WorldWideScience

Sample records for volume spatial discretization

  1. Compatible Spatial Discretizations for Partial Differential Equations

    Energy Technology Data Exchange (ETDEWEB)

    Arnold, Douglas, N, ed.

    2004-11-25

    From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical

  2. A spatial discretization of the MHD equations based on the finite volume - spectral method

    International Nuclear Information System (INIS)

    Miyoshi, Takahiro

    2000-05-01

    Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA φ , is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)

  3. Spatially localized, temporally quasiperiodic, discrete nonlinear excitations

    International Nuclear Information System (INIS)

    Cai, D.; Bishop, A.R.; Gronbech-Jensen, N.

    1995-01-01

    In contrast to the commonly discussed discrete breather, which is a spatially localized, time-periodic solution, we present an exact solution of a discrete nonlinear Schroedinger breather which is a spatially localized, temporally quasiperiodic nonlinear coherent excitation. This breather is a multiple-soliton solution in the sense of the inverse scattering transform. A discrete breather of multiple frequencies is conceptually important in studies of nonlinear lattice systems. We point out that, for this breather, the incommensurability of its frequencies is a discrete lattice effect and these frequencies become commensurate in the continuum limit. To understand the dynamical properties of the breather, we also discuss its stability and its behavior in the presence of an external potential. Finally, we indicate how to obtain an exact N-soliton breather as a discrete generalization of the continuum multiple-soliton solution

  4. Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media

    International Nuclear Information System (INIS)

    Coelho, Pedro J.

    2014-01-01

    Many methods are available for the solution of radiative heat transfer problems in participating media. Among these, the discrete ordinates method (DOM) and the finite volume method (FVM) are among the most widely used ones. They provide a good compromise between accuracy and computational requirements, and they are relatively easy to integrate in CFD codes. This paper surveys recent advances on these numerical methods. Developments concerning the grid structure (e.g., new formulations for axisymmetrical geometries, body-fitted structured and unstructured meshes, embedded boundaries, multi-block grids, local grid refinement), the spatial discretization scheme, and the angular discretization scheme are described. Progress related to the solution accuracy, solution algorithm, alternative formulations, such as the modified DOM and FVM, even-parity formulation, discrete-ordinates interpolation method and method of lines, and parallelization strategies is addressed. The application to non-gray media, variable refractive index media, and transient problems is also reviewed. - Highlights: • We survey recent advances in the discrete ordinates and finite volume methods. • Developments in spatial and angular discretization schemes are described. • Progress in solution algorithms and parallelization methods is reviewed. • Advances in the transient solution of the radiative transfer equation are appraised. • Non-gray media and variable refractive index media are briefly addressed

  5. Asymptotic analysis of spatial discretizations in implicit Monte Carlo

    International Nuclear Information System (INIS)

    Densmore, Jeffery D.

    2009-01-01

    We perform an asymptotic analysis of spatial discretizations in Implicit Monte Carlo (IMC). We consider two asymptotic scalings: one that represents a time step that resolves the mean-free time, and one that corresponds to a fixed, optically large time step. We show that only the latter scaling results in a valid spatial discretization of the proper diffusion equation, and thus we conclude that IMC only yields accurate solutions when using optically large spatial cells if time steps are also optically large. We demonstrate the validity of our analysis with a set of numerical examples.

  6. A Spatial Discretization Scheme for Solving the Transport Equation on Unstructured Grids of Polyhedra

    International Nuclear Information System (INIS)

    Thompson, K.G.

    2000-01-01

    In this work, we develop a new spatial discretization scheme that may be used to numerically solve the neutron transport equation. This new discretization extends the family of corner balance spatial discretizations to include spatial grids of arbitrary polyhedra. This scheme enforces balance on subcell volumes called corners. It produces a lower triangular matrix for sweeping, is algebraically linear, is non-negative in a source-free absorber, and produces a robust and accurate solution in thick diffusive regions. Using an asymptotic analysis, we design the scheme so that in thick diffusive regions it will attain the same solution as an accurate polyhedral diffusion discretization. We then refine the approximations in the scheme to reduce numerical diffusion in vacuums, and we attempt to capture a second order truncation error. After we develop this Upstream Corner Balance Linear (UCBL) discretization we analyze its characteristics in several limits. We complete a full diffusion limit analysis showing that we capture the desired diffusion discretization in optically thick and highly scattering media. We review the upstream and linear properties of our discretization and then demonstrate that our scheme captures strictly non-negative solutions in source-free purely absorbing media. We then demonstrate the minimization of numerical diffusion of a beam and then demonstrate that the scheme is, in general, first order accurate. We also note that for slab-like problems our method actually behaves like a second-order method over a range of cell thicknesses that are of practical interest. We also discuss why our scheme is first order accurate for truly 3D problems and suggest changes in the algorithm that should make it a second-order accurate scheme. Finally, we demonstrate 3D UCBL's performance on several very different test problems. We show good performance in diffusive and streaming problems. We analyze truncation error in a 3D problem and demonstrate robustness in a

  7. Assembly Discontinuity Factors for the Neutron Diffusion Equation discretized with the Finite Volume Method. Application to BWR

    International Nuclear Information System (INIS)

    Bernal, A.; Roman, J.E.; Miró, R.; Verdú, G.

    2016-01-01

    Highlights: • A method is proposed to solve the eigenvalue problem of the Neutron Diffusion Equation in BWR. • The Neutron Diffusion Equation is discretized with the Finite Volume Method. • The currents are calculated by using a polynomial expansion of the neutron flux. • The current continuity and boundary conditions are defined implicitly to reduce the size of the matrices. • Different structured and unstructured meshes were used to discretize the BWR. - Abstract: The neutron flux spatial distribution in Boiling Water Reactors (BWRs) can be calculated by means of the Neutron Diffusion Equation (NDE), which is a space- and time-dependent differential equation. In steady state conditions, the time derivative terms are zero and this equation is rewritten as an eigenvalue problem. In addition, the spatial partial derivatives terms are transformed into algebraic terms by discretizing the geometry and using numerical methods. As regards the geometrical discretization, BWRs are complex systems containing different components of different geometries and materials, but they are usually modelled as parallelepiped nodes each one containing only one homogenized material to simplify the solution of the NDE. There are several techniques to correct the homogenization in the node, but the most commonly used in BWRs is that based on Assembly Discontinuity Factors (ADFs). As regards numerical methods, the Finite Volume Method (FVM) is feasible and suitable to be applied to the NDE. In this paper, a FVM based on a polynomial expansion method has been used to obtain the matrices of the eigenvalue problem, assuring the accomplishment of the ADFs for a BWR. This eigenvalue problem has been solved by means of the SLEPc library.

  8. The effect of spatial discretization in LWR cell calculations with HELIOS 1.9

    International Nuclear Information System (INIS)

    Merk, B.; Koch, R.

    2008-01-01

    Cell and lattice calculations are the basis for all deterministic static and transient 3D full core calculations. The spatial discretization used for the cell and lattice calculations influences the results for these transport solutions significantly. The arising differences in the neutron flux distribution due to different spatial discretization are demonstrated. These differences in the flux distribution cause significant changes in the kinf value. An evaluation of the kinf value for the case of infinitely fine discretization is made. The influence of the discretization on the calculation of homogenized few group cross sections which are forwarded to the 3D full core calculations is investigated. Strategies for improving the discretization are developed and their influence on the calculation time is evaluated. (Authors)

  9. Spatial discretizations for self-adjoint forms of the radiative transfer equations

    International Nuclear Information System (INIS)

    Morel, Jim E.; Adams, B. Todd; Noh, Taewan; McGhee, John M.; Evans, Thomas M.; Urbatsch, Todd J.

    2006-01-01

    There are three commonly recognized second-order self-adjoint forms of the neutron transport equation: the even-parity equations, the odd-parity equations, and the self-adjoint angular flux equations. Because all of these equations contain second-order spatial derivatives and are self-adjoint for the mono-energetic case, standard continuous finite-element discretization techniques have proved quite effective when applied to the spatial variables. We first derive analogs of these equations for the case of time-dependent radiative transfer. The primary unknowns for these equations are functions of the angular intensity rather than the angular flux, hence the analog of the self-adjoint angular flux equation is referred to as the self-adjoint angular intensity equation. Then we describe a general, arbitrary-order, continuous spatial finite-element approach that is applied to each of the three equations in conjunction with backward-Euler differencing in time. We refer to it as the 'standard' technique. We also introduce an alternative spatial discretization scheme for the self-adjoint angular intensity equation that requires far fewer unknowns than the standard method, but appears to give comparable accuracy. Computational results are given that demonstrate the validity of both of these discretization schemes

  10. Spatial Treatment of the Slab-geometry Discrete Ordinates Equations Using Artificial Neural Networks

    International Nuclear Information System (INIS)

    Brantley, P S

    2001-01-01

    An artificial neural network (ANN) method is developed for treating the spatial variable of the one-group slab-geometry discrete ordinates (S N ) equations in a homogeneous medium with linearly anisotropic scattering. This ANN method takes advantage of the function approximation capability of multilayer ANNs. The discrete ordinates angular flux is approximated by a multilayer ANN with a single input representing the spatial variable x and N outputs representing the angular flux in each of the discrete ordinates angular directions. A global objective function is formulated which measures how accurately the output of the ANN approximates the solution of the discrete ordinates equations and boundary conditions at specified spatial points. Minimization of this objective function determines the appropriate values for the parameters of the ANN. Numerical results are presented demonstrating the accuracy of the method for both fixed source and incident angular flux problems

  11. Spreading speed and travelling waves for a spatially discrete SIS epidemic model

    International Nuclear Information System (INIS)

    Zhang, Kate Fang; Zhao Xiaoqiang

    2008-01-01

    This paper is devoted to the study of the asymptotic speed of spread and travelling waves for a spatially discrete SIS epidemic model. By appealing to the theory of spreading speeds and travelling waves for monotonic semiflows, we establish the existence of asymptotic speed of spread and show that it coincides with the minimal wave speed for monotonic travelling waves. This also gives an affirmative answer to an open problem presented by Rass and Radcliffe (2003 Spatial Deterministic Epidemics (Mathematical Surveys and Monographs vol 102) (Providence, RI: American Mathematical Society)) in the case of discrete spatial habitat

  12. Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation

    Science.gov (United States)

    Litaker, Eric T.

    1994-12-01

    The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.

  13. Slab geometry spatial discretization schemes with infinite-order convergence

    International Nuclear Information System (INIS)

    Adams, M.L.; Martin, W.R.

    1985-01-01

    Spatial discretization schemes for the slab geometry discrete ordinates transport equation have received considerable attention in the past several years, with particular interest shown in developing methods that are more computationally efficient that standard schemes. Here the authors apply to the discrete ordinates equations a spectral method that is significantly more efficient than previously proposed schemes for high-accuracy calculations of homogeneous problems. This is a direct consequence of the exponential (infinite-order) convergence of spectral methods for problems with every smooth solutions. For heterogeneous problems where smooth solutions do not exist and exponential convergence is not observed with spectral methods, a spectral element method is proposed which does exhibit exponential convergence

  14. A piecewise bi-linear discontinuous finite element spatial discretization of the Sn transport equation

    International Nuclear Information System (INIS)

    Bailey, Teresa S.; Warsa, James S.; Chang, Jae H.; Adams, Marvin L.

    2011-01-01

    We present a new spatial discretization of the discrete-ordinates transport equation in two dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretization that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems. (author)

  15. A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

    International Nuclear Information System (INIS)

    Bailey, T.S.; Chang, J.H.; Warsa, J.S.; Adams, M.L.

    2010-01-01

    We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

  16. A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, T S; Chang, J H; Warsa, J S; Adams, M L

    2010-12-22

    We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

  17. A new spatial multiple discrete-continuous modeling approach to land use change analysis.

    Science.gov (United States)

    2013-09-01

    This report formulates a multiple discrete-continuous probit (MDCP) land-use model within a : spatially explicit economic structural framework for land-use change decisions. The spatial : MDCP model is capable of predicting both the type and intensit...

  18. Normal scheme for solving the transport equation independently of spatial discretization

    International Nuclear Information System (INIS)

    Zamonsky, O.M.

    1993-01-01

    To solve the discrete ordinates neutron transport equation, a general order nodal scheme is used, where nodes are allowed to have different orders of approximation and the whole system reaches a final order distribution. Independence in the election of system discretization and order of approximation is obtained without loss of accuracy. The final equations and the iterative method to reach a converged order solution were implemented in a two-dimensional computer code to solve monoenergetic, isotropic scattering, external source problems. Two benchmark problems were solved using different automatic selection order methods. Results show accurate solutions without spatial discretization, regardless of the initial selection of distribution order. (author)

  19. On the influence of spatial discretization in LWR cell- and lattice calculations with HELIOS 1.9

    International Nuclear Information System (INIS)

    Merk, B.; Koch, R.

    2008-01-01

    Cell- and lattice calculations are the fundamental for all deterministic static and transient 3D full core calculations. The spatial discretization used for the cell- and lattice calculations influences the results for these transport solutions significantly. The arising differences in the neutron flux distribution due to different spatial discretization are demonstrated. These differences in the flux distribution cause significant changes in the k inf value. An evaluation of the k inf value for the case of infinitely fine discretization is made. The influence of the discretization on the calculation of homogenized few group cross-sections which are forwarded to the 3D full core calculations is investigated. Strategies for improving the discretization are developed and their influence on the calculation time is evaluated

  20. Spatial and Angular Moment Analysis of Continuous and Discretized Transport Problems

    International Nuclear Information System (INIS)

    Brantley, Patrick S.; Larsen, Edward W.

    2000-01-01

    A new theoretical tool for analyzing continuous and discretized transport equations is presented. This technique is based on a spatial and angular moment analysis of the analytic transport equation, which yields exact expressions for the 'center of mass' and 'squared radius of gyration' of the particle distribution. Essentially the same moment analysis is applied to discretized particle transport problems to determine numerical expressions for the center of mass and squared radius of gyration. Because this technique makes no assumption about the optical thickness of the spatial cells or about the amount of absorption in the system, it is applicable to problems that cannot be analyzed by a truncation analysis or an asymptotic diffusion limit analysis. The spatial differencing schemes examined (weighted- diamond, lumped linear discontinuous, and multiple balance) yield a numerically consistent expression for computing the squared radius of gyration plus an error term that depends on the mesh spacing, quadrature constants, and material properties of the system. The numerical results presented suggest that the relative accuracy of spatial differencing schemes for different types of problems can be assessed by comparing the magnitudes of these error terms

  1. A novel finite volume discretization method for advection-diffusion systems on stretched meshes

    Science.gov (United States)

    Merrick, D. G.; Malan, A. G.; van Rooyen, J. A.

    2018-06-01

    This work is concerned with spatial advection and diffusion discretization technology within the field of Computational Fluid Dynamics (CFD). In this context, a novel method is proposed, which is dubbed the Enhanced Taylor Advection-Diffusion (ETAD) scheme. The model equation employed for design of the scheme is the scalar advection-diffusion equation, the industrial application being incompressible laminar and turbulent flow. Developed to be implementable into finite volume codes, ETAD places specific emphasis on improving accuracy on stretched structured and unstructured meshes while considering both advection and diffusion aspects in a holistic manner. A vertex-centered structured and unstructured finite volume scheme is used, and only data available on either side of the volume face is employed. This includes the addition of a so-called mesh stretching metric. Additionally, non-linear blending with the existing NVSF scheme was performed in the interest of robustness and stability, particularly on equispaced meshes. The developed scheme is assessed in terms of accuracy - this is done analytically and numerically, via comparison to upwind methods which include the popular QUICK and CUI techniques. Numerical tests involved the 1D scalar advection-diffusion equation, a 2D lid driven cavity and turbulent flow case. Significant improvements in accuracy were achieved, with L2 error reductions of up to 75%.

  2. Asymptotic analysis of the spatial discretization of radiation absorption and re-emission in Implicit Monte Carlo

    International Nuclear Information System (INIS)

    Densmore, Jeffery D.

    2011-01-01

    We perform an asymptotic analysis of the spatial discretization of radiation absorption and re-emission in Implicit Monte Carlo (IMC), a Monte Carlo technique for simulating nonlinear radiative transfer. Specifically, we examine the approximation of absorption and re-emission by a spatially continuous artificial-scattering process and either a piecewise-constant or piecewise-linear emission source within each spatial cell. We consider three asymptotic scalings representing (i) a time step that resolves the mean-free time, (ii) a Courant limit on the time-step size, and (iii) a fixed time step that does not depend on any asymptotic scaling. For the piecewise-constant approximation, we show that only the third scaling results in a valid discretization of the proper diffusion equation, which implies that IMC may generate inaccurate solutions with optically large spatial cells if time steps are refined. However, we also demonstrate that, for a certain class of problems, the piecewise-linear approximation yields an appropriate discretized diffusion equation under all three scalings. We therefore expect IMC to produce accurate solutions for a wider range of time-step sizes when the piecewise-linear instead of piecewise-constant discretization is employed. We demonstrate the validity of our analysis with a set of numerical examples.

  3. On the influence of spatial discretization in LWR steady state and burnup calculations with HELIOS 1.9

    International Nuclear Information System (INIS)

    Merk, B.; Weiss, F. P.

    2009-01-01

    Cell and burnup calculations are fundamental to all deterministic static and transient 3D full core calculations for different operational states of the reactor. The spatial discretization used for the cell and burnup calculations influences significantly the results of full integral transport solutions. The influence of the discretization on k inf is shown for the steady state case and the influence on the neutron spectrum is analyzed. Moreover, the differences in k inf are presented for different spatial discretization strategies in the burnup calculation of Uranium Oxide (UOX) fuel. The resulting different flux distributions cause significant changes in the isotopic densities. The influence of the discretization strategies on the calculation of homogenized few group cross-sections is investigated. This detailed discretization study demonstrates the need for sufficiently fine discretization to produce reliable and accurate results when using integral transport methods. In contrast to the currently used discretization schemes, refined discretization is especially important in the moderator region of the unit cell to reproduce the influence on the thermal neutron spectrum. Additionally, the need for sufficient discretization affects the idea of full core calculations based on integral transport methods since it has to be discussed whether it is worth to do full core calculations with reduced discretization when facing this strong discretization effect. The computer resources required for full core calculations with fine discretization are currently not available. (authors)

  4. Structure Preserving Spatial Discretization of a 1-D Piezoelectric Timoshenko Beam

    NARCIS (Netherlands)

    Voss, T.; Scherpen, J. M. A.

    2011-01-01

    In this paper we show how to spatially discretize a distributed model of a piezoelectric beam representing the dynamics of an inflatable space reflector in port-Hamiltonian (pH) form. This model can then be used to design a controller for the shape of the inflatable structure. Inflatable structures

  5. On the influence of spatial discretization on cross section preparation with HELIOS 1.9

    International Nuclear Information System (INIS)

    Merk, B.; Koch, R.

    2008-01-01

    The aim of many reactor calculations is the determination of the neutron flux and the nuclear power distribution. These distributions are in general calculated by solving the space and energy dependent static transport equation. Thus, a reliable computation of the neutron flux distribution within the reactor core would require the solution of the space-, energy- and angle-dependent neutron transport equation for the full nuclear reactor core. It is not yet feasible to solve exactly the neutron transport equation for realistic reactor core geometries in detail in practical use. Thus deterministic reactor calculations are split into the cell and lattice calculation based on static transport and the core simulation based on nodal codes. The cell and lattice calculations are mostly based on multi group transport calculations within two dimensions considering unstructured meshes. The resulting neutron flux is used for the preparation of few group cross sections like they are used in the nodal 3D full core simulation codes. One commercial standard product is the Studsvik Scandpower code system HELIOS 1.9. ''The transport method of HELIOS is called the CCCP method, because it is based on current coupling and collision probabilities (first-flight probabilities).. the system to be calculated consists of space elements that are coupled with each other and with the boundaries by interface currents, while the properties of each space element - its responses to sources and in-currents - are obtained from collision probabilities'' [ 1]. The applied collision probabilities method is based on the flat flux approximation. ''We assume that particles are emitted isotropically and uniformly within each discrete volume. This is known as the flat flux approximation. The flat flux approximation places a restriction on the mesh: if the flux varies rapidly within a region, the mesh should be refined sufficiently to ensure that the flux is well approximated by a piecewise - constant

  6. Density perturbations due to the inhomogeneous discrete spatial structure of space-time

    International Nuclear Information System (INIS)

    Wolf, C.

    1998-01-01

    For the case that space-time permits an inhomogeneous discrete spatial structure due to varying gravitational fields or a foam-like structure of space-time, it is demonstrated that thermodynamic reasoning implies that matter-density perturbations will arise in the early universe

  7. Improvement of spatial discretization error on the semi-analytic nodal method using the scattered source subtraction method

    International Nuclear Information System (INIS)

    Yamamoto, Akio; Tatsumi, Masahiro

    2006-01-01

    In this paper, the scattered source subtraction (SSS) method is newly proposed to improve the spatial discretization error of the semi-analytic nodal method with the flat-source approximation. In the SSS method, the scattered source is subtracted from both side of the diffusion or the transport equation to make spatial variation of the source term to be small. The same neutron balance equation is still used in the SSS method. Since the SSS method just modifies coefficients of node coupling equations (those used in evaluation for the response of partial currents), its implementation is easy. Validity of the present method is verified through test calculations that are carried out in PWR multi-assemblies configurations. The calculation results show that the SSS method can significantly improve the spatial discretization error. Since the SSS method does not have any negative impact on execution time, convergence behavior and memory requirement, it will be useful to reduce the spatial discretization error of the semi-analytic nodal method with the flat-source approximation. (author)

  8. Just Roll with It? Rolling Volumes vs. Discrete Issues in Open Access Library and Information Science Journals

    Directory of Open Access Journals (Sweden)

    Jill Cirasella

    2013-08-01

    Full Text Available INTRODUCTION Articles in open access (OA journals can be published on a rolling basis, as they become ready, or in complete, discrete issues. This study examines the prevalence of and reasons for rolling volumes vs. discrete issues among scholarly OA library and information science (LIS journals based in the United States. METHODS A survey was distributed to journal editors, asking them about their publication model and their reasons for and satisfaction with that model. RESULTS Of the 21 responding journals, 12 publish in discrete issues, eight publish in rolling volumes, and one publishes in rolling volumes with an occasional special issue. Almost all editors, regardless of model, cited ease of workflow as a justification for their chosen publication model, suggesting that there is no single best workflow for all journals. However, while all rolling-volume editors reported being satisfied with their model, satisfaction was less universal among discrete-issue editors. DISCUSSION The unexpectedly high number of rolling-volume journals suggests that LIS journal editors are making forward-looking choices about publication models even though the topic has not been much addressed in the library literature. Further research is warranted; possibilities include expanding the study’s geographic scope, broadening the study to other disciplines, and investigating publication model trends across the entire scholarly OA universe. CONCLUSION Both because satisfaction is high among editors of rolling-volume journals and because readers and authors appreciate quick publication times, the rolling-volume model will likely become even more prevalent in coming years.

  9. Infrared and visual image fusion method based on discrete cosine transform and local spatial frequency in discrete stationary wavelet transform domain

    Science.gov (United States)

    Jin, Xin; Jiang, Qian; Yao, Shaowen; Zhou, Dongming; Nie, Rencan; Lee, Shin-Jye; He, Kangjian

    2018-01-01

    In order to promote the performance of infrared and visual image fusion and provide better visual effects, this paper proposes a hybrid fusion method for infrared and visual image by the combination of discrete stationary wavelet transform (DSWT), discrete cosine transform (DCT) and local spatial frequency (LSF). The proposed method has three key processing steps. Firstly, DSWT is employed to decompose the important features of the source image into a series of sub-images with different levels and spatial frequencies. Secondly, DCT is used to separate the significant details of the sub-images according to the energy of different frequencies. Thirdly, LSF is applied to enhance the regional features of DCT coefficients, and it can be helpful and useful for image feature extraction. Some frequently-used image fusion methods and evaluation metrics are employed to evaluate the validity of the proposed method. The experiments indicate that the proposed method can achieve good fusion effect, and it is more efficient than other conventional image fusion methods.

  10. The discrete ordinate method in association with the finite-volume method in non-structured mesh; Methode des ordonnees discretes associee a la methode des volumes finis en maillage non structure

    Energy Technology Data Exchange (ETDEWEB)

    Le Dez, V; Lallemand, M [Ecole Nationale Superieure de Mecanique et d` Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M; Charette, A [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees

    1997-12-31

    The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.

  11. The discrete ordinate method in association with the finite-volume method in non-structured mesh; Methode des ordonnees discretes associee a la methode des volumes finis en maillage non structure

    Energy Technology Data Exchange (ETDEWEB)

    Le Dez, V.; Lallemand, M. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M.; Charette, A. [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees

    1996-12-31

    The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.

  12. Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients

    DEFF Research Database (Denmark)

    Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter

    2011-01-01

    We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal......, whereas the convergence of the coefficients happens only with respect to the "volumetric" Lebesgue measure. Additionally, depending on whether the stationarity conditions are stated for the discretized or the original continuous problem, two distinct concepts of stationarity at a discrete level arise. We...... provide characterizations of limit points, with respect to FV mesh size, of globally optimal solutions and two types of stationary points to the discretized problems. We illustrate the practical behaviour of our cell-based FV discretization algorithm on a numerical example....

  13. Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems

    International Nuclear Information System (INIS)

    Zou, Ling; Zhao, Haihua; Zhang, Hongbin

    2015-01-01

    Highlights: • Using high-resolution spatial scheme in solving two-phase flow problems. • Fully implicit time integrations scheme. • Jacobian-free Newton–Krylov method. • Analytical solution for two-phase water faucet problem. - Abstract: The majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many nuclear thermal–hydraulics applications, it is desirable to use higher-order numerical schemes to reduce numerical errors. High-resolution spatial discretization schemes provide high order spatial accuracy in smooth regions and capture sharp spatial discontinuity without nonphysical spatial oscillations. In this work, we adapted an existing high-resolution spatial discretization scheme on staggered grids in two-phase flow applications. Fully implicit time integration schemes were also implemented to reduce numerical errors from operator-splitting types of time integration schemes. The resulting nonlinear system has been successfully solved using the Jacobian-free Newton–Krylov (JFNK) method. The high-resolution spatial discretization and high-order fully implicit time integration numerical schemes were tested and numerically verified for several two-phase test problems, including a two-phase advection problem, a two-phase advection with phase appearance/disappearance problem, and the water faucet problem. Numerical results clearly demonstrated the advantages of using such high-resolution spatial and high-order temporal numerical schemes to significantly reduce numerical diffusion and therefore improve accuracy. Our study also demonstrated that the JFNK method is stable and robust in solving two-phase flow problems, even when phase appearance/disappearance exists

  14. Discrete field theories and spatial properties of strings

    International Nuclear Information System (INIS)

    Klebanov, I.; Susskind, L.

    1988-10-01

    We use the ground-state wave function in the light-cone gauge to study the spatial properties of fundamental strings. We find that, as the cut-off in the parameter space is removed, the strings are smooth and have a divergent size. Guided by these properties, we consider a large-N lattice gauge theory which has an unstable phase where the size of strings diverges. We show that this phase exactly describes free fundamental strings. The lattice spacing does not have to be taken to zero for this equivalence to hold. Thus, exact rotation and translation invariance is restored in a discrete space. This suggests that the number of fundamental short-distance degrees of freedom in string theory is much smaller than in a conventional field theory. 11 refs., 4 figs

  15. Mimetic discretization methods

    CERN Document Server

    Castillo, Jose E

    2013-01-01

    To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and

  16. Multilevel discretized random field models with 'spin' correlations for the simulation of environmental spatial data

    Science.gov (United States)

    Žukovič, Milan; Hristopulos, Dionissios T.

    2009-02-01

    A current problem of practical significance is how to analyze large, spatially distributed, environmental data sets. The problem is more challenging for variables that follow non-Gaussian distributions. We show by means of numerical simulations that the spatial correlations between variables can be captured by interactions between 'spins'. The spins represent multilevel discretizations of environmental variables with respect to a number of pre-defined thresholds. The spatial dependence between the 'spins' is imposed by means of short-range interactions. We present two approaches, inspired by the Ising and Potts models, that generate conditional simulations of spatially distributed variables from samples with missing data. Currently, the sampling and simulation points are assumed to be at the nodes of a regular grid. The conditional simulations of the 'spin system' are forced to respect locally the sample values and the system statistics globally. The second constraint is enforced by minimizing a cost function representing the deviation between normalized correlation energies of the simulated and the sample distributions. In the approach based on the Nc-state Potts model, each point is assigned to one of Nc classes. The interactions involve all the points simultaneously. In the Ising model approach, a sequential simulation scheme is used: the discretization at each simulation level is binomial (i.e., ± 1). Information propagates from lower to higher levels as the simulation proceeds. We compare the two approaches in terms of their ability to reproduce the target statistics (e.g., the histogram and the variogram of the sample distribution), to predict data at unsampled locations, as well as in terms of their computational complexity. The comparison is based on a non-Gaussian data set (derived from a digital elevation model of the Walker Lake area, Nevada, USA). We discuss the impact of relevant simulation parameters, such as the domain size, the number of

  17. Discrete curved ray-tracing method for radiative transfer in an absorbing-emitting semitransparent slab with variable spatial refractive index

    International Nuclear Information System (INIS)

    Liu, L.H.

    2004-01-01

    A discrete curved ray-tracing method is developed to analyze the radiative transfer in one-dimensional absorbing-emitting semitransparent slab with variable spatial refractive index. The curved ray trajectory is locally treated as straight line and the complicated and time-consuming computation of ray trajectory is cut down. A problem of radiative equilibrium with linear variable spatial refractive index is taken as an example to examine the accuracy of the proposed method. The temperature distributions are determined by the proposed method and compared with the data in references, which are obtained by other different methods. The results show that the discrete curved ray-tracing method has a good accuracy in solving the radiative transfer in one-dimensional semitransparent slab with variable spatial refractive index

  18. Time Discretization Techniques

    KAUST Repository

    Gottlieb, S.; Ketcheson, David I.

    2016-01-01

    The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include

  19. Which spatial discretization for distributed hydrological models? Proposition of a methodology and illustration for medium to large-scale catchments

    Directory of Open Access Journals (Sweden)

    J. Dehotin

    2008-05-01

    Full Text Available Distributed hydrological models are valuable tools to derive distributed estimation of water balance components or to study the impact of land-use or climate change on water resources and water quality. In these models, the choice of an appropriate spatial discretization is a crucial issue. It is obviously linked to the available data, their spatial resolution and the dominant hydrological processes. For a given catchment and a given data set, the "optimal" spatial discretization should be adapted to the modelling objectives, as the latter determine the dominant hydrological processes considered in the modelling. For small catchments, landscape heterogeneity can be represented explicitly, whereas for large catchments such fine representation is not feasible and simplification is needed. The question is thus: is it possible to design a flexible methodology to represent landscape heterogeneity efficiently, according to the problem to be solved? This methodology should allow a controlled and objective trade-off between available data, the scale of the dominant water cycle components and the modelling objectives.

    In this paper, we propose a general methodology for such catchment discretization. It is based on the use of nested discretizations. The first level of discretization is composed of the sub-catchments, organised by the river network topology. The sub-catchment variability can be described using a second level of discretizations, which is called hydro-landscape units. This level of discretization is only performed if it is consistent with the modelling objectives, the active hydrological processes and data availability. The hydro-landscapes take into account different geophysical factors such as topography, land-use, pedology, but also suitable hydrological discontinuities such as ditches, hedges, dams, etc. For numerical reasons these hydro-landscapes can be further subdivided into smaller elements that will constitute the

  20. S2SA preconditioning for the Sn equations with strictly non negative spatial discretization

    International Nuclear Information System (INIS)

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

    2013-01-01

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

  1. A consistent method for finite volume discretization of body forces on collocated grids applied to flow through an actuator disk

    DEFF Research Database (Denmark)

    Troldborg, Niels; Sørensen, Niels N.; Réthoré, Pierre-Elouan

    2015-01-01

    This paper describes a consistent algorithm for eliminating the numerical wiggles appearing when solving the finite volume discretized Navier-Stokes equations with discrete body forces in a collocated grid arrangement. The proposed method is a modification of the Rhie-Chow algorithm where the for...

  2. Multilevel discretized random field models with 'spin' correlations for the simulation of environmental spatial data

    International Nuclear Information System (INIS)

    Žukovič, Milan; Hristopulos, Dionissios T

    2009-01-01

    A current problem of practical significance is how to analyze large, spatially distributed, environmental data sets. The problem is more challenging for variables that follow non-Gaussian distributions. We show by means of numerical simulations that the spatial correlations between variables can be captured by interactions between 'spins'. The spins represent multilevel discretizations of environmental variables with respect to a number of pre-defined thresholds. The spatial dependence between the 'spins' is imposed by means of short-range interactions. We present two approaches, inspired by the Ising and Potts models, that generate conditional simulations of spatially distributed variables from samples with missing data. Currently, the sampling and simulation points are assumed to be at the nodes of a regular grid. The conditional simulations of the 'spin system' are forced to respect locally the sample values and the system statistics globally. The second constraint is enforced by minimizing a cost function representing the deviation between normalized correlation energies of the simulated and the sample distributions. In the approach based on the N c -state Potts model, each point is assigned to one of N c classes. The interactions involve all the points simultaneously. In the Ising model approach, a sequential simulation scheme is used: the discretization at each simulation level is binomial (i.e., ± 1). Information propagates from lower to higher levels as the simulation proceeds. We compare the two approaches in terms of their ability to reproduce the target statistics (e.g., the histogram and the variogram of the sample distribution), to predict data at unsampled locations, as well as in terms of their computational complexity. The comparison is based on a non-Gaussian data set (derived from a digital elevation model of the Walker Lake area, Nevada, USA). We discuss the impact of relevant simulation parameters, such as the domain size, the number of

  3. Discrete elements method of neutral particle transport

    International Nuclear Information System (INIS)

    Mathews, K.A.

    1983-01-01

    A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method

  4. The linear characteristic method for spatially discretizing the discrete ordinates equations in (x,y)-geometry

    International Nuclear Information System (INIS)

    Larsen, E.W.; Alcouffe, R.E.

    1981-01-01

    In this article a new linear characteristic (LC) spatial differencing scheme for the discrete ordinates equations in (x,y)-geometry is described and numerical comparisons are given with the diamond difference (DD) method. The LC method is more stable with mesh size and is generally much more accurate than the DD method on both fine and coarse meshes, for eigenvalue and deep penetration problems. The LC method is based on computations involving the exact solution of a cell problem which has spatially linear boundary conditions and interior source. The LC method is coupled to the diffusion synthetic acceleration (DSA) algorithm in that the linear variations of the source are determined in part by the results of the DSA calculation from the previous inner iteration. An inexpensive negative-flux fixup is used which has very little effect on the accuracy of the solution. The storage requirements for LC are essentially the same as that for DD, while the computational times for LC are generally less than twice the DD computational times for the same mesh. This increase in computational cost is offset if one computes LC solutions on somewhat coarser meshes than DD; the resulting LC solutions are still generally much more accurate than the DD solutions. (orig.) [de

  5. Optimized waveform relaxation domain decomposition method for discrete finite volume non stationary convection diffusion equation

    International Nuclear Information System (INIS)

    Berthe, P.M.

    2013-01-01

    In the context of nuclear waste repositories, we consider the numerical discretization of the non stationary convection diffusion equation. Discontinuous physical parameters and heterogeneous space and time scales lead us to use different space and time discretizations in different parts of the domain. In this work, we choose the discrete duality finite volume (DDFV) scheme and the discontinuous Galerkin scheme in time, coupled by an optimized Schwarz waveform relaxation (OSWR) domain decomposition method, because this allows the use of non-conforming space-time meshes. The main difficulty lies in finding an upwind discretization of the convective flux which remains local to a sub-domain and such that the multi domain scheme is equivalent to the mono domain one. These difficulties are first dealt with in the one-dimensional context, where different discretizations are studied. The chosen scheme introduces a hybrid unknown on the cell interfaces. The idea of up winding with respect to this hybrid unknown is extended to the DDFV scheme in the two-dimensional setting. The well-posedness of the scheme and of an equivalent multi domain scheme is shown. The latter is solved by an OSWR algorithm, the convergence of which is proved. The optimized parameters in the Robin transmission conditions are obtained by studying the continuous or discrete convergence rates. Several test-cases, one of which inspired by nuclear waste repositories, illustrate these results. (author) [fr

  6. Testing Ecological Theories of Offender Spatial Decision Making Using a Discrete Choice Model

    Science.gov (United States)

    Summers, Lucia

    2015-01-01

    Research demonstrates that crime is spatially concentrated. However, most research relies on information about where crimes occur, without reference to where offenders reside. This study examines how the characteristics of neighborhoods and their proximity to offender home locations affect offender spatial decision making. Using a discrete choice model and data for detected incidents of theft from vehicles (TFV), we test predictions from two theoretical perspectives—crime pattern and social disorganization theories. We demonstrate that offenders favor areas that are low in social cohesion and closer to their home, or other age-related activity nodes. For adult offenders, choices also appear to be influenced by how accessible a neighborhood is via the street network. The implications for criminological theory and crime prevention are discussed. PMID:25866412

  7. Testing Ecological Theories of Offender Spatial Decision Making Using a Discrete Choice Model.

    Science.gov (United States)

    Johnson, Shane D; Summers, Lucia

    2015-04-01

    Research demonstrates that crime is spatially concentrated. However, most research relies on information about where crimes occur, without reference to where offenders reside. This study examines how the characteristics of neighborhoods and their proximity to offender home locations affect offender spatial decision making. Using a discrete choice model and data for detected incidents of theft from vehicles (TFV) , we test predictions from two theoretical perspectives-crime pattern and social disorganization theories. We demonstrate that offenders favor areas that are low in social cohesion and closer to their home, or other age-related activity nodes. For adult offenders, choices also appear to be influenced by how accessible a neighborhood is via the street network. The implications for criminological theory and crime prevention are discussed.

  8. A response matrix method for one-speed discrete ordinates fixed source problems in slab geometry with no spatial truncation error

    International Nuclear Information System (INIS)

    Lydia, Emilio J.; Barros, Ricardo C.

    2011-01-01

    In this paper we describe a response matrix method for one-speed slab-geometry discrete ordinates (SN) neutral particle transport problems that is completely free from spatial truncation errors. The unknowns in the method are the cell-edge angular fluxes of particles. The numerical results generated for these quantities are exactly those obtained from the analytic solution of the SN problem apart from finite arithmetic considerations. Our method is based on a spectral analysis that we perform in the SN equations with scattering inside a discretization cell of the spatial grid set up on the slab. As a result of this spectral analysis, we are able to obtain an expression for the local general solution of the SN equations. With this local general solution, we determine the response matrix and use the prescribed boundary conditions and continuity conditions to sweep across the discretization cells from left to right and from right to left across the slab, until a prescribed convergence criterion is satisfied. (author)

  9. The invisible hand illusion: multisensory integration leads to the embodiment of a discrete volume of empty space.

    Science.gov (United States)

    Guterstam, Arvid; Gentile, Giovanni; Ehrsson, H Henrik

    2013-07-01

    The dynamic integration of signals from different sensory modalities plays a key role in bodily self-perception. When visual information is used in the multisensory process of localizing and identifying one's own limbs, the sight of a body part often plays a dominant role. For example, it has repeatedly been shown that a viewed object must resemble a humanoid body part to permit illusory self-attribution of that object. Here, we report a perceptual illusion that challenges these assumptions by demonstrating that healthy (nonamputated) individuals can refer somatic sensations to a discrete volume of empty space and experience having an invisible hand. In 10 behavioral and one fMRI experiment, we characterized the perceptual rules and multisensory brain mechanisms that produced this "invisible hand illusion." Our behavioral results showed that the illusion depends on visuotactile-proprioceptive integration that obeys key spatial and temporal multisensory rules confined to near-personal space. The fMRI results associate the illusion experience with increased activity in regions related to the integration of multisensory body-related signals, most notably the bilateral ventral premotor, intraparietal, and cerebellar cortices. We further showed that a stronger feeling of having an invisible hand is associated with a higher degree of effective connectivity between the intraparietal and ventral premotor cortices. These findings demonstrate that the integration of temporally and spatially congruent multisensory signals in a premotor-intraparietal circuit is sufficient to redefine the spatial boundaries of the bodily self, even when visual information directly contradicts the presence of a physical limb at the location of the perceived illusory hand.

  10. Mixed finite element - discontinuous finite volume element discretization of a general class of multicontinuum models

    Science.gov (United States)

    Ruiz-Baier, Ricardo; Lunati, Ivan

    2016-10-01

    We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation

  11. A numerical method for multigroup slab-geometry discrete ordinates problems with no spatial truncation error

    International Nuclear Information System (INIS)

    Barros, R.C. de; Larsen, E.W.

    1991-01-01

    A generalization of the one-group Spectral Green's Function (SGF) method is developed for multigroup, slab-geometry discrete ordinates (S N ) problems. The multigroup SGF method is free from spatial truncation errors; it generated numerical values for the cell-edge and cell-average angular fluxes that agree with the analytic solution of the multigroup S N equations. Numerical results are given to illustrate the method's accuracy

  12. Factors associated with supermarket and convenience store closure: a discrete time spatial survival modelling approach.

    Science.gov (United States)

    Warren, Joshua L; Gordon-Larsen, Penny

    2018-06-01

    While there is a literature on the distribution of food stores across geographic and social space, much of this research uses cross-sectional data. Analyses attempting to understand whether the availability of stores across neighborhoods is associated with diet and/or health outcomes are limited by a lack of understanding of factors that shape the emergence of new stores and the closure of others. We used quarterly data on supermarket and convenience store locations spanning seven years (2006-2012) and tract-level census data in four US cities: Birmingham, Alabama; Chicago, Illinois; Minneapolis, Minnesota; San Francisco, California. A spatial discrete-time survival model was used to identify factors associated with an earlier and/or later closure time of a store. Sales volume was typically the strongest indicator of store survival. We identified heterogeneity in the association between tract-level poverty and racial composition with respect to store survival. Stores in high poverty, non-White tracts were often at a disadvantage in terms of survival length. The observed patterns of store survival varied by some of the same neighborhood sociodemographic factors associated with lifestyle and health outcomes, which could lead to confusion in interpretation in studies of the estimated effects of introduction of food stores into neighborhoods on health.

  13. Discrete quantum dot like emitters in monolayer MoSe{sub 2}: Spatial mapping, magneto-optics, and charge tuning

    Energy Technology Data Exchange (ETDEWEB)

    Branny, Artur; Kumar, Santosh; Gerardot, Brian D., E-mail: b.d.gerardot@hw.ac.uk [Institute of Photonics and Quantum Sciences, SUPA, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Wang, Gang; Robert, Cedric; Lassagne, Benjamin; Marie, Xavier; Urbaszek, Bernhard, E-mail: urbaszek@insa-toulouse.fr [Université de Toulouse, INSA-CNRS-UPS, LPCNO, 135 Av. Rangueil, 31077 Toulouse (France)

    2016-04-04

    Transition metal dichalcogenide monolayers such as MoSe{sub 2}, MoS{sub 2}, and WSe{sub 2} are direct bandgap semiconductors with original optoelectronic and spin-valley properties. Here we report on spectrally sharp, spatially localized emission in monolayer MoSe{sub 2}. We find this quantum dot-like emission in samples exfoliated onto gold substrates and also suspended flakes. Spatial mapping shows a correlation between the location of emitters and the existence of wrinkles (strained regions) in the flake. We tune the emission properties in magnetic and electric fields applied perpendicular to the monolayer plane. We extract an exciton g-factor of the discrete emitters close to −4, as for 2D excitons in this material. In a charge tunable sample, we record discrete jumps on the meV scale as charges are added to the emitter when changing the applied voltage.

  14. Parallel performance of the angular versus spatial domain decomposition for discrete ordinates transport methods

    International Nuclear Information System (INIS)

    Fischer, J.W.; Azmy, Y.Y.

    2003-01-01

    A previously reported parallel performance model for Angular Domain Decomposition (ADD) of the Discrete Ordinates method for solving multidimensional neutron transport problems is revisited for further validation. Three communication schemes: native MPI, the bucket algorithm, and the distributed bucket algorithm, are included in the validation exercise that is successfully conducted on a Beowulf cluster. The parallel performance model is comprised of three components: serial, parallel, and communication. The serial component is largely independent of the number of participating processors, P, while the parallel component decreases like 1/P. These two components are independent of the communication scheme, in contrast with the communication component that typically increases with P in a manner highly dependent on the global reduced algorithm. Correct trends for each component and each communication scheme were measured for the Arbitrarily High Order Transport (AHOT) code, thus validating the performance models. Furthermore, extensive experiments illustrate the superiority of the bucket algorithm. The primary question addressed in this research is: for a given problem size, which domain decomposition method, angular or spatial, is best suited to parallelize Discrete Ordinates methods on a specific computational platform? We address this question for three-dimensional applications via parallel performance models that include parameters specifying the problem size and system performance: the above-mentioned ADD, and a previously constructed and validated Spatial Domain Decomposition (SDD) model. We conclude that for large problems the parallel component dwarfs the communication component even on moderately large numbers of processors. The main advantages of SDD are: (a) scalability to higher numbers of processors of the order of the number of computational cells; (b) smaller memory requirement; (c) better performance than ADD on high-end platforms and large number of

  15. The spectral volume method as applied to transport problems

    International Nuclear Information System (INIS)

    McClarren, Ryan G.

    2011-01-01

    We present a new spatial discretization for transport problems: the spectral volume method. This method, rst developed by Wang for computational fluid dynamics, divides each computational cell into several sub-cells and enforces particle balance on each of these sub-cells. Also, these sub-cells are used to build a polynomial reconstruction in the cell. The idea of dividing cells into many cells is a generalization of the simple corner balance and other similar schemes. The spectral volume method preserves particle conservation and preserves the asymptotic diffusion limit. We present results from the method on two transport problems in slab geometry using discrete ordinates and second through sixth order spectral volume schemes. The numerical results demonstrate the accuracy and preservation of the diffusion limit of the spectral volume method. Future work will explore possible bene ts of the scheme for high-performance computing and for resolving diffusive boundary layers. (author)

  16. Beyond dizziness: virtual navigation, spatial anxiety and hippocampal volume in bilateral vestibulopathy

    Directory of Open Access Journals (Sweden)

    Olympia eKremmyda

    2016-03-01

    Full Text Available Bilateral vestibulopathy (BVP is defined as the impairment or loss of function of either the labyrinths or the eighth nerves. Patients with total BVP due to bilateral vestibular nerve section exhibit difficulties in spatial memory and navigation and show a loss of hippocampal volume. In clinical practice, most patients do not have a complete loss of function but rather an asymmetrical residual functioning of the vestibular system. The purpose of the current study was to investigate navigational ability and hippocampal atrophy in BVP patients with residual vestibular function. Fifteen patients with BVP and a group of age- and gender- matched healthy controls were examined. Self-reported questionnaires on spatial anxiety and wayfinding were used to assess the applied strategy of wayfinding and quality of life. Spatial memory and navigation were tested directly using a virtual Morris Water Maze Task. The hippocampal volume of these two groups was evaluated by voxel-based morphometry. In the patients, the questionnaire showed a higher spatial anxiety and the Morris Water Maze Task a delayed spatial learning performance. MRI revealed a significant decrease in the gray matter mid-hippocampal volume (Left: p = 0.006, Z = 4.58, Right: p < 0.001, Z = 3.63 and posterior parahippocampal volume (Right: p = 0.005, Z = 4.65, Left: p < 0.001, Z = 3.87 compared to those of healthy controls. In addition, a decrease in hippocampal formation volume correlated with a more dominant route-finding strategy. Our current findings demonstrate that even partial bilateral vestibular loss leads to anatomical and functional

  17. Effect of flux discontinuity on spatial approximations for discrete ordinates methods

    International Nuclear Information System (INIS)

    Duo, J.I.; Azmy, Y.Y.

    2005-01-01

    This work presents advances on error analysis of the spatial approximation of the discrete ordinates method for solving the neutron transport equation. Error norms for different non-collided flux problems over a two dimensional pure absorber medium are evaluated using three numerical methods. The problems are characterized by the incoming flux boundary conditions to obtain solutions with different level of differentiability. The three methods considered are the Diamond Difference (DD) method, the Arbitrarily High Order Transport method of the Nodal type (AHOT-N), and of the Characteristic type (AHOT-C). The last two methods are employed in constant, linear and quadratic orders of spatial approximation. The cell-wise error is computed as the difference between the cell-averaged flux computed by each method and the exact value, then the L 1 , L 2 , and L ∞ error norms are calculated. The results of this study demonstrate that the level of differentiability of the exact solution profoundly affects the rate of convergence of the numerical methods' solutions. Furthermore, in the case of discontinuous exact flux the methods fail to converge in the maximum error norm, or in the pointwise sense, in accordance with previous local error analysis. (authors)

  18. Spatially discrete thermal drawing of biodegradable microneedles for vascular drug delivery.

    Science.gov (United States)

    Choi, Chang Kuk; Lee, Kang Ju; Youn, Young Nam; Jang, Eui Hwa; Kim, Woong; Min, Byung-Kwon; Ryu, WonHyoung

    2013-02-01

    Spatially discrete thermal drawing is introduced as a novel method for the fabrication of biodegradable microneedles with ultra-sharp tip ends. This method provides the enhanced control of microneedle shapes by spatially controlling the temperature of drawn polymer as well as drawing steps and speeds. Particular focus is given on the formation of sharp tip ends of microneedles at the end of thermal drawing. Previous works relied on the fracture of polymer neck by fast drawing that often causes uncontrolled shapes of microneedle tips. Instead, this approach utilizes the surface energy of heated polymer to form ultra-sharp tip ends. We have investigated the effect of such temperature control, drawing speed, and drawing steps in thermal drawing process on the final shape of microneedles using biodegradable polymers. XRD analysis was performed to analyze the effect of thermal cycle on the biodegradable polymer. Load-displacement measurement also showed the dependency of mechanical strengths of microneedles on the microneedle shapes. Ex vivo vascular tissue insertion and drug delivery demonstrated microneedle insertion to tunica media layer of canine aorta and drug distribution in the tissue layer. Copyright © 2012 Elsevier B.V. All rights reserved.

  19. Finite-volume effects due to spatially non-local operators arXiv

    CERN Document Server

    Briceño, Raúl A.; Hansen, Maxwell T.; Monahan, Christopher J.

    Spatially non-local matrix elements are useful lattice-QCD observables in a variety of contexts, for example in determining hadron structure. To quote credible estimates of the systematic uncertainties in these calculations, one must understand, among other things, the size of the finite-volume effects when such matrix elements are extracted from numerical lattice calculations. In this work, we estimate finite-volume effects for matrix elements of non-local operators, composed of two currents displaced in a spatial direction by a distance $\\xi$. We find that the finite-volume corrections depend on the details of the matrix element. If the external state is the lightest degree of freedom in the theory, e.g.~the pion in QCD, then the volume corrections scale as $ e^{-m_\\pi (L- \\xi)} $, where $m_\\pi$ is the mass of the light state. For heavier external states the usual $e^{- m_\\pi L}$ form is recovered, but with a polynomial prefactor of the form $L^m/|L - \\xi|^n$ that can lead to enhanced volume effects. These ...

  20. Influence of bladder and rectal volume on spatial variability of a bladder tumor during radical radiotherapy

    International Nuclear Information System (INIS)

    Pos, Floris J.; Koedooder, Kees; Hulshof, Maarten C.C.M.; Tienhoven, Geertjan van; Gonzalez Gonzalez, Dionisio

    2003-01-01

    Purpose: To assess the spatial variability of a bladder tumor relative to the planning target volume boundaries during radical radiotherapy, and furthermore to develop strategies to reduce spatial variability. Methods and Materials: Seventeen patients with solitary T2-T4N0M0 bladder cancer were treated with a technique delivering 40 Gy/2 Gy in 20 fractions to the whole bladder with a concomitant boost to the bladder tumor of 20 Gy in 1 Gy fractions in an overall time of 4 weeks. CT scans were made weekly, immediately after treatment, and matched with the planning CT scan. Spatial variability of the tumor, as well as bladder volume and rectal diameter, were scored for each patient each week. Results: In 65% of patients, a part of the tumor appeared outside the planning target volume boundaries at least one time during the course of radiotherapy. No consistent relation of this variability with time was found. Bladder volumes and rectal diameters showed marked variability during the course of treatment. A large initial bladder volume and rectal diameter predicted a large volume variation and a large tumor spatial variability. Conclusion: In this study, a margin of 1.5 to 2 cm seemed to be inadequate in 65% of the patients with respect to spatial variability. Bladder volume and rectal diameter were found to be predictive for spatial variability of a bladder tumor during concomitant boost radiotherapy

  1. Influence of bladder and rectal volume on spatial variability of a bladder tumor during radical radiotherapy

    Energy Technology Data Exchange (ETDEWEB)

    Pos, Floris J; Koedooder, Kees; Hulshof, Maarten C.C.M.; Tienhoven, Geertjan van; Gonzalez Gonzalez, Dionisio

    2003-03-01

    Purpose: To assess the spatial variability of a bladder tumor relative to the planning target volume boundaries during radical radiotherapy, and furthermore to develop strategies to reduce spatial variability. Methods and Materials: Seventeen patients with solitary T2-T4N0M0 bladder cancer were treated with a technique delivering 40 Gy/2 Gy in 20 fractions to the whole bladder with a concomitant boost to the bladder tumor of 20 Gy in 1 Gy fractions in an overall time of 4 weeks. CT scans were made weekly, immediately after treatment, and matched with the planning CT scan. Spatial variability of the tumor, as well as bladder volume and rectal diameter, were scored for each patient each week. Results: In 65% of patients, a part of the tumor appeared outside the planning target volume boundaries at least one time during the course of radiotherapy. No consistent relation of this variability with time was found. Bladder volumes and rectal diameters showed marked variability during the course of treatment. A large initial bladder volume and rectal diameter predicted a large volume variation and a large tumor spatial variability. Conclusion: In this study, a margin of 1.5 to 2 cm seemed to be inadequate in 65% of the patients with respect to spatial variability. Bladder volume and rectal diameter were found to be predictive for spatial variability of a bladder tumor during concomitant boost radiotherapy.

  2. Finite Volume Method for Pricing European Call Option with Regime-switching Volatility

    Science.gov (United States)

    Lista Tauryawati, Mey; Imron, Chairul; Putri, Endah RM

    2018-03-01

    In this paper, we present a finite volume method for pricing European call option using Black-Scholes equation with regime-switching volatility. In the first step, we formulate the Black-Scholes equations with regime-switching volatility. we use a finite volume method based on fitted finite volume with spatial discretization and an implicit time stepping technique for the case. We show that the regime-switching scheme can revert to the non-switching Black Scholes equation, both in theoretical evidence and numerical simulations.

  3. Discrete Variational Approach for Modeling Laser-Plasma Interactions

    Science.gov (United States)

    Reyes, J. Paxon; Shadwick, B. A.

    2014-10-01

    The traditional approach for fluid models of laser-plasma interactions begins by approximating fields and derivatives on a grid in space and time, leading to difference equations that are manipulated to create a time-advance algorithm. In contrast, by introducing the spatial discretization at the level of the action, the resulting Euler-Lagrange equations have particular differencing approximations that will exactly satisfy discrete versions of the relevant conservation laws. For example, applying a spatial discretization in the Lagrangian density leads to continuous-time, discrete-space equations and exact energy conservation regardless of the spatial grid resolution. We compare the results of two discrete variational methods using the variational principles from Chen and Sudan and Brizard. Since the fluid system conserves energy and momentum, the relative errors in these conserved quantities are well-motivated physically as figures of merit for a particular method. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY-1104683.

  4. Discrimination between discrete and continuum scattering from the sub-seafloor.

    Science.gov (United States)

    Holland, Charles W; Steininger, Gavin; Dosso, Stan E

    2015-08-01

    There is growing evidence that seabed scattering is often dominated by heterogeneities within the sediment volume as opposed to seafloor roughness. From a theoretical viewpoint, sediment volume heterogeneities can be described either by a fluctuation continuum or by discrete particles. In at-sea experiments, heterogeneity characteristics generally are not known a priori. Thus, an uninformed model selection is generally made, i.e., the researcher must arbitrarily select either a discrete or continuum model. It is shown here that it is possible to (acoustically) discriminate between continuum and discrete heterogeneities in some instances. For example, when the spectral exponent γ3>4, the volume scattering cannot be described by discrete particles. Conversely, when γ3≤2, the heterogeneities likely arise from discrete particles. Furthermore, in the range 2discrete vs continuum heterogeneities via acoustic remote sensing may lead to improved observations and concomitant increased understanding of the marine benthic environment.

  5. Conservative adaptivity and two-way self-nesting using discrete wavelets

    Science.gov (United States)

    Dubos, Thomas

    2010-05-01

    In simulating atmosphere and oceans, multiscale modelling is desirable to track high-intensity weather patterns, to investigate the interactions between the various spatio-temporal scales of the climate system, and to perform assessments of climate change at scales small enough to derive impacts on society and ecosystems. The mainstream approach to multiscale modelling is to nest a fine, limited-area model into a coarse, global model. These models are then coupled, either one-way or two-way, in order to combine the global coverage of the global model and the fine details of the fine model. In the long simulations typical of climate studies, initial conditions are unimportant, except for the few quantities like mass that are exactly conserved. In this context it is crucial that numerical models conserve at least mass exactly at the discrete level. However even with elaborate strategies like adaptive mesh refinement (AMR) conservation is not straightforwardly achieved. Although the continuous wavelet transform has become a standard tool of geophysical data analysis, it is less known that discrete wavelets and the associated transforms provide the basis for spatially adaptive numerical methods. Such methods are now well-developed in the fluid dynamics community. Since they allow spatial adaptivity, they can also be seen as two-way self-nesting methods. However since they are not specifically designed for geophysical purposes they are usually not exactly conservative. I present a fairly general framework in which a wavelet-based layer is added to an existing conservative scheme (finite-volume or finite-difference) to make it spatially adaptive without breaking the exact conservation of linear invariants. Discrete wavelet transforms involve an upscaling operation by which fields are transferred from a fine grid to a coarser grid with half the resolution. The method requires that mass fluxes be upscaled in a way that is consistent with the upscaling of mass. This

  6. WATERSHED SPATIAL DISCRETIZATION FOR THE ANALYSIS OF LAND USE CHANGE IN COASTAL REGIONS

    Directory of Open Access Journals (Sweden)

    Vassiliki Terezinha Galvão Boulomytis

    Full Text Available In this study, we present a methodology to discretize a non-assessed basin based on terrain analysis using the SRTM digital elevation model (DEM and a high resolution surface model (DSM with a drainage network semi-automatic extraction process. The Juqueriquerê River Basin was used for the case study, which has the most representative non-urbanized plains of the northern coastline of São Paulo State, Brazil. The low-lying region is featured by elevations close to the sea level, mild slopes, and shallow water tables. It is also influenced by tidal variation and orographic rains. Therefore, frequent flooding occurs, even in vegetated areas. Two conflicting land use scenarios, proposed by the City Master Plan (CMP of Caraguatatuba and the Ecological-Economical Zoning (EEZ, were compared to analyze the flood vulnerability increase and geotechnical risk caused by the urbanization process. The drainage extraction techniques showed better results on high resolution DSM for low-lying regions than the SRTM DEM and determined with accuracy the locations of flood potentiality in the plains. The watershed spatial discretization allowed us to show the effects of the two different land use approaches, considering the flood vulnerability and geotechnical risk of each sub-basin

  7. Introductory discrete mathematics

    CERN Document Server

    Balakrishnan, V K

    2010-01-01

    This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv

  8. Geant4-DNA track-structure simulations for gold nanoparticles: The importance of electron discrete models in nanometer volumes.

    Science.gov (United States)

    Sakata, Dousatsu; Kyriakou, Ioanna; Okada, Shogo; Tran, Hoang N; Lampe, Nathanael; Guatelli, Susanna; Bordage, Marie-Claude; Ivanchenko, Vladimir; Murakami, Koichi; Sasaki, Takashi; Emfietzoglou, Dimitris; Incerti, Sebastien

    2018-05-01

    Gold nanoparticles (GNPs) are known to enhance the absorbed dose in their vicinity following photon-based irradiation. To investigate the therapeutic effectiveness of GNPs, previous Monte Carlo simulation studies have explored GNP dose enhancement using mostly condensed-history models. However, in general, such models are suitable for macroscopic volumes and for electron energies above a few hundred electron volts. We have recently developed, for the Geant4-DNA extension of the Geant4 Monte Carlo simulation toolkit, discrete physics models for electron transport in gold which include the description of the full atomic de-excitation cascade. These models allow event-by-event simulation of electron tracks in gold down to 10 eV. The present work describes how such specialized physics models impact simulation-based studies on GNP-radioenhancement in a context of x-ray radiotherapy. The new discrete physics models are compared to the Geant4 Penelope and Livermore condensed-history models, which are being widely used for simulation-based NP radioenhancement studies. An ad hoc Geant4 simulation application has been developed to calculate the absorbed dose in liquid water around a GNP and its radioenhancement, caused by secondary particles emitted from the GNP itself, when irradiated with a monoenergetic electron beam. The effect of the new physics models is also quantified in the calculation of secondary particle spectra, when originating in the GNP and when exiting from it. The new physics models show similar backscattering coefficients with the existing Geant4 Livermore and Penelope models in large volumes for 100 keV incident electrons. However, in submicron sized volumes, only the discrete models describe the high backscattering that should still be present around GNPs at these length scales. Sizeable differences (mostly above a factor of 2) are also found in the radial distribution of absorbed dose and secondary particles between the new and the existing Geant4

  9. Hippocampal Volume Reduction in Humans Predicts Impaired Allocentric Spatial Memory in Virtual-Reality Navigation.

    Science.gov (United States)

    Guderian, Sebastian; Dzieciol, Anna M; Gadian, David G; Jentschke, Sebastian; Doeller, Christian F; Burgess, Neil; Mishkin, Mortimer; Vargha-Khadem, Faraneh

    2015-10-21

    The extent to which navigational spatial memory depends on hippocampal integrity in humans is not well documented. We investigated allocentric spatial recall using a virtual environment in a group of patients with severe hippocampal damage (SHD), a group of patients with "moderate" hippocampal damage (MHD), and a normal control group. Through four learning blocks with feedback, participants learned the target locations of four different objects in a circular arena. Distal cues were present throughout the experiment to provide orientation. A circular boundary as well as an intra-arena landmark provided spatial reference frames. During a subsequent test phase, recall of all four objects was tested with only the boundary or the landmark being present. Patients with SHD were impaired in both phases of this task. Across groups, performance on both types of spatial recall was highly correlated with memory quotient (MQ), but not with intelligence quotient (IQ), age, or sex. However, both measures of spatial recall separated experimental groups beyond what would be expected based on MQ, a widely used measure of general memory function. Boundary-based and landmark-based spatial recall were both strongly related to bilateral hippocampal volumes, but not to volumes of the thalamus, putamen, pallidum, nucleus accumbens, or caudate nucleus. The results show that boundary-based and landmark-based allocentric spatial recall are similarly impaired in patients with SHD, that both types of recall are impaired beyond that predicted by MQ, and that recall deficits are best explained by a reduction in bilateral hippocampal volumes. In humans, bilateral hippocampal atrophy can lead to profound impairments in episodic memory. Across species, perhaps the most well-established contribution of the hippocampus to memory is not to episodic memory generally but to allocentric spatial memory. However, the extent to which navigational spatial memory depends on hippocampal integrity in humans is

  10. Finite Volumes Discretization of Topology Optimization Problems

    DEFF Research Database (Denmark)

    Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter

    , FVMs represent a standard method of discretization within engineering communities dealing with computational uid dy- namics, transport, and convection-reaction problems. Among various avours of FVMs, cell based approaches, where all variables are associated only with cell centers, are particularly...... computations is done using nite element methods (FEMs). Despite some limited recent eorts [1, 2], we have only started to develop our understanding of the interplay between the control in the coecients and FVMs. Recent advances in discrete functional analysis allow us to analyze convergence of FVM...... of the induced parametrization of the design space that allows optimization algorithms to eciently explore it, and the ease of integration with existing computational codes in a variety of application areas, the simplicity and eciency of sensitivity analyses|all stemming from the use of the same grid throughout...

  11. A study of discrete nonlinear systems

    International Nuclear Information System (INIS)

    Dhillon, H.S.

    2001-04-01

    An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)

  12. Discrete dipole approximation simulation of bead enhanced diffraction grating biosensor

    International Nuclear Information System (INIS)

    Arif, Khalid Mahmood

    2016-01-01

    We present the discrete dipole approximation simulation of light scattering from bead enhanced diffraction biosensor and report the effect of bead material, number of beads forming the grating and spatial randomness on the diffraction intensities of 1st and 0th orders. The dipole models of gratings are formed by volume slicing and image processing while the spatial locations of the beads on the substrate surface are randomly computed using discrete probability distribution. The effect of beads reduction on far-field scattering of 632.8 nm incident field, from fully occupied gratings to very coarse gratings, is studied for various bead materials. Our findings give insight into many difficult or experimentally impossible aspects of this genre of biosensors and establish that bead enhanced grating may be used for rapid and precise detection of small amounts of biomolecules. The results of simulations also show excellent qualitative similarities with experimental observations. - Highlights: • DDA was used to study the relationship between the number of beads forming gratings and ratio of first and zeroth order diffraction intensities. • A very flexible modeling program was developed to design complicated objects for DDA. • Material and spatial effects of bead distribution on surfaces were studied. • It has been shown that bead enhanced grating biosensor can be useful for fast detection of small amounts of biomolecules. • Experimental results qualitatively support the simulations and thus open a way to optimize the grating biosensors.

  13. Discrete Mathematics in the Schools. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Volume 36.

    Science.gov (United States)

    Rosenstein, Joseph G., Ed.; Franzblau, Deborah S., Ed.; Roberts, Fred S., Ed.

    This book is a collection of articles by experienced educators and explains why and how discrete mathematics should be taught in K-12 classrooms. It includes evidence for "why" and practical guidance for "how" and also discusses how discrete mathematics can be used as a vehicle for achieving the broader goals of the major…

  14. An assessment of unstructured grid finite volume schemes for cold gas hypersonic flow calculations

    Directory of Open Access Journals (Sweden)

    João Luiz F. Azevedo

    2009-06-01

    Full Text Available A comparison of five different spatial discretization schemes is performed considering a typical high speed flow application. Flowfields are simulated using the 2-D Euler equations, discretized in a cell-centered finite volume procedure on unstructured triangular meshes. The algorithms studied include a central difference-type scheme, and 1st- and 2nd-order van Leer and Liou flux-vector splitting schemes. These methods are implemented in an efficient, edge-based, unstructured grid procedure which allows for adaptive mesh refinement based on flow property gradients. Details of the unstructured grid implementation of the methods are presented together with a discussion of the data structure and of the adaptive refinement strategy. The application of interest is the cold gas flow through a typical hypersonic inlet. Results for different entrance Mach numbers and mesh topologies are discussed in order to assess the comparative performance of the various spatial discretization schemes.

  15. Quantifying spatial and temporal trends in beach-dune volumetric changes using spatial statistics

    Science.gov (United States)

    Eamer, Jordan B. R.; Walker, Ian J.

    2013-06-01

    Spatial statistics are generally underutilized in coastal geomorphology, despite offering great potential for identifying and quantifying spatial-temporal trends in landscape morphodynamics. In particular, local Moran's Ii provides a statistical framework for detecting clusters of significant change in an attribute (e.g., surface erosion or deposition) and quantifying how this changes over space and time. This study analyzes and interprets spatial-temporal patterns in sediment volume changes in a beach-foredune-transgressive dune complex following removal of invasive marram grass (Ammophila spp.). Results are derived by detecting significant changes in post-removal repeat DEMs derived from topographic surveys and airborne LiDAR. The study site was separated into discrete, linked geomorphic units (beach, foredune, transgressive dune complex) to facilitate sub-landscape scale analysis of volumetric change and sediment budget responses. Difference surfaces derived from a pixel-subtraction algorithm between interval DEMs and the LiDAR baseline DEM were filtered using the local Moran's Ii method and two different spatial weights (1.5 and 5 m) to detect statistically significant change. Moran's Ii results were compared with those derived from a more spatially uniform statistical method that uses a simpler student's t distribution threshold for change detection. Morphodynamic patterns and volumetric estimates were similar between the uniform geostatistical method and Moran's Ii at a spatial weight of 5 m while the smaller spatial weight (1.5 m) consistently indicated volumetric changes of less magnitude. The larger 5 m spatial weight was most representative of broader site morphodynamics and spatial patterns while the smaller spatial weight provided volumetric changes consistent with field observations. All methods showed foredune deflation immediately following removal with increased sediment volumes into the spring via deposition at the crest and on lobes in the lee

  16. Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

    International Nuclear Information System (INIS)

    Cui, Xia; Yuan, Guang-wei; Shen, Zhi-jun

    2016-01-01

    Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-order accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.

  17. Handbook of Spatial Statistics

    CERN Document Server

    Gelfand, Alan E

    2010-01-01

    Offers an introduction detailing the evolution of the field of spatial statistics. This title focuses on the three main branches of spatial statistics: continuous spatial variation (point referenced data); discrete spatial variation, including lattice and areal unit data; and, spatial point patterns.

  18. Laplacians on discrete and quantum geometries

    International Nuclear Information System (INIS)

    Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

    2013-01-01

    We extend discrete calculus for arbitrary (p-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular complex and its combinatorial dual. The precise implementation of geometric volume factors is not unique and, comparing the definition with a circumcentric and a barycentric dual, we argue that the latter is, in general, more appropriate because it induces a Laplacian with more desirable properties. We give the expression of the discrete Laplacian in several different sets of geometric variables, suitable for computations in different quantum gravity formalisms. Furthermore, we investigate the possibility of transforming from position to momentum space for scalar fields, thus setting the stage for the calculation of heat kernel and spectral dimension in discrete quantum geometries. (paper)

  19. Treatment plan evaluation using dose-volume histogram (DVH) and spatial dose-volume histogram (zDVH)

    International Nuclear Information System (INIS)

    Cheng, C.-W.; Das, Indra J.

    1999-01-01

    Objective: The dose-volume histogram (DVH) has been accepted as a tool for treatment-plan evaluation. However, DVH lacks spatial information. A new concept, the z-dependent dose-volume histogram (zDVH), is presented as a supplement to the DVH in three-dimensional (3D) treatment planning to provide the spatial variation, as well as the size and magnitude of the different dose regions within a region of interest. Materials and Methods: Three-dimensional dose calculations were carried out with various plans for three disease sites: lung, breast, and prostate. DVHs were calculated for the entire volume. A zDVH is defined as a differential dose-volume histogram with respect to a computed tomographic (CT) slice position. In this study, zDVHs were calculated for each CT slice in the treatment field. DVHs and zDVHs were compared. Results: In the irradiation of lung, DVH calculation indicated that the treatment plan satisfied the dose-volume constraint placed on the lung and zDVH of the lung revealed that a sizable fraction of the lung centered about the central axis (CAX) received a significant dose, a situation that warranted a modification of the treatment plan due to the removal of one lung. In the irradiation of breast with tangential fields, the DVH showed that about 7% of the breast volume received at least 110% of the prescribed dose (PD) and about 11% of the breast received less than 98% PD. However, the zDVHs of the breast volume in each of seven planes showed the existence of high-dose regions of 34% and 15%, respectively, of the volume in the two caudal-most planes and cold spots of about 40% in the two cephalic planes. In the treatment planning of prostate, DVHs showed that about 15% of the bladder and 40% of the rectum received 102% PD, whereas about 30% of the bladder and 50% of the rectum received the full dose. Taking into account the hollow structure of both the bladder and the rectum, the dose-surface histograms (DSH) showed larger hot-spot volume, about

  20. Utilization of the Discrete Differential Evolution for Optimization in Multidimensional Point Clouds.

    Science.gov (United States)

    Uher, Vojtěch; Gajdoš, Petr; Radecký, Michal; Snášel, Václav

    2016-01-01

    The Differential Evolution (DE) is a widely used bioinspired optimization algorithm developed by Storn and Price. It is popular for its simplicity and robustness. This algorithm was primarily designed for real-valued problems and continuous functions, but several modified versions optimizing both integer and discrete-valued problems have been developed. The discrete-coded DE has been mostly used for combinatorial problems in a set of enumerative variants. However, the DE has a great potential in the spatial data analysis and pattern recognition. This paper formulates the problem as a search of a combination of distinct vertices which meet the specified conditions. It proposes a novel approach called the Multidimensional Discrete Differential Evolution (MDDE) applying the principle of the discrete-coded DE in discrete point clouds (PCs). The paper examines the local searching abilities of the MDDE and its convergence to the global optimum in the PCs. The multidimensional discrete vertices cannot be simply ordered to get a convenient course of the discrete data, which is crucial for good convergence of a population. A novel mutation operator utilizing linear ordering of spatial data based on the space filling curves is introduced. The algorithm is tested on several spatial datasets and optimization problems. The experiments show that the MDDE is an efficient and fast method for discrete optimizations in the multidimensional point clouds.

  1. Multi-GPU-based acceleration of the explicit time domain volume integral equation solver using MPI-OpenACC

    KAUST Repository

    Feki, Saber

    2013-07-01

    An explicit marching-on-in-time (MOT)-based time-domain volume integral equation (TDVIE) solver has recently been developed for characterizing transient electromagnetic wave interactions on arbitrarily shaped dielectric bodies (A. Al-Jarro et al., IEEE Trans. Antennas Propag., vol. 60, no. 11, 2012). The solver discretizes the spatio-temporal convolutions of the source fields with the background medium\\'s Green function using nodal discretization in space and linear interpolation in time. The Green tensor, which involves second order spatial and temporal derivatives, is computed using finite differences on the temporal and spatial grid. A predictor-corrector algorithm is used to maintain the stability of the MOT scheme. The simplicity of the discretization scheme permits the computation of the discretized spatio-temporal convolutions on the fly during time marching; no \\'interaction\\' matrices are pre-computed or stored resulting in a memory efficient scheme. As a result, most often the applicability of this solver to the characterization of wave interactions on electrically large structures is limited by the computation time but not the memory. © 2013 IEEE.

  2. Stochastic dynamics of spatial effects in fragmentation of clusters

    International Nuclear Information System (INIS)

    Salinas-Rodriguez, E.; Rodriguez, R.F.; Zamora, J.M.

    1991-01-01

    We use a stochastic approach to study the effects of spatial in homogeneities in the kinetics of a fragmentation model which occurs in cluster breakup and polymer degradation. The analytical form of the cluster size distribution function is obtained for both the discrete and continuous limits. From it we calculate numerically the average size and volume of the clusters, their total concentration and the total scattering of the dispersion in both limits. The influence of spatial effects is explicitly shown in the last two quantities. From our description the equations for the equal-time and the two times density correlation functions are also derived in the continuous limit. Finally, the perspectives and limitations of our approach are discussed (Author)

  3. Finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws

    International Nuclear Information System (INIS)

    Botchorishvili, Ramaz; Pironneau, Olivier

    2003-01-01

    We develop here a new class of finite volume schemes on unstructured meshes for scalar conservation laws with stiff source terms. The schemes are of equilibrium type, hence with uniform bounds on approximate solutions, valid in cell entropy inequalities and exact for some equilibrium states. Convergence is investigated in the framework of kinetic schemes. Numerical tests show high computational efficiency and a significant advantage over standard cell centered discretization of source terms. Equilibrium type schemes produce accurate results even on test problems for which the standard approach fails. For some numerical tests they exhibit exponential type convergence rate. In two of our numerical tests an equilibrium type scheme with 441 nodes on a triangular mesh is more accurate than a standard scheme with 5000 2 grid points

  4. Spatial navigation impairment is proportional to right hippocampal volume

    Czech Academy of Sciences Publication Activity Database

    Nedelská, Z.; Andel, R.; Laczó, J.; Vlček, Kamil; Hořínek, D.; Lisý, J.; Sheardová, K.; Bureš, Jan; Hort, J.

    2012-01-01

    Roč. 109, č. 7 (2012), s. 2590-2594 ISSN 0027-8424 R&D Projects: GA ČR(CZ) GA309/09/1053; GA ČR(CZ) GA309/09/0286; GA MŠk(CZ) 1M0517; GA MŠk(CZ) LC554 Grant - others:GA MZd(CZ) NS10331 Institutional research plan: CEZ:AV0Z50110509 Keywords : spatial navigation * Alzheimer’s Disease * hippocampal volume Subject RIV: FH - Neurology Impact factor: 9.737, year: 2012

  5. Parallel ray tracing for one-dimensional discrete ordinate computations

    International Nuclear Information System (INIS)

    Jarvis, R.D.; Nelson, P.

    1996-01-01

    The ray-tracing sweep in discrete-ordinates, spatially discrete numerical approximation methods applied to the linear, steady-state, plane-parallel, mono-energetic, azimuthally symmetric, neutral-particle transport equation can be reduced to a parallel prefix computation. In so doing, the often severe penalty in convergence rate of the source iteration, suffered by most current parallel algorithms using spatial domain decomposition, can be avoided while attaining parallelism in the spatial domain to whatever extent desired. In addition, the reduction implies parallel algorithm complexity limits for the ray-tracing sweep. The reduction applies to all closed, linear, one-cell functional (CLOF) spatial approximation methods, which encompasses most in current popular use. Scalability test results of an implementation of the algorithm on a 64-node nCube-2S hypercube-connected, message-passing, multi-computer are described. (author)

  6. Applied geometry and discrete mathematics

    CERN Document Server

    Sturm; Gritzmann, Peter; Sturmfels, Bernd

    1991-01-01

    This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's sixty-fifth birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honor of Klee's achievements, this volume presents more than forty papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, th...

  7. Time Discretization Techniques

    KAUST Repository

    Gottlieb, S.

    2016-10-12

    The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include multistep, multistage, or multiderivative methods, as well as a combination of these approaches. The time step constraint is mainly a result of the absolute stability requirement, as well as additional conditions that mimic physical properties of the solution, such as positivity or total variation stability. These conditions may be required for stability when the solution develops shocks or sharp gradients. This chapter contains a review of some of the methods historically used for the evolution of hyperbolic PDEs, as well as cutting edge methods that are now commonly used.

  8. New non-structured discretizations for fluid flows with reinforced incompressibility

    International Nuclear Information System (INIS)

    Heib, S.

    2003-01-01

    This work deals with the discretization of Stokes and Navier-Stokes equations modeling the flow of incompressible fluids on 2-D or 3-D non-structured meshes. Triangles and tetrahedrons are used for 2-D and 3-D meshes, respectively. The developments and calculations are performed with the code Priceles (fast CEA-EdF industrial platform for large Eddy simulation). This code allows to perform simulations both on structured and non-structured meshes. A finite-volume resolution method is used: a finite difference volume (FDV) method is used for the structured meshes and a finite element volume (FEV) method is used for the non-structured meshes. The finite element used in the beginning of this work has several defects. Starting from this situation, the discretization is improved by adding modifications to this element and the new elements introduced are analyzed theoretically. In parallel to these analyses, the new discretizations are implemented in order to test them numerically and to confirm the theoretical analyses. The first chapter presents the physical and mathematical modeling used in this work. The second chapter treats of the discretization of Stokes equations and presents the FEV resolution method. Chapter 3 presents a first attempt of improvement of this finite element and leads to the proposal of a new element which is presented in details. The problem encountered with the new discretization leads to a modification presented in chapter 4. This new discretization gives all the expected convergence results and sometimes shows super-convergence properties. Chapter 5 deals with the study and discretization of the Navier-Stokes equations. The study of the filtered Navier-Stokes equations, used for large Eddy simulations, requires to give a particular attention to the discretization of the diffusive terms. Then, the convective terms are considered. The effects of the convective terms in the initial discretization and in the improved method are compared. The use of

  9. Integral and discrete inequalities and their applications

    CERN Document Server

    Qin, Yuming

    2016-01-01

    This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. It provides a useful collection and systematic presentation of known and new results, as well as many applications to differential (ODE and PDE), difference, and integral equations. With this work the author fills a gap in the literature on inequalities, offering an ideal source for researchers in these topics. The present volume is part 1 of the author’s two-volume work on inequalities. Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.

  10. Matrix albedo for discrete ordinates infinite-medium boundary condition

    International Nuclear Information System (INIS)

    Mathews, K.; Dishaw, J.

    2007-01-01

    Discrete ordinates problems with an infinite exterior medium (reflector) can be more efficiently computed by eliminating grid cells in the exterior medium and applying a matrix albedo boundary condition. The albedo matrix is a discretized bidirectional reflection distribution function (BRDF) that accounts for the angular quadrature set, spatial quadrature method, and spatial grid that would have been used to model a portion of the exterior medium. The method is exact in slab geometry, and could be used as an approximation in multiple dimensions or curvilinear coordinates. We present an adequate method for computing albedo matrices and demonstrate their use in verifying a discrete ordinates code in slab geometry by comparison with Ganapol's infinite medium semi-analytic TIEL benchmark. With sufficient resolution in the spatial and angular grids and iteration tolerance to yield solutions converged to 6 digits, the conventional (scalar) albedo boundary condition yielded 2-digit accuracy at the boundary, but the matrix albedo solution reproduced the benchmark scalar flux at the boundary to all 6 digits. (authors)

  11. Finite spatial-volume effect for π-N sigma term in lattice QCD

    International Nuclear Information System (INIS)

    Fukushima, M.; Chiba, S.; Tanigawa, T.

    2003-01-01

    We report on a finite spatial-volume effect for the pion-nucleon sigma term σ πN for quenched Wilson fermion on 8 3 x 20 and 16 3 x 20 lattices at β = 5.7 with the spatial lattice size of La∼1.12fm and La∼2.24fm, respectively. It is found that the spatial size dependence of the connected part of σ πN con is significant small. We observed the magnitude of finite size effect for the disconnected part of σ πN dis is much larger than for to connected one and an almost drastic decrease of σ πN dis amounting to 50% between La∼2.24fm to the smaller lattice size of La∼1.12fm. (author)

  12. A verification regime for the spatial discretization of the SN transport equations

    Energy Technology Data Exchange (ETDEWEB)

    Schunert, S.; Azmy, Y. [North Carolina State Univ., Dept. of Nuclear Engineering, 2500 Stinson Drive, Raleigh, NC 27695 (United States)

    2012-07-01

    The order-of-accuracy test in conjunction with the method of manufactured solutions is the current state of the art in computer code verification. In this work we investigate the application of a verification procedure including the order-of-accuracy test on a generic SN transport solver that implements the AHOTN spatial discretization. Different types of semantic errors, e.g. removal of a line of code or changing a single character, are introduced randomly into the previously verified S{sub N} code and the proposed verification procedure is used to identify the coding mistakes (if possible) and classify them. Itemized by error type we record the stage of the verification procedure where the error is detected and report the frequency with which the errors are correctly identified at various stages of the verification. Errors that remain undetected by the verification procedure are further scrutinized to determine the reason why the introduced coding mistake eluded the verification procedure. The result of this work is that the verification procedure based on an order-of-accuracy test finds almost all detectable coding mistakes but rarely, 1.44% of the time, and under certain circumstances can fail. (authors)

  13. Application of multivariate splines to discrete mathematics

    OpenAIRE

    Xu, Zhiqiang

    2005-01-01

    Using methods developed in multivariate splines, we present an explicit formula for discrete truncated powers, which are defined as the number of non-negative integer solutions of linear Diophantine equations. We further use the formula to study some classical problems in discrete mathematics as follows. First, we extend the partition function of integers in number theory. Second, we exploit the relation between the relative volume of convex polytopes and multivariate truncated powers and giv...

  14. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, T S; Adams, M L [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B; Zika, M R [Lawrence Livermore National Lab., Livermore, CA (United States)

    2005-07-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

  15. Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids

    KAUST Repository

    Chen, Huangxin

    2017-09-01

    In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i.e., the linear implicit scheme for time discretization with the finite difference method (FDM) on staggered grids for spatial discretization, pressure-correction schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations, and pressure-stabilization schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations. The energy stability estimates are obtained for the above each fully discrete scheme. The upwind scheme is used in the discretization of the convection term which plays an important role in the design of unconditionally stable discrete schemes. Numerical results are given to verify the theoretical analysis.

  16. Exponential characteristic spatial quadrature for discrete ordinates radiation transport with rectangular cells

    International Nuclear Information System (INIS)

    Minor, B.; Mathews, K.

    1995-01-01

    The exponential characteristic (EC) spatial quadrature for discrete ordinates neutral particle transport previously introduced in slab geometry is extended here to x-y geometry with rectangular cells. The method is derived and compared with current methods. It is similar to the linear characteristic (LC) quadrature (a linear-linear moments method) but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx + cy), whose parameters are rootsolved to match the known (from the previous iteration) spatial average and first moments of the source over the cell. Similarly, EC assumes exponential distributions of flux along cell edges through which particles enter the cell, with parameters chosen to match the average and first moments of flux, as passed from the adjacent, upstream cells (or as determined by boundary conditions). Like the linear adaptive (LA) method, EC is positive and nonlinear. It is more accurate than LA and does not require subdivision of cells. The nonlinearity has not interfered with convergence. The exponential moment functions, which were introduced with the slab geometry method, are extended to arbitrary dimensions (numbers of arguments) and used to avoid numerical ill conditioning. As in slab geometry, the method approaches O(Δx 4 ) global truncation error on fine-enough meshes, while the error is insensitive to mesh size for coarse meshes. Performance of the method is compared with that of the step characteristic, LC, linear nodal, step adaptive, and LA schemes. The EC method is a strong performer with scattering ratios ranging from 0 to 0.9 (the range tested), particularly so for lower scattering ratios. As in slab geometry, EC is computationally more costly per cell than current methods but can be accurate with very thick cells, leading to increased computational efficiency on appropriate problems

  17. The Impact of the discreteness of low-fluence ion beam processing on the spatial architecture of GaN nanostructures fabricated by surface charge lithography

    International Nuclear Information System (INIS)

    Tiginyanu, I.M.; Volciuc, O.; Gutowski, J.; Stevens-Kalceff, M.A.; Popa, V.; Wille, S.; Adelung, R.; Foell, H.

    2013-01-01

    We show that the discrete nature of ion beam processing used as a component in the approach of surface charge lithography leads to spatial modulation of the edges of the GaN nanostructures such as nanobelts and nanoperforated membranes. According to the performed Monte Carlo simulations, the modulation of the nanostructure edges is caused by the stochastic spatial distribution of the radiation defects generated by the impacting ions and related recoils. The obtained results pave the way for direct visualization of the networks of radiation defects induced by individual ions impacting a solid-state material. (authors)

  18. Radiative transfer on discrete spaces

    CERN Document Server

    Preisendorfer, Rudolph W; Stark, M; Ulam, S

    1965-01-01

    Pure and Applied Mathematics, Volume 74: Radiative Transfer on Discrete Spaces presents the geometrical structure of natural light fields. This book describes in detail with mathematical precision the radiometric interactions of light-scattering media in terms of a few well established principles.Organized into four parts encompassing 15 chapters, this volume begins with an overview of the derivations of the practical formulas and the arrangement of formulas leading to numerical solution procedures of radiative transfer problems in plane-parallel media. This text then constructs radiative tran

  19. Bifacial DNA origami-directed discrete, three-dimensional, anisotropic plasmonic nanoarchitectures with tailored optical chirality.

    Science.gov (United States)

    Lan, Xiang; Chen, Zhong; Dai, Gaole; Lu, Xuxing; Ni, Weihai; Wang, Qiangbin

    2013-08-07

    Discrete three-dimensional (3D) plasmonic nanoarchitectures with well-defined spatial configuration and geometry have aroused increasing interest, as new optical properties may originate from plasmon resonance coupling within the nanoarchitectures. Although spherical building blocks have been successfully employed in constructing 3D plasmonic nanoarchitectures because their isotropic nature facilitates unoriented localization, it still remains challenging to assemble anisotropic building blocks into discrete and rationally tailored 3D plasmonic nanoarchitectures. Here we report the first example of discrete 3D anisotropic gold nanorod (AuNR) dimer nanoarchitectures formed using bifacial DNA origami as a template, in which the 3D spatial configuration is precisely tuned by rationally shifting the location of AuNRs on the origami template. A distinct plasmonic chiral response was experimentally observed from the discrete 3D AuNR dimer nanoarchitectures and appeared in a spatial-configuration-dependent manner. This study represents great progress in the fabrication of 3D plasmonic nanoarchitectures with tailored optical chirality.

  20. Spatial and temporal single-cell volume estimation by a fluorescence imaging technique with application to astrocytes in primary culture

    Science.gov (United States)

    Khatibi, Siamak; Allansson, Louise; Gustavsson, Tomas; Blomstrand, Fredrik; Hansson, Elisabeth; Olsson, Torsten

    1999-05-01

    Cell volume changes are often associated with important physiological and pathological processes in the cell. These changes may be the means by which the cell interacts with its surrounding. Astroglial cells change their volume and shape under several circumstances that affect the central nervous system. Following an incidence of brain damage, such as a stroke or a traumatic brain injury, one of the first events seen is swelling of the astroglial cells. In order to study this and other similar phenomena, it is desirable to develop technical instrumentation and analysis methods capable of detecting and characterizing dynamic cell shape changes in a quantitative and robust way. We have developed a technique to monitor and to quantify the spatial and temporal volume changes in a single cell in primary culture. The technique is based on two- and three-dimensional fluorescence imaging. The temporal information is obtained from a sequence of microscope images, which are analyzed in real time. The spatial data is collected in a sequence of images from the microscope, which is automatically focused up and down through the specimen. The analysis of spatial data is performed off-line and consists of photobleaching compensation, focus restoration, filtering, segmentation and spatial volume estimation.

  1. Exponential characteristics spatial quadrature for discrete ordinates radiation transport in slab geometry

    International Nuclear Information System (INIS)

    Mathews, K.; Sjoden, G.; Minor, B.

    1994-01-01

    The exponential characteristic spatial quadrature for discrete ordinates neutral particle transport in slab geometry is derived and compared with current methods. It is similar to the linear characteristic (or, in slab geometry, the linear nodal) quadrature but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx), whose parameters are root-solved to match the known (from the previous iteration) average and first moment of the source over the cell. Like the linear adaptive method, the exponential characteristic method is positive and nonlinear but more accurate and more readily extended to other cell shapes. The nonlinearity has not interfered with convergence. The authors introduce the ''exponential moment functions,'' a generalization of the functions used by Walters in the linear nodal method, and use them to avoid numerical ill-conditioning. The method exhibits O(Δx 4 ) truncation error on fine enough meshes; the error is insensitive to mesh size for coarse meshes. In a shielding problem, it is accurate to 10% using 16-mfp-thick cells; conventional methods err by 8 to 15 orders of magnitude. The exponential characteristic method is computationally more costly per cell than current methods but can be accurate with very thick cells, leading to increased computational efficiency on appropriate problems

  2. Radiative transfer modelling in combusting systems using discrete ordinates method on three-dimensional unstructured grids; Modelisation des transferts radiatifs en combustion par methode aux ordonnees discretes sur des maillages non structures tridimensionnels

    Energy Technology Data Exchange (ETDEWEB)

    Joseph, D.

    2004-04-01

    The prediction of pollutant species such as soots and NO{sub x} emissions and lifetime of the walls in a combustion chamber is strongly dependant on heat transfer by radiation at high temperatures. This work deals with the development of a code based on the Discrete Ordinates Method (DOM) aiming at providing radiative source terms and wall fluxes with a good compromise between cpu time and accuracy. Radiative heat transfers are calculated using the unstructured grids defined by the Computational Fluid Dynamics (CFD) codes. The spectral properties of the combustion gases are taken into account by a statistical narrow bands correlated-k model (SNB-ck). Various types of angular quadrature are tested and three different spatial differencing schemes were integrated and compared. The validation tests show the limit at strong optical thicknesses of the finite volume approximation used the Discrete Ordinates Method. The first calculations performed on LES solutions are presented, it provides instantaneous radiative source terms and wall heat fluxes. Those results represent a first step towards radiation/combustion coupling. (author)

  3. Anisotropy, propagation failure, and wave speedup in traveling waves of discretizations of a Nagumo PDE

    International Nuclear Information System (INIS)

    Elmer, Christopher E.; Vleck, Erik S. van

    2003-01-01

    This article is concerned with effect of spatial and temporal discretizations on traveling wave solutions to parabolic PDEs (Nagumo type) possessing piecewise linear bistable nonlinearities. Solution behavior is compared in terms of waveforms and in terms of the so-called (a,c) relationship where a is a parameter controlling the bistable nonlinearity by varying the potential energy difference of the two phases and c is the wave speed of the traveling wave. Uniform spatial discretizations and A(α) stable linear multistep methods in time are considered. Results obtained show that although the traveling wave solutions to parabolic PDEs are stationary for only one value of the parameter a,a 0 , spatial discretization of these PDEs produce traveling waves which are stationary for a nontrivial interval of a values which include a 0 , i.e., failure of the solution to propagate in the presence of a driving force. This is true no matter how wide the interface is with respect to the discretization. For temporal discretizations at large wave speeds the set of parameter a values for which there are traveling wave solutions is constrained. An analysis of a complete discretization points out the potential for nonuniqueness in the (a,c) relationship

  4. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, T.S.; Adams, M.L. [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B.; Zika, M.R. [Lawrence Livermore National Lab., Livermore, CA (United States)

    2005-07-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

  5. A parallel algorithm for solving the multidimensional within-group discrete ordinates equations with spatial domain decomposition - 104

    International Nuclear Information System (INIS)

    Zerr, R.J.; Azmy, Y.Y.

    2010-01-01

    A spatial domain decomposition with a parallel block Jacobi solution algorithm has been developed based on the integral transport matrix formulation of the discrete ordinates approximation for solving the within-group transport equation. The new methodology abandons the typical source iteration scheme and solves directly for the fully converged scalar flux. Four matrix operators are constructed based upon the integral form of the discrete ordinates equations. A single differential mesh sweep is performed to construct these operators. The method is parallelized by decomposing the problem domain into several smaller sub-domains, each treated as an independent problem. The scalar flux of each sub-domain is solved exactly given incoming angular flux boundary conditions. Sub-domain boundary conditions are updated iteratively, and convergence is achieved when the scalar flux error in all cells meets a pre-specified convergence criterion. The method has been implemented in a computer code that was then employed for strong scaling studies of the algorithm's parallel performance via a fixed-size problem in tests ranging from one domain up to one cell per sub-domain. Results indicate that the best parallel performance compared to source iterations occurs for optically thick, highly scattering problems, the variety that is most difficult for the traditional SI scheme to solve. Moreover, the minimum execution time occurs when each sub-domain contains a total of four cells. (authors)

  6. Variable discrete ordinates method for radiation transfer in plane-parallel semi-transparent media with variable refractive index

    Science.gov (United States)

    Sarvari, S. M. Hosseini

    2017-09-01

    The traditional form of discrete ordinates method is applied to solve the radiative transfer equation in plane-parallel semi-transparent media with variable refractive index through using the variable discrete ordinate directions and the concept of refracted radiative intensity. The refractive index are taken as constant in each control volume, such that the direction cosines of radiative rays remain non-variant through each control volume, and then, the directions of discrete ordinates are changed locally by passing each control volume, according to the Snell's law of refraction. The results are compared by the previous studies in this field. Despite simplicity, the results show that the variable discrete ordinate method has a good accuracy in solving the radiative transfer equation in the semi-transparent media with arbitrary distribution of refractive index.

  7. Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids

    KAUST Repository

    Chen, Huangxin; Sun, Shuyu; Zhang, Tao

    2017-01-01

    In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i

  8. On the mixed discretization of the time domain magnetic field integral equation

    KAUST Repository

    Ulku, Huseyin Arda

    2012-09-01

    Time domain magnetic field integral equation (MFIE) is discretized using divergence-conforming Rao-Wilton-Glisson (RWG) and curl-conforming Buffa-Christiansen (BC) functions as spatial basis and testing functions, respectively. The resulting mixed discretization scheme, unlike the classical scheme which uses RWG functions as both basis and testing functions, is proper: Testing functions belong to dual space of the basis functions. Numerical results demonstrate that the marching on-in-time (MOT) solution of the mixed discretized MFIE yields more accurate results than that of classically discretized MFIE. © 2012 IEEE.

  9. On discontinuous Galerkin and discrete ordinates approximations for neutron transport equation and the critical eigenvalue

    International Nuclear Information System (INIS)

    Asadzadeh, M.; Thevenot, L.

    2010-01-01

    The objective of this paper is to give a mathematical framework for a fully discrete numerical approach for the study of the neutron transport equation in a cylindrical domain (container model,). More specifically, we consider the discontinuous Galerkin (D G) finite element method for spatial approximation of the mono-energetic, critical neutron transport equation in an infinite cylindrical domain ??in R3 with a polygonal convex cross-section ? The velocity discretization relies on a special quadrature rule developed to give optimal estimates in discrete ordinate parameters compatible with the quasi-uniform spatial mesh. We use interpolation spaces and derive optimal error estimates, up to maximal available regularity, for the fully discrete scalar flux. Finally we employ a duality argument and prove superconvergence estimates for the critical eigenvalue.

  10. Dorso- and ventro-lateral prefrontal volume and spatial working memory in schizotypal personality disorder.

    Science.gov (United States)

    Goldstein, Kim E; Hazlett, Erin A; Savage, Kimberley R; Berlin, Heather A; Hamilton, Holly K; Zelmanova, Yuliya; Look, Amy E; Koenigsberg, Harold W; Mitsis, Effie M; Tang, Cheuk Y; McNamara, Margaret; Siever, Larry J; Cohen, Barry H; New, Antonia S

    2011-04-15

    Schizotypal personality disorder (SPD) individuals and borderline personality disorder (BPD) individuals have been reported to show neuropsychological impairments and abnormalities in brain structure. However, relationships between neuropsychological function and brain structure in these groups are not well understood. This study compared visual-spatial working memory (SWM) and its associations with dorsolateral prefrontal cortex (DLPFC) and ventrolateral prefrontal cortex (VLPFC) gray matter volume in 18 unmedicated SPD patients with no BPD traits, 18 unmedicated BPD patients with no SPD traits, and 16 healthy controls (HC). Results showed impaired SWM in SPD but not BPD, compared with HC. Moreover, among the HC group, but not SPD patients, better SWM performance was associated with larger VLPFC (BA44/45) gray matter volume (Fisher's Z p-values <0.05). Findings suggest spatial working memory impairments may be a core neuropsychological deficit specific to SPD patients and highlight the role of VLPFC subcomponents in normal and dysfunctional memory performance. Published by Elsevier B.V.

  11. A robust and efficient finite volume scheme for the discretization of diffusive flux on extremely skewed meshes in complex geometries

    Science.gov (United States)

    Traoré, Philippe; Ahipo, Yves Marcel; Louste, Christophe

    2009-08-01

    In this paper an improved finite volume scheme to discretize diffusive flux on a non-orthogonal mesh is proposed. This approach, based on an iterative technique initially suggested by Khosla [P.K. Khosla, S.G. Rubin, A diagonally dominant second-order accurate implicit scheme, Computers and Fluids 2 (1974) 207-209] and known as deferred correction, has been intensively utilized by Muzaferija [S. Muzaferija, Adaptative finite volume method for flow prediction using unstructured meshes and multigrid approach, Ph.D. Thesis, Imperial College, 1994] and later Fergizer and Peric [J.H. Fergizer, M. Peric, Computational Methods for Fluid Dynamics, Springer, 2002] to deal with the non-orthogonality of the control volumes. Using a more suitable decomposition of the normal gradient, our scheme gives accurate solutions in geometries where the basic idea of Muzaferija fails. First the performances of both schemes are compared for a Poisson problem solved in quadrangular domains where control volumes are increasingly skewed in order to test their robustness and efficiency. It is shown that convergence properties and the accuracy order of the solution are not degraded even on extremely skewed mesh. Next, the very stable behavior of the method is successfully demonstrated on a randomly distorted grid as well as on an anisotropically distorted one. Finally we compare the solution obtained for quadrilateral control volumes to the ones obtained with a finite element code and with an unstructured version of our finite volume code for triangular control volumes. No differences can be observed between the different solutions, which demonstrates the effectiveness of our approach.

  12. Localized solutions for a nonlocal discrete NLS equation

    International Nuclear Information System (INIS)

    Ben, Roberto I.; Cisneros Ake, Luís; Minzoni, A.A.; Panayotaros, Panayotis

    2015-01-01

    We study spatially localized time-periodic solutions of breather type for a cubic discrete NLS equation with a nonlocal nonlinearity that models light propagation in a liquid crystal waveguide array. We show the existence of breather solutions in the limit where both linear and nonlinear intersite couplings vanish, and in the limit where the linear coupling vanishes with arbitrary nonlinear intersite coupling. Breathers of this nonlocal regime exhibit some interesting features that depart from what is seen in the NLS breathers with power nonlinearity. One property we see theoretically is the presence of higher amplitude at interfaces between sites with zero and nonzero amplitude in the vanishing linear coupling limit. A numerical study also suggests the presence of internal modes of orbitally stable localized modes. - Highlights: • Show existence of spatially localized solutions in nonlocal discrete NLS model. • Study spatial properties of localized solutions for arbitrary nonlinear nonlocal coupling. • Present numerical evidence that nonlocality leads to internal modes around stable breathers. • Present theoretical and numerical evidence for amplitude maxima at interfaces

  13. Localized solutions for a nonlocal discrete NLS equation

    Energy Technology Data Exchange (ETDEWEB)

    Ben, Roberto I. [Instituto de Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, 1613 Los Polvorines (Argentina); Cisneros Ake, Luís [Department of Mathematics, ESFM, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos Edificio 9, 07738 México D.F. (Mexico); Minzoni, A.A. [Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F. (Mexico); Panayotaros, Panayotis, E-mail: panos@mym.iimas.unam.mx [Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F. (Mexico)

    2015-09-04

    We study spatially localized time-periodic solutions of breather type for a cubic discrete NLS equation with a nonlocal nonlinearity that models light propagation in a liquid crystal waveguide array. We show the existence of breather solutions in the limit where both linear and nonlinear intersite couplings vanish, and in the limit where the linear coupling vanishes with arbitrary nonlinear intersite coupling. Breathers of this nonlocal regime exhibit some interesting features that depart from what is seen in the NLS breathers with power nonlinearity. One property we see theoretically is the presence of higher amplitude at interfaces between sites with zero and nonzero amplitude in the vanishing linear coupling limit. A numerical study also suggests the presence of internal modes of orbitally stable localized modes. - Highlights: • Show existence of spatially localized solutions in nonlocal discrete NLS model. • Study spatial properties of localized solutions for arbitrary nonlinear nonlocal coupling. • Present numerical evidence that nonlocality leads to internal modes around stable breathers. • Present theoretical and numerical evidence for amplitude maxima at interfaces.

  14. Finite-element semi-discretization of linearized compressible and resistive MHD

    International Nuclear Information System (INIS)

    Kerner, W.; Jakoby, A.; Lerbinger, K.

    1985-08-01

    The full resistive MHD equations are linearized around an equilibrium with cylindrical symmetry and solved numerically as an initial-value problem. The semi-discretization using cubic and quadratic finite elements for the spatial discretization and a fully implicit time advance yields very accurate results even for small values of the resistivity. In the application different phenomena such as waves, resistive instabilities and overstable modes are addressed. (orig.)

  15. Modeling the spatial distribution of the parameters of the coolant in the reactor volume

    International Nuclear Information System (INIS)

    Nikonov, S.P.

    2011-01-01

    In this paper the approach to the question about the spatial distribution of the parameters of the coolant in-reactor volume. To describe the in-core space is used specially developed preprocessor. When the work of the preprocessor in the first place, is recreated on the basis of available information (mostly-the original drawings) with high accuracy three-dimensional description of the structures of the reactor volume and, secondly, are prepared on this basis blocks input to the nodal system code improved estimate ATHLET, allows to take into account the hydrodynamic interaction between the spatial control volumes. As an example the special case of solutions of international standard problem on the reconstruction of the transition process in the third unit of the Kalinin nuclear power plant, due to the shutdown of one of the four Main Coolant Pumps in operation at the rated capacity (first download). Model-core area consists of approximately 58 000 control volumes and spatial relationships. It shows the influence of certain structural units of the core to the distribution of the mass floe rate of its height. It is detected a strong cross-flow coolant in the area over the baffle. Moreover, we study the distribution of the coolant temperature at the assembly head of WWER-1000 reactor. It is shown that in the region of the top of the assembly head, where we have installation of thermocouples, the flow coolant for internal assemblies core is formed by only from guide channel Reactor control and protected system Control rod flow, or a mixture of the guide channel flow and flow from the area in front of top grid head assembly (the peripheral assemblies). It is shown that the magnitude of the flow guide channels affects not only the position of control rods, but also the presence of a particular type of measuring channels (Self powered neutron detector sensors or Temperature control sensors) in the cassette. (Author)

  16. SPATIAL SEARCH IN COMMERCIAL FISHING: A DISCRETE CHOICE DYNAMIC PROGRAMMING APPROACH

    OpenAIRE

    Smith, Martin D.; Provencher, Bill

    2003-01-01

    We specify a discrete choice dynamic programming model of commercial fishing participation and location choices. This approach allows us to examine how fishermen collect information about resource abundance and whether their behavior is forward-looking.

  17. Discretization-dependent model for weakly connected excitable media

    Science.gov (United States)

    Arroyo, Pedro André; Alonso, Sergio; Weber dos Santos, Rodrigo

    2018-03-01

    Pattern formation has been widely observed in extended chemical and biological processes. Although the biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. Such approaches are usually justified by the difference of scales between the heterogeneities and the characteristic spatial size of the patterns. Under different conditions, for example, under weak coupling, discrete models are more adequate. However, discrete models may be less manageable, for instance, in terms of numerical implementation and mesh generation, than the associated continuum models. Here we study a model to approach discreteness which permits the computer implementation on general unstructured meshes. The model is cast as a partial differential equation but with a parameter that depends not only on heterogeneities sizes, as in the case of quasicontinuum models, but also on the discretization mesh. Therefore, we refer to it as a discretization-dependent model. We validate the approach in a generic excitable media that simulates three different phenomena: the propagation of action membrane potential in cardiac tissue, in myelinated axons of neurons, and concentration waves in chemical microemulsions.

  18. Dynamics of breathers in discrete nonlinear Schrodinger models

    DEFF Research Database (Denmark)

    Christiansen, Peter Leth; Johansson, Magnus; Aubry, Serge

    1998-01-01

    We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized...

  19. Discrete gradients in discrete classical mechanics

    International Nuclear Information System (INIS)

    Renna, L.

    1987-01-01

    A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated

  20. Analysis of stochastic effects in Kaldor-type business cycle discrete model

    Science.gov (United States)

    Bashkirtseva, Irina; Ryashko, Lev; Sysolyatina, Anna

    2016-07-01

    We study nonlinear stochastic phenomena in the discrete Kaldor model of business cycles. A numerical parametric analysis of stochastically forced attractors (equilibria, closed invariant curves, discrete cycles) of this model is performed using the stochastic sensitivity functions technique. A spatial arrangement of random states in stochastic attractors is modeled by confidence domains. The phenomenon of noise-induced transitions ;chaos-order; is discussed.

  1. Numerical Experiments on Advective Transport in Large Three-Dimensional Discrete Fracture Networks

    Science.gov (United States)

    Makedonska, N.; Painter, S. L.; Karra, S.; Gable, C. W.

    2013-12-01

    , computational nodes lying on fracture intersections have four associated velocities, one on each side of the intersection in each fracture plane [2]. This information is used to route particles arriving at the fracture intersection to the appropriate downstream fracture segment. Verified for small DFNs, the new simulation capability allows accurate particle tracking on more realistic representations of fractured rock sites. In the current work we focus on travel time statistics and spatial dispersion and show numerical results in DFNs of different sizes, fracture densities, and transmissivity distributions. [1] Hyman J.D., Gable C.W., Painter S.L., Automated meshing of stochastically generated discrete fracture networks, Abstract H33G-1403, 2011 AGU, San Francisco, CA, 5-9 Dec. [2] N. Makedonska, S. L. Painter, T.-L. Hsieh, Q.M. Bui, and C. W. Gable., Development and verification of a new particle tracking capability for modeling radionuclide transport in discrete fracture networks, Abstract, 2013 IHLRWM, Albuquerque, NM, Apr. 28 - May 3. [3] Lichtner, P.C., Hammond, G.E., Bisht, G., Karra, S., Mills, R.T., and Kumar, J. (2013) PFLOTRAN User's Manual: A Massively Parallel Reactive Flow Code. [4] Painter S.L., Gable C.W., Kelkar S., Pathline tracing on fully unstructured control-volume grids, Computational Geosciences, 16 (4), 2012, 1125-1134.

  2. Algebraic perturbation theory for dense liquids with discrete potentials

    Science.gov (United States)

    Adib, Artur B.

    2007-06-01

    A simple theory for the leading-order correction g1(r) to the structure of a hard-sphere liquid with discrete (e.g., square-well) potential perturbations is proposed. The theory makes use of a general approximation that effectively eliminates four-particle correlations from g1(r) with good accuracy at high densities. For the particular case of discrete perturbations, the remaining three-particle correlations can be modeled with a simple volume-exclusion argument, resulting in an algebraic and surprisingly accurate expression for g1(r) . The structure of a discrete “core-softened” model for liquids with anomalous thermodynamic properties is reproduced as an application.

  3. Synchronization of autonomous objects in discrete event simulation

    Science.gov (United States)

    Rogers, Ralph V.

    1990-01-01

    Autonomous objects in event-driven discrete event simulation offer the potential to combine the freedom of unrestricted movement and positional accuracy through Euclidean space of time-driven models with the computational efficiency of event-driven simulation. The principal challenge to autonomous object implementation is object synchronization. The concept of a spatial blackboard is offered as a potential methodology for synchronization. The issues facing implementation of a spatial blackboard are outlined and discussed.

  4. A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation

    Directory of Open Access Journals (Sweden)

    Yunying Zheng

    2011-01-01

    Full Text Available The spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis.

  5. A fully discrete energy stable scheme for a phase filed moving contact line model with variable densities and viscosities

    KAUST Repository

    Zhu, Guangpu

    2018-01-26

    In this paper, a fully discrete scheme which considers temporal and spatial discretizations is presented for the coupled Cahn-Hilliard equation in conserved form with the dynamic contact line condition and the Navier-Stokes equation with the generalized Navier boundary condition. Variable densities and viscosities are incorporated in this model. A rigorous proof of energy stability is provided for the fully discrete scheme based on a semi-implicit temporal discretization and a finite difference method on the staggered grids for the spatial discretization. A splitting method based on the pressure stabilization is implemented to solve the Navier-Stokes equation, while the stabilization approach is also used for the Cahn-Hilliard equation. Numerical results in both 2-D and 3-D demonstrate the accuracy, efficiency and decaying property of discrete energy of the proposed scheme.

  6. Parallel PWTD-Accelerated Explicit Solution of the Time Domain Electric Field Volume Integral Equation

    KAUST Repository

    Liu, Yang

    2016-03-25

    A parallel plane-wave time-domain (PWTD)-accelerated explicit marching-on-in-time (MOT) scheme for solving the time domain electric field volume integral equation (TD-EFVIE) is presented. The proposed scheme leverages pulse functions and Lagrange polynomials to spatially and temporally discretize the electric flux density induced throughout the scatterers, and a finite difference scheme to compute the electric fields from the Hertz electric vector potentials radiated by the flux density. The flux density is explicitly updated during time marching by a predictor-corrector (PC) scheme and the vector potentials are efficiently computed by a scalar PWTD scheme. The memory requirement and computational complexity of the resulting explicit PWTD-PC-EFVIE solver scale as ( log ) s s O N N and ( ) s t O N N , respectively. Here, s N is the number of spatial basis functions and t N is the number of time steps. A scalable parallelization of the proposed MOT scheme on distributed- memory CPU clusters is described. The efficiency, accuracy, and applicability of the resulting (parallelized) PWTD-PC-EFVIE solver are demonstrated via its application to the analysis of transient electromagnetic wave interactions on canonical and real-life scatterers represented with up to 25 million spatial discretization elements.

  7. Parallel PWTD-Accelerated Explicit Solution of the Time Domain Electric Field Volume Integral Equation

    KAUST Repository

    Liu, Yang; Al-Jarro, Ahmed; Bagci, Hakan; Michielssen, Eric

    2016-01-01

    A parallel plane-wave time-domain (PWTD)-accelerated explicit marching-on-in-time (MOT) scheme for solving the time domain electric field volume integral equation (TD-EFVIE) is presented. The proposed scheme leverages pulse functions and Lagrange polynomials to spatially and temporally discretize the electric flux density induced throughout the scatterers, and a finite difference scheme to compute the electric fields from the Hertz electric vector potentials radiated by the flux density. The flux density is explicitly updated during time marching by a predictor-corrector (PC) scheme and the vector potentials are efficiently computed by a scalar PWTD scheme. The memory requirement and computational complexity of the resulting explicit PWTD-PC-EFVIE solver scale as ( log ) s s O N N and ( ) s t O N N , respectively. Here, s N is the number of spatial basis functions and t N is the number of time steps. A scalable parallelization of the proposed MOT scheme on distributed- memory CPU clusters is described. The efficiency, accuracy, and applicability of the resulting (parallelized) PWTD-PC-EFVIE solver are demonstrated via its application to the analysis of transient electromagnetic wave interactions on canonical and real-life scatterers represented with up to 25 million spatial discretization elements.

  8. Decompositions of bubbly flow PIV velocity fields using discrete wavelets multi-resolution and multi-section image method

    International Nuclear Information System (INIS)

    Choi, Je-Eun; Takei, Masahiro; Doh, Deog-Hee; Jo, Hyo-Jae; Hassan, Yassin A.; Ortiz-Villafuerte, Javier

    2008-01-01

    Currently, wavelet transforms are widely used for the analyses of particle image velocimetry (PIV) velocity vector fields. This is because the wavelet provides not only spatial information of the velocity vectors, but also of the time and frequency domains. In this study, a discrete wavelet transform is applied to real PIV images of bubbly flows. The vector fields obtained by a self-made cross-correlation PIV algorithm were used for the discrete wavelet transform. The performances of the discrete wavelet transforms were investigated by changing the level of power of discretization. The images decomposed by wavelet multi-resolution showed conspicuous characteristics of the bubbly flows for the different levels. A high spatial bubble concentrated area could be evaluated by the constructed discrete wavelet transform algorithm, in which high-leveled wavelets play dominant roles in revealing the flow characteristics

  9. Discrete mKdV and discrete sine-Gordon flows on discrete space curves

    International Nuclear Information System (INIS)

    Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

    2014-01-01

    In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym–Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces. (paper)

  10. Foundations of the probabilistic mechanics of discrete media

    CERN Document Server

    Axelrad, D R

    1984-01-01

    This latest volume in the Foundations & Philosophy of Science & Technology series provides an account of probabilistic functional analysis and shows its applicability in the formulation of the behaviour of discrete media with the inclusion of microstructural effects. Although quantum mechanics have long been recognized as a stochastic theory, the introduction of probabilistic concepts and principles to classical mechanics has in general not been attempted. In this study the author takes the view that the significant field quantities of a discrete medium are random variables or functions of s

  11. Discrete Curvatures and Discrete Minimal Surfaces

    KAUST Repository

    Sun, Xiang

    2012-06-01

    This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.

  12. Finite Volumes for Complex Applications VII

    CERN Document Server

    Ohlberger, Mario; Rohde, Christian

    2014-01-01

    The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications. The second volume of the proceedings covers reviewed contributions reporting successful applications in the fields of fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory and other topics. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative propert...

  13. Discrete Events as Units of Perceived Time

    Science.gov (United States)

    Liverence, Brandon M.; Scholl, Brian J.

    2012-01-01

    In visual images, we perceive both space (as a continuous visual medium) and objects (that inhabit space). Similarly, in dynamic visual experience, we perceive both continuous time and discrete events. What is the relationship between these units of experience? The most intuitive answer may be similar to the spatial case: time is perceived as an…

  14. Temporal dynamics of divided spatial attention.

    Science.gov (United States)

    Itthipuripat, Sirawaj; Garcia, Javier O; Serences, John T

    2013-05-01

    In naturalistic settings, observers often have to monitor multiple objects dispersed throughout the visual scene. However, the degree to which spatial attention can be divided across spatially noncontiguous objects has long been debated, particularly when those objects are in close proximity. Moreover, the temporal dynamics of divided attention are unclear: is the process of dividing spatial attention gradual and continuous, or does it onset in a discrete manner? To address these issues, we recorded steady-state visual evoked potentials (SSVEPs) as subjects covertly monitored two flickering targets while ignoring an intervening distractor that flickered at a different frequency. All three stimuli were clustered within either the lower left or the lower right quadrant, and our dependent measure was SSVEP power at the target and distractor frequencies measured over time. In two experiments, we observed a temporally discrete increase in power for target- vs. distractor-evoked SSVEPs extending from ∼350 to 150 ms prior to correct (but not incorrect) responses. The divergence in SSVEP power immediately prior to a correct response suggests that spatial attention can be divided across noncontiguous locations, even when the targets are closely spaced within a single quadrant. In addition, the division of spatial attention appears to be relatively discrete, as opposed to slow and continuous. Finally, the predictive relationship between SSVEP power and behavior demonstrates that these neurophysiological measures of divided attention are meaningfully related to cognitive function.

  15. Compartmentalization analysis using discrete fracture network models

    Energy Technology Data Exchange (ETDEWEB)

    La Pointe, P.R.; Eiben, T.; Dershowitz, W. [Golder Associates, Redmond, VA (United States); Wadleigh, E. [Marathon Oil Co., Midland, TX (United States)

    1997-08-01

    This paper illustrates how Discrete Fracture Network (DFN) technology can serve as a basis for the calculation of reservoir engineering parameters for the development of fractured reservoirs. It describes the development of quantitative techniques for defining the geometry and volume of structurally controlled compartments. These techniques are based on a combination of stochastic geometry, computational geometry, and graph the theory. The parameters addressed are compartment size, matrix block size and tributary drainage volume. The concept of DFN models is explained and methodologies to compute these parameters are demonstrated.

  16. Discrete and mesoscopic regimes of finite-size wave turbulence

    International Nuclear Information System (INIS)

    L'vov, V. S.; Nazarenko, S.

    2010-01-01

    Bounding volume results in discreteness of eigenmodes in wave systems. This leads to a depletion or complete loss of wave resonances (three-wave, four-wave, etc.), which has a strong effect on wave turbulence (WT) i.e., on the statistical behavior of broadband sets of weakly nonlinear waves. This paper describes three different regimes of WT realizable for different levels of the wave excitations: discrete, mesoscopic and kinetic WT. Discrete WT comprises chaotic dynamics of interacting wave 'clusters' consisting of discrete (often finite) number of connected resonant wave triads (or quarters). Kinetic WT refers to the infinite-box theory, described by well-known wave-kinetic equations. Mesoscopic WT is a regime in which either the discrete and the kinetic evolutions alternate or when none of these two types is purely realized. We argue that in mesoscopic systems the wave spectrum experiences a sandpile behavior. Importantly, the mesoscopic regime is realized for a broad range of wave amplitudes which typically spans over several orders on magnitude, and not just for a particular intermediate level.

  17. On the convergence of multigroup discrete-ordinates approximations

    International Nuclear Information System (INIS)

    Victory, H.D. Jr.; Allen, E.J.; Ganguly, K.

    1987-01-01

    Our analysis is divided into two distinct parts which we label for convenience as Part A and Part B. In Part A, we demonstrate that the multigroup discrete-ordinates approximations are well-defined and converge to the exact transport solution in any subcritical setting. For the most part, we focus on transport in two-dimensional Cartesian geometry. A Nystroem technique is used to extend the discrete ordinates multigroup approximates to all values of the angular and energy variables. Such an extension enables us to employ collectively compact operator theory to deduce stability and convergence of the approximates. In Part B, we perform a thorough convergence analysis for the multigroup discrete-ordinates method for an anisotropically-scattering subcritical medium in slab geometry. The diamond-difference and step-characteristic spatial approximation methods are each studied. The multigroup neutron fluxes are shown to converge in a Banach space setting under realistic smoothness conditions on the solution. This is the first thorough convergence analysis for the fully-discretized multigroup neutron transport equations

  18. Averaged multivalued solutions and time discretization for conservation laws

    International Nuclear Information System (INIS)

    Brenier, Y.

    1985-01-01

    It is noted that the correct shock solutions can be approximated by averaging in some sense the multivalued solution given by the method of characteristics for the nonlinear scalar conservation law (NSCL). A time discretization for the NSCL equation based on this principle is considered. An equivalent analytical formulation is shown to lead quite easily to a convergence result, and a third formulation is introduced which can be generalized for the systems of conservation laws. Various numerical schemes are constructed from the proposed time discretization. The first family of schemes is obtained by using a spatial grid and projecting the results of the time discretization. Many known schemes are then recognized (mainly schemes by Osher, Roe, and LeVeque). A second way to discretize leads to a particle scheme without space grid, which is very efficient (at least in the scalar case). Finally, a close relationship between the proposed method and the Boltzmann type schemes is established. 14 references

  19. Evaluating sample allocation and effort in detecting population differentiation for discrete and continuously distributed individuals

    Science.gov (United States)

    Erin L. Landguth; Michael K. Schwartz

    2014-01-01

    One of the most pressing issues in spatial genetics concerns sampling. Traditionally, substructure and gene flow are estimated for individuals sampled within discrete populations. Because many species may be continuously distributed across a landscape without discrete boundaries, understanding sampling issues becomes paramount. Given large-scale, geographically broad...

  20. High-order discrete ordinate transport in non-conforming 2D Cartesian meshes

    International Nuclear Information System (INIS)

    Gastaldo, L.; Le Tellier, R.; Suteau, C.; Fournier, D.; Ruggieri, J. M.

    2009-01-01

    We present in this paper a numerical scheme for solving the time-independent first-order form of the Boltzmann equation in non-conforming 2D Cartesian meshes. The flux solution technique used here is the discrete ordinate method and the spatial discretization is based on discontinuous finite elements. In order to have p-refinement capability, we have chosen a hierarchical polynomial basis based on Legendre polynomials. The h-refinement capability is also available and the element interface treatment has been simplified by the use of special functions decomposed over the mesh entities of an element. The comparison to a classical S N method using the Diamond Differencing scheme as spatial approximation confirms the good behaviour of the method. (authors)

  1. Discrete variable theory of triatomic photodissociation

    International Nuclear Information System (INIS)

    Heather, R.W.; Light, J.C.

    1983-01-01

    The coupled equations describing the photodissociation process are expressed in the discrete variable representation (DVR) in which the coupled equations are labeled by quadrature points rather than by internal basis functions. A large reduction in the dimensionality of the coupled equations can be realized since the spatially localized bound state nuclear wave function vanishes at most of the quadrature points, making only certain orientations of the fragments important in the region of strong interaction (small separation). The discrete variable theory of photodissociation is applied to the model dissociation of bent HCN in which the CN fragment is treated as a rigid rotor. The truncated DVR rotational distributions are compared with the exact close coupled rotational distributions, and excellent agreement with greatly reduced dimensionality of the equations is found

  2. Development and comparison of different spatial numerical schemes for the radiative transfer equation resolution using three-dimensional unstructured meshes

    International Nuclear Information System (INIS)

    Capdevila, R.; Perez-Segarra, C.D.; Oliva, A.

    2010-01-01

    In the present work four different spatial numerical schemes have been developed with the aim of reducing the false-scattering of the numerical solutions obtained with the discrete ordinates (DOM) and the finite volume (FVM) methods. These schemes have been designed specifically for unstructured meshes by means of the extrapolation of nodal values of intensity on the studied radiative direction. The schemes have been tested and compared in several 3D benchmark test cases using both structured orthogonal and unstructured grids.

  3. Asymmetry in Nature-Discrete Symmetries in Particle Physics and ...

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 7; Issue 3. Asymmetry in Nature - Discrete Symmetries in Particle Physics and their Violation - Background and ... Theoretical Studies, Indian Institute of Science, Bangalore 560012, India. Indian Institute of Technology, Chennai. Aligarh Muslim University.

  4. Discrete-State Stochastic Models of Calcium-Regulated Calcium Influx and Subspace Dynamics Are Not Well-Approximated by ODEs That Neglect Concentration Fluctuations

    Science.gov (United States)

    Weinberg, Seth H.; Smith, Gregory D.

    2012-01-01

    Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough (e.g., 10−17 liters) that local signaling may involve 1–100 calcium ions. Is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of fluctuating subspace calcium concentration (a result that accounts for the small subspace volume) with the corresponding deterministic model (an approximation that assumes large system size). When subspace calcium did not regulate calcium influx, the deterministic and stochastic descriptions agreed. However, when calcium binding altered channel activity in the model, the continuous deterministic description often deviated significantly from the discrete stochastic model, unless the subspace volume is unrealistically large and/or the kinetics of the calcium binding are sufficiently fast. This principle was also demonstrated using a physiologically realistic model of calmodulin regulation of L-type calcium channels introduced by Yue and coworkers. PMID:23509597

  5. An efficient fully-implicit multislope MUSCL method for multiphase flow with gravity in discrete fractured media

    Science.gov (United States)

    Jiang, Jiamin; Younis, Rami M.

    2017-06-01

    The first-order methods commonly employed in reservoir simulation for computing the convective fluxes introduce excessive numerical diffusion leading to severe smoothing of displacement fronts. We present a fully-implicit cell-centered finite-volume (CCFV) framework that can achieve second-order spatial accuracy on smooth solutions, while at the same time maintain robustness and nonlinear convergence performance. A novel multislope MUSCL method is proposed to construct the required values at edge centroids in a straightforward and effective way by taking advantage of the triangular mesh geometry. In contrast to the monoslope methods in which a unique limited gradient is used, the multislope concept constructs specific scalar slopes for the interpolations on each edge of a given element. Through the edge centroids, the numerical diffusion caused by mesh skewness is reduced, and optimal second order accuracy can be achieved. Moreover, an improved smooth flux-limiter is introduced to ensure monotonicity on non-uniform meshes. The flux-limiter provides high accuracy without degrading nonlinear convergence performance. The CCFV framework is adapted to accommodate a lower-dimensional discrete fracture-matrix (DFM) model. Several numerical tests with discrete fractured system are carried out to demonstrate the efficiency and robustness of the numerical model.

  6. New diffusion-sythetic acceleration methods for the SN equations with corner balance spatial differencing

    International Nuclear Information System (INIS)

    Wareing, T.A.

    1993-01-01

    New methods are presented for diffusion-synthetic accelerating the S N equations in slab and x-y geometries with the corner balance spatial differencing scheme. With the standard diffusion-synthetic acceleration method, the discretized diffusion problem is derived from the discretized S N problem to insure stability through consistent differencing. The major difference between our new methods and standard diffusion-synthetic acceleration is that the discretized diffusion problem is derived from a discretization of the P 1 equations, independently of the discretized S N problem. We present theoretical and numerical results to show that these new methods are unconditionally efficient in slab and x-y geometries with rectangular spatial meshes and isotropic scattering. (orig.)

  7. Discrete element modeling of deformable particles in YADE

    Directory of Open Access Journals (Sweden)

    Martin Haustein

    2017-01-01

    Full Text Available In this paper we describe the open-source discrete element framework YADE and the implementation of a new deformation engine. YADE is a highly expandable software package that allows the simulation of current industrial problems in the field of granular materials using particle-based numerical methods. The description of the compaction of powders and granular material like metal pellets is now possible with a pure and simple discrete element approach in a modern DEM-framework. The deformation is realized by expanding the radius of the spherical particles, depending on their overlap, so that the volume of the material is kept constant.

  8. Fractured reservoir discrete feature network technologies. Final report, March 7, 1996 to September 30, 1998

    Energy Technology Data Exchange (ETDEWEB)

    Dershowitz, William S.; Einstein, Herbert H.; LaPoint, Paul R.; Eiben, Thorsten; Wadleigh, Eugene; Ivanova, Violeta

    1998-12-01

    This report summarizes research conducted for the Fractured Reservoir Discrete Feature Network Technologies Project. The five areas studied are development of hierarchical fracture models; fractured reservoir compartmentalization, block size, and tributary volume analysis; development and demonstration of fractured reservoir discrete feature data analysis tools; development of tools for data integration and reservoir simulation through application of discrete feature network technologies for tertiary oil production; quantitative evaluation of the economic value of this analysis approach.

  9. Parallel, explicit, and PWTD-enhanced time domain volume integral equation solver

    KAUST Repository

    Liu, Yang

    2013-07-01

    Time domain volume integral equations (TDVIEs) are useful for analyzing transient scattering from inhomogeneous dielectric objects in applications as varied as photonics, optoelectronics, and bioelectromagnetics. TDVIEs typically are solved by implicit marching-on-in-time (MOT) schemes [N. T. Gres et al., Radio Sci., 36, 379-386, 2001], requiring the solution of a system of equations at each and every time step. To reduce the computational cost associated with such schemes, [A. Al-Jarro et al., IEEE Trans. Antennas Propagat., 60, 5203-5215, 2012] introduced an explicit MOT-TDVIE method that uses a predictor-corrector technique to stably update field values throughout the scatterer. By leveraging memory-efficient nodal spatial discretization and scalable parallelization schemes [A. Al-Jarro et al., in 28th Int. Rev. Progress Appl. Computat. Electromagn., 2012], this solver has been successfully applied to the analysis of scattering phenomena involving 0.5 million spatial unknowns. © 2013 IEEE.

  10. Emissivity of discretized diffusion problems

    International Nuclear Information System (INIS)

    Densmore, Jeffery D.; Davidson, Gregory; Carrington, David B.

    2006-01-01

    The numerical modeling of radiative transfer by the diffusion approximation can produce artificially damped radiation propagation if spatial cells are too optically thick. In this paper, we investigate this nonphysical behavior at external problem boundaries by examining the emissivity of the discretized diffusion approximation. We demonstrate that the standard cell-centered discretization produces an emissivity that is too low for optically thick cells, a situation that leads to the lack of radiation propagation. We then present a modified boundary condition that yields an accurate emissivity regardless of cell size. This modified boundary condition can be used with a deterministic calculation or as part of a hybrid transport-diffusion method for increasing the efficiency of Monte Carlo simulations. We also discuss the range of applicability, as a function of cell size and material properties, when this modified boundary condition is employed in a hybrid technique. With a set of numerical calculations, we demonstrate the accuracy and usefulness of this modified boundary condition

  11. Final Report for DOE grant DE-FG02-07ER64432 "New Grid and Discretization Technologies for Ocean and Ice Simulations"

    Energy Technology Data Exchange (ETDEWEB)

    Gunzburger, Max

    2013-03-12

    The work reported is in pursuit of these goals: high-quality unstructured, non-uniform Voronoi and Delaunay grids; improved finite element and finite volume discretization schemes; and improved finite element and finite volume discretization schemes. These are sought for application to spherical and three-dimensional applications suitable for ocean, atmosphere, ice-sheet, and other climate modeling applications.

  12. A fully discrete energy stable scheme for a phase filed moving contact line model with variable densities and viscosities

    KAUST Repository

    Zhu, Guangpu; Chen, Huangxin; Sun, Shuyu; Yao, Jun

    2018-01-01

    In this paper, a fully discrete scheme which considers temporal and spatial discretizations is presented for the coupled Cahn-Hilliard equation in conserved form with the dynamic contact line condition and the Navier-Stokes equation

  13. Coding Model and Mapping Method of Spherical Diamond Discrete Grids Based on Icosahedron

    Directory of Open Access Journals (Sweden)

    LIN Bingxian

    2016-12-01

    Full Text Available Discrete Global Grid(DGG provides a fundamental environment for global-scale spatial data's organization and management. DGG's encoding scheme, which blocks coordinate transformation between different coordination reference frames and reduces the complexity of spatial analysis, contributes a lot to the multi-scale expression and unified modeling of spatial data. Compared with other kinds of DGGs, Diamond Discrete Global Grid(DDGG based on icosahedron is beneficial to the spherical spatial data's integration and expression for much better geometric properties. However, its structure seems more complicated than DDGG on octahedron due to its initial diamond's edges cannot fit meridian and parallel. New challenges are posed when it comes to the construction of hierarchical encoding system and mapping relationship with geographic coordinates. On this issue, this paper presents a DDGG's coding system based on the Hilbert curve and designs conversion methods between codes and geographical coordinates. The study results indicate that this encoding system based on the Hilbert curve can express space scale and location information implicitly with the similarity between DDG and planar grid put into practice, and balances efficiency and accuracy of conversion between codes and geographical coordinates in order to support global massive spatial data's modeling, integrated management and all kinds of spatial analysis.

  14. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2011-01-01

    The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

  15. Continuous time modelling of dynamical spatial lattice data observed at sparsely distributed times

    DEFF Research Database (Denmark)

    Rasmussen, Jakob Gulddahl; Møller, Jesper

    2007-01-01

    Summary. We consider statistical and computational aspects of simulation-based Bayesian inference for a spatial-temporal model based on a multivariate point process which is only observed at sparsely distributed times. The point processes are indexed by the sites of a spatial lattice......, and they exhibit spatial interaction. For specificity we consider a particular dynamical spatial lattice data set which has previously been analysed by a discrete time model involving unknown normalizing constants. We discuss the advantages and disadvantages of using continuous time processes compared...... with discrete time processes in the setting of the present paper as well as other spatial-temporal situations....

  16. A high-order method for the integration of the Galerkin semi-discretized nuclear reactor kinetics equations

    International Nuclear Information System (INIS)

    Vargas, L.

    1988-01-01

    The numerical approximate solution of the space-time nuclear reactor kinetics equation is investigated using a finite-element discretization of the space variable and a high order integration scheme for the resulting semi-discretized parabolic equation. The Galerkin method with spatial piecewise polynomial Lagrange basis functions are used to obtained a continuous time semi-discretized form of the space-time reactor kinetics equation. A temporal discretization is then carried out with a numerical scheme based on the Iterated Defect Correction (IDC) method using piecewise quadratic polynomials or exponential functions. The kinetics equations are thus solved with in a general finite element framework with respect to space as well as time variables in which the order of convergence of the spatial and temporal discretizations is consistently high. A computer code GALFEM/IDC is developed, to implement the numerical schemes described above. This issued to solve a one space dimensional benchmark problem. The results of the numerical experiments confirm the theoretical arguments and show that the convergence is very fast and the overall procedure is quite efficient. This is due to the good asymptotic properties of the numerical scheme which is of third order in the time interval

  17. Baecklund transformations for discrete Painleve equations: Discrete PII-PV

    International Nuclear Information System (INIS)

    Sakka, A.; Mugan, U.

    2006-01-01

    Transformation properties of discrete Painleve equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painleve equations, discrete P II -P V , with different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the classical special functions of discrete Painleve equations can also be obtained from these transformations

  18. On the mixed discretization of the time domain magnetic field integral equation

    KAUST Repository

    Ulku, Huseyin Arda; Bogaert, Ignace; Cools, Kristof; Andriulli, Francesco P.; Bagci, Hakan

    2012-01-01

    Time domain magnetic field integral equation (MFIE) is discretized using divergence-conforming Rao-Wilton-Glisson (RWG) and curl-conforming Buffa-Christiansen (BC) functions as spatial basis and testing functions, respectively. The resulting mixed

  19. Relativity and the question of discretization in astronomy

    CERN Document Server

    Edelen, Dominic G B

    1970-01-01

    Theoretical researches in general relativity and observational data from galactic astronomy combine in this volume in contributions to one of the oldest questions of natural philosophy: Is the structure of the physical world more adequately described by a continuous or a discrete mode of representation? Since the days of the Pythagoreans, this question has surfaced from time to time in various guises in science as well as in philosophy. One of the most bitterly contested and illuminating controversies between the continuous and the discrete viewpoints is to be found in the wave versus corpuscular description of optical phenom­ enae. This controversy was not resolved to the satisfaction of most of its protaganists until the development of the quantum theory. However, several obscurities that still becloud the question suggest that some deeper formulation may be necessary before more satisfactory answers can be given 1. The firm establishment of the validity of quantized structure and discrete energy distribut...

  20. Mass, momentum and energy conserving (MaMEC) discretizations on general grids for the compressible Euler and shallow water equations

    International Nuclear Information System (INIS)

    Hof, Bas van’t; Veldman, Arthur E.P.

    2012-01-01

    The paper explains a method by which discretizations of the continuity and momentum equations can be designed, such that they can be combined with an equation of state into a discrete energy equation. The resulting ‘MaMEC’ discretizations conserve mass, momentum as well as energy, although no explicit conservation law for the total energy is present. Essential ingredients are (i) discrete convection that leaves the discrete energy invariant, and (ii) discrete consistency between the thermodynamic terms. Of particular relevance is the way in which finite volume fluxes are related to nodal values. The method is an extension of existing methods based on skew-symmetry of discrete operators, because it allows arbitrary equations of state and a larger class of grids than earlier methods. The method is first illustrated with a one-dimensional example on a highly stretched staggered grid, in which the MaMEC method calculates qualitatively correct results and a non-skew-symmetric finite volume method becomes unstable. A further example is a two-dimensional shallow water calculation on a rectilinear grid as well as on an unstructured grid. The conservation of mass, momentum and energy is checked, and losses are found negligible up to machine accuracy.

  1. First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

    Science.gov (United States)

    Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

    2018-01-01

    A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development

  2. First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

    International Nuclear Information System (INIS)

    Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

    2016-01-01

    A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development

  3. First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

    Energy Technology Data Exchange (ETDEWEB)

    Mishchenko, Michael I., E-mail: michael.i.mishchenko@nasa.gov [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Dlugach, Janna M. [Main Astronomical Observatory of the National Academy of Sciences of Ukraine, 27 Zabolotny Str., 03680, Kyiv (Ukraine); Yurkin, Maxim A. [Voevodsky Institute of Chemical Kinetics and Combustion, SB RAS, Institutskaya str. 3, 630090 Novosibirsk (Russian Federation); Novosibirsk State University, Pirogova 2, 630090 Novosibirsk (Russian Federation); Bi, Lei [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Cairns, Brian [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Liu, Li [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Columbia University, 2880 Broadway, New York, NY 10025 (United States); Panetta, R. Lee [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Travis, Larry D. [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Yang, Ping [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Zakharova, Nadezhda T. [Trinnovim LLC, 2880 Broadway, New York, NY 10025 (United States)

    2016-05-16

    A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development

  4. First-Principles Modeling Of Electromagnetic Scattering By Discrete and Discretely Heterogeneous Random Media

    Science.gov (United States)

    Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

    2016-01-01

    A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell- Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of

  5. Spatially-protected Topology and Group Cohomology in Band Insulators

    Science.gov (United States)

    Alexandradinata, A.

    This thesis investigates band topologies which rely fundamentally on spatial symmetries. A basic geometric property that distinguishes spatial symmetry regards their transformation of the spatial origin. Point groups consist of spatial transformations that preserve the spatial origin, while un-split extensions of the point groups by spatial translations are referred to as nonsymmorphic space groups. The first part of the thesis addresses topological phases with discretely-robust surface properties: we introduce theories for the Cnv point groups, as well as certain nonsymmorphic groups that involve glide reflections. These band insulators admit a powerful characterization through the geometry of quasimomentum space; parallel transport in this space is represented by the Wilson loop. The non-symmorphic topology we study is naturally described by a further extension of the nonsymmorphic space group by quasimomentum translations (the Wilson loop), thus placing real and quasimomentum space on equal footing -- here, we introduce the language of group cohomology into the theory of band insulators. The second part of the thesis addresses topological phases without surface properties -- their only known physical consequences are discrete signatures in parallel transport. We provide two such case studies with spatial-inversion and discrete-rotational symmetries respectively. One lesson learned here regards the choice of parameter loops in which we carry out transport -- the loop must be chosen to exploit the symmetry that protects the topology. While straight loops are popular for their connection with the geometric theory of polarization, we show that bent loops also have utility in topological band theory.

  6. High-order solution methods for grey discrete ordinates thermal radiative transfer

    Energy Technology Data Exchange (ETDEWEB)

    Maginot, Peter G., E-mail: maginot1@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States); Morel, Jim E., E-mail: morel@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States)

    2016-12-15

    This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.

  7. Parallel Jacobian-free Newton Krylov solution of the discrete ordinates method with flux limiters for 3D radiative transfer

    International Nuclear Information System (INIS)

    Godoy, William F.; Liu Xu

    2012-01-01

    The present study introduces a parallel Jacobian-free Newton Krylov (JFNK) general minimal residual (GMRES) solution for the discretized radiative transfer equation (RTE) in 3D, absorbing, emitting and scattering media. For the angular and spatial discretization of the RTE, the discrete ordinates method (DOM) and the finite volume method (FVM) including flux limiters are employed, respectively. Instead of forming and storing a large Jacobian matrix, JFNK methods allow for large memory savings as the required Jacobian-vector products are rather approximated by semiexact and numerical formulations, for which convergence and computational times are presented. Parallelization of the GMRES solution is introduced in a combined memory-shared/memory-distributed formulation that takes advantage of the fact that only large vector arrays remain in the JFNK process. Results are presented for 3D test cases including a simple homogeneous, isotropic medium and a more complex non-homogeneous, non-isothermal, absorbing–emitting and anisotropic scattering medium with collimated intensities. Additionally, convergence and stability of Gram–Schmidt and Householder orthogonalizations for the Arnoldi process in the parallel GMRES algorithms are discussed and analyzed. Overall, the introduction of JFNK methods results in a parallel, yet scalable to the tested 2048 processors, and memory affordable solution to 3D radiative transfer problems without compromising the accuracy and convergence of a Newton-like solution.

  8. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, Teresa S. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: baileyte@tamu.edu; Adams, Marvin L. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: mladams@tamu.edu; Yang, Brian [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Zika, Michael R. [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States)], E-mail: zika@llnl.gov

    2008-04-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.

  9. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    International Nuclear Information System (INIS)

    Bailey, Teresa S.; Adams, Marvin L.; Yang, Brian; Zika, Michael R.

    2008-01-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids

  10. Discrete Curvatures and Discrete Minimal Surfaces

    KAUST Repository

    Sun, Xiang

    2012-01-01

    This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads

  11. Domain of composition and finite volume schemes on non-matching grids; Decomposition de domaine et schemas volumes finis sur maillages non-conformes

    Energy Technology Data Exchange (ETDEWEB)

    Saas, L.

    2004-05-01

    This Thesis deals with sedimentary basin modeling whose goal is the prediction through geological times of the localizations and appraisal of hydrocarbons quantities present in the ground. Due to the natural and evolutionary decomposition of the sedimentary basin in blocks and stratigraphic layers, domain decomposition methods are requested to simulate flows of waters and of hydrocarbons in the ground. Conservations laws are used to model the flows in the ground and form coupled partial differential equations which must be discretized by finite volume method. In this report we carry out a study on finite volume methods on non-matching grids solved by domain decomposition methods. We describe a family of finite volume schemes on non-matching grids and we prove that the associated global discretized problem is well posed. Then we give an error estimate. We give two examples of finite volume schemes on non matching grids and the corresponding theoretical results (Constant scheme and Linear scheme). Then we present the resolution of the global discretized problem by a domain decomposition method using arbitrary interface conditions (for example Robin conditions). Finally we give numerical results which validate the theoretical results and study the use of finite volume methods on non-matching grids for basin modeling. (author)

  12. Laser-induced fluorescence imaging of subsurface tissue structures with a volume holographic spatial-spectral imaging system.

    Science.gov (United States)

    Luo, Yuan; Gelsinger-Austin, Paul J; Watson, Jonathan M; Barbastathis, George; Barton, Jennifer K; Kostuk, Raymond K

    2008-09-15

    A three-dimensional imaging system incorporating multiplexed holographic gratings to visualize fluorescence tissue structures is presented. Holographic gratings formed in volume recording materials such as a phenanthrenquinone poly(methyl methacrylate) photopolymer have narrowband angular and spectral transmittance filtering properties that enable obtaining spatial-spectral information within an object. We demonstrate this imaging system's ability to obtain multiple depth-resolved fluorescence images simultaneously.

  13. Regional volumes and spatial volumetric distribution of gray matter in the gender dysphoric brain.

    Science.gov (United States)

    Hoekzema, Elseline; Schagen, Sebastian E E; Kreukels, Baudewijntje P C; Veltman, Dick J; Cohen-Kettenis, Peggy T; Delemarre-van de Waal, Henriette; Bakker, Julie

    2015-05-01

    The sexual differentiation of the brain is primarily driven by gonadal hormones during fetal development. Leading theories on the etiology of gender dysphoria (GD) involve deviations herein. To examine whether there are signs of a sex-atypical brain development in GD, we quantified regional neural gray matter (GM) volumes in 55 female-to-male and 38 male-to-female adolescents, 44 boys and 52 girls without GD and applied both univariate and multivariate analyses. In girls, more GM volume was observed in the left superior medial frontal cortex, while boys had more volume in the bilateral superior posterior hemispheres of the cerebellum and the hypothalamus. Regarding the GD groups, at whole-brain level they differed only from individuals sharing their gender identity but not from their natal sex. Accordingly, using multivariate pattern recognition analyses, the GD groups could more accurately be automatically discriminated from individuals sharing their gender identity than those sharing their natal sex based on spatially distributed GM patterns. However, region of interest analyses indicated less GM volume in the right cerebellum and more volume in the medial frontal cortex in female-to-males in comparison to girls without GD, while male-to-females had less volume in the bilateral cerebellum and hypothalamus than natal boys. Deviations from the natal sex within sexually dimorphic structures were also observed in the untreated subsamples. Our findings thus indicate that GM distribution and regional volumes in GD adolescents are largely in accordance with their respective natal sex. However, there are subtle deviations from the natal sex in sexually dimorphic structures, which can represent signs of a partial sex-atypical differentiation of the brain. Copyright © 2015 Elsevier Ltd. All rights reserved.

  14. Hybrid finite volume/ finite element method for radiative heat transfer in graded index media

    Science.gov (United States)

    Zhang, L.; Zhao, J. M.; Liu, L. H.; Wang, S. Y.

    2012-09-01

    The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J. Coelho, J. Quant. Spectrosc. Radiat. Transf., vol. 93, pp. 89-101, 2005) is extended to solve the radiative heat transfer in two-dimensional absorbing-emitting-scattering graded index media, in which the spatial discretization is carried out using a FVM, while the angular discretization is by a FEM. The FEM angular discretization is demonstrated to be preferable in dealing with the redistribution terms in the GRTE. Two stiff matrix assembly schemes of the angular FEM discretization, namely, the traditional assembly approach and a new spherical assembly approach (assembly on the unit sphere of the solid angular space), are discussed. The spherical assembly scheme is demonstrated to give better results than the traditional assembly approach. The predicted heat flux distributions and temperature distributions in radiative equilibrium are determined by the proposed method and compared with the results available in other references. The proposed hybrid FVM/FEM method can predict the radiative heat transfer in absorbing-emitting-scattering graded index medium with good accuracy.

  15. Hybrid finite volume/ finite element method for radiative heat transfer in graded index media

    International Nuclear Information System (INIS)

    Zhang, L.; Zhao, J.M.; Liu, L.H.; Wang, S.Y.

    2012-01-01

    The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J. Coelho, J. Quant. Spectrosc. Radiat. Transf., vol. 93, pp. 89-101, 2005) is extended to solve the radiative heat transfer in two-dimensional absorbing-emitting-scattering graded index media, in which the spatial discretization is carried out using a FVM, while the angular discretization is by a FEM. The FEM angular discretization is demonstrated to be preferable in dealing with the redistribution terms in the GRTE. Two stiff matrix assembly schemes of the angular FEM discretization, namely, the traditional assembly approach and a new spherical assembly approach (assembly on the unit sphere of the solid angular space), are discussed. The spherical assembly scheme is demonstrated to give better results than the traditional assembly approach. The predicted heat flux distributions and temperature distributions in radiative equilibrium are determined by the proposed method and compared with the results available in other references. The proposed hybrid FVM/FEM method can predict the radiative heat transfer in absorbing-emitting-scattering graded index medium with good accuracy.

  16. Higher-order Spatial Accuracy in Diffeomorphic Image Registration

    DEFF Research Database (Denmark)

    Jacobs, Henry O.; Sommer, Stefan

    -jets. We show that the solutions convergence to optimal solutions of the original cost functional as the number of particles increases with a convergence rate of O(hd+k) where h is a resolution parameter. The effect of this approach over traditional particle methods is illustrated on synthetic examples......We discretize a cost functional for image registration problems by deriving Taylor expansions for the matching term. Minima of the discretized cost functionals can be computed with no spatial discretization error, and the optimal solutions are equivalent to minimal energy curves in the space of kk...

  17. A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids

    Directory of Open Access Journals (Sweden)

    J. Thuburn

    2014-05-01

    Full Text Available A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank–Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV. The algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

  18. Arbitrary-Lagrangian-Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

    Science.gov (United States)

    Boscheri, Walter; Dumbser, Michael

    2017-10-01

    We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total

  19. The role of the Stripa phase 3 project in the development of practical discrete fracture modelling technology

    International Nuclear Information System (INIS)

    Dershowitz, W.S.

    1994-01-01

    The Stripa project has played a major role in developing discrete fracture analysis from a theoretical research topic to a practical repository evaluation tool. The Site Characterization and Validation (SCV) program positively answered questions regarding: (1) the validation of discrete fracture models, (2) the feasibility of collecting data for discrete fracture models, (3) the ability of discrete fracture models to simulate flow in a rock volume of approximately 10 6 cubic meters using modest computing resources, and (4) the ability to model transport in discrete fractures. The SCV program also made progress on such continuing issues as the importance of in-plane fracture heterogeneity and coupled effects. (author). 16 refs., 2 tabs., 6 figs

  20. In search of fundamental discreteness in (2 + 1)-dimensional quantum gravity

    NARCIS (Netherlands)

    Budd, T.G.; Loll, R.

    2009-01-01

    Inspired by previous work in (2 + 1)-dimensional quantum gravity, which found evidence for a discretization of time in the quantum theory, we reexamine the issue for the case of pure Lorentzian gravity with vanishing cosmological constant and spatially compact universes of genus g ≥ 2. Taking the

  1. A method for partial volume correction of PET-imaged tumor heterogeneity using expectation maximization with a spatially varying point spread function

    International Nuclear Information System (INIS)

    Barbee, David L; Holden, James E; Nickles, Robert J; Jeraj, Robert; Flynn, Ryan T

    2010-01-01

    Tumor heterogeneities observed in positron emission tomography (PET) imaging are frequently compromised by partial volume effects which may affect treatment prognosis, assessment or future implementations such as biologically optimized treatment planning (dose painting). This paper presents a method for partial volume correction of PET-imaged heterogeneous tumors. A point source was scanned on a GE Discovery LS at positions of increasing radii from the scanner's center to obtain the spatially varying point spread function (PSF). PSF images were fit in three dimensions to Gaussian distributions using least squares optimization. Continuous expressions were devised for each Gaussian width as a function of radial distance, allowing for generation of the system PSF at any position in space. A spatially varying partial volume correction (SV-PVC) technique was developed using expectation maximization (EM) and a stopping criterion based on the method's correction matrix generated for each iteration. The SV-PVC was validated using a standard tumor phantom and a tumor heterogeneity phantom and was applied to a heterogeneous patient tumor. SV-PVC results were compared to results obtained from spatially invariant partial volume correction (SINV-PVC), which used directionally uniform three-dimensional kernels. SV-PVC of the standard tumor phantom increased the maximum observed sphere activity by 55 and 40% for 10 and 13 mm diameter spheres, respectively. Tumor heterogeneity phantom results demonstrated that as net changes in the EM correction matrix decreased below 35%, further iterations improved overall quantitative accuracy by less than 1%. SV-PVC of clinically observed tumors frequently exhibited changes of ±30% in regions of heterogeneity. The SV-PVC method implemented spatially varying kernel widths and automatically determined the number of iterations for optimal restoration, parameters which are arbitrarily chosen in SINV-PVC. Comparing SV-PVC to SINV-PVC demonstrated

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

    Science.gov (United States)

    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

  3. An effective FEM-based approach for discrete 3D crack growth

    DEFF Research Database (Denmark)

    Nielsen, Morten Eggert; Lambertsen, Søren Heide; Pedersen, Erik B.

    2015-01-01

    A new geometric approach for discrete crack growth modeling is proposed and implemented in a commercial FEM software. The basic idea is to model the crack growth by removing volumes of material as the crack front advances. Thereby, adaptive meshing techniques, found in commercial software, is wel...

  4. Development and application of the discrete ordinate method in orthogonal curvilinear coordinates; Developpement et application de la methode des ordonnees discretes en coordonnees curvilignes orthogonales

    Energy Technology Data Exchange (ETDEWEB)

    Vaillon, R; Lallemand, M; Lemonnier, D [Ecole Nationale Superieure de Mecanique et d` Aerotechnique (ENSMA), 86 - Poitiers (France)

    1997-12-31

    The method of discrete ordinates, which is more and more widely used in radiant heat transfer studies, is mainly developed in Cartesian, (r,z) and (r,{Theta}) cylindrical, and spherical coordinates. In this study, the approach of this method is performed in orthogonal curvilinear coordinates: determination of the radiant heat transfer equation, treatment of the angular redistribution terms, numerical procedure. Some examples of application are described in 2-D geometry defined in curvilinear coordinates along a curve and at the thermal equilibrium. A comparison is made with the discrete ordinates method in association with the finite-volumes method in non structured mesh. (J.S.) 27 refs.

  5. Development and application of the discrete ordinate method in orthogonal curvilinear coordinates; Developpement et application de la methode des ordonnees discretes en coordonnees curvilignes orthogonales

    Energy Technology Data Exchange (ETDEWEB)

    Vaillon, R.; Lallemand, M.; Lemonnier, D. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France)

    1996-12-31

    The method of discrete ordinates, which is more and more widely used in radiant heat transfer studies, is mainly developed in Cartesian, (r,z) and (r,{Theta}) cylindrical, and spherical coordinates. In this study, the approach of this method is performed in orthogonal curvilinear coordinates: determination of the radiant heat transfer equation, treatment of the angular redistribution terms, numerical procedure. Some examples of application are described in 2-D geometry defined in curvilinear coordinates along a curve and at the thermal equilibrium. A comparison is made with the discrete ordinates method in association with the finite-volumes method in non structured mesh. (J.S.) 27 refs.

  6. Nonlinear wave propagation in discrete and continuous systems

    Science.gov (United States)

    Rothos, V. M.

    2016-09-01

    In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.

  7. Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions

    OpenAIRE

    Cresson, Jacky; Pierret, Frédéric

    2015-01-01

    We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the Hamiltonian setting. Several applications are discussed.

  8. A suspended-particle rosette multi-sampler for discrete biogeochemical sampling in low-particle-density waters

    Energy Technology Data Exchange (ETDEWEB)

    Breier, J. A.; Rauch, C. G.; McCartney, K.; Toner, B. M.; Fakra, S. C.; White, S. N.; German, C. R.

    2010-06-22

    To enable detailed investigations of early stage hydrothermal plume formation and abiotic and biotic plume processes we developed a new oceanographic tool. The Suspended Particulate Rosette sampling system has been designed to collect geochemical and microbial samples from the rising portion of deep-sea hydrothermal plumes. It can be deployed on a remotely operated vehicle for sampling rising plumes, on a wire-deployed water rosette for spatially discrete sampling of non-buoyant hydrothermal plumes, or on a fixed mooring in a hydrothermal vent field for time series sampling. It has performed successfully during both its first mooring deployment at the East Pacific Rise and its first remotely-operated vehicle deployments along the Mid-Atlantic Ridge. It is currently capable of rapidly filtering 24 discrete large-water-volume samples (30-100 L per sample) for suspended particles during a single deployment (e.g. >90 L per sample at 4-7 L per minute through 1 {mu}m pore diameter polycarbonate filters). The Suspended Particulate Rosette sampler has been designed with a long-term goal of seafloor observatory deployments, where it can be used to collect samples in response to tectonic or other events. It is compatible with in situ optical sensors, such as laser Raman or visible reflectance spectroscopy systems, enabling in situ particle analysis immediately after sample collection and before the particles alter or degrade.

  9. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2011-01-01

    ; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

  10. Digital Discretion

    DEFF Research Database (Denmark)

    Busch, Peter Andre; Zinner Henriksen, Helle

    2018-01-01

    discretion is suggested to reduce this footprint by influencing or replacing their discretionary practices using ICT. What is less researched is whether digital discretion can cause changes in public policy outcomes, and under what conditions such changes can occur. Using the concept of public service values......This study reviews 44 peer-reviewed articles on digital discretion published in the period from 1998 to January 2017. Street-level bureaucrats have traditionally had a wide ability to exercise discretion stirring debate since they can add their personal footprint on public policies. Digital......, we suggest that digital discretion can strengthen ethical and democratic values but weaken professional and relational values. Furthermore, we conclude that contextual factors such as considerations made by policy makers on the macro-level and the degree of professionalization of street...

  11. Quantum cosmology based on discrete Feynman paths

    International Nuclear Information System (INIS)

    Chew, Geoffrey F.

    2002-01-01

    Although the rules for interpreting local quantum theory imply discretization of process, Lorentz covariance is usually regarded as precluding time quantization. Nevertheless a time-discretized quantum representation of redshifting spatially-homogeneous universe may be based on discrete-step Feynman paths carrying causal Lorentz-invariant action--paths that not only propagate the wave function but provide a phenomenologically-promising elementary-particle Hilbert-space basis. In a model under development, local path steps are at Planck scale while, at a much larger ''wave-function scale'', global steps separate successive wave-functions. Wave-function spacetime is but a tiny fraction of path spacetime. Electromagnetic and gravitational actions are ''at a distance'' in Wheeler-Feynman sense while strong (color) and weak (isospin) actions, as well as action of particle motion, are ''local'' in a sense paralleling the action of local field theory. ''Nonmaterial'' path segments and ''trivial events'' collaborate to define energy and gravity. Photons coupled to conserved electric charge enjoy privileged model status among elementary fermions and vector bosons. Although real path parameters provide no immediate meaning for ''measurement'', the phase of the complex wave function allows significance for ''information'' accumulated through ''gentle'' electromagnetic events involving charged matter and ''soft'' photons. Through its soft-photon content the wave function is an ''information reservoir''

  12. Discrete excitation of mode pulses using a diode-pumped solid-state digital laser

    CSIR Research Space (South Africa)

    Ngcobo, Sandile

    2016-02-01

    Full Text Available In this paper, we experimentally demonstrate novel method of generating discrete excitation of on-demand Lagaurre-Gaussian (LG) mode pulses, in a diode pumped solid-state digital laser. The digital laser comprises of an intra-cavity spatial light...

  13. Development and analysis of finite volume methods

    International Nuclear Information System (INIS)

    Omnes, P.

    2010-05-01

    This document is a synthesis of a set of works concerning the development and the analysis of finite volume methods used for the numerical approximation of partial differential equations (PDEs) stemming from physics. In the first part, the document deals with co-localized Godunov type schemes for the Maxwell and wave equations, with a study on the loss of precision of this scheme at low Mach number. In the second part, discrete differential operators are built on fairly general, in particular very distorted or nonconforming, bidimensional meshes. These operators are used to approach the solutions of PDEs modelling diffusion, electro and magneto-statics and electromagnetism by the discrete duality finite volume method (DDFV) on staggered meshes. The third part presents the numerical analysis and some a priori as well as a posteriori error estimations for the discretization of the Laplace equation by the DDFV scheme. The last part is devoted to the order of convergence in the L2 norm of the finite volume approximation of the solution of the Laplace equation in one dimension and on meshes with orthogonality properties in two dimensions. Necessary and sufficient conditions, relatively to the mesh geometry and to the regularity of the data, are provided that ensure the second-order convergence of the method. (author)

  14. Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

    2013-01-01

    In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

  15. Periodic, quasiperiodic, and chaotic breathers in two-dimensional discrete β-Fermi—Pasta—Ulam lattice

    International Nuclear Information System (INIS)

    Xu Quan; Tian Qiang

    2013-01-01

    Using numerical method, we investigate whether periodic, quasiperiodic, and chaotic breathers are supported by the two-dimensional discrete Fermi—Pasta—Ulam (FPU) lattice with linear dispersion term. The spatial profile and time evolution of the two-dimensional discrete β-FPU lattice are segregated by the method of separation of variables, and the numerical simulations suggest that the discrete breathers (DBs) are supported by the system. By introducing a periodic interaction into the linear interaction between the atoms, we achieve the coupling of two incommensurate frequencies for a single DB, and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system, too. (condensed matter: structural, mechanical, and thermal properties)

  16. Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

    KAUST Repository

    Mohamed, Mamdouh S.

    2017-05-23

    A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.

  17. Helmholtz Natural Modes: the universal and discrete spatial fabric of electromagnetic wavefields

    International Nuclear Information System (INIS)

    El Gawhary, Omar

    2017-01-01

    The interaction of electromagnetic waves with matter is at the foundation of the way we perceive and explore the world around us. In fact, when a field interacts with an object, signatures on the object’s geometry and physical properties are recorded in the resulting scattered field and are transported away from the object, where they can eventually be detected and processed. An optical field can transport information through its spectral content, its polarization state, and its spatial distribution. Generally speaking, the field’s spatial structure is typically subjected to changes under free-space propagation and any information therein encoded gets reshuffled by the propagation process. We must ascribe to this fundamental reason the fact that spectroscopy was known to the ancient civilizations already, and founded as modern science in the middle of seventeenth century, while to date we do not have an established scientific of field of ‘spatial spectroscopy’ yet. In this work we tackle this issue and we show how any field, whose evolution is dictated by Helmholtz equation, contains a universal and invariant spatial structure. When expressed in the framework of this spatial fabric, the spatial information content carried by any field reveals its invariant nature. This opens the way to novel paradigms in optical digital communications, inverse scattering, materials inspection, nanometrology and quantum optics. (paper)

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

    Science.gov (United States)

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

    2018-01-04

    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

  19. High Statistics Analysis using Anisotropic Clover Lattices: (IV) The Volume Dependence of the Light Hadron Masses

    Energy Technology Data Exchange (ETDEWEB)

    Beane, S R; Detmold, W; Lin, H W; Luu, T C; Orginos, K; Parreno, A; Savage, M J; Torok, A; Walker-Loud, A

    2011-07-01

    The volume dependence of the octet baryon masses and relations among them are explored with Lattice QCD. Calculations are performed with nf = 2 + 1 clover fermion discretization in four lattice volumes, with spatial extent L ? 2.0, 2.5, 3.0 and 4.0 fm, with an anisotropic lattice spacing of b_s ? 0.123 fm in the spatial direction, and b_t = b_s/3.5 in the time direction, and at a pion mass of m_\\pi ? 390 MeV. The typical precision of the ground-state baryon mass determination is volume dependence of the masses, the Gell-Mann Okubo mass-relation, and of other mass combinations. A comparison with the predictions of heavy baryon chiral perturbation theory is performed in both the SU(2)L ? SU(2)R and SU(3)L ? SU(3)R expansions. Predictions of the three-flavor expansion for the hadron masses are found to describe the observed volume dependences reasonably well. Further, the ?N? axial coupling constant is extracted from the volume dependence of the nucleon mass in the two-flavor expansion, with only small modifications in the three-flavor expansion from the inclusion of kaons and eta's. At a given value of m?L, the finite-volume contributions to the nucleon mass are predicted to be significantly smaller at m_\\pi ? 140 MeV than at m_\\pi ? 390 MeV due to a coefficient that scales as ? m_\\pi^3. This is relevant for the design of future ensembles of lattice gauge-field configurations. Finally, the volume dependence of the pion and kaon masses are analyzed with two-flavor and three-flavor chiral perturbation theory.

  20. Compatible discrete operator schemes on polyhedral meshes for elliptic and Stokes equations

    International Nuclear Information System (INIS)

    Bonelle, Jerome

    2014-01-01

    This thesis presents a new class of spatial discretization schemes on polyhedral meshes, called Compatible Discrete Operator (CDO) schemes and their application to elliptic and Stokes equations In CDO schemes, preserving the structural properties of the continuous equations is the leading principle to design the discrete operators. De Rham maps define the degrees of freedom according to the physical nature of fields to discretize. CDO schemes operate a clear separation between topological relations (balance equations) and constitutive relations (closure laws). Topological relations are related to discrete differential operators, and constitutive relations to discrete Hodge operators. A feature of CDO schemes is the explicit use of a second mesh, called dual mesh, to build the discrete Hodge operator. Two families of CDO schemes are considered: vertex-based schemes where the potential is located at (primal) mesh vertices, and cell-based schemes where the potential is located at dual mesh vertices (dual vertices being in one-to-one correspondence with primal cells). The CDO schemes related to these two families are presented and their convergence is analyzed. A first analysis hinges on an algebraic definition of the discrete Hodge operator and allows one to identify three key properties: symmetry, stability, and P0-consistency. A second analysis hinges on a definition of the discrete Hodge operator using reconstruction operators, and the requirements on these reconstruction operators are identified. In addition, CDO schemes provide a unified vision on a broad class of schemes proposed in the literature (finite element, finite element, mimetic schemes... ). Finally, the reliability and the efficiency of CDO schemes are assessed on various test cases and several polyhedral meshes. (author)

  1. Spiral waves are stable in discrete element models of two-dimensional homogeneous excitable media

    Science.gov (United States)

    Feldman, A. B.; Chernyak, Y. B.; Cohen, R. J.

    1998-01-01

    The spontaneous breakup of a single spiral wave of excitation into a turbulent wave pattern has been observed in both discrete element models and continuous reaction-diffusion models of spatially homogeneous 2D excitable media. These results have attracted considerable interest, since spiral breakup is thought to be an important mechanism of transition from the heart rhythm disturbance ventricular tachycardia to the fatal arrhythmia ventricular fibrillation. It is not known whether this process can occur in the absence of disease-induced spatial heterogeneity of the electrical properties of the ventricular tissue. Candidate mechanisms for spiral breakup in uniform 2D media have emerged, but the physical validity of the mechanisms and their applicability to myocardium require further scrutiny. In this letter, we examine the computer simulation results obtained in two discrete element models and show that the instability of each spiral is an artifact resulting from an unphysical dependence of wave speed on wave front curvature in the medium. We conclude that spiral breakup does not occur in these two models at the specified parameter values and that great care must be exercised in the representation of a continuous excitable medium via discrete elements.

  2. ML-Space: Hybrid Spatial Gillespie and Particle Simulation of Multi-Level Rule-Based Models in Cell Biology.

    Science.gov (United States)

    Bittig, Arne T; Uhrmacher, Adelinde M

    2017-01-01

    Spatio-temporal dynamics of cellular processes can be simulated at different levels of detail, from (deterministic) partial differential equations via the spatial Stochastic Simulation algorithm to tracking Brownian trajectories of individual particles. We present a spatial simulation approach for multi-level rule-based models, which includes dynamically hierarchically nested cellular compartments and entities. Our approach ML-Space combines discrete compartmental dynamics, stochastic spatial approaches in discrete space, and particles moving in continuous space. The rule-based specification language of ML-Space supports concise and compact descriptions of models and to adapt the spatial resolution of models easily.

  3. Asynchronous discrete event schemes for PDEs

    Science.gov (United States)

    Stone, D.; Geiger, S.; Lord, G. J.

    2017-08-01

    A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations is introduced, based on the principle of allowing quanta of mass to pass through faces of a (regular, structured) Cartesian finite volume grid. The timescales of these events are linked to the flux on the face. The resulting schemes are self-adaptive, and local in both time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate reference solutions where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased, and we outline a framework for analysis.

  4. Adaptive discrete-ordinates algorithms and strategies

    International Nuclear Information System (INIS)

    Stone, J.C.; Adams, M.L.

    2005-01-01

    We present our latest algorithms and strategies for adaptively refined discrete-ordinates quadrature sets. In our basic strategy, which we apply here in two-dimensional Cartesian geometry, the spatial domain is divided into regions. Each region has its own quadrature set, which is adapted to the region's angular flux. Our algorithms add a 'test' direction to the quadrature set if the angular flux calculated at that direction differs by more than a user-specified tolerance from the angular flux interpolated from other directions. Different algorithms have different prescriptions for the method of interpolation and/or choice of test directions and/or prescriptions for quadrature weights. We discuss three different algorithms of different interpolation orders. We demonstrate through numerical results that each algorithm is capable of generating solutions with negligible angular discretization error. This includes elimination of ray effects. We demonstrate that all of our algorithms achieve a given level of error with far fewer unknowns than does a standard quadrature set applied to an entire problem. To address a potential issue with other algorithms, we present one algorithm that retains exact integration of high-order spherical-harmonics functions, no matter how much local refinement takes place. To address another potential issue, we demonstrate that all of our methods conserve partial currents across interfaces where quadrature sets change. We conclude that our approach is extremely promising for solving the long-standing problem of angular discretization error in multidimensional transport problems. (authors)

  5. Switching between bistable states in a discrete nonlinear model with long-range dispersion

    DEFF Research Database (Denmark)

    Johansson, Magnus; Gaididei, Yuri B.; Christiansen, Peter Leth

    1998-01-01

    In the framework of a discrete nonlinear Schrodinger equation with long-range dispersion, we propose a general mechanism for obtaining a controlled switching between bistable localized excitations. We show that the application of a spatially symmetric kick leads to the excitation of an internal...

  6. Towards models of strategic spatial choice behaviour: theory and application issues

    NARCIS (Netherlands)

    Han, Q.; Timmermans, H.J.P.

    2005-01-01

    Models of spatial choice behaviour have been around in urban planning for decades to assess the feasibility of planning actions or to predict external (competition) effects on existing destinations. The well known spatial interaction models of the 1970s have gradually been replaced by discrete

  7. Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

    Science.gov (United States)

    Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

    2015-05-01

    We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

  8. A necessary condition for dispersal driven growth of populations with discrete patch dynamics.

    Science.gov (United States)

    Guiver, Chris; Packman, David; Townley, Stuart

    2017-07-07

    We revisit the question of when can dispersal-induced coupling between discrete sink populations cause overall population growth? Such a phenomenon is called dispersal driven growth and provides a simple explanation of how dispersal can allow populations to persist across discrete, spatially heterogeneous, environments even when individual patches are adverse or unfavourable. For two classes of mathematical models, one linear and one non-linear, we provide necessary conditions for dispersal driven growth in terms of the non-existence of a common linear Lyapunov function, which we describe. Our approach draws heavily upon the underlying positive dynamical systems structure. Our results apply to both discrete- and continuous-time models. The theory is illustrated with examples and both biological and mathematical conclusions are drawn. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

  9. Discrete kinematic modeling of the 3-D deformation of sedimentary basins; Modelisation cinematique discrete de la deformation 3D des bassins sedimentaires

    Energy Technology Data Exchange (ETDEWEB)

    Cornu, T.

    2001-01-01

    The present work deals with three-dimensional deformation of sedimentary basins. The main goal of the work was to propose new ways to study tectonic deformation and to insert it into basin-modeling environment for hydrocarbon migration applications. To handle the complexity of the deformation, the model uses kinematic laws, a discrete approach, and the construction of a code that allows the greatest diversity in the deformation mechanisms we can take into account. The 3-D-volume deformation is obtained through the calculation of the behavior of the neutral surface of each basin layer. The main idea is to deform the neutral surface of each layer with the help of geometrical laws and to use the result to rebuild the volume deformation of the basin. The constitutive algorithm includes three characteristic features. The first one deals with the mathematical operator we use to describe the flexural-slip mechanism which is a combination of the translation of the neutral surface nodes and the rotation of the vertical edges attached to these nodes. This performs the reversibility that was required for the basin modeling. The second one is about. the use of a discrete approach, which gives a better description of the global deformation and offers to locally control volume evolutions. The knowledge of volume variations can become a powerful tool in structural geology analysis and the perfect complement for a field study. The last one concerns the modularity of the developed code. Indeed, the proposed model uses three main mechanisms of deformation. But the architecture of the code allows the insertion of new mechanisms or a better interaction between them. The model has been validated first with 2-D cases, then with 3-D natural cases. They give good results from a qualitative point of view. They also show the capacity of the model to provide a deformation path that is geologically acceptable, and its ability to control the volume variations of the basin through the

  10. Dynamic illumination of spatially restricted or large brain volumes via a single tapered optical fiber.

    Science.gov (United States)

    Pisanello, Ferruccio; Mandelbaum, Gil; Pisanello, Marco; Oldenburg, Ian A; Sileo, Leonardo; Markowitz, Jeffrey E; Peterson, Ralph E; Della Patria, Andrea; Haynes, Trevor M; Emara, Mohamed S; Spagnolo, Barbara; Datta, Sandeep Robert; De Vittorio, Massimo; Sabatini, Bernardo L

    2017-08-01

    Optogenetics promises precise spatiotemporal control of neural processes using light. However, the spatial extent of illumination within the brain is difficult to control and cannot be adjusted using standard fiber optics. We demonstrate that optical fibers with tapered tips can be used to illuminate either spatially restricted or large brain volumes. Remotely adjusting the light input angle to the fiber varies the light-emitting portion of the taper over several millimeters without movement of the implant. We use this mode to activate dorsal versus ventral striatum of individual mice and reveal different effects of each manipulation on motor behavior. Conversely, injecting light over the full numerical aperture of the fiber results in light emission from the entire taper surface, achieving broader and more efficient optogenetic activation of neurons, compared to standard flat-faced fiber stimulation. Thus, tapered fibers permit focal or broad illumination that can be precisely and dynamically matched to experimental needs.

  11. A Calderón multiplicative preconditioner for coupled surface-volume electric field integral equations

    KAUST Repository

    Bagci, Hakan

    2010-08-01

    A well-conditioned coupled set of surface (S) and volume (V) electric field integral equations (S-EFIE and V-EFIE) for analyzing wave interactions with densely discretized composite structures is presented. Whereas the V-EFIE operator is well-posed even when applied to densely discretized volumes, a classically formulated S-EFIE operator is ill-posed when applied to densely discretized surfaces. This renders the discretized coupled S-EFIE and V-EFIE system ill-conditioned, and its iterative solution inefficient or even impossible. The proposed scheme regularizes the coupled set of S-EFIE and V-EFIE using a Calderón multiplicative preconditioner (CMP)-based technique. The resulting scheme enables the efficient analysis of electromagnetic interactions with composite structures containing fine/subwavelength geometric features. Numerical examples demonstrate the efficiency of the proposed scheme. © 2006 IEEE.

  12. CEPXS/ONELD: A one-dimensional coupled electron-photon discrete ordinates code package

    International Nuclear Information System (INIS)

    Lorence, L.J. Jr.; Morel, J.E.

    1992-01-01

    CEPXS/ONELD is a discrete ordinates transport code package that can model the electron-photon cascade from 100 MeV to 1 keV. The CEPXS code generates fully-coupled multigroup-Legendre cross section data. This data is used by the general-purpose discrete ordinates code, ONELD, which is derived from the Los Alamos ONEDANT and ONBTRAN codes. Version 1.0 of CEPXS/ONELD was released in 1989 and has been primarily used to analyze the effect of radiation environments on electronics. Version 2.0 is under development and will include user-friendly features such as the automatic selection of group structure, spatial mesh structure, and S N order

  13. Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

    KAUST Repository

    Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

    2017-01-01

    A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy

  14. Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System

    Science.gov (United States)

    Rovny, Jared; Blum, Robert L.; Barrett, Sean E.

    2018-05-01

    A discrete time crystal (DTC) is a robust phase of driven systems that breaks the discrete time translation symmetry of the driving Hamiltonian. Recent experiments have observed DTC signatures in two distinct systems. Here we show nuclear magnetic resonance observations of DTC signatures in a third, strikingly different system: an ordered spatial crystal. We use a novel DTC echo experiment to probe the coherence of the driven system. Finally, we show that interactions during the pulse of the DTC sequence contribute to the decay of the signal, complicating attempts to measure the intrinsic lifetime of the DTC.

  15. Spatial Discrete Soliton in Two dimensional with Kerr medium

    International Nuclear Information System (INIS)

    Aghdami, M.; Mostafavi, D.; Mokhtari, F.; Keradmand, R.

    2012-01-01

    In this theoretical work propagation of the Gaussian beam through a two dimensional waveguides array is numerically investigated, in which each waveguide contains medium with Kerr nonlinearity considering coupling to vertical, horizontal and diagonal neighbor through light electric field. Different values of intensity, nonlinear coefficient Kerr and Gaussian beam width of incident Gaussian beam are examined and finally suitable parameters for providing central spatial solitons are obtained.

  16. Development of a spatially uniform fast ionization wave in a large-volume discharge

    International Nuclear Information System (INIS)

    Zatsepin, D.V.; Starikovskaya, S.M.; Starikovskii, A.Yu.

    1998-01-01

    A study is made of a high-voltage nanosecond breakdown in the form of a fast ionization wave produced in a large-volume (401) discharge chamber. The propagation speed of the wave front and the integral energy deposition in a plasma are measured for various regimes of the air discharge at pressures of 10 -2 -4 Torr. A high degree of both the spatial uniformity of the discharge and the reproducibility of the discharge parameters is obtained. The possibility of the development of a fast ionization wave in an electrodeless system is demonstrated. A transition of the breakdown occurring in the form of a fast ionization wave into the streamer breakdown is observed. It is shown that such discharges are promising for technological applications

  17. DISCRETE MATHEMATICS/NUMBER THEORY

    OpenAIRE

    Mrs. Manju Devi*

    2017-01-01

    Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...

  18. Resonance and web structure in discrete soliton systems: the two-dimensional Toda lattice and its fully discrete and ultra-discrete analogues

    International Nuclear Information System (INIS)

    Maruno, Ken-ichi; Biondini, Gino

    2004-01-01

    We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable systems such as differential-difference equations, difference equations and cellular automata (ultra-discrete equations)

  19. Singular characteristic tracking algorithm for improved solution accuracy of the discrete ordinates method with isotropic scattering

    International Nuclear Information System (INIS)

    Duo, J. I.; Azmy, Y. Y.

    2007-01-01

    A new method, the Singular Characteristics Tracking algorithm, is developed to account for potential non-smoothness across the singular characteristics in the exact solution of the discrete ordinates approximation of the transport equation. Numerical results show improved rate of convergence of the solution to the discrete ordinates equations in two spatial dimensions with isotropic scattering using the proposed methodology. Unlike the standard Weighted Diamond Difference methods, the new algorithm achieves local convergence in the case of discontinuous angular flux along the singular characteristics. The method also significantly reduces the error for problems where the angular flux presents discontinuous spatial derivatives across these lines. For purposes of verifying the results, the Method of Manufactured Solutions is used to generate analytical reference solutions that permit estimating the local error in the numerical solution. (authors)

  20. Development of a Discrete Spatial-Temporal SEIR Simulator for Modeling Infectious Diseases

    Energy Technology Data Exchange (ETDEWEB)

    McKenna, S.A.

    2000-11-01

    Multiple techniques have been developed to model the temporal evolution of infectious diseases. Some of these techniques have also been adapted to model the spatial evolution of the disease. This report examines the application of one such technique, the SEIR model, to the spatial and temporal evolution of disease. Applications of the SEIR model are reviewed briefly and an adaptation to the traditional SEIR model is presented. This adaptation allows for modeling the spatial evolution of the disease stages at the individual level. The transmission of the disease between individuals is modeled explicitly through the use of exposure likelihood functions rather than the global transmission rate applied to populations in the traditional implementation of the SEIR model. These adaptations allow for the consideration of spatially variable (heterogeneous) susceptibility and immunity within the population. The adaptations also allow for modeling both contagious and non-contagious diseases. The results of a number of numerical experiments to explore the effect of model parameters on the spread of an example disease are presented.

  1. Geometry intuitive, discrete, and convex : a tribute to László Fejes Tóth

    CERN Document Server

    Böröczky, Károly; Tóth, Gábor; Pach, János

    2013-01-01

    The present volume is a collection of a dozen survey articles, dedicated to the memory of the famous Hungarian geometer, László Fejes Tóth, on the 99th anniversary of his birth. Each article reviews recent progress in an important field in intuitive, discrete, and convex geometry. The mathematical work and perspectives of all editors and most contributors of this volume were deeply influenced by László Fejes Tóth.

  2. Modelling light distributions of homogeneous versus discrete absorbers in light irradiated turbid media

    NARCIS (Netherlands)

    Verkruysse, W.; Lucassen, G. W.; de Boer, J. F.; Smithies, D. J.; Nelson, J. S.; van Gemert, M. J.

    1997-01-01

    Laser treatment of port wine stains has often been modelled assuming that blood is distributed homogeneously over the dermal volume, instead of enclosed within discrete vessels. The purpose of this paper is to analyse the consequences of this assumption. Due to strong light absorption by blood,

  3. A non-conformal finite element/finite volume scheme for the non-structured grid-based approximation of low Mach number flows; Un schema elements finis non-conformes/volumes finis pour l'approximation en maillages non-structures des ecoulements a faible nombre de Mach

    Energy Technology Data Exchange (ETDEWEB)

    Ansanay-Alex, G.

    2009-06-17

    The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)

  4. An element-based finite-volume method approach for naturally fractured compositional reservoir simulation

    Energy Technology Data Exchange (ETDEWEB)

    Marcondes, Francisco [Federal University of Ceara, Fortaleza (Brazil). Dept. of Metallurgical Engineering and Material Science], e-mail: marcondes@ufc.br; Varavei, Abdoljalil; Sepehrnoori, Kamy [The University of Texas at Austin (United States). Petroleum and Geosystems Engineering Dept.], e-mails: varavei@mail.utexas.edu, kamys@mail.utexas.edu

    2010-07-01

    An element-based finite-volume approach in conjunction with unstructured grids for naturally fractured compositional reservoir simulation is presented. In this approach, both the discrete fracture and the matrix mass balances are taken into account without any additional models to couple the matrix and discrete fractures. The mesh, for two dimensional domains, can be built of triangles, quadrilaterals, or a mix of these elements. However, due to the available mesh generator to handle both matrix and discrete fractures, only results using triangular elements will be presented. The discrete fractures are located along the edges of each element. To obtain the approximated matrix equation, each element is divided into three sub-elements and then the mass balance equations for each component are integrated along each interface of the sub-elements. The finite-volume conservation equations are assembled from the contribution of all the elements that share a vertex, creating a cell vertex approach. The discrete fracture equations are discretized only along the edges of each element and then summed up with the matrix equations in order to obtain a conservative equation for both matrix and discrete fractures. In order to mimic real field simulations, the capillary pressure is included in both matrix and discrete fracture media. In the implemented model, the saturation field in the matrix and discrete fractures can be different, but the potential of each phase in the matrix and discrete fracture interface needs to be the same. The results for several naturally fractured reservoirs are presented to demonstrate the applicability of the method. (author)

  5. Trees and spatial topology change in CDT

    DEFF Research Database (Denmark)

    Ambjorn, Jan; Budd, Timothy George

    2013-01-01

    Generalized causal dynamical triangulations (generalized CDT) is a model of two-dimensional quantum gravity in which a limited number of spatial topology changes is allowed to occur. We solve the model at the discretized level using bijections between quadrangulations and trees. In the continuum...

  6. Spatial domain decomposition for neutron transport problems

    International Nuclear Information System (INIS)

    Yavuz, M.; Larsen, E.W.

    1989-01-01

    A spatial Domain Decomposition method is proposed for modifying the Source Iteration (SI) and Diffusion Synthetic Acceleration (DSA) algorithms for solving discrete ordinates problems. The method, which consists of subdividing the spatial domain of the problem and performing the transport sweeps independently on each subdomain, has the advantage of being parallelizable because the calculations in each subdomain can be performed on separate processors. In this paper we describe the details of this spatial decomposition and study, by numerical experimentation, the effect of this decomposition on the SI and DSA algorithms. Our results show that the spatial decomposition has little effect on the convergence rates until the subdomains become optically thin (less than about a mean free path in thickness)

  7. Diffusion of multiple species with excluded-volume effects

    KAUST Repository

    Bruna, Maria; Chapman, S. Jonathan

    2012-01-01

    Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial differential equations. In this paper we consider multiple interacting subpopulations/species and study how the inter-species competition emerges at the population level. Each individual is described as a finite-size hard core interacting particle undergoing Brownian motion. The link between the discrete stochastic equations of motion and the continuum model is considered systematically using the method of matched asymptotic expansions. The system for two species leads to a nonlinear cross-diffusion system for each subpopulation, which captures the enhancement of the effective diffusion rate due to excluded-volume interactions between particles of the same species, and the diminishment due to particles of the other species. This model can explain two alternative notions of the diffusion coefficient that are often confounded, namely collective diffusion and self-diffusion. Simulations of the discrete system show good agreement with the analytic results. © 2012 American Institute of Physics.

  8. Discrete mode laser diodes for FTTH/PON applications up to 10 Gbit/s

    NARCIS (Netherlands)

    O'Carroll, J.; Phelan, R.; Kelly, B.; Byrne, D.; Latkowski, S.; Anandarajah, P.M.; Barry, L.P.

    2012-01-01

    Discrete Mode Laser Diodes (DMLDs) present an economic approach with a focus on high volume manufacturability of single mode lasers using a single step fabrication process. We report on a DMLD designed for operation in the 1550 nm window with high Side Mode Suppression Ratio (SMSR) over a wide

  9. Effects of image charges, interfacial charge discreteness, and surface roughness on the zeta potential of spherical electric double layers.

    Science.gov (United States)

    Gan, Zecheng; Xing, Xiangjun; Xu, Zhenli

    2012-07-21

    We investigate the effects of image charges, interfacial charge discreteness, and surface roughness on spherical electric double layer structures in electrolyte solutions with divalent counterions in the setting of the primitive model. By using Monte Carlo simulations and the image charge method, the zeta potential profile and the integrated charge distribution function are computed for varying surface charge strengths and salt concentrations. Systematic comparisons were carried out between three distinct models for interfacial charges: (1) SURF1 with uniform surface charges, (2) SURF2 with discrete point charges on the interface, and (3) SURF3 with discrete interfacial charges and finite excluded volume. By comparing the integrated charge distribution function and the zeta potential profile, we argue that the potential at the distance of one ion diameter from the macroion surface is a suitable location to define the zeta potential. In SURF2 model, we find that image charge effects strongly enhance charge inversion for monovalent interfacial charges, and strongly suppress charge inversion for multivalent interfacial charges. For SURF3, the image charge effect becomes much smaller. Finally, with image charges in action, we find that excluded volumes (in SURF3) suppress charge inversion for monovalent interfacial charges and enhance charge inversion for multivalent interfacial charges. Overall, our results demonstrate that all these aspects, i.e., image charges, interfacial charge discreteness, their excluding volumes, have significant impacts on zeta potentials of electric double layers.

  10. Discrete control systems

    CERN Document Server

    Okuyama, Yoshifumi

    2014-01-01

    Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...

  11. Influence of macular pigment optical density spatial distribution on intraocular scatter.

    Science.gov (United States)

    Putnam, Christopher M; Bland, Pauline J; Bassi, Carl J

    This study evaluated the summed measures of macular pigment optical density (MPOD) spatial distribution and their effects on intraocular scatter using a commercially available device (C-Quant, Oculus, USA). A customized heterochromatic flicker photometer (cHFP) device was used to measure MPOD spatial distribution across the central 16° using a 1° stimulus. MPOD was calculated as a discrete measure and summed measures across the central 1°, 3.3°, 10° and 16° diameters. Intraocular scatter was determined as a mean of 5 trials in which reliability and repeatability measures were met using the C-Quant. MPOD spatial distribution maps were constructed and the effects of both discrete and summed values on intraocular scatter were examined. Spatial mapping identified mean values for discrete MPOD [0.32 (s.d.=0.08)], MPOD summed across central 1° [0.37 (s.d.=0.11)], MPOD summed across central 3.3° [0.85 (s.d.=0.20)], MPOD summed across central 10° [1.60 (s.d.=0.35)] and MPOD summed across central 16° [1.78 (s.d.=0.39)]. Mean intraocular scatter was 0.83 (s.d.=0.16) log units. While there were consistent trends for an inverse relationship between MPOD and scatter, these relationships were not statistically significant. Correlations between the highest and lowest quartiles of MPOD within the central 1° were near significance. While there was an overall trend of decreased intraocular forward scatter with increased MPOD consistent with selective short wavelength visible light attenuation, neither discrete nor summed values of MPOD significantly influence intraocular scatter as measured by the C-Quant device. Published by Elsevier España, S.L.U.

  12. An energy recondensation method using the discrete generalized multigroup energy expansion theory

    International Nuclear Information System (INIS)

    Zhu Lei; Forget, Benoit

    2011-01-01

    Highlights: → Discrete-generalized multigroup method was implemented as a recondensation scheme. → Coarse group cross-sections were recondensed from core-level solution. → Neighboring effect of reflector and MOX bundle was improved. → Methodology was shown to be fully consistent when a flat angular flux approximation is used. - Abstract: In this paper, the discrete generalized multigroup (DGM) method was used to recondense the coarse group cross-sections using the core level solution, thus providing a correction for neighboring effect found at the core level. This approach was tested using a discrete ordinates implementation in both 1-D and 2-D. Results indicate that 2 or 3 iterations can substantially improve the flux and fission density errors associated with strong interfacial spectral changes as found in the presence of strong absorbers, reflector of mixed-oxide fuel. The methodology is also proven to be fully consistent with the multigroup methodology as long as a flat-flux approximation is used spatially.

  13. Simulation techniques for spatially evolving instabilities in compressible flow over a flat plate

    NARCIS (Netherlands)

    Wasistho, B.; Geurts, Bernardus J.; Kuerten, Johannes G.M.

    1997-01-01

    In this paper we present numerical techniques suitable for a direct numerical simulation in the spatial setting. We demonstrate the application to the simulation of compressible flat plate flow instabilities. We compare second and fourth order accurate spatial discretization schemes in combination

  14. Discrete hierarchical organization of social group sizes.

    Science.gov (United States)

    Zhou, W-X; Sornette, D; Hill, R A; Dunbar, R I M

    2005-02-22

    The 'social brain hypothesis' for the evolution of large brains in primates has led to evidence for the coevolution of neocortical size and social group sizes, suggesting that there is a cognitive constraint on group size that depends, in some way, on the volume of neural material available for processing and synthesizing information on social relationships. More recently, work on both human and non-human primates has suggested that social groups are often hierarchically structured. We combine data on human grouping patterns in a comprehensive and systematic study. Using fractal analysis, we identify, with high statistical confidence, a discrete hierarchy of group sizes with a preferred scaling ratio close to three: rather than a single or a continuous spectrum of group sizes, humans spontaneously form groups of preferred sizes organized in a geometrical series approximating 3-5, 9-15, 30-45, etc. Such discrete scale invariance could be related to that identified in signatures of herding behaviour in financial markets and might reflect a hierarchical processing of social nearness by human brains.

  15. A complete characterization of the (m,n-cubes and combinatorial applications in imaging, vision and discrete geometry

    Directory of Open Access Journals (Sweden)

    Daniel Khoshnoudirad

    2015-11-01

    Full Text Available The aim of this work is to provide a complete characterization of a (m,n-cube. The latter are the pieces of discrete planes appearing in Theoretical Computer Science, Discrete Geometry and Combinatorics. This characterization in three dimensions is the exact equivalent of the preimage for a discrete segment as it has been introduced by McIlroy. Further this characterization, which avoids the redundancies, reduces the combinatorial problem of determining the cardinality of the (m,n-cubes to a new combinatorial problem consisting of determining the volumic regions formed by the crossing of planes. This work can find applications in Imaging, Vision, and pattern recognition for instance.

  16. The number of bound states for a discrete Schroedinger operator on ZN, N≥1, lattices

    International Nuclear Information System (INIS)

    Karachalios, N I

    2008-01-01

    We consider the discrete Schroedinger operator -Δ d +U in Z N , N≥1 in the case of a potential with negative part in an appropriate l σ -space (decays with an appropriate rate). We present a discrete analog of the method of Li and Yau (1983 Commun. Math. Phys. 88 309-18), proving an explicit upper estimate on the number of bound states N d (0)={j:μ j ≤0}, which is independent of the dimension of the lattice. This is a major difference with the continuous counterpart estimate, which is not valid when N = 1, 2. As a consequence, a dimension-independent smallness criterion for the existence of bound states is derived in contrast to the continuous case as well as to the discrete case of vanishing potential. A short comment is made on possible applications of the results to the study of the dynamics of some particular spatially discrete nonlinear systems

  17. Discrete Element Modeling

    Energy Technology Data Exchange (ETDEWEB)

    Morris, J; Johnson, S

    2007-12-03

    The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.

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

    Science.gov (United States)

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

    2015-01-01

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

  19. A non-conformal finite element/finite volume scheme for the non-structured grid-based approximation of low Mach number flows

    International Nuclear Information System (INIS)

    Ansanay-Alex, G.

    2009-01-01

    The development of simulation codes aimed at a precise simulation of fires requires a precise approach of flame front phenomena by using very fine grids. The need to take different spatial scale into consideration leads to a local grid refinement and to a discretization with homogeneous grid for computing time and memory purposes. The author reports the approximation of the non-linear convection term, the scalar advection-diffusion in finite volumes, numerical simulations of a flow in a bent tube, of a three-dimensional laminar flame and of a low Mach number an-isotherm flow. Non conformal finite elements are also presented (Rannacher-Turek and Crouzeix-Raviart elements)

  20. Lattice fluid dynamics from perfect discretizations of continuum flows

    International Nuclear Information System (INIS)

    Katz, E.; Wiese, U.

    1998-01-01

    We use renormalization group methods to derive equations of motion for large scale variables in fluid dynamics. The large scale variables are averages of the underlying continuum variables over cubic volumes and naturally exist on a lattice. The resulting lattice dynamics represents a perfect discretization of continuum physics, i.e., grid artifacts are completely eliminated. Perfect equations of motion are derived for static, slow flows of incompressible, viscous fluids. For Hagen-Poiseuille flow in a channel with a square cross section the equations reduce to a perfect discretization of the Poisson equation for the velocity field with Dirichlet boundary conditions. The perfect large scale Poisson equation is used in a numerical simulation and is shown to represent the continuum flow exactly. For nonsquare cross sections one can use a numerical iterative procedure to derive flow equations that are approximately perfect. copyright 1998 The American Physical Society

  1. WE-H-207A-05: Spatial Co-Localization of F-18 NaF Vs. F-18 FDG Defined Disease Volumes

    Energy Technology Data Exchange (ETDEWEB)

    Ferjancic, P; Harmon, S; Jeraj, R [University of Wisconsin, Madison, WI (United States); Chen, S [1st Hospital of China Medical University, Shenyang, Liaoning (China); Simoncic, U [Jozef Stefan Institute, Ljubljana (Slovenia)

    2016-06-15

    Purpose: Both [F-18]NaF and [F-18]FDG show promise for quantitative PET/CT assessment in metastatic prostate cancer to bone. Broad agreement between the tracers has been shown but voxel-wise correspondence has not been explored in depth. This study evaluates the spatial co-localization of [F-18]NaF PET and [F-18]FDG PET in bone lesions. Methods: Seventy-three lesion contours were identified in six patients receiving dynamic NaF PET/CT and FDG PET/CT scans two hours apart using identical fields-of-view. Tracer uptake (SUV) reflecting 60 minutes post-injection was modeled from kinetic parameters. Lesions were segmented by a physician separately on NaF PET and FDG PET. PET images were rigidly aligned using skeletal references on CT images. Lesion size, degree of overlap, voxel-wise tracer uptake values (SUV), and CT density distributions were compared using Dice coefficient, Positive Predictive Value (PPV), and Spearman rank correlation tests. Results: Across all patients, 42 lesions were identified on NaF PET (median 1.4 cm{sup 3}, range <1–204 cm{sup 3}) compared to 31 using FDG PET (median 1.8 cm{sup 3}, range <1–244 cm{sup 3}). Spatial cooccurrence was found in 25 lesion pairs. Lesions on NaF PET had PPV of 0.91 and on FDG a PPV of 0.65. Overall, NaF-defined lesions were 47% (±24%) larger by volume with moderate overlap to FDG, resulting in mean Dice coefficient of 34% (±22%). In areas of overlap, voxel-wise correlation of NaF and FDG SUV was moderate (ρ=0.56). Expanding to regions of non-spatial overlap, voxels contained in FDG-only contours were almost exclusively low HU (median 118), compared to dense regions of NaF-only voxels (median 250). In sclerotic sub-volumes (HU > 300) NaF-defined contours encompassed 83% of total FDG volume. Conclusion: Moderate voxel-wise correlation of FDG and NaF PET/CT uptake was observed. Spatial discrepancies in FDG and NaF PET/CT imaging of boney metastases could be influenced by poor sensitivity of FDG PET/CT in

  2. Location Aggregation of Spatial Population CTMC Models

    Directory of Open Access Journals (Sweden)

    Luca Bortolussi

    2016-10-01

    Full Text Available In this paper we focus on spatial Markov population models, describing the stochastic evolution of populations of agents, explicitly modelling their spatial distribution, representing space as a discrete, finite graph. More specifically, we present a heuristic approach to aggregating spatial locations, which is designed to preserve the dynamical behaviour of the model whilst reducing the computational cost of analysis. Our approach combines stochastic approximation ideas (moment closure, linear noise, with computational statistics (spectral clustering to obtain an efficient aggregation, which is experimentally shown to be reasonably accurate on two case studies: an instance of epidemic spreading and a London bike sharing scenario.

  3. Health and safety impacts from discrete sources of naturally-occurring and accelerator-produced radioactive materials (NARM)

    International Nuclear Information System (INIS)

    Nussbaumer, D.; Wiblin, C.; Welch, L.

    1993-02-01

    This report characterizes discrete sources of naturally-occurring and accelerator-produced radioactive material (NARM) and estimates risks posed by the possession, use and disposal of them. A distinction between discrete and diffuse NARM sources is made with discrete sources being high activity, low volume and diffuse sources being low activity, high volume. Two nanocuries per gram is used as a separation guide between high and low activity, although use of this value does not impact the report's conclusions. Most NARM is under regulatory control of States that either license or register users but reporting requirements are not uniform. Use in consumer products has declined with virtually no production today; however, lack of information available concerning radiation exposures resulting form possession of ageing radium sources precludes a quantitative risk assessment in this report. The report identifies the type of information needed to permit such an assessment. Regarding accelerator-produced radioactive material (ARM), use of this material in nuclear medicine programs has recently increased. Available radiation exposure data regarding ARM handling and use indicates that the risk to workers and the public is low at this time

  4. CONTAMINATED SOIL VOLUME ESTIMATE TRACKING METHODOLOGY

    International Nuclear Information System (INIS)

    Durham, L.A.; Johnson, R.L.; Rieman, C.; Kenna, T.; Pilon, R.

    2003-01-01

    The U.S. Army Corps of Engineers (USACE) is conducting a cleanup of radiologically contaminated properties under the Formerly Utilized Sites Remedial Action Program (FUSRAP). The largest cost element for most of the FUSRAP sites is the transportation and disposal of contaminated soil. Project managers and engineers need an estimate of the volume of contaminated soil to determine project costs and schedule. Once excavation activities begin and additional remedial action data are collected, the actual quantity of contaminated soil often deviates from the original estimate, resulting in cost and schedule impacts to the project. The project costs and schedule need to be frequently updated by tracking the actual quantities of excavated soil and contaminated soil remaining during the life of a remedial action project. A soil volume estimate tracking methodology was developed to provide a mechanism for project managers and engineers to create better project controls of costs and schedule. For the FUSRAP Linde site, an estimate of the initial volume of in situ soil above the specified cleanup guidelines was calculated on the basis of discrete soil sample data and other relevant data using indicator geostatistical techniques combined with Bayesian analysis. During the remedial action, updated volume estimates of remaining in situ soils requiring excavation were calculated on a periodic basis. In addition to taking into account the volume of soil that had been excavated, the updated volume estimates incorporated both new gamma walkover surveys and discrete sample data collected as part of the remedial action. A civil survey company provided periodic estimates of actual in situ excavated soil volumes. By using the results from the civil survey of actual in situ volumes excavated and the updated estimate of the remaining volume of contaminated soil requiring excavation, the USACE Buffalo District was able to forecast and update project costs and schedule. The soil volume

  5. Simultaneous storage of medical images in the spatial and frequency domain: A comparative study

    Directory of Open Access Journals (Sweden)

    Acharya U Rajendra

    2004-06-01

    Full Text Available Abstract Background Digital watermarking is a technique of hiding specific identification data for copyright authentication. This technique is adapted here for interleaving patient information with medical images, to reduce storage and transmission overheads. Methods The patient information is encrypted before interleaving with images to ensure greater security. The bio-signals are compressed and subsequently interleaved with the image. This interleaving is carried out in the spatial domain and Frequency domain. The performance of interleaving in the spatial, Discrete Fourier Transform (DFT, Discrete Cosine Transform (DCT and Discrete Wavelet Transform (DWT coefficients is studied. Differential pulse code modulation (DPCM is employed for data compression as well as encryption and results are tabulated for a specific example. Results It can be seen from results, the process does not affect the picture quality. This is attributed to the fact that the change in LSB of a pixel changes its brightness by 1 part in 256. Spatial and DFT domain interleaving gave very less %NRMSE as compared to DCT and DWT domain. Conclusion The Results show that spatial domain the interleaving, the %NRMSE was less than 0.25% for 8-bit encoded pixel intensity. Among the frequency domain interleaving methods, DFT was found to be very efficient.

  6. Spatial Economics Model Predicting Transport Volume

    Directory of Open Access Journals (Sweden)

    Lu Bo

    2016-10-01

    Full Text Available It is extremely important to predict the logistics requirements in a scientific and rational way. However, in recent years, the improvement effect on the prediction method is not very significant and the traditional statistical prediction method has the defects of low precision and poor interpretation of the prediction model, which cannot only guarantee the generalization ability of the prediction model theoretically, but also cannot explain the models effectively. Therefore, in combination with the theories of the spatial economics, industrial economics, and neo-classical economics, taking city of Zhuanghe as the research object, the study identifies the leading industry that can produce a large number of cargoes, and further predicts the static logistics generation of the Zhuanghe and hinterlands. By integrating various factors that can affect the regional logistics requirements, this study established a logistics requirements potential model from the aspect of spatial economic principles, and expanded the way of logistics requirements prediction from the single statistical principles to an new area of special and regional economics.

  7. Splines and their reciprocal-bases in volume-integral equations

    International Nuclear Information System (INIS)

    Sabbagh, H.A.

    1993-01-01

    The authors briefly outline the use of higher-order splines and their reciprocal-bases in discretizing the volume-integral equations of electromagnetics. The discretization is carried out by means of the method of moments, in which the expansion functions are the higher-order splines, and the testing functions are the corresponding reciprocal-basis functions. These functions satisfy an orthogonality condition with respect to the spline expansion functions. Thus, the method is not Galerkin, but the structure of the resulting equations is quite regular, nevertheless. The theory is applied to the volume-integral equations for the unknown current density, or unknown electric field, within a scattering body, and to the equations for eddy-current nondestructive evaluation. Numerical techniques for computing the matrix elements are also given

  8. A Discrete Spectral Problem and Related Hierarchy of Discrete Hamiltonian Lattice Equations

    International Nuclear Information System (INIS)

    Xu Xixiang; Cao Weili

    2007-01-01

    Staring from a discrete matrix spectral problem, a hierarchy of lattice soliton equations is presented though discrete zero curvature representation. The resulting lattice soliton equations possess non-local Lax pairs. The Hamiltonian structures are established for the resulting hierarchy by the discrete trace identity. Liouville integrability of resulting hierarchy is demonstrated.

  9. A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation

    International Nuclear Information System (INIS)

    Banks, J.W.; Hittinger, J.A.

    2010-01-01

    Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.

  10. Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

    KAUST Repository

    Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

    2016-01-01

    A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a

  11. Evidence for discrete landmark use by pigeons during homing.

    Science.gov (United States)

    Mora, Cordula V; Ross, Jeremy D; Gorsevski, Peter V; Chowdhury, Budhaditya; Bingman, Verner P

    2012-10-01

    Considerable efforts have been made to investigate how homing pigeons (Columba livia f. domestica) are able to return to their loft from distant, unfamiliar sites while the mechanisms underlying navigation in familiar territory have received less attention. With the recent advent of global positioning system (GPS) data loggers small enough to be carried by pigeons, the role of visual environmental features in guiding navigation over familiar areas is beginning to be understood, yet, surprisingly, we still know very little about whether homing pigeons can rely on discrete, visual landmarks to guide navigation. To assess a possible role of discrete, visual landmarks in navigation, homing pigeons were first trained to home from a site with four wind turbines as salient landmarks as well as from a control site without any distinctive, discrete landmark features. The GPS-recorded flight paths of the pigeons on the last training release were straighter and more similar among birds from the turbine site compared with those from the control site. The pigeons were then released from both sites following a clock-shift manipulation. Vanishing bearings from the turbine site continued to be homeward oriented as 13 of 14 pigeons returned home. By contrast, at the control site the vanishing bearings were deflected in the expected clock-shift direction and only 5 of 13 pigeons returned home. Taken together, our results offer the first strong evidence that discrete, visual landmarks are one source of spatial information homing pigeons can utilize to navigate when flying over a familiar area.

  12. Asymptotic behavior of discrete holomorphic maps z^c, log(z) and discrete Painleve transcedents

    OpenAIRE

    Agafonov, S. I.

    2005-01-01

    It is shown that discrete analogs of z^c and log(z) have the same asymptotic behavior as their smooth counterparts. These discrete maps are described in terms of special solutions of discrete Painleve-II equations, asymptotics of these solutions providing the behaviour of discrete z^c and log(z) at infinity.

  13. Applying Spatial-Temporal Model and Game Theory to Asymmetric Threat Prediction

    National Research Council Canada - National Science Library

    Wei, Mo; Chen, Genshe; Cruz, Jr., Jose B; Haynes, Leonard; Kruger, Martin

    2007-01-01

    .... In most Command and Control "C2" applications, the existing techniques, such as spatial-temporal point models for ECOA prediction or Discrete Choice Model "DCM", assume that insurgent attack features...

  14. Lung ventilation injures areas with discrete alveolar flooding, in a surface tension-dependent fashion.

    Science.gov (United States)

    Wu, You; Kharge, Angana Banerjee; Perlman, Carrie E

    2014-10-01

    With proteinaceous-liquid flooding of discrete alveoli, a model of the edema pattern in the acute respiratory distress syndrome, lung inflation over expands aerated alveoli adjacent to flooded alveoli. Theoretical considerations suggest that the overexpansion may be proportional to surface tension, T. Yet recent evidence indicates proteinaceous edema liquid may not elevate T. Thus whether the overexpansion is injurious is not known. Here, working in the isolated, perfused rat lung, we quantify fluorescence movement from the vasculature to the alveolar liquid phase as a measure of overdistension injury to the alveolar-capillary barrier. We label the perfusate with fluorescence; micropuncture a surface alveolus and instill a controlled volume of nonfluorescent liquid to obtain a micropunctured-but-aerated region (control group) or a region with discrete alveolar flooding; image the region at a constant transpulmonary pressure of 5 cmH2O; apply five ventilation cycles with a positive end-expiratory pressure of 0-20 cmH2O and tidal volume of 6 or 12 ml/kg; return the lung to a constant transpulmonary pressure of 5 cmH2O; and image for an additional 10 min. In aerated areas, ventilation is not injurious. With discrete alveolar flooding, all ventilation protocols cause sustained injury. Greater positive end-expiratory pressure or tidal volume increases injury. Furthermore, we determine T and find injury increases with T. Inclusion of either plasma proteins or Survanta in the flooding liquid does not alter T or injury. Inclusion of 2.7-10% albumin and 1% Survanta together, however, lowers T and injury. Contrary to expectation, albumin inclusion in our model facilitates exogenous surfactant activity. Copyright © 2014 the American Physiological Society.

  15. Space discretization in SN methods: Features, improvements and convergence patterns

    International Nuclear Information System (INIS)

    Coppa, G.G.M.; Lapenta, G.; Ravetto, P.

    1990-01-01

    A comparative analysis of the space discretization schemes currently used in S N methods is performed and special attention is devoted to direct integration techniques. Some improvements are proposed in one- and two-dimensional applications, which are based on suitable choices for the spatial variation of the collision source. A study of the convergence pattern is carried out for eigenvalue calculations within the space asymptotic approximation by means of both analytical and numerical investigations. (orig.) [de

  16. Adaptive Microwave Staring Correlated Imaging for Targets Appearing in Discrete Clusters.

    Science.gov (United States)

    Tian, Chao; Jiang, Zheng; Chen, Weidong; Wang, Dongjin

    2017-10-21

    Microwave staring correlated imaging (MSCI) can achieve ultra-high resolution in real aperture staring radar imaging using the correlated imaging process (CIP) under all-weather and all-day circumstances. The CIP must combine the received echo signal with the temporal-spatial stochastic radiation field. However, a precondition of the CIP is that the continuous imaging region must be discretized to a fine grid, and the measurement matrix should be accurately computed, which makes the imaging process highly complex when the MSCI system observes a wide area. This paper proposes an adaptive imaging approach for the targets in discrete clusters to reduce the complexity of the CIP. The approach is divided into two main stages. First, as discrete clustered targets are distributed in different range strips in the imaging region, the transmitters of the MSCI emit narrow-pulse waveforms to separate the echoes of the targets in different strips in the time domain; using spectral entropy, a modified method robust against noise is put forward to detect the echoes of the discrete clustered targets, based on which the strips with targets can be adaptively located. Second, in a strip with targets, the matched filter reconstruction algorithm is used to locate the regions with targets, and only the regions of interest are discretized to a fine grid; sparse recovery is used, and the band exclusion is used to maintain the non-correlation of the dictionary. Simulation results are presented to demonstrate that the proposed approach can accurately and adaptively locate the regions with targets and obtain high-quality reconstructed images.

  17. Recent advances in marching-on-in-time schemes for solving time domain volume integral equations

    KAUST Repository

    Sayed, Sadeed Bin; Ulku, Huseyin Arda; Bagci, Hakan

    2015-01-01

    Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are constructed by setting the summation of the incident and scattered field intensities to the total field intensity on the volumetric support of the scatterer. The unknown can be the field intensity or flux/current density. Representing the total field intensity in terms of the unknown using the relevant constitutive relation and the scattered field intensity in terms of the spatiotemporal convolution of the unknown with the Green function yield the final form of the TDVIE. The unknown is expanded in terms of local spatial and temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation at discrete times yield a system of equations that is solved by the marching on-in-time (MOT) scheme. At each time step, a smaller system of equations, termed MOT system is solved for the coefficients of the expansion. The right-hand side of this system consists of the tested incident field and discretized spatio-temporal convolution of the unknown samples computed at the previous time steps with the Green function.

  18. Recent advances in marching-on-in-time schemes for solving time domain volume integral equations

    KAUST Repository

    Sayed, Sadeed Bin

    2015-05-16

    Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are constructed by setting the summation of the incident and scattered field intensities to the total field intensity on the volumetric support of the scatterer. The unknown can be the field intensity or flux/current density. Representing the total field intensity in terms of the unknown using the relevant constitutive relation and the scattered field intensity in terms of the spatiotemporal convolution of the unknown with the Green function yield the final form of the TDVIE. The unknown is expanded in terms of local spatial and temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation at discrete times yield a system of equations that is solved by the marching on-in-time (MOT) scheme. At each time step, a smaller system of equations, termed MOT system is solved for the coefficients of the expansion. The right-hand side of this system consists of the tested incident field and discretized spatio-temporal convolution of the unknown samples computed at the previous time steps with the Green function.

  19. Discrete port-Hamiltonian systems

    NARCIS (Netherlands)

    Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der

    2006-01-01

    Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling

  20. Applied discrete-time queues

    CERN Document Server

    Alfa, Attahiru S

    2016-01-01

    This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are includ...

  1. Does cooperation mean kinship between spatially discrete ant nests?

    Science.gov (United States)

    Procter, Duncan S; Cottrell, Joan E; Watts, Kevin; A'Hara, Stuart W; Hofreiter, Michael; Robinson, Elva J H

    2016-12-01

    Eusociality is one of the most complex forms of social organization, characterized by cooperative and reproductive units termed colonies. Altruistic behavior of workers within colonies is explained by inclusive fitness, with indirect fitness benefits accrued by helping kin. Members of a social insect colony are expected to be more closely related to one another than they are to other conspecifics. In many social insects, the colony can extend to multiple socially connected but spatially separate nests (polydomy). Social connections, such as trails between nests, promote cooperation and resource exchange, and we predict that workers from socially connected nests will have higher internest relatedness than those from socially unconnected, and noncooperating, nests. We measure social connections, resource exchange, and internest genetic relatedness in the polydomous wood ant Formica lugubris to test whether (1) socially connected but spatially separate nests cooperate, and (2) high internest relatedness is the underlying driver of this cooperation. Our results show that socially connected nests exhibit movement of workers and resources, which suggests they do cooperate, whereas unconnected nests do not. However, we find no difference in internest genetic relatedness between socially connected and unconnected nest pairs, both show high kinship. Our results suggest that neighboring pairs of connected nests show a social and cooperative distinction, but no genetic distinction. We hypothesize that the loss of a social connection may initiate ecological divergence within colonies. Genetic divergence between neighboring nests may build up only later, as a consequence rather than a cause of colony separation.

  2. A discrete model for compressible flows in heterogeneous media

    International Nuclear Information System (INIS)

    Le Metayer, O.; Massol, A.; Favrie, N.; Hank, S.

    2011-01-01

    This work deals with the building of a discrete model able to describe and to predict the evolution of complex gas flows in heterogeneous media. In many physical applications, large scales numerical simulation is no longer possible because of a lack of computing resources. Indeed the medium topology may be complex due to the presence of many obstacles (walls, pipes, equipments, geometric singularities etc.). Aircraft powerplant compartments are examples where topology is complex due to the presence of pipes, ducts, coolers and other equipment. Other important examples are gas explosions and large scale dispersion of hazardous materials in urban places, cities or underground involving obstacles such as buildings and various infrastructures. In all cases efficient safety responses are required. Then a new discrete model is built and solved in reasonable execution times for large cells volumes including such obstacles. Quantitative comparisons between experimental and numerical results are shown for different significant test cases, showing excellent agreement.

  3. Discrete repulsive oscillator wavefunctions

    International Nuclear Information System (INIS)

    Munoz, Carlos A; Rueda-Paz, Juvenal; Wolf, Kurt Bernardo

    2009-01-01

    For the study of infinite discrete systems on phase space, the three-dimensional Lorentz algebra and group, so(2,1) and SO(2,1), provide a discrete model of the repulsive oscillator. Its eigenfunctions are found in the principal irreducible representation series, where the compact generator-that we identify with the position operator-has the infinite discrete spectrum of the integers Z, while the spectrum of energies is a double continuum. The right- and left-moving wavefunctions are given by hypergeometric functions that form a Dirac basis for l 2 (Z). Under contraction, the discrete system limits to the well-known quantum repulsive oscillator. Numerical computations of finite approximations raise further questions on the use of Dirac bases for infinite discrete systems.

  4. Performance comparisons of enhanced tubes with discrete and wavy disruption shapes

    Energy Technology Data Exchange (ETDEWEB)

    Arman, B.; Rabas, T.J.

    1993-08-01

    This paper presents comparisons of the friction factors and heat-transfer coefficients obtained with enhanced tubes with transverse discrete and almost transverse wavy two-dimensional disruptions. Both experimental data and numerical predictions were used for the comparisons. For the latter a two-layer turbulence model incorporated in a body-fitted, finite-volume method was used. The disruption shape, discrete or wavy, depends on the manufacturing process. If an extrusion process is used, discrete disruptions (ribs) of various profiles are obtained that are separated from each other by a flat or unaltered inside diameter. If a spirally indenting process is used, a wavy proflie is obtained with a continuously varying inside diameter between two adjacent disruption peaks. These disruptions are transverse or almost transverse to the tube axis and separated by a distance that exceeds the reattachment length. Based on these comparisons, the following conclusions are obtained: (1) the disruption shape is not an important correlating parameter for discrete disruptions, (2) only the friction factor is influenced by the shape for wavy disruptions, and (3) there are major differences between both the friction-factor and heat-transfer performance of discrete and wavy disruptions with the same maximum disruption height and spacing. However, the most important finding is that the groove radius of spirally indented tubes should be increased because of the substantial reduction of the friction factor but only a small decrease in the thermal performance. Additional comparisons of predicted results were made to obtain a fundamental understanding of the influence of these different shapes.

  5. Spatial effects in meta-foodwebs.

    Science.gov (United States)

    Barter, Edmund; Gross, Thilo

    2017-08-30

    In ecology it is widely recognised that many landscapes comprise a network of discrete patches of habitat. The species that inhabit the patches interact with each other through a foodweb, the network of feeding interactions. The meta-foodweb model proposed by Pillai et al. combines the feeding relationships at each patch with the dispersal of species between patches, such that the whole system is represented by a network of networks. Previous work on meta-foodwebs has focussed on landscape networks that do not have an explicit spatial embedding, but in real landscapes the patches are usually distributed in space. Here we compare the dispersal of a meta-foodweb on Erdős-Rényi networks, that do not have a spatial embedding, and random geometric networks, that do have a spatial embedding. We found that local structure and large network distances in spatially embedded networks, lead to meso-scale patterns of patch occupation by both specialist and omnivorous species. In particular, we found that spatial separations make the coexistence of competing species more likely. Our results highlight the effects of spatial embeddings for meta-foodweb models, and the need for new analytical approaches to them.

  6. Discrete Hamiltonian evolution and quantum gravity

    International Nuclear Information System (INIS)

    Husain, Viqar; Winkler, Oliver

    2004-01-01

    We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization

  7. Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

    KAUST Repository

    Mohamed, Mamdouh S.

    2016-02-11

    A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

  8. Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

    Science.gov (United States)

    Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

    2016-05-01

    A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

  9. Naval Medical Research and Development News. Volume 8, Issue 3

    Science.gov (United States)

    2016-03-01

    concentration of an airborne spatial repellent (SR) product and the resulting change in mosquito behavior. The NAMRU-D team will leverage their years of...discrete, known airborne concentrations of spatial repellent (SR) compounds. This project could establish a standard product evaluation process and...resistance microarray, massively multiplexed PCR and sequencing, and shotgun metagenomics sequencing) that can be used to rapidly characterize the

  10. Analysis for preliminary evaluation of discrete fracture flow and large-scale permeability in sedimentary rocks

    International Nuclear Information System (INIS)

    Kanehiro, B.Y.; Lai, C.H.; Stow, S.H.

    1987-05-01

    Conceptual models for sedimentary rock settings that could be used in future evaluation and suitability studies are being examined through the DOE Repository Technology Program. One area of concern for the hydrologic aspects of these models is discrete fracture flow analysis as related to the estimation of the size of the representative elementary volume, evaluation of the appropriateness of continuum assumptions and estimation of the large-scale permeabilities of sedimentary rocks. A basis for preliminary analysis of flow in fracture systems of the types that might be expected to occur in low permeability sedimentary rocks is presented. The approach used involves numerical modeling of discrete fracture flow for the configuration of a large-scale hydrologic field test directed at estimation of the size of the representative elementary volume and large-scale permeability. Analysis of fracture data on the basis of this configuration is expected to provide a preliminary indication of the scale at which continuum assumptions can be made

  11. Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization

    International Nuclear Information System (INIS)

    Fernandez, P.; Wang, Q.

    2017-01-01

    We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed.

  12. Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization

    Science.gov (United States)

    Fernandez, P.; Wang, Q.

    2017-12-01

    We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed.

  13. How does the sparse memory "engram" neurons encode the memory of a spatial-temporal event?

    Directory of Open Access Journals (Sweden)

    Ji-Song Guan

    2016-08-01

    Full Text Available Episodic memory in human brain is not a fixed 2-D picture but a highly dynamic movie serial, integrating information at both the temporal and the spatial domains. Recent studies in neuroscience reveal that memory storage and recall are closely related to the activities in discrete memory engram (trace neurons within the dentate gyrus region of hippocampus and the layer 2/3 of neocortex. More strikingly, optogenetic reactivation of those memory trace neurons is able to trigger the recall of naturally encoded memory. It is still unknown how the discrete memory traces encode and reactivate the memory. Considering a particular memory normally represents a natural event, which consists of information at both the temporal and spatial domains, it is unknown how the discrete trace neurons could reconstitute such enriched information in the brain. Furthermore, as the optogenetic-stimuli induced recall of memory did not depend on firing pattern of the memory traces, it is most likely that the spatial activation pattern, but not the temporal activation pattern of the discrete memory trace neurons encodes the memory in the brain. How does the neural circuit convert the activities in the spatial domain into the temporal domain to reconstitute memory of a natural event? By reviewing the literature, here we present how the memory engram (trace neurons are selected and consolidated in the brain. Then, we will discuss the main challenges in the memory trace theory. In the end, we will provide a plausible model of memory trace cell network, underlying the conversion of neural activities between the spatial domain and the temporal domain. We will also discuss on how the activation of sparse memory trace neurons might trigger the replay of neural activities in specific temporal patterns.

  14. Modeling of asphalt by means of discrete element method – an initial study

    DEFF Research Database (Denmark)

    Feng, Huan; Hededal, Ole; Stang, Henrik

    of conducting time-consuming and lab-costly procedures. The use of numerical models, capable of reducing greatly the testing cost, has shown great potential in characterizing asphalt-aggregate mixtures for both material evaluation and structural design purposes, [1],[2]. Discrete element method (DEM) is one...... – will be applied. The work presented here will focus on the discrete element method as a tool for modelling composite materials, i.e. determination of a representative volume; boundary conditions; characterisation of the components mastic (binder + filler) and aggregates; and establishment of virtual test samples....... Results from initial tests will be presented and the future development of the model towards characterising asphalt from its composition will be outlined....

  15. Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

    International Nuclear Information System (INIS)

    Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

    2012-01-01

    We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms of the τ function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation. (paper)

  16. Estimation of Interchannel Time Difference in Frequency Subbands Based on Nonuniform Discrete Fourier Transform

    Directory of Open Access Journals (Sweden)

    Qiu Bo

    2008-01-01

    Full Text Available Binaural cue coding (BCC is an efficient technique for spatial audio rendering by using the side information such as interchannel level difference (ICLD, interchannel time difference (ICTD, and interchannel correlation (ICC. Of the side information, the ICTD plays an important role to the auditory spatial image. However, inaccurate estimation of the ICTD may lead to the audio quality degradation. In this paper, we develop a novel ICTD estimation algorithm based on the nonuniform discrete Fourier transform (NDFT and integrate it with the BCC approach to improve the decoded auditory image. Furthermore, a new subjective assessment method is proposed for the evaluation of auditory image widths of decoded signals. The test results demonstrate that the NDFT-based scheme can achieve much wider and more externalized auditory image than the existing BCC scheme based on the discrete Fourier transform (DFT. It is found that the present technique, regardless of the image width, does not deteriorate the sound quality at the decoder compared to the traditional scheme without ICTD estimation.

  17. A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

    Science.gov (United States)

    Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

    2017-09-01

    Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

  18. Dynamical barrier for the formation of solitary waves in discrete lattices

    International Nuclear Information System (INIS)

    Kevrekidis, P.G.; Espinola-Rocha, J.A.; Drossinos, Y.; Stefanov, A.

    2008-01-01

    We consider the problem of the existence of a dynamical barrier of 'mass' that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schroedinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. The existence of a sufficient condition for the excitation of localized modes in the non-integrable, discrete, nonlinear Schroedinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schroedinger equation

  19. Macular pigment spatial distribution effects on glare disability.

    Science.gov (United States)

    Putnam, Christopher M; Bassi, Carl J

    2015-01-01

    This project explored the relationship of the macular pigment optical density (MPOD) spatial profile with measures of glare disability (GD) across the macula. A novel device was used to measure MPOD across the central 16° of retina along four radii using customized heterochromatic flicker photometry (cHFP)at eccentricities of 0°, 2°, 4°, 6° and 8°. MPOD was measured as discrete and integrated values at all measured retinal loci. GD was calculated as a difference in contrast sensitivity (CS) between no glare and glare conditions using identical stimuli presented at the same eccentricities. GD was defined as [(CSNo Glare-CSGlare)/CSNo Glare] in order to isolate the glare attenuation effects of MPOD by controlling for CS variability among the subject sample. Correlations of the discrete and integrated MPOD with GD were compared. The cHFP identified reliable MPOD spatial distribution maps demonstrating a 1st-order exponential decay as a function of increasing eccentricity. There was a significant negative correlation between both measures of foveal MPOD and GD using 6 cycles per degree (cpd) and 9 cpd stimuli. Significant correlations were found between corresponding parafoveal MPOD measures and GD at 2 and 4° of eccentricity using 9 cpd stimuli with greater MPOD associated with less glare disability. These results are consistent with the glare attenuation effects of MP at higher spatial frequencies and support the hypothesis that discrete and integrated measures of MPOD have similar correlations with glare attenuation effects across the macula. Additionally, peak foveal MPOD appears to influence GD across the macula. Copyright © 2014 Spanish General Council of Optometry. Published by Elsevier Espana. All rights reserved.

  20. Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials

    International Nuclear Information System (INIS)

    Aquilanti, V; Marinelli, D; Marzuoli, A

    2014-01-01

    Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schrödinger–like equation which provides a semiclassical Hamiltonian picture of the evolution of a 'quantum of space', as shown by the authors in [1]. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed

  1. Implantable bladder volume sensor based on resistor ladder network composed of conductive hydrogel composite.

    Science.gov (United States)

    Mi Kyung Kim; Hyojung Kim; Jung, Yeon Su; Adem, Kenana M A; Bawazir, Sarah S; Stefanini, Cesare; Lee, Hyunjoo J

    2017-07-01

    An accurate bladder volume monitoring system is a critical component in diagnosis and treatment of urological disorders. Here, we report an implantable bladder volume sensor with a multi-level resistor ladder which estimates the bladder volume through discrete resistance values. Discretization allows the sensor output to be resilient to the long-term drift, hysteresis, and degradation of the sensor materials. Our sensor is composed of biocompatible polypyrrole/agarose hydrogel composite. Because Young's modulus of this composite is comparable to that of the bladder wall, the effect of mechanical loading of the sensor on the bladder movement is minimized which allows more accurate volume monitoring. We also demonstrate the patterning and molding capability of this material by fabrication various structures. Lastly, we successfully demonstrate the functionality of the multi-level resistor ladder sensor as a bladder volume sensor by attaching the sensor on the pig's bladder and observing the impedance change of the sensor.

  2. High-order discrete ordinate transport in hexagonal geometry: A new capability in ERANOS

    International Nuclear Information System (INIS)

    Le Tellier, R.; Suteau, C.; Fournier, D.; Ruggieri, J.M.

    2010-01-01

    This paper presents the implementation of an arbitrary order discontinuous Galerkin scheme within the framework of a discrete ordinate solver of the neutron transport equation for nuclear reactor calculations. More precisely, it deals with non-conforming spatial meshes for the 2 D and 3 D modeling of core geometries based on hexagonal assemblies. This work aims at improving the capabilities of the ERANOS code system dedicated to fast reactor analysis and design. Both the angular quadrature and spatial scheme peculiarities for hexagonal geometries are presented. A particular focus is set on the spatial non-conforming mesh and variable order capabilities of this scheme in anticipation to the development of spatial adaptiveness algorithms. These features are illustrated on a 3 D numerical benchmark with comparison to a Monte Carlo reference and a 2 D benchmark that shows the potential of this scheme for both h-and p-adaptation.

  3. A discrete exterior approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems

    NARCIS (Netherlands)

    Seslija, Marko; Scherpen, Jacquelien M.A.; van der Schaft, Arjan

    2011-01-01

    This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce simplicial Dirac structures as discrete analogues of the Stokes-Dirac structure and demonstrate

  4. Discrete integrable couplings associated with Toda-type lattice and two hierarchies of discrete soliton equations

    International Nuclear Information System (INIS)

    Zhang Yufeng; Fan Engui; Zhang Yongqing

    2006-01-01

    With the help of two semi-direct sum Lie algebras, an efficient way to construct discrete integrable couplings is proposed. As its applications, the discrete integrable couplings of the Toda-type lattice equations are obtained. The approach can be devoted to establishing other discrete integrable couplings of the discrete lattice integrable hierarchies of evolution equations

  5. Discrete exterior geometry approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems

    NARCIS (Netherlands)

    Seslija, Marko; van der Schaft, Arjan; Scherpen, Jacquelien M.A.

    This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a discrete analogue of the Stokes-Dirac structure and demonstrate

  6. a Novel Approach of Indexing and Retrieving Spatial Polygons for Efficient Spatial Region Queries

    Science.gov (United States)

    Zhao, J. H.; Wang, X. Z.; Wang, F. Y.; Shen, Z. H.; Zhou, Y. C.; Wang, Y. L.

    2017-10-01

    Spatial region queries are more and more widely used in web-based applications. Mechanisms to provide efficient query processing over geospatial data are essential. However, due to the massive geospatial data volume, heavy geometric computation, and high access concurrency, it is difficult to get response in real time. Spatial indexes are usually used in this situation. In this paper, based on k-d tree, we introduce a distributed KD-Tree (DKD-Tree) suitbable for polygon data, and a two-step query algorithm. The spatial index construction is recursive and iterative, and the query is an in memory process. Both the index and query methods can be processed in parallel, and are implemented based on HDFS, Spark and Redis. Experiments on a large volume of Remote Sensing images metadata have been carried out, and the advantages of our method are investigated by comparing with spatial region queries executed on PostgreSQL and PostGIS. Results show that our approach not only greatly improves the efficiency of spatial region query, but also has good scalability, Moreover, the two-step spatial range query algorithm can also save cluster resources to support a large number of concurrent queries. Therefore, this method is very useful when building large geographic information systems.

  7. A NOVEL APPROACH OF INDEXING AND RETRIEVING SPATIAL POLYGONS FOR EFFICIENT SPATIAL REGION QUERIES

    Directory of Open Access Journals (Sweden)

    J. H. Zhao

    2017-10-01

    Full Text Available Spatial region queries are more and more widely used in web-based applications. Mechanisms to provide efficient query processing over geospatial data are essential. However, due to the massive geospatial data volume, heavy geometric computation, and high access concurrency, it is difficult to get response in real time. Spatial indexes are usually used in this situation. In this paper, based on k-d tree, we introduce a distributed KD-Tree (DKD-Tree suitbable for polygon data, and a two-step query algorithm. The spatial index construction is recursive and iterative, and the query is an in memory process. Both the index and query methods can be processed in parallel, and are implemented based on HDFS, Spark and Redis. Experiments on a large volume of Remote Sensing images metadata have been carried out, and the advantages of our method are investigated by comparing with spatial region queries executed on PostgreSQL and PostGIS. Results show that our approach not only greatly improves the efficiency of spatial region query, but also has good scalability, Moreover, the two-step spatial range query algorithm can also save cluster resources to support a large number of concurrent queries. Therefore, this method is very useful when building large geographic information systems.

  8. Spectrum Control through Discrete Frequency Diffraction in the Presence of Photonic Gauge Potentials

    Science.gov (United States)

    Qin, Chengzhi; Zhou, Feng; Peng, Yugui; Sounas, Dimitrios; Zhu, Xuefeng; Wang, Bing; Dong, Jianji; Zhang, Xinliang; Alù; , Andrea; Lu, Peixiang

    2018-03-01

    By using optical phase modulators in a fiber-optical circuit, we theoretically and experimentally demonstrate large control over the spectrum of an impinging signal, which may evolve analogously to discrete diffraction in spatial waveguide arrays. The modulation phase acts as a photonic gauge potential in the frequency dimension, realizing efficient control of the central frequency and bandwidth of frequency combs. We experimentally achieve a 50 GHz frequency shift and threefold bandwidth expansion of an impinging comb, as well as the frequency analogue of various refraction phenomena, including negative refraction and perfect focusing in the frequency domain, both for discrete and continuous incident spectra. Our study paves a promising way towards versatile frequency management for optical communications and signal processing using time modulation schemes.

  9. Avoidance of transmission line pressure oscillations in discrete hydraulic systems – by shaping of valve opening characteristics

    DEFF Research Database (Denmark)

    Hansen, Anders Hedegaard; Pedersen, Henrik C.; Bech, Michael Møller

    2015-01-01

    The architecture of multi pressure line discrete fluid power force systems imposes rapid pressure shifts in the actuator volumes. These fast shifts between pressure levels often introduce pressure oscillations in the actuator chamber and connecting pipes. The topic of this paper is to perform...... pressure shifts by changing the connection between various fixed pressure lines without introducing significant pressure oscillation. As a case study a discrete force system is utilised is a Power Take Off(PTO) system of a wave energy converter. Four pressure shifting algorithms are proposed...

  10. Congruence Approximations for Entrophy Endowed Hyperbolic Systems

    Science.gov (United States)

    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.

  11. Scattering in discrete random media with implications to propagation through rain. Ph.D. Thesis George Washingtion Univ., Washington, D.C.

    Science.gov (United States)

    Ippolito, L. J., Jr.

    1977-01-01

    The multiple scattering effects on wave propagation through a volume of discrete scatterers were investigated. The mean field and intensity for a distribution of scatterers was developed using a discrete random media formulation, and second order series expansions for the mean field and total intensity derived for one-dimensional and three-dimensional configurations. The volume distribution results were shown to proceed directly from the one-dimensional results. The multiple scattering intensity expansion was compared to the classical single scattering intensity and the classical result was found to represent only the first three terms in the total intensity expansion. The Foldy approximation to the mean field was applied to develop the coherent intensity, and was found to exactly represent all coherent terms of the total intensity.

  12. On the Linear Stability of the Fifth-Order WENO Discretization

    KAUST Repository

    Motamed, Mohammad

    2010-10-03

    We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the forward Euler method or a two-stage, second-order Runge-Kutta method is linearly stable provided very small time step-sizes are taken. We also consider fifth-order multistep time discretizations whose stability domains do not include the imaginary axis. These are found to be linearly stable with moderate time steps when combined with WENO5. In particular, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis. © Springer Science+Business Media, LLC 2010.

  13. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2010-01-01

    The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...

  14. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2010-01-01

    The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...

  15. Two new discrete integrable systems

    International Nuclear Information System (INIS)

    Chen Xiao-Hong; Zhang Hong-Qing

    2013-01-01

    In this paper, we focus on the construction of new (1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra à 1 . By designing two new (1+1)-dimensional discrete spectral problems, two new discrete integrable systems are obtained, namely, a 2-field lattice hierarchy and a 3-field lattice hierarchy. When deriving the two new discrete integrable systems, we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy. Moreover, we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity

  16. Space-Time Discrete KPZ Equation

    Science.gov (United States)

    Cannizzaro, G.; Matetski, K.

    2018-03-01

    We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.

  17. Discrete density of states

    International Nuclear Information System (INIS)

    Aydin, Alhun; Sisman, Altug

    2016-01-01

    By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.

  18. Discrete ordinates transport methods for problems with highly forward-peaked scattering

    International Nuclear Information System (INIS)

    Pautz, S.D.

    1998-04-01

    The author examines the solutions of the discrete ordinates (S N ) method for problems with highly forward-peaked scattering kernels. He derives conditions necessary to obtain reasonable solutions in a certain forward-peaked limit, the Fokker-Planck (FP) limit. He also analyzes the acceleration of the iterative solution of such problems and offer improvements to it. He extends the analytic Fokker-Planck limit analysis to the S N equations. This analysis shows that in this asymptotic limit the S N solution satisfies a pseudospectral discretization of the FP equation, provided that the scattering term is handled in a certain way (which he describes) and that the analytic transport solution satisfies an analytic FP equation. Similar analyses of various spatially discretized S N equations reveal that they too produce solutions that satisfy discrete FP equations, given the same provisions. Numerical results agree with these theoretical predictions. He defines a multidimensional angular multigrid (ANMG) method to accelerate the iterative solution of highly forward-peaked problems. The analyses show that a straightforward application of this scheme is subject to high-frequency instabilities. However, by applying a diffusive filter to the ANMG corrections he is able to stabilize this method. Fourier analyses of model problems show that the resulting method is effective at accelerating the convergence rate when the scattering is forward-peaked. The numerical results demonstrate that these analyses are good predictors of the actual performance of the ANMG method

  19. Poisson hierarchy of discrete strings

    International Nuclear Information System (INIS)

    Ioannidou, Theodora; Niemi, Antti J.

    2016-01-01

    The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

  20. Poisson hierarchy of discrete strings

    Energy Technology Data Exchange (ETDEWEB)

    Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)

    2016-01-28

    The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

  1. Discrete energy formulation of neutron transport theory applied to solving the discrete ordinates equations

    International Nuclear Information System (INIS)

    Ching, J.; Oblow, E.M.; Goldstein, H.

    1976-01-01

    An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated that allows the development of a discrete energy, discrete ordinates method for the solution of radiation transport problems. In the discrete energy method, the group averaging required in the cross-section processing for multigroup calculations is replaced by a faster numerical quadrature scheme capable of generating transfer cross sections describing all the physical processes of interest on a fine point-energy grid. Test calculations in which the discrete energy method is compared with the multigroup method show that, for the same energy grid, the discrete energy method is much faster, although somewhat less accurate, than the multigroup method. However, the accuracy of the discrete energy method increases rapidly as the spacing between energy grid points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum, the discrete energy method is therefore expected to be far more economical than the multigroup technique for equivalent accuracy solutions. This advantage of the point method is demonstrated by application to the study of neutron transport in a thick iron slab

  2. 3-D Discrete Analytical Ridgelet Transform

    OpenAIRE

    Helbert , David; Carré , Philippe; Andrès , Éric

    2006-01-01

    International audience; In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines:...

  3. Discrete traits of the sternum and ribs: a useful contribution to identification in forensic anthropology and medicine.

    Science.gov (United States)

    Verna, Emeline; Piercecchi-Marti, Marie-Dominique; Chaumoitre, Kathia; Bartoli, Christophe; Leonetti, Georges; Adalian, Pascal

    2013-05-01

    During forensic anthropological investigation, biological profile is determined by age, sex, ancestry, and stature. However, several individuals may share the same profile. Observation of discrete traits can yield useful information and contribute to identification. This research establishes the frequency of discrete traits of the sternum and ribs in a modern population in southern France, using 500 computer tomography (CT) scans of individuals aged 15-60 years. Only discrete traits with a frequency lower than 10% according to the literature were considered, a total of eight traits. All scans examined were three-dimensional (3D) volume renderings from DICOM images. In our population, the frequency of all the discrete traits was lower than 5%. None were associated with sex or age, with the exception of a single trait, the end of the xiphoid process. Our findings can usefully be applied for identification purposes in forensic anthropology and medicine. © 2013 American Academy of Forensic Sciences.

  4. Quantum volume hologram

    International Nuclear Information System (INIS)

    Vasilyev, Denis V.; Sokolov, Ivan V.; Polzik, Eugene S.

    2010-01-01

    We propose a scheme for parallel spatially multimode quantum memory for light. The scheme is based on a counterpropagating quantum signal wave and a strong classical reference wave as in a classical volume hologram and therefore can be called a quantum volume hologram. The medium for the hologram consists of a spatially extended ensemble of atoms placed in a magnetic field. The write-in and readout of this quantum hologram is as simple as that of its classical counterpart and consists of a single-pass illumination. In addition, we show that the present scheme for a quantum hologram is less sensitive to diffraction and therefore is capable of achieving a higher density of storage of spatial modes as compared to previous proposals. We present a feasibility study and show that experimental implementation is possible with available cold atomic samples. A quantum hologram capable of storing entangled images can become an important ingredient in quantum information processing and quantum imaging.

  5. Discrete fractional calculus

    CERN Document Server

    Goodrich, Christopher

    2015-01-01

    This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...

  6. Chaotic properties between the nonintegrable discrete nonlinear Schroedinger equation and a nonintegrable discrete Heisenberg model

    International Nuclear Information System (INIS)

    Ding Qing

    2007-01-01

    We prove that the integrable-nonintegrable discrete nonlinear Schroedinger equation (AL-DNLS) introduced by Cai, Bishop and Gronbech-Jensen (Phys. Rev. Lett. 72 591(1994)) is the discrete gauge equivalent to an integrable-nonintegrable discrete Heisenberg model from the geometric point of view. Then we study whether the transmission and bifurcation properties of the AL-DNLS equation are preserved under the action of discrete gauge transformations. Our results reveal that the transmission property of the AL-DNLS equation is completely preserved and the bifurcation property is conditionally preserved to those of the integrable-nonintegrable discrete Heisenberg model

  7. An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids

    Science.gov (United States)

    English, R. Elliot; Qiu, Linhai; Yu, Yue; Fedkiw, Ronald

    2013-12-01

    We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we address separately through the development of a method for solving the heat diffusion equations. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. Internal curved boundaries such as at solid interfaces are handled using a simple immersed boundary approach which is directly applied to the Voronoi mesh in both the viscosity and pressure solves. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with stationary and moving solid bodies.

  8. Discrete density of states

    Energy Technology Data Exchange (ETDEWEB)

    Aydin, Alhun; Sisman, Altug, E-mail: sismanal@itu.edu.tr

    2016-03-22

    By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.

  9. Homogenization of discrete media

    International Nuclear Information System (INIS)

    Pradel, F.; Sab, K.

    1998-01-01

    Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.)

  10. Homogenization of discrete media

    Energy Technology Data Exchange (ETDEWEB)

    Pradel, F.; Sab, K. [CERAM-ENPC, Marne-la-Vallee (France)

    1998-11-01

    Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.) 7 refs.

  11. Dynamical barrier for the formation of solitary waves in discrete lattices

    Energy Technology Data Exchange (ETDEWEB)

    Kevrekidis, P.G. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003 (United States)], E-mail: kevrekid@math.umass.edu; Espinola-Rocha, J.A. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003 (United States); Drossinos, Y. [European Commission, Joint Research Centre, I-21020 Ispra (Vatican City State, Holy See,) (Italy); School of Mechanical and Systems Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU (United Kingdom); Stefanov, A. [Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd., Lawrence, KS 66045-7523 (United States)

    2008-03-24

    We consider the problem of the existence of a dynamical barrier of 'mass' that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schroedinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. The existence of a sufficient condition for the excitation of localized modes in the non-integrable, discrete, nonlinear Schroedinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schroedinger equation.

  12. sGD: software for estimating spatially explicit indices of genetic diversity.

    Science.gov (United States)

    Shirk, A J; Cushman, S A

    2011-09-01

    Anthropogenic landscape changes have greatly reduced the population size, range and migration rates of many terrestrial species. The small local effective population size of remnant populations favours loss of genetic diversity leading to reduced fitness and adaptive potential, and thus ultimately greater extinction risk. Accurately quantifying genetic diversity is therefore crucial to assessing the viability of small populations. Diversity indices are typically calculated from the multilocus genotypes of all individuals sampled within discretely defined habitat patches or larger regional extents. Importantly, discrete population approaches do not capture the clinal nature of populations genetically isolated by distance or landscape resistance. Here, we introduce spatial Genetic Diversity (sGD), a new spatially explicit tool to estimate genetic diversity based on grouping individuals into potentially overlapping genetic neighbourhoods that match the population structure, whether discrete or clinal. We compared the estimates and patterns of genetic diversity using patch or regional sampling and sGD on both simulated and empirical populations. When the population did not meet the assumptions of an island model, we found that patch and regional sampling generally overestimated local heterozygosity, inbreeding and allelic diversity. Moreover, sGD revealed fine-scale spatial heterogeneity in genetic diversity that was not evident with patch or regional sampling. These advantages should provide a more robust means to evaluate the potential for genetic factors to influence the viability of clinal populations and guide appropriate conservation plans. © 2011 Blackwell Publishing Ltd.

  13. Effective Spatial Dimension of Extremal Nondilatonic Black p-Branes and the Description on the World Volume

    International Nuclear Information System (INIS)

    Cai, R.

    1997-01-01

    By investigating the critical behavior appearing at the extremal limit of the nondilatonic, black p-branes in (d+p) dimensions, we find that some critical exponents related to the critical point obey the scaling laws. From the scaling laws we obtain that the effective spatial dimension of the nondilatonic black holes and black strings is one, and is p for the nondilatonic black p-branes. For the dilatonic black holes and black p-branes, the effective dimension will depend on the parameters in theories. Thus, we give an interpretation why the Bekenstein-Hawking entropy may be given a simple world volume interpretation only for the nondilatonic black p-branes. copyright 1997 The American Physical Society

  14. Discrete differential geometry. Consistency as integrability

    OpenAIRE

    Bobenko, Alexander I.; Suris, Yuri B.

    2005-01-01

    A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...

  15. Advances in discrete differential geometry

    CERN Document Server

    2016-01-01

    This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...

  16. Splitting Method for Solving the Coarse-Mesh Discretized Low-Order Quasi-Diffusion Equations

    International Nuclear Information System (INIS)

    Hiruta, Hikaru; Anistratov, Dmitriy Y.; Adams, Marvin L.

    2005-01-01

    In this paper, the development is presented of a splitting method that can efficiently solve coarse-mesh discretized low-order quasi-diffusion (LOQD) equations. The LOQD problem can reproduce exactly the transport scalar flux and current. To solve the LOQD equations efficiently, a splitting method is proposed. The presented method splits the LOQD problem into two parts: (a) the D problem that captures a significant part of the transport solution in the central parts of assemblies and can be reduced to a diffusion-type equation and (b) the Q problem that accounts for the complicated behavior of the transport solution near assembly boundaries. Independent coarse-mesh discretizations are applied: the D problem equations are approximated by means of a finite element method, whereas the Q problem equations are discretized using a finite volume method. Numerical results demonstrate the efficiency of the methodology presented. This methodology can be used to modify existing diffusion codes for full-core calculations (which already solve a version of the D problem) to account for transport effects

  17. Spatially Partitioned Embedded Runge--Kutta Methods

    KAUST Repository

    Ketcheson, David I.

    2013-10-30

    We study spatially partitioned embedded Runge--Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in space. We focus on embedded partitioned methods as they offer greater efficiency and avoid the order reduction that may occur in nonembedded schemes. We demonstrate that the lack of conservation in partitioned schemes can lead to nonphysical effects and propose conservative additive schemes based on partitioning the fluxes rather than the ordinary differential equations. A variety of SPERK schemes are presented, including an embedded pair suitable for the time evolution of fifth-order weighted nonoscillatory spatial discretizations. Numerical experiments are provided to support the theory.

  18. Spatially Partitioned Embedded Runge--Kutta Methods

    KAUST Repository

    Ketcheson, David I.; MacDonald, Colin B.; Ruuth, Steven J.

    2013-01-01

    We study spatially partitioned embedded Runge--Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in space. We focus on embedded partitioned methods as they offer greater efficiency and avoid the order reduction that may occur in nonembedded schemes. We demonstrate that the lack of conservation in partitioned schemes can lead to nonphysical effects and propose conservative additive schemes based on partitioning the fluxes rather than the ordinary differential equations. A variety of SPERK schemes are presented, including an embedded pair suitable for the time evolution of fifth-order weighted nonoscillatory spatial discretizations. Numerical experiments are provided to support the theory.

  19. The finite volume element (FVE) and multigrid method for the incompressible Navier-Stokes equations

    International Nuclear Information System (INIS)

    Gu Lizhen; Bao Weizhu

    1992-01-01

    The authors apply FVE method to discrete INS equations with the original variable, in which the bilinear square finite element and the square finite volume are chosen. The discrete schemes of INS equations are presented. The FMV multigrid algorithm is applied to solve that discrete system, where DGS iteration is used as smoother, DGS distributive mode for the INS discrete system is also presented. The sample problems for the square cavity flow with Reynolds number Re≤100 are successfully calculated. The numerical solutions show that the results with 1 FMV is satisfactory and when Re is not large, The FVE discrete scheme of the conservative INS equations and that of non-conservative INS equations with linearization both can provide almost same accuracy

  20. Discrete elements method of neutron transport

    International Nuclear Information System (INIS)

    Mathews, K.A.

    1988-01-01

    In this paper a new neutron transport method, called discrete elements (L N ) is derived and compared to discrete ordinates methods, theoretically and by numerical experimentation. The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The discrete elements method is shown to be more cost-effective than discrete ordinates, in terms of accuracy versus execution time and storage, for the cases tested. In a two-dimensional test case, a vacuum duct in a shield, the L N method is more consistently convergent toward a Monte Carlo benchmark solution

  1. Comparison of different precondtioners for nonsymmtric finite volume element methods

    Energy Technology Data Exchange (ETDEWEB)

    Mishev, I.D.

    1996-12-31

    We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.

  2. Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

    Science.gov (United States)

    LeMesurier, Brenton

    2012-01-01

    A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

  3. Zero of the discrete beta function in SU(3) lattice gauge theory with color sextet fermions

    International Nuclear Information System (INIS)

    Shamir, Yigal; Svetitsky, Benjamin; DeGrand, Thomas

    2008-01-01

    We have carried out a Schrodinger functional calculation for the SU(3) lattice gauge theory with two flavors of Wilson fermions in the sextet representation of the gauge group. We find that the discrete beta function, which governs the change in the running coupling under a discrete change of spatial scale, changes sign when the Schrodinger functional renormalized coupling is in the neighborhood of g 2 =2.0. The simplest explanation is that the theory has an infrared-attractive fixed point, but more complicated possibilities are allowed by the data. While we compare rescalings by factors of 2 and 4/3, we work at a single lattice spacing.

  4. Uncertainty modelling and analysis of volume calculations based on a regular grid digital elevation model (DEM)

    Science.gov (United States)

    Li, Chang; Wang, Qing; Shi, Wenzhong; Zhao, Sisi

    2018-05-01

    The accuracy of earthwork calculations that compute terrain volume is critical to digital terrain analysis (DTA). The uncertainties in volume calculations (VCs) based on a DEM are primarily related to three factors: 1) model error (ME), which is caused by an adopted algorithm for a VC model, 2) discrete error (DE), which is usually caused by DEM resolution and terrain complexity, and 3) propagation error (PE), which is caused by the variables' error. Based on these factors, the uncertainty modelling and analysis of VCs based on a regular grid DEM are investigated in this paper. Especially, how to quantify the uncertainty of VCs is proposed by a confidence interval based on truncation error (TE). In the experiments, the trapezoidal double rule (TDR) and Simpson's double rule (SDR) were used to calculate volume, where the TE is the major ME, and six simulated regular grid DEMs with different terrain complexity and resolution (i.e. DE) were generated by a Gauss synthetic surface to easily obtain the theoretical true value and eliminate the interference of data errors. For PE, Monte-Carlo simulation techniques and spatial autocorrelation were used to represent DEM uncertainty. This study can enrich uncertainty modelling and analysis-related theories of geographic information science.

  5. Pedestrian temporal and spatial gap acceptance at mid-block street crossing in developing world.

    Science.gov (United States)

    Pawar, Digvijay S; Patil, Gopal R

    2015-02-01

    Most of the midblock pedestrian crossings on urban roads in India are uncontrolled; wherein the high degree of discretion in pedestrians' behavior while crossing the traffic stream, has made the situation complex to analyze. Vehicles do not yield to pedestrians, even though the traffic laws give priority to pedestrians over motorized vehicles at unsignalized pedestrian crossings. Therefore, a pedestrian has to decide if an available gap is safe or not for crossing. This paper aims to investigate pedestrian temporal and spatial gap acceptance for midblock street crossings. Field data were collected using video camera at two midblock pedestrian crossings. The data extraction in laboratory resulted in 1107 pedestrian gaps. Available gaps, pedestrians' decision, traffic volume, etc. were extracted from the videos. While crossing a road with multiple lanes, rolling gap acceptance behavior was observed. Using binary logit analysis, six utility models were developed, three each for temporal and spatial gaps. The 50th percentile temporal and spatial gaps ranged from 4.1 to 4.8s and 67 to 79 m respectively, whereas the 85th percentile temporal and spatial gaps ranged from 5 to 5.8s and 82 to 95 m respectively. These gap values were smaller than that reported in the studies in developed countries. The speed of conflicting vehicle was found to be significant in spatial gap but not in temporal gap acceptance. The gap acceptance decision was also found to be affected by the type of conflicting vehicles. The insights from this study can be used for the safety and performance evaluation of uncontrolled midblock street crossings in developing countries. Copyright © 2014 Elsevier Ltd and National Safety Council. All rights reserved.

  6. Improved Discretization of Grounding Lines and Calving Fronts using an Embedded-Boundary Approach in BISICLES

    Science.gov (United States)

    Martin, D. F.; Cornford, S. L.; Schwartz, P.; Bhalla, A.; Johansen, H.; Ng, E.

    2017-12-01

    Correctly representing grounding line and calving-front dynamics is of fundamental importance in modeling marine ice sheets, since the configuration of these interfaces exerts a controlling influence on the dynamics of the ice sheet. Traditional ice sheet models have struggled to correctly represent these regions without very high spatial resolution. We have developed a front-tracking discretization for grounding lines and calving fronts based on the Chombo embedded-boundary cut-cell framework. This promises better representation of these interfaces vs. a traditional stair-step discretization on Cartesian meshes like those currently used in the block-structured AMR BISICLES code. The dynamic adaptivity of the BISICLES model complements the subgrid-scale discretizations of this scheme, producing a robust approach for tracking the evolution of these interfaces. Also, the fundamental discontinuous nature of flow across grounding lines is respected by mathematically treating it as a material phase change. We present examples of this approach to demonstrate its effectiveness.

  7. Discrete Sparse Coding.

    Science.gov (United States)

    Exarchakis, Georgios; Lücke, Jörg

    2017-11-01

    Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1) we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2) use image patches of natural images and discuss the role of the prior for the extraction of image components, (3) use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.

  8. Double-pass quantum volume hologram

    International Nuclear Information System (INIS)

    Vasilyev, Denis V.; Sokolov, Ivan V.

    2011-01-01

    We propose a scheme for parallel, spatially multimode quantum memory for light. The scheme is based on the propagation in different directions of a quantum signal wave and strong classical reference wave, like in a classical volume hologram and the previously proposed quantum volume hologram [D. V. Vasilyev et al., Phys. Rev. A 81, 020302(R) (2010)]. The medium for the hologram consists of a spatially extended ensemble of cold spin-polarized atoms. In the absence of the collective spin rotation during the interaction, two passes of light for both storage and retrieval are required, and therefore the present scheme can be called a double-pass quantum volume hologram. The scheme is less sensitive to diffraction and therefore is capable of achieving a higher density of storage of spatial modes as compared to the previously proposed thin quantum hologram [D. V. Vasilyev et al., Phys. Rev. A 77, 020302(R) (2008)], which also requires two passes of light for both storage and retrieval. However, the present scheme allows one to achieve a good memory performance with a lower optical depth of the atomic sample as compared to the quantum volume hologram. A quantum hologram capable of storing entangled images can become an important ingredient in quantum information processing and quantum imaging.

  9. A paradigm for discrete physics

    International Nuclear Information System (INIS)

    Noyes, H.P.; McGoveran, D.; Etter, T.; Manthey, M.J.; Gefwert, C.

    1987-01-01

    An example is outlined for constructing a discrete physics using as a starting point the insight from quantum physics that events are discrete, indivisible and non-local. Initial postulates are finiteness, discreteness, finite computability, absolute nonuniqueness (i.e., homogeneity in the absence of specific cause) and additivity

  10. Discrete-Event Simulation

    Directory of Open Access Journals (Sweden)

    Prateek Sharma

    2015-04-01

    Full Text Available Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of events in time. So this paper aims at introducing about Discrete-Event Simulation and analyzing how it is beneficial to the real world systems.

  11. Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site.

    Science.gov (United States)

    Jason, Peter; Johansson, Magnus

    2016-01-01

    We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.

  12. A discrete model of Ostwald ripening based on multiple pairwise interactions

    Science.gov (United States)

    Di Nunzio, Paolo Emilio

    2018-06-01

    A discrete multi-particle model of Ostwald ripening based on direct pairwise interactions is developed for particles with incoherent interfaces as an alternative to the classical LSW mean field theory. The rate of matter exchange depends on the average surface-to-surface interparticle distance, a characteristic feature of the system which naturally incorporates the effect of volume fraction of second phase. The multi-particle diffusion is described through the definition of an interaction volume containing all the particles involved in the exchange of solute. At small volume fractions this is proportional to the size of the central particle, at higher volume fractions it gradually reduces as a consequence of diffusion screening described on a geometrical basis. The topological noise present in real systems is also included. For volume fractions below about 0.1 the model predicts broad and right-skewed stationary size distributions resembling a lognormal function. Above this value, a transition to sharper, more symmetrical but still right-skewed shapes occurs. An excellent agreement with experiments is obtained for 3D particle size distributions of solid-solid and solid-liquid systems with volume fraction 0.07, 0.30, 0.52 and 0.74. The kinetic constant of the model depends on the cube root of volume fraction up to about 0.1, then increases rapidly with an upward concavity. It is in good agreement with the available literature data on solid-liquid mixtures in the volume fraction range from 0.20 to about 0.75.

  13. Discrete dynamics versus analytic dynamics

    DEFF Research Database (Denmark)

    Toxværd, Søren

    2014-01-01

    For discrete classical Molecular dynamics obtained by the “Verlet” algorithm (VA) with the time increment h there exists a shadow Hamiltonian H˜ with energy E˜(h) , for which the discrete particle positions lie on the analytic trajectories for H˜ . Here, we proof that there, independent...... of such an analytic analogy, exists an exact hidden energy invariance E * for VA dynamics. The fact that the discrete VA dynamics has the same invariances as Newtonian dynamics raises the question, which of the formulations that are correct, or alternatively, the most appropriate formulation of classical dynamics....... In this context the relation between the discrete VA dynamics and the (general) discrete dynamics investigated by Lee [Phys. Lett. B122, 217 (1983)] is presented and discussed....

  14. Volume of discrete brain structures in complex dissociative disorders : preliminary findings

    NARCIS (Netherlands)

    Ehling, T.; Nijenhuis, E. R. S.; Krikke, A. P.; DeKloet, ER; Vermetten, E

    2007-01-01

    Based on findings in traumatized animals and patients with posttraumatic stress disorder, and on traumatogenic models of complex dissociative disorders, it was hypothesized that (1) patients with complex dissociative disorders have smaller volumes of hippocampus, parahippocampal gyrus, and amygdala

  15. 3-D discrete analytical ridgelet transform.

    Science.gov (United States)

    Helbert, David; Carré, Philippe; Andres, Eric

    2006-12-01

    In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines: 3-D discrete radial lines going through the origin defined from their orthogonal projections and 3-D planes covered with 2-D discrete line segments. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a 3-D DART adapted to a specific application. Indeed, the 3-D DART representation is not orthogonal, It is associated with a flexible redundancy factor. The 3-D DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this new discrete transform, we apply the 3-D DART and its extension to the Local-DART (with smooth windowing) to the denoising of 3-D image and color video. These experimental results show that the simple thresholding of the 3-D DART coefficients is efficient.

  16. Analysis of Discrete Mittag - Leffler Functions

    Directory of Open Access Journals (Sweden)

    N. Shobanadevi

    2015-03-01

    Full Text Available Discrete Mittag - Leffler functions play a major role in the development of the theory of discrete fractional calculus. In the present article, we analyze qualitative properties of discrete Mittag - Leffler functions and establish sufficient conditions for convergence, oscillation and summability of the infinite series associated with discrete Mittag - Leffler functions.

  17. Associations between volume changes and spatial dose metrics for the urinary bladder during local versus pelvic irradiation for prostate cancer.

    Science.gov (United States)

    Casares-Magaz, Oscar; Moiseenko, Vitali; Hopper, Austin; Pettersson, Niclas Johan; Thor, Maria; Knopp, Rick; Deasy, Joseph O; Muren, Ludvig Paul; Einck, John

    2017-06-01

    Inter-fractional variation in urinary bladder volumes during the course of radiotherapy (RT) for prostate cancer causes deviations between planned and delivered doses. This study compared planned versus daily cone-beam CT (CBCT)-based spatial bladder dose distributions, for prostate cancer patients receiving local prostate treatment (local treatment) versus prostate including pelvic lymph node irradiation (pelvic treatment). Twenty-seven patients (N = 15 local treatment; N = 12 pelvic treatment) were treated using daily image-guided RT (1.8 Gy@43-45 fx), adhering to a full bladder/empty rectum protocol. For each patient, 9-10 CBCTs were registered to the planning CT, using the clinically applied translations. The urinary bladder was manually segmented on each CBCT, 3 mm inner shells were generated, and semi and quadrant sectors were created using axial/coronal cuts. Planned and delivered DVH metrics were compared across patients and between the two groups of treatment (t-test, p bladder volume variations and the dose-volume histograms (DVH) of the bladder and its sectors were evaluated (Spearman's rank correlation coefficient, r s ). Bladder volumes varied considerably during RT (coefficient of variation: 16-58%). The population-averaged planned and delivered DVH metrics were not significantly different at any dose level. Larger treatment bladder volumes resulted in increased absolute volume of the posterior/inferior bladder sector receiving intermediate-high doses, in both groups. The superior bladder sector received less dose with larger bladder volumes for local treatments (r s  ± SD: -0.47 ± 0.32), but larger doses for pelvic treatments (r s  ± SD: 0.74 ± 0.24). Substantial bladder volume changes during the treatment course occurred even though patients were treated under a full bladder/daily image-guided protocol. Larger bladder volumes resulted in less bladder wall spared at the posterior-inferior sector, regardless the

  18. Difference Discrete Variational Principles, Euler-Lagrange Cohomology and Symplectic, Multisymplectic Structures I: Difference Discrete Variational Principle

    Institute of Scientific and Technical Information of China (English)

    GUO Han-Ying,; LI Yu-Qi; WU Ke1; WANG Shi-Kun

    2002-01-01

    In this first paper of a series, we study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncommutative differential geometry. Regarding the difference as an entire geometric object, the difference discrete version of Legendre transformation can be introduced. By virtue of this variational principle, we can discretely deal with the variation problems in both the Lagrangian and Hamiltonian formalisms to get difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory.

  19. Influence of spatial discretization, underground water storage and glacier melt on a physically-based hydrological model of the Upper Durance River basin

    Science.gov (United States)

    Lafaysse, M.; Hingray, B.; Etchevers, P.; Martin, E.; Obled, C.

    2011-06-01

    SummaryThe SAFRAN-ISBA-MODCOU hydrological model ( Habets et al., 2008) presents severe limitations for alpine catchments. Here we propose possible model adaptations. For the catchment discretization, Relatively Homogeneous Hydrological Units (RHHUs) are used instead of the classical 8 km square grid. They are defined from the dilineation of hydrological subbasins, elevation bands, and aspect classes. Glacierized and non-glacierized areas are also treated separately. In addition, new modules are included in the model for the simulation of glacier melt, and retention of underground water. The improvement resulting from each model modification is analysed for the Upper Durance basin. RHHUs allow the model to better account for the high spatial variability of the hydrological processes (e.g. snow cover). The timing and the intensity of the spring snowmelt floods are significantly improved owing to the representation of water retention by aquifers. Despite the relatively small area covered by glaciers, accounting for glacier melt is necessary for simulating the late summer low flows. The modified model is robust over a long simulation period and it produces a good reproduction of the intra and interannual variability of discharge, which is a necessary condition for its application in a modified climate context.

  20. Discrete mechanics

    CERN Document Server

    Caltagirone, Jean-Paul

    2014-01-01

    This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling.  The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the H

  1. Discrete mechanics

    International Nuclear Information System (INIS)

    Lee, T.D.

    1985-01-01

    This paper reviews the role of time throughout all phases of mechanics: classical mechanics, non-relativistic quantum mechanics, and relativistic quantum theory. As an example of the relativistic quantum field theory, the case of a massless scalar field interacting with an arbitrary external current is discussed. The comparison between the new discrete theory and the usual continuum formalism is presented. An example is given of a two-dimensional random lattice and its duel. The author notes that there is no evidence that the discrete mechanics is more appropriate than the usual continuum mechanics

  2. A posteriori error estimator and AMR for discrete ordinates nodal transport methods

    International Nuclear Information System (INIS)

    Duo, Jose I.; Azmy, Yousry Y.; Zikatanov, Ludmil T.

    2009-01-01

    In the development of high fidelity transport solvers, optimization of the use of available computational resources and access to a tool for assessing quality of the solution are key to the success of large-scale nuclear systems' simulation. In this regard, error control provides the analyst with a confidence level in the numerical solution and enables for optimization of resources through Adaptive Mesh Refinement (AMR). In this paper, we derive an a posteriori error estimator based on the nodal solution of the Arbitrarily High Order Transport Method of the Nodal type (AHOT-N). Furthermore, by making assumptions on the regularity of the solution, we represent the error estimator as a function of computable volume and element-edges residuals. The global L 2 error norm is proved to be bound by the estimator. To lighten the computational load, we present a numerical approximation to the aforementioned residuals and split the global norm error estimator into local error indicators. These indicators are used to drive an AMR strategy for the spatial discretization. However, the indicators based on forward solution residuals alone do not bound the cell-wise error. The estimator and AMR strategy are tested in two problems featuring strong heterogeneity and highly transport streaming regime with strong flux gradients. The results show that the error estimator indeed bounds the global error norms and that the error indicator follows the cell-error's spatial distribution pattern closely. The AMR strategy proves beneficial to optimize resources, primarily by reducing the number of unknowns solved for to achieve prescribed solution accuracy in global L 2 error norm. Likewise, AMR achieves higher accuracy compared to uniform refinement when resolving sharp flux gradients, for the same number of unknowns

  3. Combined discrete nebulization and microextraction process for molybdenum determination by flame atomic absorption spectrometry (FAAS)

    International Nuclear Information System (INIS)

    Oviedo, Jenny A.; Jesus, Amanda M.D. de; Fialho, Lucimar L.; Pereira-Filho, Edenir R.

    2014-01-01

    Simple and sensitive procedures for the extraction/preconcentration of molybdenum based on vortex-assisted solidified floating organic drop microextraction (VA-SFODME) and cloud point combined with flame absorption atomic spectrometry (FAAS) and discrete nebulization were developed. The influence of the discrete nebulization on the sensitivity of the molybdenum preconcentration processes was studied. An injection volume of 200 μ resulted in a lower relative standard deviation with both preconcentration procedures. Enrichment factors of 31 and 67 and limits of detection of 25 and 5 μ L -1 were obtained for cloud point and VA-SFODME, respectively. The developed procedures were applied to the determination of Mo in mineral water and multivitamin samples. (author)

  4. An exact and consistent adjoint method for high-fidelity discretization of the compressible flow equations

    Science.gov (United States)

    Subramanian, Ramanathan Vishnampet Ganapathi

    , with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that its accuracy is limited only by computing precision, and we demonstrate it on the aeroacoustic control of a mixing layer with a challengingly broad range of turbulence scales. For comparison, the error from a corresponding discretization of the continuous-adjoint equations is quantified to potentially explain its limited success in past efforts to control jet noise. The differences are illuminating: the continuous-adjoint is shown to suffer from exponential error growth in (reverse) time even for the best-resolved largest turbulence scales. Though the gradient from our fully discrete adjoint is formally exact, it does include sensitivity to numerical solutions that are only an artifact of the discretization. These are typically saw-tooth type features, such as seen in under-resolved numerical simulations. Since these have no physical analog, for physical analysis or design of realistic actuators, such solutions are in a sense spurious. This has been addressed without sacrificing accuracy by redesigning the basic discretization to be dual-consistent, for which the discrete-adjoint is consistent with the adjoint of the continuous system, and thus, free from spurious numerical sensitivity modes. We extend our exact discrete-adjoint to a spatially dual-consistent discretization of the compressible flow equations and demonstrate its practical application for aeroacoustic control of a Mach 1.3 turbulent jet. The formulation admits a broad class of finite-difference schemes that satisfy a summation by-parts rule, and extends to multi-block curvilinear grids for efficient handling of complex geometries. The formulation is developed for several boundary conditions commonly used in simulation of free-shear and wall-bounded flows. In addition, the proposed discretization leads to superconvergent approximations of functionals

  5. Synchronization Techniques in Parallel Discrete Event Simulation

    OpenAIRE

    Lindén, Jonatan

    2018-01-01

    Discrete event simulation is an important tool for evaluating system models in many fields of science and engineering. To improve the performance of large-scale discrete event simulations, several techniques to parallelize discrete event simulation have been developed. In parallel discrete event simulation, the work of a single discrete event simulation is distributed over multiple processing elements. A key challenge in parallel discrete event simulation is to ensure that causally dependent ...

  6. Discrete-Feature Model Implementation of SDM-Site Forsmark

    Energy Technology Data Exchange (ETDEWEB)

    Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (United States))

    2010-03-15

    A discrete-feature model (DFM) was implemented for the Forsmark repository site based on the final site descriptive model from surface based investigations. The discrete-feature conceptual model represents deformation zones, individual fractures, and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which, in the present study, is treated as impermeable. This approximation is reasonable for sites in crystalline rock which has very low permeability, apart from that which results from macroscopic fracturing. Models are constructed based on the geological and hydrogeological description of the sites and engineering designs. Hydraulic heads and flows through the network of water-conducting features are calculated by the finite-element method, and are used in turn to simulate migration of non-reacting solute by a particle-tracking method, in order to estimate the properties of pathways by which radionuclides could be released to the biosphere. Stochastic simulation is used to evaluate portions of the model that can only be characterized in statistical terms, since many water-conducting features within the model volume cannot be characterized deterministically. Chapter 2 describes the methodology by which discrete features are derived to represent water-conducting features around the hypothetical repository at Forsmark (including both natural features and features that result from the disturbance of excavation), and then assembled to produce a discrete-feature network model for numerical simulation of flow and transport. Chapter 3 describes how site-specific data and repository design are adapted to produce the discrete-feature model. Chapter 4 presents results of the calculations. These include utilization factors for deposition tunnels based on the emplacement criteria that have been set forth by the implementers, flow distributions to the deposition holes, and calculated properties of discharge paths as well as

  7. Discrete-Feature Model Implementation of SDM-Site Forsmark

    International Nuclear Information System (INIS)

    Geier, Joel

    2010-03-01

    A discrete-feature model (DFM) was implemented for the Forsmark repository site based on the final site descriptive model from surface based investigations. The discrete-feature conceptual model represents deformation zones, individual fractures, and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which, in the present study, is treated as impermeable. This approximation is reasonable for sites in crystalline rock which has very low permeability, apart from that which results from macroscopic fracturing. Models are constructed based on the geological and hydrogeological description of the sites and engineering designs. Hydraulic heads and flows through the network of water-conducting features are calculated by the finite-element method, and are used in turn to simulate migration of non-reacting solute by a particle-tracking method, in order to estimate the properties of pathways by which radionuclides could be released to the biosphere. Stochastic simulation is used to evaluate portions of the model that can only be characterized in statistical terms, since many water-conducting features within the model volume cannot be characterized deterministically. Chapter 2 describes the methodology by which discrete features are derived to represent water-conducting features around the hypothetical repository at Forsmark (including both natural features and features that result from the disturbance of excavation), and then assembled to produce a discrete-feature network model for numerical simulation of flow and transport. Chapter 3 describes how site-specific data and repository design are adapted to produce the discrete-feature model. Chapter 4 presents results of the calculations. These include utilization factors for deposition tunnels based on the emplacement criteria that have been set forth by the implementers, flow distributions to the deposition holes, and calculated properties of discharge paths as well as

  8. Production Optimization of Oil Reservoirs

    DEFF Research Database (Denmark)

    Völcker, Carsten

    with emphasis on optimal control of water ooding with the use of smartwell technology. We have implemented immiscible ow of water and oil in isothermal reservoirs with isotropic heterogenous permeability elds. We use the method of lines for solution of the partial differential equation (PDE) system that governs...... the uid ow. We discretize the the two-phase ow model spatially using the nite volume method (FVM), and we use the two point ux approximation (TPFA) and the single-point upstream (SPU) scheme for computing the uxes. We propose a new formulation of the differential equation system that arise...... as a consequence of the spatial discretization of the two-phase ow model. Upon discretization in time, the proposed equation system ensures the mass conserving property of the two-phase ow model. For the solution of the spatially discretized two-phase ow model, we develop mass conserving explicit singly diagonally...

  9. Discrete gauge symmetries in discrete MSSM-like orientifolds

    International Nuclear Information System (INIS)

    Ibáñez, L.E.; Schellekens, A.N.; Uranga, A.M.

    2012-01-01

    Motivated by the necessity of discrete Z N symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)'s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1) factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)'s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1) and U(3)×Sp(2)×U(1)×U(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5) GUT models. We find examples of models with Z 2 (R-parity) and Z 3 symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.

  10. Darboux and binary Darboux transformations for discrete integrable systems I. Discrete potential KdV equation

    International Nuclear Information System (INIS)

    Shi, Ying; Zhang, Da-jun; Nimmo, Jonathan J C

    2014-01-01

    The Hirota–Miwa equation can be written in ‘nonlinear’ form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation. For both systems, we consider the Darboux and binary Darboux transformations, expressed in terms of the continuous variable, and obtain exact solutions in Wronskian and Grammian form. We discuss reductions of both systems to the discrete KdV and discrete potential KdV equation, respectively, and exploit this connection to find the Darboux and binary Darboux transformations and exact solutions of these equations. (paper)

  11. Finite Discrete Gabor Analysis

    DEFF Research Database (Denmark)

    Søndergaard, Peter Lempel

    2007-01-01

    frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... can also be related by sampling and periodization. This thesis extends on this theory by showing new results for window construction. It also provides a discussion of the problems associated to discrete Gabor bases. The sampling and periodization connection is handy because it allows Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...

  12. Adaptive Discrete Hypergraph Matching.

    Science.gov (United States)

    Yan, Junchi; Li, Changsheng; Li, Yin; Cao, Guitao

    2018-02-01

    This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.

  13. Principles of discrete time mechanics

    CERN Document Server

    Jaroszkiewicz, George

    2014-01-01

    Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, beginning with the historical, physical and mathematical background to the chronon hypothesis. Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.

  14. Discrete Calculus by Analogy

    CERN Document Server

    Izadi, F A; Bagirov, G

    2009-01-01

    With its origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology, especially in discrete mathematics, numerical analysis, statistics and probability theory as well as in electrical engineering, but our viewpoint here is that these topics belong to a much more general realm of mathematics; namely calculus and differential equations because of the remarkable analogy of the subject to this branch of mathemati

  15. Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves

    International Nuclear Information System (INIS)

    Feng Baofeng; Maruno, Ken-ichi; Inoguchi, Jun-ichi; Kajiwara, Kenji; Ohta, Yasuhiro

    2011-01-01

    We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sine-Gordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the Euler-Lagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations. (paper)

  16. Multiple and dependent scattering by densely packed discrete spheres: Comparison of radiative transfer and Maxwell theory

    International Nuclear Information System (INIS)

    Ma, L.X.; Tan, J.Y.; Zhao, J.M.; Wang, F.Q.; Wang, C.A.

    2017-01-01

    The radiative transfer equation (RTE) has been widely used to deal with multiple scattering of light by sparsely and randomly distributed discrete particles. However, for densely packed particles, the RTE becomes questionable due to strong dependent scattering effects. This paper examines the accuracy of RTE by comparing with the exact electromagnetic theory. For an imaginary spherical volume filled with randomly distributed, densely packed spheres, the RTE is solved by the Monte Carlo method combined with the Percus–Yevick hard model to consider the dependent scattering effect, while the electromagnetic calculation is based on the multi-sphere superposition T-matrix method. The Mueller matrix elements of the system with different size parameters and volume fractions of spheres are obtained using both methods. The results verify that the RTE fails to deal with the systems with a high-volume fraction due to the dependent scattering effects. Apart from the effects of forward interference scattering and coherent backscattering, the Percus–Yevick hard sphere model shows good accuracy in accounting for the far-field interference effects for medium or smaller size parameters (up to 6.964 in this study). For densely packed discrete spheres with large size parameters (equals 13.928 in this study), the improvement of dependent scattering correction tends to deteriorate. The observations indicate that caution must be taken when using RTE in dealing with the radiative transfer in dense discrete random media even though the dependent scattering correction is applied. - Highlights: • The Muller matrix of randomly distributed, densely packed spheres are investigated. • The effects of multiple scattering and dependent scattering are analyzed. • The accuracy of radiative transfer theory for densely packed spheres is discussed. • Dependent scattering correction takes effect at medium size parameter or smaller. • Performance of dependent scattering correction

  17. Modern approaches to discrete curvature

    CERN Document Server

    Romon, Pascal

    2017-01-01

     This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.

  18. Numerical electromagnetic frequency domain analysis with discrete exterior calculus

    Science.gov (United States)

    Chen, Shu C.; Chew, Weng Cho

    2017-12-01

    In this paper, we perform a numerical analysis in frequency domain for various electromagnetic problems based on discrete exterior calculus (DEC) with an arbitrary 2-D triangular or 3-D tetrahedral mesh. We formulate the governing equations in terms of DEC for 3-D and 2-D inhomogeneous structures, and also show that the charge continuity relation is naturally satisfied. Then we introduce a general construction for signed dual volume to incorporate material information and take into account the case when circumcenters fall outside triangles or tetrahedrons, which may lead to negative dual volume without Delaunay triangulation. Then we examine the boundary terms induced by the dual mesh and provide a systematical treatment of various boundary conditions, including perfect magnetic conductor (PMC), perfect electric conductor (PEC), Dirichlet, periodic, and absorbing boundary conditions (ABC) within this method. An excellent agreement is achieved through the numerical calculation of several problems, including homogeneous waveguides, microstructured fibers, photonic crystals, scattering by a 2-D PEC, and resonant cavities.

  19. Planning "discrete" movements using a continuous system: insights from a dynamic field theory of movement preparation.

    Science.gov (United States)

    Schutte, Anne R; Spencer, John P

    2007-04-01

    The timed-initiation paradigm developed by Ghez and colleagues (1997) has revealed two modes of motor planning: continuous and discrete. Continuous responding occurs when targets are separated by less than 60 degrees of spatial angle, and discrete responding occurs when targets are separated by greater than 60 degrees . Although these two modes are thought to reflect the operation of separable strategic planning systems, a new theory of movement preparation, the Dynamic Field Theory, suggests that two modes emerge flexibly from the same system. Experiment 1 replicated continuous and discrete performance using a task modified to allow for a critical test of the single system view. In Experiment 2, participants were allowed to correct their movements following movement initiation (the standard task does not allow corrections). Results showed continuous planning performance at large and small target separations. These results are consistent with the proposal that the two modes reflect the time-dependent "preshaping" of a single planning system.

  20. Noether symmetries of discrete mechanico–electrical systems

    International Nuclear Information System (INIS)

    Fu Jingli; Xie Fengping; Chen Benyong

    2008-01-01

    This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electrical systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange–Maxwell equations, the discrete analogue of Noether theorems for Lagrange–Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results. (general)

  1. High order backward discretization of the neutron diffusion equation

    Energy Technology Data Exchange (ETDEWEB)

    Ginestar, D.; Bru, R.; Marin, J. [Universidad Politecnica de Valencia (Spain). Departamento de Matematica Aplicada; Verdu, G.; Munoz-Cobo, J.L. [Universidad Politecnica de Valencia (Spain). Departamento de Ingenieria Quimica y Nuclear; Vidal, V. [Universidad Politecnica de Valencia (Spain). Departamento de Sistemas Informaticos y Computacion

    1997-11-21

    Fast codes capable of dealing with three-dimensional geometries, are needed to be able to simulate spatially complicated transients in a nuclear reactor. We propose a new discretization technique for the time integration of the neutron diffusion equation, based on the backward difference formulas for systems of stiff ordinary differential equations. This method needs to solve a system of linear equations for each integration step, and for this purpose, we have developed an iterative block algorithm combined with a variational acceleration technique. We tested the algorithm with two benchmark problems, and compared the results with those provided by other codes, concluding that the performance and overall agreement are very good. (author).

  2. Exact discretization of Schrödinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

    2016-01-08

    There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

  3. Exact discretization of Schrödinger equation

    International Nuclear Information System (INIS)

    Tarasov, Vasily E.

    2016-01-01

    There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

  4. Finite approximations in discrete-time stochastic control quantized models and asymptotic optimality

    CERN Document Server

    Saldi, Naci; Yüksel, Serdar

    2018-01-01

    In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original mo...

  5. Discrete Localized States and Localization Dynamics in Discrete Nonlinear Schrödinger Equations

    DEFF Research Database (Denmark)

    Christiansen, Peter Leth; Gaididei, Yu.B.; Mezentsev, V.K.

    1996-01-01

    Dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity is taken into account. Stability properties of the stationary solutions...

  6. Multi-dimensional, fully-implicit, spectral method for the Vlasov-Maxwell equations with exact conservation laws in discrete form

    Science.gov (United States)

    Delzanno, G. L.

    2015-11-01

    A spectral method for the numerical solution of the multi-dimensional Vlasov-Maxwell equations is presented. The plasma distribution function is expanded in Fourier (for the spatial part) and Hermite (for the velocity part) basis functions, leading to a truncated system of ordinary differential equations for the expansion coefficients (moments) that is discretized with an implicit, second order accurate Crank-Nicolson time discretization. The discrete non-linear system is solved with a preconditioned Jacobian-Free Newton-Krylov method. It is shown analytically that the Fourier-Hermite method features exact conservation laws for total mass, momentum and energy in discrete form. Standard tests involving plasma waves and the whistler instability confirm the validity of the conservation laws numerically. The whistler instability test also shows that we can step over the fastest time scale in the system without incurring in numerical instabilities. Some preconditioning strategies are presented, showing that the number of linear iterations of the Krylov solver can be drastically reduced and a significant gain in performance can be obtained.

  7. Cherenkov detectors for spatial imaging applications using discrete-energy photons

    Energy Technology Data Exchange (ETDEWEB)

    Rose, Paul B.; Erickson, Anna S., E-mail: erickson@gatech.edu [Georgia Institute of Technology, Nuclear and Radiological Engineering, G.W. Woodruff School of Mechanical Engineering, 770 State St., Atlanta, Georgia 30332 (United States)

    2016-08-14

    Cherenkov detectors can offer a significant advantage in spatial imaging applications when excellent timing response, low noise and cross talk, large area coverage, and the ability to operate in magnetic fields are required. We show that an array of Cherenkov detectors with crude energy resolution coupled with monochromatic photons resulting from a low-energy nuclear reaction can be used to produce a sharp image of material while providing large and inexpensive detector coverage. The analysis of the detector response to relative transmission of photons with various energies allows for reconstruction of material's effective atomic number further aiding in high-Z material identification.

  8. The spatial rotator

    DEFF Research Database (Denmark)

    Rasmusson, Allan; Hahn, Ute; Larsen, Jytte Overgaard

    2013-01-01

    This paper presents a new local volume estimator, the spatial rotator, which is based on measurements on a virtual 3D probe, using computer assisted microscopy. The basic design of the probe builds upon the rotator principle which requires only a few manual intersection markings, thus making...

  9. The discrete null space method for the energy-consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics

    International Nuclear Information System (INIS)

    Leyendecker, Sigrid; Betsch, Peter; Steinmann, Paul

    2008-01-01

    In the present work, the unified framework for the computational treatment of rigid bodies and nonlinear beams developed by Betsch and Steinmann (Multibody Syst. Dyn. 8, 367-391, 2002) is extended to the realm of nonlinear shells. In particular, a specific constrained formulation of shells is proposed which leads to the semi-discrete equations of motion characterized by a set of differential-algebraic equations (DAEs). The DAEs provide a uniform description for rigid bodies, semi-discrete beams and shells and, consequently, flexible multibody systems. The constraints may be divided into two classes: (i) internal constraints which are intimately connected with the assumption of rigidity of the bodies, and (ii) external constraints related to the presence of joints in a multibody framework. The present approach thus circumvents the use of rotational variables throughout the whole time discretization, facilitating the design of energy-momentum methods for flexible multibody dynamics. After the discretization has been completed a size-reduction of the discrete system is performed by eliminating the constraint forces. Numerical examples dealing with a spatial slider-crank mechanism and with intersecting shells illustrate the performance of the proposed method

  10. Predicted stand volume for Eucalyptus plantations by spatial analysis

    Science.gov (United States)

    Latifah, Siti; Teodoro, RV; Myrna, GC; Nathaniel, CB; Leonardo, M. F.

    2018-03-01

    The main objective of the present study was to assess nonlinear models generated by integrating the stand volume growth rate to estimate the growth and yield of Eucalyptus. The primary data was done for point of interest (POI) of permanent sample plots (PSPs) and inventory sample plots, in Aek Nauli sector, Simalungun regency,North Sumatera Province,Indonesia. from December 2008- March 2009. Today,the demand for forestry information has continued to grow over recent years. Because many forest managers and decision makers face complex decisions, reliable information has become the necessity. In the assessment of natural resources including plantation forests have been widely used geospatial technology.The yield of Eucalyptus plantations represented by merchantable volume as dependent variable while factors affecting yield namely stands variables and the geographic variables as independent variables. The majority of the areas in the study site has stand volume class 0 - 50 m3/ha with 16.59 ha or 65.85 % of the total study site.

  11. Observability of discretized partial differential equations

    Science.gov (United States)

    Cohn, Stephen E.; Dee, Dick P.

    1988-01-01

    It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.

  12. Delineating Facies Spatial Distribution by Integrating Ensemble Data Assimilation and Indicator Geostatistics with Level Set Transformation.

    Energy Technology Data Exchange (ETDEWEB)

    Hammond, Glenn Edward; Song, Xuehang; Ye, Ming; Dai, Zhenxue; Zachara, John; Chen, Xingyuan

    2017-03-01

    A new approach is developed to delineate the spatial distribution of discrete facies (geological units that have unique distributions of hydraulic, physical, and/or chemical properties) conditioned not only on direct data (measurements directly related to facies properties, e.g., grain size distribution obtained from borehole samples) but also on indirect data (observations indirectly related to facies distribution, e.g., hydraulic head and tracer concentration). Our method integrates for the first time ensemble data assimilation with traditional transition probability-based geostatistics. The concept of level set is introduced to build shape parameterization that allows transformation between discrete facies indicators and continuous random variables. The spatial structure of different facies is simulated by indicator models using conditioning points selected adaptively during the iterative process of data assimilation. To evaluate the new method, a two-dimensional semi-synthetic example is designed to estimate the spatial distribution and permeability of two distinct facies from transient head data induced by pumping tests. The example demonstrates that our new method adequately captures the spatial pattern of facies distribution by imposing spatial continuity through conditioning points. The new method also reproduces the overall response in hydraulic head field with better accuracy compared to data assimilation with no constraints on spatial continuity on facies.

  13. Discrete Mathematics Re "Tooled."

    Science.gov (United States)

    Grassl, Richard M.; Mingus, Tabitha T. Y.

    1999-01-01

    Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)

  14. Euler-Poincare reduction for discrete field theories

    International Nuclear Information System (INIS)

    Vankerschaver, Joris

    2007-01-01

    In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed

  15. Positivity for Convective Semi-discretizations

    KAUST Repository

    Fekete, Imre

    2017-04-19

    We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations of 1D scalar hyperbolic conservation laws. This technique is a generalization of the approach suggested in Khalsaraei (J Comput Appl Math 235(1): 137–143, 2010). We give more relaxed conditions on the time-step for positivity preservation for slope-limited semi-discretizations integrated in time with explicit Runge–Kutta methods. We show that the step-size restrictions derived are sharp in a certain sense, and that many higher-order explicit Runge–Kutta methods, including the classical 4th-order method and all non-confluent methods with a negative Butcher coefficient, cannot generally maintain positivity for these semi-discretizations under any positive step size. We also apply the proposed technique to centered finite difference discretizations of scalar hyperbolic and parabolic problems.

  16. Infrared images target detection based on background modeling in the discrete cosine domain

    Science.gov (United States)

    Ye, Han; Pei, Jihong

    2018-02-01

    Background modeling is the critical technology to detect the moving target for video surveillance. Most background modeling techniques are aimed at land monitoring and operated in the spatial domain. A background establishment becomes difficult when the scene is a complex fluctuating sea surface. In this paper, the background stability and separability between target are analyzed deeply in the discrete cosine transform (DCT) domain, on this basis, we propose a background modeling method. The proposed method models each frequency point as a single Gaussian model to represent background, and the target is extracted by suppressing the background coefficients. Experimental results show that our approach can establish an accurate background model for seawater, and the detection results outperform other background modeling methods in the spatial domain.

  17. A numerical simulation of wheel spray for simplified vehicle model based on discrete phase method

    Directory of Open Access Journals (Sweden)

    Xingjun Hu

    2015-07-01

    Full Text Available Road spray greatly affects vehicle body soiling and driving safety. The study of road spray has attracted increasing attention. In this article, computational fluid dynamics software with widely used finite volume method code was employed to investigate the numerical simulation of spray induced by a simplified wheel model and a modified square-back model proposed by the Motor Industry Research Association. Shear stress transport k-omega turbulence model, discrete phase model, and Eulerian wall-film model were selected. In the simulation process, the phenomenon of breakup and coalescence of drops were considered, and the continuous and discrete phases were treated as two-way coupled in momentum and turbulent motion. The relationship between the vehicle external flow structure and body soiling was also discussed.

  18. Integrable discretizations of the short pulse equation

    International Nuclear Information System (INIS)

    Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro

    2010-01-01

    In this paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key construction is the bilinear form and determinant structure of solutions of the SP equation. We also give the determinant formulas of N-soliton solutions of the semi-discrete and full-discrete analogues of the SP equations, from which the multi-loop and multi-breather solutions can be generated. In the continuous limit, the full-discrete SP equation converges to the semi-discrete SP equation, and then to the continuous SP equation. Based on the semi-discrete SP equation, an integrable numerical scheme, i.e. a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short pulse equation.

  19. Discrete computational structures

    CERN Document Server

    Korfhage, Robert R

    1974-01-01

    Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasize

  20. The quantitative modelling of human spatial habitability

    Science.gov (United States)

    Wise, James A.

    1988-01-01

    A theoretical model for evaluating human spatial habitability (HuSH) in the proposed U.S. Space Station is developed. Optimizing the fitness of the space station environment for human occupancy will help reduce environmental stress due to long-term isolation and confinement in its small habitable volume. The development of tools that operationalize the behavioral bases of spatial volume for visual kinesthetic, and social logic considerations is suggested. This report further calls for systematic scientific investigations of how much real and how much perceived volume people need in order to function normally and with minimal stress in space-based settings. The theoretical model presented in this report can be applied to any size or shape interior, at any scale of consideration, for the Space Station as a whole to an individual enclosure or work station. Using as a point of departure the Isovist model developed by Dr. Michael Benedikt of the U. of Texas, the report suggests that spatial habitability can become as amenable to careful assessment as engineering and life support concerns.

  1. Discrete integrable systems and deformations of associative algebras

    International Nuclear Information System (INIS)

    Konopelchenko, B G

    2009-01-01

    Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. Theory of deformations for associative algebras is presented. Closed left ideal generated by the elements representing the multiplication table plays a central role in this theory. Deformations of the structure constants are generated by the deformation driving algebra and governed by the central system of equations. It is demonstrated that many discrete equations such as discrete Boussinesq equation, discrete WDVV equation, discrete Schwarzian KP and BKP equations, discrete Hirota-Miwa equations for KP and BKP hierarchies are particular realizations of the central system. An interaction between the theories of discrete integrable systems and discrete deformations of associative algebras is reciprocal and fruitful. An interpretation of the Menelaus relation (discrete Schwarzian KP equation), discrete Hirota-Miwa equation for KP hierarchy, consistency around the cube as the associativity conditions and the concept of gauge equivalence, for instance, between the Menelaus and KP configurations are particular examples.

  2. Stochastic analysis in discrete and continuous settings with normal martingales

    CERN Document Server

    Privault, Nicolas

    2009-01-01

    This volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance.

  3. Discrete Surface Evolution and Mesh Deformation for Aircraft Icing Applications

    Science.gov (United States)

    Thompson, David; Tong, Xiaoling; Arnoldus, Qiuhan; Collins, Eric; McLaurin, David; Luke, Edward; Bidwell, Colin S.

    2013-01-01

    Robust, automated mesh generation for problems with deforming geometries, such as ice accreting on aerodynamic surfaces, remains a challenging problem. Here we describe a technique to deform a discrete surface as it evolves due to the accretion of ice. The surface evolution algorithm is based on a smoothed, face-offsetting approach. We also describe a fast algebraic technique to propagate the computed surface deformations into the surrounding volume mesh while maintaining geometric mesh quality. Preliminary results presented here demonstrate the ecacy of the approach for a sphere with a prescribed accretion rate, a rime ice accretion, and a more complex glaze ice accretion.

  4. Bit-string physics a finite and discrete approach to natural philosophy

    CERN Document Server

    Noyes, H Pierre

    2001-01-01

    We could be on the threshold of a scientific revolution. Quantum mechanics is based on unique, finite, and discrete events. General relativity assumes a continuous, curved space-time. Reconciling the two remains the most fundamental unsolved scientific problem left over from the last century. The papers of H Pierre Noyes collected in this volume reflect one attempt to achieve that unification by replacing the continuum with the bit-string events of computer science. Three principles are used: physics can determine whether two quantities are the same or different; measurement can tell something

  5. An Evaluation of Different Training Sample Allocation Schemes for Discrete and Continuous Land Cover Classification Using Decision Tree-Based Algorithms

    Directory of Open Access Journals (Sweden)

    René Roland Colditz

    2015-07-01

    Full Text Available Land cover mapping for large regions often employs satellite images of medium to coarse spatial resolution, which complicates mapping of discrete classes. Class memberships, which estimate the proportion of each class for every pixel, have been suggested as an alternative. This paper compares different strategies of training data allocation for discrete and continuous land cover mapping using classification and regression tree algorithms. In addition to measures of discrete and continuous map accuracy the correct estimation of the area is another important criteria. A subset of the 30 m national land cover dataset of 2006 (NLCD2006 of the United States was used as reference set to classify NADIR BRDF-adjusted surface reflectance time series of MODIS at 900 m spatial resolution. Results show that sampling of heterogeneous pixels and sample allocation according to the expected area of each class is best for classification trees. Regression trees for continuous land cover mapping should be trained with random allocation, and predictions should be normalized with a linear scaling function to correctly estimate the total area. From the tested algorithms random forest classification yields lower errors than boosted trees of C5.0, and Cubist shows higher accuracies than random forest regression.

  6. Continuum and discrete approach in modeling biofilm development and structure: a review.

    Science.gov (United States)

    Mattei, M R; Frunzo, L; D'Acunto, B; Pechaud, Y; Pirozzi, F; Esposito, G

    2018-03-01

    The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

  7. Geometry and Hamiltonian mechanics on discrete spaces

    International Nuclear Information System (INIS)

    Talasila, V; Clemente-Gallardo, J; Schaft, A J van der

    2004-01-01

    Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed

  8. Seasonal and spatial distribution of Bacterioplankton in a fluvial-lagunar system of a tropical region: density, biomass, cellular volume and morphologic variation

    Directory of Open Access Journals (Sweden)

    Magnólia Fernandes Florêncio de Araújo

    2008-02-01

    Full Text Available The temporal and spatial fluctuations of Bacterioplankton in a fluvial-lagunar system of a tropical region (Pitimbu River and Jiqui Lake, RN were studied during the dry and the rainy periods. The bacterial abundance varied from 2.67 to 5.1 Cells10(7mL-1 and did not show a typical temporal variation, presenting only small oscillations between the rainy and the dry periods. The bacterial biomass varied from 123 µgC L-1 to 269 µgC L-1 in the sampling sites and the average cellular volume varied from 0.12 to 0.54µm³, showing a predominance of the rods. The temperature showed a positive correlation with the cellular volume of the rods (R=0.55; p=0.02 and vibrio (R=0.53; p=0.03. Significant spatial differences of biomass (Mann Whitney: p=0.01 and cellular volume of the morphotypes (Mann Whitney: p=0.003 were found between the sampling sites. The strong positive correlations of the water temperature and oxygen with bacterioplankton showed a probable high bacterial activity in this system.A variação temporal e espacial do bacterioplâncton em um sistema fluvial-lagunar de região tropical foi estudada em períodos seco e chuvoso. As médias da abundância bacteriana variaram de 2,67 a 5,1 x 10(7 e não exibiram uma variação temporal marcante, tendo apresentado apenas pequenas oscilações entre os períodos chuvoso e seco. A biomassa bacteriana variou de 123 µg C L-1 a 269 µg C L-1 entre os locais de coleta e o volume celular médio de 0,12µm³ a 0,54µm³, ocorrendo predominância de bacilos. A temperatura mostrou correlação positiva com o volume celular de bacilos (R=0,55; p=0,02 e de vibriões (R=0,53; p=0,03. Foram encontradas diferenças espaciais significativas de biomassa (Mann Whitney: p=0,01 e volume celular dos morfotipos (Mann Whitney: p= 0,003, entre os locais de coleta. As fortes correlações positivas da temperatura da água e do oxigênio, com o bacterioplâncton, são sugestivas de uma provavelmente elevada atividade

  9. Spatial cluster modelling

    CERN Document Server

    Lawson, Andrew B

    2002-01-01

    Research has generated a number of advances in methods for spatial cluster modelling in recent years, particularly in the area of Bayesian cluster modelling. Along with these advances has come an explosion of interest in the potential applications of this work, especially in epidemiology and genome research. In one integrated volume, this book reviews the state-of-the-art in spatial clustering and spatial cluster modelling, bringing together research and applications previously scattered throughout the literature. It begins with an overview of the field, then presents a series of chapters that illuminate the nature and purpose of cluster modelling within different application areas, including astrophysics, epidemiology, ecology, and imaging. The focus then shifts to methods, with discussions on point and object process modelling, perfect sampling of cluster processes, partitioning in space and space-time, spatial and spatio-temporal process modelling, nonparametric methods for clustering, and spatio-temporal ...

  10. Integrable structure in discrete shell membrane theory.

    Science.gov (United States)

    Schief, W K

    2014-05-08

    We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory.

  11. Discrete port-Hamiltonian systems : mixed interconnections

    NARCIS (Netherlands)

    Talasila, Viswanath; Clemente-Gallardo, J.; Schaft, A.J. van der

    2005-01-01

    Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling

  12. Discrete diffusion Lyman α radiative transfer

    Science.gov (United States)

    Smith, Aaron; Tsang, Benny T.-H.; Bromm, Volker; Milosavljević, Miloš

    2018-06-01

    Due to its accuracy and generality, Monte Carlo radiative transfer (MCRT) has emerged as the prevalent method for Lyα radiative transfer in arbitrary geometries. The standard MCRT encounters a significant efficiency barrier in the high optical depth, diffusion regime. Multiple acceleration schemes have been developed to improve the efficiency of MCRT but the noise from photon packet discretization remains a challenge. The discrete diffusion Monte Carlo (DDMC) scheme has been successfully applied in state-of-the-art radiation hydrodynamics (RHD) simulations. Still, the established framework is not optimal for resonant line transfer. Inspired by the DDMC paradigm, we present a novel extension to resonant DDMC (rDDMC) in which diffusion in space and frequency are treated on equal footing. We explore the robustness of our new method and demonstrate a level of performance that justifies incorporating the method into existing Lyα codes. We present computational speedups of ˜102-106 relative to contemporary MCRT implementations with schemes that skip scattering in the core of the line profile. This is because the rDDMC runtime scales with the spatial and frequency resolution rather than the number of scatterings—the latter is typically ∝τ0 for static media, or ∝(aτ0)2/3 with core-skipping. We anticipate new frontiers in which on-the-fly Lyα radiative transfer calculations are feasible in 3D RHD. More generally, rDDMC is transferable to any computationally demanding problem amenable to a Fokker-Planck approximation of frequency redistribution.

  13. Discrete conservation laws and the convergence of long time simulations of the mkdv equation

    Science.gov (United States)

    Gorria, C.; Alejo, M. A.; Vega, L.

    2013-02-01

    Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solutions present a structural instability which make difficult to approximate their evolution in long time intervals with enough accuracy. The standard numerical methods do not guarantee the convergence to the proper solution of the initial value problem and often fail by approaching solutions associated to different initial conditions. In this frame the numerical schemes that preserve the discrete invariants related to some conservation laws of this equation produce better results than the methods which only take care of a high consistency order. Pseudospectral spatial discretization appear as the most robust of the numerical methods, but finite difference schemes are useful in order to analyze the rule played by the conservation of the invariants in the convergence.

  14. A low noise discrete velocity method for the Boltzmann equation with quantized rotational and vibrational energy

    Science.gov (United States)

    Clarke, Peter; Varghese, Philip; Goldstein, David

    2018-01-01

    A discrete velocity method is developed for gas mixtures of diatomic molecules with both rotational and vibrational energy states. A full quantized model is described, and rotation-translation and vibration-translation energy exchanges are simulated using a Larsen-Borgnakke exchange model. Elastic and inelastic molecular interactions are modeled during every simulated collision to help produce smooth internal energy distributions. The method is verified by comparing simulations of homogeneous relaxation by our discrete velocity method to numerical solutions of the Jeans and Landau-Teller equations, and to direct simulation Monte Carlo. We compute the structure of a 1D shock using this method, and determine how the rotational energy distribution varies with spatial location in the shock and with position in velocity space.

  15. IMA’s 2014-2015 Annual Thematic Program on Discrete Structures: Analysis and Applications

    CERN Document Server

    Madiman, Mokshay; Werner, Elisabeth

    2017-01-01

    This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute of Mathematics and its Applications during the Spring 2015 where geometric analysis, convex geometry and concentration phenomena were the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The volume is organized into two parts. Part I contains those contributions that focus primarily on problems motivated by probability theory, while Part II contains those contributions that focus primarily on problems motivated by convex geometry and geometric analysis. This book will be of use to those who research convex geometry, geometric analysis and probability directly or apply such methods in other fields.

  16. Channel-facilitated molecular transport: The role of strength and spatial distribution of interactions

    Energy Technology Data Exchange (ETDEWEB)

    Uppulury, Karthik, E-mail: karthik.uppulury@gmail.com [Department of Chemistry, Texas Tech University, Lubbock, TX 79409 (United States); Kolomeisky, Anatoly B. [Department of Chemistry, Department of Chemical and Biomolecular Engineering, Center for Theoretical Biological Physics, Rice University, Houston, TX 77005 (United States)

    2016-12-20

    Highlights: • Molecular flux strongly depends on the strength of the molecule-pore interactions. • There exists an optimal molecule-pore interaction potential for maximal flux. • Volume of interactions depends inversely on the strength for maximal flux. • Stronger interactions need more number of attractive sites for maximal flux. • Channels with few special sites need more attractive sites for higher flux. - Abstract: Molecular transport across channels and pores is critically important for multiple natural and industrial processes. Recent advances in single-molecule techniques have allowed researchers to probe translocation through nanopores with unprecedented spatial and temporal resolution. However, our understanding of the mechanisms of channel-facilitated molecular transport is still not complete. We present a theoretical approach that investigates the role of molecular interactions in the transport through channels. It is based on the discrete-state stochastic analysis that provides a fully analytical description of this complex process. It is found that a spatial distribution of the interactions strongly influences the translocation dynamics. We predict that there is the optimal distribution that leads to the maximal flux through the channel. It is also argued that the channel transport depends on the strength of the molecule-pore interactions, on the shape of interaction potentials and on the relative contributions of entrance and diffusion processes in the system. These observations are discussed using simple physical-chemical arguments.

  17. Channel-facilitated molecular transport: The role of strength and spatial distribution of interactions

    International Nuclear Information System (INIS)

    Uppulury, Karthik; Kolomeisky, Anatoly B.

    2016-01-01

    Highlights: • Molecular flux strongly depends on the strength of the molecule-pore interactions. • There exists an optimal molecule-pore interaction potential for maximal flux. • Volume of interactions depends inversely on the strength for maximal flux. • Stronger interactions need more number of attractive sites for maximal flux. • Channels with few special sites need more attractive sites for higher flux. - Abstract: Molecular transport across channels and pores is critically important for multiple natural and industrial processes. Recent advances in single-molecule techniques have allowed researchers to probe translocation through nanopores with unprecedented spatial and temporal resolution. However, our understanding of the mechanisms of channel-facilitated molecular transport is still not complete. We present a theoretical approach that investigates the role of molecular interactions in the transport through channels. It is based on the discrete-state stochastic analysis that provides a fully analytical description of this complex process. It is found that a spatial distribution of the interactions strongly influences the translocation dynamics. We predict that there is the optimal distribution that leads to the maximal flux through the channel. It is also argued that the channel transport depends on the strength of the molecule-pore interactions, on the shape of interaction potentials and on the relative contributions of entrance and diffusion processes in the system. These observations are discussed using simple physical-chemical arguments.

  18. Discrete Event Simulation of Patient Admissions to a Neurovascular Unit

    Directory of Open Access Journals (Sweden)

    S. Hahn-Goldberg

    2014-01-01

    Full Text Available Evidence exists that clinical outcomes improve for stroke patients admitted to specialized Stroke Units. The Toronto Western Hospital created a Neurovascular Unit (NVU using beds from general internal medicine, Neurology and Neurosurgery to care for patients with stroke and acute neurovascular conditions. Using patient-level data for NVU-eligible patients, a discrete event simulation was created to study changes in patient flow and length of stay pre- and post-NVU implementation. Varying patient volumes and resources were tested to determine the ideal number of beds under various conditions. In the first year of operation, the NVU admitted 507 patients, over 66% of NVU-eligible patient volumes. With the introduction of the NVU, length of stay decreased by around 8%. Scenario testing showed that the current level of 20 beds is sufficient for accommodating the current demand and would continue to be sufficient with an increase in demand of up to 20%.

  19. Cuspidal discrete series for projective hyperbolic spaces

    DEFF Research Database (Denmark)

    Andersen, Nils Byrial; Flensted-Jensen, Mogens

    2013-01-01

    Abstract. We have in [1] proposed a definition of cusp forms on semisimple symmetric spaces G/H, involving the notion of a Radon transform and a related Abel transform. For the real non-Riemannian hyperbolic spaces, we showed that there exists an infinite number of cuspidal discrete series......, and at most finitely many non-cuspidal discrete series, including in particular the spherical discrete series. For the projective spaces, the spherical discrete series are the only non-cuspidal discrete series. Below, we extend these results to the other hyperbolic spaces, and we also study the question...

  20. Discrete-Event Simulation

    OpenAIRE

    Prateek Sharma

    2015-01-01

    Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of ev...

  1. Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations

    Science.gov (United States)

    Vescovi, D.; Berzi, D.; Richard, P.; Brodu, N.

    2014-05-01

    We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature.

  2. Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations

    International Nuclear Information System (INIS)

    Vescovi, D.; Berzi, D.; Richard, P.; Brodu, N.

    2014-01-01

    We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature

  3. Positivity for Convective Semi-discretizations

    KAUST Repository

    Fekete, Imre; Ketcheson, David I.; Loczi, Lajos

    2017-01-01

    We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations

  4. Perfect discretization of reparametrization invariant path integrals

    International Nuclear Information System (INIS)

    Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian

    2011-01-01

    To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.

  5. Perfect discretization of reparametrization invariant path integrals

    Science.gov (United States)

    Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian

    2011-05-01

    To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.

  6. A proton therapy model using discrete difference equations with an example of treating hepatocellular carcinoma.

    Science.gov (United States)

    Bodine, Erin N; Monia, K Lars

    2017-08-01

    Proton therapy is a type of radiation therapy used to treat cancer. It provides more localized particle exposure than other types of radiotherapy (e.g., x-ray and electron) thus reducing damage to tissue surrounding a tumor and reducing unwanted side effects. We have developed a novel discrete difference equation model of the spatial and temporal dynamics of cancer and healthy cells before, during, and after the application of a proton therapy treatment course. Specifically, the model simulates the growth and diffusion of the cancer and healthy cells in and surrounding a tumor over one spatial dimension (tissue depth) and the treatment of the tumor with discrete bursts of proton radiation. We demonstrate how to use data from in vitro and clinical studies to parameterize the model. Specifically, we use data from studies of Hepatocellular carcinoma, a common form of liver cancer. Using the parameterized model we compare the ability of different clinically used treatment courses to control the tumor. Our results show that treatment courses which use conformal proton therapy (targeting the tumor from multiple angles) provides better control of the tumor while using lower treatment doses than a non-conformal treatment course, and thus should be recommend for use when feasible.

  7. Assessing the Suitability of Future Multi- and Hyperspectral Satellite Systems for Mapping the Spatial Distribution of Norway Spruce Timber Volume

    Directory of Open Access Journals (Sweden)

    Sascha Nink

    2015-09-01

    Full Text Available The availability of accurate and timely information on timber volume is important for supporting operational forest management. One option is to combine statistical concepts (e.g., small area estimates with specifically designed terrestrial sampling strategies to provide estimations also on the level of administrative units such as forest districts. This may suffice for economic assessments, but still fails to provide spatially explicit information on the distribution of timber volume within these management units. This type of information, however, is needed for decision-makers to design and implement appropriate management operations. The German federal state of Rhineland-Palatinate is currently implementing an object-oriented database that will also allow the direct integration of Earth observation data products. This work analyzes the suitability of forthcoming multi- and hyperspectral satellite imaging systems for producing local distribution maps for timber volume of Norway spruce, one of the most economically important tree species. In combination with site-specific inventory data, fully processed hyperspectral data sets (HyMap were used to simulate datasets of the forthcoming EnMAP and Sentinel-2 systems to establish adequate models for estimating timber volume maps. The analysis included PLS regression and the k-NN method. Root Mean Square Errors between 21.6% and 26.5% were obtained, where k-NN performed slightly better than PLSR. It was concluded that the datasets of both simulated sensor systems fulfill accuracy requirements to support local forest management operations and could be used in synergy. Sentinel-2 can provide meaningful volume distribution maps in higher geometric resolution, while EnMAP, due to its hyperspectral coverage, can contribute complementary information, e.g., on biophysical conditions.

  8. Discrete Curvature Theories and Applications

    KAUST Repository

    Sun, Xiang

    2016-08-25

    Discrete Di erential Geometry (DDG) concerns discrete counterparts of notions and methods in di erential geometry. This thesis deals with a core subject in DDG, discrete curvature theories on various types of polyhedral surfaces that are practically important for free-form architecture, sunlight-redirecting shading systems, and face recognition. Modeled as polyhedral surfaces, the shapes of free-form structures may have to satisfy di erent geometric or physical constraints. We study a combination of geometry and physics { the discrete surfaces that can stand on their own, as well as having proper shapes for the manufacture. These proper shapes, known as circular and conical meshes, are closely related to discrete principal curvatures. We study curvature theories that make such surfaces possible. Shading systems of freeform building skins are new types of energy-saving structures that can re-direct the sunlight. From these systems, discrete line congruences across polyhedral surfaces can be abstracted. We develop a new curvature theory for polyhedral surfaces equipped with normal congruences { a particular type of congruences de ned by linear interpolation of vertex normals. The main results are a discussion of various de nitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula. In addition to architecture, we consider the role of discrete curvatures in face recognition. We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold, which is an extension of the classical notion of asymptotic directions. We get a simple expression of these cones for polyhedral surfaces, as well as convergence and approximation theorems. We use the asymptotic cones as facial descriptors and demonstrate the

  9. Application of a discrete-energy, discrete-ordinates technique to the study of neutron transport in iron

    International Nuclear Information System (INIS)

    Ching, J.T.

    1975-01-01

    An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated which allows the development of a discrete-energy, discrete-ordinates method for the solution of radiation transport problems. The method utilizes a modified version of a cross section processing scheme devised for the moments method code BMT and the transport equation solution algorithm from the one-dimensional discrete-ordinates transport code ANISN. The combined system, identified as MOMANS, computes fluxes directly from point cross sections in a single operation. In the cross-section processing, the group averaging required for multigroup calculations is replaced by a fast numerical scheme capable of generating a set of transfer cross sections containing all the physical features of interest, thereby increasing the detail in the calculated results. Test calculations in which the discrete-energy method was compared with the multigroup method have shown that for the same energy grid (number of points = number of groups), the discrete-energy method is faster but somewhat less accurate than the multigroup method. However, the accuracy of the discrete-energy method increases rapidly as the spacing between energy points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum the discrete-energy method has therefore proven to be as accurate as, and more economical than, the multigroup technique. This was demonstrated by the application of the method to the study of the transport of neutrons in an iron sphere. Using the capability of the discrete-energy method for rapidly treating changes in cross-section sets, the propagation of neutrons from a 14 MeV source in a 22 cm radius sphere of iron was analyzed for sensitivity to changes in the microscopic scattering mechanisms

  10. Weak form of Stokes-Dirac structures and geometric discretization of port-Hamiltonian systems

    Science.gov (United States)

    Kotyczka, Paul; Maschke, Bernhard; Lefèvre, Laurent

    2018-05-01

    We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.

  11. Perfect discretization of path integrals

    International Nuclear Information System (INIS)

    Steinhaus, Sebastian

    2012-01-01

    In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.

  12. Perfect discretization of path integrals

    Science.gov (United States)

    Steinhaus, Sebastian

    2012-05-01

    In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.

  13. Combined spatial/angular domain decomposition SN algorithms for shared memory parallel machines

    International Nuclear Information System (INIS)

    Hunter, M.A.; Haghighat, A.

    1993-01-01

    Several parallel processing algorithms on the basis of spatial and angular domain decomposition methods are developed and incorporated into a two-dimensional discrete ordinates transport theory code. These algorithms divide the spatial and angular domains into independent subdomains so that the flux calculations within each subdomain can be processed simultaneously. Two spatial parallel algorithms (Block-Jacobi, red-black), one angular parallel algorithm (η-level), and their combinations are implemented on an eight processor CRAY Y-MP. Parallel performances of the algorithms are measured using a series of fixed source RZ geometry problems. Some of the results are also compared with those executed on an IBM 3090/600J machine. (orig.)

  14. 8th conference on Finite Volumes for Complex Applications

    CERN Document Server

    Omnes, Pascal

    2017-01-01

    This first volume of the proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017) covers various topics including convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers comparing advanced numerical methods for Stokes and Navier–Stokes equations on a benchmark, as well as reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods, offering a comprehensive overview of the state of the art in the field. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including m...

  15. A Finite-Volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction

    Science.gov (United States)

    Daude, F.; Galon, P.

    2018-06-01

    A Finite-Volume scheme for the numerical computations of compressible single- and two-phase flows in flexible pipelines is proposed based on an approximate Godunov-type approach. The spatial discretization is here obtained using the HLLC scheme. In addition, the numerical treatment of abrupt changes in area and network including several pipelines connected at junctions is also considered. The proposed approach is based on the integral form of the governing equations making it possible to tackle general equations of state. A coupled approach for the resolution of fluid-structure interaction of compressible fluid flowing in flexible pipes is considered. The structural problem is solved using Euler-Bernoulli beam finite elements. The present Finite-Volume method is applied to ideal gas and two-phase steam-water based on the Homogeneous Equilibrium Model (HEM) in conjunction with a tabulated equation of state in order to demonstrate its ability to tackle general equations of state. The extensive application of the scheme for both shock tube and other transient flow problems demonstrates its capability to resolve such problems accurately and robustly. Finally, the proposed 1-D fluid-structure interaction model appears to be computationally efficient.

  16. Control of Discrete Event Systems

    NARCIS (Netherlands)

    Smedinga, Rein

    1989-01-01

    Systemen met discrete gebeurtenissen spelen in vele gebieden een rol. In dit proefschrift staat de volgorde van gebeurtenissen centraal en worden tijdsaspecten buiten beschouwing gelaten. In dat geval kunnen systemen met discrete gebeurtenissen goed worden gemodelleerd door gebruik te maken van

  17. Connections on discrete fibre bundles

    International Nuclear Information System (INIS)

    Manton, N.S.; Cambridge Univ.

    1987-01-01

    A new approach to gauge fields on a discrete space-time is proposed, in which the fundamental object is a discrete version of a principal fibre bundle. If the bundle is twisted, the gauge fields are topologically non-trivial automatically. (orig.)

  18. An efficient permeability scaling-up technique applied to the discretized flow equations

    Energy Technology Data Exchange (ETDEWEB)

    Urgelli, D.; Ding, Yu [Institut Francais du Petrole, Rueil Malmaison (France)

    1997-08-01

    Grid-block permeability scaling-up for numerical reservoir simulations has been discussed for a long time in the literature. It is now recognized that a full permeability tensor is needed to get an accurate reservoir description at large scale. However, two major difficulties are encountered: (1) grid-block permeability cannot be properly defined because it depends on boundary conditions; (2) discretization of flow equations with a full permeability tensor is not straightforward and little work has been done on this subject. In this paper, we propose a new method, which allows us to get around both difficulties. As the two major problems are closely related, a global approach will preserve the accuracy. So, in the proposed method, the permeability up-scaling technique is integrated in the discretized numerical scheme for flow simulation. The permeability is scaled-up via the transmissibility term, in accordance with the fluid flow calculation in the numerical scheme. A finite-volume scheme is particularly studied, and the transmissibility scaling-up technique for this scheme is presented. Some numerical examples are tested for flow simulation. This new method is compared with some published numerical schemes for full permeability tensor discretization where the full permeability tensor is scaled-up through various techniques. Comparing the results with fine grid simulations shows that the new method is more accurate and more efficient.

  19. Time varying, multivariate volume data reduction

    Energy Technology Data Exchange (ETDEWEB)

    Ahrens, James P [Los Alamos National Laboratory; Fout, Nathaniel [UC DAVIS; Ma, Kwan - Liu [UC DAVIS

    2010-01-01

    Large-scale supercomputing is revolutionizing the way science is conducted. A growing challenge, however, is understanding the massive quantities of data produced by large-scale simulations. The data, typically time-varying, multivariate, and volumetric, can occupy from hundreds of gigabytes to several terabytes of storage space. Transferring and processing volume data of such sizes is prohibitively expensive and resource intensive. Although it may not be possible to entirely alleviate these problems, data compression should be considered as part of a viable solution, especially when the primary means of data analysis is volume rendering. In this paper we present our study of multivariate compression, which exploits correlations among related variables, for volume rendering. Two configurations for multidimensional compression based on vector quantization are examined. We emphasize quality reconstruction and interactive rendering, which leads us to a solution using graphics hardware to perform on-the-fly decompression during rendering. In this paper we present a solution which addresses the need for data reduction in large supercomputing environments where data resulting from simulations occupies tremendous amounts of storage. Our solution employs a lossy encoding scheme to acrueve data reduction with several options in terms of rate-distortion behavior. We focus on encoding of multiple variables together, with optional compression in space and time. The compressed volumes can be rendered directly with commodity graphics cards at interactive frame rates and rendering quality similar to that of static volume renderers. Compression results using a multivariate time-varying data set indicate that encoding multiple variables results in acceptable performance in the case of spatial and temporal encoding as compared to independent compression of variables. The relative performance of spatial vs. temporal compression is data dependent, although temporal compression has the

  20. Pediatric blood volumes: a one-page reference guide.

    Science.gov (United States)

    Smiley, J; Reitan, J

    1998-10-01

    At our institution, a multidisciplinary team met to work out a blood volume policy for our pediatric patients' laboratory testing. Because we are a cancer center, many of our patients are on protocols and/or are in the hospital for an extended period of time. These factors result in multiple blood draws. It is important to manage the volumes used so that we do not compromise the hematological status of our pediatric patients. The concerns of nurses and laboratory technologists were discussed and a three-tiered system was designed consisting of adult volumes, volumes for inflexibility to verify or add to the original order without resticking the patient increase at each tier. It is imperative to the overall quality of care for all patients that discretion is used when following these guidelines. When it is medically prudent to restrict the blood volumes taken from any patient, it should be done. However, when it is not medically necessary, the increased costs and potential decrease in the quality of laboratory service outweighs the desire to use smaller blood volumes.

  1. A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media

    KAUST Repository

    Saad, Bilal Mohammed; Saad, Mazen Naufal B M

    2014-01-01

    We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.

  2. A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media

    KAUST Repository

    Saad, Bilal Mohammed

    2014-06-28

    We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.

  3. Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation

    International Nuclear Information System (INIS)

    Common, Alan K; Hone, Andrew N W

    2008-01-01

    The Yablonskii-Vorob'ev polynomials y n (t), which are defined by a second-order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second Painleve equation (P II ). Here we define two-variable polynomials Y n (t, h) on a lattice with spacing h, by considering rational solutions of the discrete time Toda lattice as introduced by Suris. These polynomials are shown to have many properties that are analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce when h = 0. They also provide rational solutions for a particular discretization of P II , namely the so-called alternate discrete P II , and this connection leads to an expression in terms of the Umemura polynomials for the third Painleve equation (P III ). It is shown that the Baecklund transformation for the alternate discrete Painleve equation is a symplectic map, and the shift in time is also symplectic. Finally we present a Lax pair for the alternate discrete P II , which recovers Jimbo and Miwa's Lax pair for P II in the continuum limit h → 0

  4. A practical discrete-adjoint method for high-fidelity compressible turbulence simulations

    International Nuclear Information System (INIS)

    Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.

    2015-01-01

    Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that

  5. Handbook on modelling for discrete optimization

    CERN Document Server

    Pitsoulis, Leonidas; Williams, H

    2006-01-01

    The primary objective underlying the Handbook on Modelling for Discrete Optimization is to demonstrate and detail the pervasive nature of Discrete Optimization. While its applications cut across an incredibly wide range of activities, many of the applications are only known to specialists. It is the aim of this handbook to correct this. It has long been recognized that "modelling" is a critically important mathematical activity in designing algorithms for solving these discrete optimization problems. Nevertheless solving the resultant models is also often far from straightforward. In recent years it has become possible to solve many large-scale discrete optimization problems. However, some problems remain a challenge, even though advances in mathematical methods, hardware, and software technology have pushed the frontiers forward. This handbook couples the difficult, critical-thinking aspects of mathematical modeling with the hot area of discrete optimization. It will be done in an academic handbook treatment...

  6. Urbanisation and 3d Spatial - a Geometric Approach

    Science.gov (United States)

    Duncan, E. E.; Rahman, A. Abdul

    2013-09-01

    Urbanisation creates immense competition for space, this may be attributed to an increase in population owing to domestic and external tourism. Most cities are constantly exploring all avenues in maximising its limited space. Hence, urban or city authorities need to plan, expand and use such three dimensional (3D) space above, on and below the city space. Thus, difficulties in property ownership and the geometric representation of the 3D city space is a major challenge. This research, investigates the concept of representing a geometric topological 3D spatial model capable of representing 3D volume parcels for man-made constructions above and below the 3D surface volume parcel. A review of spatial data models suggests that the 3D TIN (TEN) model is significant and can be used as a unified model. The concepts, logical and physical models of 3D TIN for 3D volumes using tetrahedrons as the base geometry is presented and implemented to show man-made constructions above and below the surface parcel within a user friendly graphical interface. Concepts for 3D topology and 3D analysis are discussed. Simulations of this model for 3D cadastre are implemented. This model can be adopted by most countries to enhance and streamline geometric 3D property ownership for urban centres. 3D TIN concept for spatial modelling can be adopted for the LA_Spatial part of the Land Administration Domain Model (LADM) (ISO/TC211, 2012), this satisfies the concept of 3D volumes.

  7. On time discretizations for the simulation of the batch settling-compression process in one dimension.

    Science.gov (United States)

    Bürger, Raimund; Diehl, Stefan; Mejías, Camilo

    2016-01-01

    The main purpose of the recently introduced Bürger-Diehl simulation model for secondary settling tanks was to resolve spatial discretization problems when both hindered settling and the phenomena of compression and dispersion are included. Straightforward time integration unfortunately means long computational times. The next step in the development is to introduce and investigate time-integration methods for more efficient simulations, but where other aspects such as implementation complexity and robustness are equally considered. This is done for batch settling simulations. The key findings are partly a new time-discretization method and partly its comparison with other specially tailored and standard methods. Several advantages and disadvantages for each method are given. One conclusion is that the new linearly implicit method is easier to implement than another one (semi-implicit method), but less efficient based on two types of batch sedimentation tests.

  8. A coarse-mesh diffusion synthetic acceleration of the scattering source iteration scheme for one-speed slab-geometry discrete ordinates problems

    International Nuclear Information System (INIS)

    Santos, Frederico P.; Alves Filho, Hermes; Barros, Ricardo C.; Xavier, Vinicius S.

    2011-01-01

    The scattering source iterative (SI) scheme is traditionally applied to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S N ) neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as initial guess for the fine-mesh scattering source, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the classical S N prescribed boundary conditions, including vacuum boundary conditions. Therefore, we first implement a spectral nodal method that generates coarse-mesh diffusion solution that is completely free from spatial truncation errors, then we reconstruct this coarse-mesh solution within each spatial cell of the discretization grid, to further yield the initial guess for the fine-mesh scattering source in the first S N transport sweep (μm > 0 and μm < 0, m = 1:N) across the spatial grid. We consider a number of numerical experiments to illustrate the efficiency of the offered diffusion synthetic acceleration (DSA) technique. (author)

  9. Discrete Gabor transform and discrete Zak transform

    NARCIS (Netherlands)

    Bastiaans, M.J.; Namazi, N.M.; Matthews, K.

    1996-01-01

    Gabor's expansion of a discrete-time signal into a set of shifted and modulated versions of an elementary signal or synthesis window is introduced, along with the inverse operation, i.e. the Gabor transform, which uses an analysis window that is related to the synthesis window and with the help of

  10. Discrete Feature Model (DFM) User Documentation

    Energy Technology Data Exchange (ETDEWEB)

    Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (United States))

    2008-06-15

    This manual describes the Discrete-Feature Model (DFM) software package for modelling groundwater flow and solute transport in networks of discrete features. A discrete-feature conceptual model represents fractures and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which is usually treated as impermeable. This approximation may be valid for crystalline rocks such as granite or basalt, which have very low permeability if macroscopic fractures are excluded. A discrete feature is any entity that can conduct water and permit solute transport through bedrock, and can be reasonably represented as a piecewise-planar conductor. Examples of such entities may include individual natural fractures (joints or faults), fracture zones, and disturbed-zone features around tunnels (e.g. blasting-induced fractures or stress-concentration induced 'onion skin' fractures around underground openings). In a more abstract sense, the effectively discontinuous nature of pathways through fractured crystalline bedrock may be idealized as discrete, equivalent transmissive features that reproduce large-scale observations, even if the details of connective paths (and unconnected domains) are not precisely known. A discrete-feature model explicitly represents the fundamentally discontinuous and irregularly connected nature of systems of such systems, by constraining flow and transport to occur only within such features and their intersections. Pathways for flow and solute transport in this conceptualization are a consequence not just of the boundary conditions and hydrologic properties (as with continuum models), but also the irregularity of connections between conductive/transmissive features. The DFM software package described here is an extensible code for investigating problems of flow and transport in geological (natural or human-altered) systems that can be characterized effectively in terms of discrete features. With this

  11. Discrete Feature Model (DFM) User Documentation

    International Nuclear Information System (INIS)

    Geier, Joel

    2008-06-01

    This manual describes the Discrete-Feature Model (DFM) software package for modelling groundwater flow and solute transport in networks of discrete features. A discrete-feature conceptual model represents fractures and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which is usually treated as impermeable. This approximation may be valid for crystalline rocks such as granite or basalt, which have very low permeability if macroscopic fractures are excluded. A discrete feature is any entity that can conduct water and permit solute transport through bedrock, and can be reasonably represented as a piecewise-planar conductor. Examples of such entities may include individual natural fractures (joints or faults), fracture zones, and disturbed-zone features around tunnels (e.g. blasting-induced fractures or stress-concentration induced 'onion skin' fractures around underground openings). In a more abstract sense, the effectively discontinuous nature of pathways through fractured crystalline bedrock may be idealized as discrete, equivalent transmissive features that reproduce large-scale observations, even if the details of connective paths (and unconnected domains) are not precisely known. A discrete-feature model explicitly represents the fundamentally discontinuous and irregularly connected nature of systems of such systems, by constraining flow and transport to occur only within such features and their intersections. Pathways for flow and solute transport in this conceptualization are a consequence not just of the boundary conditions and hydrologic properties (as with continuum models), but also the irregularity of connections between conductive/transmissive features. The DFM software package described here is an extensible code for investigating problems of flow and transport in geological (natural or human-altered) systems that can be characterized effectively in terms of discrete features. With this software, the

  12. Distribution of the Discretization and Algebraic Error in Numerical Solution of Partial Differential Equations

    Czech Academy of Sciences Publication Activity Database

    Papež, Jan; Liesen, J.; Strakoš, Z.

    2014-01-01

    Roč. 449, 15 May (2014), s. 89-114 ISSN 0024-3795 R&D Projects: GA AV ČR IAA100300802; GA ČR GA201/09/0917 Grant - others:GA MŠk(CZ) LL1202; GA UK(CZ) 695612 Institutional support: RVO:67985807 Keywords : numerical solution of partial differential equations * finite element method * adaptivity * a posteriori error analysis * discretization error * algebra ic error * spatial distribution of the error Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014

  13. Sparse Jacobian construction for mapped grid visco-resistive magnetohydrodynamics

    KAUST Repository

    Reynolds, Daniel R.; Samtaney, Ravi

    2012-01-01

    employs a fully implicit formulation in time, and a mapped finite volume spatial discretization. We solve this model using inexact Newton-Krylov methods. Of critical importance in these iterative solvers is the development of an effective preconditioner

  14. Discrete-Time Biomedical Signal Encryption

    Directory of Open Access Journals (Sweden)

    Victor Grigoraş

    2017-12-01

    Full Text Available Chaotic modulation is a strong method of improving communication security. Analog and discrete chaotic systems are presented in actual literature. Due to the expansion of digital communication, discrete-time systems become more efficient and closer to actual technology. The present contribution offers an in-depth analysis of the effects chaos encryption produce on 1D and 2D biomedical signals. The performed simulations show that modulating signals are precisely recovered by the synchronizing receiver if discrete systems are digitally implemented and the coefficients precisely correspond. Channel noise is also applied and its effects on biomedical signal demodulation are highlighted.

  15. The origin of discrete particles

    CERN Document Server

    Bastin, T

    2009-01-01

    This book is a unique summary of the results of a long research project undertaken by the authors on discreteness in modern physics. In contrast with the usual expectation that discreteness is the result of mathematical tools for insertion into a continuous theory, this more basic treatment builds up the world from the discrimination of discrete entities. This gives an algebraic structure in which certain fixed numbers arise. As such, one agrees with the measured value of the fine-structure constant to one part in 10,000,000 (10 7 ). Sample Chapter(s). Foreword (56 KB). Chapter 1: Introduction

  16. Finite difference techniques for nonlinear hyperbolic conservation laws

    International Nuclear Information System (INIS)

    Sanders, R.

    1985-01-01

    The present study is concerned with numerical approximations to the initial value problem for nonlinear systems of conservative laws. Attention is given to the development of a class of conservation form finite difference schemes which are based on the finite volume method (i.e., the method of averages). These schemes do not fit into the classical framework of conservation form schemes discussed by Lax and Wendroff (1960). The finite volume schemes are specifically intended to approximate solutions of multidimensional problems in the absence of rectangular geometries. In addition, the development is reported of different schemes which utilize the finite volume approach for time discretization. Particular attention is given to local time discretization and moving spatial grids. 17 references

  17. Time-Discrete Higher-Order ALE Formulations: Stability

    KAUST Repository

    Bonito, Andrea; Kyza, Irene; Nochetto, Ricardo H.

    2013-01-01

    on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time

  18. Wayfinding in the Blind: Larger Hippocampal Volume and Supranormal Spatial Navigation

    Science.gov (United States)

    Fortin, Madeleine; Voss, Patrice; Lord, Catherine; Lassonde, Maryse; Pruessner, Jens; Saint-Amour, Dave; Rainville, Constant; Lepore, Franco

    2008-01-01

    In the absence of visual input, the question arises as to how complex spatial abilities develop and how the brain adapts to the absence of this modality. We explored navigational skills in both early and late blind individuals and structural differences in the hippocampus, a brain region well known to be involved in spatial processing.…

  19. Fermion systems in discrete space-time

    International Nuclear Information System (INIS)

    Finster, Felix

    2007-01-01

    Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure

  20. Fermion systems in discrete space-time

    Energy Technology Data Exchange (ETDEWEB)

    Finster, Felix [NWF I - Mathematik, Universitaet Regensburg, 93040 Regensburg (Germany)

    2007-05-15

    Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.

  1. Fermion Systems in Discrete Space-Time

    OpenAIRE

    Finster, Felix

    2006-01-01

    Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.

  2. Fermion systems in discrete space-time

    Science.gov (United States)

    Finster, Felix

    2007-05-01

    Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.

  3. Discrete ellipsoidal statistical BGK model and Burnett equations

    Science.gov (United States)

    Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua; Wang, Pei

    2018-06-01

    A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.

  4. SR 97 - Alternative models project. Discrete fracture network modelling for performance assessment of Aberg

    International Nuclear Information System (INIS)

    Dershowitz, B.; Eiben, T.; Follin, S.; Andersson, Johan

    1999-08-01

    As part of studies into the siting of a deep repository for nuclear waste, Swedish Nuclear Fuel and Waste Management Company (SKB) has commissioned the Alternative Models Project (AMP). The AMP is a comparison of three alternative modeling approaches for geosphere performance assessment for a single hypothetical site. The hypothetical site, arbitrarily named Aberg is based on parameters from the Aespoe Hard Rock Laboratory in southern Sweden. The Aberg model domain, boundary conditions and canister locations are defined as a common reference case to facilitate comparisons between approaches. This report presents the results of a discrete fracture pathways analysis of the Aberg site, within the context of the SR 97 performance assessment exercise. The Aberg discrete fracture network (DFN) site model is based on consensus Aberg parameters related to the Aespoe HRL site. Discrete fracture pathways are identified from canister locations in a prototype repository design to the surface of the island or to the sea bottom. The discrete fracture pathways analysis presented in this report is used to provide the following parameters for SKB's performance assessment transport codes FARF31 and COMP23: * F-factor: Flow wetted surface normalized with regards to flow rate (yields an appreciation of the contact area available for diffusion and sorption processes) [TL -1 ]. * Travel Time: Advective transport time from a canister location to the environmental discharge [T]. * Canister Flux: Darcy flux (flow rate per unit area) past a representative canister location [LT -1 ]. In addition to the above, the discrete fracture pathways analysis in this report also provides information about: additional pathway parameters such as pathway length, pathway width, transport aperture, reactive surface area and transmissivity, percentage of canister locations with pathways to the surface discharge, spatial pattern of pathways and pathway discharges, visualization of pathways, and statistical

  5. SR 97 - Alternative models project. Discrete fracture network modelling for performance assessment of Aberg

    Energy Technology Data Exchange (ETDEWEB)

    Dershowitz, B.; Eiben, T. [Golder Associates Inc., Seattle (United States); Follin, S.; Andersson, Johan [Golder Grundteknik KB, Stockholm (Sweden)

    1999-08-01

    As part of studies into the siting of a deep repository for nuclear waste, Swedish Nuclear Fuel and Waste Management Company (SKB) has commissioned the Alternative Models Project (AMP). The AMP is a comparison of three alternative modeling approaches for geosphere performance assessment for a single hypothetical site. The hypothetical site, arbitrarily named Aberg is based on parameters from the Aespoe Hard Rock Laboratory in southern Sweden. The Aberg model domain, boundary conditions and canister locations are defined as a common reference case to facilitate comparisons between approaches. This report presents the results of a discrete fracture pathways analysis of the Aberg site, within the context of the SR 97 performance assessment exercise. The Aberg discrete fracture network (DFN) site model is based on consensus Aberg parameters related to the Aespoe HRL site. Discrete fracture pathways are identified from canister locations in a prototype repository design to the surface of the island or to the sea bottom. The discrete fracture pathways analysis presented in this report is used to provide the following parameters for SKB's performance assessment transport codes FARF31 and COMP23: * F-factor: Flow wetted surface normalized with regards to flow rate (yields an appreciation of the contact area available for diffusion and sorption processes) [TL{sup -1}]. * Travel Time: Advective transport time from a canister location to the environmental discharge [T]. * Canister Flux: Darcy flux (flow rate per unit area) past a representative canister location [LT{sup -1}]. In addition to the above, the discrete fracture pathways analysis in this report also provides information about: additional pathway parameters such as pathway length, pathway width, transport aperture, reactive surface area and transmissivity, percentage of canister locations with pathways to the surface discharge, spatial pattern of pathways and pathway discharges, visualization of pathways, and

  6. Memorized discrete systems and time-delay

    CERN Document Server

    Luo, Albert C J

    2017-01-01

    This book examines discrete dynamical systems with memory—nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability and bifurcations of time-delay dynamical systems that can be investigated through memorized dynamical systems as well as bifurcations of memorized nonlinear dynamical systems, discretization methods of time-delay systems, and periodic motions to chaos in nonlinear time-delay systems. The book helps readers find analytical solutions of MDS, change traditional perturbation analysis in time-delay systems, detect motion complexity and singularity in MDS; and determine stability, bifurcation, and chaos in any time-delay system.

  7. Discrete Mathematics and Curriculum Reform.

    Science.gov (United States)

    Kenney, Margaret J.

    1996-01-01

    Defines discrete mathematics as the mathematics necessary to effect reasoned decision making in finite situations and explains how its use supports the current view of mathematics education. Discrete mathematics can be used by curriculum developers to improve the curriculum for students of all ages and abilities. (SLD)

  8. Multicriteria optimization of the spatial dose distribution

    International Nuclear Information System (INIS)

    Schlaefer, Alexander; Viulet, Tiberiu; Muacevic, Alexander; Fürweger, Christoph

    2013-01-01

    Purpose: Treatment planning for radiation therapy involves trade-offs with respect to different clinical goals. Typically, the dose distribution is evaluated based on few statistics and dose–volume histograms. Particularly for stereotactic treatments, the spatial dose distribution represents further criteria, e.g., when considering the gradient between subregions of volumes of interest. The authors have studied how to consider the spatial dose distribution using a multicriteria optimization approach.Methods: The authors have extended a stepwise multicriteria optimization approach to include criteria with respect to the local dose distribution. Based on a three-dimensional visualization of the dose the authors use a software tool allowing interaction with the dose distribution to map objectives with respect to its shape to a constrained optimization problem. Similarly, conflicting criteria are highlighted and the planner decides if and where to relax the shape of the dose distribution.Results: To demonstrate the potential of spatial multicriteria optimization, the tool was applied to a prostate and meningioma case. For the prostate case, local sparing of the rectal wall and shaping of a boost volume are achieved through local relaxations and while maintaining the remaining dose distribution. For the meningioma, target coverage is improved by compromising low dose conformality toward noncritical structures. A comparison of dose–volume histograms illustrates the importance of spatial information for achieving the trade-offs.Conclusions: The results show that it is possible to consider the location of conflicting criteria during treatment planning. Particularly, it is possible to conserve already achieved goals with respect to the dose distribution, to visualize potential trade-offs, and to relax constraints locally. Hence, the proposed approach facilitates a systematic exploration of the optimal shape of the dose distribution

  9. Exact analysis of discrete data

    CERN Document Server

    Hirji, Karim F

    2005-01-01

    Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...

  10. Solution algorithms for a PN-1 - Equivalent SN angular discretization of the transport equation in one-dimensional spherical coordinates

    International Nuclear Information System (INIS)

    Warsa, J. S.; Morel, J. E.

    2007-01-01

    Angular discretizations of the S N transport equation in curvilinear coordinate systems may result in a streaming-plus-removal operator that is dense in the angular variable or that is not lower-triangular. We investigate numerical solution algorithms for such angular discretizations using relationships given by Chandrasekhar to compute the angular derivatives in the one-dimensional S N transport equation in spherical coordinates with Gauss quadrature. This discretization makes the S N transport equation P N-1 - equivalent, but it also makes the sweep operator dense at every spatial point because the N angular derivatives are expressed in terms of the N angular fluxes. To avoid having to invert the sweep operator directly, we must work with the angular fluxes to solve the equations iteratively. We show how we can use approximations to the sweep operator to precondition the full P N-1 equivalent S N equations. We show that these pre-conditioners affect the operator enough such that convergence of a Krylov iterative method improves. (authors)

  11. On spatial coalescents with multiple mergers in two dimensions.

    Science.gov (United States)

    Heuer, Benjamin; Sturm, Anja

    2013-08-01

    We consider the genealogy of a sample of individuals taken from a spatially structured population when the variance of the offspring distribution is relatively large. The space is structured into discrete sites of a graph G. If the population size at each site is large, spatial coalescents with multiple mergers, so called spatial Λ-coalescents, for which ancestral lines migrate in space and coalesce according to some Λ-coalescent mechanism, are shown to be appropriate approximations to the genealogy of a sample of individuals. We then consider as the graph G the two dimensional torus with side length 2L+1 and show that as L tends to infinity, and time is rescaled appropriately, the partition structure of spatial Λ-coalescents of individuals sampled far enough apart converges to the partition structure of a non-spatial Kingman coalescent. From a biological point of view this means that in certain circumstances both the spatial structure as well as larger variances of the underlying offspring distribution are harder to detect from the sample. However, supplemental simulations show that for moderately large L the different structure is still evident. Copyright © 2012 Elsevier Inc. All rights reserved.

  12. Lévy matters IV estimation for discretely observed Lévy processes

    CERN Document Server

    Belomestny, Denis; Genon-Catalot, Valentine; Masuda, Hiroki; Reiß, Markus

    2015-01-01

    The aim of this volume is to provide an extensive account of the most recent advances in statistics for discretely observed Lévy processes. These days, statistics for stochastic processes is a lively topic, driven by the needs of various fields of application, such as finance, the biosciences, and telecommunication. The three chapters of this volume are completely dedicated to the estimation of Lévy processes, and are written by experts in the field. The first chapter by Denis Belomestny and Markus Reiß treats the low frequency situation, and estimation methods are based on the empirical characteristic function. The second chapter by Fabienne Comte and Valery Genon-Catalon is dedicated to non-parametric estimation mainly covering the high-frequency data case. A distinctive feature of this part is the construction of adaptive estimators, based on deconvolution or projection or kernel methods. The last chapter by Hiroki Masuda considers the parametric situation. The chapters cover the main aspects of the est...

  13. Improved stochastic approximation methods for discretized parabolic partial differential equations

    Science.gov (United States)

    Guiaş, Flavius

    2016-12-01

    We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).

  14. Discrete systems and integrability

    CERN Document Server

    Hietarinta, J; Nijhoff, F W

    2016-01-01

    This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thoroug...

  15. Development op finite volume methods for fluid dynamics; Developpement de methodes de volumes finis pour la mecanique des fluides

    Energy Technology Data Exchange (ETDEWEB)

    Delcourte, S

    2007-09-15

    We aim to develop a finite volume method which applies to a greater class of meshes than other finite volume methods, restricted by orthogonality constraints. We build discrete differential operators over the three staggered tessellations needed for the construction of the method. These operators verify some analogous properties to those of the continuous operators. At first, the method is applied to the Div-Curl problem, which can be viewed as a building block of the Stokes problem. Then, the Stokes problem is dealt with with various boundary conditions. It is well known that when the computational domain is polygonal and non-convex, the order of convergence of numerical methods is deteriorated. Consequently, we have studied how an appropriate local refinement is able to restore the optimal order of convergence for the Laplacian problem. At last, we have discretized the non-linear Navier-Stokes problem, using the rotational formulation of the convection term, associated to the Bernoulli pressure. With an iterative algorithm, we are led to solve a saddle-point problem at each iteration. We give a particular interest to this linear problem by testing some pre-conditioners issued from finite elements, which we adapt to our method. Each problem is illustrated by numerical results on arbitrary meshes, such as strongly non-conforming meshes. (author)

  16. Perspectives on spatial data analysis

    CERN Document Server

    Rey, Sergio

    2010-01-01

    This book takes both a retrospective and prospective view of the field of spatial analysis by combining selected reprints of classic articles by Arthur Getis with current observations by leading experts in the field. Four main aspects are highlighted, dealing with spatial analysis, pattern analysis, local statistics as well as illustrative empirical applications. Researchers and students will gain an appreciation of Getis' methodological contributions to spatial analysis and the broad impact of the methods he has helped pioneer on an impressively broad array of disciplines including spatial epidemiology, demography, economics, and ecology. The volume is a compilation of high impact original contributions, as evidenced by citations, and the latest thinking on the field by leading scholars. This makes the book ideal for advanced seminars and courses in spatial analysis as well as a key resource for researchers seeking a comprehensive overview of recent advances and future directions in the field.

  17. Discrete random walk models for space-time fractional diffusion

    International Nuclear Information System (INIS)

    Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo

    2002-01-01

    A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order α is part of (0,2] and skewness θ (moduleθ≤{α,2-α}), and the first-order time derivative with a Caputo derivative of order β is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation

  18. Airborne Lidar: Advances in Discrete Return Technology for 3D Vegetation Mapping

    Directory of Open Access Journals (Sweden)

    Valerie Ussyshkin

    2011-02-01

    Full Text Available Conventional discrete return airborne lidar systems, used in the commercial sector for efficient generation of high quality spatial data, have been considered for the past decade to be an ideal choice for various mapping applications. Unlike two-dimensional aerial imagery, the elevation component of airborne lidar data provides the ability to represent vertical structure details with very high precision, which is an advantage for many lidar applications focusing on the analysis of elevated features such as 3D vegetation mapping. However, the use of conventional airborne discrete return lidar systems for some of these applications has often been limited, mostly due to relatively coarse vertical resolution and insufficient number of multiple measurements in vertical domain. For this reason, full waveform airborne sensors providing more detailed representation of target vertical structure have often been considered as a preferable choice in some areas of 3D vegetation mapping application, such as forestry research. This paper presents an overview of the specific features of airborne lidar technology concerning 3D mapping applications, particularly vegetation mapping. Certain key performance characteristics of lidar sensors important for the quality of vegetation mapping are discussed and illustrated by the advanced capabilities of the ALTM-Orion, a new discrete return sensor manufactured by Optech Incorporated. It is demonstrated that advanced discrete return sensors with enhanced 3D mapping capabilities can produce data of enhanced quality, which can represent complex structures of vegetation targets at the level of details equivalent in some aspects to the content of full waveform data. It is also shown that recent advances in conventional airborne lidar technology bear the potential to create a new application niche, where high quality dense point clouds, enhanced by fully recorded intensity for multiple returns, may provide sufficient

  19. Discrete Painlevé equations: an integrability paradigm

    International Nuclear Information System (INIS)

    Grammaticos, B; Ramani, A

    2014-01-01

    In this paper we present a review of results on discrete Painlevé equations. We begin with an introduction which serves as a refresher on the continuous Painlevé equations. Next, in the first, main part of the paper, we introduce the discrete Painlevé equations, the various methods for their derivation, and their properties as well as their classification scheme. Along the way we present a brief summary of the two major discrete integrability detectors and of Quispel–Roberts–Thompson mapping, which plays a primordial role in the derivation of discrete Painlevé equations. The second part of the paper is more technical and focuses on the presentation of new results on what are called asymmetric discrete Painlevé equations. (comment)

  20. A linear multiple balance method for discrete ordinates neutron transport equations

    International Nuclear Information System (INIS)

    Park, Chang Je; Cho, Nam Zin

    2000-01-01

    A linear multiple balance method (LMB) is developed to provide more accurate and positive solutions for the discrete ordinates neutron transport equations. In this multiple balance approach, one mesh cell is divided into two subcells with quadratic approximation of angular flux distribution. Four multiple balance equations are used to relate center angular flux with average angular flux by Simpson's rule. From the analysis of spatial truncation error, the accuracy of the linear multiple balance scheme is ο(Δ 4 ) whereas that of diamond differencing is ο(Δ 2 ). To accelerate the linear multiple balance method, we also describe a simplified additive angular dependent rebalance factor scheme which combines a modified boundary projection acceleration scheme and the angular dependent rebalance factor acceleration schme. It is demonstrated, via fourier analysis of a simple model problem as well as numerical calculations, that the additive angular dependent rebalance factor acceleration scheme is unconditionally stable with spectral radius < 0.2069c (c being the scattering ration). The numerical results tested so far on slab-geometry discrete ordinates transport problems show that the solution method of linear multiple balance is effective and sufficiently efficient

  1. Discrete non-parametric kernel estimation for global sensitivity analysis

    International Nuclear Information System (INIS)

    Senga Kiessé, Tristan; Ventura, Anne

    2016-01-01

    This work investigates the discrete kernel approach for evaluating the contribution of the variance of discrete input variables to the variance of model output, via analysis of variance (ANOVA) decomposition. Until recently only the continuous kernel approach has been applied as a metamodeling approach within sensitivity analysis framework, for both discrete and continuous input variables. Now the discrete kernel estimation is known to be suitable for smoothing discrete functions. We present a discrete non-parametric kernel estimator of ANOVA decomposition of a given model. An estimator of sensitivity indices is also presented with its asymtotic convergence rate. Some simulations on a test function analysis and a real case study from agricultural have shown that the discrete kernel approach outperforms the continuous kernel one for evaluating the contribution of moderate or most influential discrete parameters to the model output. - Highlights: • We study a discrete kernel estimation for sensitivity analysis of a model. • A discrete kernel estimator of ANOVA decomposition of the model is presented. • Sensitivity indices are calculated for discrete input parameters. • An estimator of sensitivity indices is also presented with its convergence rate. • An application is realized for improving the reliability of environmental models.

  2. A coarse-mesh diffusion synthetic acceleration of the source iteration scheme for one-speed discrete ordinates transport calculations in Slab geometry

    International Nuclear Information System (INIS)

    Santos, Frederico P.; Xavier, Vinicius S.; Alves Filho, Hermes; Barros, Ricardo C.

    2011-01-01

    The scattering source iterative (SI) scheme is traditionally applied to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S N ) neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as initial guess for the fine-mesh scattering source, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the classical S N prescribed boundary conditions, including vacuum boundary conditions. Therefore, we first implement a spectral nodal method that generates coarse-mesh diffusion solution that is completely free from spatial truncation errors, then we reconstruct this coarse-mesh solution within each spatial cell of the discretization grid, to further yield the initial guess for the fine-mesh scattering source in the first S N transport sweep (μm > 0 and μm < 0, m = 1:N) across the spatial grid. We consider a number of numerical experiments to illustrate the efficiency of the offered diffusion synthetic acceleration (DSA) technique. (author)

  3. From the continuous PV to discrete Painleve equations

    International Nuclear Information System (INIS)

    Tokihiro, T.; Grammaticos, B.; Ramani, A.

    2002-01-01

    We study the discrete transformations that are associated with the auto-Baecklund of the (continuous) P V equation. We show that several two-parameter discrete Painleve equations can be obtained as contiguity relations of P V . Among them we find the asymmetric d-P II equation which is a well-known form of discrete P III . The relation between the ternary P I (previously obtained through the discrete dressing approach) and P V is also established. A new discrete Painleve equation is also derived. (author)

  4. A hybrid finite-volume and finite difference scheme for depth-integrated non-hydrostatic model

    Science.gov (United States)

    Yin, Jing; Sun, Jia-wen; Wang, Xing-gang; Yu, Yong-hai; Sun, Zhao-chen

    2017-06-01

    A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.

  5. A Multiscale Time-Splitting Discrete Fracture Model of Nanoparticles Transport in Fractured Porous Media

    KAUST Repository

    El-Amin, Mohamed F.; Kou, Jisheng; Sun, Shuyu

    2017-01-01

    Recently, applications of nanoparticles have been considered in many branches of petroleum engineering, especially, enhanced oil recovery. The current paper is devoted to investigate the problem of nanoparticles transport in fractured porous media, numerically. We employed the discrete-fracture model (DFM) to represent the flow and transport in the fractured formations. The system of the governing equations consists of the mass conservation law, Darcy's law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat. The variation of porosity and permeability due to the nanoparticles deposition/entrapment on/in the pores is also considered. We employ the multiscale time-splitting strategy to control different time-step sizes for different physics, such as pressure and concentration. The cell-centered finite difference (CCFD) method is used for the spatial discretization. Numerical examples are provided to demonstrate the efficiency of the proposed multiscale time splitting approach.

  6. A Multiscale Time-Splitting Discrete Fracture Model of Nanoparticles Transport in Fractured Porous Media

    KAUST Repository

    El-Amin, Mohamed F.

    2017-06-06

    Recently, applications of nanoparticles have been considered in many branches of petroleum engineering, especially, enhanced oil recovery. The current paper is devoted to investigate the problem of nanoparticles transport in fractured porous media, numerically. We employed the discrete-fracture model (DFM) to represent the flow and transport in the fractured formations. The system of the governing equations consists of the mass conservation law, Darcy\\'s law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat. The variation of porosity and permeability due to the nanoparticles deposition/entrapment on/in the pores is also considered. We employ the multiscale time-splitting strategy to control different time-step sizes for different physics, such as pressure and concentration. The cell-centered finite difference (CCFD) method is used for the spatial discretization. Numerical examples are provided to demonstrate the efficiency of the proposed multiscale time splitting approach.

  7. The analytical evolution of NLS solitons due to the numerical discretization error

    Science.gov (United States)

    Hoseini, S. M.; Marchant, T. R.

    2011-12-01

    Soliton perturbation theory is used to obtain analytical solutions describing solitary wave tails or shelves, due to numerical discretization error, for soliton solutions of the nonlinear Schrödinger equation. Two important implicit numerical schemes for the nonlinear Schrödinger equation, with second-order temporal and spatial discretization errors, are considered. These are the Crank-Nicolson scheme and a scheme, due to Taha [1], based on the inverse scattering transform. The first-order correction for the solitary wave tail, or shelf, is in integral form and an explicit expression is found for large time. The shelf decays slowly, at a rate of t^{-{1\\over 2}}, which is characteristic of the nonlinear Schrödinger equation. Singularity theory, usually used for combustion problems, is applied to the explicit large-time expression for the solitary wave tail. Analytical results are then obtained, such as the parameter regions in which qualitatively different types of solitary wave tails occur, the location of zeros and the location and amplitude of peaks. It is found that three different types of tail occur for the Crank-Nicolson and Taha schemes and that the Taha scheme exhibits some unusual symmetry properties, as the tails for left and right moving solitary waves are different. Optimal choices of the discretization parameters for the numerical schemes are also found, which minimize the amplitude of the solitary wave tail. The analytical solutions are compared with numerical simulations, and an excellent comparison is found.

  8. The analytical evolution of NLS solitons due to the numerical discretization error

    International Nuclear Information System (INIS)

    Hoseini, S M; Marchant, T R

    2011-01-01

    Soliton perturbation theory is used to obtain analytical solutions describing solitary wave tails or shelves, due to numerical discretization error, for soliton solutions of the nonlinear Schrödinger equation. Two important implicit numerical schemes for the nonlinear Schrödinger equation, with second-order temporal and spatial discretization errors, are considered. These are the Crank–Nicolson scheme and a scheme, due to Taha, based on the inverse scattering transform. The first-order correction for the solitary wave tail, or shelf, is in integral form and an explicit expression is found for large time. The shelf decays slowly, at a rate of t -1/2 , which is characteristic of the nonlinear Schrödinger equation. Singularity theory, usually used for combustion problems, is applied to the explicit large-time expression for the solitary wave tail. Analytical results are then obtained, such as the parameter regions in which qualitatively different types of solitary wave tails occur, the location of zeros and the location and amplitude of peaks. It is found that three different types of tail occur for the Crank–Nicolson and Taha schemes and that the Taha scheme exhibits some unusual symmetry properties, as the tails for left and right moving solitary waves are different. Optimal choices of the discretization parameters for the numerical schemes are also found, which minimize the amplitude of the solitary wave tail. The analytical solutions are compared with numerical simulations, and an excellent comparison is found. (paper)

  9. Discrete Routh reduction

    International Nuclear Information System (INIS)

    Jalnapurkar, Sameer M; Leok, Melvin; Marsden, Jerrold E; West, Matthew

    2006-01-01

    This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical J 2 correction, as well as the double spherical pendulum. The J 2 problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a non-trivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the non-canonical nature of the symplectic structure

  10. Foundations of a discrete physics

    International Nuclear Information System (INIS)

    McGoveran, D.; Noyes, P.

    1988-01-01

    Starting from the principles of finiteness, discreteness, finite computability and absolute nonuniqueness, we develop the ordering operator calculus, a strictly constructive mathematical system having the empirical properties required by quantum mechanical and special relativistic phenomena. We show how to construct discrete distance functions, and both rectangular and spherical coordinate systems(with a discrete version of ''π''). The richest discrete space constructible without a preferred axis and preserving translational and rotational invariance is shown to be a discrete 3-space with the usual symmetries. We introduce a local ordering parameter with local (proper) time-like properties and universal ordering parameters with global (cosmological) time-like properties. Constructed ''attribute velocities'' connect ensembles with attributes that are invariant as the appropriate time-like parameter increases. For each such attribute, we show how to construct attribute velocities which must satisfy the '' relativistic Doppler shift'' and the ''relativistic velocity composition law,'' as well as the Lorentz transformations. By construction, these velocities have finite maximum and minimum values. In the space of all attributes, the minimum of these maximum velocities will predominate in all multiple attribute computations, and hence can be identified as a fundamental limiting velocity, General commutation relations are constructed which under the physical interpretation are shown to reduce to the usual quantum mechanical commutation relations. 50 refs., 18 figs

  11. A Calderón multiplicative preconditioner for coupled surface-volume electric field integral equations

    KAUST Repository

    Bagci, Hakan; Andriulli, Francesco P.; Cools, Kristof; Olyslager, Femke; Michielssen, Eric

    2010-01-01

    A well-conditioned coupled set of surface (S) and volume (V) electric field integral equations (S-EFIE and V-EFIE) for analyzing wave interactions with densely discretized composite structures is presented. Whereas the V-EFIE operator is well

  12. Distributed mean curvature on a discrete manifold for Regge calculus

    International Nuclear Information System (INIS)

    Conboye, Rory; Miller, Warner A; Ray, Shannon

    2015-01-01

    The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector. (paper)

  13. Distributed mean curvature on a discrete manifold for Regge calculus

    Science.gov (United States)

    Conboye, Rory; Miller, Warner A.; Ray, Shannon

    2015-09-01

    The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector.

  14. Theoretical Basics of Teaching Discrete Mathematics

    Directory of Open Access Journals (Sweden)

    Y. A. Perminov

    2012-01-01

    Full Text Available  The paper deals with the research findings concerning the process of mastering the theoretical basics of discrete mathematics by the students of vocational pedagogic profile. The methodological analysis is based on the subject and functions of the modern discrete mathematics and its role in mathematical modeling and computing. The modern discrete mathematics (i.e. mathematics of the finite type structures plays the important role in modernization of vocational training. It is especially rele- vant to training students for vocational pedagogic qualifications, as in the future they will be responsible for training the middle and the senior level specialists in engineer- ing and technical spheres. Nowadays in different industries, there arise the problems which require for their solving both continual – based on the classical mathematical methods – and discrete modeling. The teaching course of discrete mathematics for the future vocational teachers should be relevant to the target qualification and aimed at mastering the mathematical modeling, systems of computer mathematics and computer technologies. The author emphasizes the fundamental role of mastering the language of algebraic and serial structures, as well as the logical, algorithmic, combinatory schemes dominating in dis- crete mathematics. The guidelines for selecting the content of the course in discrete mathematics are specified. The theoretical findings of the research can be put into practice whilst developing curricula and working programs for bachelors and masters’ training. 

  15. Discrete symmetries and their stringy origin

    International Nuclear Information System (INIS)

    Mayorga Pena, Damian Kaloni

    2014-05-01

    Discrete symmetries have proven to be very useful in controlling the phenomenology of theories beyond the standard model. In this work we explore how these symmetries emerge from string compactifications. Our approach is twofold: On the one hand, we consider the heterotic string on orbifold backgrounds. In this case the discrete symmetries can be derived from the orbifold conformal field theory, and it can be shown that they are in close relation with the orbifold geometry. We devote special attention to R-symmetries, which arise from discrete remnants of the Lorentz group in compact space. Further we discuss the physical implications of these symmetries both in the heterotic mini-landscape and in newly constructed models based on the Z 2 x Z 4 orbifold. In both cases we observe that the discrete symmetries favor particular locations in the orbifold where the particles of standard model should live. On the other hand we consider a class of F-theory models exhibiting an SU(5) gauge group, times additional U(1) symmetries. In this case, the smooth compactification background does not permit us to track the discrete symmetries as transparently as in orbifold models. Hence, we follow a different approach and search for discrete subgroups emerging after the U(1)s are broken. We observe that in this approach it is possible to obtain the standard Z 2 matter parity of the MSSM.

  16. Exterior difference systems and invariance properties of discrete mechanics

    International Nuclear Information System (INIS)

    Xie Zheng; Xie Duanqiang; Li Hongbo

    2008-01-01

    Invariance properties describe the fundamental physical laws in discrete mechanics. Can those properties be described in a geometric way? We investigate an exterior difference system called the discrete Euler-Lagrange system, whose solution has one-to-one correspondence with solutions of discrete Euler-Lagrange equations, and use it to define the first integrals. The preservation of the discrete symplectic form along the discrete Hamilton phase flows and the discrete Noether's theorem is also described in the language of difference forms

  17. Discrete breathers in graphane: Effect of temperature

    Energy Technology Data Exchange (ETDEWEB)

    Baimova, J. A., E-mail: julia.a.baimova@gmail.com [Russian Academy of Sciences, Institute of Metal Physics, Ural Branch (Russian Federation); Murzaev, R. T.; Lobzenko, I. P.; Dmitriev, S. V. [Russian Academy of Sciences, Institute for Metals Superplasticity Problems (Russian Federation); Zhou, Kun [Nanyang Technological University, School of Mechanical and Aerospace Engineering (Singapore)

    2016-05-15

    The discrete breathers in graphane in thermodynamic equilibrium in the temperature range 50–600 K are studied by molecular dynamics simulation. A discrete breather is a hydrogen atom vibrating along the normal to a sheet of graphane at a high amplitude. As was found earlier, the lifetime of a discrete breather at zero temperature corresponds to several tens of thousands of vibrations. The effect of temperature on the decay time of discrete breathers and the probability of their detachment from a sheet of graphane are studied in this work. It is shown that closely spaced breathers can exchange energy with each other at zero temperature. The data obtained suggest that thermally activated discrete breathers can be involved in the dehydrogenation of graphane, which is important for hydrogen energetics.

  18. Computational domain discretization in numerical analysis of flow within granular materials

    Science.gov (United States)

    Sosnowski, Marcin

    2018-06-01

    The discretization of computational domain is a crucial step in Computational Fluid Dynamics (CFD) because it influences not only the numerical stability of the analysed model but also the agreement of obtained results and real data. Modelling flow in packed beds of granular materials is a very challenging task in terms of discretization due to the existence of narrow spaces between spherical granules contacting tangentially in a single point. Standard approach to this issue results in a low quality mesh and unreliable results in consequence. Therefore the common method is to reduce the diameter of the modelled granules in order to eliminate the single-point contact between the individual granules. The drawback of such method is the adulteration of flow and contact heat resistance among others. Therefore an innovative method is proposed in the paper: single-point contact is extended to a cylinder-shaped volume contact. Such approach eliminates the low quality mesh elements and simultaneously introduces only slight distortion to the flow as well as contact heat transfer. The performed analysis of numerous test cases prove the great potential of the proposed method of meshing the packed beds of granular materials.

  19. An integrable semi-discretization of the Boussinesq equation

    International Nuclear Information System (INIS)

    Zhang, Yingnan; Tian, Lixin

    2016-01-01

    Highlights: • A new integrable semi-discretization of the Boussinesq equation is present. • A Bäcklund transformation and a Lax pair for the differential-difference system is derived by using Hirota's bilinear method. • The soliton solutions of 'good' Boussinesq equation and numerical algorithms are investigated. - Abstract: In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the ‘time’ variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Bäcklund transformation and a Lax pair of the differential-difference system. For the case of ‘good’ Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.

  20. Discretization of 3d gravity in different polarizations

    Science.gov (United States)

    Dupuis, Maïté; Freidel, Laurent; Girelli, Florian

    2017-10-01

    We study the discretization of three-dimensional gravity with Λ =0 following the loop quantum gravity framework. In the process, we realize that different choices of polarization are possible. This allows us to introduce a new discretization based on the triad as opposed to the connection as in the standard loop quantum gravity framework. We also identify the classical nontrivial symmetries of discrete gravity, namely the Drinfeld double, given in terms of momentum maps. Another choice of polarization is given by the Chern-Simons formulation of gravity. Our framework also provides a new discretization scheme of Chern-Simons, which keeps track of the link between the continuum variables and the discrete ones. We show how the Poisson bracket we recover between the Chern-Simons holonomies allows us to recover the Goldman bracket. There is also a transparent link between the discrete Chern-Simons formulation and the discretization of gravity based on the connection (loop gravity) or triad variables (dual loop gravity).

  1. Discrete fractional solutions of a Legendre equation

    Science.gov (United States)

    Yılmazer, Resat

    2018-01-01

    One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus has also an important position in fractional calculus. In this work, we acquire new discrete fractional solutions of the homogeneous and non homogeneous Legendre differential equation by using discrete fractional nabla operator.

  2. Discrete Mathematics and Its Applications

    Science.gov (United States)

    Oxley, Alan

    2010-01-01

    The article gives ideas that lecturers of undergraduate Discrete Mathematics courses can use in order to make the subject more interesting for students and encourage them to undertake further studies in the subject. It is possible to teach Discrete Mathematics with little or no reference to computing. However, students are more likely to be…

  3. Current density and continuity in discretized models

    International Nuclear Information System (INIS)

    Boykin, Timothy B; Luisier, Mathieu; Klimeck, Gerhard

    2010-01-01

    Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schroedinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying discrete models, students can encounter conceptual difficulties with the representation of the current and its divergence because different finite-difference expressions, all of which reduce to the current density in the continuous limit, measure different physical quantities. Understanding these different discrete currents is essential and requires a careful analysis of the current operator, the divergence of the current and the continuity equation. Here we develop point forms of the current and its divergence valid for an arbitrary mesh and basis. We show that in discrete models currents exist only along lines joining atomic sites (or mesh points). Using these results, we derive a discrete analogue of the divergence theorem and demonstrate probability conservation in a purely localized-basis approach.

  4. Discrete Calculus as a Bridge between Scales

    Science.gov (United States)

    Degiuli, Eric; McElwaine, Jim

    2012-02-01

    Understanding how continuum descriptions of disordered media emerge from the microscopic scale is a fundamental challenge in condensed matter physics. In many systems, it is necessary to coarse-grain balance equations at the microscopic scale to obtain macroscopic equations. We report development of an exact, discrete calculus, which allows identification of discrete microscopic equations with their continuum equivalent [1]. This allows the application of powerful techniques of calculus, such as the Helmholtz decomposition, the Divergence Theorem, and Stokes' Theorem. We illustrate our results with granular materials. In particular, we show how Newton's laws for a single grain reproduce their continuum equivalent in the calculus. This allows introduction of a discrete Airy stress function, exactly as in the continuum. As an application of the formalism, we show how these results give the natural mean-field variation of discrete quantities, in agreement with numerical simulations. The discrete calculus thus acts as a bridge between discrete microscale quantities and continuous macroscale quantities. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310

  5. A study of MRI gradient echo signals from discrete magnetic particles with considerations of several parameters in simulations.

    Science.gov (United States)

    Kokeny, Paul; Cheng, Yu-Chung N; Xie, He

    2018-05-01

    Modeling MRI signal behaviors in the presence of discrete magnetic particles is important, as magnetic particles appear in nanoparticle labeled cells, contrast agents, and other biological forms of iron. Currently, many models that take into account the discrete particle nature in a system have been used to predict magnitude signal decays in the form of R2* or R2' from one single voxel. Little work has been done for predicting phase signals. In addition, most calculations of phase signals rely on the assumption that a system containing discrete particles behaves as a continuous medium. In this work, numerical simulations are used to investigate MRI magnitude and phase signals from discrete particles, without diffusion effects. Factors such as particle size, number density, susceptibility, volume fraction, particle arrangements for their randomness, and field of view have been considered in simulations. The results are compared to either a ground truth model, theoretical work based on continuous mediums, or previous literature. Suitable parameters used to model particles in several voxels that lead to acceptable magnetic field distributions around particle surfaces and accurate MR signals are identified. The phase values as a function of echo time from a central voxel filled by particles can be significantly different from those of a continuous cubic medium. However, a completely random distribution of particles can lead to an R2' value which agrees with the prediction from the static dephasing theory. A sphere with a radius of at least 4 grid points used in simulations is found to be acceptable to generate MR signals equivalent from a larger sphere. Increasing number of particles with a fixed volume fraction in simulations reduces the resulting variance in the phase behavior, and converges to almost the same phase value for different particle numbers at each echo time. The variance of phase values is also reduced when increasing the number of particles in a fixed

  6. Integrals of Motion for Discrete-Time Optimal Control Problems

    OpenAIRE

    Torres, Delfim F. M.

    2003-01-01

    We obtain a discrete time analog of E. Noether's theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasi-invariance properties of the discrete time Lagrangian and discrete time control system. As corollaries, results for first-order and higher-order discrete problems of the calculus of variations are obtained.

  7. A spatial error model with continuous random effects and an application to growth convergence

    Science.gov (United States)

    Laurini, Márcio Poletti

    2017-10-01

    We propose a spatial error model with continuous random effects based on Matérn covariance functions and apply this model for the analysis of income convergence processes (β -convergence). The use of a model with continuous random effects permits a clearer visualization and interpretation of the spatial dependency patterns, avoids the problems of defining neighborhoods in spatial econometrics models, and allows projecting the spatial effects for every possible location in the continuous space, circumventing the existing aggregations in discrete lattice representations. We apply this model approach to analyze the economic growth of Brazilian municipalities between 1991 and 2010 using unconditional and conditional formulations and a spatiotemporal model of convergence. The results indicate that the estimated spatial random effects are consistent with the existence of income convergence clubs for Brazilian municipalities in this period.

  8. Further results on geometric operators in quantum gravity

    NARCIS (Netherlands)

    Loll, R.

    1996-01-01

    We investigate some properties of geometric operators in canonical quantum gravity in the connection approach `a la Ashtekar, which are associated with volume, area and length of spatial regions. We motivate the construction of analogous discretized lattice quantities, compute various quantum

  9. Effective Hamiltonian for travelling discrete breathers

    Science.gov (United States)

    MacKay, Robert S.; Sepulchre, Jacques-Alexandre

    2002-05-01

    Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.

  10. Mittag-Leffler function for discrete fractional modelling

    Directory of Open Access Journals (Sweden)

    Guo-Cheng Wu

    2016-01-01

    Full Text Available From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta’s sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function.

  11. Simplified discrete ordinates method in spherical geometry

    International Nuclear Information System (INIS)

    Elsawi, M.A.; Abdurrahman, N.M.; Yavuz, M.

    1999-01-01

    The authors extend the method of simplified discrete ordinates (SS N ) to spherical geometry. The motivation for such an extension is that the appearance of the angular derivative (redistribution) term in the spherical geometry transport equation makes it difficult to decide which differencing scheme best approximates this term. In the present method, the angular derivative term is treated implicitly and thus avoids the need for the approximation of such term. This method can be considered to be analytic in nature with the advantage of being free from spatial truncation errors from which most of the existing transport codes suffer. In addition, it treats the angular redistribution term implicitly with the advantage of avoiding approximations to that term. The method also can handle scattering in a very general manner with the advantage of spending almost the same computational effort for all scattering modes. Moreover, the methods can easily be applied to higher-order S N calculations

  12. Discrete/PWM Ballast-Resistor Controller

    Science.gov (United States)

    King, Roger J.

    1994-01-01

    Circuit offers low switching loss and automatic compensation for failure of ballast resistor. Discrete/PWM ballast-resistor controller improved shunt voltage-regulator circuit designed to supply power from high-resistance source to low-impedance bus. Provides both coarse discrete voltage levels (by switching of ballast resistors) and continuous fine control of voltage via pulse-width modulation.

  13. Discretization of four types of Weyl group orbit functions

    International Nuclear Information System (INIS)

    Hrivnák, Jiří

    2013-01-01

    The discrete Fourier calculus of the four families of special functions, called C–, S–, S s – and S l -functions, is summarized. Functions from each of the four families of special functions are discretely orthogonal over a certain finite set of points. The generalizations of discrete cosine and sine transforms of one variable — the discrete S s – and S l -transforms of the group F 4 — are considered in detail required for their exploitation in discrete Fourier spectral methods. The continuous interpolations, induced by the discrete expansions, are presented

  14. Faster-Than-Real-Time Simulation of Lithium Ion Batteries with Full Spatial and Temporal Resolution

    Directory of Open Access Journals (Sweden)

    Sandip Mazumder

    2013-01-01

    Full Text Available A one-dimensional coupled electrochemical-thermal model of a lithium ion battery with full temporal and normal-to-electrode spatial resolution is presented. Only a single pair of electrodes is considered in the model. It is shown that simulation of a lithium ion battery with the inclusion of detailed transport phenomena and electrochemistry is possible with faster-than-real-time compute times. The governing conservation equations of mass, charge, and energy are discretized using the finite volume method and solved using an iterative procedure. The model is first successfully validated against experimental data for both charge and discharge processes in a LixC6-LiyMn2O4 battery. Finally, it is demonstrated for an arbitrary rapidly changing transient load typical of a hybrid electric vehicle drive cycle. The model is able to predict the cell voltage of a 15-minute drive cycle in less than 12 seconds of compute time on a laptop with a 2.33 GHz Intel Pentium 4 processor.

  15. On organizing principles of discrete differential geometry. Geometry of spheres

    International Nuclear Information System (INIS)

    Bobenko, Alexander I; Suris, Yury B

    2007-01-01

    Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.

  16. Reaction-Transport Systems Mesoscopic Foundations, Fronts, and Spatial Instabilities

    CERN Document Server

    Horsthemke, Werner; Mendez, Vicenc

    2010-01-01

    This book is an introduction to the dynamics of reaction-diffusion systems, with a focus on fronts and stationary spatial patterns. Emphasis is on systems that are non-standard in the sense that either the transport is not simply classical diffusion (Brownian motion) or the system is not homogeneous. A important feature is the derivation of the basic phenomenological equations from the mesoscopic system properties. Topics addressed include transport with inertia, described by persistent random walks and hyperbolic reaction-transport equations and transport by anomalous diffusion, in particular subdiffusion, where the mean square displacement grows sublinearly with time. In particular reaction-diffusion systems are studied where the medium is in turn either spatially inhomogeneous, compositionally heterogeneous or spatially discrete. Applications span a vast range of interdisciplinary fields and the systems considered can be as different as human or animal groups migrating under external influences, population...

  17. Effective lagrangian description on discrete gauge symmetries

    International Nuclear Information System (INIS)

    Banks, T.

    1989-01-01

    We exhibit a simple low-energy lagrangian which describes a system with a discrete remnant of a spontaneously broken continuous gauge symmetry. The lagrangian gives a simple description of the effects ascribed to such systems by Krauss and Wilczek: black holes carry discrete hair and interact with cosmic strings, and wormholes cannot lead to violation of discrete gauge symmetries. (orig.)

  18. An integrable semi-discretization of the Boussinesq equation

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Yingnan, E-mail: ynzhang@njnu.edu.cn [Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu (China); Tian, Lixin, E-mail: tianlixin@njnu.edu.cn [Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu (China); Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang, Jiangsu (China)

    2016-10-23

    Highlights: • A new integrable semi-discretization of the Boussinesq equation is present. • A Bäcklund transformation and a Lax pair for the differential-difference system is derived by using Hirota's bilinear method. • The soliton solutions of 'good' Boussinesq equation and numerical algorithms are investigated. - Abstract: In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the ‘time’ variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Bäcklund transformation and a Lax pair of the differential-difference system. For the case of ‘good’ Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.

  19. A 2+1 non-isospectral discrete integrable system and its discrete integrable coupling system

    International Nuclear Information System (INIS)

    Yu Fajun; Zhang Hongqing

    2006-01-01

    In this Letter by considering a (2+1)-dimensional discrete non-isospectral linear problem, a new (2+1)-dimensional integrable lattice hierarchy is constructed. It shows that generalization of the Blaszak-Marciniak lattice hierarchy can be obtained as a reduction. Then an extended algebraic system X-bar of X is presented, from which the integrable coupling system of the (2+1)-dimensional discrete non-isospectral Blaszak-Marciniak lattice equations are obtained

  20. Hairs of discrete symmetries and gravity

    Energy Technology Data Exchange (ETDEWEB)

    Choi, Kang Sin [Scranton Honors Program, Ewha Womans University, Seodaemun-Gu, Seoul 03760 (Korea, Republic of); Center for Fields, Gravity and Strings, CTPU, Institute for Basic Sciences, Yuseong-Gu, Daejeon 34047 (Korea, Republic of); Kim, Jihn E., E-mail: jihnekim@gmail.com [Department of Physics, Kyung Hee University, 26 Gyungheedaero, Dongdaemun-Gu, Seoul 02447 (Korea, Republic of); Center for Axion and Precision Physics Research (IBS), 291 Daehakro, Yuseong-Gu, Daejeon 34141 (Korea, Republic of); Kyae, Bumseok [Department of Physics, Pusan National University, 2 Busandaehakro-63-Gil, Geumjeong-Gu, Busan 46241 (Korea, Republic of); Nam, Soonkeon [Department of Physics, Kyung Hee University, 26 Gyungheedaero, Dongdaemun-Gu, Seoul 02447 (Korea, Republic of)

    2017-06-10

    Gauge symmetries are known to be respected by gravity because gauge charges carry flux lines, but global charges do not carry flux lines and are not conserved by gravitational interaction. For discrete symmetries, they are spontaneously broken in the Universe, forming domain walls. Since the realization of discrete symmetries in the Universe must involve the vacuum expectation values of Higgs fields, a string-like configuration (hair) at the intersection of domain walls in the Higgs vacua can be realized. Therefore, we argue that discrete charges are also respected by gravity.