2 and $$\\mathbb Z$$ 4.This opens up a whole new arena for model building with discrete global symmetries in F-theory. In these three manifolds, we also find codimension two I 2-fibers supporting matter charged only under these discrete gauge groups. Their 6D matter multiplicities are computed employing ideal techniques and the associated Jacobian fibrations. Here, we also show that the Jacobian of the biquadric fibration has one rational section, yielding one U(1)-gauge field in F-theory. Furthermore, the elliptically fibered Calabi-Yau manifold based on dP 1 has a U(1)-gauge field induced by a non-toric rational section. In this model, we find the first F-theory realization of matter with U(1)-charge q = 3.« less

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

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

A Hybrid MPI/OpenMP Approach for Parallel Groundwater Model Calibration on Multicore Computers

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

Tang, Guoping; D'Azevedo, Ed F; Zhang, Fan

2010-01-01

Groundwater model calibration is becoming increasingly computationally time intensive. We describe a hybrid MPI/OpenMP approach to exploit two levels of parallelism in software and hardware to reduce calibration time on multicore computers with minimal parallelization effort. At first, HydroGeoChem 5.0 (HGC5) is parallelized using OpenMP for a uranium transport model with over a hundred species involving nearly a hundred reactions, and a field scale coupled flow and transport model. In the first application, a single parallelizable loop is identified to consume over 97% of the total computational time. With a few lines of OpenMP compiler directives inserted into the code,more » the computational time reduces about ten times on a compute node with 16 cores. The performance is further improved by selectively parallelizing a few more loops. For the field scale application, parallelizable loops in 15 of the 174 subroutines in HGC5 are identified to take more than 99% of the execution time. By adding the preconditioned conjugate gradient solver and BICGSTAB, and using a coloring scheme to separate the elements, nodes, and boundary sides, the subroutines for finite element assembly, soil property update, and boundary condition application are parallelized, resulting in a speedup of about 10 on a 16-core compute node. The Levenberg-Marquardt (LM) algorithm is added into HGC5 with the Jacobian calculation and lambda search parallelized using MPI. With this hybrid approach, compute nodes at the number of adjustable parameters (when the forward difference is used for Jacobian approximation), or twice that number (if the center difference is used), are used to reduce the calibration time from days and weeks to a few hours for the two applications. This approach can be extended to global optimization scheme and Monte Carol analysis where thousands of compute nodes can be efficiently utilized.« less

SU-F-J-80: Deformable Image Registration for Residual Organ Motion Estimation in Respiratory Gated Treatments with Scanned Carbon Ion Beams

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

Meschini, G; Seregni, M; Pella, A

Purpose: At the Centro Nazionale di Adroterapia Oncologica (CNAO, Pavia, Italy) C-ions respiratory gated treatments of patients with abdominal tumours started in 2014. In these cases, the therapeutic dose is delivered around end-exhale. We propose the use of a respiratory motion model to evaluate residual tumour motion. Such a model requires motion fields obtained from deformable image registration (DIR) between 4DCT phases, estimating anatomical motion through interpolation. The aim of this work is to identify the optimal DIR technique to be integrated in the modeling pipeline. Methods: We used 4DCT datasets from 4 patients to test 4 DIR algorithms: Bspline,more » demons, log-domain and symmetric log domain diffeomorphic demons. We evaluate DIR performance in terms of registration accuracy (RMSE between registered images) and anatomical consistency of the motion field (Jacobian) when registering end-inhale to end-exhale. We subsequently employed the model to estimate the tumour trajectory within the ideal gating window. Results: Within the liver contour, the RMSE is in the range 31–46 HU for the best performing algorithm (Bspline) and 43–145 HU for the worst one (demons). The Jacobians featured zero negative voxels (which indicate singularities in the motion field) for the Bspline fields in 3 of 4 patients, whereas diffeomorphic demons fields showed a non-null number of negative voxels in every case. GTV motion in the gating window measured less than 7 mm for every patient, displaying a predominant superior-inferior (SI) component. Conclusion: The Bspline algorithm allows for acceptable DIR results in the abdominal region, exhibiting the property of anatomical consistency of the computed field. Computed trajectories are in agreement with clinical expectations (small and prevalent SI displacements), since patients lie wearing semi-rigid immobilizing masks. In future, the model could be used for retrospective estimation of organ motion during treatment, as guided by the breathing surrogate signal.« less

Deploy production sliding mesh capability with linear solver benchmarking.

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

Domino, Stefan P.; Thomas, Stephen; Barone, Matthew F.

Wind applications require the ability to simulate rotating blades. To support this use-case, a novel design-order sliding mesh algorithm has been developed and deployed. The hybrid method combines the control volume finite element methodology (CVFEM) with concepts found within a discontinuous Galerkin (DG) finite element method (FEM) to manage a sliding mesh. The method has been demonstrated to be design-order for the tested polynomial basis (P=1 and P=2) and has been deployed to provide production simulation capability for a Vestas V27 (225 kW) wind turbine. Other stationary and canonical rotating ow simulations are also presented. As the majority of wind-energymore » applications are driving extensive usage of hybrid meshes, a foundational study that outlines near-wall numerical behavior for a variety of element topologies is presented. Results indicate that the proposed nonlinear stabilization operator (NSO) is an effective stabilization methodology to control Gibbs phenomena at large cell Peclet numbers. The study also provides practical mesh resolution guidelines for future analysis efforts. Application-driven performance and algorithmic improvements have been carried out to increase robustness of the scheme on hybrid production wind energy meshes. Specifically, the Kokkos-based Nalu Kernel construct outlined in the FY17/Q4 ExaWind milestone has been transitioned to the hybrid mesh regime. This code base is exercised within a full V27 production run. Simulation timings for parallel search and custom ghosting are presented. As the low-Mach application space requires implicit matrix solves, the cost of matrix reinitialization has been evaluated on a variety of production meshes. Results indicate that at low element counts, i.e., fewer than 100 million elements, matrix graph initialization and preconditioner setup times are small. However, as mesh sizes increase, e.g., 500 million elements, simulation time associated with \\setup-up" costs can increase to nearly 50% of overall simulation time when using the full Tpetra solver stack and nearly 35% when using a mixed Tpetra- Hypre-based solver stack. The report also highlights the project achievement of surpassing the 1 billion element mesh scale for a production V27 hybrid mesh. A detailed timing breakdown is presented that again suggests work to be done in the setup events associated with the linear system. In order to mitigate these initialization costs, several application paths have been explored, all of which are designed to reduce the frequency of matrix reinitialization. Methods such as removing Jacobian entries on the dynamic matrix columns (in concert with increased inner equation iterations), and lagging of Jacobian entries have reduced setup times at the cost of numerical stability. Artificially increasing, or bloating, the matrix stencil to ensure that full Jacobians are included is developed with results suggesting that this methodology is useful in decreasing reinitialization events without loss of matrix contributions. With the above foundational advances in computational capability, the project is well positioned to begin scientific inquiry on a variety of wind-farm physics such as turbine/turbine wake interactions.« less

Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Bailey, Harry E.; Beam, Richard M.

1991-01-01

Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.

About the coupling of turbulence closure models with averaged Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Vandromme, D.; Ha Minh, H.

1986-01-01

The MacCormack implicit predictor-corrector model (1981) for numerical solution of the coupled Navier-Stokes equations for turbulent flows is extended to nonconservative multiequation turbulence models, as well as the inclusion of second-order Reynolds stress turbulence closure. A scalar effective pressure turbulent contribution to the pressure field is defined to approximate the effects of the Reynolds stress in strongly sheared flows. The Jacobian matrices of the transport equations are diagonalized to reduce the required computer memory and run time. Techniques are defined for including turbulence in the diagonalization. Application of the method is demonstrated with solutions generated for transonic nozzle flow and for the interaction between a supersonic flat plate boundary layer and a 12 deg compression-expansion ramp.

Estimation of regional lung expansion via 3D image registration

NASA Astrophysics Data System (ADS)

Pan, Yan; Kumar, Dinesh; Hoffman, Eric A.; Christensen, Gary E.; McLennan, Geoffrey; Song, Joo Hyun; Ross, Alan; Simon, Brett A.; Reinhardt, Joseph M.

2005-04-01

A method is described to estimate regional lung expansion and related biomechanical parameters using multiple CT images of the lungs, acquired at different inflation levels. In this study, the lungs of two sheep were imaged utilizing a multi-detector row CT at different lung inflations in the prone and supine positions. Using the lung surfaces and the airway branch points for guidance, a 3D inverse consistent image registration procedure was used to match different lung volumes at each orientation. The registration was validated using a set of implanted metal markers. After registration, the Jacobian of the deformation field was computed to express regional expansion or contraction. The regional lung expansion at different pressures and different orientations are compared.

Convergence Estimates for Multidisciplinary Analysis and Optimization

NASA Technical Reports Server (NTRS)

Arian, Eyal

1997-01-01

A quantitative analysis of coupling between systems of equations is introduced. This analysis is then applied to problems in multidisciplinary analysis, sensitivity, and optimization. For the sensitivity and optimization problems both multidisciplinary and single discipline feasibility schemes are considered. In all these cases a "convergence factor" is estimated in terms of the Jacobians and Hessians of the system, thus it can also be approximated by existing disciplinary analysis and optimization codes. The convergence factor is identified with the measure for the "coupling" between the disciplines in the system. Applications to algorithm development are discussed. Demonstration of the convergence estimates and numerical results are given for a system composed of two non-linear algebraic equations, and for a system composed of two PDEs modeling aeroelasticity.

Study of chaos in chaotic satellite systems

NASA Astrophysics Data System (ADS)

Khan, Ayub; Kumar, Sanjay

2018-01-01

In this paper, we study the qualitative behaviour of satellite systems using bifurcation diagrams, Poincaré section, Lyapunov exponents, dissipation, equilibrium points, Kaplan-Yorke dimension etc. Bifurcation diagrams with respect to the known parameters of satellite systems are analysed. Poincaré sections with different sowing axes of the satellite are drawn. Eigenvalues of Jacobian matrices for the satellite system at different equilibrium points are calculated to justify the unstable regions. Lyapunov exponents are estimated. From these studies, chaos in satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the considered system.

Three-dimensional unstructured grid Euler computations using a fully-implicit, upwind method

NASA Technical Reports Server (NTRS)

Whitaker, David L.

1993-01-01

A method has been developed to solve the Euler equations on a three-dimensional unstructured grid composed of tetrahedra. The method uses an upwind flow solver with a linearized, backward-Euler time integration scheme. Each time step results in a sparse linear system of equations which is solved by an iterative, sparse matrix solver. Local-time stepping, switched evolution relaxation (SER), preconditioning and reuse of the Jacobian are employed to accelerate the convergence rate. Implicit boundary conditions were found to be extremely important for fast convergence. Numerical experiments have shown that convergence rates comparable to that of a multigrid, central-difference scheme are achievable on the same mesh. Results are presented for several grids about an ONERA M6 wing.

Numerical Solution of the Gyrokinetic Poisson Equation in TEMPEST

NASA Astrophysics Data System (ADS)

Dorr, Milo; Cohen, Bruce; Cohen, Ronald; Dimits, Andris; Hittinger, Jeffrey; Kerbel, Gary; Nevins, William; Rognlien, Thomas; Umansky, Maxim; Xiong, Andrew; Xu, Xueqiao

2006-10-01

The gyrokinetic Poisson (GKP) model in the TEMPEST continuum gyrokinetic edge plasma code yields the electrostatic potential due to the charge density of electrons and an arbitrary number of ion species including the effects of gyroaveraging in the limit kρ1. The TEMPEST equations are integrated as a differential algebraic system involving a nonlinear system solve via Newton-Krylov iteration. The GKP preconditioner block is inverted using a multigrid preconditioned conjugate gradient (CG) algorithm. Electrons are treated as kinetic or adiabatic. The Boltzmann relation in the adiabatic option employs flux surface averaging to maintain neutrality within field lines and is solved self-consistently with the GKP equation. A decomposition procedure circumvents the near singularity of the GKP Jacobian block that otherwise degrades CG convergence.

Proposal for chiral-boson search at LHC via their unique new signature

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

Chizhov, M. V.; Bednyakov, V. A.; Budagov, J. A.

The resonance production of new chiral spin-1 bosons and their detection through the Drell-Yan process at the CERN LHC is considered. Quantitative evaluations of various differential cross sections of the chiral-boson production are made within the CalcHEP package. The new neutral chiral bosons can be observed as a Breit-Wigner resonance peak in the invariant-dilepton-mass distribution, as usual. However, unique new signatures of the chiral bosons exist. First, there is no Jacobian peak in the lepton transverse-momentum distribution. Second, the lepton angular distribution in the Collins-Soper frame for the high on-peak invariant masses of the lepton pairs has a peculiar 'swallowtail'more » shape.« less

Design and Optimization of a Hybrid-Driven Waist Rehabilitation Robot

PubMed Central

Zi, Bin; Yin, Guangcai; Zhang, Dan

2016-01-01

In this paper a waist rehabilitation robot driven by cables and pneumatic artificial muscles (PAMs) has been conceptualized and designed. In the process of mechanism design, the human body structure, the waist movement characteristics, and the actuators’ driving characteristics are the main considerable factors to make the hybrid-driven waist rehabilitation robot (HWRR) cost-effective, safe, flexible, and well-adapted. A variety of sensors are chosen to measure the position and orientation of the recovery patient to ensure patient safety at the same time as the structure design. According to the structure specialty and function, the HWRR is divided into two independent parallel robots: the waist twist device and the lower limb traction device. Then these two devices are analyzed and evaluated, respectively. Considering the characters of the human body in the HWRR, the inverse kinematics and statics are studied when the waist and the lower limb are considered as a spring and link, respectively. Based on the inverse kinematics and statics, the effect of the contraction parameter of the PAM is considered in the optimization of the waist twist device, and the lower limb traction device is optimized using particle swarm optimization (PSO) to minimize the global conditioning number over the feasible workspace. As a result of the optimization, an optimal rehabilitation robot design is obtained and the condition number of the Jacobian matrix over the feasible workspace is also calculated. PMID:27983626

Dynamic Modeling and Interactive Performance of PARM: A Parallel Upper-Limb Rehabilitation Robot Using Impedance Control for Patients after Stroke.

PubMed

Guang, Hui; Ji, Linhong; Shi, Yingying; Misgeld, Berno J E

2018-01-01

The robot-assisted therapy has been demonstrated to be effective in the improvements of limb function and even activities of daily living for patients after stroke. This paper presents an interactive upper-limb rehabilitation robot with a parallel mechanism and an isometric screen embedded in the platform to display trajectories. In the dynamic modeling for impedance control, the effects of friction and inertia are reduced by introducing the principle of virtual work and derivative of Jacobian matrix. To achieve the assist-as-needed impedance control for arbitrary trajectories, the strategy based on orthogonal deviations is proposed. Simulations and experiments were performed to validate the dynamic modeling and impedance control. Besides, to investigate the influence of the impedance in practice, a subject participated in experiments and performed two types of movements with the robot, that is, rectilinear and circular movements, under four conditions, that is, with/without resistance or impedance, respectively. The results showed that the impedance and resistance affected both mean absolute error and standard deviation of movements and also demonstrated the significant differences between movements with/without impedance and resistance ( p < 0.001). Furthermore, the error patterns were discussed, which suggested that the impedance environment was capable of alleviating movement deviations by compensating the synergetic inadequacy between the shoulder and elbow joints.

Dynamic Modeling and Interactive Performance of PARM: A Parallel Upper-Limb Rehabilitation Robot Using Impedance Control for Patients after Stroke

PubMed Central

Shi, Yingying; Misgeld, Berno J. E.

2018-01-01

The robot-assisted therapy has been demonstrated to be effective in the improvements of limb function and even activities of daily living for patients after stroke. This paper presents an interactive upper-limb rehabilitation robot with a parallel mechanism and an isometric screen embedded in the platform to display trajectories. In the dynamic modeling for impedance control, the effects of friction and inertia are reduced by introducing the principle of virtual work and derivative of Jacobian matrix. To achieve the assist-as-needed impedance control for arbitrary trajectories, the strategy based on orthogonal deviations is proposed. Simulations and experiments were performed to validate the dynamic modeling and impedance control. Besides, to investigate the influence of the impedance in practice, a subject participated in experiments and performed two types of movements with the robot, that is, rectilinear and circular movements, under four conditions, that is, with/without resistance or impedance, respectively. The results showed that the impedance and resistance affected both mean absolute error and standard deviation of movements and also demonstrated the significant differences between movements with/without impedance and resistance (p < 0.001). Furthermore, the error patterns were discussed, which suggested that the impedance environment was capable of alleviating movement deviations by compensating the synergetic inadequacy between the shoulder and elbow joints. PMID:29850004

GARLIC - A general purpose atmospheric radiative transfer line-by-line infrared-microwave code: Implementation and evaluation

NASA Astrophysics Data System (ADS)

Schreier, Franz; Gimeno García, Sebastián; Hedelt, Pascal; Hess, Michael; Mendrok, Jana; Vasquez, Mayte; Xu, Jian

2014-04-01

A suite of programs for high resolution infrared-microwave atmospheric radiative transfer modeling has been developed with emphasis on efficient and reliable numerical algorithms and a modular approach appropriate for simulation and/or retrieval in a variety of applications. The Generic Atmospheric Radiation Line-by-line Infrared Code - GARLIC - is suitable for arbitrary observation geometry, instrumental field-of-view, and line shape. The core of GARLIC's subroutines constitutes the basis of forward models used to implement inversion codes to retrieve atmospheric state parameters from limb and nadir sounding instruments. This paper briefly introduces the physical and mathematical basics of GARLIC and its descendants and continues with an in-depth presentation of various implementation aspects: An optimized Voigt function algorithm combined with a two-grid approach is used to accelerate the line-by-line modeling of molecular cross sections; various quadrature methods are implemented to evaluate the Schwarzschild and Beer integrals; and Jacobians, i.e. derivatives with respect to the unknowns of the atmospheric inverse problem, are implemented by means of automatic differentiation. For an assessment of GARLIC's performance, a comparison of the quadrature methods for solution of the path integral is provided. Verification and validation are demonstrated using intercomparisons with other line-by-line codes and comparisons of synthetic spectra with spectra observed on Earth and from Venus.

Topology-induced bifurcations for the nonlinear Schrödinger equation on the tadpole graph.

PubMed

Cacciapuoti, Claudio; Finco, Domenico; Noja, Diego

2015-01-01

In this paper we give the complete classification of solitons for a cubic nonlinear Schrödinger equation on the simplest network with a nontrivial topology: the tadpole graph, i.e., a ring with a half line attached to it and free boundary conditions at the junction. This is a step toward the modelization of condensate propagation and confinement in quasi-one-dimensional traps. The model, although simple, exhibits a surprisingly rich behavior and in particular we show that it admits: (i) a denumerable family of continuous branches of embedded solitons vanishing on the half line and bifurcating from linear eigenstates and threshold resonances of the system; (ii) a continuous branch of edge solitons bifurcating from the previous families at the threshold of the continuous spectrum with a pitchfork bifurcation; and (iii) a finite family of continuous branches of solitons without linear analog. All the solutions are explicitly constructed in terms of elliptic Jacobian functions. Moreover we show that families of nonlinear bound states of the above kind continue to exist in the presence of a uniform magnetic field orthogonal to the plane of the ring when a well definite flux quantization condition holds true. In this sense the magnetic field acts as a control parameter. Finally we highlight the role of resonances in the linearization as a signature of the occurrence of bifurcations of solitons from the continuous spectrum.

Design and Optimization of a Hybrid-Driven Waist Rehabilitation Robot.

PubMed

Zi, Bin; Yin, Guangcai; Zhang, Dan

2016-12-14

In this paper a waist rehabilitation robot driven by cables and pneumatic artificial muscles (PAMs) has been conceptualized and designed. In the process of mechanism design, the human body structure, the waist movement characteristics, and the actuators' driving characteristics are the main considerable factors to make the hybrid-driven waist rehabilitation robot (HWRR) cost-effective, safe, flexible, and well-adapted. A variety of sensors are chosen to measure the position and orientation of the recovery patient to ensure patient safety at the same time as the structure design. According to the structure specialty and function, the HWRR is divided into two independent parallel robots: the waist twist device and the lower limb traction device. Then these two devices are analyzed and evaluated, respectively. Considering the characters of the human body in the HWRR, the inverse kinematics and statics are studied when the waist and the lower limb are considered as a spring and link, respectively. Based on the inverse kinematics and statics, the effect of the contraction parameter of the PAM is considered in the optimization of the waist twist device, and the lower limb traction device is optimized using particle swarm optimization (PSO) to minimize the global conditioning number over the feasible workspace. As a result of the optimization, an optimal rehabilitation robot design is obtained and the condition number of the Jacobian matrix over the feasible workspace is also calculated.

The use of computational thermodynamics for the determination of surface tension and Gibbs-Thomson coefficient of multicomponent alloys

NASA Astrophysics Data System (ADS)

Ferreira, D. J. S.; Bezerra, B. N.; Collyer, M. N.; Garcia, A.; Ferreira, I. L.

2018-04-01

The simulation of casting processes demands accurate information on the thermophysical properties of the alloy; however, such information is scarce in the literature for multicomponent alloys. Generally, metallic alloys applied in industry have more than three solute components. In the present study, a general solution of Butler's formulation for surface tension is presented for multicomponent alloys and is applied in quaternary Al-Cu-Si-Fe alloys, thus permitting the Gibbs-Thomson coefficient to be determined. Such coefficient is a determining factor to the reliability of predictions furnished by microstructure growth models and by numerical computations of solidification thermal parameters, which will depend on the thermophysical properties assumed in the calculations. The Gibbs-Thomson coefficient for ternary and quaternary alloys is seldom reported in the literature. A numerical model based on Powell's hybrid algorithm and a finite difference Jacobian approximation has been coupled to a Thermo-Calc TCAPI interface to assess the excess Gibbs energy of the liquid phase, permitting liquidus temperature, latent heat, alloy density, surface tension and Gibbs-Thomson coefficient for Al-Cu-Si-Fe hypoeutectic alloys to be calculated, as an example of calculation capabilities for multicomponent alloys of the proposed method. The computed results are compared with thermophysical properties of binary Al-Cu and ternary Al-Cu-Si alloys found in the literature and presented as a function of the Cu solute composition.

Efficient 3D inversions using the Richards equation

NASA Astrophysics Data System (ADS)

Cockett, Rowan; Heagy, Lindsey J.; Haber, Eldad

2018-07-01

Fluid flow in the vadose zone is governed by the Richards equation; it is parameterized by hydraulic conductivity, which is a nonlinear function of pressure head. Investigations in the vadose zone typically require characterizing distributed hydraulic properties. Water content or pressure head data may include direct measurements made from boreholes. Increasingly, proxy measurements from hydrogeophysics are being used to supply more spatially and temporally dense data sets. Inferring hydraulic parameters from such datasets requires the ability to efficiently solve and optimize the nonlinear time domain Richards equation. This is particularly important as the number of parameters to be estimated in a vadose zone inversion continues to grow. In this paper, we describe an efficient technique to invert for distributed hydraulic properties in 1D, 2D, and 3D. Our technique does not store the Jacobian matrix, but rather computes its product with a vector. Existing literature for the Richards equation inversion explicitly calculates the sensitivity matrix using finite difference or automatic differentiation, however, for large scale problems these methods are constrained by computation and/or memory. Using an implicit sensitivity algorithm enables large scale inversion problems for any distributed hydraulic parameters in the Richards equation to become tractable on modest computational resources. We provide an open source implementation of our technique based on the SimPEG framework, and show it in practice for a 3D inversion of saturated hydraulic conductivity using water content data through time.

A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

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

Manzini, Gianmarco; Delzanno, Gian Luca; Vencels, Juris

In this study, we present the design and implementation of an L 2-stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations ismore » iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L 2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.« less

A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system

DOE PAGES

Manzini, Gianmarco; Delzanno, Gian Luca; Vencels, Juris; ...

2016-04-22

In this study, we present the design and implementation of an L 2-stable spectral method for the discretization of the Vlasov–Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank–Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations ismore » iteratively solved at any time cycle by a Jacobian-Free Newton–Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre–Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L 2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.« less

Agradient velocity, vortical motion and gravity waves in a rotating shallow-water model

NASA Astrophysics Data System (ADS)

Sutyrin Georgi, G.

2004-07-01

A new approach to modelling slow vortical motion and fast inertia-gravity waves is suggested within the rotating shallow-water primitive equations with arbitrary topography. The velocity is exactly expressed as a sum of the gradient wind, described by the Bernoulli function,B, and the remaining agradient part, proportional to the velocity tendency. Then the equation for inverse potential vorticity,Q, as well as momentum equations for agradient velocity include the same source of intrinsic flow evolution expressed as a single term J (B, Q), where J is the Jacobian operator (for any steady state J (B, Q) = 0). Two components of agradient velocity are responsible for the fast inertia-gravity wave propagation similar to the traditionally used divergence and ageostrophic vorticity. This approach allows for the construction of balance relations for vortical dynamics and potential vorticity inversion schemes even for moderate Rossby and Froude numbers assuming the characteristic value of |J(B, Q)| = to be small. The components of agradient velocity are used as the fast variables slaved to potential vorticity that allows for diagnostic estimates of the velocity tendency, the direct potential vorticity inversion with the accuracy of 2 and the corresponding potential vorticity-conserving agradient velocity balance model (AVBM). The ultimate limitations of constructing the balance are revealed in the form of the ellipticity condition for balanced tendency of the Bernoulli function which incorporates both known criteria of the formal stability: the gradient wind modified by the characteristic vortical Rossby wave phase speed should be subcritical. The accuracy of the AVBM is illustrated by considering the linear normal modes and coastal Kelvin waves in the f-plane channel with topography.

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

DOE PAGES

Bunting, Gregory; Prakash, Arun; Walsh, Timothy; ...

2018-01-26

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

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

Bunting, Gregory; Prakash, Arun; Walsh, Timothy

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Exact self-similarity solution of the Navier-Stokes equations for a porous channel with orthogonally moving walls

NASA Astrophysics Data System (ADS)

Dauenhauer, Eric C.; Majdalani, Joseph

2003-06-01

This article describes a self-similarity solution of the Navier-Stokes equations for a laminar, incompressible, and time-dependent flow that develops within a channel possessing permeable, moving walls. The case considered here pertains to a channel that exhibits either injection or suction across two opposing porous walls while undergoing uniform expansion or contraction. Instances of direct application include the modeling of pulsating diaphragms, sweat cooling or heating, isotope separation, filtration, paper manufacturing, irrigation, and the grain regression during solid propellant combustion. To start, the stream function and the vorticity equation are used in concert to yield a partial differential equation that lends itself to a similarity transformation. Following this similarity transformation, the original problem is reduced to solving a fourth-order differential equation in one similarity variable η that combines both space and time dimensions. Since two of the four auxiliary conditions are of the boundary value type, a numerical solution becomes dependent upon two initial guesses. In order to achieve convergence, the governing equation is first transformed into a function of three variables: The two guesses and η. At the outset, a suitable numerical algorithm is applied by solving the resulting set of twelve first-order ordinary differential equations with two unspecified start-up conditions. In seeking the two unknown initial guesses, the rapidly converging inverse Jacobian method is applied in an iterative fashion. Numerical results are later used to ascertain a deeper understanding of the flow character. The numerical scheme enables us to extend the solution range to physical settings not considered in previous studies. Moreover, the numerical approach broadens the scope to cover both suction and injection cases occurring with simultaneous wall motion.

Application of the generalized vertical coordinate ocean model for better representing satellite data

NASA Technical Reports Server (NTRS)

Song, Y. T.

2002-01-01

It is found that two adaptive parametric functions can be introduced into the basic ocean equations for utilizing the optimal or hybrid features of commonly used z-level, terrain- following, isopycnal, and pressure coordinates in numerical ocean models. The two parametric functions are formulated by combining three techniques: the arbitrary vertical coordinate system of Kasahara (1 974), the Jacobian pressure gradient formulation of Song (1 998), and a newly developed metric factor that permits both compressible (non-Boussinesq) and incompressible (Boussinesq) approximations. Based on the new formulation, an adaptive modeling strategy is proposed and a staggered finite volume method is designed to ensure conservation of important physical properties and numerical accuracy. Implementation of the combined techniques to SCRUM (Song and Haidvogel1994) shows that the adaptive modeling strategy can be applied to any existing ocean model without incurring computational expense or altering the original numerical schemes. Such a generalized coordinate model is expected to benefit diverse ocean modelers for easily choosing optimal vertical structures and sharing modeling resources based on a common model platform. Several representing oceanographic problems with different scales and characteristics, such as coastal canyons, basin-scale circulation, and global ocean circulation, are used to demonstrate the model's capability for multiple applications. New results show that the model is capable of simultaneously resolving both Boussinesq and non-Boussinesq, and both small- and large-scale processes well. This talk will focus on its applications of multiple satellite sensing data in eddy-resolving simulations of Asian Marginal Sea and Kurosio. Attention will be given to how Topex/Poseidon SSH, TRMM SST; and GRACE ocean bottom pressure can be correctly represented in a non- Boussinesq model.

Localized bulging in an inflated cylindrical tube of arbitrary thickness - the effect of bending stiffness

NASA Astrophysics Data System (ADS)

Fu, Y. B.; Liu, J. L.; Francisco, G. S.

2016-05-01

We study localized bulging of a cylindrical hyperelastic tube of arbitrary thickness when it is subjected to the combined action of inflation and axial extension. It is shown that with the internal pressure P and resultant axial force F viewed as functions of the azimuthal stretch on the inner surface and the axial stretch, the bifurcation condition for the initiation of a localized bulge is that the Jacobian of the vector function (P , F) should vanish. This is established using the dynamical systems theory by first computing the eigenvalues of a certain eigenvalue problem governing incremental deformations, and then deriving the bifurcation condition explicitly. The bifurcation condition is valid for all loading conditions, and in the special case of fixed resultant axial force it gives the expected result that the initiation pressure for localized bulging is precisely the maximum pressure in uniform inflation. It is shown that even if localized bulging cannot take place when the axial force is fixed, it is still possible if the axial stretch is fixed instead. The explicit bifurcation condition also provides a means to quantify precisely the effect of bending stiffness on the initiation pressure. It is shown that the (approximate) membrane theory gives good predictions for the initiation pressure, with a relative error less than 5%, for thickness/radius ratios up to 0.67. A two-term asymptotic bifurcation condition for localized bulging that incorporates the effect of bending stiffness is proposed, and is shown to be capable of giving extremely accurate predictions for the initiation pressure for thickness/radius ratios up to as large as 1.2.

A quasi-Newton algorithm for large-scale nonlinear equations.

PubMed

Huang, Linghua

2017-01-01

In this paper, the algorithm for large-scale nonlinear equations is designed by the following steps: (i) a conjugate gradient (CG) algorithm is designed as a sub-algorithm to obtain the initial points of the main algorithm, where the sub-algorithm's initial point does not have any restrictions; (ii) a quasi-Newton algorithm with the initial points given by sub-algorithm is defined as main algorithm, where a new nonmonotone line search technique is presented to get the step length [Formula: see text]. The given nonmonotone line search technique can avoid computing the Jacobian matrix. The global convergence and the [Formula: see text]-order convergent rate of the main algorithm are established under suitable conditions. Numerical results show that the proposed method is competitive with a similar method for large-scale problems.

Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

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

Tronko, Natalia; Brizard, Alain J.

A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center Lagrangian constraint onmore » the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.« less

Ranking of stopping criteria for log domain diffeomorphic demons application in clinical radiation therapy.

PubMed

Peroni, M; Golland, P; Sharp, G C; Baroni, G

2011-01-01

Deformable Image Registration is a complex optimization algorithm with the goal of modeling a non-rigid transformation between two images. A crucial issue in this field is guaranteeing the user a robust but computationally reasonable algorithm. We rank the performances of four stopping criteria and six stopping value computation strategies for a log domain deformable registration. The stopping criteria we test are: (a) velocity field update magnitude, (b) vector field Jacobian, (c) mean squared error, and (d) harmonic energy. Experiments demonstrate that comparing the metric value over the last three iterations with the metric minimum of between four and six previous iterations is a robust and appropriate strategy. The harmonic energy and vector field update magnitude metrics give the best results in terms of robustness and speed of convergence.

Modelling and simulation of a moving interface problem: freeze drying of black tea extract

NASA Astrophysics Data System (ADS)

Aydin, Ebubekir Sıddık; Yucel, Ozgun; Sadikoglu, Hasan

2017-06-01

The moving interface separates the material that is subjected to the freeze drying process as dried and frozen. Therefore, the accurate modeling the moving interface reduces the process time and energy consumption by improving the heat and mass transfer predictions during the process. To describe the dynamic behavior of the drying stages of the freeze-drying, a case study of brewed black tea extract in storage trays including moving interface was modeled that the heat and mass transfer equations were solved using orthogonal collocation method based on Jacobian polynomial approximation. Transport parameters and physical properties describing the freeze drying of black tea extract were evaluated by fitting the experimental data using Levenberg-Marquardt algorithm. Experimental results showed good agreement with the theoretical predictions.

Implicit and Multigrid Method for Ideal Multigrid Convergence: Direct Numerical Simulation of Separated Flow Around NACA 0012 Airfoil

NASA Technical Reports Server (NTRS)

Liu, Chao-Qun; Shan, H.; Jiang, L.

1999-01-01

Numerical investigation of flow separation over a NACA 0012 airfoil at large angles of attack has been carried out. The numerical calculation is performed by solving the full Navier-Stokes equations in generalized curvilinear coordinates. The second-order LU-SGS implicit scheme is applied for time integration. This scheme requires no tridiagonal inversion and is capable of being completely vectorized, provided the corresponding Jacobian matrices are properly selected. A fourth-order centered compact scheme is used for spatial derivatives. In order to reduce numerical oscillation, a sixth-order implicit filter is employed. Non-reflecting boundary conditions are imposed at the far-field and outlet boundaries to avoid possible non-physical wave reflection. Complex flow separation and vortex shedding phenomenon have been observed and discussed.

A trajectory generation and system characterization model for cislunar low-thrust spacecraft. Volume 2: Technical manual

NASA Technical Reports Server (NTRS)

Korsmeyer, David J.; Pinon, Elfego, III; Oconnor, Brendan M.; Bilby, Curt R.

1990-01-01

The documentation of the Trajectory Generation and System Characterization Model for the Cislunar Low-Thrust Spacecraft is presented in Technical and User's Manuals. The system characteristics and trajectories of low thrust nuclear electric propulsion spacecraft can be generated through the use of multiple system technology models coupled with a high fidelity trajectory generation routine. The Earth to Moon trajectories utilize near Earth orbital plane alignment, midcourse control dependent upon the spacecraft's Jacobian constant, and capture to target orbit utilizing velocity matching algorithms. The trajectory generation is performed in a perturbed two-body equinoctial formulation and the restricted three-body formulation. A single control is determined by the user for the interactive midcourse portion of the trajectory. The full spacecraft system characteristics and trajectory are provided as output.

Stability analysis of the phytoplankton effect model on changes in nitrogen concentration on integrated multi-trophic aquaculture systems

NASA Astrophysics Data System (ADS)

Widowati; Putro, S. P.; Silfiana

2018-05-01

Integrated Multi-Trophic Aquaculture (IMTA) is a polyculture with several biotas maintained in it to optimize waste recycling as a food source. The interaction between phytoplankton and nitrogen as waste in fish cultivation including ammonia, nitrite, and nitrate studied in the form of mathematical models. The form model is non-linear systems of differential equations with the four variables. The analytical analysis was used to study the dynamic behavior of this model. Local stability analysis is performed at the equilibrium point with the first step linearized model by using Taylor series, then determined the Jacobian matrix. If all eigenvalues have negative real parts, then the equilibrium of the system is locally asymptotic stable. Some numerical simulations were also demonstrated to verify our analytical result.

A robust direct-integration method for rotorcraft maneuver and periodic response

NASA Technical Reports Server (NTRS)

Panda, Brahmananda

1992-01-01

The Newmark-Beta method and the Newton-Raphson iteration scheme are combined to develop a direct-integration method for evaluating the maneuver and periodic-response expressions for rotorcraft. The method requires the generation of Jacobians and includes higher derivatives in the formulation of the geometric stiffness matrix to enhance the convergence of the system. The method leads to effective convergence with nonlinear structural dynamics and aerodynamic terms. Singularities in the matrices can be addressed with the method as they arise from a Lagrange multiplier approach for coupling equations with nonlinear constraints. The method is also shown to be general enough to handle singularities from quasisteady control-system models. The method is shown to be more general and robust than the similar 2GCHAS method for analyzing rotorcraft dynamics.

New experimental results in atlas-based brain morphometry

NASA Astrophysics Data System (ADS)

Gee, James C.; Fabella, Brian A.; Fernandes, Siddharth E.; Turetsky, Bruce I.; Gur, Ruben C.; Gur, Raquel E.

1999-05-01

In a previous meeting, we described a computational approach to MRI morphometry, in which a spatial warp mapping a reference or atlas image into anatomic alignment with the subject is first inferred. Shape differences with respect to the atlas are then studied by calculating the pointwise Jacobian determinant for the warp, which provides a measure of the change in differential volume about a point in the reference as it transforms to its corresponding position in the subject. In this paper, the method is used to analyze sex differences in the shape and size of the corpus callosum in an ongoing study of a large population of normal controls. The preliminary results of the current analysis support findings in the literature that have observed the splenium to be larger in females than in males.

Two fast approximate wavelet algorithms for image processing, classification, and recognition

NASA Astrophysics Data System (ADS)

Wickerhauser, Mladen V.

1994-07-01

We use large libraries of template waveforms with remarkable orthogonality properties to recast the relatively complex principal orthogonal decomposition (POD) into an optimization problem with a fast solution algorithm. Then it becomes practical to use POD to solve two related problems: recognizing or classifying images, and inverting a complicated map from a low-dimensional configuration space to a high-dimensional measurement space. In the case where the number N of pixels or measurements is more than 1000 or so, the classical O(N3) POD algorithms becomes very costly, but it can be replaced with an approximate best-basis method that has complexity O(N2logN). A variation of POD can also be used to compute an approximate Jacobian for the complicated map.

Symplectic maps and chromatic optics in particle accelerators

DOE PAGES

Cai, Yunhai

2015-07-06

Here, we have applied the nonlinear map method to comprehensively characterize the chromatic optics in particle accelerators. Our approach is built on the foundation of symplectic transfer maps of magnetic elements. The chromatic lattice parameters can be transported from one element to another by the maps. We also introduce a Jacobian operator that provides an intrinsic linkage between the maps and the matrix with parameter dependence. The link allows us to directly apply the formulation of the linear optics to compute the chromatic lattice parameters. As an illustration, we analyze an alternating-gradient cell with nonlinear sextupoles, octupoles, and decapoles andmore » derive analytically their settings for the local chromatic compensation. Finally, the cell becomes nearly perfect up to the third-order of the momentum deviation.« less

On structure-exploiting trust-region regularized nonlinear least squares algorithms for neural-network learning.

PubMed

Mizutani, Eiji; Demmel, James W

2003-01-01

This paper briefly introduces our numerical linear algebra approaches for solving structured nonlinear least squares problems arising from 'multiple-output' neural-network (NN) models. Our algorithms feature trust-region regularization, and exploit sparsity of either the 'block-angular' residual Jacobian matrix or the 'block-arrow' Gauss-Newton Hessian (or Fisher information matrix in statistical sense) depending on problem scale so as to render a large class of NN-learning algorithms 'efficient' in both memory and operation costs. Using a relatively large real-world nonlinear regression application, we shall explain algorithmic strengths and weaknesses, analyzing simulation results obtained by both direct and iterative trust-region algorithms with two distinct NN models: 'multilayer perceptrons' (MLP) and 'complementary mixtures of MLP-experts' (or neuro-fuzzy modular networks).

Finite element implementation of state variable-based viscoplasticity models

NASA Technical Reports Server (NTRS)

Iskovitz, I.; Chang, T. Y. P.; Saleeb, A. F.

1991-01-01

The implementation of state variable-based viscoplasticity models is made in a general purpose finite element code for structural applications of metals deformed at elevated temperatures. Two constitutive models, Walker's and Robinson's models, are studied in conjunction with two implicit integration methods: the trapezoidal rule with Newton-Raphson iterations and an asymptotic integration algorithm. A comparison is made between the two integration methods, and the latter method appears to be computationally more appealing in terms of numerical accuracy and CPU time. However, in order to make the asymptotic algorithm robust, it is necessary to include a self adaptive scheme with subincremental step control and error checking of the Jacobian matrix at the integration points. Three examples are given to illustrate the numerical aspects of the integration methods tested.

A fully-implicit high-order system thermal-hydraulics model for advanced non-LWR safety analyses

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

Hu, Rui

An advanced system analysis tool is being developed for advanced reactor safety analysis. This paper describes the underlying physics and numerical models used in the code, including the governing equations, the stabilization schemes, the high-order spatial and temporal discretization schemes, and the Jacobian Free Newton Krylov solution method. The effects of the spatial and temporal discretization schemes are investigated. Additionally, a series of verification test problems are presented to confirm the high-order schemes. Furthermore, it is demonstrated that the developed system thermal-hydraulics model can be strictly verified with the theoretical convergence rates, and that it performs very well for amore » wide range of flow problems with high accuracy, efficiency, and minimal numerical diffusions.« less

A fully-implicit high-order system thermal-hydraulics model for advanced non-LWR safety analyses

DOE PAGES

Hu, Rui

2016-11-19

An advanced system analysis tool is being developed for advanced reactor safety analysis. This paper describes the underlying physics and numerical models used in the code, including the governing equations, the stabilization schemes, the high-order spatial and temporal discretization schemes, and the Jacobian Free Newton Krylov solution method. The effects of the spatial and temporal discretization schemes are investigated. Additionally, a series of verification test problems are presented to confirm the high-order schemes. Furthermore, it is demonstrated that the developed system thermal-hydraulics model can be strictly verified with the theoretical convergence rates, and that it performs very well for amore » wide range of flow problems with high accuracy, efficiency, and minimal numerical diffusions.« less

Solving coupled groundwater flow systems using a Jacobian Free Newton Krylov method

NASA Astrophysics Data System (ADS)

Mehl, S.

2012-12-01

Jacobian Free Newton Kyrlov (JFNK) methods can have several advantages for simulating coupled groundwater flow processes versus conventional methods. Conventional methods are defined here as those based on an iterative coupling (rather than a direct coupling) and/or that use Picard iteration rather than Newton iteration. In an iterative coupling, the systems are solved separately, coupling information is updated and exchanged between the systems, and the systems are re-solved, etc., until convergence is achieved. Trusted simulators, such as Modflow, are based on these conventional methods of coupling and work well in many cases. An advantage of the JFNK method is that it only requires calculation of the residual vector of the system of equations and thus can make use of existing simulators regardless of how the equations are formulated. This opens the possibility of coupling different process models via augmentation of a residual vector by each separate process, which often requires substantially fewer changes to the existing source code than if the processes were directly coupled. However, appropriate perturbation sizes need to be determined for accurate approximations of the Frechet derivative, which is not always straightforward. Furthermore, preconditioning is necessary for reasonable convergence of the linear solution required at each Kyrlov iteration. Existing preconditioners can be used and applied separately to each process which maximizes use of existing code and robust preconditioners. In this work, iteratively coupled parent-child local grid refinement models of groundwater flow and groundwater flow models with nonlinear exchanges to streams are used to demonstrate the utility of the JFNK approach for Modflow models. Use of incomplete Cholesky preconditioners with various levels of fill are examined on a suite of nonlinear and linear models to analyze the effect of the preconditioner. Comparisons of convergence and computer simulation time are made using conventional iteratively coupled methods and those based on Picard iteration to those formulated with JFNK to gain insights on the types of nonlinearities and system features that make one approach advantageous. Results indicate that nonlinearities associated with stream/aquifer exchanges are more problematic than those resulting from unconfined flow.

A Numerical Testbed for Remote Sensing of Aerosols, and its Demonstration for Evaluating Retrieval Synergy from a Geostationary Satellite Constellation of GEO-CAPE and GOES-R

NASA Technical Reports Server (NTRS)

Wang, Jun; Xu, Xiaoguang; Ding, Shouguo; Zeng, Jing; Spurr, Robert; Liu, Xiong; Chance, Kelly; Mishchenko, Michael I.

2014-01-01

We present a numerical testbed for remote sensing of aerosols, together with a demonstration for evaluating retrieval synergy from a geostationary satellite constellation. The testbed combines inverse (optimal-estimation) software with a forward model containing linearized code for computing particle scattering (for both spherical and non-spherical particles), a kernel-based (land and ocean) surface bi-directional reflectance facility, and a linearized radiative transfer model for polarized radiance. Calculation of gas absorption spectra uses the HITRAN (HIgh-resolution TRANsmission molecular absorption) database of spectroscopic line parameters and other trace species cross-sections. The outputs of the testbed include not only the Stokes 4-vector elements and their sensitivities (Jacobians) with respect to the aerosol single scattering and physical parameters (such as size and shape parameters, refractive index, and plume height), but also DFS (Degree of Freedom for Signal) values for retrieval of these parameters. This testbed can be used as a tool to provide an objective assessment of aerosol information content that can be retrieved for any constellation of (planned or real) satellite sensors and for any combination of algorithm design factors (in terms of wavelengths, viewing angles, radiance and/or polarization to be measured or used). We summarize the components of the testbed, including the derivation and validation of analytical formulae for Jacobian calculations. Benchmark calculations from the forward model are documented. In the context of NASA's Decadal Survey Mission GEOCAPE (GEOstationary Coastal and Air Pollution Events), we demonstrate the use of the testbed to conduct a feasibility study of using polarization measurements in and around the O2 A band for the retrieval of aerosol height information from space, as well as an to assess potential improvement in the retrieval of aerosol fine and coarse mode aerosol optical depth (AOD) through the synergic use of two future geostationary satellites, GOES-R (Geostationary Operational Environmental Satellite R-series) and TEMPO (Tropospheric Emissions: Monitoring of Pollution). Strong synergy between GEOS-R and TEMPO are found especially in their characterization of surface bi-directional reflectance, and thereby, can potentially improve the AOD retrieval to the accuracy required by GEO-CAPE.

Non-pairwise additivity of the leading-order dispersion energy

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

Hollett, Joshua W., E-mail: j.hollett@uwinnipeg.ca

2015-02-28

The leading-order (i.e., dipole-dipole) dispersion energy is calculated for one-dimensional (1D) and two-dimensional (2D) infinite lattices, and an infinite 1D array of infinitely long lines, of doubly occupied locally harmonic wells. The dispersion energy is decomposed into pairwise and non-pairwise additive components. By varying the force constant and separation of the wells, the non-pairwise additive contribution to the dispersion energy is shown to depend on the overlap of density between neighboring wells. As well separation is increased, the non-pairwise additivity of the dispersion energy decays. The different rates of decay for 1D and 2D lattices of wells is explained inmore » terms of a Jacobian effect that influences the number of nearest neighbors. For an array of infinitely long lines of wells spaced 5 bohrs apart, and an inter-well spacing of 3 bohrs within a line, the non-pairwise additive component of the leading-order dispersion energy is −0.11 kJ mol{sup −1} well{sup −1}, which is 7% of the total. The polarizability of the wells and the density overlap between them are small in comparison to that of the atomic densities that arise from the molecular density partitioning used in post-density-functional theory (DFT) damped dispersion corrections, or DFT-D methods. Therefore, the nonadditivity of the leading-order dispersion observed here is a conservative estimate of that in molecular clusters.« less

Subcortical shape and volume abnormalities in an elderly HIV+ cohort

NASA Astrophysics Data System (ADS)

Wade, Benjamin S. C.; Valcour, Victor; Busovaca, Edgar; Esmaeili-Firidouni, Pardis; Joshi, Shantanu H.; Wang, Yalin; Thompson, Paul M.

2015-03-01

Over 50% of HIV+ individuals show significant impairment in psychomotor functioning, processing speed, working memory and attention [1, 2]. Patients receiving combination antiretroviral therapy may still have subcortical atrophy, but the profile of HIV-associated brain changes is poorly understood. With parametric surface-based shape analyses, we mapped the 3D profile of subcortical morphometry in 63 elderly HIV+ subjects (4 female; age=65.35 ± 2.21) and 31 uninfected elderly controls (2 female; age=64.68 ± 4.57) scanned with MRI as part of a San Francisco Bay Area study of elderly people with HIV. We also investigated whether morphometry was associated with nadir CD4+ (T-cell) counts, viral load and illness duration among HIV+ participants. FreeSurfer was used to segment the thalamus, caudate, putamen, pallidum, hippocampus, amygdala, accumbens, brainstem, callosum and ventricles from brain MRI scans. To study subcortical shape, we analyzed: (1) the Jacobian determinant (JD) indexed over structures' surface coordinates and (2) radial distances (RD) of structure surfaces from a medial curve. A JD less than 1 reflects regional tissue atrophy and greater than 1 reflects expansion. The volumes of several subcortical regions were found to be associated with HIV status. No regional volumes showed detectable associations with CD4 counts, viral load or illness duration. The shapes of numerous subcortical regions were significantly linked to HIV status, detectability of viral RNA and illness duration. Our results show subcortical brain differences in HIV+ subjects in both shape and volumetric domains.

Assessment of Polarization Effect on Efficiency of Levenberg-Marquardt Algorithm in Case of Thin Atmosphere Over Black Surface

NASA Technical Reports Server (NTRS)

Korkin, S.; Lyapustin, A.

2012-01-01

The Levenberg-Marquardt algorithm [1, 2] provides a numerical iterative solution to the problem of minimization of a function over a space of its parameters. In our work, the Levenberg-Marquardt algorithm retrieves optical parameters of a thin (single scattering) plane parallel atmosphere irradiated by collimated infinitely wide monochromatic beam of light. Black ground surface is assumed. Computational accuracy, sensitivity to the initial guess and the presence of noise in the signal, and other properties of the algorithm are investigated in scalar (using intensity only) and vector (including polarization) modes. We consider an atmosphere that contains a mixture of coarse and fine fractions. Following [3], the fractions are simulated using Henyey-Greenstein model. Though not realistic, this assumption is very convenient for tests [4, p.354]. In our case it yields analytical evaluation of Jacobian matrix. Assuming the MISR geometry of observation [5] as an example, the average scattering cosines and the ratio of coarse and fine fractions, the atmosphere optical depth, and the single scattering albedo, are the five parameters to be determined numerically. In our implementation of the algorithm, the system of five linear equations is solved using the fast Cramer s rule [6]. A simple subroutine developed by the authors, makes the algorithm independent from external libraries. All Fortran 90/95 codes discussed in the presentation will be available immediately after the meeting from sergey.v.korkin@nasa.gov by request.

Brain Surface Conformal Parameterization Using Riemann Surface Structure

PubMed Central

Wang, Yalin; Lui, Lok Ming; Gu, Xianfeng; Hayashi, Kiralee M.; Chan, Tony F.; Toga, Arthur W.; Thompson, Paul M.; Yau, Shing-Tung

2011-01-01

In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable (their solutions tend to be smooth functions and the boundary conditions of the Dirichlet problem can be enforced). Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3-D brain surface manifolds to modified PDEs on a two-dimensional parameter domain. Since the Jacobian matrix of a conformal parameterization is diagonal, the modified PDE on the parameter domain is readily solved. To illustrate our techniques, we computed parameterizations for several types of anatomical surfaces in 3-D magnetic resonance imaging scans of the brain, including the cerebral cortex, hippocampi, and lateral ventricles. For surfaces that are topologically homeomorphic to each other and have similar geometrical structures, we show that the parameterization results are consistent and the subdivided surfaces can be matched to each other. Finally, we present an automatic sulcal landmark location algorithm by solving PDEs on cortical surfaces. The landmark detection results are used as constraints for building conformal maps between surfaces that also match explicitly defined landmarks. PMID:17679336

Implementation of Radiation, Ablation, and Free Energy Minimization Modules for Coupled Simulations of Hypersonic Flow

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.; Johnston, Christopher O.; Thompson, Richard A.

2009-01-01

A description of models and boundary conditions required for coupling radiation and ablation physics to a hypersonic flow simulation is provided. Chemical equilibrium routines for varying elemental mass fraction are required in the flow solver to integrate with the equilibrium chemistry assumption employed in the ablation models. The capability also enables an equilibrium catalytic wall boundary condition in the non-ablating case. The paper focuses on numerical implementation issues using FIRE II, Mars return, and Apollo 4 applications to provide context for discussion. Variable relaxation factors applied to the Jacobian elements of partial equilibrium relations required for convergence are defined. Challenges of strong radiation coupling in a shock capturing algorithm are addressed. Results are presented to show how the current suite of models responds to a wide variety of conditions involving coupled radiation and ablation.

MOOSE: A PARALLEL COMPUTATIONAL FRAMEWORK FOR COUPLED SYSTEMS OF NONLINEAR EQUATIONS.

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

G. Hansen; C. Newman; D. Gaston

Systems of coupled, nonlinear partial di?erential equations often arise in sim- ulation of nuclear processes. MOOSE: Multiphysics Ob ject Oriented Simulation Environment, a parallel computational framework targeted at solving these systems is presented. As opposed to traditional data / ?ow oriented com- putational frameworks, MOOSE is instead founded on mathematics based on Jacobian-free Newton Krylov (JFNK). Utilizing the mathematical structure present in JFNK, physics are modularized into “Kernels” allowing for rapid production of new simulation tools. In addition, systems are solved fully cou- pled and fully implicit employing physics based preconditioning allowing for a large amount of ?exibility even withmore » large variance in time scales. Background on the mathematics, an inspection of the structure of MOOSE and several rep- resentative solutions from applications built on the framework are presented.« less

On the Hardy Space Theory of Compensated Compactness Quantities

NASA Astrophysics Data System (ADS)

Lindberg, Sauli

2017-05-01

We make progress on a problem of Coifman et al. (J Math Pures Appl (9) 72(3): 247-286, 1993) by showing that the Jacobian operator J does not map {W^{1,n}(Rn, Rn) onto the Hardy space H1(Rn) for any {n ≥ 2}. The related question about the surjectivity of {J : dot{W}^{1,n}(Rn,Rn) to H1(Rn) is still open. The second main result and its variants reduce the proof of H1 regularity of a large class of compensated compactness quantities to an integration by parts or easy arithmetic, and applications are presented. Furthermore, we exhibit a class of nonlinear partial differential operators in which weak sequential continuity is a strictly stronger condition than H1 regularity, shedding light on another question of Coifman, Lions, Meyer and Semmes.

Improving the accuracy of central difference schemes

NASA Technical Reports Server (NTRS)

Turkel, Eli

1988-01-01

General difference approximations to the fluid dynamic equations require an artificial viscosity in order to converge to a steady state. This artificial viscosity serves two purposes. One is to suppress high frequency noise which is not damped by the central differences. The second purpose is to introduce an entropy-like condition so that shocks can be captured. These viscosities need a coefficient to measure the amount of viscosity to be added. In the standard scheme, a scalar coefficient is used based on the spectral radius of the Jacobian of the convective flux. However, this can add too much viscosity to the slower waves. Hence, it is suggested that a matrix viscosity be used. This gives an appropriate viscosity for each wave component. With this matrix valued coefficient, the central difference scheme becomes closer to upwind biased methods.

Kinematics of the six-degree-of-freedom force-reflecting Kraft Master

NASA Technical Reports Server (NTRS)

Williams, Robert L., II

1991-01-01

Presented here are kinematic equations for a six degree of freedom force-reflecting hand controller. The forward kinematics solution is developed and shown in simplified form. The Jacobian matrix, which uses terms from the forward kinematics solution, is derived. Both of these kinematic solutions require joint angle inputs. A calibration method is presented to determine the hand controller joint angles given the respective potentiometer readings. The kinematic relationship describing the mechanical coupling between the hand and controller shoulder and elbow joints is given. These kinematic equations may be used in an algorithm to control the hand controller as a telerobotic system component. The purpose of the hand controller is two-fold: operator commands to the telerobotic system are entered using the hand controller, and contact forces and moments from the task are reflected to the operator via the hand controller.

Computer coordination of limb motion for a three-legged walking robot

NASA Technical Reports Server (NTRS)

Klein, C. A.; Patterson, M. R.

1980-01-01

Coordination of the limb motion of a vehicle which could perform assembly and maintenance operations on large structures in space is described. Manipulator kinematics and walking robots are described. The basic control scheme of the robot is described. The control of the individual arms are described. Arm velocities are generally described in Cartesian coordinates. Cartesian velocities are converted to joint velocities using the Jacobian matrix. The calculation of a trajectory for an arm given a sequence of points through which it is to pass is described. The free gait algorithm which controls the lifting and placing of legs for the robot is described. The generation of commanded velocities for the robot, and the implementation of those velocities by the algorithm are discussed. Suggestions for further work in the area of robot legged locomotion are presented.

A spatial operator algebra for manipulator modeling and control

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Kreutz, K.; Milman, M.

1988-01-01

A powerful new spatial operator algebra for modeling, control, and trajectory design of manipulators is discussed along with its implementation in the Ada programming language. Applications of this algebra to robotics include an operator representation of the manipulator Jacobian matrix; the robot dynamical equations formulated in terms of the spatial algebra, showing the complete equivalence between the recursive Newton-Euler formulations to robot dynamics; the operator factorization and inversion of the manipulator mass matrix which immediately results in O(N) recursive forward dynamics algorithms; the joint accelerations of a manipulator due to a tip contact force; the recursive computation of the equivalent mass matrix as seen at the tip of a manipulator; and recursive forward dynamics of a closed chain system. Finally, additional applications and current research involving the use of the spatial operator algebra are discussed in general terms.

MOOSE: A parallel computational framework for coupled systems of nonlinear equations.

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

Derek Gaston; Chris Newman; Glen Hansen

Systems of coupled, nonlinear partial differential equations (PDEs) often arise in simulation of nuclear processes. MOOSE: Multiphysics Object Oriented Simulation Environment, a parallel computational framework targeted at the solution of such systems, is presented. As opposed to traditional data-flow oriented computational frameworks, MOOSE is instead founded on the mathematical principle of Jacobian-free Newton-Krylov (JFNK) solution methods. Utilizing the mathematical structure present in JFNK, physics expressions are modularized into `Kernels,'' allowing for rapid production of new simulation tools. In addition, systems are solved implicitly and fully coupled, employing physics based preconditioning, which provides great flexibility even with large variance in timemore » scales. A summary of the mathematics, an overview of the structure of MOOSE, and several representative solutions from applications built on the framework are presented.« less

On the dynamics of a small body under the influence of a Maxwell ring-type N-body system with a spheroidal central body: Focal curves

NASA Astrophysics Data System (ADS)

Kalvouridis, T.; Fakis, D.

2013-09-01

One of the most interesting aspects which characterize the dynamics of a small body under the influence of a regular polygon formation of N bodies with a spheroidal central primary, is related to the zero-velocity surfaces which, for a given set of the problem's parameters, separate the regions where particle planar motion is permitted from those where this motion is impossible. The non-sphericity of the central primary is here described by adding an inverse cube corrective term to Newton's law of gravitation, when applied both between the central primary and a peripheral one and between this primary and the small body. A similar expression of the potential including a corrective term was proposed by Manev in 1924 in his effort to describe some special physical properties of a body like radiation emission, or to explain some relativistic effects without using the theory of relativity. The version of the problem we deal with, is characterized by three parameters, namely, the number ?=N-1 of the peripheral primaries, the mass parameter (ratio of the central mass m0 to the mass m of a peripheral body) and the oblateness parameter e, which appears in the non-Newtonian term of the force function related to the central primary. Parameter ? takes only positive values, while parameter e can take small real values either positive (oblate body) or negative (prolate body). By using the existing Jacobian-type integral which characterizes the planar motion of the particle in the synodic coordinate system Oxyz located at the mass center O of the system, and by superposing the zerovelocity surfaces C=C(x,y, z=0; ?, e) (where C is the Jacobian constant) drawn for a given configuration ?, we observe that: (i) when e is kept constant and ? varies, then the central parts of all these surfaces ,which evolve around the central primary, intersect along one continuous curve while, (ii) when ? is kept constant and e varies, then, depending on either positive or negative values of e, the central parts of all these surfaces intersect along either one or two common continuous curves respectively. We call these curves focal curves due to their aforementioned property. As it is expected, they display all the symmetry elements of the primaries arrangement in rotations around an axis perpendicular to the xy-plane through an angle 2?/?. We shall prove that in case (i) the focal curve is independent of parameter e, while in case (ii) the focal curves (or curve) are independent of parameter ?. It should be noted that, a similar property concerning the zero-velocity surfaces has been discovered by one of the present authors (Kalvouridis, 2004) during the investigation of the particle dynamics in the Newtonian field of a regular polygon formation of N spherical massive bodies. Another aspect dealt with in the present paper, is the mechanism of the parametric evolution of the focal curves and the effects of this property on the equilibrium locations and the periodic motions of the particle.

Singularity and workspace analysis of three isoconstrained parallel manipulators with schoenflies motion

NASA Astrophysics Data System (ADS)

Lee, Po-Chih; Lee, Jyh-Jone

2012-06-01

This paper presents the analysis of three parallel manipulators with Schoenflies-motion. Each parallel manipulator possesses two limbs in structure and the end-effector has three DOFs (degree of freedom) in the translational motion and one DOF in rotational motion about a given direction axis with respect to the world coordinate system. The three isoconstrained parallel manipulators have the structures denoted as C{u/u}UwHw-//-C{v/v}UwHw, CuR{u/u}Uhw-//-CvR{v/v}Uhw and CuPuUhw-//-CvPvUhw. The kinematic equations are first introduced for each manipulator. Then, Jacobian matrix, singularity, workspace, and performance index for each mechanism are subsequently derived and analysed for the first time. The results can be helpful for the engineers to evaluate such kind of parallel robots for possible application in industry where pick-and-place motion is required.

Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity, and Linear Models

DOE PAGES

Bernstein, Andrey; Wang, Cong; Dall'Anese, Emiliano; ...

2018-01-01

This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the Z-bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations. Explicit conditions for existence and uniqueness of load-flow solutions are presented. These conditions also guarantee convergence of the load-flow algorithm to the unique solution. The proposed methodology is applicable to generic systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. Further, a sufficient condition for themore » non-singularity of the load-flow Jacobian is proposed. Finally, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders.« less

1D-VAR Retrieval Using Superchannels

NASA Technical Reports Server (NTRS)

Liu, Xu; Zhou, Daniel; Larar, Allen; Smith, William L.; Schluessel, Peter; Mango, Stephen; SaintGermain, Karen

2008-01-01

Since modern ultra-spectral remote sensors have thousands of channels, it is difficult to include all of them in a 1D-var retrieval system. We will describe a physical inversion algorithm, which includes all available channels for the atmospheric temperature, moisture, cloud, and surface parameter retrievals. Both the forward model and the inversion algorithm compress the channel radiances into super channels. These super channels are obtained by projecting the radiance spectra onto a set of pre-calculated eigenvectors. The forward model provides both super channel properties and jacobian in EOF space directly. For ultra-spectral sensors such as Infrared Atmospheric Sounding Interferometer (IASI) and the NPOESS Airborne Sounder Testbed Interferometer (NAST), a compression ratio of more than 80 can be achieved, leading to a significant reduction in computations involved in an inversion process. Results will be shown applying the algorithm to real IASI and NAST data.

Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons

NASA Astrophysics Data System (ADS)

Bao, L.; Kleinschmidt, A.; Nilsson, B. E. W.; Persson, D.; Pioline, B.

2013-12-01

Type IIA string theory compactified on a rigid Calabi-Yau threefold gives rise to a classical moduli space that carries an isometric action of U(2, 1). Various quantum corrections break this continuous isometry to a discrete subgroup. Focussing on the case where the intermediate Jacobian of the Calabi-Yau admits complex multiplication by the ring of quadratic imaginary integers d, we argue that the remaining quantum duality group is an arithmetic Picard modular group PU(2, 1; d). Based on this proposal we construct an Eisenstein series invariant under this duality group and study its non-Abelian Fourier expansion. This allows the prediction of non-perturbative effects, notably the contribution of D2- and NS5-brane instantons. The present work extends our previous analysis in 0909.4299 which was restricted to the special case of the Gaussian integers 1 = Bbb Z[i].

Combinatorial Algorithms to Enable Computational Science and Engineering: Work from the CSCAPES Institute

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

Boman, Erik G.; Catalyurek, Umit V.; Chevalier, Cedric

2015-01-16

This final progress report summarizes the work accomplished at the Combinatorial Scientific Computing and Petascale Simulations Institute. We developed Zoltan, a parallel mesh partitioning library that made use of accurate hypergraph models to provide load balancing in mesh-based computations. We developed several graph coloring algorithms for computing Jacobian and Hessian matrices and organized them into a software package called ColPack. We developed parallel algorithms for graph coloring and graph matching problems, and also designed multi-scale graph algorithms. Three PhD students graduated, six more are continuing their PhD studies, and four postdoctoral scholars were advised. Six of these students and Fellowsmore » have joined DOE Labs (Sandia, Berkeley), as staff scientists or as postdoctoral scientists. We also organized the SIAM Workshop on Combinatorial Scientific Computing (CSC) in 2007, 2009, and 2011 to continue to foster the CSC community.« less

Oscillator strengths, first-order properties, and nuclear gradients for local ADC(2).

PubMed

Schütz, Martin

2015-06-07

We describe theory and implementation of oscillator strengths, orbital-relaxed first-order properties, and nuclear gradients for the local algebraic diagrammatic construction scheme through second order. The formalism is derived via time-dependent linear response theory based on a second-order unitary coupled cluster model. The implementation presented here is a modification of our previously developed algorithms for Laplace transform based local time-dependent coupled cluster linear response (CC2LR); the local approximations thus are state specific and adaptive. The symmetry of the Jacobian leads to considerable simplifications relative to the local CC2LR method; as a result, a gradient evaluation is about four times less expensive. Test calculations show that in geometry optimizations, usually very similar geometries are obtained as with the local CC2LR method (provided that a second-order method is applicable). As an exemplary application, we performed geometry optimizations on the low-lying singlet states of chlorophyllide a.

Random Weighting, Strong Tracking, and Unscented Kalman Filter for Soft Tissue Characterization.

PubMed

Shin, Jaehyun; Zhong, Yongmin; Oetomo, Denny; Gu, Chengfan

2018-05-21

This paper presents a new nonlinear filtering method based on the Hunt-Crossley model for online nonlinear soft tissue characterization. This method overcomes the problem of performance degradation in the unscented Kalman filter due to contact model error. It adopts the concept of Mahalanobis distance to identify contact model error, and further incorporates a scaling factor in predicted state covariance to compensate identified model error. This scaling factor is determined according to the principle of innovation orthogonality to avoid the cumbersome computation of Jacobian matrix, where the random weighting concept is adopted to improve the estimation accuracy of innovation covariance. A master-slave robotic indentation system is developed to validate the performance of the proposed method. Simulation and experimental results as well as comparison analyses demonstrate that the efficacy of the proposed method for online characterization of soft tissue parameters in the presence of contact model error.

Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity, and Linear Models

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

Bernstein, Andrey; Wang, Cong; Dall'Anese, Emiliano

This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the Z-bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations. Explicit conditions for existence and uniqueness of load-flow solutions are presented. These conditions also guarantee convergence of the load-flow algorithm to the unique solution. The proposed methodology is applicable to generic systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. Further, a sufficient condition for themore » non-singularity of the load-flow Jacobian is proposed. Finally, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders.« less

Optimal trajectories for aeroassisted orbital transfer

NASA Technical Reports Server (NTRS)

Miele, A.; Venkataraman, P.

1983-01-01

Consideration is given to classical and minimax problems involved in aeroassisted transfer from high earth orbit (HEO) to low earth orbit (LEO). The transfer is restricted to coplanar operation, with trajectory control effected by means of lift modulation. The performance of the maneuver is indexed to the energy expenditure or, alternatively, the time integral of the heating rate. Firist-order optimality conditions are defined for the classical approach, as are a sequential gradient-restoration algorithm and a combined gradient-restoration algorithm. Minimization techniques are presented for the aeroassisted transfer energy consumption and time-delay integral of the heating rate, as well as minimization of the pressure. It is shown that the eigenvalues of the Jacobian matrix of the differential system is both stiff and unstable, implying that the sequential gradient restoration algorithm in its present version is unsuitable. A new method, involving a multipoint approach to the two-poing boundary value problem, is recommended.

A Feasibility Study on a Parallel Mechanism for Examining the Space Shuttle Orbiter Payload Bay Radiators

NASA Technical Reports Server (NTRS)

Roberts, Rodney G.; LopezdelCastillo, Eduardo

1996-01-01

The goal of the project was to develop the necessary analysis tools for a feasibility study of a cable suspended robot system for examining the space shuttle orbiter payload bay radiators These tools were developed to address design issues such as workspace size, tension requirements on the cable, the necessary accuracy and resolution requirements and the stiffness and movement requirements of the system. This report describes the mathematical models for studying the inverse kinematics, statics, and stiffness of the robot. Each model is described by a matrix. The manipulator Jacobian was also related to the stiffness matrix, which characterized the stiffness of the system. Analysis tools were then developed based on the singular value decomposition (SVD) of the corresponding matrices. It was demonstrated how the SVD can be used to quantify the robot's performance and to provide insight into different design issues.

Multirate Particle-in-Cell Time Integration Techniques of Vlasov-Maxwell Equations for Collisionless Kinetic Plasma Simulations

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

Chen, Guangye; Chacon, Luis; Knoll, Dana Alan

2015-07-31

A multi-rate PIC formulation was developed that employs large timesteps for slow field evolution, and small (adaptive) timesteps for particle orbit integrations. Implementation is based on a JFNK solver with nonlinear elimination and moment preconditioning. The approach is free of numerical instabilities (ω peΔt >>1, and Δx >> λ D), and requires many fewer dofs (vs. explicit PIC) for comparable accuracy in challenging problems. Significant gains (vs. conventional explicit PIC) may be possible for large scale simulations. The paper is organized as follows: Vlasov-Maxwell Particle-in-cell (PIC) methods for plasmas; Explicit, semi-implicit, and implicit time integrations; Implicit PIC formulation (Jacobian-Free Newton-Krylovmore » (JFNK) with nonlinear elimination allows different treatments of disparate scales, discrete conservation properties (energy, charge, canonical momentum, etc.)); Some numerical examples; and Summary.« less

Implementation of a kappa-epsilon turbulence model to RPLUS3D code

NASA Technical Reports Server (NTRS)

Chitsomboon, Tawit

1992-01-01

The RPLUS3D code has been developed at the NASA Lewis Research Center to support the National Aerospace Plane (NASP) project. The code has the ability to solve three dimensional flowfields with finite rate combustion of hydrogen and air. The combustion process of the hydrogen-air system are simulated by an 18 reaction path, 8 species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though a fully implicit numerical algorithm is used. A k-epsilon turbulence model has recently been incorporated into the code. Initial validations have been conducted for a flow over a flat plate. Results of the validation studies are shown. Some difficulties in implementing the k-epsilon equations to the code are also discussed.

Implementation of a kappa-epsilon turbulence model to RPLUS3D code

NASA Astrophysics Data System (ADS)

Chitsomboon, Tawit

1992-02-01

The RPLUS3D code has been developed at the NASA Lewis Research Center to support the National Aerospace Plane (NASP) project. The code has the ability to solve three dimensional flowfields with finite rate combustion of hydrogen and air. The combustion process of the hydrogen-air system are simulated by an 18 reaction path, 8 species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though a fully implicit numerical algorithm is used. A k-epsilon turbulence model has recently been incorporated into the code. Initial validations have been conducted for a flow over a flat plate. Results of the validation studies are shown. Some difficulties in implementing the k-epsilon equations to the code are also discussed.

On coupling fluid plasma and kinetic neutral physics models

DOE PAGES

Joseph, I.; Rensink, M. E.; Stotler, D. P.; ...

2017-03-01

The coupled fluid plasma and kinetic neutral physics equations are analyzed through theory and simulation of benchmark cases. It is shown that coupling methods that do not treat the coupling rates implicitly are restricted to short time steps for stability. Fast charge exchange, ionization and recombination coupling rates exist, even after constraining the solution by requiring that the neutrals are at equilibrium. For explicit coupling, the present implementation of Monte Carlo correlated sampling techniques does not allow for complete convergence in slab geometry. For the benchmark case, residuals decay with particle number and increase with grid size, indicating that theymore » scale in a manner that is similar to the theoretical prediction for nonlinear bias error. Progress is reported on implementation of a fully implicit Jacobian-free Newton–Krylov coupling scheme. The present block Jacobi preconditioning method is still sensitive to time step and methods that better precondition the coupled system are under investigation.« less

The generalized DMPK equation revisited: towards a systematic derivation

NASA Astrophysics Data System (ADS)

Douglas, Andrew; Markoš, Peter; Muttalib, K. A.

2014-03-01

The generalized Dorokov-Mello-Pereyra-Kumar (DMPK) equation has recently been used to obtain a family of very broad and highly asymmetric conductance distributions for three-dimensional disordered conductors. However, there are two major criticisms of the derivation of the generalized DMPK equation: (1) certain eigenvector correlations were neglected based on qualitative arguments that cannot be valid for all strengths of disorder, and (2) the repulsion between two closely spaced eigenvalues were not rigorously governed by symmetry considerations. In this work we show that it is possible to address both criticisms by including the eigenvalue and eigenvector correlations in a systematic and controlled way. It turns out that the added correlations determine the evolution of the Jacobian, without affecting the evaluation of the conductance distributions. They also guarantee the symmetry requirements. In addition, we obtain an exact relationship between the eigenvectors and the Lyapunov exponents leading to a sum rule for the latter at all disorder strengths.

Fluid preconditioning for Newton–Krylov-based, fully implicit, electrostatic particle-in-cell simulations

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

Chen, G., E-mail: gchen@lanl.gov; Chacón, L.; Leibs, C.A.

2014-02-01

A recent proof-of-principle study proposes an energy- and charge-conserving, nonlinearly implicit electrostatic particle-in-cell (PIC) algorithm in one dimension [9]. The algorithm in the reference employs an unpreconditioned Jacobian-free Newton–Krylov method, which ensures nonlinear convergence at every timestep (resolving the dynamical timescale of interest). Kinetic enslavement, which is one key component of the algorithm, not only enables fully implicit PIC as a practical approach, but also allows preconditioning the kinetic solver with a fluid approximation. This study proposes such a preconditioner, in which the linearized moment equations are closed with moments computed from particles. Effective acceleration of the linear GMRES solvemore » is demonstrated, on both uniform and non-uniform meshes. The algorithm performance is largely insensitive to the electron–ion mass ratio. Numerical experiments are performed on a 1D multi-scale ion acoustic wave test problem.« less

Second- and third-order upwind difference schemes for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Yang, J. Y.

1984-01-01

Second- and third-order two time-level five-point explicit upwind-difference schemes are described for the numerical solution of hyperbolic systems of conservation laws and applied to the Euler equations of inviscid gas dynamics. Nonliner smoothing techniques are used to make the schemes total variation diminishing. In the method both hyperbolicity and conservation properties of the hyperbolic conservation laws are combined in a very natural way by introducing a normalized Jacobian matrix of the hyperbolic system. Entropy satisfying shock transition operators which are consistent with the upwind differencing are locally introduced when transonic shock transition is detected. Schemes thus constructed are suitable for shockcapturing calculations. The stability and the global order of accuracy of the proposed schemes are examined. Numerical experiments for the inviscid Burgers equation and the compressible Euler equations in one and two space dimensions involving various situations of aerodynamic interest are included and compared.

Newton-Krylov-Schwarz: An implicit solver for CFD

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Keyes, David E.; Venkatakrishnan, V.

1995-01-01

Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton's method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on aerodynamics applications emphasizing comparisons with a standard defect-correction approach, subdomain preconditioner consistency, subdomain preconditioner quality, and the effect of a coarse grid.

Fast calculation of the sensitivity matrix in magnetic induction tomography by tetrahedral edge finite elements and the reciprocity theorem.

PubMed

Hollaus, K; Magele, C; Merwa, R; Scharfetter, H

2004-02-01

Magnetic induction tomography of biological tissue is used to reconstruct the changes in the complex conductivity distribution by measuring the perturbation of an alternating primary magnetic field. To facilitate the sensitivity analysis and the solution of the inverse problem a fast calculation of the sensitivity matrix, i.e. the Jacobian matrix, which maps the changes of the conductivity distribution onto the changes of the voltage induced in a receiver coil, is needed. The use of finite differences to determine the entries of the sensitivity matrix does not represent a feasible solution because of the high computational costs of the basic eddy current problem. Therefore, the reciprocity theorem was exploited. The basic eddy current problem was simulated by the finite element method using symmetric tetrahedral edge elements of second order. To test the method various simulations were carried out and discussed.

Solar Sail Attitude Control Performance Comparison

NASA Technical Reports Server (NTRS)

Bladt, Jeff J.; Lawrence, Dale A.

2005-01-01

Performance of two solar sail attitude control implementations is evaluated. One implementation employs four articulated reflective vanes located at the periphery of the sail assembly to generate control torque about all three axes. A second attitude control configuration uses mass on a gimbaled boom to alter the center-of-mass location relative to the center-of-pressure producing roll and pitch torque along with a pair of articulated control vanes for yaw control. Command generation algorithms employ linearized dynamics with a feedback inversion loop to map desired vehicle attitude control torque into vane and/or gimbal articulation angle commands. We investigate the impact on actuator deflection angle behavior due to variations in how the Jacobian matrix is incorporated into the feedback inversion loop. Additionally, we compare how well each implementation tracks a commanded thrust profile, which has been generated to follow an orbit trajectory from the sun-earth L1 point to a sub-L1 station.

Inflow/Outflow Boundary Conditions with Application to FUN3D

NASA Technical Reports Server (NTRS)

Carlson, Jan-Renee

2011-01-01

Several boundary conditions that allow subsonic and supersonic flow into and out of the computational domain are discussed. These boundary conditions are demonstrated in the FUN3D computational fluid dynamics (CFD) code which solves the three-dimensional Navier-Stokes equations on unstructured computational meshes. The boundary conditions are enforced through determination of the flux contribution at the boundary to the solution residual. The boundary conditions are implemented in an implicit form where the Jacobian contribution of the boundary condition is included and is exact. All of the flows are governed by the calorically perfect gas thermodynamic equations. Three problems are used to assess these boundary conditions. Solution residual convergence to machine zero precision occurred for all cases. The converged solution boundary state is compared with the requested boundary state for several levels of mesh densities. The boundary values converged to the requested boundary condition with approximately second-order accuracy for all of the cases.

A method to approximate a closest loadability limit using multiple load flow solutions

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

Yorino, Naoto; Harada, Shigemi; Cheng, Haozhong

A new method is proposed to approximate a closest loadability limit (CLL), or closest saddle node bifurcation point, using a pair of multiple load flow solutions. More strictly, the obtainable points by the method are the stationary points including not only CLL but also farthest and saddle points. An operating solution and a low voltage load flow solution are used to efficiently estimate the node injections at a CLL as well as the left and right eigenvectors corresponding to the zero eigenvalue of the load flow Jacobian. They can be used in monitoring loadability margin, in identification of weak spotsmore » in a power system and in the examination of an optimal control against voltage collapse. Most of the computation time of the proposed method is taken in calculating the load flow solution pair. The remaining computation time is less than that of an ordinary load flow.« less

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

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

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

Real time markerless motion tracking using linked kinematic chains

DOEpatents

Luck, Jason P [Arvada, CO; Small, Daniel E [Albuquerque, NM

2007-08-14

A markerless method is described for tracking the motion of subjects in a three dimensional environment using a model based on linked kinematic chains. The invention is suitable for tracking robotic, animal or human subjects in real-time using a single computer with inexpensive video equipment, and does not require the use of markers or specialized clothing. A simple model of rigid linked segments is constructed of the subject and tracked using three dimensional volumetric data collected by a multiple camera video imaging system. A physics based method is then used to compute forces to align the model with subsequent volumetric data sets in real-time. The method is able to handle occlusion of segments and accommodates joint limits, velocity constraints, and collision constraints and provides for error recovery. The method further provides for elimination of singularities in Jacobian based calculations, which has been problematic in alternative methods.

A simple extension of Roe's scheme for real gases

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

Arabi, Sina, E-mail: sina.arabi@polymtl.ca; Trépanier, Jean-Yves; Camarero, Ricardo

The purpose of this paper is to develop a highly accurate numerical algorithm to model real gas flows in local thermodynamic equilibrium (LTE). The Euler equations are solved using a finite volume method based on Roe's flux difference splitting scheme including real gas effects. A novel algorithm is proposed to calculate the Jacobian matrix which satisfies the flux difference splitting exactly in the average state for a general equation of state. This algorithm increases the robustness and accuracy of the method, especially around the contact discontinuities and shock waves where the gas properties jump appreciably. The results are compared withmore » an exact solution of the Riemann problem for the shock tube which considers the real gas effects. In addition, the method is applied to a blunt cone to illustrate the capability of the proposed extension in solving two dimensional flows.« less

Human low vision image warping - Channel matching considerations

NASA Technical Reports Server (NTRS)

Juday, Richard D.; Smith, Alan T.; Loshin, David S.

1992-01-01

We are investigating the possibility that a video image may productively be warped prior to presentation to a low vision patient. This could form part of a prosthesis for certain field defects. We have done preliminary quantitative studies on some notions that may be valid in calculating the image warpings. We hope the results will help make best use of time to be spent with human subjects, by guiding the selection of parameters and their range to be investigated. We liken a warping optimization to opening the largest number of spatial channels between the pixels of an input imager and resolution cells in the visual system. Some important effects are not quantified that will require human evaluation, such as local 'squashing' of the image, taken as the ratio of eigenvalues of the Jacobian of the transformation. The results indicate that the method shows quantitative promise. These results have identified some geometric transformations to evaluate further with human subjects.

Optimization of Time-Dependent Particle Tracing Using Tetrahedral Decomposition

NASA Technical Reports Server (NTRS)

Kenwright, David; Lane, David

1995-01-01

An efficient algorithm is presented for computing particle paths, streak lines and time lines in time-dependent flows with moving curvilinear grids. The integration, velocity interpolation and step-size control are all performed in physical space which avoids the need to transform the velocity field into computational space. This leads to higher accuracy because there are no Jacobian matrix approximations or expensive matrix inversions. Integration accuracy is maintained using an adaptive step-size control scheme which is regulated by the path line curvature. The problem of cell-searching, point location and interpolation in physical space is simplified by decomposing hexahedral cells into tetrahedral cells. This enables the point location to be done analytically and substantially faster than with a Newton-Raphson iterative method. Results presented show this algorithm is up to six times faster than particle tracers which operate on hexahedral cells yet produces almost identical particle trajectories.

Exploiting the MODIS albedos with the Two-stream Inversion Package (JRC-TIP): 2. Fractions of transmitted and absorbed fluxes in the vegetation and soil layers

NASA Astrophysics Data System (ADS)

Pinty, B.; Clerici, M.; Andredakis, I.; Kaminski, T.; Taberner, M.; Verstraete, M. M.; Gobron, N.; Plummer, S.; Widlowski, J.-L.

2011-05-01

The two-stream model parameters and associated uncertainties retrieved by inversion against MODIS broadband visible and near-infrared white sky surface albedos were discussed in a companion paper. The present paper concentrates on the partitioning of the solar radiation fluxes delivered by the Joint Research Centre Two-stream Inversion Package (JRC-TIP). The estimation of the various flux fractions related to the vegetation and the background layers separately capitalizes on the probability density functions of the model parameters discussed in the companion paper. The propagation of uncertainties from the observations to the model parameters is achieved via the Hessian of the cost function and yields a covariance matrix of posterior parameter uncertainties. This matrix is propagated to the radiation fluxes via the model's Jacobian matrix of first derivatives. Results exhibit a rather good spatiotemporal consistency given that the prior values on the model parameters are not specified as a function of land cover type and/or vegetation phenological states. A specific investigation based on a scenario imposing stringent conditions of leaf absorbing and scattering properties highlights the impact of such constraints that are, as a matter of fact, currently adopted in vegetation index approaches. Special attention is also given to snow-covered and snow-contaminated areas since these regions encompass significant reflectance changes that strongly affect land surface processes. A definite asset of the JRC-TIP lies in its capability to control and ultimately relax a number of assumptions that are often implicit in traditional approaches. These features greatly help us understand the discrepancies between the different data sets of land surface properties and fluxes that are currently available. Through a series of selected examples, the inverse procedure implemented in the JRC-TIP is shown to be robust, reliable, and compliant with large-scale processing requirements. Furthermore, this package ensures the physical consistency between the set of observations, the two-stream model parameters, and radiation fluxes. It also documents the retrieval of associated uncertainties.

MIND Demons for MR-to-CT Deformable Image Registration In Image-Guided Spine Surgery

PubMed Central

Reaungamornrat, S.; De Silva, T.; Uneri, A.; Wolinsky, J.-P.; Khanna, A. J.; Kleinszig, G.; Vogt, S.; Prince, J. L.; Siewerdsen, J. H.

2016-01-01

Purpose Localization of target anatomy and critical structures defined in preoperative MR images can be achieved by means of multi-modality deformable registration to intraoperative CT. We propose a symmetric diffeomorphic deformable registration algorithm incorporating a modality independent neighborhood descriptor (MIND) and a robust Huber metric for MR-to-CT registration. Method The method, called MIND Demons, solves for the deformation field between two images by optimizing an energy functional that incorporates both the forward and inverse deformations, smoothness on the velocity fields and the diffeomorphisms, a modality-insensitive similarity function suitable to multi-modality images, and constraints on geodesics in Lagrangian coordinates. Direct optimization (without relying on an exponential map of stationary velocity fields used in conventional diffeomorphic Demons) is carried out using a Gauss-Newton method for fast convergence. Registration performance and sensitivity to registration parameters were analyzed in simulation, in phantom experiments, and clinical studies emulating application in image-guided spine surgery, and results were compared to conventional mutual information (MI) free-form deformation (FFD), local MI (LMI) FFD, and normalized MI (NMI) Demons. Result The method yielded sub-voxel invertibility (0.006 mm) and nonsingular spatial Jacobians with capability to preserve local orientation and topology. It demonstrated improved registration accuracy in comparison to the reference methods, with mean target registration error (TRE) of 1.5 mm compared to 10.9, 2.3, and 4.6 mm for MI FFD, LMI FFD, and NMI Demons methods, respectively. Validation in clinical studies demonstrated realistic deformation with sub-voxel TRE in cases of cervical, thoracic, and lumbar spine. Conclusions A modality-independent deformable registration method has been developed to estimate a viscoelastic diffeomorphic map between preoperative MR and intraoperative CT. The method yields registration accuracy suitable to application in image-guided spine surgery across a broad range of anatomical sites and modes of deformation. PMID:27330239

MIND Demons for MR-to-CT deformable image registration in image-guided spine surgery

NASA Astrophysics Data System (ADS)

Reaungamornrat, S.; De Silva, T.; Uneri, A.; Wolinsky, J.-P.; Khanna, A. J.; Kleinszig, G.; Vogt, S.; Prince, J. L.; Siewerdsen, J. H.

2016-03-01

Purpose: Localization of target anatomy and critical structures defined in preoperative MR images can be achieved by means of multi-modality deformable registration to intraoperative CT. We propose a symmetric diffeomorphic deformable registration algorithm incorporating a modality independent neighborhood descriptor (MIND) and a robust Huber metric for MR-to-CT registration. Method: The method, called MIND Demons, solves for the deformation field between two images by optimizing an energy functional that incorporates both the forward and inverse deformations, smoothness on the velocity fields and the diffeomorphisms, a modality-insensitive similarity function suitable to multi-modality images, and constraints on geodesics in Lagrangian coordinates. Direct optimization (without relying on an exponential map of stationary velocity fields used in conventional diffeomorphic Demons) is carried out using a Gauss-Newton method for fast convergence. Registration performance and sensitivity to registration parameters were analyzed in simulation, in phantom experiments, and clinical studies emulating application in image-guided spine surgery, and results were compared to conventional mutual information (MI) free-form deformation (FFD), local MI (LMI) FFD, and normalized MI (NMI) Demons. Result: The method yielded sub-voxel invertibility (0.006 mm) and nonsingular spatial Jacobians with capability to preserve local orientation and topology. It demonstrated improved registration accuracy in comparison to the reference methods, with mean target registration error (TRE) of 1.5 mm compared to 10.9, 2.3, and 4.6 mm for MI FFD, LMI FFD, and NMI Demons methods, respectively. Validation in clinical studies demonstrated realistic deformation with sub-voxel TRE in cases of cervical, thoracic, and lumbar spine. Conclusions: A modality-independent deformable registration method has been developed to estimate a viscoelastic diffeomorphic map between preoperative MR and intraoperative CT. The method yields registration accuracy suitable to application in image-guided spine surgery across a broad range of anatomical sites and modes of deformation.

MIND Demons for MR-to-CT Deformable Image Registration In Image-Guided Spine Surgery.

PubMed

Reaungamornrat, S; De Silva, T; Uneri, A; Wolinsky, J-P; Khanna, A J; Kleinszig, G; Vogt, S; Prince, J L; Siewerdsen, J H

2016-02-27

Localization of target anatomy and critical structures defined in preoperative MR images can be achieved by means of multi-modality deformable registration to intraoperative CT. We propose a symmetric diffeomorphic deformable registration algorithm incorporating a modality independent neighborhood descriptor (MIND) and a robust Huber metric for MR-to-CT registration. The method, called MIND Demons, solves for the deformation field between two images by optimizing an energy functional that incorporates both the forward and inverse deformations, smoothness on the velocity fields and the diffeomorphisms, a modality-insensitive similarity function suitable to multi-modality images, and constraints on geodesics in Lagrangian coordinates. Direct optimization (without relying on an exponential map of stationary velocity fields used in conventional diffeomorphic Demons) is carried out using a Gauss-Newton method for fast convergence. Registration performance and sensitivity to registration parameters were analyzed in simulation, in phantom experiments, and clinical studies emulating application in image-guided spine surgery, and results were compared to conventional mutual information (MI) free-form deformation (FFD), local MI (LMI) FFD, and normalized MI (NMI) Demons. The method yielded sub-voxel invertibility (0.006 mm) and nonsingular spatial Jacobians with capability to preserve local orientation and topology. It demonstrated improved registration accuracy in comparison to the reference methods, with mean target registration error (TRE) of 1.5 mm compared to 10.9, 2.3, and 4.6 mm for MI FFD, LMI FFD, and NMI Demons methods, respectively. Validation in clinical studies demonstrated realistic deformation with sub-voxel TRE in cases of cervical, thoracic, and lumbar spine. A modality-independent deformable registration method has been developed to estimate a viscoelastic diffeomorphic map between preoperative MR and intraoperative CT. The method yields registration accuracy suitable to application in image-guided spine surgery across a broad range of anatomical sites and modes of deformation.

Inversion of Attributes and Full Waveforms of Ground Penetrating Radar Data Using PEST

NASA Astrophysics Data System (ADS)

Jazayeri, S.; Kruse, S.; Esmaeili, S.

2015-12-01

We seek to establish a method, based on freely available software, for inverting GPR signals for the underlying physical properties (electrical permittivity, magnetic permeability, target geometries). Such a procedure should be useful for classroom instruction and for analyzing surface GPR surveys over simple targets. We explore the applicability of the PEST parameter estimation software package for GPR inversion (www.pesthomepage.org). PEST is designed to invert data sets with large numbers of parameters, and offers a variety of inversion methods. Although primarily used in hydrogeology, the code has been applied to a wide variety of physical problems. The PEST code requires forward model input; the forward model of the GPR signal is done with the GPRMax package (www.gprmax.com). The problem of extracting the physical characteristics of a subsurface anomaly from the GPR data is highly nonlinear. For synthetic models of simple targets in homogeneous backgrounds, we find PEST's nonlinear Gauss-Marquardt-Levenberg algorithm is preferred. This method requires an initial model, for which the weighted differences between model-generated data and those of the "true" synthetic model (the objective function) are calculated. In order to do this, the Jacobian matrix and the derivatives of the observation data in respect to the model parameters are computed using a finite differences method. Next, the iterative process of building new models by updating the initial values starts in order to minimize the objective function. Another measure of the goodness of the final acceptable model is the correlation coefficient which is calculated based on the method of Cooley and Naff. An accepted final model satisfies both of these conditions. Models to date show that physical properties of simple isolated targets against homogeneous backgrounds can be obtained from multiple traces from common-offset surface surveys. Ongoing work examines the inversion capabilities with more complex target geometries and heterogeneous soils.

WE-AB-202-06: Correlating Lung CT HU with Transformation-Based and Xe-CT Derived Ventilation

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

Du, K; Patton, T; Bayouth, J

Purpose: Regional lung ventilation is useful to reduce radiation-induced function damage during lung cancer radiation therapy. Recently a new direct HU (Hounsfield unit)-based method was proposed to estimate the ventilation potential without image registration. The purpose of this study is to examine if there is a functional dependence between HU values and transformation-based or Xe-CT derived ventilation. Methods: 4DCT images acquired from 13 patients prior to radiation therapy and 4 mechanically ventilated sheep subjects which also have associated Xe-CT images were used for this analysis. Transformation-based ventilation was computed using Jacobian determinant of the transformation field between peak-exhale and peak-inhalemore » 4DCT images. Both transformation and Xe-CT derived ventilation was computed for each HU bin. Color scatter plot and cumulative histogram were used to compare and validate the direct HU-based method. Results: There was little change of the center and shape of the HU histograms between free breathing CT and 4DCT average, with or without smoothing, and between the repeated 4DCT scans. HU of −750 and −630 were found to have the greatest transformation-based ventilation for human and sheep subjects, respectively. Maximum Xe-CT derived ventilation was found to locate at HU of −600 in sheep subjects. The curve between Xe-CT ventilation and HU was noisy for tissue above HU −400, possibly due to less intensity change of Xe gas during wash-out and wash-in phases. Conclusion: Both transformation-based and Xe-CT ventilation demonstrated that lung tissues with HU values in the range of (-750, −600) HU have the maximum ventilation potential. The correlation between HU and ventilation suggests that HU might be used to help guide the ventilation calculation and make it more robust to noise and image registration errors. Research support from NIH grants CA166703 and CA166119 and a gift from Roger Koch.« less

Three-dimensional variational assimilation of MODIS aerosol optical depth: Implementation and application to a dust storm over East Asia

NASA Astrophysics Data System (ADS)

Liu, Zhiquan; Liu, Quanhua; Lin, Hui-Chuan; Schwartz, Craig S.; Lee, Yen-Huei; Wang, Tijian

2011-12-01

Assimilation of the Moderate Resolution Imaging Spectroradiometer (MODIS) total aerosol optical depth (AOD) retrieval products (at 550 nm wavelength) from both Terra and Aqua satellites have been developed within the National Centers for Environmental Prediction (NCEP) Gridpoint Statistical Interpolation (GSI) three-dimensional variational (3DVAR) data assimilation system. This newly developed algorithm allows, in a one-step procedure, the analysis of 3-D mass concentration of 14 aerosol variables from the Goddard Chemistry Aerosol Radiation and Transport (GOCART) module. The Community Radiative Transfer Model (CRTM) was extended to calculate AOD using GOCART aerosol variables as input. Both the AOD forward model and corresponding Jacobian model were developed within the CRTM and used in the 3DVAR minimization algorithm to compute the AOD cost function and its gradient with respect to 3-D aerosol mass concentration. The impact of MODIS AOD data assimilation was demonstrated by application to a dust storm from 17 to 24 March 2010 over East Asia. The aerosol analyses initialized Weather Research and Forecasting/Chemistry (WRF/Chem) model forecasts. Results indicate that assimilating MODIS AOD substantially improves aerosol analyses and subsequent forecasts when compared to MODIS AOD, independent AOD observations from the Aerosol Robotic Network (AERONET) and Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) instrument, and surface PM10 (particulate matter with diameters less than 10 μm) observations. The newly developed AOD data assimilation system can serve as a tool to improve simulations of dust storms and general air quality analyses and forecasts.

Path planning for assembly of strut-based structures. Thesis

NASA Technical Reports Server (NTRS)

Muenger, Rolf

1991-01-01

A path planning method with collision avoidance for a general single chain nonredundant or redundant robot is proposed. Joint range boundary overruns are also avoided. The result is a sequence of joint vectors which are passed to a trajectory planner. A potential field algorithm in joint space computes incremental joint vectors delta-q = delta-q(sub a) + delta-q(sub c) + delta-q(sub r). Adding delta-q to the robot's current joint vector leads to the next step in the path. Delta-q(sub a) is obtained by computing the minimum norm solution of the underdetermined linear system J delta-q(sub a) = x(sub a) where x(sub a) is a translational and rotational force vector that attracts the robot to its goal position and orientation. J is the manipulator Jacobian. Delta-q(sub c) is a collision avoidance term encompassing collisions between the robot (links and payload) and obstacles in the environment as well as collisions among links and payload of the robot themselves. It is obtained in joint space directly. Delta-q(sub r) is a function of the current joint vector and avoids joint range overruns. A higher level discrete search over candidate safe positions is used to provide alternatives in case the potential field algorithm encounters a local minimum and thus fails to reach the goal. The best first search algorithm A* is used for graph search. Symmetry properties of the payload and equivalent rotations are exploited to further enlarge the number of alternatives passed to the potential field algorithm.

Mean template for tensor-based morphometry using deformation tensors.

PubMed

Leporé, Natasha; Brun, Caroline; Pennec, Xavier; Chou, Yi-Yu; Lopez, Oscar L; Aizenstein, Howard J; Becker, James T; Toga, Arthur W; Thompson, Paul M

2007-01-01

Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In, it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is 'closest' to all subjects' anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework. The control brain B that is already the closest to 'average' is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling's T2 test on the deformation tensors. These results are compared to the ones found using the 'best' control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the p-values in maps of inter-group differences.

Computational aeroelasticity using a pressure-based solver

NASA Astrophysics Data System (ADS)

Kamakoti, Ramji

A computational methodology for performing fluid-structure interaction computations for three-dimensional elastic wing geometries is presented. The flow solver used is based on an unsteady Reynolds-Averaged Navier-Stokes (RANS) model. A well validated k-ε turbulence model with wall function treatment for near wall region was used to perform turbulent flow calculations. Relative merits of alternative flow solvers were investigated. The predictor-corrector-based Pressure Implicit Splitting of Operators (PISO) algorithm was found to be computationally economic for unsteady flow computations. Wing structure was modeled using Bernoulli-Euler beam theory. A fully implicit time-marching scheme (using the Newmark integration method) was used to integrate the equations of motion for structure. Bilinear interpolation and linear extrapolation techniques were used to transfer necessary information between fluid and structure solvers. Geometry deformation was accounted for by using a moving boundary module. The moving grid capability was based on a master/slave concept and transfinite interpolation techniques. Since computations were performed on a moving mesh system, the geometric conservation law must be preserved. This is achieved by appropriately evaluating the Jacobian values associated with each cell. Accurate computation of contravariant velocities for unsteady flows using the momentum interpolation method on collocated, curvilinear grids was also addressed. Flutter computations were performed for the AGARD 445.6 wing at subsonic, transonic and supersonic Mach numbers. Unsteady computations were performed at various dynamic pressures to predict the flutter boundary. Results showed favorable agreement of experiment and previous numerical results. The computational methodology exhibited capabilities to predict both qualitative and quantitative features of aeroelasticity.

SU-E-J-120: Comparing 4D CT Computed Ventilation to Lung Function Measured with Hyperpolarized Xenon-129 MRI

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

Neal, B; Chen, Q

2015-06-15

Purpose: To correlate ventilation parameters computed from 4D CT to ventilation, profusion, and gas exchange measured with hyperpolarized Xenon-129 MRI for a set of lung cancer patients. Methods: Hyperpolarized Xe-129 MRI lung scans were acquired for lung cancer patients, before and after radiation therapy, measuring ventilation, perfusion, and gas exchange. In the standard clinical workflow, these patients also received 4D CT scans before treatment. Ventilation was computed from 4D CT using deformable image registration (DIR). All phases of the 4D CT scan were registered using a B-spline deformable registration. Ventilation at the voxel level was then computed for each phasemore » based on a Jacobian volume expansion metric, yielding phase sorted ventilation images. Ventilation based upon 4D CT and Xe-129 MRI were co-registered, allowing qualitative visual comparison and qualitative comparison via the Pearson correlation coefficient. Results: Analysis shows a weak correlation between hyperpolarized Xe-129 MRI and 4D CT DIR ventilation, with a Pearson correlation coefficient of 0.17 to 0.22. Further work will refine the DIR parameters to optimize the correlation. The weak correlation could be due to the limitations of 4D CT, registration algorithms, or the Xe-129 MRI imaging. Continued development will refine parameters to optimize correlation. Conclusion: Current analysis yields a minimal correlation between 4D CT DIR and Xe-129 MRI ventilation. Funding provided by the 2014 George Amorino Pilot Grant in Radiation Oncology at the University of Virginia.« less

Launching and controlling Gaussian beams from point sources via planar transformation media

NASA Astrophysics Data System (ADS)

Odabasi, Hayrettin; Sainath, Kamalesh; Teixeira, Fernando L.

2018-02-01

Based on operations prescribed under the paradigm of complex transformation optics (CTO) [F. Teixeira and W. Chew, J. Electromagn. Waves Appl. 13, 665 (1999), 10.1163/156939399X01104; F. L. Teixeira and W. C. Chew, Int. J. Numer. Model. 13, 441 (2000), 10.1002/1099-1204(200009/10)13:5%3C441::AID-JNM376%3E3.0.CO;2-J; H. Odabasi, F. L. Teixeira, and W. C. Chew, J. Opt. Soc. Am. B 28, 1317 (2011), 10.1364/JOSAB.28.001317; B.-I. Popa and S. A. Cummer, Phys. Rev. A 84, 063837 (2011), 10.1103/PhysRevA.84.063837], it was recently shown in [G. Castaldi, S. Savoia, V. Galdi, A. Alù, and N. Engheta, Phys. Rev. Lett. 110, 173901 (2013), 10.1103/PhysRevLett.110.173901] that a complex source point (CSP) can be mimicked by parity-time (PT ) transformation media. Such coordinate transformation has a mirror symmetry for the imaginary part, and results in a balanced loss/gain metamaterial slab. A CSP produces a Gaussian beam and, consequently, a point source placed at the center of such a metamaterial slab produces a Gaussian beam propagating away from the slab. Here, we extend the CTO analysis to nonsymmetric complex coordinate transformations as put forth in [S. Savoia, G. Castaldi, and V. Galdi, J. Opt. 18, 044027 (2016), 10.1088/2040-8978/18/4/044027] and verify that, by using simply a (homogeneous) doubly anisotropic gain-media metamaterial slab, one can still mimic a CSP and produce Gaussian beam. In addition, we show that a Gaussian-like beams can be produced by point sources placed outside the slab as well. By making use of the extra degrees of freedom (the real and imaginary parts of the coordinate transformation) provided by CTO, the near-zero requirement on the real part of the resulting constitutive parameters can be relaxed to facilitate potential realization of Gaussian-like beams. We illustrate how beam properties such as peak amplitude and waist location can be controlled by a proper choice of (complex-valued) CTO Jacobian elements. In particular, the beam waist location may be moved bidirectionally by allowing for negative entries in the Jacobian (equivalent to inducing negative refraction effects). These results are then interpreted in light of the ensuing CSP location.

A practical implementation of wave front construction for 3-D isotropic media

NASA Astrophysics Data System (ADS)

Chambers, K.; Kendall, J.-M.

2008-06-01

Wave front construction (WFC) methods are a useful tool for tracking wave fronts and are a natural extension to standard ray shooting methods. Here we describe and implement a simple WFC method that is used to interpolate wavefield properties throughout a 3-D heterogeneous medium. Our approach differs from previous 3-D WFC procedures primarily in the use of a ray interpolation scheme, based on approximating the wave front as a `locally spherical' surface and a `first arrival mode', which reduces computation times, where only first arrivals are required. Both of these features have previously been included in 2-D WFC algorithms; however, until now they have not been extended to 3-D systems. The wave front interpolation scheme allows for rays to be traced from a nearly arbitrary distribution of take-off angles, and the calculation of derivatives with respect to take-off angles is not required for wave front interpolation. However, in regions of steep velocity gradient, the locally spherical approximation is not valid, and it is necessary to backpropagate rays to a sufficiently homogenous region before interpolation of the new ray. Our WFC technique is illustrated using a realistic velocity model, based on a North Sea oil reservoir. We examine wavefield quantities such as traveltimes, ray angles, source take-off angles and geometrical spreading factors, all of which are interpolated on to a regular grid. We compare geometrical spreading factors calculated using two methods: using the ray Jacobian and by taking the ratio of a triangular area of wave front to the corresponding solid angle at the source. The results show that care must be taken when using ray Jacobians to calculate geometrical spreading factors, as the poles of the source coordinate system produce unreliable values, which can be spread over a large area, as only a few initial rays are traced in WFC. We also show that the use of the first arrival mode can reduce computation time by ~65 per cent, with the accuracy of the interpolated traveltimes, ray angles and source take-off angles largely unchanged. However, the first arrival mode does lead to inaccuracies in interpolated angles near caustic surfaces, as well as small variations in geometrical spreading factors for ray tubes that have passed through caustic surfaces.

Issues in quantification of registered respiratory gated PET/CT in the lung.

PubMed

Cuplov, Vesna; Holman, Beverley F; McClelland, Jamie; Modat, Marc; Hutton, Brian F; Thielemans, Kris

2017-12-14

PET/CT quantification of lung tissue is limited by several difficulties: the lung density and local volume changes during respiration, the anatomical mismatch between PET and CT and the relative contributions of tissue, air and blood to the PET signal (the tissue fraction effect). Air fraction correction (AFC) has been shown to improve PET image quantification in the lungs. Methods to correct for the movement and anatomical mismatch involve respiratory gating and image registration techniques. While conventional registration methods only account for spatial mismatch, the Jacobian determinant of the deformable registration transformation field can be used to estimate local volume changes and could therefore potentially be used to correct (i.e. Jacobian Correction, JC) the PET signal for changes in concentration due to local volume changes. This work aims to investigate the relationship between variations in the lung due to respiration, specifically density, tracer concentration and local volume changes. In particular, we study the effect of AFC and JC on PET quantitation after registration of respiratory gated PET/CT patient data. Six patients suffering from lung cancer with solitary pulmonary nodules underwent [Formula: see text]F-FDG PET/cine-CT. The PET data were gated into six respiratory gates using displacement gating based on a real-time position management (RPM) signal and reconstructed with matched gated CT. The PET tracer concentration and tissue density were extracted from registered gated PET and CT images before and after corrections (AFC or JC) and compared to the values from the reference images. Before correction, we observed a linear correlation between the PET tracer concentration values and density. Across all gates and patients, the maximum relative change in PET tracer concentration before (after) AFC was found to be 16.2% (4.1%) and the maximum relative change in tissue density and PET tracer concentration before (after) JC was found to be 17.1% (5.5%) and 16.2% (6.8%) respectively. Overall our results show that both AFC or JC largely explain the observed changes in PET tracer activity over the respiratory cycle. We also speculate that a second order effect is related to change in fluid content but this needs further investigation. Consequently, either AFC or JC is recommended when combining lung PET images from different gates to reduce noise.

Issues in quantification of registered respiratory gated PET/CT in the lung

NASA Astrophysics Data System (ADS)

Cuplov, Vesna; Holman, Beverley F.; McClelland, Jamie; Modat, Marc; Hutton, Brian F.; Thielemans, Kris

2018-01-01

PET/CT quantification of lung tissue is limited by several difficulties: the lung density and local volume changes during respiration, the anatomical mismatch between PET and CT and the relative contributions of tissue, air and blood to the PET signal (the tissue fraction effect). Air fraction correction (AFC) has been shown to improve PET image quantification in the lungs. Methods to correct for the movement and anatomical mismatch involve respiratory gating and image registration techniques. While conventional registration methods only account for spatial mismatch, the Jacobian determinant of the deformable registration transformation field can be used to estimate local volume changes and could therefore potentially be used to correct (i.e. Jacobian Correction, JC) the PET signal for changes in concentration due to local volume changes. This work aims to investigate the relationship between variations in the lung due to respiration, specifically density, tracer concentration and local volume changes. In particular, we study the effect of AFC and JC on PET quantitation after registration of respiratory gated PET/CT patient data. Six patients suffering from lung cancer with solitary pulmonary nodules underwent 18 F-FDG PET/cine-CT. The PET data were gated into six respiratory gates using displacement gating based on a real-time position management (RPM) signal and reconstructed with matched gated CT. The PET tracer concentration and tissue density were extracted from registered gated PET and CT images before and after corrections (AFC or JC) and compared to the values from the reference images. Before correction, we observed a linear correlation between the PET tracer concentration values and density. Across all gates and patients, the maximum relative change in PET tracer concentration before (after) AFC was found to be 16.2% (4.1%) and the maximum relative change in tissue density and PET tracer concentration before (after) JC was found to be 17.1% (5.5%) and 16.2% (6.8%) respectively. Overall our results show that both AFC or JC largely explain the observed changes in PET tracer activity over the respiratory cycle. We also speculate that a second order effect is related to change in fluid content but this needs further investigation. Consequently, either AFC or JC is recommended when combining lung PET images from different gates to reduce noise.

A Voxel-by-Voxel Comparison of Deformable Vector Fields Obtained by Three Deformable Image Registration Algorithms Applied to 4DCT Lung Studies.

PubMed

Fatyga, Mirek; Dogan, Nesrin; Weiss, Elizabeth; Sleeman, William C; Zhang, Baoshe; Lehman, William J; Williamson, Jeffrey F; Wijesooriya, Krishni; Christensen, Gary E

2015-01-01

Commonly used methods of assessing the accuracy of deformable image registration (DIR) rely on image segmentation or landmark selection. These methods are very labor intensive and thus limited to relatively small number of image pairs. The direct voxel-by-voxel comparison can be automated to examine fluctuations in DIR quality on a long series of image pairs. A voxel-by-voxel comparison of three DIR algorithms applied to lung patients is presented. Registrations are compared by comparing volume histograms formed both with individual DIR maps and with a voxel-by-voxel subtraction of the two maps. When two DIR maps agree one concludes that both maps are interchangeable in treatment planning applications, though one cannot conclude that either one agrees with the ground truth. If two DIR maps significantly disagree one concludes that at least one of the maps deviates from the ground truth. We use the method to compare 3 DIR algorithms applied to peak inhale-peak exhale registrations of 4DFBCT data obtained from 13 patients. All three algorithms appear to be nearly equivalent when compared using DICE similarity coefficients. A comparison based on Jacobian volume histograms shows that all three algorithms measure changes in total volume of the lungs with reasonable accuracy, but show large differences in the variance of Jacobian distribution on contoured structures. Analysis of voxel-by-voxel subtraction of DIR maps shows differences between algorithms that exceed a centimeter for some registrations. Deformation maps produced by DIR algorithms must be treated as mathematical approximations of physical tissue deformation that are not self-consistent and may thus be useful only in applications for which they have been specifically validated. The three algorithms tested in this work perform fairly robustly for the task of contour propagation, but produce potentially unreliable results for the task of DVH accumulation or measurement of local volume change. Performance of DIR algorithms varies significantly from one image pair to the next hence validation efforts, which are exhaustive but performed on a small number of image pairs may not reflect the performance of the same algorithm in practical clinical situations. Such efforts should be supplemented by validation based on a longer series of images of clinical quality.

What dementia reveals about proverb interpretation and its neuroanatomical correlates.

PubMed

Kaiser, Natalie C; Lee, Grace J; Lu, Po H; Mather, Michelle J; Shapira, Jill; Jimenez, Elvira; Thompson, Paul M; Mendez, Mario F

2013-08-01

Neuropsychologists frequently include proverb interpretation as a measure of executive abilities. A concrete interpretation of proverbs, however, may reflect semantic impairments from anterior temporal lobes, rather than executive dysfunction from frontal lobes. The investigation of proverb interpretation among patients with different dementias with varying degrees of temporal and frontal dysfunction may clarify the underlying brain-behavior mechanisms for abstraction from proverbs. We propose that patients with behavioral variant frontotemporal dementia (bvFTD), who are characteristically more impaired on proverb interpretation than those with Alzheimer's disease (AD), are disproportionately impaired because of anterior temporal-mediated semantic deficits. Eleven patients with bvFTD and 10 with AD completed the Delis-Kaplan Executive Function System (D-KEFS) Proverbs Test and a series of neuropsychological measures of executive and semantic functions. The analysis included both raw and age-adjusted normed data for multiple choice responses on the D-KEFS Proverbs Test using independent samples t-tests. Tensor-based morphometry (TBM) applied to 3D T1-weighted MRI scans mapped the association between regional brain volume and proverb performance. Computations of mean Jacobian values within select regions of interest provided a numeric summary of regional volume, and voxel-wise regression yielded 3D statistical maps of the association between tissue volume and proverb scores. The patients with bvFTD were significantly worse than those with AD in proverb interpretation. The worse performance of the bvFTD patients involved a greater number of concrete responses to common, familiar proverbs, but not to uncommon, unfamiliar ones. These concrete responses to common proverbs correlated with semantic measures, whereas concrete responses to uncommon proverbs correlated with executive functions. After controlling for dementia diagnosis, TBM analyses indicated significant correlations between impaired proverb interpretation and the anterior temporal lobe region (left>right). Among two dementia groups, those with bvFTD, demonstrated a greater number of concrete responses to common proverbs compared to those with AD, and this performance correlated with semantic deficits and the volume of the left anterior lobe, the hub of semantic knowledge. The findings of this study suggest that common proverb interpretation is greatly influenced by semantic dysfunction and that the use of proverbs for testing executive functions needs to include the interpretation of unfamiliar proverbs. Published by Elsevier Ltd.

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

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

Zhu, Hongyu; Petra, Noemi; Stadler, Georg

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE PAGES

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; ...

2016-07-13

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

NASA Astrophysics Data System (ADS)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar

2016-07-01

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

Local linear approximation of the Jacobian matrix better captures phase resetting of neural limit cycle oscillators.

PubMed

Oprisan, Sorinel Adrian

2014-01-01

One effect of any external perturbations, such as presynaptic inputs, received by limit cycle oscillators when they are part of larger neural networks is a transient change in their firing rate, or phase resetting. A brief external perturbation moves the figurative point outside the limit cycle, a geometric perturbation that we mapped into a transient change in the firing rate, or a temporal phase resetting. In order to gain a better qualitative understanding of the link between the geometry of the limit cycle and the phase resetting curve (PRC), we used a moving reference frame with one axis tangent and the others normal to the limit cycle. We found that the stability coefficients associated with the unperturbed limit cycle provided good quantitative predictions of both the tangent and the normal geometric displacements induced by external perturbations. A geometric-to-temporal mapping allowed us to correctly predict the PRC while preserving the intuitive nature of this geometric approach.

Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion

NASA Astrophysics Data System (ADS)

Philip, B.; Wang, Z.; Berrill, M. A.; Birke, M.; Pernice, M.

2014-04-01

The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered often exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multi-physics systems: implicit time integration for efficient long term time integration of stiff multi-physics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

Computational aspects of helicopter trim analysis and damping levels from Floquet theory

NASA Technical Reports Server (NTRS)

Gaonkar, Gopal H.; Achar, N. S.

1992-01-01

Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.

Application of a fast Newton-Krylov solver for equilibrium simulations of phosphorus and oxygen

NASA Astrophysics Data System (ADS)

Fu, Weiwei; Primeau, François

2017-11-01

Model drift due to inadequate spinup is a serious problem that complicates the interpretation of climate change simulations. Even after a 300 year spinup we show that solutions are not only still drifting but often drifting away from their eventual equilibrium over large parts of the ocean. Here we present a Newton-Krylov solver for computing cyclostationary equilibrium solutions of a biogeochemical model for the cycling of phosphorus and oxygen. In addition to using previously developed preconditioning strategies - time-averaging and coarse-graining the Jacobian matrix - we also introduce a new strategy: the adiabatic elimination of a fast variable (particulate organic phosphorus) by slaving it to a slow variable (dissolved inorganic phosphorus). We use transport matrices derived from the Community Earth System Model (CESM) with a nominal horizontal resolution of 1° × 1° and 60 vertical levels to implement and test the solver. We find that the new solver obtains seasonally-varying equilibrium solutions with no visible drift using no more than 80 simulation years.

Optimizing some 3-stage W-methods for the time integration of PDEs

NASA Astrophysics Data System (ADS)

Gonzalez-Pinto, S.; Hernandez-Abreu, D.; Perez-Rodriguez, S.

2017-07-01

The optimization of some W-methods for the time integration of time-dependent PDEs in several spatial variables is considered. In [2, Theorem 1] several three-parametric families of three-stage W-methods for the integration of IVPs in ODEs were studied. Besides, the optimization of several specific methods for PDEs when the Approximate Matrix Factorization Splitting (AMF) is used to define the approximate Jacobian matrix (W ≈ fy(yn)) was carried out. Also, some convergence and stability properties were presented [2]. The derived methods were optimized on the base that the underlying explicit Runge-Kutta method is the one having the largest Monotonicity interval among the thee-stage order three Runge-Kutta methods [1]. Here, we propose an optimization of the methods by imposing some additional order condition [7] to keep order three for parabolic PDE problems [6] but at the price of reducing substantially the length of the nonlinear Monotonicity interval of the underlying explicit Runge-Kutta method.

Monte Carlo based method for fluorescence tomographic imaging with lifetime multiplexing using time gates

PubMed Central

Chen, Jin; Venugopal, Vivek; Intes, Xavier

2011-01-01

Time-resolved fluorescence optical tomography allows 3-dimensional localization of multiple fluorophores based on lifetime contrast while providing a unique data set for improved resolution. However, to employ the full fluorescence time measurements, a light propagation model that accurately simulates weakly diffused and multiple scattered photons is required. In this article, we derive a computationally efficient Monte Carlo based method to compute time-gated fluorescence Jacobians for the simultaneous imaging of two fluorophores with lifetime contrast. The Monte Carlo based formulation is validated on a synthetic murine model simulating the uptake in the kidneys of two distinct fluorophores with lifetime contrast. Experimentally, the method is validated using capillaries filled with 2.5nmol of ICG and IRDye™800CW respectively embedded in a diffuse media mimicking the average optical properties of mice. Combining multiple time gates in one inverse problem allows the simultaneous reconstruction of multiple fluorophores with increased resolution and minimal crosstalk using the proposed formulation. PMID:21483610

Vibration-based damage detection in a concrete beam under temperature variations using AR models and state-space approaches

NASA Astrophysics Data System (ADS)

Clément, A.; Laurens, S.

2011-07-01

The Structural Health Monitoring of civil structures subjected to ambient vibrations is very challenging. Indeed, the variations of environmental conditions and the difficulty to characterize the excitation make the damage detection a hard task. Auto-regressive (AR) models coefficients are often used as damage sensitive feature. The presented work proposes a comparison of the AR approach with a state-space feature formed by the Jacobian matrix of the dynamical process. Since the detection of damage can be formulated as a novelty detection problem, Mahalanobis distance is applied to track new points from an undamaged reference collection of feature vectors. Data from a concrete beam subjected to temperature variations and damaged by several static loading are analyzed. It is observed that the damage sensitive features are effectively sensitive to temperature variations. However, the use of the Mahalanobis distance makes possible the detection of cracking with both of them. Early damage (before cracking) is only revealed by the AR coefficients with a good sensibility.

Robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks.

PubMed

Yan, Zheng; Wang, Jun

2014-03-01

This paper presents a neural network approach to robust model predictive control (MPC) for constrained discrete-time nonlinear systems with unmodeled dynamics affected by bounded uncertainties. The exact nonlinear model of underlying process is not precisely known, but a partially known nominal model is available. This partially known nonlinear model is first decomposed to an affine term plus an unknown high-order term via Jacobian linearization. The linearization residue combined with unmodeled dynamics is then modeled using an extreme learning machine via supervised learning. The minimax methodology is exploited to deal with bounded uncertainties. The minimax optimization problem is reformulated as a convex minimization problem and is iteratively solved by a two-layer recurrent neural network. The proposed neurodynamic approach to nonlinear MPC improves the computational efficiency and sheds a light for real-time implementability of MPC technology. Simulation results are provided to substantiate the effectiveness and characteristics of the proposed approach.

State and force observers based on multibody models and the indirect Kalman filter

NASA Astrophysics Data System (ADS)

Sanjurjo, Emilio; Dopico, Daniel; Luaces, Alberto; Naya, Miguel Ángel

2018-06-01

The aim of this work is to present two new methods to provide state observers by combining multibody simulations with indirect extended Kalman filters. One of the methods presented provides also input force estimation. The observers have been applied to two mechanism with four different sensor configurations, and compared to other multibody-based observers found in the literature to evaluate their behavior, namely, the unscented Kalman filter (UKF), and the indirect extended Kalman filter with simplified Jacobians (errorEKF). The new methods have some more computational cost than the errorEKF, but still much less than the UKF. Regarding their accuracy, both are better than the errorEKF. The method with input force estimation outperforms also the UKF, while the method without force estimation achieves results almost identical to those of the UKF. All the methods have been implemented as a reusable MATLAB® toolkit which has been released as Open Source in https://github.com/MBDS/mbde-matlab.

Fluid-structure interaction simulations of deformable structures with non-linear thin shell elements

NASA Astrophysics Data System (ADS)

Asgharzadeh, Hafez; Hedayat, Mohammadali; Borazjani, Iman; Scientific Computing; Biofluids Laboratory Team

2017-11-01

Large deformation of structures in a fluid is simulated using a strongly coupled partitioned fluid-structure interaction (FSI) approach which is stabilized with under-relaxation and the Aitken acceleration technique. The fluid is simulated using a recently developed implicit Newton-Krylov method with a novel analytical Jacobian. Structures are simulated using a triangular thin-shell finite element formulation, which considers only translational degrees of freedom. The thin-shell method is developed on the top of a previously implemented membrane finite element formulation. A sharp interface immersed boundary method is used to handle structures in the fluid domain. The developed FSI framework is validated against two three-dimensional experiments: (1) a flexible aquatic vegetation in the fluid and (2) a heaving flexible panel in fluid. Furthermore, the developed FSI framework is used to simulate tissue heart valves, which involve large deformations and non-linear material properties. This work was supported by American Heart Association (AHA) Grant 13SDG17220022 and the Center of Computational Research (CCR) of University at Buffalo.

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

Stimpson, Shane G.

Activities to incorporate fuel performance capabilities into the Virtual Environment for Reactor Applications (VERA) are receiving increasing attention. The multiphysics emphasis is expanding as the neutronics (MPACT) and thermal-hydraulics (CTF) packages are becoming more mature. Capturing the finer details of fuel phenomena (swelling, densification, relocation, gap closure, etc.) is the natural next step in the VERA Core Simulator (VERA-CS) development process since these phenomena are currently not directly taken into account. While several codes could be used to accomplish this, the BISON fuel performance code being developed by the Idaho National Laboratory (INL) is the focus of ongoing work inmore » the Consortium for Advanced Simulation of Light Water Reactors (CASL). Built on INL’s MOOSE framework, BISON uses the finite element method for geometric representation and a Jacobian-free Newton-Krylov (JFNK) scheme to solve systems of partial differential equations for various fuel characteristic relationships. There are several modes of operation in BISON, but, for this work, it uses a 2D azimuthally symmetric (R-Z) smeared-pellet model.« less

Discontinuous Galerkin Methods for NonLinear Differential Systems

NASA Technical Reports Server (NTRS)

Barth, Timothy; Mansour, Nagi (Technical Monitor)

2001-01-01

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

Chaotic, informational and synchronous behaviour of multiplex networks

NASA Astrophysics Data System (ADS)

Baptista, M. S.; Szmoski, R. M.; Pereira, R. F.; Pinto, S. E. De Souza

2016-03-01

The understanding of the relationship between topology and behaviour in interconnected networks would allow to charac- terise and predict behaviour in many real complex networks since both are usually not simultaneously known. Most previous studies have focused on the relationship between topology and synchronisation. In this work, we provide analytical formulas that shows how topology drives complex behaviour: chaos, information, and weak or strong synchronisation; in multiplex net- works with constant Jacobian. We also study this relationship numerically in multiplex networks of Hindmarsh-Rose neurons. Whereas behaviour in the analytically tractable network is a direct but not trivial consequence of the spectra of eigenvalues of the Laplacian matrix, where behaviour may strongly depend on the break of symmetry in the topology of interconnections, in Hindmarsh-Rose neural networks the nonlinear nature of the chemical synapses breaks the elegant mathematical connec- tion between the spectra of eigenvalues of the Laplacian matrix and the behaviour of the network, creating networks whose behaviour strongly depends on the nature (chemical or electrical) of the inter synapses.

An Implicit Solver on A Parallel Block-Structured Adaptive Mesh Grid for FLASH

NASA Astrophysics Data System (ADS)

Lee, D.; Gopal, S.; Mohapatra, P.

2012-07-01

We introduce a fully implicit solver for FLASH based on a Jacobian-Free Newton-Krylov (JFNK) approach with an appropriate preconditioner. The main goal of developing this JFNK-type implicit solver is to provide efficient high-order numerical algorithms and methodology for simulating stiff systems of differential equations on large-scale parallel computer architectures. A large number of natural problems in nonlinear physics involve a wide range of spatial and time scales of interest. A system that encompasses such a wide magnitude of scales is described as "stiff." A stiff system can arise in many different fields of physics, including fluid dynamics/aerodynamics, laboratory/space plasma physics, low Mach number flows, reactive flows, radiation hydrodynamics, and geophysical flows. One of the big challenges in solving such a stiff system using current-day computational resources lies in resolving time and length scales varying by several orders of magnitude. We introduce FLASH's preliminary implementation of a time-accurate JFNK-based implicit solver in the framework of FLASH's unsplit hydro solver.

A Fast and Sensitive New Satellite SO2 Retrieval Algorithm based on Principal Component Analysis: Application to the Ozone Monitoring Instrument

NASA Technical Reports Server (NTRS)

Li, Can; Joiner, Joanna; Krotkov, A.; Bhartia, Pawan K.

2013-01-01

We describe a new algorithm to retrieve SO2 from satellite-measured hyperspectral radiances. We employ the principal component analysis technique in regions with no significant SO2 to capture radiance variability caused by both physical processes (e.g., Rayleigh and Raman scattering and ozone absorption) and measurement artifacts. We use the resulting principal components and SO2 Jacobians calculated with a radiative transfer model to directly estimate SO2 vertical column density in one step. Application to the Ozone Monitoring Instrument (OMI) radiance spectra in 310.5-340 nm demonstrates that this approach can greatly reduce biases in the operational OMI product and decrease the noise by a factor of 2, providing greater sensitivity to anthropogenic emissions. The new algorithm is fast, eliminates the need for instrument-specific radiance correction schemes, and can be easily adapted to other sensors. These attributes make it a promising technique for producing longterm, consistent SO2 records for air quality and climate research.

Joint inversion of acoustic and resistivity data for the estimation of gas hydrate concentration

USGS Publications Warehouse

Lee, Myung W.

2002-01-01

Downhole log measurements, such as acoustic or electrical resistivity logs, are frequently used to estimate in situ gas hydrate concentrations in the pore space of sedimentary rocks. Usually the gas hydrate concentration is estimated separately based on each log measurement. However, measurements are related to each other through the gas hydrate concentration, so the gas hydrate concentrations can be estimated by jointly inverting available logs. Because the magnitude of slowness of acoustic and resistivity values differs by more than an order of magnitude, a least-squares method, weighted by the inverse of the observed values, is attempted. Estimating the resistivity of connate water and gas hydrate concentration simultaneously is problematic, because the resistivity of connate water is independent of acoustics. In order to overcome this problem, a coupling constant is introduced in the Jacobian matrix. In the use of different logs to estimate gas hydrate concentration, a joint inversion of different measurements is preferred to the averaging of each inversion result.

EIT image reconstruction based on a hybrid FE-EFG forward method and the complete-electrode model.

PubMed

Hadinia, M; Jafari, R; Soleimani, M

2016-06-01

This paper presents the application of the hybrid finite element-element free Galerkin (FE-EFG) method for the forward and inverse problems of electrical impedance tomography (EIT). The proposed method is based on the complete electrode model. Finite element (FE) and element-free Galerkin (EFG) methods are accurate numerical techniques. However, the FE technique has meshing task problems and the EFG method is computationally expensive. In this paper, the hybrid FE-EFG method is applied to take both advantages of FE and EFG methods, the complete electrode model of the forward problem is solved, and an iterative regularized Gauss-Newton method is adopted to solve the inverse problem. The proposed method is applied to compute Jacobian in the inverse problem. Utilizing 2D circular homogenous models, the numerical results are validated with analytical and experimental results and the performance of the hybrid FE-EFG method compared with the FE method is illustrated. Results of image reconstruction are presented for a human chest experimental phantom.

Post-Newtonian Circular Restricted 3-Body Problem: Schwarzschild primaries

NASA Astrophysics Data System (ADS)

Dubeibe, F. L.; Lora-Clavijo, F. D.; González, G. A.

2017-07-01

The restricted three-body problem (RTBP) has been extensively studied to investigate the stability of the solar system, extra-solar subsystems, asteroid capture, and the dynamics of two massive black holes orbited by a sun. In the present work, we study the stability of the planar circular restricted three-body problem in the context of post-Newtonian approximations. First of all, we review the results obtained from the post-Newtonian equations of motion calculated in the framework of the Einstein-Infeld-Hoffmann formalism (EIH). Therefore, using the Fodor-Hoenselers-Perjes formalism (FHP), we have performed an expansion of the gravitational potential for two primaries, deriving a new system of equations of motion, which unlike the EIH-approach, preserves the Jacobian integral of motion. Additionally, we have obtained approximate expressions for the Lagrange points in terms of a mass parameter μ, where it is found that the deviations from the classical regime are larger for the FHP than for the EIH equations.

Analysis of physics-based preconditioning for single-phase subchannel equations

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

Hansel, J. E.; Ragusa, J. C.; Allu, S.

2013-07-01

The (single-phase) subchannel approximations are used throughout nuclear engineering to provide an efficient flow simulation because the computational burden is much smaller than for computational fluid dynamics (CFD) simulations, and empirical relations have been developed and validated to provide accurate solutions in appropriate flow regimes. Here, the subchannel equations have been recast in a residual form suitable for a multi-physics framework. The Eigen spectrum of the Jacobian matrix, along with several potential physics-based preconditioning approaches, are evaluated, and the the potential for improved convergence from preconditioning is assessed. The physics-based preconditioner options include several forms of reduced equations that decouplemore » the subchannels by neglecting crossflow, conduction, and/or both turbulent momentum and energy exchange between subchannels. Eigen-scopy analysis shows that preconditioning moves clusters of eigenvalues away from zero and toward one. A test problem is run with and without preconditioning. Without preconditioning, the solution failed to converge using GMRES, but application of any of the preconditioners allowed the solution to converge. (authors)« less

An Object-Oriented Finite Element Framework for Multiphysics Phase Field Simulations

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

Michael R Tonks; Derek R Gaston; Paul C Millett

2012-01-01

The phase field approach is a powerful and popular method for modeling microstructure evolution. In this work, advanced numerical tools are used to create a phase field framework that facilitates rapid model development. This framework, called MARMOT, is based on Idaho National Laboratory's finite element Multiphysics Object-Oriented Simulation Environment. In MARMOT, the system of phase field partial differential equations (PDEs) are solved simultaneously with PDEs describing additional physics, such as solid mechanics and heat conduction, using the Jacobian-Free Newton Krylov Method. An object-oriented architecture is created by taking advantage of commonalities in phase fields models to facilitate development of newmore » models with very little written code. In addition, MARMOT provides access to mesh and time step adaptivity, reducing the cost for performing simulations with large disparities in both spatial and temporal scales. In this work, phase separation simulations are used to show the numerical performance of MARMOT. Deformation-induced grain growth and void growth simulations are included to demonstrate the muliphysics capability.« less

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

Wannamaker, Philip E.

We have developed an algorithm for the inversion of magnetotelluric (MT) data to a 3D earth resistivity model based upon the finite element method. Hexahedral edge finite elements are implemented to accommodate discontinuities in the electric field across resistivity boundaries, and to accurately simulate topographic variations. All matrices are reduced and solved using direct solution modules which avoids ill-conditioning endemic to iterative solvers such as conjugate gradients, principally PARDISO for the finite element system and PLASMA for the parameter step estimate. Large model parameterizations can be handled by transforming the Gauss-Newton estimator to data-space form. Accuracy of the forward problemmore » and jacobians has been checked by comparison to integral equations results and by limiting asymptotes. Inverse accuracy and performance has been verified against the public Dublin Secret Test Model 2 and the well-known Mount St Helens 3D MT data set. This algorithm we believe is the most capable yet for forming 3D images of earth resistivity structure and their implications for geothermal fluids and pathways.« less

An hp symplectic pseudospectral method for nonlinear optimal control

NASA Astrophysics Data System (ADS)

Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong

2017-01-01

An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

Dynamic analysis of flexible gear trains/transmissions - An automated approach

NASA Technical Reports Server (NTRS)

Amirouche, F. M. L.; Shareef, N. H.; Xie, M.

1992-01-01

In this paper an automated algorithmic method is presented for the dynamic analysis of geared trains/transmissions. These are treated as a system of interconnected flexible bodies. The procedure developed explains the switching of constraints with time as a result of the change in the contacting areas at the gear teeth. The elastic behavior of the system is studied through the employment of three-dimensional isoparametric elements having six degrees-of-freedom at each node. The contact between the bodies is assumed at the various nodes, which could be either a line or a plane. The kinematical expressions, together with the equations of motion using Kane's method, strain energy concepts, are presented in a matrix form suitable for computer implementation. The constraint Jacobian matrices are generated automatically based on the contact information between the bodies. The concepts of the relative velocity at the contacting points at the tooth pairs and the subsequent use of the transmission ratios in the analysis is presented.

A stationary phase solution for mountain waves with application to mesospheric mountain waves generated by Auckland Island

NASA Astrophysics Data System (ADS)

Broutman, Dave; Eckermann, Stephen D.; Knight, Harold; Ma, Jun

2017-01-01

A relatively general stationary phase solution is derived for mountain waves from localized topography. It applies to hydrostatic, nonhydrostatic, or anelastic dispersion relations, to arbitrary localized topography, and to arbitrary smooth vertically varying background temperature and vector wind profiles. A simple method is introduced to compute the ray Jacobian that quantifies the effects of horizontal geometrical spreading in the stationary phase solution. The stationary phase solution is applied to mesospheric mountain waves generated by Auckland Island during the Deep Propagating Gravity Wave Experiment. The results are compared to a Fourier solution. The emphasis is on interpretations involving horizontal geometrical spreading. The results show larger horizontal geometrical spreading for nonhydrostatic waves than for hydrostatic waves in the region directly above the island; the dominant effect of horizontal geometrical spreading in the lower ˜30 km of the atmosphere, compared to the effects of refraction and background density variation; and the enhanced geometrical spreading due to directional wind in the approach to a critical layer in the mesosphere.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Observational constraints on transverse gravity: A generalization of unimodular gravity

NASA Astrophysics Data System (ADS)

Lopez-Villarejo, J. J.

2010-04-01

We explore the hypothesis that the set of symmetries enjoyed by the theory that describes gravity is not the full group of diffeomorphisms (Diff(M)), as in General Relativity, but a maximal subgroup of it (TransverseDiff(M)), with its elements having a jacobian equal to unity; at the infinitesimal level, the parameter describing the coordinate change xμ → xμ + ξμ(x) is transverse, i.e., δμξμ = 0. Incidentally, this is the smaller symmetry one needs to propagate consistently a graviton, which is a great theoretical motivation for considering these theories. Also, the determinant of the metric, g, behaves as a "transverse scalar", so that these theories can be seen as a generalization of the better-known unimodular gravity. We present our results on the observational constraints on transverse gravity, in close relation with the claim of equivalence with general scalar-tensor theory. We also comment on the structure of the divergences of the quantum theory to the one-loop order.

Assessing the Hydraulic Criticality of Deep Ocean Overflows

NASA Astrophysics Data System (ADS)

Pratt, L. J.; Helfrich, K. R.

2004-12-01

Two methods for assessing the hydraulic criticality of a modelled or observed deep overflow are discussed. The methods should be of use in determining the position of the control section, which is needed to establish the transport relation helpful for long-term monitoring from upstream. Both approaches are based on a multiple streamtube idealization in which the observed flow at a particular section is divided up into subsections (streamtubes). There are no restrictions on the bottom topography or potential vorticity distribution. The first criteria involves evauation of a generalized Jacobian condition based on the conservation laws for each streamtube; the second involves direct calculation of the long-wave phase speeds. We also comment on the significance of the local Froude number F of the flow and argue that F must pass through unity across a section of hydraulic control. These criteria are applied to some numerically modelled flows and are used in the companion presentation (Girton, et al.) to evaluate the hydraulic criticality of the Faroe Bank Channel.

Steering Law Design for Redundant Single Gimbal Control Moment Gyro Systems. M.S. Thesis - Massachusetts Inst. of Technology.

NASA Technical Reports Server (NTRS)

Bedrossian, Nazareth Sarkis

1987-01-01

The correspondence between robotic manipulators and single gimbal Control Moment Gyro (CMG) systems was exploited to aid in the understanding and design of single gimbal CMG Steering laws. A test for null motion near a singular CMG configuration was derived which is able to distinguish between escapable and unescapable singular states. Detailed analysis of the Jacobian matrix null-space was performed and results were used to develop and test a variety of single gimbal CMG steering laws. Computer simulations showed that all existing singularity avoidance methods are unable to avoid Elliptic internal singularities. A new null motion algorithm using the Moore-Penrose pseudoinverse, however, was shown by simulation to avoid Elliptic type singularities under certain conditions. The SR-inverse, with appropriate null motion was proposed as a general approach to singularity avoidance, because of its ability to avoid singularities through limited introduction of torque error. Simulation results confirmed the superior performance of this method compared to the other available and proposed pseudoinverse-based Steering laws.

An accelerated photo-magnetic imaging reconstruction algorithm based on an analytical forward solution and a fast Jacobian assembly method

NASA Astrophysics Data System (ADS)

Nouizi, F.; Erkol, H.; Luk, A.; Marks, M.; Unlu, M. B.; Gulsen, G.

2016-10-01

We previously introduced photo-magnetic imaging (PMI), an imaging technique that illuminates the medium under investigation with near-infrared light and measures the induced temperature increase using magnetic resonance thermometry (MRT). Using a multiphysics solver combining photon migration and heat diffusion, PMI models the spatiotemporal distribution of temperature variation and recovers high resolution optical absorption images using these temperature maps. In this paper, we present a new fast non-iterative reconstruction algorithm for PMI. This new algorithm uses analytic methods during the resolution of the forward problem and the assembly of the sensitivity matrix. We validate our new analytic-based algorithm with the first generation finite element method (FEM) based reconstruction algorithm previously developed by our team. The validation is performed using, first synthetic data and afterwards, real MRT measured temperature maps. Our new method accelerates the reconstruction process 30-fold when compared to a single iteration of the FEM-based algorithm.

Fully implicit adaptive mesh refinement solver for 2D MHD

NASA Astrophysics Data System (ADS)

Philip, B.; Chacon, L.; Pernice, M.

2008-11-01

Application of implicit adaptive mesh refinement (AMR) to simulate resistive magnetohydrodynamics is described. Solving this challenging multi-scale, multi-physics problem can improve understanding of reconnection in magnetically-confined plasmas. AMR is employed to resolve extremely thin current sheets, essential for an accurate macroscopic description. Implicit time stepping allows us to accurately follow the dynamical time scale of the developing magnetic field, without being restricted by fast Alfven time scales. At each time step, the large-scale system of nonlinear equations is solved by a Jacobian-free Newton-Krylov method together with a physics-based preconditioner. Each block within the preconditioner is solved optimally using the Fast Adaptive Composite grid method, which can be considered as a multiplicative Schwarz method on AMR grids. We will demonstrate the excellent accuracy and efficiency properties of the method with several challenging reduced MHD applications, including tearing, island coalescence, and tilt instabilities. B. Philip, L. Chac'on, M. Pernice, J. Comput. Phys., in press (2008)

Theory and praxis pf map analsys in CHEF part 1: Linear normal form

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

Michelotti, Leo; /Fermilab

2008-10-01

This memo begins a series which, put together, could comprise the 'CHEF Documentation Project' if there were such a thing. The first--and perhaps only--three will telegraphically describe theory, algorithms, implementation and usage of the normal form map analysis procedures encoded in CHEF's collection of libraries. [1] This one will begin the sequence by explaining the linear manipulations that connect the Jacobian matrix of a symplectic mapping to its normal form. It is a 'Reader's Digest' version of material I wrote in Intermediate Classical Dynamics (ICD) [2] and randomly scattered across technical memos, seminar viewgraphs, and lecture notes for the pastmore » quarter century. Much of its content is old, well known, and in some places borders on the trivial.1 Nevertheless, completeness requires their inclusion. The primary objective is the 'fundamental theorem' on normalization written on page 8. I plan to describe the nonlinear procedures in a subsequent memo and devote a third to laying out algorithms and lines of code, connecting them with equations written in the first two. Originally this was to be done in one short paper, but I jettisoned that approach after its first section exceeded a dozen pages. The organization of this document is as follows. A brief description of notation is followed by a section containing a general treatment of the linear problem. After the 'fundamental theorem' is proved, two further subsections discuss the generation of equilibrium distributions and issue of 'phase'. The final major section reviews parameterizations--that is, lattice functions--in two and four dimensions with a passing glance at the six-dimensional version. Appearances to the contrary, for the most part I have tried to restrict consideration to matters needed to understand the code in CHEF's libraries.« less

Accuracy analysis and design of A3 parallel spindle head

NASA Astrophysics Data System (ADS)

Ni, Yanbing; Zhang, Biao; Sun, Yupeng; Zhang, Yuan

2016-03-01

As functional components of machine tools, parallel mechanisms are widely used in high efficiency machining of aviation components, and accuracy is one of the critical technical indexes. Lots of researchers have focused on the accuracy problem of parallel mechanisms, but in terms of controlling the errors and improving the accuracy in the stage of design and manufacturing, further efforts are required. Aiming at the accuracy design of a 3-DOF parallel spindle head(A3 head), its error model, sensitivity analysis and tolerance allocation are investigated. Based on the inverse kinematic analysis, the error model of A3 head is established by using the first-order perturbation theory and vector chain method. According to the mapping property of motion and constraint Jacobian matrix, the compensatable and uncompensatable error sources which affect the accuracy in the end-effector are separated. Furthermore, sensitivity analysis is performed on the uncompensatable error sources. The sensitivity probabilistic model is established and the global sensitivity index is proposed to analyze the influence of the uncompensatable error sources on the accuracy in the end-effector of the mechanism. The results show that orientation error sources have bigger effect on the accuracy in the end-effector. Based upon the sensitivity analysis results, the tolerance design is converted into the issue of nonlinearly constrained optimization with the manufacturing cost minimum being the optimization objective. By utilizing the genetic algorithm, the allocation of the tolerances on each component is finally determined. According to the tolerance allocation results, the tolerance ranges of ten kinds of geometric error sources are obtained. These research achievements can provide fundamental guidelines for component manufacturing and assembly of this kind of parallel mechanisms.

3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids

NASA Astrophysics Data System (ADS)

Jahandari, H.; Farquharson, C. G.

2017-11-01

Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.

IceChrono v1: a probabilistic model to compute a common and optimal chronology for several ice cores

NASA Astrophysics Data System (ADS)

Parrenin, Frédéric

2015-04-01

Polar ice cores provide exceptional archives of past environmental conditions. The dating of ice cores is essential to interpret the paleo records that they contain, but it is a complicated problem since it involves different dating methods. Here I present IceChrono v1, a new probabilistic model to combine different kinds of chronological information to obtain a common and optimized chronology for several ice cores, as well as its uncertainty. It is based on the inversion of three quantities: the surface accumulation rate, the Lock-In Depth (LID) of air bubbles and the vertical thinning function. The chronological information used are: models of the sedimentation process (accumulation of snow, densification of snow into ice and air trapping, ice flow), ice and gas dated horizons, ice and gas dated depth intervals, Δdepth observations (depth shift between synchronous events recorded in the ice and in the air), stratigraphic links in between ice cores (ice-ice, air-air or mix ice-air and air-ice links). The optimization problem is formulated as a least squares problems, that is, all densities of probabilities are assumed gaussian. It is numerically solved using the Levenberg-Marquardt algorithm and a numerical evaluation of the model's Jacobian. IceChrono is similar in scope to the Datice model, but has differences from the mathematical, numerical and programming point of views. I apply IceChrono on an AICC2012-like experiment and I find similar results than Datice within a few centuries, which is a confirmation of both IceChrono and Datice codes. IceChrono v1 is freely available under the GPL v3 open source license.

Numerical study of comparison of vorticity and passive vectors in turbulence and inviscid flows

NASA Astrophysics Data System (ADS)

Ohkitani, Koji

2002-04-01

The nonlinear vortex stretching in incompressible Navier-Stokes turbulence is compared with a linear stretching process of passive vectors (PVs). In particular, we pay special attention to the difference of these processes under long and short time evolutions. For finite time evolution, we confirm our previous finding that the stretching effect of vorticity is weaker than that of general passive vectors for a majority of the initial conditions with the same energy spectra. The above difference can be explained qualitatively by examining the Biot-Savart formula. In order to see to what extent infinitesimal time development explains the above difference, we examine the probability density functions (PDFs) of the stretching rates of the passive vectors in the vicinity of a solution of Navier-Stokes equations. It is found that the PDFs are found to have a Gaussian distribution, suggesting that there are equally many PVs that stretched less and more than the vorticity. This suggests the importance of the vorticity-strain correlation built up over finite time in turbulence. We also discuss the case of Euler equations, where the dynamics of the Jacobian matrix relating the physical and material coordinates is examined numerically. A kind of alignment problem associated with the Cauchy-Green tensor is proposed and studied using the results of numerical simulations. It is found that vorticity tends to align itself with the most compressing eigenvector of the Cauchy-Green tensor. A two-dimensional counterpart of active-passive comparison is briefly studied. There is no essential difference between stretching of vorticity gradients and that of passive scalar gradients and a physical interpretation is given to it.

An open source software tool to assign the material properties of bone for ABAQUS finite element simulations.

PubMed

Pegg, Elise C; Gill, Harinderjit S

2016-09-06

A new software tool to assign the material properties of bone to an ABAQUS finite element mesh was created and compared with Bonemat, a similar tool originally designed to work with Ansys finite element models. Our software tool (py_bonemat_abaqus) was written in Python, which is the chosen scripting language for ABAQUS. The purpose of this study was to compare the software packages in terms of the material assignment calculation and processing speed. Three element types were compared (linear hexahedral (C3D8), linear tetrahedral (C3D4) and quadratic tetrahedral elements (C3D10)), both individually and as part of a mesh. Comparisons were made using a CT scan of a hemi-pelvis as a test case. A small difference, of -0.05kPa on average, was found between Bonemat version 3.1 (the current version) and our Python package. Errors were found in the previous release of Bonemat (version 3.0 downloaded from www.biomedtown.org) during calculation of the quadratic tetrahedron Jacobian, and conversion of the apparent density to modulus when integrating over the Young׳s modulus field. These issues caused up to 2GPa error in the modulus assignment. For these reasons, we recommend users upgrade to the most recent release of Bonemat. Processing speeds were assessed for the three different element types. Our Python package took significantly longer (110s on average) to perform the calculations compared with the Bonemat software (10s). Nevertheless, the workflow advantages of the package and added functionality makes 'py_bonemat_abaqus' a useful tool for ABAQUS users. Copyright © 2016 Elsevier Ltd. All rights reserved.

Diastolic chamber properties of the left ventricle assessed by global fitting of pressure-volume data: improving the gold standard of diastolic function.

PubMed

Bermejo, Javier; Yotti, Raquel; Pérez del Villar, Candelas; del Álamo, Juan C; Rodríguez-Pérez, Daniel; Martínez-Legazpi, Pablo; Benito, Yolanda; Antoranz, J Carlos; Desco, M Mar; González-Mansilla, Ana; Barrio, Alicia; Elízaga, Jaime; Fernández-Avilés, Francisco

2013-08-15

In cardiovascular research, relaxation and stiffness are calculated from pressure-volume (PV) curves by separately fitting the data during the isovolumic and end-diastolic phases (end-diastolic PV relationship), respectively. This method is limited because it assumes uncoupled active and passive properties during these phases, it penalizes statistical power, and it cannot account for elastic restoring forces. We aimed to improve this analysis by implementing a method based on global optimization of all PV diastolic data. In 1,000 Monte Carlo experiments, the optimization algorithm recovered entered parameters of diastolic properties below and above the equilibrium volume (intraclass correlation coefficients = 0.99). Inotropic modulation experiments in 26 pigs modified passive pressure generated by restoring forces due to changes in the operative and/or equilibrium volumes. Volume overload and coronary microembolization caused incomplete relaxation at end diastole (active pressure > 0.5 mmHg), rendering the end-diastolic PV relationship method ill-posed. In 28 patients undergoing PV cardiac catheterization, the new algorithm reduced the confidence intervals of stiffness parameters by one-fifth. The Jacobian matrix allowed visualizing the contribution of each property to instantaneous diastolic pressure on a per-patient basis. The algorithm allowed estimating stiffness from single-beat PV data (derivative of left ventricular pressure with respect to volume at end-diastolic volume intraclass correlation coefficient = 0.65, error = 0.07 ± 0.24 mmHg/ml). Thus, in clinical and preclinical research, global optimization algorithms provide the most complete, accurate, and reproducible assessment of global left ventricular diastolic chamber properties from PV data. Using global optimization, we were able to fully uncouple relaxation and passive PV curves for the first time in the intact heart.

Algebraic dynamic multilevel method for compositional flow in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Cusini, Matteo; Fryer, Barnaby; van Kruijsdijk, Cor; Hajibeygi, Hadi

2018-02-01

This paper presents the algebraic dynamic multilevel method (ADM) for compositional flow in three dimensional heterogeneous porous media in presence of capillary and gravitational effects. As a significant advancement compared to the ADM for immiscible flows (Cusini et al., 2016) [33], here, mass conservation equations are solved along with k-value based thermodynamic equilibrium equations using a fully-implicit (FIM) coupling strategy. Two different fine-scale compositional formulations are considered: (1) the natural variables and (2) the overall-compositions formulation. At each Newton's iteration the fine-scale FIM Jacobian system is mapped to a dynamically defined (in space and time) multilevel nested grid. The appropriate grid resolution is chosen based on the contrast of user-defined fluid properties and on the presence of specific features (e.g., well source terms). Consistent mapping between different resolutions is performed by the means of sequences of restriction and prolongation operators. While finite-volume restriction operators are employed to ensure mass conservation at all resolutions, various prolongation operators are considered. In particular, different interpolation strategies can be used for the different primary variables, and multiscale basis functions are chosen as pressure interpolators so that fine scale heterogeneities are accurately accounted for across different resolutions. Several numerical experiments are conducted to analyse the accuracy, efficiency and robustness of the method for both 2D and 3D domains. Results show that ADM provides accurate solutions by employing only a fraction of the number of grid-cells employed in fine-scale simulations. As such, it presents a promising approach for large-scale simulations of multiphase flow in heterogeneous reservoirs with complex non-linear fluid physics.

Multi-equilibrium property of metabolic networks: SSI module.

PubMed

Lei, Hong-Bo; Zhang, Ji-Feng; Chen, Luonan

2011-06-20

Revealing the multi-equilibrium property of a metabolic network is a fundamental and important topic in systems biology. Due to the complexity of the metabolic network, it is generally a difficult task to study the problem as a whole from both analytical and numerical viewpoint. On the other hand, the structure-oriented modularization idea is a good choice to overcome such a difficulty, i.e. decomposing the network into several basic building blocks and then studying the whole network through investigating the dynamical characteristics of the basic building blocks and their interactions. Single substrate and single product with inhibition (SSI) metabolic module is one type of the basic building blocks of metabolic networks, and its multi-equilibrium property has important influence on that of the whole metabolic networks. In this paper, we describe what the SSI metabolic module is, characterize the rates of the metabolic reactions by Hill kinetics and give a unified model for SSI modules by using a set of nonlinear ordinary differential equations with multi-variables. Specifically, a sufficient and necessary condition is first given to describe the injectivity of a class of nonlinear systems, and then, the sufficient condition is used to study the multi-equilibrium property of SSI modules. As a main theoretical result, for the SSI modules in which each reaction has no more than one inhibitor, a sufficient condition is derived to rule out multiple equilibria, i.e. the Jacobian matrix of its rate function is nonsingular everywhere. In summary, we describe SSI modules and give a general modeling framework based on Hill kinetics, and provide a sufficient condition for ruling out multiple equilibria of a key type of SSI module.

Multi-equilibrium property of metabolic networks: SSI module

PubMed Central

2011-01-01

Background Revealing the multi-equilibrium property of a metabolic network is a fundamental and important topic in systems biology. Due to the complexity of the metabolic network, it is generally a difficult task to study the problem as a whole from both analytical and numerical viewpoint. On the other hand, the structure-oriented modularization idea is a good choice to overcome such a difficulty, i.e. decomposing the network into several basic building blocks and then studying the whole network through investigating the dynamical characteristics of the basic building blocks and their interactions. Single substrate and single product with inhibition (SSI) metabolic module is one type of the basic building blocks of metabolic networks, and its multi-equilibrium property has important influence on that of the whole metabolic networks. Results In this paper, we describe what the SSI metabolic module is, characterize the rates of the metabolic reactions by Hill kinetics and give a unified model for SSI modules by using a set of nonlinear ordinary differential equations with multi-variables. Specifically, a sufficient and necessary condition is first given to describe the injectivity of a class of nonlinear systems, and then, the sufficient condition is used to study the multi-equilibrium property of SSI modules. As a main theoretical result, for the SSI modules in which each reaction has no more than one inhibitor, a sufficient condition is derived to rule out multiple equilibria, i.e. the Jacobian matrix of its rate function is nonsingular everywhere. Conclusions In summary, we describe SSI modules and give a general modeling framework based on Hill kinetics, and provide a sufficient condition for ruling out multiple equilibria of a key type of SSI module. PMID:21689474

Elimination of secular terms from the differential equations for the elements of perturbed two-body motion

NASA Technical Reports Server (NTRS)

Bond, Victor R.; Fraietta, Michael F.

1991-01-01

In 1961, Sperling linearized and regularized the differential equations of motion of the two-body problem by changing the independent variable from time to fictitious time by Sundman's transformation (r = dt/ds) and by embedding the two-body energy integral and the Laplace vector. In 1968, Burdet developed a perturbation theory which was uniformly valid for all types of orbits using a variation of parameters approach on the elements which appeared in Sperling's equations for the two-body solution. In 1973, Bond and Hanssen improved Burdet's set of differential equations by embedding the total energy (which is a constant when the potential function is explicitly dependent upon time.) The Jacobian constant was used as an element to replace the total energy in a reformulation of the differential equations of motion. In the process, another element which is proportional to a component of the angular momentum was introduced. Recently trajectories computed during numerical studies of atmospheric entry from circular orbits and low thrust beginning in near-circular orbits exhibited numerical instability when solved by the method of Bond and Gottlieb (1989) for long time intervals. It was found that this instability was due to secular terms which appear on the righthand sides of the differential equations of some of the elements. In this paper, this instability is removed by the introduction of another vector integral called the delta integral (which replaces the Laplace Vector) and another scalar integral which removes the secular terms. The introduction of these integrals requires a new derivation of the differential equations for most of the elements. For this rederivation, the Lagrange method of variation of parameters is used, making the development more concise. Numerical examples of this improvement are presented.

IceChrono1: a probabilistic model to compute a common and optimal chronology for several ice cores

NASA Astrophysics Data System (ADS)

Parrenin, Frédéric; Bazin, Lucie; Capron, Emilie; Landais, Amaëlle; Lemieux-Dudon, Bénédicte; Masson-Delmotte, Valérie

2016-04-01

Polar ice cores provide exceptional archives of past environmental conditions. The dating of ice cores and the estimation of the age scale uncertainty are essential to interpret the climate and environmental records that they contain. It is however a complex problem which involves different methods. Here, we present IceChrono1, a new probabilistic model integrating various sources of chronological information to produce a common and optimized chronology for several ice cores, as well as its uncertainty. IceChrono1 is based on the inversion of three quantities: the surface accumulation rate, the Lock-In Depth (LID) of air bubbles and the thinning function. The chronological information integrated into the model are: models of the sedimentation process (accumulation of snow, densification of snow into ice and air trapping, ice flow), ice and air dated horizons, ice and air depth intervals with known durations, Δdepth observations (depth shift between synchronous events recorded in the ice and in the air) and finally air and ice stratigraphic links in between ice cores. The optimization is formulated as a least squares problem, implying that all densities of probabilities are assumed to be Gaussian. It is numerically solved using the Levenberg-Marquardt algorithm and a numerical evaluation of the model's Jacobian. IceChrono follows an approach similar to that of the Datice model which was recently used to produce the AICC2012 chronology for 4 Antarctic ice cores and 1 Greenland ice core. IceChrono1 provides improvements and simplifications with respect to Datice from the mathematical, numerical and programming point of views. The capabilities of IceChrono is demonstrated on a case study similar to the AICC2012 dating experiment. We find results similar to those of Datice, within a few centuries, which is a confirmation of both IceChrono and Datice codes. We also test new functionalities with respect to the original version of Datice: observations as ice intervals with known durations, correlated observations, observations as gas intervals with known durations and observations as mixed ice-air stratigraphic links. IceChrono1 is freely available under the GPL v3 open source license.

IceChrono1: a probabilistic model to compute a common and optimal chronology for several ice cores

NASA Astrophysics Data System (ADS)

Parrenin, F.; Bazin, L.; Capron, E.; Landais, A.; Lemieux-Dudon, B.; Masson-Delmotte, V.

2015-05-01

Polar ice cores provide exceptional archives of past environmental conditions. The dating of ice cores and the estimation of the age-scale uncertainty are essential to interpret the climate and environmental records that they contain. It is, however, a complex problem which involves different methods. Here, we present IceChrono1, a new probabilistic model integrating various sources of chronological information to produce a common and optimized chronology for several ice cores, as well as its uncertainty. IceChrono1 is based on the inversion of three quantities: the surface accumulation rate, the lock-in depth (LID) of air bubbles and the thinning function. The chronological information integrated into the model are models of the sedimentation process (accumulation of snow, densification of snow into ice and air trapping, ice flow), ice- and air-dated horizons, ice and air depth intervals with known durations, depth observations (depth shift between synchronous events recorded in the ice and in the air) and finally air and ice stratigraphic links in between ice cores. The optimization is formulated as a least squares problem, implying that all densities of probabilities are assumed to be Gaussian. It is numerically solved using the Levenberg-Marquardt algorithm and a numerical evaluation of the model's Jacobian. IceChrono follows an approach similar to that of the Datice model which was recently used to produce the AICC2012 (Antarctic ice core chronology) for four Antarctic ice cores and one Greenland ice core. IceChrono1 provides improvements and simplifications with respect to Datice from the mathematical, numerical and programming point of views. The capabilities of IceChrono1 are demonstrated on a case study similar to the AICC2012 dating experiment. We find results similar to those of Datice, within a few centuries, which is a confirmation of both IceChrono1 and Datice codes. We also test new functionalities with respect to the original version of Datice: observations as ice intervals with known durations, correlated observations, observations as air intervals with known durations and observations as mixed ice-air stratigraphic links. IceChrono1 is freely available under the General Public License v3 open source license.

Kinematic synthesis of bevel-gear-type robotic wrist mechanisms

NASA Astrophysics Data System (ADS)

Lin, Chen-Chou

Bevel-gear-type robotic wrist mechanisms are commonly used in industry. The reasons for their popularity are that they are compact, light-weight, and relatively inexpensive. However, there are singularities in their workspace, which substantially degrade their manipulative performance. The objective of this research is to develop an atlas of three-degree-of-freedom bevel-gear-type wrist mechanisms, and through dimensional synthesis to improve their kinematic performance. The dissertation contains two major parts: the first is structural analysis and synthesis, the other is kinematic analysis and dimensional synthesis. To synthesize the kinematic structures of bevel-gear-type wrist mechanisms, the kinematic structures are separated from their functional considerations. All kinematic structures which satisfy the mobility condition are enumerated in an unbiased, systematic manner. Then the bevel-gear-type wrist mechanisms are identified by applying the functional requirements. Structural analysis shows that a three-degree-of-freedom wrist mechanism usually consists of non-fractionated, two degree-of-freedom epicyclic gear train jointed with the base link. Therefore, the structural synthesis can be simplified into a problem of examining the atlas of non-fractionated, two-degree-of-freedom epicyclic gear trains. The resulting bevel-gear-type wrist mechanism has been categorized and evaluated. It is shown that three-degree-of-freedom, four-jointed wrist mechanisms are promising for further improving the kinematic performance. It is found that a spherical planetary gear train is necessarily imbedded in a three-degree-of-freedom, four-jointed wrist mechanism. Therefore, to study the workspace and singularity problems of three-degree-of-freedom four-jointed spherical wrist mechanisms, we have to study the trajectories of spherical planetary gear trains. The parametric equations of the trajectories and some useful geometric properties for the analysis and synthesis of workplace are derived. The workspace boundary equations can be derived via both geometric consideration and Jacobian analysis. The workspace is divided by inner and outer boundaries into regions of accessibility of zero, two, and four. The design criteria of full workspace and a maximum four-root region are established.

Numerical simulations of induction and MWD logging tools and data inversion method with X-window interface on a UNIX workstation

NASA Astrophysics Data System (ADS)

Tian, Xiang-Dong

The purpose of this research is to simulate induction and measuring-while-drilling (MWD) logs. In simulation of logs, there are two tasks. The first task, the forward modeling procedure, is to compute the logs from known formation. The second task, the inversion procedure, is to determine the unknown properties of the formation from the measured field logs. In general, the inversion procedure requires the solution of a forward model. In this study, a stable numerical method to simulate induction and MWD logs is presented. The proposed algorithm is based on a horizontal eigenmode expansion method. Vertical propagation of modes is modeled by a three-layer module. The multilayer cases are treated as a cascade of these modules. The mode tracing algorithm possesses stable characteristics that are superior to other methods. This method is applied to simulate the logs in the formations with both vertical and horizontal layers, and also used to study the groove effects of the MWD tool. The results are very good. Two-dimensional inversion of induction logs is an nonlinear problem. Nonlinear functions of the apparent conductivity are expanded into a Taylor series. After truncating the high order terms in this Taylor series, the nonlinear functions are linearized. An iterative procedure is then devised to solve the inversion problem. In each iteration, the Jacobian matrix is calculated, and a small variation computed using the least-squares method is used to modify the background medium. Finally, the inverted medium is obtained. The horizontal eigenstate method is used to solve the forward problem. It is found that a good inverted formation can be obtained by using measurements. In order to help the user simulate the induction logs conveniently, a Wellog Simulator, based on the X-window system, is developed. The application software (FORTRAN codes) embedded in the Simulator is designed to simulate the responses of the induction tools in the layered formation with dipping beds. The graphic user-interface part of the Wellog Simulator is implemented with C and Motif. Through the user interface, the user can prepare the simulation data, select the tools, simulate the logs and plot the results.

Characterizing species interactions to understand press perturbations: What is the community matrix?

USGS Publications Warehouse

Novak, Mark; Yeakel, Justin D.; Noble, Andrew E.; Doak, Daniel F.; Emmerson, Mark; Estes, James A.; Jacob, Ute; Tinker, M. Tim; Wootton, J. Timothy

2016-01-01

The community matrix is among ecology's most important mathematical abstractions, formally encapsulating the interconnected network of effects that species have on one another's populations. Despite its importance, the term `community matrix' has been applied to matrices having differing interpretations. This has hindered the application of theory for understanding community structure and perturbation responses, particularly in the contexts of ecosystem-based management and conservation. Here we clarify the correspondence and distinctions between the Interaction matrix, the Alpha matrix and the Jacobian matrix, terms which are frequently used interchangeably and have numerous synonyms, including the term Community matrix. We illustrate how these matrices correspond to different ways of characterizing interaction strengths, how they permit insights regarding different types of press perturbations of species growth rates or abundances, and how these are related by a simple scaling relationship. Connections to additional interaction strength characterizations encapsulated by the Beta matrix, the Gamma matrix, and the Removal matrix are also discussed. Our synthesis highlights the empirical challenges that remain in using these mathematical tools to understand actual communities.

A computationally efficient method for full-core conjugate heat transfer modeling of sodium fast reactors

DOE PAGES

Hu, Rui; Yu, Yiqi

2016-09-08

For efficient and accurate temperature predictions of sodium fast reactor structures, a 3-D full-core conjugate heat transfer modeling capability is developed for an advanced system analysis tool, SAM. The hexagon lattice core is modeled with 1-D parallel channels representing the subassembly flow, and 2-D duct walls and inter-assembly gaps. The six sides of the hexagon duct wall and near-wall coolant region are modeled separately to account for different temperatures and heat transfer between coolant flow and each side of the duct wall. The Jacobian Free Newton Krylov (JFNK) solution method is applied to solve the fluid and solid field simultaneouslymore » in a fully coupled fashion. The 3-D full-core conjugate heat transfer modeling capability in SAM has been demonstrated by a verification test problem with 7 fuel assemblies in a hexagon lattice layout. In addition, the SAM simulation results are compared with RANS-based CFD simulations. Very good agreements have been achieved between the results of the two approaches.« less

Domain decomposition methods for the parallel computation of reacting flows

NASA Technical Reports Server (NTRS)

Keyes, David E.

1988-01-01

Domain decomposition is a natural route to parallel computing for partial differential equation solvers. Subdomains of which the original domain of definition is comprised are assigned to independent processors at the price of periodic coordination between processors to compute global parameters and maintain the requisite degree of continuity of the solution at the subdomain interfaces. In the domain-decomposed solution of steady multidimensional systems of PDEs by finite difference methods using a pseudo-transient version of Newton iteration, the only portion of the computation which generally stands in the way of efficient parallelization is the solution of the large, sparse linear systems arising at each Newton step. For some Jacobian matrices drawn from an actual two-dimensional reacting flow problem, comparisons are made between relaxation-based linear solvers and also preconditioned iterative methods of Conjugate Gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately 10-fold speedup on 16 processors.

Reply to "Comment on 'Hydrodynamics of fractal continuum flow' and 'Map of fluid flow in fractal porous medium into fractal continuum flow'".

PubMed

Balankin, Alexander S; Elizarraraz, Benjamin Espinoza

2013-11-01

The aim of this Reply is to elucidate the difference between the fractal continuum models used in the preceding Comment and the models of fractal continuum flow which were put forward in our previous articles [Phys. Rev. E 85, 025302(R) (2012); 85, 056314 (2012)]. In this way, some drawbacks of the former models are highlighted. Specifically, inconsistencies in the definitions of the fractal derivative, the Jacobian of transformation, the displacement vector, and angular momentum are revealed. The proper forms of the Reynolds' transport theorem and angular momentum principle for the fractal continuum are reaffirmed in a more illustrative manner. Consequently, we emphasize that in the absence of any internal angular momentum, body couples, and couple stresses, the Cauchy stress tensor in the fractal continuum should be symmetric. Furthermore, we stress that the approach based on the Cartesian product measured and used in the preceding Comment cannot be employed to study the path-connected fractals, such as a flow in a fractally permeable medium. Thus, all statements of our previous works remain unchallenged.

Diffeomorphic demons: efficient non-parametric image registration.

PubMed

Vercauteren, Tom; Pennec, Xavier; Perchant, Aymeric; Ayache, Nicholas

2009-03-01

We propose an efficient non-parametric diffeomorphic image registration algorithm based on Thirion's demons algorithm. In the first part of this paper, we show that Thirion's demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. We provide strong theoretical roots to the different variants of Thirion's demons algorithm. This analysis predicts a theoretical advantage for the symmetric forces variant of the demons algorithm. We show on controlled experiments that this advantage is confirmed in practice and yields a faster convergence. In the second part of this paper, we adapt the optimization procedure underlying the demons algorithm to a space of diffeomorphic transformations. In contrast to many diffeomorphic registration algorithms, our solution is computationally efficient since in practice it only replaces an addition of displacement fields by a few compositions. Our experiments show that in addition to being diffeomorphic, our algorithm provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the gold standard, available in controlled experiments, in terms of Jacobians.

Rate-Based Model Predictive Control of Turbofan Engine Clearance

NASA Technical Reports Server (NTRS)

DeCastro, Jonathan A.

2006-01-01

An innovative model predictive control strategy is developed for control of nonlinear aircraft propulsion systems and sub-systems. At the heart of the controller is a rate-based linear parameter-varying model that propagates the state derivatives across the prediction horizon, extending prediction fidelity to transient regimes where conventional models begin to lose validity. The new control law is applied to a demanding active clearance control application, where the objectives are to tightly regulate blade tip clearances and also anticipate and avoid detrimental blade-shroud rub occurrences by optimally maintaining a predefined minimum clearance. Simulation results verify that the rate-based controller is capable of satisfying the objectives during realistic flight scenarios where both a conventional Jacobian-based model predictive control law and an unconstrained linear-quadratic optimal controller are incapable of doing so. The controller is evaluated using a variety of different actuators, illustrating the efficacy and versatility of the control approach. It is concluded that the new strategy has promise for this and other nonlinear aerospace applications that place high importance on the attainment of control objectives during transient regimes.

Collective relaxation dynamics of small-world networks

NASA Astrophysics Data System (ADS)

Grabow, Carsten; Grosskinsky, Stefan; Kurths, Jürgen; Timme, Marc

2015-05-01

Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph Laplacian, or a similar linear operator. The structure of networks with regular, small-world, and random connectivities are reasonably well understood, but their collective dynamical properties remain largely unknown. Here we present a two-stage mean-field theory to derive analytic expressions for network spectra. A single formula covers the spectrum from regular via small-world to strongly randomized topologies in Watts-Strogatz networks, explaining the simultaneous dependencies on network size N , average degree k , and topological randomness q . We present simplified analytic predictions for the second-largest and smallest eigenvalue, and numerical checks confirm our theoretical predictions for zero, small, and moderate topological randomness q , including the entire small-world regime. For large q of the order of one, we apply standard random matrix theory, thereby overarching the full range from regular to randomized network topologies. These results may contribute to our analytic and mechanistic understanding of collective relaxation phenomena of network dynamical systems.

Kinematically Optimal Robust Control of Redundant Manipulators

NASA Astrophysics Data System (ADS)

Galicki, M.

2017-12-01

This work deals with the problem of the robust optimal task space trajectory tracking subject to finite-time convergence. Kinematic and dynamic equations of a redundant manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the endeffector. Furthermore, the movement is to be accomplished in such a way as to minimize both the manipulator torques and their oscillations thus eliminating the potential robot vibrations. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of chattering-free robust kinematically optimal controllers, based on the estimation of transpose Jacobian, which seem to be effective in counteracting both uncertain kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a redundant manipulator of a SCARA type consisting of the three revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers as well as comparisons with other well known control schemes.

Robust Task Space Trajectory Tracking Control of Robotic Manipulators

NASA Astrophysics Data System (ADS)

Galicki, M.

2016-08-01

This work deals with the problem of the accurate task space trajectory tracking subject to finite-time convergence. Kinematic and dynamic equations of a redundant manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the end-effector. Furthermore, the movement is to be accomplished in such a way as to reduce both the manipulator torques and their oscillations thus eliminating the potential robot vibrations. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we propose a class of chattering-free robust controllers, based on the estimation of transpose Jacobian, which seem to be effective in counteracting both uncertain kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a redundant manipulator of a SCARA type consisting of the three revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers as well as comparisons with other well known control schemes.

Revisiting arithmetic solutions to the W =0 condition

NASA Astrophysics Data System (ADS)

Kanno, Keita; Watari, Taizan

2017-11-01

The gravitino mass is expected not to be much smaller than the Planck scale for a large fraction of vacua in flux compactifications. There is no continuous parameter to tune even by hand, and it seems that the gravitino mass can be small only as a result of accidental cancellation among period integrals weighted by integer-valued flux quanta. DeWolfe et al. [J. High Energy Phys. 02 (2005) 037, 10.1088/1126-6708/2005/02/037] proposed paying close attention to vacua where the Hodge decomposition is possible within a number field, so that the precise cancellation takes place as a result of algebra. We focus on a subclass of those vacua—those with complex multiplication—and explore more on the idea in this article. It turns out, in Type IIB compactifications, that those vacua admit nontrivial supersymmetric flux configurations if and only if the reflex field of the Weil intermediate Jacobian is isomorphic to the quadratic imaginary field generated by the axidilaton vacuum expectation value. We also found that flux statistics are highly enriched on such vacua, as F-term conditions become linearly dependent.