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Sample records for adjoint transport equation

  1. Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport

    SciTech Connect

    Liscum-Powell, J.L.; Lorence, L.J. Jr.; Morel, J.E.; Prinja, A.K.

    1999-07-08

    Recently, Morel and McGhee described an alternate second-order form of the transport equation called the self adjoint angular flux (SAAF) equation that has the angular flux as its unknown. The SAAF formulation has all the advantages of the traditional even- and odd-parity self-adjoint equations, with the added advantages that it yields the full angular flux when it is numerically solved, it is significantly easier to implement reflective and reflective-like boundary conditions, and in the appropriate form it can be solved in void regions. The SAAF equation has the disadvantage that the angular domain is the full unit sphere and, like the even- and odd- parity form, S{sub n} source iteration cannot be implemented using the standard sweeping algorithm. Also, problems arise in pure scattering media. Morel and McGhee demonstrated the efficacy of the SAAF formulation for neutral particle transport. Here we apply the SAAF formulation to coupled electron-photon transport problems using multigroup cross-sections from the CEPXS code and S{sub n} discretization.

  2. Nonlinear acceleration of a continuous finite element discretization of the self-adjoint angular flux form of the transport equation

    SciTech Connect

    Sanchez, R.

    2012-07-01

    Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self adjoint angular flux (SAAF) form of the transport equation and use a post processing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a formal derivation of the boundary conditions for the SAAF. (authors)

  3. Nonlinear Acceleration of a Continuous Finite Element Discretization of the Self-Adjoint Angular Flux Form of the Transport Equation

    SciTech Connect

    Richard Sanchez; Cristian Rabiti; Yaqi Wang

    2013-11-01

    Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self-adjoint angular flux (SAAF) form of the transport equation and use a postprocessing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a novel formal derivation of the boundary conditions for the SAAF.

  4. The compressible adjoint equations in geodynamics: equations and numerical assessment

    NASA Astrophysics Data System (ADS)

    Ghelichkhan, Siavash; Bunge, Hans-Peter

    2016-04-01

    The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.

  5. FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

    NASA Astrophysics Data System (ADS)

    Ibragimov, N. H.; Torrisi, M.; Tracinà, R.

    2010-11-01

    In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.

  6. Adjoint Function: Physical Basis of Variational & Perturbation Theory in Transport

    2009-07-27

    Version 00 Dr. J.D. Lewins has now released the following legacy book for free distribution: Importance: The Adjoint Function: The Physical Basis of Variational and Perturbation Theory in Transport and Diffusion Problems, North-Holland Publishing Company - Amsterdam, 582 pages, 1966 Introduction: Continuous Systems and the Variational Principle 1. The Fundamental Variational Principle 2. The Importance Function 3. Adjoint Equations 4. Variational Methods 5. Perturbation and Iterative Methods 6. Non-Linear Theory

  7. A new mathematical adjoint for the modified SAAF-SN equations

    SciTech Connect

    Schunert, Sebastian; Wang, Yaqi; Martineau, Richard; DeHart, Mark D.

    2015-01-01

    We present a new adjoint FEM weak form, which can be directly used for evaluating the mathematical adjoint, suitable for perturbation calculations, of the self-adjoint angular flux SN equations (SAAF-SN) without construction and transposition of the underlying coefficient matrix. Stabilization schemes incorporated in the described SAAF-SN method make the mathematical adjoint distinct from the physical adjoint, i.e. the solution of the continuous adjoint equation with SAAF-SN . This weak form is implemented into RattleSnake, the MOOSE (Multiphysics Object-Oriented Simulation Environment) based transport solver. Numerical results verify the correctness of the implementation and show its utility both for fixed source and eigenvalue problems.

  8. Self-adjointness and conservation laws of difference equations

    NASA Astrophysics Data System (ADS)

    Peng, Linyu

    2015-06-01

    A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference Lagrangian. It is proved that the system, combined by the original system and its adjoint system, is governed by a variational principle, which inherits all symmetries of the original system. Noether's theorem can then be applied. With some special techniques, e.g. self-adjointness properties, this allows us to obtain conservation laws for difference equations, which are not necessary governed by Lagrangian formalisms.

  9. Eulerian-Lagrangian localized adjoint methods for reactive transport in groundwater

    SciTech Connect

    Ewing, R.E.; Wang, Hong

    1996-12-31

    In this paper, we present Eulerian-Lagrangian localized adjoint methods (ELLAM) to solve convection-diffusion-reaction equations governing contaminant transport in groundwater flowing through an adsorbing porous medium. These ELLAM schemes can treat various combinations of boundary conditions and conserve mass. Numerical results are presented to demonstrate the strong potential of ELLAM schemes.

  10. Nonlinear self-adjointness and conservation laws of Klein-Gordon-Fock equation with central symmetry

    NASA Astrophysics Data System (ADS)

    Abdulwahhab, Muhammad Alim

    2015-05-01

    The concept of nonlinear self-adjointness, introduced by Ibragimov, has significantly extends approaches to constructing conservation laws associated with symmetries since it incorporates the strict self-adjointness, the quasi self-adjointness as well as the usual linear self-adjointness. Using this concept, the nonlinear self-adjointness condition for the Klein-Gordon-Fock equation was established and subsequently used to construct simplified but infinitely many nontrivial and independent conserved vectors. The Noether's theorem was further applied to the Klein-Gordon-Fock equation to explore more distinct first integrals, result shows that conservation laws constructed through this approach are exactly the same as those obtained under strict self-adjointness of Ibragimov's method.

  11. Periodic differential equations with self-adjoint monodromy operator

    NASA Astrophysics Data System (ADS)

    Yudovich, V. I.

    2001-04-01

    A linear differential equation \\dot u=A(t)u with p-periodic (generally speaking, unbounded) operator coefficient in a Euclidean or a Hilbert space \\mathbb H is considered. It is proved under natural constraints that the monodromy operator U_p is self-adjoint and strictly positive if A^*(-t)=A(t) for all t\\in\\mathbb R.It is shown that Hamiltonian systems in the class under consideration are usually unstable and, if they are stable, then the operator U_p reduces to the identity and all solutions are p-periodic.For higher frequencies averaged equations are derived. Remarkably, high-frequency modulation may double the number of critical values.General results are applied to rotational flows with cylindrical components of the velocity a_r=a_z=0, a_\\theta=\\lambda c(t)r^\\beta, \\beta<-1, c(t) is an even p-periodic function, and also to several problems of free gravitational convection of fluids in periodic fields.

  12. Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures

    SciTech Connect

    Kim, Min-Geun; Jang, Hong-Lae; Cho, Seonho

    2013-05-01

    An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems. A reduced atomic system and the adjoint system are constructed in a locally confined region, utilizing generalized Langevin equation (GLE) for periodic lattice structures. Due to the translational symmetry of lattice structures, the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atom’s degrees of freedom. For the problems of highly nonlinear design variables, the finite difference method is impractical for its inefficiency and inaccuracy. However, the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint GLE. Through numerical examples, the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity.

  13. Development of CO2 inversion system based on the adjoint of the global coupled transport model

    NASA Astrophysics Data System (ADS)

    Belikov, Dmitry; Maksyutov, Shamil; Chevallier, Frederic; Kaminski, Thomas; Ganshin, Alexander; Blessing, Simon

    2014-05-01

    We present the development of an inverse modeling system employing an adjoint of the global coupled transport model consisting of the National Institute for Environmental Studies (NIES) Eulerian transport model (TM) and the Lagrangian plume diffusion model (LPDM) FLEXPART. NIES TM is a three-dimensional atmospheric transport model, which solves the continuity equation for a number of atmospheric tracers on a grid spanning the entire globe. Spatial discretization is based on a reduced latitude-longitude grid and a hybrid sigma-isentropic coordinate in the vertical. NIES TM uses a horizontal resolution of 2.5°×2.5°. However, to resolve synoptic-scale tracer distributions and to have the ability to optimize fluxes at resolutions of 0.5° and higher we coupled NIES TM with the Lagrangian model FLEXPART. The Lagrangian component of the forward and adjoint models uses precalculated responses of the observed concentration to the surface fluxes and 3-D concentrations field simulated with the FLEXPART model. NIES TM and FLEXPART are driven by JRA-25/JCDAS reanalysis dataset. Construction of the adjoint of the Lagrangian part is less complicated, as LPDMs calculate the sensitivity of measurements to the surrounding emissions field by tracking a large number of "particles" backwards in time. Developing of the adjoint to Eulerian part was performed with automatic differentiation tool the Transformation of Algorithms in Fortran (TAF) software (http://www.FastOpt.com). This method leads to the discrete adjoint of NIES TM. The main advantage of the discrete adjoint is that the resulting gradients of the numerical cost function are exact, even for nonlinear algorithms. The overall advantages of our method are that: 1. No code modification of Lagrangian model is required, making it applicable to combination of global NIES TM and any Lagrangian model; 2. Once run, the Lagrangian output can be applied to any chemically neutral gas; 3. High-resolution results can be obtained over

  14. Adjoint-based deviational Monte Carlo methods for phonon transport calculations

    NASA Astrophysics Data System (ADS)

    Péraud, Jean-Philippe M.; Hadjiconstantinou, Nicolas G.

    2015-06-01

    In the field of linear transport, adjoint formulations exploit linearity to derive powerful reciprocity relations between a variety of quantities of interest. In this paper, we develop an adjoint formulation of the linearized Boltzmann transport equation for phonon transport. We use this formulation for accelerating deviational Monte Carlo simulations of complex, multiscale problems. Benefits include significant computational savings via direct variance reduction, or by enabling formulations which allow more efficient use of computational resources, such as formulations which provide high resolution in a particular phase-space dimension (e.g., spectral). We show that the proposed adjoint-based methods are particularly well suited to problems involving a wide range of length scales (e.g., nanometers to hundreds of microns) and lead to computational methods that can calculate quantities of interest with a cost that is independent of the system characteristic length scale, thus removing the traditional stiffness of kinetic descriptions. Applications to problems of current interest, such as simulation of transient thermoreflectance experiments or spectrally resolved calculation of the effective thermal conductivity of nanostructured materials, are presented and discussed in detail.

  15. A numerical adjoint parabolic equation (PE) method for tomography and geoacoustic inversion in shallow water

    NASA Astrophysics Data System (ADS)

    Hermand, Jean-Pierre; Berrada, Mohamed; Meyer, Matthias; Asch, Mark

    2005-09-01

    Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer and Hermand, J. Acoust. Soc. Am. 117, 2937-2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a spectral integral representation of the nonlocal boundary condition. The adjoint model is generated numerically and the inversion is carried out jointly across multiple frequencies. The paper further discusses the application of the numerical adjoint PE method for ocean acoustic tomography. To show the effectiveness of the implemented numerical adjoint, preliminary inversion results of water sound-speed profile and bottom acoustic properties will be shown for the YELLOW SHARK '94 experimental conditions.

  16. Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation

    NASA Astrophysics Data System (ADS)

    Yaşar, Emrullah; San, Sait; Özkan, Yeşim Sağlam

    2016-01-01

    In this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.

  17. Adjoint equations and analysis of complex systems: Application to virus infection modelling

    NASA Astrophysics Data System (ADS)

    Marchuk, G. I.; Shutyaev, V.; Bocharov, G.

    2005-12-01

    Recent development of applied mathematics is characterized by ever increasing attempts to apply the modelling and computational approaches across various areas of the life sciences. The need for a rigorous analysis of the complex system dynamics in immunology has been recognized since more than three decades ago. The aim of the present paper is to draw attention to the method of adjoint equations. The methodology enables to obtain information about physical processes and examine the sensitivity of complex dynamical systems. This provides a basis for a better understanding of the causal relationships between the immune system's performance and its parameters and helps to improve the experimental design in the solution of applied problems. We show how the adjoint equations can be used to explain the changes in hepatitis B virus infection dynamics between individual patients.

  18. A Least-Squares Transport Equation Compatible with Voids

    SciTech Connect

    Hansen, Jon; Peterson, Jacob; Morel, Jim; Ragusa, Jean; Wang, Yaqi

    2014-12-01

    Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transport equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares Sn formulation represents an excellent alternative to existing second-order Sn transport formulations

  19. Neural network training by integration of adjoint systems of equations forward in time

    NASA Technical Reports Server (NTRS)

    Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)

    1992-01-01

    A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically, it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved, but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. The trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

  20. Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time

    NASA Technical Reports Server (NTRS)

    Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)

    1999-01-01

    A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically. it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved. but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. Tbc trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

  1. A finite-volume Eulerian-Lagrangian localized adjoint method for solution of the advection-dispersion equation

    USGS Publications Warehouse

    Healy, R.W.; Russell, T.F.

    1993-01-01

    Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods for solute transport problems that are dominated by advection. FVELLAM systematically conserves mass globally with all types of boundary conditions. Integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking of characteristic lines intersecting inflow boundaries. FVELLAM extends previous results by obtaining mass conservation locally on Lagrangian space-time elements. -from Authors

  2. A new least-squares transport equation compatible with voids

    SciTech Connect

    Hansen, J. B.; Morel, J. E.

    2013-07-01

    We define a new least-squares transport equation that is applicable in voids, can be solved using source iteration with diffusion-synthetic acceleration, and requires only the solution of an independent set of second-order self-adjoint equations for each direction during each source iteration. We derive the equation, discretize it using the S{sub n} method in conjunction with a linear-continuous finite-element method in space, and computationally demonstrate various of its properties. (authors)

  3. Construction of the adjoint MIT ocean general circulation model and application to Atlantic heat transport sensitivity

    NASA Astrophysics Data System (ADS)

    Marotzke, Jochem; Giering, Ralf; Zhang, Kate Q.; Stammer, Detlef; Hill, Chris; Lee, Tong

    1999-12-01

    We first describe the principles and practical considerations behind the computer generation of the adjoint to the Massachusetts Institute of Technology ocean general circulation model (GCM) using R. Giering's software tool Tangent-Linear and Adjoint Model Compiler (TAMC). The TAMC's recipe for (FORTRAN-) line-by-line generation of adjoint code is explained by interpreting an adjoint model strictly as the operator that gives the sensitivity of the output of a model to its input. Then, the sensitivity of 1993 annual mean heat transport across 29°N in the Atlantic, to the hydrography on January 1, 1993, is calculated from a global solution of the GCM. The "kinematic sensitivity" to initial temperature variations is isolated, showing how the latter would influence heat transport if they did not affect the density and hence the flow. Over 1 year the heat transport at 29°N is influenced kinematically from regions up to 20° upstream in the western boundary current and up to 5° upstream in the interior. In contrast, the dynamical influences of initial temperature (and salinity) perturbations spread from as far as the rim of the Labrador Sea to the 29°N section along the western boundary. The sensitivities calculated with the adjoint compare excellently to those from a perturbation calculation with the dynamical model. Perturbations in initial interior salinity influence meridional overturning and heat transport when they have propagated to the western boundary and can thus influence the integrated east-west density difference. Our results support the notion that boundary monitoring of meridional mass and heat transports is feasible.

  4. Solution of the self-adjoint radiative transfer equation on hybrid computer systems

    NASA Astrophysics Data System (ADS)

    Gasilov, V. A.; Kuchugov, P. A.; Olkhovskaya, O. G.; Chetverushkin, B. N.

    2016-06-01

    A new technique for simulating three-dimensional radiative energy transfer for the use in the software designed for the predictive simulation of plasma with high energy density on parallel computers is proposed. A highly scalable algorithm that takes into account the angular dependence of the radiation intensity and is free of the ray effect is developed based on the solution of a second-order equation with a self-adjoint operator. A distinctive feature of this algorithm is a preliminary transformation of rotation to eliminate mixed derivatives with respect to the spatial variables, simplify the structure of the difference operator, and accelerate the convergence of the iterative solution of the equation. It is shown that the proposed method correctly reproduces the limiting cases—isotropic radiation and the directed radiation with a δ-shaped angular distribution.

  5. An adjoint view on flux consistency and strong wall boundary conditions to the Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Stück, Arthur

    2015-11-01

    Inconsistent discrete expressions in the boundary treatment of Navier-Stokes solvers and in the definition of force objective functionals can lead to discrete-adjoint boundary treatments that are not a valid representation of the boundary conditions to the corresponding adjoint partial differential equations. The underlying problem is studied for an elementary 1D advection-diffusion problem first using a node-centred finite-volume discretisation. The defect of the boundary operators in the inconsistently defined discrete-adjoint problem leads to oscillations and becomes evident with the additional insight of the continuous-adjoint approach. A homogenisation of the discretisations for the primal boundary treatment and the force objective functional yields second-order functional accuracy and eliminates the defect in the discrete-adjoint boundary treatment. Subsequently, the issue is studied for aerodynamic Reynolds-averaged Navier-Stokes problems in conjunction with a standard finite-volume discretisation on median-dual grids and a strong implementation of noslip walls, found in many unstructured general-purpose flow solvers. Going out from a base-line discretisation of force objective functionals which is independent of the boundary treatment in the flow solver, two improved flux-consistent schemes are presented; based on either body wall-defined or farfield-defined control-volumes they resolve the dual inconsistency. The behaviour of the schemes is investigated on a sequence of grids in 2D and 3D.

  6. A three-dimensional finite-volume Eulerian-Lagrangian Localized Adjoint Method (ELLAM) for solute-transport modeling

    USGS Publications Warehouse

    Heberton, C.I.; Russell, T.F.; Konikow, L.F.; Hornberger, G.Z.

    2000-01-01

    This report documents the U.S. Geological Survey Eulerian-Lagrangian Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.

  7. Adjoint transport calculations for sensitivity analysis of the Hiroshima air-over-ground environment

    SciTech Connect

    Broadhead, B.L.; Cacuci, D.G.; Pace, J.V. III

    1984-01-01

    A major effort within the US Dose Reassessment Program is aimed at recalculating the transport of initial nuclear radiation in an air-over-ground environment. This paper is the first report of results from adjoint calculations in the Hiroshima air-over-ground environment. The calculations use a Hiroshima/Nagasaki multi-element ground, ENDF/B-V nuclear data, one-dimensional ANISN flux weighting for neutron and gamma cross sections, a source obtained by two-dimensional hydrodynamic and three-dimensional transport calculations, and best-estimate atmospheric conditions from Japanese sources. 7 references, 2 figures.

  8. Solution of the advection-dispersion equation by a finite-volume eulerian-lagrangian local adjoint method

    USGS Publications Warehouse

    Healy, R.W.; Russell, T.F.

    1992-01-01

    A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.

  9. A family of Eulerian-Lagrangian localized adjoint methods for multi-dimensional advection-reaction equations

    SciTech Connect

    Wang, H.; Man, S.; Ewing, R.E.; Qin, G.; Lyons, S.L.; Al-Lawatia, M.

    1999-06-10

    Many difficult problems arise in the numerical simulation of fluid flow processes within porous media in petroleum reservoir simulation and in subsurface contaminant transport and remediation. The authors develop a family of Eulerian-Lagrangian localized adjoint methods for the solution of the initial-boundary value problems for first-order advection-reaction equations on general multi-dimensional domains. Different tracking algorithms, including the Euler and Runge-Kutta algorithms, are used. The derived schemes, which are full mass conservative, naturally incorporate inflow boundary conditions into their formulations and do not need any artificial outflow boundary conditions. Moreover, they have regularly structured, well-conditioned, symmetric, and positive-definite coefficient matrices, which can be efficiently solved by the conjugate gradient method in an optimal order number of iterations without any preconditioning needed. Numerical results are presented to compare the performance of the ELLAM schemes with many well studied and widely used methods, including the upwind finite difference method, the Galerkin and the Petrov-Galerkin finite element methods with backward-Euler or Crank-Nicolson temporal discretization, the streamline diffusion finite element methods, the monotonic upstream-centered scheme for conservation laws (MUSCL), and the Minmod scheme.

  10. Adjoint Sensitivity Analysis of Radiative Transfer Equation: Temperature and Gas Mixing Ratio Weighting Functions for Remote Sensing of Scattering Atmospheres in Thermal IR

    NASA Technical Reports Server (NTRS)

    Ustinov, E.

    1999-01-01

    Sensitivity analysis based on using of the adjoint equation of radiative transfer is applied to the case of atmospheric remote sensing in the thermal spectral region with non-negligeable atmospheric scattering.

  11. Optimization of the Direct Discrete Method Using the Solution of the Adjoint Equation and its Application in the Multi-Group Neutron Diffusion Equation

    SciTech Connect

    Ayyoubzadeh, Seyed Mohsen; Vosoughi, Naser

    2011-09-14

    Obtaining the set of algebraic equations that directly correspond to a physical phenomenon has been viable in the recent direct discrete method (DDM). Although this method may find its roots in physical and geometrical considerations, there are still some degrees of freedom that one may suspect optimize-able. Here we have used the information embedded in the corresponding adjoint equation to form a local functional, which in turn by its minimization, yield suitable dual mesh positioning.

  12. Variational data assimilation with a semi-Lagrangian semi-implicit global shallow-water equation model and its adjoint

    NASA Technical Reports Server (NTRS)

    Li, Y.; Navon, I. M.; Courtier, P.; Gauthier, P.

    1993-01-01

    An adjoint model is developed for variational data assimilation using the 2D semi-Lagrangian semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-Lagrangian scheme is preserved during the minimization process, related to the variational data assimilation procedure.

  13. Adjoint-Based Design of Rotors Using the Navier-Stokes Equations in a Noninertial Reference Frame

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Jones, William T.

    2010-01-01

    Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated by using comparisons with a complex-variable technique, and a number of single- and multipoint optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

  14. Adjoint-Based Design of Rotors using the Navier-Stokes Equations in a Noninertial Reference Frame

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.; Lee-Rausch, Elizabeth M.; Jones, William T.

    2009-01-01

    Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated using comparisons with a complex-variable technique, and a number of single- and multi-point optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

  15. Calculation of the response of cylindrical targets to collimated beams of particles using one-dimensional adjoint transport techniques. [LMFBR

    SciTech Connect

    Dupree, S. A.

    1980-06-01

    The use of adjoint techniques to determine the interaction of externally incident collimated beams of particles with cylindrical targets is a convenient means of examining a class of problems important in radiation transport studies. The theory relevant to such applications is derived, and a simple example involving a fissioning target is discussed. Results from both discrete ordinates and Monte Carlo transport-code calculations are presented, and comparisons are made with results obtained from forward calculations. The accuracy of the discrete ordinates adjoint results depends on the order of angular quadrature used in the calculation. Reasonable accuracy by using EQN quadratures can be expected from order S/sub 16/ or higher.

  16. Analytical solution for the advection-dispersion transport equation in layered media

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The advection-dispersion transport equation with first-order decay was solved analytically for multi-layered media using the classic integral transform technique (CITT). The solution procedure used an associated non-self-adjoint advection-diffusion eigenvalue problem that had the same form and coef...

  17. Transport equations in tokamak plasmas

    SciTech Connect

    Callen, J. D.; Hegna, C. C.; Cole, A. J.

    2010-05-15

    Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes. Also, ad hoc terms are added for neoclassical effects on the parallel Ohm's law, fluctuation-induced transport, heating, current-drive and flow sources and sinks, small magnetic field nonaxisymmetries, magnetic field transients, etc. A set of self-consistent second order in gyroradius fluid-moment-based transport equations for nearly axisymmetric tokamak plasmas has been developed using a kinetic-based approach. The derivation uses neoclassical-based parallel viscous force closures, and includes all the effects noted above. Plasma processes on successive time scales and constraints they impose are considered sequentially: compressional Alfven waves (Grad-Shafranov equilibrium, ion radial force balance), sound waves (pressure constant along field lines, incompressible flows within a flux surface), and collisions (electrons, parallel Ohm's law; ions, damping of poloidal flow). Radial particle fluxes are driven by the many second order in gyroradius toroidal angular torques on a plasma species: seven ambipolar collision-based ones (classical, neoclassical, etc.) and eight nonambipolar ones (fluctuation-induced, polarization flows from toroidal rotation transients, etc.). The plasma toroidal rotation equation results from setting to zero the net radial current induced by the nonambipolar fluxes. The radial particle flux consists of the collision-based intrinsically ambipolar fluxes plus the nonambipolar fluxes evaluated at the ambipolarity-enforcing toroidal plasma rotation (radial electric field). The energy transport equations do not involve an ambipolar constraint and hence are more directly obtained. The 'mean field' effects of microturbulence on the parallel Ohm's law, poloidal ion flow, particle fluxes, and toroidal momentum and energy transport are all included self-consistently. The

  18. Numerical Computation of Sensitivities and the Adjoint Approach

    NASA Technical Reports Server (NTRS)

    Lewis, Robert Michael

    1997-01-01

    We discuss the numerical computation of sensitivities via the adjoint approach in optimization problems governed by differential equations. We focus on the adjoint problem in its weak form. We show how one can avoid some of the problems with the adjoint approach, such as deriving suitable boundary conditions for the adjoint equation. We discuss the convergence of numerical approximations of the costate computed via the weak form of the adjoint problem and show the significance for the discrete adjoint problem.

  19. Source identification of benzene emissions in Texas City using an adjoint neighborhood scale transport model

    NASA Astrophysics Data System (ADS)

    Guven, B.; Olaguer, E. P.; Herndon, S. C.; Kolb, C. E.; Cuclis, A.

    2012-12-01

    During the "Formaldehyde and Olefins from Large Industrial Sources" (FLAIR) study in 2009, the Aerodyne Research Inc. (ARI) mobile laboratory performed real-time in situ measurements of VOCs, NOx and HCHO in Texas City, TX on May 7, 2009 from 11 am to 3 pm. This high resolution dataset collected in a predominantly industrial area provides an ideal test bed for advanced source attribution. Our goal was to identify and quantify emission sources within the largest facility in Texas City most likely responsible for measured benzene concentrations. For this purpose, fine horizontal resolution (200 m x 200 m) 4D variational (4Dvar) inverse modeling was performed by running the HARC air quality transport model in adjoint mode based on ambient concentrations measured by the mobile laboratory. The simulations were conducted with a horizontal domain size of 4 km x 4 km for a four-hour period (11 am to 3 pm). Potential emission unit locations within the facility were specified using a high spatial resolution digital model of the largest industrial complex in the area. The HARC model was used to infer benzene emission rates from all potential source locations that would account for the benzene concentrations measured by the Aerodyne mobile laboratory in the vicinity of the facility. A Positive Matrix Factorization receptor model was also applied to the concentrations of other compounds measured by the mobile lab to support the source attribution by the inverse model. Although previous studies attributed measured benzene concentrations during the same time period to a cooling tower unit at the industrial complex, this study found that some of the flare units in the facility were also associated with the elevated benzene concentrations. The emissions of some of these flare units were found to be greater than reported in emission inventories, by up to two orders of magnitude.

  20. Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method

    USGS Publications Warehouse

    Healy, R.W.; Russell, T.F.

    1998-01-01

    We extend the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.

  1. Shape optimization governed by the Euler equations using an adjoint method

    NASA Technical Reports Server (NTRS)

    Iollo, Angelo; Salas, Manuel D.; Taasan, Shlomo

    1993-01-01

    A numerical approach for the treatment of optimal shape problems governed by the Euler equations is discussed. Focus is on flows with embedded shocks. A very simple problem is considered: the design of a quasi-one-dimensional Laval nozzle. A cost function and a set of Lagrange multipliers are introduced to achieve the minimum. The nature of the resulting costate equations is discussed. A theoretical difficulty that arises for cases with embedded shocks is pointed out and solved. Finally, some results are given to illustrate the effectiveness of the method.

  2. AN EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION

    EPA Science Inventory

    Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...

  3. EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION

    EPA Science Inventory

    Many numerical methods use characteristic analysis to accommodate the advective component of transport. uch characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. eneralization of characteristic...

  4. Adjoint of the global Eulerian-Lagrangian coupled atmospheric transport model (A-GELCA v1.0): development and validation

    NASA Astrophysics Data System (ADS)

    Belikov, Dmitry A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander

    2016-02-01

    We present the development of the Adjoint of the Global Eulerian-Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e-14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated

  5. Solving the transport equation with quadratic finite elements: Theory and applications

    SciTech Connect

    Ferguson, J.M.

    1997-12-31

    At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids.

  6. Diagnositcs With Adjoint Modelling

    NASA Astrophysics Data System (ADS)

    Blessing, S.; Fraedrich, K.; Kirk, E.; Lunkeit, F.

    The potential usefulness of an adjoint primitive equations global atmospheric circu- lation model for climate diagnostics is demonstrated in a feasibility study. A daily NAO-type index is calculated as one-point correlation of the 300 hPa streamfunction anomaly. By application of the adjoint model we diagnose its temperature forcing on short timescales in terms of spatial temperature sensitivity patterns at different time lags, which, in a first order approximation, induce growth of the index. The dynamical relevance of these sensitivity patterns is confirmed by lag-correlating the index time series and the projection time series of the model temperature on these sensitivity patterns.

  7. Langevin equation approach to reactor noise analysis: stochastic transport equation

    SciTech Connect

    Akcasu, A.Z. ); Stolle, A.M. )

    1993-01-01

    The application of the Langevin equation method to the study of fluctuations in the space- and velocity-dependent neutron density as well as in the detector outputs in nuclear reactors is presented. In this case, the Langevin equation is the stochastic linear neutron transport equation with a space- and velocity-dependent random neutron source, often referred to as the noise equivalent source (NES). The power spectral densities (PSDs) of the NESs in the transport equation, as well as in the accompanying detection rate equations, are obtained, and the cross- and auto-power spectral densities of the outputs of pairs of detectors are explicitly calculated. The transport-level expression for the R([omega]) ratio measured in the [sup 252]Cf source-driven noise analysis method is also derived. Finally, the implementation of the Langevin equation approach at different levels of approximation is discussed, and the stochastic one-speed transport and one-group P[sub 1] equations are derived by first integrating the stochastic transport equation over speed and then eliminating the angular dependence by a spherical harmonics expansion. By taking the large transport rate limit in the P[sub 1] description, the stochastic diffusion equation is obtained as well as the PSD of the NES in it. This procedure also leads directly to the stochastic Fick's law.

  8. Top-Down Inversion of Aerosol Emissions through Adjoint Integration of Satellite Radiance and GEOS-Chem Chemical Transport Model

    NASA Astrophysics Data System (ADS)

    Xu, X.; Wang, J.; Henze, D. K.; Qu, W.; Kopacz, M.

    2012-12-01

    The knowledge of aerosol emissions from both natural and anthropogenic sources are needed to study the impacts of tropospheric aerosol on atmospheric composition, climate, and human health, but large uncertainties persist in quantifying the aerosol sources with the current bottom-up methods. This study presents a new top-down approach that spatially constrains the amount of aerosol emissions from satellite (MODIS) observed reflectance with the adjoint of a chemistry transport model (GEOS-Chem). We apply this technique with a one-month case study (April 2008) over the East Asia. The bottom-up estimated sulfate-nitrate-ammonium precursors, such as sulfur dioxide (SO2), ammonia (NH3), and nitrogen oxides (NOx), all from INTEX-B 2006 inventory, emissions of black carbon (BC), organic carbon (OC) from Bond-2007 inventory, and mineral dust simulated from DEAD dust mobilization scheme, are spatially optimized from the GEOS-Chem model and its adjoint constrained by the aerosol optical depth (AOD) that are derived from MODIS reflectance with the GEOS-Chem aerosol single scattering properties. The adjoint inverse modeling for the study period yields notable decreases in anthropogenic aerosol emissions over China: 436 Gg (33.5%) for SO2, 378 Gg (34.5%) for NH3, 319 (18.8%) for NOx, 10 Gg (9.1%) for BC, and 30 Gg (15.0%) for OC. The total amount of the mineral dust emission is reduced by 56.4% from the DEAD mobilization module which simulates dust production of 19020 Gg. Sub-regional adjustments are significant and directions of changes are spatially different. The model simulation with optimized aerosol emissions shows much better agreement with independent observations from sun-spectrophotometer observed AOD from AERONET, MISR (Multi-angle Imaging SpectroRadiometer) AOD, OMI (Ozone Monitoring Instrument) NO2 and SO2 columns, and surface aerosol concentrations measured over both anthropogenic pollution and dust source regions. Assuming the used bottom-up anthropogenic

  9. The gBL transport equations

    SciTech Connect

    Mynick, H.E.

    1989-05-01

    The transport equations arising from the ''generalized Balescu- Lenard'' (gBL) collision operator are obtained, and some of their properties examined. The equations contain neoclassical and turbulent transport as two special cases, having the same structure. The resultant theory offers potential explanation for a number of results not well understood, including the anomalous pinch, observed ratios of Q/GAMMAT on TFTR, and numerical reproduction of ASDEX profiles by a model for turbulent transport invoked without derivation, but by analogy to neoclassical theory. The general equations are specialized to consideration of a number of particular transport mechanisms of interest. 10 refs.

  10. Variational Determination of the Neutron Integral Transport Equation Eigenvalues Using Space Asymptotic Trial Functions

    NASA Astrophysics Data System (ADS)

    Colombo, V.; Ravetto, P.; Sumini, M.

    1988-08-01

    An approximate determination of the critical eigenvalue of the neutron transport equation in integral form, within both the one speed and energy multigroup models, for a homogeneous medium, is achieved by means of a variational technique. The space asymptotic solutions for both the direct and adjoint problems are used as trial functions. A variational procedure is also developed and numerically exploited within the Fourier transformed domain, where noticeable theoretical features can be demonstrated. It is evidenced that excellent results can be obtained with little computational effort, and a set of critical calculations in plane geometry is presented and discussed.

  11. Variational determination of the neutron integral transport equation eigenvalues using space asymptotic trial functions

    SciTech Connect

    Colombo, V.; Ravetto, P.; Sumini, M.

    1988-08-01

    An approximate determination of the critical eigenvalue of the neutron transport equation in integral form, within both the one speed and energy multigroup models, for a homogeneous medium, is achieved by means of a variational technique. The space asymptotic solutions for both the direct and adjoint problems are used as trial functions. A variational procedure is also developed and numerically exploited within the Fourier transformed domain, where noticeable theoretical features can be demonstrated. It is evidenced that excellent results can be obtained with little computational effort, and a set of critical calculations in plane geometry is presented and discussed. copyright 1988 Academic Press, Inc.

  12. Solving Parker's transport equation with stochastic differential equations on GPUs

    NASA Astrophysics Data System (ADS)

    Dunzlaff, P.; Strauss, R. D.; Potgieter, M. S.

    2015-07-01

    The numerical solution of transport equations for energetic charged particles in space is generally very costly in terms of time. Besides the use of multi-core CPUs and computer clusters in order to decrease the computation times, high performance calculations on graphics processing units (GPUs) have become available during the last years. In this work we introduce and describe a GPU-accelerated implementation of Parker's equation using Stochastic Differential Equations (SDEs) for the simulation of the transport of energetic charged particles with the CUDA toolkit, which is the focus of this work. We briefly discuss the set of SDEs arising from Parker's transport equation and their application to boundary value problems such as that of the Jovian magnetosphere. We compare the runtimes of the GPU code with a CPU version of the same algorithm. Compared to the CPU implementation (using OpenMP and eight threads) we find a performance increase of about a factor of 10-60, depending on the assumed set of parameters. Furthermore, we benchmark our simulation using the results of an existing SDE implementation of Parker's transport equation.

  13. Fractional transport equation on random fractals

    NASA Astrophysics Data System (ADS)

    Zeng, Qiuhua; Li, Houqiang; Fang, Yaquan

    1998-12-01

    According to the ways of H.E. Roman and M. Giona with the constitutive equation of diffusive particles in isotropic and homogeneous three dimensions and the Laplace transform we derive the multiscaling fractional transport equation in disordered fractal media, whose solution is consistent with literature results.

  14. Dual Diagonalization of Reactive Transport Equations

    NASA Astrophysics Data System (ADS)

    Yeh, G.; Tsai, C.

    2013-12-01

    One solves a system of species transport equations in the primitive approach to reactive transport modeling. This approach is not able to decouple equilibrium reaction rates from species concentrations. This problem has been overcome with the approach to diagonalizing the reaction matrix since mid 1990's, which yields the same number of transport equations for reaction-extents. In the diagonalization approach, first, a subset of reaction- extent transport equations is solved for concentrations of components and kinetic-variables. Then, the component, kinetic-variable, and mass action equations are solved for all species concentrations. Finally, the equilibrium reaction rates are posterior computed. The difficulty in this approach is that the solution of species concentrations in the second step is a stiff problem when the concentrations of master species are small compared to those of equilibrium species. To overcome the problem of stiffness, we propose a dual diagonalization approach. Here, a second diagonalization is performed on the decomposed unit matrix to yield species concentrations, each as a linear function of reaction extents. In this dual diagonalization approach, four steps are needed to complete the modeling. First, component and kinetic-variable transport equations are solved for the concentrations of components (a subset of reaction-extents) and kinetic-variables (another subset of reaction-extents). Second, the set of mass action equations written in terms of reaction extents are solved for equilibrium-variables (yet another subset of reaction-extents). Third, species concentrations are posterior obtained by solving the set of linear equations defining reaction-extents. Fourth, equilibrium rates are posterior calculated with transport equations for equilibrium-variables. Several example problems will be used to demonstrate the efficiency of this approach. Keywords: Reactive Transport, Reaction-Extent, Component, Kinetic-Variable, Equilibrium

  15. Extraction of macroscopic and microscopic adjoint concepts using a lattice Boltzmann method and discrete adjoint approach.

    PubMed

    Hekmat, Mohamad Hamed; Mirzaei, Masoud

    2015-01-01

    In the present research, we tried to improve the performance of the lattice Boltzmann (LB) -based adjoint approach by utilizing the mesoscopic inherent of the LB method. In this regard, two macroscopic discrete adjoint (MADA) and microscopic discrete adjoint (MIDA) approaches are used to answer the following two challenging questions. Is it possible to extend the concept of the macroscopic and microscopic variables of the flow field to the corresponding adjoint ones? Further, similar to the conservative laws in the LB method, is it possible to find the comparable conservation equations in the adjoint approach? If so, then a definite framework, similar to that used in the flow solution by the LB method, can be employed in the flow sensitivity analysis by the MIDA approach. This achievement can decrease the implementation cost and coding efforts of the MIDA method in complicated sensitivity analysis problems. First, the MADA and MIDA equations are extracted based on the LB method using the duality viewpoint. Meanwhile, using an elementary case, inverse design of a two-dimensional unsteady Poiseuille flow in a periodic channel with constant body forces, the procedure of analytical evaluation of the adjoint variables is described. The numerical results show that similar correlations between the distribution functions can be seen between the corresponding adjoint ones. Besides, the results are promising, emphasizing the flow field adjoint variables can be evaluated via the adjoint distribution functions. Finally, the adjoint conservative laws are introduced. PMID:25679735

  16. Introduction to Adjoint Models

    NASA Technical Reports Server (NTRS)

    Errico, Ronald M.

    2015-01-01

    In this lecture, some fundamentals of adjoint models will be described. This includes a basic derivation of tangent linear and corresponding adjoint models from a parent nonlinear model, the interpretation of adjoint-derived sensitivity fields, a description of methods of automatic differentiation, and the use of adjoint models to solve various optimization problems, including singular vectors. Concluding remarks will attempt to correct common misconceptions about adjoint models and their utilization.

  17. The telegraph equation in charged particle transport

    NASA Technical Reports Server (NTRS)

    Gombosi, T. I.; Jokipii, J. R.; Kota, J.; Lorencz, K.; Williams, L. L.

    1993-01-01

    We present a new derivation of the telegraph equation which modifies its coefficients. First, an infinite order partial differential equation is obtained for the velocity space solid angle-averaged phase-space distribution of particles which underwent at least a few collisions. It is shown that, in the lowest order asymptotic expansion, this equation simplifies to the well-known diffusion equation. The second-order asymptotic expansion for isotropic small-angle scattering results in a modified telegraph equation with a signal propagation speed of v(5/11) exp 1/2 instead of the usual v/3 exp 1/2. Our derivation of a modified telegraph equation follows from an expansion of the Boltzmann equation in the relevant smallness parameters and not from a truncation of an eigenfunction expansion. This equation is consistent with causality. It is shown that, under steady state conditions in a convecting plasma, the telegraph equation may be regarded as a diffusion equation with a modified transport coefficient, which describes a combination of diffusion and cosmic-ray inertia.

  18. Alternative formulation of the monokinetic transport equation

    SciTech Connect

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

    1985-03-01

    After recalling a technique already exploited in stationary neutron transport, the dynamic linear monokinetic equation for general geometry is cast into an integro-differential form where a second order space Laplace operator and both a second and first time derivatives appear. The introduced unknowns are given a physical interpretation for plane geometry and their relations with the total flux and current are derived.

  19. Code System to Solve the Few-Group Neutron Diffusion Equation Utilizing the Nodal Expansion Method (NEM) for Eigenvalue, Adjoint, and Fixed-Source

    2004-04-21

    Version 04 NESTLE solves the few-group neutron diffusion equation utilizing the NEM. The NESTLE code can solve the eigenvalue (criticality), eigenvalue adjoint, external fixed-source steady-state, and external fixed-source or eigenvalue initiated transient problems. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two- ormore » four-energy groups can be utilized, with all energy groups being thermal groups (i.e., upscatter exits) if desired. Core geometries modeled include Cartesian and hexagonal. Three-, two-, and one-dimensional models can be utilized with various symmetries. The thermal conditions predicted by the thermal-hydraulic model of the core are used to correct cross sections for temperature and density effects. Cross sections are parameterized by color, control rod state (i.e., in or out), and burnup, allowing fuel depletion to be modeled. Either a macroscopic or microscopic model may be employed.« less

  20. Pdf - Transport equations for chemically reacting flows

    NASA Technical Reports Server (NTRS)

    Kollmann, W.

    1989-01-01

    The closure problem for the transport equations for pdf and the characteristic functions of turbulent, chemically reacting flows is addressed. The properties of the linear and closed equations for the characteristic functional for Eulerian and Lagrangian variables are established, and the closure problem for the finite-dimensional case is discussed for pdf and characteristic functions. It is shown that the closure for the scalar dissipation term in the pdf equation developed by Dopazo (1979) and Kollmann et al. (1982) results in a single integral, in contrast to the pdf, where double integration is required. Some recent results using pdf methods obtained for turbulent flows with combustion, including effects of chemical nonequilibrium, are discussed.

  1. Dispersion in tidally averaged transport equation

    USGS Publications Warehouse

    Cheng, R.T.; Casulli, V.

    1992-01-01

    A general governing inter-tidal transport equation for conservative solutes has been derived without invoking the weakly nonlinear approximation. The governing inter-tidal transport equation is a convection-dispersion equation in which the convective velocity is a mean Lagrangian residual current, and the inter-tidal dispersion coefficient is defined by a dispersion patch. When the weakly nonlinear condition is violated, the physical significance of the Stokes' drift, as used in tidal dynamics, becomes questionable. For nonlinear problems, analytical solutions for the mean Lagrangian residual current and for the inter-tidal dispersion coefficient do not exist, they must be determined numerically. A rectangular tidal inlet with a constriction is used in the first example. The solutions of the residual currents and the computed properties of the inter-tidal dispersion coefficient are used to illuminate the mechanisms of the inter-tidal transport processes. Then, the present formulation is tested in a geometrically complex tidal estuary – San Francisco Bay, California. The computed inter-tidal dispersion coefficients are in the range between 5×104 and 5×106 cm2/sec., which are consistent with the values reported in the literature

  2. A transport equation for eddy viscosity

    NASA Technical Reports Server (NTRS)

    Durbin, P. A.; Yang, Z.

    1992-01-01

    A transport equation for eddy viscosity is proposed for wall bounded turbulent flows. The proposed model reduces to a quasi-homogeneous form far from surfaces. Near to a surface, the nonhomogeneous effect of the wall is modeled by an elliptic relaxation model. All the model terms are expressed in local variables and are coordinate independent; the model is intended to be used in complex flows. Turbulent channel flow and turbulent boundary layer flows with/without pressure gradient are calculated using the present model. Comparisons between model calculations and direct numerical simulation or experimental data show good agreement.

  3. Nonlinear diffusion acceleration for the multigroup transport equation discretized with S{sub N} and continuous FEM with rattlesnake

    SciTech Connect

    Wang, Y.

    2013-07-01

    Nonlinear diffusion acceleration (NDA) can improve the performance of a neutron transport solver significantly especially for the multigroup eigenvalue problems. The high-order transport equation and the transport-corrected low-order diffusion equation form a nonlinear system in NDA, which can be solved via a Picard iteration. The consistency of the correction of the low-order equation is important to ensure the stabilization and effectiveness of the iteration. It also makes the low-order equation preserve the scalar flux of the high-order equation. In this paper, the consistent correction for a particular discretization scheme, self-adjoint angular flux (SAAF) formulation with discrete ordinates method (S{sub N}) and continuous finite element method (CFEM) is proposed for the multigroup neutron transport equation. Equations with the anisotropic scatterings and a void treatment are included. The Picard iteration with this scheme has been implemented and tested with RattleS{sub N}ake, a MOOSE-based application at INL. Convergence results are presented. (authors)

  4. Maximal stochastic transport in the Lorenz equations

    NASA Astrophysics Data System (ADS)

    Agarwal, Sahil; Wettlaufer, J. S.

    2016-01-01

    We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh-Bénard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.

  5. Application of adjoint operators to neural learning

    NASA Technical Reports Server (NTRS)

    Barhen, J.; Toomarian, N.; Gulati, S.

    1990-01-01

    A technique for the efficient analytical computation of such parameters of the neural architecture as synaptic weights and neural gain is presented as a single solution of a set of adjoint equations. The learning model discussed concentrates on the adiabatic approximation only. A problem of interest is represented by a system of N coupled equations, and then adjoint operators are introduced. A neural network is formalized as an adaptive dynamical system whose temporal evolution is governed by a set of coupled nonlinear differential equations. An approach based on the minimization of a constrained neuromorphic energylike function is applied, and the complete learning dynamics are obtained as a result of the calculations.

  6. On diagonalization of coupled hydrologic transport and geochemical reaction equations

    SciTech Connect

    Yeh, Gour-Tsyh; Cheng, Hwai-Ping

    1996-12-31

    Two basic ingredients present in modeling the transport of reactive multi-components: the transport is described by a set of advection-dispersion-reactive partial differential equations (PDEs) based on the principle of mass balance; the chemical reactions, under the assumptions of local equilibrium, are described by a set of highly nonlinear algebraic equations (AEs) base on the principles of mole balance and mass action. For a typical application, the complete set of nonlinear PDEs and AEs consist of more than one hundred simultaneous equations. Thus, it is impractical to solve this set of equations simultaneously. General practice is to divide this set of equations into two subsets: one is the primary governing equations (PGEs) consisting of mainly the transport equations and the other one is the secondary governing equations consisting of mainly the geochemical reaction equations. The PGEs are solved for the chosen primary dependent variables (PDVs) and the SGEs are used to compute for the secondary dependent variables (SDVs). The major difficulties in simulating the reactive transport is the numerical solution of PGEs. From the computational point of view, the solution of the set of highly nonlinear PDEs are solved either with the direct substitution approach (DSA) or with the sequential iteration approach (SIA). For DSA, geochemical equilibrium reaction equations are substituted into the hydrologic transport equations to results in a set of nonlinear partial differential equations.

  7. Stable Difference Schemes for the Neutron Transport Equation

    SciTech Connect

    Ashyralyev, Allaberen; Taskin, Abdulgafur

    2011-09-22

    The initial boundary value problem for the neutron transport equation is considered. The first and second orders of accuracy difference schemes for the approximate solution of this problem are presented. In applications, the stability estimates for solutions of difference schemes for the approximate solution of the neutron transport equation are obtained. Numerical techniques are developed and algorithms are tested on an example in MATLAB.

  8. Transport equations for multicomponent anisotropic space plasmas - A review

    NASA Technical Reports Server (NTRS)

    Barakat, A. R.; Schunk, R. W.

    1982-01-01

    An attempt is made to present a unified approach to the study of transport phenomena in multicomponent anisotropic space plasmas. In particular, a system of generalized transport equations is presented that can be applied to widely different plasma flow conditions. The generalized transport equations can describe subsonic and supersonic flows, collision-dominated and collisionless flows, plasma flows in rapidly changing magnetic field configurations, multicomponent plasma flows with large temperature differences between the interacting species, and plasma flows that contain anisotropic temperature distributions. In addition, if Maxwell's equations of electricity and magnetism are added to the system of transport equations, they can be used to model electrostatic shocks, double layers, and magnetic merging processes. These transport equations also contain terms which act to regulate both the heat flow and temperature anisotropy, processes which appear to be operating in the solar wind.

  9. Adjoint methods for external beam inverse treatment planning

    NASA Astrophysics Data System (ADS)

    Kowalok, Michael E.

    Forward and adjoint radiation transport methods may both be used to determine the dosimetric relationship between source parameters and voxel elements of a phantom. Forward methods consider one specific tuple of source parameters and calculate the response in all voxels of interest. This response is often cast as the dose delivered per unit source-weight. Adjoint transport methods, conversely, consider one particular voxel and calculate the response of that voxel in relation to all possible source parameters. In this regard, adjoint methods provide an "adjoint function" in addition to a dose value. Although the dose is for a single voxel only, the adjoint function illustrates the source parameters, (e.g. beam positions and directions) that are most important to delivering the dose to that voxel. In this regard, adjoint methods of analysis lend themselves in a natural way to optimization problems and perturbation studies. This work investigates the utility of adjoint analytic methods for treatment planning and for Monte Carlo dose calculations. Various methods for implementing this approach are discussed, along with their strengths and weaknesses. The complementary nature of adjoint and forward techniques is illustrated and exploited. Also, several features of the Monte Carlo codes MCNP and MCNPX are reviewed for treatment planning applications.

  10. Adjoint-Based Uncertainty Quantification with MCNP

    SciTech Connect

    Seifried, Jeffrey E.

    2011-09-01

    This work serves to quantify the instantaneous uncertainties in neutron transport simulations born from nuclear data and statistical counting uncertainties. Perturbation and adjoint theories are used to derive implicit sensitivity expressions. These expressions are transformed into forms that are convenient for construction with MCNP6, creating the ability to perform adjoint-based uncertainty quantification with MCNP6. These new tools are exercised on the depleted-uranium hybrid LIFE blanket, quantifying its sensitivities and uncertainties to important figures of merit. Overall, these uncertainty estimates are small (< 2%). Having quantified the sensitivities and uncertainties, physical understanding of the system is gained and some confidence in the simulation is acquired.

  11. Transport equations for partially ionized reactive plasma in magnetic field

    NASA Astrophysics Data System (ADS)

    Zhdanov, V. M.; Stepanenko, A. A.

    2016-06-01

    Transport equations for partially ionized reactive plasma in magnetic field taking into account the internal degrees of freedom and electronic excitation of plasma particles are derived. As a starting point of analysis the kinetic equation with a binary collision operator written in the Wang-Chang and Uhlenbeck form and with a reactive collision integral allowing for arbitrary chemical reactions is used. The linearized variant of Grad's moment method is applied to deduce the systems of moment equations for plasma and also full and reduced transport equations for plasma species nonequilibrium parameters.

  12. Aerodynamic design optimization by using a continuous adjoint method

    NASA Astrophysics Data System (ADS)

    Luo, JiaQi; Xiong, JunTao; Liu, Feng

    2014-07-01

    This paper presents the fundamentals of a continuous adjoint method and the applications of this method to the aerodynamic design optimization of both external and internal flows. General formulation of the continuous adjoint equations and the corresponding boundary conditions are derived. With the adjoint method, the complete gradient information needed in the design optimization can be obtained by solving the governing flow equations and the corresponding adjoint equations only once for each cost function, regardless of the number of design parameters. An inverse design of airfoil is firstly performed to study the accuracy of the adjoint gradient and the effectiveness of the adjoint method as an inverse design method. Then the method is used to perform a series of single and multiple point design optimization problems involving the drag reduction of airfoil, wing, and wing-body configuration, and the aerodynamic performance improvement of turbine and compressor blade rows. The results demonstrate that the continuous adjoint method can efficiently and significantly improve the aerodynamic performance of the design in a shape optimization problem.

  13. Fully automatic adjoints: a robust and efficient mechanism for generating adjoint ocean models

    NASA Astrophysics Data System (ADS)

    Ham, D. A.; Farrell, P. E.; Funke, S. W.; Rognes, M. E.

    2012-04-01

    The problem of generating and maintaining adjoint models is sufficiently difficult that typically only the most advanced and well-resourced community ocean models achieve it. There are two current technologies which each suffer from their own limitations. Algorithmic differentiation, also called automatic differentiation, is employed by models such as the MITGCM [2] and the Alfred Wegener Institute model FESOM [3]. This technique is very difficult to apply to existing code, and requires a major initial investment to prepare the code for automatic adjoint generation. AD tools may also have difficulty with code employing modern software constructs such as derived data types. An alternative is to formulate the adjoint differential equation and to discretise this separately. This approach, known as the continuous adjoint and employed in ROMS [4], has the disadvantage that two different model code bases must be maintained and manually kept synchronised as the model develops. The discretisation of the continuous adjoint is not automatically consistent with that of the forward model, producing an additional source of error. The alternative presented here is to formulate the flow model in the high level language UFL (Unified Form Language) and to automatically generate the model using the software of the FEniCS project. In this approach it is the high level code specification which is differentiated, a task very similar to the formulation of the continuous adjoint [5]. However since the forward and adjoint models are generated automatically, the difficulty of maintaining them vanishes and the software engineering process is therefore robust. The scheduling and execution of the adjoint model, including the application of an appropriate checkpointing strategy is managed by libadjoint [1]. In contrast to the conventional algorithmic differentiation description of a model as a series of primitive mathematical operations, libadjoint employs a new abstraction of the simulation

  14. Goal-based angular adaptivity applied to a wavelet-based discretisation of the neutral particle transport equation

    SciTech Connect

    Goffin, Mark A.; Buchan, Andrew G.; Dargaville, Steven; Pain, Christopher C.; Smith, Paul N.; Smedley-Stevenson, Richard P.

    2015-01-15

    A method for applying goal-based adaptive methods to the angular resolution of the neutral particle transport equation is presented. The methods are applied to an octahedral wavelet discretisation of the spherical angular domain which allows for anisotropic resolution. The angular resolution is adapted across both the spatial and energy dimensions. The spatial domain is discretised using an inner-element sub-grid scale finite element method. The goal-based adaptive methods optimise the angular discretisation to minimise the error in a specific functional of the solution. The goal-based error estimators require the solution of an adjoint system to determine the importance to the specified functional. The error estimators and the novel methods to calculate them are described. Several examples are presented to demonstrate the effectiveness of the methods. It is shown that the methods can significantly reduce the number of unknowns and computational time required to obtain a given error. The novelty of the work is the use of goal-based adaptive methods to obtain anisotropic resolution in the angular domain for solving the transport equation. -- Highlights: •Wavelet angular discretisation used to solve transport equation. •Adaptive method developed for the wavelet discretisation. •Anisotropic angular resolution demonstrated through the adaptive method. •Adaptive method provides improvements in computational efficiency.

  15. ADGEN: ADjoint GENerator for computer models

    SciTech Connect

    Worley, B.A.; Pin, F.G.; Horwedel, J.E.; Oblow, E.M.

    1989-05-01

    This paper presents the development of a FORTRAN compiler and an associated supporting software library called ADGEN. ADGEN reads FORTRAN models as input and produces and enhanced version of the input model. The enhanced version reproduces the original model calculations but also has the capability to calculate derivatives of model results of interest with respect to any and all of the model data and input parameters. The method for calculating the derivatives and sensitivities is the adjoint method. Partial derivatives are calculated analytically using computer calculus and saved as elements of an adjoint matrix on direct assess storage. The total derivatives are calculated by solving an appropriate adjoint equation. ADGEN is applied to a major computer model of interest to the Low-Level Waste Community, the PRESTO-II model. PRESTO-II sample problem results reveal that ADGEN correctly calculates derivatives of response of interest with respect to 300 parameters. The execution time to create the adjoint matrix is a factor of 45 times the execution time of the reference sample problem. Once this matrix is determined, the derivatives with respect to 3000 parameters are calculated in a factor of 6.8 that of the reference model for each response of interest. For a single 3000 for determining these derivatives by parameter perturbations. The automation of the implementation of the adjoint technique for calculating derivatives and sensitivities eliminates the costly and manpower-intensive task of direct hand-implementation by reprogramming and thus makes the powerful adjoint technique more amenable for use in sensitivity analysis of existing models. 20 refs., 1 fig., 5 tabs.

  16. Relativistic transport equations for electromagnetic scalar, and pseudoscalar potentials

    SciTech Connect

    Shin, G.R.; Rafelski, J.

    1995-10-01

    The authors propose a particular form of relativistic transport equations arising from the classical limit of single-time Wigner function for Dirac particles evolving in the presence of scalar, pseudoscalar, and electromagnetic fields. These relativistic Vlasov-type equations for the particle and the antiparticle sector of the Fock space can be also obtained assuming the validity of the Liouville`s equation given a suitable classical Hamiltonian and the associated force. 11 refs.

  17. Onsager's-principle-consistent 13-moment transport equations

    NASA Astrophysics Data System (ADS)

    Singh, Narendra; Agrawal, Amit

    2016-06-01

    A new set of generalized transport equations is derived for higher-order moments which are generated in evolution equation for stress tensor and heat flux vector in 13-moment equations. The closure we employ satisfies Onsager's symmetry principle. In the derivation, we do not employ a phase density function based on Hermite polynomial series in terms of higher-order moments, unlike Grad's approach. The distribution function is rather chosen to satisfy collision invariance, and H-theorem and capture relatively strong deviations from equilibrium. The phase density function satisfies the linearized Boltzmann equation and provides the correct value of the Prandtl number for monatomic gas. The derived equations are compared with Grad's 13-moments equations for gas modeled as Maxwellian molecule. The merits of the proposed equations against Grad's and R13 equations are discussed. In particular, it is noted that the proposed equations contain higher-order terms compared to these equations but require a fewer number of boundary conditions as compared to the R13 equations. The Knudsen number envelope which can be covered to describe flows with these equations is therefore expected to be larger as compared to the earlier equations.

  18. Adjoint affine fusion and tadpoles

    NASA Astrophysics Data System (ADS)

    Urichuk, Andrew; Walton, Mark A.

    2016-06-01

    We study affine fusion with the adjoint representation. For simple Lie algebras, elementary and universal formulas determine the decomposition of a tensor product of an integrable highest-weight representation with the adjoint representation. Using the (refined) affine depth rule, we prove that equally striking results apply to adjoint affine fusion. For diagonal fusion, a coefficient equals the number of nonzero Dynkin labels of the relevant affine highest weight, minus 1. A nice lattice-polytope interpretation follows and allows the straightforward calculation of the genus-1 1-point adjoint Verlinde dimension, the adjoint affine fusion tadpole. Explicit formulas, (piecewise) polynomial in the level, are written for the adjoint tadpoles of all classical Lie algebras. We show that off-diagonal adjoint affine fusion is obtained from the corresponding tensor product by simply dropping non-dominant representations.

  19. Central role of the observable electric potential in transport equations.

    PubMed

    Garrido, J; Compañ, V; López, M L

    2001-07-01

    Nonequilibrium systems are usually studied in the framework of transport equations that involve the true electric potential (TEP), a nonobservable variable. Nevertheless another electric potential, the observable electric potential (OEP), may be defined to construct a useful set of transport equations. In this paper several basic characteristics of the OEP are deduced and emphasized: (i) the OEP distribution depends on thermodynamic state of the solution, (ii) the observable equations have a reference value for all other transport equations, (iii) the bridge that connects the OEP with a certain TEP is usually defined by the ion activity coefficient, (iv) the electric charge density is a nonobservable variable, and (v) the OEP formulation constitutes a natural model for studying the fluxes in membrane systems. PMID:11461346

  20. Kinetic theory of transport processes in partially ionized reactive plasma, I: General transport equations

    NASA Astrophysics Data System (ADS)

    Zhdanov, V. M.; Stepanenko, A. A.

    2016-03-01

    In this paper we derive the set of general transport equations for multicomponent partially ionized reactive plasma in the presence of electric and magnetic fields taking into account the internal degrees of freedom and electronic excitation of plasma particles. Our starting point is a generalized Boltzmann equation with the collision integral in the Wang-Chang and Uhlenbeck form and a reactive collision integral. We obtain a set of conservation equations for such plasma and employ a linearized variant of Grad's moment method to derive the system of moment (or transport) equations for the plasma species nonequilibrium parameters. Full and reduced transport equations, resulting from the linearized system of moment equations, are presented, which can be used to obtain transport relations and expressions for transport coefficients of electrons and heavy plasma particles (molecules, atoms and ions) in partially ionized reactive plasma.

  1. Volume transport and generalized hydrodynamic equations for monatomic fluids.

    PubMed

    Eu, Byung Chan

    2008-10-01

    In this paper, the effects of volume transport on the generalized hydrodynamic equations for a pure simple fluid are examined from the standpoint of statistical mechanics and, in particular, kinetic theory of fluids. First, we derive the generalized hydrodynamic equations, namely, the constitutive equations for the stress tensor and heat flux for a single-component monatomic fluid, from the generalized Boltzmann equation in the presence of volume transport. Then their linear steady-state solutions are derived and examined with regard to the effects of volume transport on them. The generalized hydrodynamic equations and linear constitutive relations obtained for nonconserved variables make it possible to assess Brenner's proposition [Physica A 349, 11 (2005); Physica A 349, 60 (2005)] for volume transport and attendant mass and volume velocities as well as the effects of volume transport on the Newtonian law of viscosity, compression/dilatation (bulk viscosity) phenomena, and Fourier's law of heat conduction. On the basis of study made, it is concluded that the notion of volume transport is sufficiently significant to retain in irreversible thermodynamics of fluids and fluid mechanics. PMID:19045107

  2. Diffusion Acceleration Schemes for Self-Adjoint Angular Flux Formulation with a Void Treatment

    SciTech Connect

    Yaqi Wang; Hongbin Zhang; Richard C. Martineau

    2014-02-01

    A Galerkin weak form for the monoenergetic neutron transport equation with a continuous finite element method and discrete ordinate method is developed based on self-adjoint angular flux formulation. This weak form is modified for treating void regions. A consistent diffusion scheme is developed with projection. Correction terms of the diffusion scheme are derived to reproduce the transport scalar flux. A source iteration that decouples the solution of all directions with both linear and nonlinear diffusion accelerations is developed and demonstrated. One-dimensional Fourier analysis is conducted to demonstrate the stability of the linear and nonlinear diffusion accelerations. Numerical results of these schemes are presented.

  3. Transport equations for the inflationary trispectrum

    SciTech Connect

    Anderson, Gemma J.; Seery, David; Mulryne, David J. E-mail: D.Mulryne@qmul.ac.uk

    2012-10-01

    We use transport techniques to calculate the trispectrum produced in multiple-field inflationary models with canonical kinetic terms. Our method allows the time evolution of the local trispectrum parameters, τ{sub NL} and g{sub NL}, to be tracked throughout the inflationary phase. We illustrate our approach using examples. We give a simplified method to calculate the superhorizon part of the relation between field fluctuations on spatially flat hypersurfaces and the curvature perturbation on uniform density slices, ζ, and obtain its third-order part for the first time. We clarify how the 'backwards' formalism of Yokoyama et al. relates to our analysis and other recent work. We supply explicit formulae which enable each inflationary observable to be computed in any canonical model of interest, using a suitable first-order ODE solver.

  4. Magnetohydrodynamic transport equations for high current propagation in overdense plasmas

    NASA Astrophysics Data System (ADS)

    Zha, Xuejun; Wang, Yan; Han, Shensheng

    2008-10-01

    In this paper, it is presented that the full set of magnetohydrodynamic (MHD) equations which may be used to study the transport mechanism for the high current relativistic electron beams (current intensity 100˜1000 MA, electron energy ˜ MeV) by the laser in background overdense plasma (1022-1026cm). The transport of intense relativistic electron beams (REB) has two basic characteristics: the first is that the forward current is a giga-ampere and the forward current density is about 10 14 A/cm 2 which exceeds the Alfven current limit [M. Tabak et al., Phys. Plasmas 12, 057305 (2005)]; the second is the propagation of the intense forward current in the presence of a background overdense plasma which may have very strong MHD instability. The transport problem can be solved by MHD equations that describe the dynamic, self consistent collisional and electromagnetic interaction of REB with overdense hydrogenic plasmas or arbitrary atomic-number plasmas. The full set of equations consists of the REB transport equations which are coupled to Maxwell's equations through the electromagnetic-field terms and two-fluid plasma dynamical equations for the background overdense plasma through the collision term.

  5. Transport equations for superconductors in the presence of spin interaction

    NASA Astrophysics Data System (ADS)

    Konschelle, François

    2014-05-01

    Quasi-classical theory of superconductivity provides a powerful and yet simple description of the superconductivity phenomenology. In particular, the Eilenberger and Usadel equations provide a neat simplification of the description of the superconducting state in the presence of disorder and electromagnetic interaction. However, the modern aspects of superconductivity require a correct description of the spin interaction as well. Here, we generalize the transport equations of superconductivity in order to take into account space-time dependent electromagnetic and spin interactions on equal footing. Using a gauge-covariant Wigner transformation for the Green-Gor'kov correlation functions, we establish the correspondence between the Dyson-Gor'kov equation and the quasi-classical transport equation in the time-dependent phase-space. We give the expressions for the gauge-covariant current and charge densities (quasi-particle, electric and spin) in the transport formulation. The generalized Eilenberger and Usadel limits of the transport equation are given, too. This study is devoted to the formal derivation of the equations of motion in the electromagnetic plus spin plus particle-hole space. The studies of some specific systems are postponed to future works.

  6. Optical Testing Using the Transport-of-Intensity Equation

    SciTech Connect

    Dorrer, C; Zuegel, J.D.

    2008-03-12

    The transport-of-intensity equation links the intensity and phase of an optical source to the longitudinal variation of its intensity in the presence of Fresnel diffraction. This equation can be used to provide a simple, accurate spatial-phase measurement for optical testing of flat surfaces. The properties of this approach are derived. The experimental demonstration is performed by quantifying the surface variations induced by the magnetorheological finishing process on laser rods.

  7. Adjoint-based uncertainty quantification and sensitivity analysis for reactor depletion calculations

    NASA Astrophysics Data System (ADS)

    Stripling, Hayes Franklin

    Depletion calculations for nuclear reactors model the dynamic coupling between the material composition and neutron flux and help predict reactor performance and safety characteristics. In order to be trusted as reliable predictive tools and inputs to licensing and operational decisions, the simulations must include an accurate and holistic quantification of errors and uncertainties in its outputs. Uncertainty quantification is a formidable challenge in large, realistic reactor models because of the large number of unknowns and myriad sources of uncertainty and error. We present a framework for performing efficient uncertainty quantification in depletion problems using an adjoint approach, with emphasis on high-fidelity calculations using advanced massively parallel computing architectures. This approach calls for a solution to two systems of equations: (a) the forward, engineering system that models the reactor, and (b) the adjoint system, which is mathematically related to but different from the forward system. We use the solutions of these systems to produce sensitivity and error estimates at a cost that does not grow rapidly with the number of uncertain inputs. We present the framework in a general fashion and apply it to both the source-driven and k-eigenvalue forms of the depletion equations. We describe the implementation and verification of solvers for the forward and ad- joint equations in the PDT code, and we test the algorithms on realistic reactor analysis problems. We demonstrate a new approach for reducing the memory and I/O demands on the host machine, which can be overwhelming for typical adjoint algorithms. Our conclusion is that adjoint depletion calculations using full transport solutions are not only computationally tractable, they are the most attractive option for performing uncertainty quantification on high-fidelity reactor analysis problems.

  8. Theory of contributon transport

    SciTech Connect

    Painter, J.W.; Gerstl, S.A.W.; Pomraning, G.C.

    1980-10-01

    A general discussion of the physics of contributon transport is presented. To facilitate this discussion, a Boltzmann-like transport equation for contributons is obtained, and special contributon cross sections are defined. However, the main goal of this study is to identify contributon transport equations and investigate possible deterministic solution techniques. Four approaches to the deterministic solution of the contributon transport problem are investigated. These approaches are an attempt to exploit certain attractive properties of the contributon flux, psi = phi phi/sup +/, where phi and phi/sup +/ are the solutions to the forward and adjoint Boltzmann transport equations.

  9. MCNP: Multigroup/adjoint capabilities

    SciTech Connect

    Wagner, J.C.; Redmond, E.L. II; Palmtag, S.P.; Hendricks, J.S.

    1994-04-01

    This report discusses various aspects related to the use and validity of the general purpose Monte Carlo code MCNP for multigroup/adjoint calculations. The increased desire to perform comparisons between Monte Carlo and deterministic codes, along with the ever-present desire to increase the efficiency of large MCNP calculations has produced a greater user demand for the multigroup/adjoint capabilities. To more fully utilize these capabilities, we review the applications of the Monte Carlo multigroup/adjoint method, describe how to generate multigroup cross sections for MCNP with the auxiliary CRSRD code, describe how to use the multigroup/adjoint capability in MCNP, and provide examples and results indicating the effectiveness and validity of the MCNP multigroup/adjoint treatment. This information should assist users in taking advantage of the MCNP multigroup/adjoint capabilities.

  10. Quantum Non-Markovian Langevin Equations and Transport Coefficients

    SciTech Connect

    Sargsyan, V.V.; Antonenko, N.V.; Kanokov, Z.; Adamian, G.G.

    2005-12-01

    Quantum diffusion equations featuring explicitly time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytic expressions for calculating the friction and diffusion coefficients in nuclear processes are obtained. The asymptotic behavior of the transport coefficients and correlation functions for a damped harmonic oscillator that is linearly coupled in momentum to a heat bath is studied. The coupling to a heat bath in momentum is responsible for the appearance of the diffusion coefficient in coordinate. The problem of regression of correlations in quantum dissipative systems is analyzed.

  11. A rain splash transport equation assimilating field and laboratory measurements

    USGS Publications Warehouse

    Dunne, T.; Malmon, D.V.; Mudd, S.M.

    2010-01-01

    Process-based models of hillslope evolution require transport equations relating sediment flux to its major controls. An equation for rain splash transport in the absence of overland flow was constructed by modifying an approach developed by Reeve (1982) and parameterizing it with measurements from single-drop laboratory experiments and simulated rainfall on a grassland in East Africa. The equation relates rain splash to hillslope gradient, the median raindrop diameter of a storm, and ground cover density; the effect of soil texture on detachability can be incorporated from other published results. The spatial and temporal applicability of such an equation for rain splash transport in the absence of overland flow on uncultivated hillslopes can be estimated from hydrological calculations. The predicted transport is lower than landscape-averaged geologic erosion rates from Kenya but is large enough to modify short, slowly eroding natural hillslopes as well as microtopographic interrill surfaces between which overland flow transports the mobilized sediment. Copyright 2010 by the American Geophysical Union. Copyright 2010 by the American Geophysical Union.

  12. Conservation Laws of a Family of Reaction-Diffusion-Convection Equations

    NASA Astrophysics Data System (ADS)

    Bruzón, M. S.; Gandarias, M. L.; de la Rosa, R.

    Ibragimov introduced the concept of nonlinear self-adjoint equations. This definition generalizes the concept of self-adjoint and quasi-self-adjoint equations. Gandarias defined the concept of weak self-adjoint. In this paper, we found a class of nonlinear self-adjoint nonlinear reaction-diffusion-convection equations which are neither self-adjoint nor quasi-self-adjoint nor weak self-adjoint. From a general theorem on conservation laws proved by Ibragimov we obtain conservation laws for these equations.

  13. Multilevel methods for transport equations in diffusive regimes

    NASA Technical Reports Server (NTRS)

    Manteuffel, Thomas A.; Ressel, Klaus

    1993-01-01

    We consider the numerical solution of the single-group, steady state, isotropic transport equation. An analysis by means of the moment equations shows that a discrete ordinate S(sub N) discretization in direction (angle) with a least squares finite element discretization in space does not behave properly in the diffusion limit. A scaling of the S(sub N) equations is introduced so that the least squares discretization has the correct diffusion limit. For the resulting discrete system a full multigrid algorithm was developed.

  14. Admitting the Inadmissible: Adjoint Formulation for Incomplete Cost Functionals in Aerodynamic Optimization

    NASA Technical Reports Server (NTRS)

    Arian, Eyal; Salas, Manuel D.

    1997-01-01

    We derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as "inadmissible." For example, a cost functional which depends on the density, rather than on the pressure, is considered "inadmissible" for an optimization problem governed by the Euler equations. We show that for such problems additional terms should be included in the Lagrangian functional when deriving the adjoint equations. These terms are obtained from the restriction of the interior PDE to the control surface. Demonstrations of the explicit derivation of the adjoint equations for "inadmissible" cost functionals are given for the potential, Euler, and Navier-Stokes equations.

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

    SciTech Connect

    Wang, Chi-Jen

    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.

  16. Singular perturbation analysis of the neutron transport equation

    SciTech Connect

    Losey, D.C.; Lee, J.C.

    1996-07-01

    A singular perturbation technique is applied to the one-speed, one- dimensional neutron transport equation with isotropic scattering. Our technique extends previous singular perturbation applications to higher-order and reduces the transport problem to a series of diffusion theory problems in the interior medium and a series of analytically solvable transport problems in the boundary layers. Asymptotic matching links the two solutions, yielding boundary conditions and a composite expansion valid throughout the media. Our formulation generates an accurate correction for the material interface condition used in global diffusion theory calculations.

  17. Analysis of Transition-Sensitized Turbulent Transport Equations

    NASA Technical Reports Server (NTRS)

    Rumsey, Christopher L.; Thacker, William D.; Gatski, Thomas B.; Grosch, Chester E,

    2005-01-01

    The dynamics of an ensemble of linear disturbances in boundary-layer flows at various Reynolds numbers is studied through an analysis of the transport equations for the mean disturbance kinetic energy and energy dissipation rate. Effects of adverse and favorable pressure-gradients on the disturbance dynamics are also included in the analysis Unlike the fully turbulent regime where nonlinear phase scrambling of the fluctuations affects the flow field even in proximity to the wall, the early stage transition regime fluctuations studied here are influenced cross the boundary layer by the solid boundary. The dominating dynamics in the disturbance kinetic energy and dissipation rate equations are described. These results are then used to formulate transition-sensitized turbulent transport equations, which are solved in a two-step process and applied to zero-pressure-gradient flow over a flat plate. Computed results are in good agreement with experimental data.

  18. Adjoint-Operator Learning For A Neural Network

    NASA Technical Reports Server (NTRS)

    Barhen, Jacob; Toomarian, Nikzad

    1993-01-01

    Electronic neural networks made to synthesize initially unknown mathematical models of time-dependent phenomena or to learn temporally evolving patterns by use of algorithms based on adjoint operators. Algorithms less complicated, involve less computation and solve learning equations forward in time possibly simultaneously with equations of evolution of neural network, thereby both increasing computational efficiency and making real-time applications possible.

  19. Adjoint-Based Methodology for Time-Dependent Optimization

    NASA Technical Reports Server (NTRS)

    Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.

    2008-01-01

    This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.

  20. A bedload transport equation for the Cerastoderma edule cockle

    NASA Astrophysics Data System (ADS)

    Anta, Jose; Peña, Enrique; Puertas, Jerónimo; Cea, Luis

    2013-02-01

    Hydrodynamics play an important role in the structure of many marine ecosystems of bivalves. After severe storm periods, large amounts of the Cerastoderma edule stocks were transported from the Lombos do Ulla shellfish bed (Spain). This paper presents the results of laboratory experiments carried out to analyze the bedload transport of this bivalve emulating the stormy shellfish bed conditions. Flow velocities were measured using particle image velocimetry and the double averaged methodology was applied to determine the main flow characteristics over different cockle patches. The flow structure exhibits properties of skimming and isolated flows depending on the density of bivalves. Bed shear stress was determined from the log-law and the cockles were geometrically characterized in order to derive specific bedload transport equations in a conventional deterministic sediment transport framework. The obtained formulas can be implemented in common numerical codes to further analyze mollusk stability, bedload transport and dispersal in their aquatic systems.

  1. A Posteriori Analysis for Hydrodynamic Simulations Using Adjoint Methodologies

    SciTech Connect

    Woodward, C S; Estep, D; Sandelin, J; Wang, H

    2009-02-26

    This report contains results of analysis done during an FY08 feasibility study investigating the use of adjoint methodologies for a posteriori error estimation for hydrodynamics simulations. We developed an approach to adjoint analysis for these systems through use of modified equations and viscosity solutions. Targeting first the 1D Burgers equation, we include a verification of the adjoint operator for the modified equation for the Lax-Friedrichs scheme, then derivations of an a posteriori error analysis for a finite difference scheme and a discontinuous Galerkin scheme applied to this problem. We include some numerical results showing the use of the error estimate. Lastly, we develop a computable a posteriori error estimate for the MAC scheme applied to stationary Navier-Stokes.

  2. Numerical Study of Fractional Ensemble Average Transport Equations

    NASA Astrophysics Data System (ADS)

    Kim, S.; Park, Y.; Gyeong, C. B.; Lee, O.

    2014-12-01

    In this presentation, a newly developed theory is applied to the case of stationary and non-stationary stochastic advective flow field, and a numerical solution method is presented for the resulting fractional Fokker-Planck equation (fFPE), which describes the evolution of the probability density function (PDF) of contaminant concentration. The derived fFPE is evaluated for three different form: 1) purely advective form, 2) second-order moment form and 3) second-order cumulant form. The Monte Carlo analysis of the fractional governing equation is then performed in a stochastic flow field, generated by a fractional Brownian motion for the stationary and non-stationary stochastic advection, in order to provide a benchmark for the results obtained from the fFPEs. When compared to the Monte Carlo simulation based PDFs and their ensemble average, the second-order cumulant form gives a good fit in terms of the shape and mode of the PDF of the contaminant concentration. Therefore, it is quite promising that the non-Fickian transport behavior can be modeled by the derived fractional ensemble average transport equations either by means of the long memory in the underlying stochastic flow, or by means of the time-space non-stationarity of the underlying stochastic flow, or by means of the time and space fractional derivatives of the transport equations. This subject is supported by Korea Ministry of Environment as "The Eco Innovation Project : Non-point source pollution control research group"

  3. Moment transport equations for the primordial curvature perturbation

    SciTech Connect

    Mulryne, David J.; Seery, David; Wesley, Daniel E-mail: d.seery@sussex.ac.uk

    2011-04-01

    In a recent publication, we proposed that inflationary perturbation theory can be reformulated in terms of a probability transport equation, whose moments determine the correlation properties of the primordial curvature perturbation. In this paper we generalize this formulation to an arbitrary number of fields. We deduce ordinary differential equations for the evolution of the moments of ζ on superhorizon scales, which can be used to obtain an evolution equation for the dimensionless bispectrum, f{sub NL}. Our equations are covariant in field space and allow identification of the source terms responsible for evolution of f{sub NL}. In a model with M scalar fields, the number of numerical integrations required to obtain solutions of these equations scales like O(M{sup 3}). The performance of the moment transport algorithm means that numerical calculations with M >> 1 fields are straightforward. We illustrate this performance with a numerical calculation of f{sub NL} in Nflation models containing M ∼ 10{sup 2} fields, finding agreement with existing analytic calculations. We comment briefly on extensions of the method beyond the slow-roll approximation, or to calculate higher order parameters such as g{sub NL}.

  4. Wing planform optimization via an adjoint method

    NASA Astrophysics Data System (ADS)

    Leoviriyakit, Kasidit

    This dissertation focuses on the problem of wing planform optimization for transonic aircraft based on flow simulation using Computational Fluid Dynamics (CFD) combined with an adjoint-gradient based numerical optimization procedure. The adjoint method, traditionally used for wing section design has been extended to cover planform variations and to compute the sensitivities of the structural weight of both the wing section and planform variations. The two relevant disciplines accounted for are the aerodynamics and structural weight. A simplified structural weight model is used for the optimization. Results of a variety of long range transports indicate that significant improvement in both aerodynamics and structures can be achieved simultaneously. The proof-of-concept optimal results indicate large improvements for both drag and structural weight. The work is an "enabling step" towards a realistic automated wing designed by a computer.

  5. Unsteady adjoint of a gas turbine inlet guide vane

    NASA Astrophysics Data System (ADS)

    Talnikar, Chaitanya; Wang, Qiqi

    2015-11-01

    Unsteady fluid flow simulations like large eddy simulation have been shown to be crucial in accurately predicting heat transfer in turbomachinery applications like transonic flow over an inlet guide vane. To compute sensitivities of aerothermal objectives for a vane with respect to design parameters an unsteady adjoint is required. In this talk we present unsteady adjoint solutions for a vane from VKI using pressure loss and heat transfer over the vane surface as the objectives. The boundary layer on the suction side near the trailing edge of the vane is turbulent and this poses a challenge for an adjoint solver. The chaotic dynamics cause the adjoint solution to diverge exponentially to infinity from that region when simulated backwards in time. The prospect of adding artificial viscosity to the adjoint equations to dampen the adjoint fields is investigated. Results for the vane from simulations performed on the Titan supercomputer will be shown and the effect of the additional viscosity on the accuracy of the sensitivities will be discussed.

  6. A transport equation for reaction rate in turbulent flows

    NASA Astrophysics Data System (ADS)

    Sabelnikov, V. A.; Lipatnikov, A. N.; Chakraborty, N.; Nishiki, S.; Hasegawa, T.

    2016-08-01

    New transport equations for chemical reaction rate and its mean value in turbulent flows have been derived and analyzed. Local perturbations of the reaction zone by turbulent eddies are shown to play a pivotal role even for weakly turbulent flows. The mean-reaction-rate transport equation is shown to involve two unclosed dominant terms and a joint closure relation for the sum of these two terms is developed. Obtained analytical results and, in particular, the closure relation are supported by processing two widely recognized sets of data obtained from earlier direct numerical simulations of statistically planar 1D premixed flames associated with both weak large-scale and intense small-scale turbulence.

  7. Transport equations for lower hybrid waves in a turbulent plasma

    NASA Astrophysics Data System (ADS)

    Mendonca, J. T.; Horton, W.; Galvao, R. M. O.; Elskens, Y.

    2014-10-01

    Injection and control of intense lower hybrid (LH) wave spectra is required to achieve steady state tokamak operation in the new WEST tokamak at CEA France. The tungsten [W] environment [E] steadytstate [S] tokamak [T] has two high-power [20 MW] lower hybrid antennas launching 3.7 GHz polarized waves for steady fusion-grade plasmas control. The wave propagation and scattering is described in by ray equations in the presence of the drift wave turbulence. Theory for the wave transport equations for propagation of the wave momentum and energy densities are derived from the Wigner function method of QM. The limits of the diffraction and scattering for ray transport theory are established. Comparisons are made between the wave propagation in WEST and ITER tokamaks. Supported by the University of Texas at Austin; PIIM/CNRS at Aix-Marseille University and University of Sao Paulo.

  8. Adjoint operator approach to shape design for internal incompressible flows

    NASA Technical Reports Server (NTRS)

    Cabuk, H.; Sung, C.-H.; Modi, V.

    1991-01-01

    The problem of determining the profile of a channel or duct that provides the maximum static pressure rise is solved. Incompressible, laminar flow governed by the steady state Navier-Stokes equations is assumed. Recent advances in computational resources and algorithms have made it possible to solve the direct problem of determining such a flow through a body of known geometry. It is possible to obtain a set of adjoint equations, the solution to which permits the calculation of the direction and relative magnitude of change in the diffuser profile that leads to a higher pressure rise. The solution to the adjoint problem can be shown to represent an artificially constructed flow. This interpretation provides a means to construct numerical solutions to the adjoint equations that do not compromise the fully viscous nature of the problem. The algorithmic and computational aspects of solving the adjoint equations are addressed. The form of these set of equations is similar but not identical to the Navier-Stokes equations. In particular some issues related to boundary conditions and stability are discussed.

  9. Sonic Boom Mitigation Through Aircraft Design and Adjoint Methodology

    NASA Technical Reports Server (NTRS)

    Rallabhandi, Siriam K.; Diskin, Boris; Nielsen, Eric J.

    2012-01-01

    This paper presents a novel approach to design of the supersonic aircraft outer mold line (OML) by optimizing the A-weighted loudness of sonic boom signature predicted on the ground. The optimization process uses the sensitivity information obtained by coupling the discrete adjoint formulations for the augmented Burgers Equation and Computational Fluid Dynamics (CFD) equations. This coupled formulation links the loudness of the ground boom signature to the aircraft geometry thus allowing efficient shape optimization for the purpose of minimizing the impact of loudness. The accuracy of the adjoint-based sensitivities is verified against sensitivities obtained using an independent complex-variable approach. The adjoint based optimization methodology is applied to a configuration previously optimized using alternative state of the art optimization methods and produces additional loudness reduction. The results of the optimizations are reported and discussed.

  10. Learning a trajectory using adjoint functions and teacher forcing

    NASA Technical Reports Server (NTRS)

    Toomarian, Nikzad B.; Barhen, Jacob

    1992-01-01

    A new methodology for faster supervised temporal learning in nonlinear neural networks is presented which builds upon the concept of adjoint operators to allow fast computation of the gradients of an error functional with respect to all parameters of the neural architecture, and exploits the concept of teacher forcing to incorporate information on the desired output into the activation dynamics. The importance of the initial or final time conditions for the adjoint equations is discussed. A new algorithm is presented in which the adjoint equations are solved simultaneously (i.e., forward in time) with the activation dynamics of the neural network. We also indicate how teacher forcing can be modulated in time as learning proceeds. The results obtained show that the learning time is reduced by one to two orders of magnitude with respect to previously published results, while trajectory tracking is significantly improved. The proposed methodology makes hardware implementation of temporal learning attractive for real-time applications.

  11. Global Adjoint Tomography

    NASA Astrophysics Data System (ADS)

    Bozdag, Ebru; Lefebvre, Matthieu; Lei, Wenjie; Peter, Daniel; Smith, James; Komatitsch, Dimitri; Tromp, Jeroen

    2015-04-01

    We will present our initial results of global adjoint tomography based on 3D seismic wave simulations which is one of the most challenging examples in seismology in terms of intense computational requirements and vast amount of high-quality seismic data that can potentially be assimilated in inversions. Using a spectral-element method, we incorporate full 3D wave propagation in seismic tomography by running synthetic seismograms and adjoint simulations to compute exact sensitivity kernels in realistic 3D background models. We run our global simulations on the Oak Ridge National Laboratory's Cray XK7 "Titan" system taking advantage of the GPU version of the SPECFEM3D_GLOBE package. We have started iterations with initially selected 253 earthquakes within the magnitude range of 5.5 < Mw < 7.0 and numerical simulations having resolution down to ~27 s to invert for a transversely isotropic crust and mantle model using a non-linear conjugate gradient algorithm. The measurements are currently based on frequency-dependent traveltime misfits. We use both minor- and major-arc body and surface waves by running 200 min simulations where inversions are performed with more than 2.6 million measurements. Our initial results after 12 iterations already indicate several prominent features such as enhanced slab (e.g., Hellenic, Japan, Bismarck, Sandwich), plume/hotspot (e.g., the Pacific superplume, Caroline, Yellowstone, Hawaii) images, etc. To improve the resolution and ray coverage, particularly in the lower mantle, our aim is to increase the resolution of numerical simulations first going down to ~17 s and then to ~9 s to incorporate high-frequency body waves in inversions. While keeping track of the progress and illumination of features in our models with a limited data set, we work towards to assimilate all available data in inversions from all seismic networks and earthquakes in the global CMT catalogue.

  12. Numerical solution of the radiation transport equation in disk geometry

    NASA Technical Reports Server (NTRS)

    Spagna, George F., Jr.; Leung, Chun Ming

    1987-01-01

    An efficient numerical method for solving the problem of radiation transport in a dusty medium with two dimensional (2-D) disk geometry is described. It is a generalization of the one-dimensional quasi-diffusion method in which the transport equation is cast in diffusion form and then solved as a boundary value problem. The method should be applicable to a variety of astronomical sources, the dynamics of which are angular-momentum dominated and hence not accurately treated by spherical geometry, e.g., protoplanetary nebulae, circumstellar disks, interstellar molecular clouds, accretion disks, and disk galaxies. The computational procedure and practical considerations for implementing the method are described in detail. To illustrate the effects of 2-D radiation transport, some model results (dust temperature distributions and IR flux spectra) for externally heated, interstellar dust clouds with spherically symmetric and disk geometry are compared.

  13. Inverse problems for homogeneous transport equations: II. The multidimensional case

    NASA Astrophysics Data System (ADS)

    Bal, Guillaume

    2000-08-01

    A companion paper by Bal (Bal G 2000 Inverse Problems 16 997) and this paper are parts I and II of a series dealing with the reconstruction from boundary measurements of the scattering operator of homogeneous linear transport equations. This part II deals with the case of convex bounded domains in dimensions higher than one. We distinguish the analysis of smooth boundaries from that of boundaries with discontinuities such as corners. We propose a reconstruction in the case of degenerate symmetric scattering operators and show the well-posedness of the inverse problem. The proof of well-posedness is based on a decomposition of angular moments of the transport solution into unbounded and bounded components. This decomposition allows us to show the linear independence of a sufficiently large number of angular moments of the transport solution that are used to construct an invertible system for the scattering coefficients to be reconstructed.

  14. Adjoint simulation of stream depletion due to aquifer pumping.

    PubMed

    Neupauer, Roseanna M; Griebling, Scott A

    2012-01-01

    If an aquifer is hydraulically connected to an adjacent stream, a pumping well operating in the aquifer will draw some water from aquifer storage and some water from the stream, causing stream depletion. Several analytical, semi-analytical, and numerical approaches have been developed to estimate stream depletion due to pumping. These approaches are effective if the well location is known. If a new well is to be installed, it may be desirable to install the well at a location where stream depletion is minimal. If several possible locations are considered for the location of a new well, stream depletion would have to be estimated for all possible well locations, which can be computationally inefficient. The adjoint approach for estimating stream depletion is a more efficient alternative because with one simulation of the adjoint model, stream depletion can be estimated for pumping at a well at any location. We derive the adjoint equations for a coupled system with a confined aquifer, an overlying unconfined aquifer, and a river that is hydraulically connected to the unconfined aquifer. We assume that the stage in the river is known, and is independent of the stream depletion, consistent with the assumptions of the MODFLOW river package. We describe how the adjoint equations can be solved using MODFLOW. In an illustrative example, we show that for this scenario, the adjoint approach is as accurate as standard forward numerical simulation methods, and requires substantially less computational effort. PMID:22182421

  15. Mesh-free adjoint methods for nonlinear filters

    NASA Astrophysics Data System (ADS)

    Daum, Fred

    2005-09-01

    We apply a new industrial strength numerical approximation, called the "mesh-free adjoint method", to solve the nonlinear filtering problem. This algorithm exploits the smoothness of the problem, unlike particle filters, and hence we expect that mesh-free adjoints are superior to particle filters for many practical applications. The nonlinear filter problem is equivalent to solving the Fokker-Planck equation in real time. The key idea is to use a good adaptive non-uniform quantization of state space to approximate the solution of the Fokker-Planck equation. In particular, the adjoint method computes the location of the nodes in state space to minimize errors in the final answer. This use of an adjoint is analogous to optimal control algorithms, but it is more interesting. The adjoint method is also analogous to importance sampling in particle filters, but it is better for four reasons: (1) it exploits the smoothness of the problem; (2) it explicitly minimizes the errors in the relevant functional; (3) it explicitly models the dynamics in state space; and (4) it can be used to compute a corrected value for the desired functional using the residuals. We will attempt to make this paper accessible to normal engineers who do not have PDEs for breakfast.

  16. Application of the Broyden method to stiff transport equations

    NASA Astrophysics Data System (ADS)

    Carlsson, Johan; Cary, John R.; Cohen, Ron

    2002-11-01

    Plasma turbulence generates fluxes (of particles, energy, etc.) that are said to be stiff, that is a small change in temperature, density, or some other quantity, can lead to a large change in flux. The dependence of the diffusivities on the temperature and density profiles, and their gradients, also introduces nonlinearity. Irrespective of whether the fluxes are given by transport models, such as IFS/PPPL, GLF23, or MMM95, or are directly calculated, the resulting system of transport equations is thus numerically challenging to solve. Efficient transport solvers must also take into account that the evaluation of the diffusivities (or their gradients: the fluxes) is numerically costly. We have developed a new iterative transport solver that combines the stability of a relaxation scheme with the fast convergence of a Newton solver. The new solver uses a gradually decreasing relaxation parameter for the first few iterations and once it is inside the radius of convergence it switches over to a quasi-Newton method where a Broyden-like scheme is used to approximate the Jacobian. By taking advantage of the structure of the matrix (tri-diagonal if a second-order spatial finite differencing is used) the Broyden algorithm[1] gives a good approximation of the Jacobian after only a few iterations. We have implemented the new transport solver in the form of a C++ library called the Transport Analysis Tool. To make the library easy to access from codes written in other languages, a C interface is also provided. We will present the new transport solver in detail, as well as benchmark results and examples of how to use the Transport Analysis Tool library. [1] C. G. Broyden, in Mathematics of Computation, vol. 19, 1965, pp. 577--593.

  17. Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq Equations

    NASA Astrophysics Data System (ADS)

    Brenier, Yann

    2009-10-01

    We establish a connection between optimal transport theory (see Villani in Topics in optimal transportation. Graduate studies in mathematics, vol. 58, AMS, Providence, 2003, for instance) and classical convection theory for geophysical flows (Pedlosky, in Geophysical fluid dynamics, Springer, New York, 1979). Our starting point is the model designed few years ago by Angenent, Haker, and Tannenbaum (SIAM J. Math. Anal. 35:61-97, 2003) to solve some optimal transport problems. This model can be seen as a generalization of the Darcy-Boussinesq equations, which is a degenerate version of the Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate different variants of the NSB equations (in particular what we call the generalized hydrostatic-Boussinesq equations) to various models involving optimal transport (and the related Monge-Ampère equation, Brenier in Commun. Pure Appl. Math. 64:375-417, 1991; Caffarelli in Commun. Pure Appl. Math. 45:1141-1151, 1992). This includes the 2D semi-geostrophic equations (Hoskins in Annual review of fluid mechanics, vol. 14, pp. 131-151, Palo Alto, 1982; Cullen et al. in SIAM J. Appl. Math. 51:20-31, 1991, Arch. Ration. Mech. Anal. 185:341-363, 2007; Benamou and Brenier in SIAM J. Appl. Math. 58:1450-1461, 1998; Loeper in SIAM J. Math. Anal. 38:795-823, 2006) and some fully nonlinear versions of the so-called high-field limit of the Vlasov-Poisson system (Nieto et al. in Arch. Ration. Mech. Anal. 158:29-59, 2001) and of the Keller-Segel for Chemotaxis (Keller and Segel in J. Theor. Biol. 30:225-234, 1971; Jäger and Luckhaus in Trans. Am. Math. Soc. 329:819-824, 1992; Chalub et al. in Mon. Math. 142:123-141, 2004). Mathematically speaking, we establish some existence theorems for local smooth, global smooth or global weak solutions of the different models. We also justify that the inertia terms can be rigorously neglected under appropriate scaling assumptions in the generalized Navier-Stokes-Boussinesq equations

  18. Implicitly causality enforced solution of multidimensional transient photon transport equation.

    PubMed

    Handapangoda, Chintha C; Premaratne, Malin

    2009-12-21

    A novel method for solving the multidimensional transient photon transport equation for laser pulse propagation in biological tissue is presented. A Laguerre expansion is used to represent the time dependency of the incident short pulse. Owing to the intrinsic causal nature of Laguerre functions, our technique automatically always preserve the causality constrains of the transient signal. This expansion of the radiance using a Laguerre basis transforms the transient photon transport equation to the steady state version. The resulting equations are solved using the discrete ordinates method, using a finite volume approach. Therefore, our method enables one to handle general anisotropic, inhomogeneous media using a single formulation but with an added degree of flexibility owing to the ability to invoke higher-order approximations of discrete ordinate quadrature sets. Therefore, compared with existing strategies, this method offers the advantage of representing the intensity with a high accuracy thus minimizing numerical dispersion and false propagation errors. The application of the method to one, two and three dimensional geometries is provided. PMID:20052050

  19. Renormalization group methods for the Reynolds stress transport equations

    NASA Technical Reports Server (NTRS)

    Rubinstein, R.

    1992-01-01

    The Yakhot-Orszag renormalization group is used to analyze the pressure gradient-velocity correlation and return to isotropy terms in the Reynolds stress transport equations. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher order nonlinear models by approximating the sums more accurately. The Yakhot-Orszag renormalization group provides a systematic procedure for deriving turbulence models. Typical applications have included theoretical derivation of the universal constants of isotropic turbulence theory, such as the Kolmogorov constant, and derivation of two equation models, again with theoretically computed constants and low Reynolds number forms of the equations. Recent work has applied this formalism to Reynolds stress modeling, previously in the form of a nonlinear eddy viscosity representation of the Reynolds stresses, which can be used to model the simplest normal stress effects. The present work attempts to apply the Yakhot-Orszag formalism to Reynolds stress transport modeling.

  20. Is Onsager symmetry relevant in the transport equations for magnetically confined plasmas

    SciTech Connect

    Balescu, R. )

    1991-03-01

    A global, algebraic view of the transport processes in a magnetically confined plasma is developed. Both the neoclassical (banana) and the anomalous transport matrices are represented in a factorized form, thus separating the roles of the dynamics and of the geometric constraints. The self-adjointness of the collision operator (the sole condition for classical Onsager symmetry) is shown to be a necessary, but not sufficient condition for this symmetry in confined plasmas. The latter results for the banana transport matrix from a delicate relationship between dynamic and geometric components. This structure is not present in the anomalous transport matrix, and the Onsager symmetry is broken in this case. It is stressed that the symmetry breaking does not violate any general principles.

  1. Quantum-mechanical transport equation for atomic systems.

    NASA Technical Reports Server (NTRS)

    Berman, P. R.

    1972-01-01

    A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

  2. Vorticity Preserving Flux Corrected Transport Scheme for the Acoustic Equations

    SciTech Connect

    Lung, Tyler B.; Roe, Phil; Morgan, Nathaniel R.

    2012-08-15

    Long term research goals are to develop an improved cell-centered Lagrangian Hydro algorithm with the following qualities: 1. Utilizes Flux Corrected Transport (FCT) to achieve second order accuracy with multidimensional physics; 2. Does not rely on the one-dimensional Riemann problem; and 3. Implements a form of vorticity control. Short term research goals are to devise and implement a 2D vorticity preserving FCT solver for the acoustic equations on an Eulerian mesh: 1. Develop a flux limiting mechanism for systems of governing equations with symmetric wave speeds; 2. Verify the vorticity preserving properties of the scheme; and 3. Compare the performance of the scheme to traditional MUSCL-Hancock and other algorithms.

  3. Proton transport model in the ionosphere 1. Multistream approach of the transport equations

    NASA Astrophysics Data System (ADS)

    Galand, M.; Lilensten, J.; Kofman, W.; Sidje, R. B.

    1997-09-01

    The suprathermal particles, electrons and protons, coming from the magnetosphere and precipitating into the high-latitude atmosphere are an energy source of the Earth's ionosphere. They interact with ambient thermal gas through inelastic and elastic collisions. The physical quantities perturbed by these precipitations, such as the heating rate, the electron production rate, or the emission intensities, can be provided in solving the kinetic stationary Boltzmann equation. This equation yields particle fluxes as a function of altitude, energy, and pitch angle. While this equation has been solved through different ways for the electron transport and fully tested, the proton transport is more complicated. Because of charge-changing reactions, the latter is a set of two-coupled transport equations that must be solved: one for protons and the other for H atoms. We present here a new approach that solves the multistream proton/hydrogen transport equations encompassing the collision angular redistributions and the magnetic mirroring effect. In order to validate our model we discuss the energy conservation and we compare with another model under the same inputs and with rocket observations. The influence of the angular redistributions is discussed in a forthcoming paper.

  4. Towards Global Adjoint Tomography

    NASA Astrophysics Data System (ADS)

    Bozdag, E.; Zhu, H.; Peter, D. B.; Tromp, J.

    2012-12-01

    Seismic tomography is at a stage where we can harness entire seismograms using the opportunities offered by advances in numerical wave propagation solvers and high-performance computing. Adjoint methods provide an efficient way for incorporating full nonlinearity of wave propagation and 3D Fréchet kernels in iterative seismic inversions which have so far given promising results at continental and regional scales. Our goal is to take adjoint tomography forward to image the entire planet. Using an iterative conjugate gradient scheme, we initially set the aim to obtain a global crustal and mantle model with confined transverse isotropy in the upper mantle. We have started with around 255 global CMT events having moment magnitudes between 5.8 and 7, and used GSN stations as well as some local networks such as USArray, European stations etc. Prior to the structure inversion, we reinvert global CMT solutions by computing Green functions in our 3D reference model to take into account effects of crustal variations on source parameters. Using the advantages of numerical simulations, our strategy is to invert crustal and mantle structure together to avoid any bias introduced into upper-mantle images due to "crustal corrections", which are commonly used in classical tomography. 3D simulations dramatically increase the usable amount of data so that, with the current earthquake-station setup, we perform each iteration with more than two million measurements. Multi-resolution smoothing based on ray density is applied to the gradient to better deal with the imperfect source-station distribution on the globe and extract more information underneath regions with dense ray coverage and vice versa. Similar to frequency domain approach, we reduce nonlinearities by starting from long periods and gradually increase the frequency content of data after successive model updates. To simplify the problem, we primarily focus on the elastic structure and therefore our measurements are based on

  5. Geometric Correction for Diffusive Expansion of Steady Neutron Transport Equation

    NASA Astrophysics Data System (ADS)

    Wu, Lei; Guo, Yan

    2015-06-01

    We revisit the diffusive limit of a steady neutron transport equation in a two-dimensional unit disk with one-speed velocity. A classical theorem by Bensoussan et al. (Publ Res Inst Math Sci 15(1):53-157, 1979) states that its solution can be approximated in L ∞ by the leading order interior solution plus the Knudsen layer in the diffusive limit. In this paper, we construct a counterexample to this result via a different boundary layer expansion with geometric correction.

  6. Modeling tracer transport in randomly heterogeneous porous media by nonlocal moment equations: Anomalous transport

    NASA Astrophysics Data System (ADS)

    Morales-Casique, E.; Lezama-Campos, J. L.; Guadagnini, A.; Neuman, S. P.

    2013-05-01

    Modeling tracer transport in geologic porous media suffers from the corrupt characterization of the spatial distribution of hydrogeologic properties of the system and the incomplete knowledge of processes governing transport at multiple scales. Representations of transport dynamics based on a Fickian model of the kind considered in the advection-dispersion equation (ADE) fail to capture (a) the temporal variation associated with the rate of spreading of a tracer, and (b) the distribution of early and late arrival times which are often observed in field and/or laboratory scenarios and are considered as the signature of anomalous transport. Elsewhere we have presented exact stochastic moment equations to model tracer transport in randomly heterogeneous aquifers. We have also developed a closure scheme which enables one to provide numerical solutions of such moment equations at different orders of approximations. The resulting (ensemble) average and variance of concentration fields were found to display a good agreement against Monte Carlo - based simulation results for mildly heterogeneous (or well-conditioned strongly heterogeneous) media. Here we explore the ability of the moment equations approach to describe the distribution of early arrival times and late time tailing effects which can be observed in Monte-Carlo based breakthrough curves (BTCs) of the (ensemble) mean concentration. We show that BTCs of mean resident concentration calculated at a fixed space location through higher-order approximations of moment equations display long tailing features of the kind which is typically associated with anomalous transport behavior and are not represented by an ADE model with constant dispersive parameter, such as the zero-order approximation.

  7. The fast neutron fluence and the activation detector activity calculations using the effective source method and the adjoint function

    SciTech Connect

    Hep, J.; Konecna, A.; Krysl, V.; Smutny, V.

    2011-07-01

    This paper describes the application of effective source in forward calculations and the adjoint method to the solution of fast neutron fluence and activation detector activities in the reactor pressure vessel (RPV) and RPV cavity of a VVER-440 reactor. Its objective is the demonstration of both methods on a practical task. The effective source method applies the Boltzmann transport operator to time integrated source data in order to obtain neutron fluence and detector activities. By weighting the source data by time dependent decay of the detector activity, the result of the calculation is the detector activity. Alternatively, if the weighting is uniform with respect to time, the result is the fluence. The approach works because of the inherent linearity of radiation transport in non-multiplying time-invariant media. Integrated in this way, the source data are referred to as the effective source. The effective source in the forward calculations method thereby enables the analyst to replace numerous intensive transport calculations with a single transport calculation in which the time dependence and magnitude of the source are correctly represented. In this work, the effective source method has been expanded slightly in the following way: neutron source data were performed with few group method calculation using the active core calculation code MOBY-DICK. The follow-up neutron transport calculation was performed using the neutron transport code TORT to perform multigroup calculations. For comparison, an alternative method of calculation has been used based upon adjoint functions of the Boltzmann transport equation. Calculation of the three-dimensional (3-D) adjoint function for each required computational outcome has been obtained using the deterministic code TORT and the cross section library BGL440. Adjoint functions appropriate to the required fast neutron flux density and neutron reaction rates have been calculated for several significant points within the RPV

  8. Transport equations of electrodiffusion processes in the laboratory reference frame.

    PubMed

    Garrido, Javier

    2006-02-23

    The transport equations of electrodiffusion processes use three reference frames for defining the fluxes: Fick's reference in diffusion, solvent-fixed reference in transference numbers, and laboratory fluxes in electric conductivity. The convenience of using only one reference frame is analyzed here from the point of view of the thermodynamics of irreversible processes. A relation between the fluxes of ions and solvent and the electric current density is deduced first from a mass and volume balance. This is then used to show that (i) the laboratory and Fick's diffusion coefficients are identical and (ii) the transference numbers of both the solvent and the ion in the laboratory reference frame are related. Finally, four experimental methods for the measurement of ion transference numbers are analyzed critically. New expressions for evaluating transference numbers for the moving boundary method and the chronopotentiometry technique are deduced. It is concluded that the ion transport equation in the laboratory reference frame plays a key role in the description of electrodiffusion processes. PMID:16494340

  9. Modeling of Flow Transition Using an Intermittency Transport Equation

    NASA Technical Reports Server (NTRS)

    Suzen, Y. B.; Huang, P. G.

    1999-01-01

    A new transport equation for intermittency factor is proposed to model transitional flows. The intermittent behavior of the transitional flows is incorporated into the computations by modifying the eddy viscosity, mu(sub t), obtainable from a turbulence model, with the intermittency factor, gamma: mu(sub t, sup *) = gamma.mu(sub t). In this paper, Menter's SST model (Menter, 1994) is employed to compute mu(sub t) and other turbulent quantities. The proposed intermittency transport equation can be considered as a blending of two models - Steelant and Dick (1996) and Cho and Chung (1992). The former was proposed for near-wall flows and was designed to reproduce the streamwise variation of the intermittency factor in the transition zone following Dhawan and Narasimha correlation (Dhawan and Narasimha, 1958) and the latter was proposed for free shear flows and was used to provide a realistic cross-stream variation of the intermittency profile. The new model was used to predict the T3 series experiments assembled by Savill (1993a, 1993b) including flows with different freestream turbulence intensities and two pressure-gradient cases. For all test cases good agreements between the computed results and the experimental data are observed.

  10. A New 2D-Transport, 1D-Diffusion Approximation of the Boltzmann Transport equation

    SciTech Connect

    Larsen, Edward

    2013-06-17

    The work performed in this project consisted of the derivation, implementation, and testing of a new, computationally advantageous approximation to the 3D Boltz- mann transport equation. The solution of the Boltzmann equation is the neutron flux in nuclear reactor cores and shields, but solving this equation is difficult and costly. The new “2D/1D” approximation takes advantage of a special geometric feature of typical 3D reactors to approximate the neutron transport physics in a specific (ax- ial) direction, but not in the other two (radial) directions. The resulting equation is much less expensive to solve computationally, and its solutions are expected to be sufficiently accurate for many practical problems. In this project we formulated the new equation, discretized it using standard methods, developed a stable itera- tion scheme for solving the equation, implemented the new numerical scheme in the MPACT code, and tested the method on several realistic problems. All the hoped- for features of this new approximation were seen. For large, difficult problems, the resulting 2D/1D solution is highly accurate, and is calculated about 100 times faster than a 3D discrete ordinates simulation.

  11. A unified transport equation for both cosmic rays and thermal particles

    NASA Technical Reports Server (NTRS)

    Williams, L. L.; Schwadron, N.; Jokipii, J. R.; Gombosi, T. I.

    1993-01-01

    We present a unified transport equation that is valid for particles of all energies if the particle mean free paths are much smaller than macroscopic fluid length scales. If restricted to particles with random speeds much greater than fluid flow speeds, this equation reduces to the previously discussed extended cosmic-ray transport equation. It is significant that this allows one to describe the acceleration of particles from thermal energies to cosmic-ray energies using one transport equation. This is in contrast to previous transport equations (the Parker equation and the extended cosmic-ray transport equation), which were restricted to fast particles. The close connection to the extended cosmic-ray transport equation is demonstrated.

  12. Neglected transport equations: extended Rankine-Hugoniot conditions and J -integrals for fracture

    NASA Astrophysics Data System (ADS)

    Davey, K.; Darvizeh, R.

    2016-03-01

    Transport equations in integral form are well established for analysis in continuum fluid dynamics but less so for solid mechanics. Four classical continuum mechanics transport equations exist, which describe the transport of mass, momentum, energy and entropy and thus describe the behaviour of density, velocity, temperature and disorder, respectively. However, one transport equation absent from the list is particularly pertinent to solid mechanics and that is a transport equation for movement, from which displacement is described. This paper introduces the fifth transport equation along with a transport equation for mechanical energy and explores some of the corollaries resulting from the existence of these equations. The general applicability of transport equations to discontinuous physics is discussed with particular focus on fracture mechanics. It is well established that bulk properties can be determined from transport equations by application of a control volume methodology. A control volume can be selected to be moving, stationary, mass tracking, part of, or enclosing the whole system domain. The flexibility of transport equations arises from their ability to tolerate discontinuities. It is insightful thus to explore the benefits derived from the displacement and mechanical energy transport equations, which are shown to be beneficial for capturing the physics of fracture arising from a displacement discontinuity. Extended forms of the Rankine-Hugoniot conditions for fracture are established along with extended forms of J -integrals.

  13. Nodal collocation approximation for the multidimensional PL equations applied to transport source problems

    SciTech Connect

    Verdu, G.; Capilla, M.; Talavera, C. F.; Ginestar, D.

    2012-07-01

    PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)

  14. Transport Code for Regular Triangular Geometry

    1993-06-09

    DIAMANT2 solves the two-dimensional static multigroup neutron transport equation in planar regular triangular geometry. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective or input specified boundary flux conditions are solved. Anisotropy is allowed for the scattering source. Volume and surface sources are allowed for inhomogeneous problems.

  15. Probability density adjoint for sensitivity analysis of the Mean of Chaos

    SciTech Connect

    Blonigan, Patrick J. Wang, Qiqi

    2014-08-01

    Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. This paper presents a new method for sensitivity analysis of ergodic chaotic dynamical systems, the density adjoint method. The method involves solving the governing equations for the system's invariant measure and its adjoint on the system's attractor manifold rather than in phase-space. This new approach is derived for and demonstrated on one-dimensional chaotic maps and the three-dimensional Lorenz system. It is found that the density adjoint computes very finely detailed adjoint distributions and accurate sensitivities, but suffers from large computational costs.

  16. Adjoint Based Data Assimilation for an Ionospheric Model

    NASA Astrophysics Data System (ADS)

    Rosen, I. G.; Hajj, G. A.; Hajj, G. A.; Pi, X.; Pi, X.; Wang, C.; Wilson, B. D.

    2001-05-01

    The success of ionospheric modeling depends primarily on accurate knowledge of the forces (drivers) which enter into the collisional plasma hydrodynamic equations for the ionosphere and control the ionization as well as other dynamical and chemical processes. These include solar EUV and UV radiation, magnetospheric electric fields, particle precipitation, dynamo electric fields, thermospheric winds, neutral densities, and temperature. The determination of these model parameters from observational data is known as data assimilation. The data assimilation problem is formulated as a problem of minimizing a nonlinear functional, J (typically least squares) under a system of constraints consisting primarily of the underlying model equations. The performance index, J, can, in principle, be minimized using standard techniques such as the Newton's steepest decent method. There are however major technical challenges in practice. Since J is highly nonlinear and each evaluation of the functional requires the integration of the ionospheric model equations, computing the gradient vector of J with respect to the unknown parameters is time consuming. This problem is solved by use of the adjoint method. The ionospheric model used in this effort is for mid- and low-latitudes and consists of solving the continuity and momentum partial differential equations in four dimensional (three spatial dimensions and time) to compute the O+ density in the ionosphere and plasmasphere. We have developed codes for solving the forward model on a fixed grid. This makes it relatively straight forward to apply the adjoint method for computing gradients when doing nonlinear least squares based data assimilation. Because of the significant cost (in computational effort and CPU time) involved in performing a forward integration of the underlying 3-D model at any reasonable grid resolution, the use of the adjoint method for computing the gradients is indispensable. The adjoint method provides an elegant

  17. Local-in-Time Adjoint-Based Method for Optimal Control/Design Optimization of Unsteady Compressible Flows

    NASA Technical Reports Server (NTRS)

    Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.

    2009-01-01

    .We study local-in-time adjoint-based methods for minimization of ow matching functionals subject to the 2-D unsteady compressible Euler equations. The key idea of the local-in-time method is to construct a very accurate approximation of the global-in-time adjoint equations and the corresponding sensitivity derivative by using only local information available on each time subinterval. In contrast to conventional time-dependent adjoint-based optimization methods which require backward-in-time integration of the adjoint equations over the entire time interval, the local-in-time method solves local adjoint equations sequentially over each time subinterval. Since each subinterval contains relatively few time steps, the storage cost of the local-in-time method is much lower than that of the global adjoint formulation, thus making the time-dependent optimization feasible for practical applications. The paper presents a detailed comparison of the local- and global-in-time adjoint-based methods for minimization of a tracking functional governed by the Euler equations describing the ow around a circular bump. Our numerical results show that the local-in-time method converges to the same optimal solution obtained with the global counterpart, while drastically reducing the memory cost as compared to the global-in-time adjoint formulation.

  18. Variational Phase Imaging Using the Transport-of-Intensity Equation.

    PubMed

    Bostan, Emrah; Froustey, Emmanuel; Nilchian, Masih; Sage, Daniel; Unser, Michael

    2016-02-01

    We introduce a variational phase retrieval algorithm for the imaging of transparent objects. Our formalism is based on the transport-of-intensity equation (TIE), which relates the phase of an optical field to the variation of its intensity along the direction of propagation. TIE practically requires one to record a set of defocus images to measure the variation of intensity. We first investigate the effect of the defocus distance on the retrieved phase map. Based on our analysis, we propose a weighted phase reconstruction algorithm yielding a phase map that minimizes a convex functional. The method is nonlinear and combines different ranges of spatial frequencies - depending on the defocus value of the measurements - in a regularized fashion. The minimization task is solved iteratively via the alternating-direction method of multipliers. Our simulations outperform commonly used linear and nonlinear TIE solvers. We also illustrate and validate our method on real microscopy data of HeLa cells. PMID:26685242

  19. Renormalization group analysis of the Reynolds stress transport equation

    NASA Technical Reports Server (NTRS)

    Rubinstein, R.; Barton, J. M.

    1992-01-01

    The pressure velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot-Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the epsilon-expansion of the Yakhot-Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest order Pade approximations to the sums of these series produce a fast pressure strain model of the form proposed by Launder, Reece, and Rodi, and a return to isotropy model of the form proposed by Rotta. In both cases, the model constant are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of driving higher order nonlinear models by approximating the sums more accurately.

  20. A discrete formulation of the Wigner transport equation

    NASA Astrophysics Data System (ADS)

    Kim, Kyoung-Youm

    2007-12-01

    A discrete formulation of the Wigner distribution function (WDF) and the Wigner transport equation (WTE) is proposed, where the "discreteness" of the WDF and WTE is not just a practical, mathematical feature of discretization for the possible computations, but reveals a fundamental physics regarding the maximum correlation length of potentials (an essential quantum-mechanical feature of the WTE): it is set by the positional uncertainty due to the discrete values of momentum in evaluating the discrete WDF. Our formulation also shows that the weighting function to the potential-correlation term can be derived naturally from a mathematical necessity related to the antiperiodicity of the discrete density operator. In addition, we propose a mutually independent discretization scheme for the diagonal and cross-diagonal coordinates of the density operator, which results in a numerically effective discrete WTE in that it requires much less computational resources without significant loss in accuracy.

  1. Heat conduction in multifunctional nanotrusses studied using Boltzmann transport equation

    NASA Astrophysics Data System (ADS)

    Dou, Nicholas G.; Minnich, Austin J.

    2016-01-01

    Materials that possess low density, low thermal conductivity, and high stiffness are desirable for engineering applications, but most materials cannot realize these properties simultaneously due to the coupling between them. Nanotrusses, which consist of hollow nanoscale beams architected into a periodic truss structure, can potentially break these couplings due to their lattice architecture and nanoscale features. In this work, we study heat conduction in the exact nanotruss geometry by solving the frequency-dependent Boltzmann transport equation using a variance-reduced Monte Carlo algorithm. We show that their thermal conductivity can be described with only two parameters, solid fraction and wall thickness. Our simulations predict that nanotrusses can realize unique combinations of mechanical and thermal properties that are challenging to achieve in typical materials.

  2. A simple Boltzmann transport equation for ballistic to diffusive transient heat transport

    NASA Astrophysics Data System (ADS)

    Maassen, Jesse; Lundstrom, Mark

    2015-04-01

    Developing simplified, but accurate, theoretical approaches to treat heat transport on all length and time scales is needed to further enable scientific insight and technology innovation. Using a simplified form of the Boltzmann transport equation (BTE), originally developed for electron transport, we demonstrate how ballistic phonon effects and finite-velocity propagation are easily and naturally captured. We show how this approach compares well to the phonon BTE, and readily handles a full phonon dispersion and energy-dependent mean-free-path. This study of transient heat transport shows (i) how fundamental temperature jumps at the contacts depend simply on the ballistic thermal resistance, (ii) that phonon transport at early times approach the ballistic limit in samples of any length, and (iii) perceived reductions in heat conduction, when ballistic effects are present, originate from reductions in temperature gradient. Importantly, this framework can be recast exactly as the Cattaneo and hyperbolic heat equations, and we discuss how the key to capturing ballistic heat effects is to use the correct physical boundary conditions.

  3. A simple Boltzmann transport equation for ballistic to diffusive transient heat transport

    SciTech Connect

    Maassen, Jesse Lundstrom, Mark

    2015-04-07

    Developing simplified, but accurate, theoretical approaches to treat heat transport on all length and time scales is needed to further enable scientific insight and technology innovation. Using a simplified form of the Boltzmann transport equation (BTE), originally developed for electron transport, we demonstrate how ballistic phonon effects and finite-velocity propagation are easily and naturally captured. We show how this approach compares well to the phonon BTE, and readily handles a full phonon dispersion and energy-dependent mean-free-path. This study of transient heat transport shows (i) how fundamental temperature jumps at the contacts depend simply on the ballistic thermal resistance, (ii) that phonon transport at early times approach the ballistic limit in samples of any length, and (iii) perceived reductions in heat conduction, when ballistic effects are present, originate from reductions in temperature gradient. Importantly, this framework can be recast exactly as the Cattaneo and hyperbolic heat equations, and we discuss how the key to capturing ballistic heat effects is to use the correct physical boundary conditions.

  4. Transport equations for linear surface waves with random underlying flows

    NASA Astrophysics Data System (ADS)

    Bal, Guillaume; Chou, Tom

    1999-11-01

    We define the Wigner distribution and use it to develop equations for linear surface capillary-gravity wave propagation in the transport regime. The energy density a(r, k) contained in waves propagating with wavevector k at field point r is given by dota(r,k) + nabla_k[U_⊥(r,z=0) \\cdotk + Ω(k)]\\cdotnabla_ra [13pt] \\: hspace1in - (nabla_r\\cdotU_⊥)a - nabla_r(k\\cdotU_⊥)\\cdotnabla_ka = Σ(δU^2) where U_⊥(r, z=0) is a slowly varying surface current, and Ω(k) = √(k^3+k)tanh kh is the free capillary-gravity dispersion relation. Note that nabla_r\\cdotU_⊥(r,z=0) neq 0, and that the surface currents exchange energy density with the propagating waves. When an additional weak random current √\\varepsilon δU(r/\\varepsilon) varying on the scale of k-1 is included, we find an additional scattering term Σ(δU^2) as a function of correlations in δU. Our results can be applied to the study of surface wave energy transport over a turbulent ocean.

  5. Generalized parallel heat transport equations in collisional to weakly collisional plasmas

    NASA Astrophysics Data System (ADS)

    Zawaideh, Emad; Kim, N. S.; Najmabadi, Farrokh

    1988-11-01

    A new set of two-fluid heat-transport equations for heat conduction in collisional to weakly collisional plasmas was derived on the basis of gyrokinetic equations in flux coordinates. In these equations, no restrictions on the anisotropy of the ion distribution function or the collisionality are imposed. In the highly collisional limit, these equations reduce to the classical heat conduction equation of Spitzer and Haerm (1953), while in the weakly collisional limit, they describe a saturated heat flux. Numerical examples comparing these equations with conventional heat transport equations are presented.

  6. Ab initio electronic transport model with explicit solution to the linearized Boltzmann transport equation

    NASA Astrophysics Data System (ADS)

    Faghaninia, Alireza; Ager, Joel W.; Lo, Cynthia S.

    2015-06-01

    Accurate models of carrier transport are essential for describing the electronic properties of semiconductor materials. To the best of our knowledge, the current models following the framework of the Boltzmann transport equation (BTE) either rely heavily on experimental data (i.e., semiempirical), or utilize simplifying assumptions, such as the constant relaxation time approximation (BTE-cRTA). While these models offer valuable physical insights and accurate calculations of transport properties in some cases, they often lack sufficient accuracy—particularly in capturing the correct trends with temperature and carrier concentration. We present here a transport model for calculating low-field electrical drift mobility and Seebeck coefficient of n -type semiconductors, by explicitly considering relevant physical phenomena (i.e., elastic and inelastic scattering mechanisms). We first rewrite expressions for the rates of elastic scattering mechanisms, in terms of ab initio properties, such as the band structure, density of states, and polar optical phonon frequency. We then solve the linear BTE to obtain the perturbation to the electron distribution—resulting from the dominant scattering mechanisms—and use this to calculate the overall mobility and Seebeck coefficient. Therefore, we have developed an ab initio model for calculating mobility and Seebeck coefficient using the Boltzmann transport (aMoBT) equation. Using aMoBT, we accurately calculate electrical transport properties of the compound n -type semiconductors, GaAs and InN, over various ranges of temperature and carrier concentration. aMoBT is fully predictive and provides high accuracy when compared to experimental measurements on both GaAs and InN, and vastly outperforms both semiempirical models and the BTE-cRTA. Therefore, we assert that this approach represents a first step towards a fully ab initio carrier transport model that is valid in all compound semiconductors.

  7. Multigroup Three-Dimensional Direct Integration Method Radiation Transport Analysis Code System.

    1987-09-18

    Version 00 TRISTAN solves the three-dimensional, fixed-source, Boltzmann transport equation for neutrons or gamma rays in rectangular geometry. The code can solve an adjoint problem as well as a usual transport problem. TRISTAN is a suitable tool to analyze radiation shielding problems such as streaming and deep penetration problems.

  8. Transport in the spatially tempered, fractional Fokker-Planck equation

    NASA Astrophysics Data System (ADS)

    Kullberg, A.; del-Castillo-Negrete, D.

    2012-06-01

    A study of truncated Lévy flights in super-diffusive transport in the presence of an external potential is presented. The study is based on the spatially tempered, fractional Fokker-Planck (TFFP) equation in which the fractional diffusion operator is replaced by a tempered fractional diffusion (TFD) operator. We focus on harmonic (quadratic) potentials and periodic potentials with broken spatial symmetry. The main objective is to study the dependence of the steady-state probability density function (PDF), and the current (in the case of periodic potentials) on the level of tempering, λ, and on the order of the fractional derivative in space, α. An expansion of the TFD operator for large λ is presented, and the corresponding equation for the coarse grained PDF is obtained. The steady-state PDF solution of the TFFP equation for a harmonic potential is computed numerically. In the limit λ → ∞, the PDF approaches the expected Boltzmann distribution. However, nontrivial departures from this distribution are observed for finite (λ > 0) truncations, and α ≠ 2. In the study of periodic potentials, we use two complementary numerical methods: a finite-difference scheme based on the Grunwald-Letnikov discretization of the truncated fractional derivatives and a Fourier-based spectral method. In the limit λ → ∞, the PDFs converges to the Boltzmann distribution and the current vanishes. However, for α ≠ 2, the PDF deviates from the Boltzmann distribution and a finite non-equilibrium ratchet current appears for any λ > 0. The current is observed to converge exponentially in time to the steady-state value. The steady-state current exhibits algebraical decay with λ, as J ˜ λ-ζ, for α ⩾ 1.75. However, for α ⩽ 1.5, the steady-state current decays exponentially with λ, as J ˜ e-ξλ. In the presence of an asymmetry in the TFD operator, the tempering can lead to a current reversal. A detailed numerical study is presented on the dependence of the

  9. Transport in the spatially tempered, fractional Fokker-Planck equation

    SciTech Connect

    Kullberg, A.; Del-Castillo-Negrete, Diego B

    2012-01-01

    A study of truncated Levy flights in super-diffusive transport in the presence of an external potential is presented. The study is based on the spatially tempered, fractional Fokker-Planck (TFFP) equation in which the fractional diffusion operator is replaced by a tempered fractional diffusion (TFD) operator. We focus on harmonic (quadratic) potentials and periodic potentials with broken spatial symmetry. The main objective is to study the dependence of the steady-state probability density function (PDF), and the current (in the case of periodic potentials) on the level of tempering, lambda, and on the order of the fractional derivative in space, alpha. An expansion of the TFD operator for large lambda is presented, and the corresponding equation for the coarse grained PDF is obtained. The steady-state PDF solution of the TFFP equation for a harmonic potential is computed numerically. In the limit lambda -> infinity, the PDF approaches the expected Boltzmann distribution. However, nontrivial departures from this distribution are observed for finite (lambda > 0) truncations, and alpha not equal 2. In the study of periodic potentials, we use two complementary numerical methods: a finite-difference scheme based on the Grunwald-Letnikov discretization of the truncated fractional derivatives and a Fourier-based spectral method. In the limit lambda -> infinity, the PDFs converges to the Boltzmann distribution and the current vanishes. However, for alpha not equal 2, the PDF deviates from the Boltzmann distribution and a finite non-equilibrium ratchet current appears for any lambda > 0. The current is observed to converge exponentially in time to the steady-state value. The steady-state current exhibits algebraical decay with lambda, as J similar to lambda(-zeta), for alpha >= 1.75. However, for alpha <= 1.5, the steady-state current decays exponentially with lambda, as J similar to e(-xi lambda). In the presence of an asymmetry in the TFD operator, the tempering can lead

  10. Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.; Diskin, Boris; Yamaleev, Nail K.

    2009-01-01

    An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of time-integration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.

  11. Adjoint Formulation for an Embedded-Boundary Cartesian Method

    NASA Technical Reports Server (NTRS)

    Nemec, Marian; Aftosmis, Michael J.; Murman, Scott M.; Pulliam, Thomas H.

    2004-01-01

    Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code

  12. Adjoint active surfaces for localization and imaging.

    PubMed

    Cook, Daniel A; Mueller, Martin Fritz; Fedele, Francesco; Yezzi, Anthony J

    2015-01-01

    This paper addresses the problem of localizing and segmenting regions embedded within a surrounding medium by characterizing their boundaries, as opposed to imaging the entirety of the volume. Active surfaces are used to directly reconstruct the shape of the region of interest. We describe the procedure for finding the optimal surface, which is computed iteratively via gradient descent that exploits the sensitivity of an error minimization functional to changes of the active surface. In doing so, we introduce the adjoint model to compute the sensitivity, and in this respect, the method shares common ground with several other disciplines, such as optimal control. Finally, we illustrate the proposed active surface technique in the framework of wave propagation governed by the scalar Helmholtz equation. Potential applications include electromagnetics, acoustics, geophysics, nondestructive testing, and medical imaging. PMID:25438311

  13. One-dimensional transport equation models for sound energy propagation in long spaces: simulations and experiments.

    PubMed

    Jing, Yun; Xiang, Ning

    2010-04-01

    In this paper, the accuracy and efficiency of the previously discussed one-dimensional transport equation models [Y. Jing et al., J. Acoust. Soc. Am. 127, 2312-2322 (2010)] are examined both numerically and experimentally. The finite element method is employed to solve the equations. Artificial diffusion is applied in the numerical implementation to suppress oscillations of the solution. The transport equation models are then compared with the ray-tracing based method for different scenarios. In general, they are in good agreement, and the transport equation models are substantially less time consuming. In addition, the two-group model is found to yield more accurate results than the one-group model for the tested cases. Lastly, acoustic experimental results obtained from a 1:10 long room scale-model are used to verify the transport equation models. The results suggest that the transport equation models are able to accurately model the sound field in a long space. PMID:20370014

  14. Drift-diffusion equation for ballistic transport in nanoscale metal-oxide-semiconductor field effect transistors

    NASA Astrophysics Data System (ADS)

    Rhew, Jung-Hoon; Lundstrom, Mark S.

    2002-11-01

    We develop a drift-diffusion equation that describes ballistic transport in a nanoscale metal-oxide-semiconductor field effect transistor (MOSFET). We treat injection from different contacts separately, and describe each injection with a set of extended McKelvey one-flux equations [Phys. Rev. 123, 51 (1961); 125, 1570 (1962)] that include hierarchy closure approximations appropriate for high-field ballistic transport and degenerate carrier statistics. We then reexpress the extended one-flux equations in a drift-diffusion form with a properly defined Einstein relationship. The results obtained for a nanoscale MOSFET show excellent agreement with the solution of the ballistic Boltzmann transport equation with no fitting parameters. These results show that a macroscopic transport model based on the moments of the Boltzmann transport equation can describe ballistic transport.

  15. Accurate adjoint design sensitivities for nano metal optics.

    PubMed

    Hansen, Paul; Hesselink, Lambertus

    2015-09-01

    We present a method for obtaining accurate numerical design sensitivities for metal-optical nanostructures. Adjoint design sensitivity analysis, long used in fluid mechanics and mechanical engineering for both optimization and structural analysis, is beginning to be used for nano-optics design, but it fails for sharp-cornered metal structures because the numerical error in electromagnetic simulations of metal structures is highest at sharp corners. These locations feature strong field enhancement and contribute strongly to design sensitivities. By using high-accuracy FEM calculations and rounding sharp features to a finite radius of curvature we obtain highly-accurate design sensitivities for 3D metal devices. To provide a bridge to the existing literature on adjoint methods in other fields, we derive the sensitivity equations for Maxwell's equations in the PDE framework widely used in fluid mechanics. PMID:26368483

  16. Adjoint-Based Methods for Estimating CO2 Sources and Sinks from Atmospheric Concentration Data

    NASA Technical Reports Server (NTRS)

    Andrews, Arlyn E.

    2003-01-01

    Work to develop adjoint-based methods for estimating CO2 sources and sinks from atmospheric concentration data was initiated in preparation for last year's summer institute on Carbon Data Assimilation (CDAS) at the National Center for Atmospheric Research in Boulder, CO. The workshop exercises used the GSFC Parameterized Chemistry and Transport Model and its adjoint. Since the workshop, a number of simulations have been run to evaluate the performance of the model adjoint. Results from these simulations will be presented, along with an outline of challenges associated with incorporating a variety of disparate data sources, from sparse, but highly precise, surface in situ observations to less accurate, global future satellite observations.

  17. A Photon Free Method to Solve Radiation Transport Equations

    SciTech Connect

    Chang, B

    2006-09-05

    The multi-group discrete-ordinate equations of radiation transfer is solved for the first time by Newton's method. It is a photon free method because the photon variables are eliminated from the radiation equations to yield a N{sub group}XN{sub direction} smaller but equivalent system of equations. The smaller set of equations can be solved more efficiently than the original set of equations. Newton's method is more stable than the Semi-implicit Linear method currently used by conventional radiation codes.

  18. Phonon-limited low-field mobility in silicon: Quantum transport vs. linearized Boltzmann Transport Equation

    NASA Astrophysics Data System (ADS)

    Rhyner, Reto; Luisier, Mathieu

    2013-12-01

    We propose to check and validate the approximations made in dissipative quantum transport (QT) simulations solved in the Non-equilibrium Green's Function formalism by comparing them with the exact solution of the linearized Boltzmann Transport Equation (LB) in the stationary regime. For that purpose, we calculate the phonon-limited electron and hole mobility in bulk Si and ultra-scaled Si nanowires for different crystal orientations ⟨100⟩, ⟨110⟩, and ⟨111⟩. In both QT and LB simulations, we use the same sp3d5s* tight-binding model to describe the electron/hole properties and the same valence-force-field approach to account for the phonon properties. It is found that the QT simplifications work well for electrons, but are less accurate for holes, where a renormalization of the phonon scattering strength is proved useful to improve the results.

  19. Moment-based effective transport equations for energy straggling.

    SciTech Connect

    Prinja, A. K.; Klein, V.; Hughes, H. G.

    2002-01-01

    Ion energy straggling is accomodated in condensed history (CH) Monte Carlo simulation by sampling energy-losses at the end of a fixed spatial step from precomputed, pathlength dependent energy-loss distributions. These distributions are essentially solutions to a straight ahead transport equation given by {partial_derivative}{psi}(s,E)/{partial_derivative}s = {integral}{sub Q{sub min}}{sup Q{sub max}} dQ {sigma}{sub e}(E,Q){psi}(s, E + Q) - {sigma}{sub e}(E){psi}(s,E), 8 {ge} 0, with monoenergetic incidence {psi}(0, E) = {delta}(E{sub 0} - E). In Eq.(1), s is the pathlength variable, {sigma}{sub e}(E,Q) is the differential cross section for energy loss Q, typically given by the relativistic Rutherford cross section for hard collisions, {sigma}{sub e}(E) is the total ion-electron scattering cross section, and Q{sub min} and Q{sub max} are, respectively, the minimum and maximum energy transfer per collision. Direct solution of Eq.( 1) by stochastic or deterministic numerical techniques is not feasible because of the very small energy transfers and very small mean free paths that characterize charged particle interactions. Condensed history codes typically employ an approximate solution due to Vavilov, obtained assuming a constant mean free path and thus restricted to short step sizes. This solution is formal and its numerical evaluation can be computationally laborious, especially for small step sizes. In practice, Monte Carlo codes have incorporated the Vavilov theory through elaborate numerical approximations, such as truncated Edgeworth expansions, curve-fitting approximations using Moyal functions for small penetration depths or higher energies, and special treatments for the large energy-loss tail of the distribution. In this paper we propose an alternative approach which is also valid under the conditions of the Vavilov theory but has the potential of being computationally more efficient.

  20. ANISORROPIA: the adjoint of the aerosol thermodynamic model ISORROPIA

    NASA Astrophysics Data System (ADS)

    Capps, S. L.; Henze, D. K.; Hakami, A.; Russell, A. G.; Nenes, A.

    2011-08-01

    We present the development of ANISORROPIA, the discrete adjoint of the ISORROPIA thermodynamic equilibrium model that treats the Na+-SO42--HSO4--NH4+-NO3--Cl--H2O aerosol system, and we demonstrate its sensitivity analysis capabilities. ANISORROPIA calculates sensitivities of an inorganic species in aerosol or gas phase with respect to the total concentrations of each species present with only a two-fold increase in computational time over the forward model execution. Due to the highly nonlinear and discontinuous solution surface of ISORROPIA, evaluation of the adjoint required a new, complex-variable version of the the model, which determines first-order sensitivities with machine precision and avoids cancellation errors arising from finite difference calculations. The adjoint is verified over an atmospherically relevant range of concentrations, temperature, and relative humidity. We apply ANISORROPIA to recent field campaign results from Atlanta, GA, USA, and Mexico City, Mexico, to characterize the inorganic aerosol sensitivities of these distinct urban air masses. The variability in the relationship between PM2.5 mass and precursor concentrations shown has important implications for air quality and climate. ANISORROPIA enables efficient elucidation of aerosol concentration dependence on aerosol precursor emissions in the context of atmospheric chemical transport model adjoints.

  1. Cable Connected Spinning Spacecraft, 1. the Canonical Equations, 2. Urban Mass Transportation, 3

    NASA Technical Reports Server (NTRS)

    Sitchin, A.

    1972-01-01

    Work on the dynamics of cable-connected spinning spacecraft was completed by formulating the equations of motion by both the canonical equations and Lagrange's equations and programming them for numerical solution on a digital computer. These energy-based formulations will permit future addition of the effect of cable mass. Comparative runs indicate that the canonical formulation requires less computer time. Available literature on urban mass transportation was surveyed. Areas of the private rapid transit concept of urban transportation are also studied.

  2. Self-adjointness of deformed unbounded operators

    SciTech Connect

    Much, Albert

    2015-09-15

    We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem, we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.

  3. On the derivation of vector radiative transfer equation for polarized radiative transport in graded index media

    NASA Astrophysics Data System (ADS)

    Zhao, J. M.; Tan, J. Y.; Liu, L. H.

    2012-02-01

    Light transport in graded index media follows a curved trajectory determined by Fermat's principle. Besides the effect of variation of the refractive index on the transport of radiative intensity, the curved ray trajectory will induce geometrical effects on the transport of polarization ellipse. This paper presents a complete derivation of vector radiative transfer equation for polarized radiation transport in absorption, emission and scattering graded index media. The derivation is based on the analysis of the conserved quantities for polarized light transport along curved trajectory and a novel approach. The obtained transfer equation can be considered as a generalization of the classic vector radiative transfer equation that is only valid for uniform refractive index media. Several variant forms of the transport equation are also presented, which include the form for Stokes parameters defined with a fixed reference and the Eulerian forms in the ray coordinate and in several common orthogonal coordinate systems.

  4. Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

    NASA Technical Reports Server (NTRS)

    Nemec, Marian; Aftosmis, Michael J.

    2004-01-01

    Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented

  5. Adjoint-Based Algorithms for Adaptation and Design Optimizations on Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.

    2006-01-01

    Schemes based on discrete adjoint algorithms present several exciting opportunities for significantly advancing the current state of the art in computational fluid dynamics. Such methods provide an extremely efficient means for obtaining discretely consistent sensitivity information for hundreds of design variables, opening the door to rigorous, automated design optimization of complex aerospace configuration using the Navier-Stokes equation. Moreover, the discrete adjoint formulation provides a mathematically rigorous foundation for mesh adaptation and systematic reduction of spatial discretization error. Error estimates are also an inherent by-product of an adjoint-based approach, valuable information that is virtually non-existent in today's large-scale CFD simulations. An overview of the adjoint-based algorithm work at NASA Langley Research Center is presented, with examples demonstrating the potential impact on complex computational problems related to design optimization as well as mesh adaptation.

  6. 2D/1D approximations to the 3D neutron transport equation. II: Numerical comparisons

    SciTech Connect

    Kelley, B. W.; Collins, B.; Larsen, E. W.

    2013-07-01

    In a companion paper [1], (i) several new '2D/1D equations' are introduced as accurate approximations to the 3D Boltzmann transport equation, (ii) the simplest of these approximate equations is systematically discretized, and (iii) a theoretically stable iteration scheme is developed to solve the discrete equations. In this paper, numerical results are presented that confirm the theoretical predictions made in [1]. (authors)

  7. Unsteady Adjoint Approach for Design Optimization of Flapping Airfoils

    NASA Technical Reports Server (NTRS)

    Lee, Byung Joon; Liou, Meng-Sing

    2012-01-01

    This paper describes the work for optimizing the propulsive efficiency of flapping airfoils, i.e., improving the thrust under constraining aerodynamic work during the flapping flights by changing their shape and trajectory of motion with the unsteady discrete adjoint approach. For unsteady problems, it is essential to properly resolving time scales of motion under consideration and it must be compatible with the objective sought after. We include both the instantaneous and time-averaged (periodic) formulations in this study. For the design optimization with shape parameters or motion parameters, the time-averaged objective function is found to be more useful, while the instantaneous one is more suitable for flow control. The instantaneous objective function is operationally straightforward. On the other hand, the time-averaged objective function requires additional steps in the adjoint approach; the unsteady discrete adjoint equations for a periodic flow must be reformulated and the corresponding system of equations solved iteratively. We compare the design results from shape and trajectory optimizations and investigate the physical relevance of design variables to the flapping motion at on- and off-design conditions.

  8. Velocity-Field Theory, Boltzmann's Transport Equation and Geometry

    NASA Astrophysics Data System (ADS)

    Ichinose, Shoichi

    Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the velocity-field plays the central role. The matter (constituent particles) fields appear as the density and the viscosity. Fluctuation is examined, and is clearly discriminated from the quantum effect. The time variable is emergently introduced through the computational process step. The collision term, for the (velocity)**4 potential (4-body interaction), is explicitly obtained and the (statistical) fluctuation is closely explained. The present field theory model does not conserve energy and is an open-system model. (One dimensional) Navier-Stokes equation or Burger's equation, appears. In the latter part, we present a way to directly define the distribution function by use of the geometry, appearing in the mechanical dynamics, and Feynman's path-integral.

  9. Three-Dimensional Turbulent RANS Adjoint-Based Error Correction

    NASA Technical Reports Server (NTRS)

    Park, Michael A.

    2003-01-01

    Engineering problems commonly require functional outputs of computational fluid dynamics (CFD) simulations with specified accuracy. These simulations are performed with limited computational resources. Computable error estimates offer the possibility of quantifying accuracy on a given mesh and predicting a fine grid functional on a coarser mesh. Such an estimate can be computed by solving the flow equations and the associated adjoint problem for the functional of interest. An adjoint-based error correction procedure is demonstrated for transonic inviscid and subsonic laminar and turbulent flow. A mesh adaptation procedure is formulated to target uncertainty in the corrected functional and terminate when error remaining in the calculation is less than a user-specified error tolerance. This adaptation scheme is shown to yield anisotropic meshes with corrected functionals that are more accurate for a given number of grid points then isotropic adapted and uniformly refined grids.

  10. Time-Dependent Ginzburg-Landau Equation and Boltzmann Transport Equation for Charge-Density-Wave Conductors

    NASA Astrophysics Data System (ADS)

    Takane, Yositake; Hayashi, Masahiko; Ebisawa, Hiromichi

    2016-08-01

    The time-dependent Ginzburg-Landau equation and the Boltzmann transport equation for charge-density-wave (CDW) conductors are derived from a microscopic one-dimensional model by applying the Keldysh Green's function approach under a quasiclassical approximation. The effects of an external electric field and impurity pinning of the CDW are fully taken into account without relying on a phenomenological argument. These equations simultaneously describe the spatiotemporal dynamics of both the CDW and quasiparticles; thus, they serve as a starting point to develop a general framework to analyze various nonequilibrium phenomena, such as current conversion between the CDW condensate and quasiparticles, in realistic CDW conductors. It is shown that, in typical situations, the equations correctly describe the nonlinear behavior of electric conductivity in a simpler manner.

  11. Mapping pan-Arctic methane emissions at high spatial resolution using an adjoint atmospheric transport and inversion method and process-based wetland and lake biogeochemical models

    NASA Astrophysics Data System (ADS)

    Tan, Z.; Zhuang, Q.; Henze, D. K.; Frankenberg, C.; Dlugokencky, E.; Sweeney, C.; Turner, A. J.

    2015-11-01

    Understanding methane emissions from the Arctic, a fast warming carbon reservoir, is important for projecting changes in the global methane cycle under future climate scenarios. Here we optimize Arctic methane emissions with a nested-grid high-resolution inverse model by assimilating both high-precision surface measurements and column-average SCIAMACHY satellite retrievals of methane mole fraction. For the first time, methane emissions from lakes are integrated into an atmospheric transport and inversion estimate, together with prior wetland emissions estimated by six different biogeochemical models. We find that, the global methane emissions during July 2004-June 2005 ranged from 496.4 to 511.5 Tg yr-1, with wetland methane emissions ranging from 130.0 to 203.3 Tg yr-1. The Arctic methane emissions during July 2004-June 2005 were in the range of 14.6-30.4 Tg yr-1, with wetland and lake emissions ranging from 8.8 to 20.4 Tg yr-1 and from 5.4 to 7.9 Tg yr-1 respectively. Canadian and Siberian lakes contributed most of the estimated lake emissions. Due to insufficient measurements in the region, Arctic methane emissions are less constrained in northern Russia than in Alaska, northern Canada and Scandinavia. Comparison of different inversions indicates that the distribution of global and Arctic methane emissions is sensitive to prior wetland emissions. Evaluation with independent datasets shows that the global and Arctic inversions improve estimates of methane mixing ratios in boundary layer and free troposphere. The high-resolution inversions provide more details about the spatial distribution of methane emissions in the Arctic.

  12. Simple jumping process with memory: Transport equation and diffusion

    NASA Astrophysics Data System (ADS)

    Kamińska, A.; Srokowski, T.

    2004-06-01

    We present a stochastic jumping process, defined in terms of jump-size probability density and jumping rate, which is a generalization of the well-known kangaroo process. The definition takes into account two process values: after and before the jump. Therefore, the process is able to preserve memory about its previous values. It possesses a simple stationary limit. Its master equation is interpreted as the kinetic equation with variable collision rate. The process can be easily applied to model systems which relax to distributions other than Maxwellian. The case of a constant jumping rate corresponds to the diffusion process, either normal or ballistic.

  13. Adjoint Error Estimation for Linear Advection

    SciTech Connect

    Connors, J M; Banks, J W; Hittinger, J A; Woodward, C S

    2011-03-30

    An a posteriori error formula is described when a statistical measurement of the solution to a hyperbolic conservation law in 1D is estimated by finite volume approximations. This is accomplished using adjoint error estimation. In contrast to previously studied methods, the adjoint problem is divorced from the finite volume method used to approximate the forward solution variables. An exact error formula and computable error estimate are derived based on an abstractly defined approximation of the adjoint solution. This framework allows the error to be computed to an arbitrary accuracy given a sufficiently well resolved approximation of the adjoint solution. The accuracy of the computable error estimate provably satisfies an a priori error bound for sufficiently smooth solutions of the forward and adjoint problems. The theory does not currently account for discontinuities. Computational examples are provided that show support of the theory for smooth solutions. The application to problems with discontinuities is also investigated computationally.

  14. Consistent Adjoint Driven Importance Sampling using Space, Energy and Angle

    SciTech Connect

    Peplow, Douglas E.; Mosher, Scott W; Evans, Thomas M

    2012-08-01

    For challenging radiation transport problems, hybrid methods combine the accuracy of Monte Carlo methods with the global information present in deterministic methods. One of the most successful hybrid methods is CADIS Consistent Adjoint Driven Importance Sampling. This method uses a deterministic adjoint solution to construct a biased source distribution and consistent weight windows to optimize a specific tally in a Monte Carlo calculation. The method has been implemented into transport codes using just the spatial and energy information from the deterministic adjoint and has been used in many applications to compute tallies with much higher figures-of-merit than analog calculations. CADIS also outperforms user-supplied importance values, which usually take long periods of user time to develop. This work extends CADIS to develop weight windows that are a function of the position, energy, and direction of the Monte Carlo particle. Two types of consistent source biasing are presented: one method that biases the source in space and energy while preserving the original directional distribution and one method that biases the source in space, energy, and direction. Seven simple example problems are presented which compare the use of the standard space/energy CADIS with the new space/energy/angle treatments.

  15. The radiative transport equation in flatland with separation of variables

    NASA Astrophysics Data System (ADS)

    Machida, Manabu

    2016-07-01

    The linear Boltzmann equation can be solved with separation of variables in one dimension, i.e., in three-dimensional space with planar symmetry. In this method, solutions are given by superpositions of eigenmodes which are sometimes called singular eigenfunctions. In this paper, we explore the singular-eigenfunction approach in flatland or two-dimensional space.

  16. Gluon transport equations with condensate in the small angle approximation

    NASA Astrophysics Data System (ADS)

    Blaizot, Jean-Paul; Liao, Jinfeng

    2016-05-01

    We derive the set of kinetic equations that control the evolution of gluons in the presence of a condensate. We show that the dominant singularities remain logarithmic when the scattering involves particles in the condensate. This allows us to define a consistent small angle approximation.

  17. Solving parallel transport equations in the higher-dimensional Kerr-NUT-(A)dS spacetimes

    SciTech Connect

    Connell, Patrick; Frolov, Valeri P.; Kubiznak, David

    2008-07-15

    We obtain and study the equations describing the parallel transport of orthonormal frames along geodesics in a spacetime admitting a nondegenerate, principal, conformal Killing-Yano tensor h. We demonstrate that the operator F, obtained by a projection of h to a subspace orthogonal to the velocity, has in a generic case eigenspaces of dimension not greater than 2. Each of these eigenspaces is independently parallel propagated. This allows one to reduce the parallel transport equations to a set of first order, ordinary, differential equations for the angles of rotation in the 2D eigenspaces. General analysis is illustrated by studying the equations of the parallel transport in the Kerr-NUT-(A)dS metrics. Examples of three-, four-, and five-dimensional Kerr-NUT-(A)dS are considered, and it is shown that the obtained first order equations can be solved by a separation of variables.

  18. Solving parallel transport equations in the higher-dimensional Kerr-NUT-(A)dS spacetimes

    NASA Astrophysics Data System (ADS)

    Connell, Patrick; Frolov, Valeri P.; Kubizňák, David

    2008-07-01

    We obtain and study the equations describing the parallel transport of orthonormal frames along geodesics in a spacetime admitting a nondegenerate, principal, conformal Killing-Yano tensor h. We demonstrate that the operator F, obtained by a projection of h to a subspace orthogonal to the velocity, has in a generic case eigenspaces of dimension not greater than 2. Each of these eigenspaces is independently parallel propagated. This allows one to reduce the parallel transport equations to a set of first order, ordinary, differential equations for the angles of rotation in the 2D eigenspaces. General analysis is illustrated by studying the equations of the parallel transport in the Kerr-NUT-(A)dS metrics. Examples of three-, four-, and five-dimensional Kerr-NUT-(A)dS are considered, and it is shown that the obtained first order equations can be solved by a separation of variables.

  19. Differential equation of exospheric lateral transport and its application to terrestrial hydrogen

    NASA Technical Reports Server (NTRS)

    Hodges, R. R., Jr.

    1973-01-01

    The differential equation description of exospheric lateral transport of Hodges and Johnson is reformulated to extend its utility to light gases. Accuracy of the revised equation is established by applying it to terrestrial hydrogen. The resulting global distributions for several static exobase models are shown to be essentially the same as those that have been computed by Quessette using an integral equation approach. The present theory is subsequently used to elucidate the effects of nonzero lateral flow, exobase rotation, and diurnal tidal winds on the hydrogen distribution. Finally it is shown that the differential equation of exospheric transport is analogous to a diffusion equation. Hence it is practical to consider exospheric transport as a continuation of thermospheric diffusion, a concept that alleviates the need for an artificial exobase dividing thermosphere and exosphere.

  20. A practical discrete-adjoint method for high-fidelity compressible turbulence simulations

    NASA Astrophysics Data System (ADS)

    Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.

    2015-03-01

    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 its

  1. A practical discrete-adjoint method for high-fidelity compressible turbulence simulations

    SciTech Connect

    Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.

    2015-03-15

    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

  2. Stratospheric Water Vapor and the Asian Monsoon: An Adjoint Model Investigation

    NASA Technical Reports Server (NTRS)

    Olsen, Mark A.; Andrews, Arlyn E.

    2003-01-01

    A new adjoint model of the Goddard Parameterized Chemistry and Transport Model is used to investigate the role that the Asian monsoon plays in transporting water to the stratosphere. The adjoint model provides a unique perspective compared to non-diffusive and non-mixing Lagrangian trajectory analysis. The quantity of water vapor transported from the monsoon and the pathways into the stratosphere are examined. The emphasis is on the amount of water originating from the monsoon that contributes to the tropical tape recorder signal. The cross-tropopause flux of water from the monsoon to the midlatitude lower stratosphere will also be discussed.

  3. AN EXACT PEAK CAPTURING AND OSCILLATION-FREE SCHEME TO SOLVE ADVECTION-DISPERSION TRANSPORT EQUATIONS

    EPA Science Inventory

    An exact peak capturing and essentially oscillation-free (EPCOF) algorithm, consisting of advection-dispersion decoupling, backward method of characteristics, forward node tracking, and adaptive local grid refinement, is developed to solve transport equations. This algorithm repr...

  4. A Generalized Adjoint Approach for Quantifying Reflector Assembly Discontinuity Factor Uncertainties

    SciTech Connect

    Yankov, Artem; Collins, Benjamin; Jessee, Matthew Anderson; Downar, Thomas

    2012-01-01

    Sensitivity-based uncertainty analysis of assembly discontinuity factors (ADFs) can be readily performed using adjoint methods for infinite lattice models. However, there is currently no adjoint-based methodology to obtain uncertainties for ADFs along an interface between a fuel and reflector region. To accommodate leakage effects in a reflector region, a 1D approximation is usually made in order to obtain the homogeneous interface flux required to calculate the ADF. Within this 1D framework an adjoint-based method is proposed that is capable of efficiently calculating ADF uncertainties. In the proposed method the sandwich rule is utilized to relate the covariance of the input parameters of 1D diffusion theory in the reflector region to the covariance of the interface ADFs. The input parameters covariance matrix can be readily obtained using sampling-based codes such as XSUSA or adjoint-based codes such as TSUNAMI. The sensitivity matrix is constructed using a fixed-source adjoint approach for inputs characterizing the reflector region. An analytic approach is then used to determine the sensitivity of the ADFs to fuel parameters using the neutron balance equation. A stochastic approach is used to validate the proposed adjoint-based method.

  5. Generalized adjoint consistent treatment of wall boundary conditions for compressible flows

    NASA Astrophysics Data System (ADS)

    Hartmann, Ralf; Leicht, Tobias

    2015-11-01

    In this article, we revisit the adjoint consistency analysis of Discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations with application to the Reynolds-averaged Navier-Stokes and k- ω turbulence equations. Here, particular emphasis is laid on the discretization of wall boundary conditions. While previously only one specific combination of discretizations of wall boundary conditions and of aerodynamic force coefficients has been shown to give an adjoint consistent discretization, in this article we generalize this analysis and provide a discretization of the force coefficients for any consistent discretization of wall boundary conditions. Furthermore, we demonstrate that a related evaluation of the cp- and cf-distributions is required. The freedom gained in choosing the discretization of boundary conditions without loosing adjoint consistency is used to devise a new adjoint consistent discretization including numerical fluxes on the wall boundary which is more robust than the adjoint consistent discretization known up to now. While this work is presented in the framework of Discontinuous Galerkin discretizations, the insight gained is also applicable to (and thus valuable for) other discretization schemes. In particular, the discretization of integral quantities, like the drag, lift and moment coefficients, as well as the discretization of local quantities at the wall like surface pressure and skin friction should follow as closely as possible the discretization of the flow equations and boundary conditions at the wall boundary.

  6. Transport in driven plasmas

    SciTech Connect

    Fisch, N.J.

    1985-03-01

    A plasma in contact with an external source of power, especially a source that interacts specifically with high-velocity electrons, exhibits transport properties, such as conductivity, different from those of an isolated plasma near thermal equilibrium. This is true even when the bulk of the particles in the driven plasma are near thermal equilibrium. To describe the driven plasma we derive an adjoint equation to the inhomogeneous, linearized, dynamic Boltzmann equation. The Green's functions for a variety of plasma responses can then be generated. It is possible to modify the Chapman-Enskog expansion in order to incorporate the response functions derived here.

  7. General solution of a fractional diffusion-advection equation for solar cosmic-ray transport

    NASA Astrophysics Data System (ADS)

    Rocca, M. C.; Plastino, A. R.; Plastino, A.; Ferri, G. L.; de Paoli, A.

    2016-04-01

    In this effort we exactly solve the fractional diffusion-advection equation for solar cosmic-ray transport and give its general solution in terms of hypergeometric distributions. Numerical analysis of this equation shows that its solutions resemble power-laws.

  8. Numerical evaluation of the intensity transport equation for well-known wavefronts and intensity distributions

    NASA Astrophysics Data System (ADS)

    Campos-García, Manuel; Granados-Agustín, Fermín.; Cornejo-Rodríguez, Alejandro; Estrada-Molina, Amilcar; Avendaño-Alejo, Maximino; Moreno-Oliva, Víctor Iván.

    2013-11-01

    In order to obtain a clearer interpretation of the Intensity Transport Equation (ITE), in this work, we propose an algorithm to solve it for some particular wavefronts and its corresponding intensity distributions. By simulating intensity distributions in some planes, the ITE is turns into a Poisson equation with Neumann boundary conditions. The Poisson equation is solved by means of the iterative algorithm SOR (Simultaneous Over-Relaxation).

  9. Electrophoretic transport equations - Electrophoretic models based on migration only and their interrelationships

    NASA Technical Reports Server (NTRS)

    Thormann, Wolfgang; Mosher, Richard A.

    1985-01-01

    The general equations which describe the electrophoretic transport of components in solution are restated using Newman's general concept of mobilities. A concise derivation of the moving boundary equation and the regulating function from the continuity equation is presented. Various other regulating principles across moving and stationary boundaries are also discussed, which permits a review of the features and interrelationships of the electrophoretic models based on electromigration only. The effect of considering an interactive (dissociating) solvent on the mathematical treatment is discussed.

  10. Adjoint Data Assimilative Model Study of the Gulf of Maine Coastal Circulation

    NASA Astrophysics Data System (ADS)

    He, R.; McGillicuddy, D. J.; Lynch, D. R.

    2004-12-01

    Data assimilation (DA) in the coastal ocean can be divided into category of either sequential estimation or variational adjoint. Sequential estimation techniques blend models with observations directly, using a variety of algorithms with which the relative weights of data and model are calculated. Variational adjoint techniques infer model control variables (e.g. parameters, forcing functions, boundary conditions, etc.) that minimize the misfit between observations and predictions. The advantage of the latter techniques over the former is that the resulting model solutions obey model dynamics. In this study, the Gulf of Maine coastal circulation and the material property transport are investigated with the Dartmouth variational adjoint DA modeling system, which assimilates in-situ data via inversion for the unknown sea level elevation at open boundaries. In-situ observations include ADCP currents and coastal sea levels. The adjoint DA model skill is evaluated by the inter-comparisons between modeled and observed drifter trajectories. Excellent model skill is found, demonstrating the utility and effectiveness of the adjoint DA modeling system in bridging in-situ observations with coastal ocean model simulations. Implications of the adjoint DA strategy on the emergent coastal ocean observing systems are discussed.

  11. Southern California Adjoint Source Inversions

    NASA Astrophysics Data System (ADS)

    Tromp, J.; Kim, Y.

    2007-12-01

    Southern California Centroid-Moment Tensor (CMT) solutions with 9 components (6 moment tensor elements, latitude, longitude, and depth) are sought to minimize a misfit function computed from waveform differences. The gradient of a misfit function is obtained based upon two numerical simulations for each earthquake: one forward calculation for the southern California model, and an adjoint calculation that uses time-reversed signals at the receivers. Conjugate gradient and square-root variable metric methods are used to iteratively improve the earthquake source model while reducing the misfit function. The square-root variable metric algorithm has the advantage of providing a direct approximation to the posterior covariance operator. We test the inversion procedure by perturbing each component of the CMT solution, and see how the algorithm converges. Finally, we demonstrate full inversion capabilities using data for real Southern California earthquakes.

  12. Surface harmonics method equations for solving the time-dependent neutron transport problems and their verification

    SciTech Connect

    Boyarinov, V. F.; Kondrushin, A. E.; Fomichenko, P. A.

    2012-07-01

    Finite-difference time-dependent equations of Surface Harmonics method have been obtained for plane geometry. Verification of these equations has been carried out by calculations of tasks from 'Benchmark Problem Book ANL-7416'. The capacity and efficiency of the Surface Harmonics method have been demonstrated by solution of the time-dependent neutron transport equation in diffusion approximation. The results of studies showed that implementation of Surface Harmonics method for full-scale calculations will lead to a significant progress in the efficient solution of the time-dependent neutron transport problems in nuclear reactors. (authors)

  13. A two-equation integral model for particle transport in renewal statistical media

    SciTech Connect

    Zuchuat, O.; Sanchez, R.

    1995-12-31

    The authors consider the problem of particle transport including scattering in renewal statistical media. The general description of this problem leads to an infinite hierarchy of equations. A new closure scheme is developed to obtain a more tractable set of equations. Numerical results in planar geometry are given which compare the predictions of this new closure with exact benchmark results as well as with a previous model available in the literature. The development of the new closure and the comparisons the authors make underline the importance of having a physical basis in the elaboration of closure schemes for the hierarchy of equations describing the transport of particle with collisions in stochastic mixtures.

  14. The Dissipation Rate Transport Equation and Subgrid-Scale Models in Rotating Turbulence

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert; Ye, Zhou

    1997-01-01

    The dissipation rate transport equation remains the most uncertain part of turbulence modeling. The difficulties arc increased when external agencies like rotation prevent straightforward dimensional analysis from determining the correct form of the modelled equation. In this work, the dissipation rate transport equation and subgrid scale models for rotating turbulence are derived from an analytical statistical theory of rotating turbulence. In the strong rotation limit, the theory predicts a turbulent steady state in which the inertial range energy spectrum scales as k(sup -2) and the turbulent time scale is the inverse rotation rate. This scaling has been derived previously by heuristic arguments.

  15. FRACTIONAL SOLUTE TRANSPORT EQUATION EVALUATED WITH THE MISCIBLE DISPLACEMENT EXPERIMENTAL DATA

    Technology Transfer Automated Retrieval System (TEKTRAN)

    A new solute transport model has been recently developed assuming that the movements of solute particles in hierarchically-structured porous media belongs to the family of Lévy motions rather than to the Brownian motion. The one-dimensional fractional advective-dispersive transport equation, or FADE...

  16. Fractional Advective-Dispersive Equation as a Model of Solute Transport in Porous Media

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Understanding and modeling transport of solutes in porous media is a critical issue in the environmental protection. The common model is the advective-dispersive equation (ADE) describing the superposition of the advective transport and the Brownian motion in water-filled pore space. Deviations from...

  17. Conservative differencing of the electron Fokker-Planck transport equation

    SciTech Connect

    Langdon, A.B.

    1981-01-12

    We need to extend the applicability and improve the accuracy of kinetic electron transport codes. In this paper, special attention is given to modelling of e-e collisions, including the dominant contributions arising from anisotropy. The electric field and spatial gradient terms are also considered. I construct finite-difference analogues to the Fokker-Planck integral-differential collision operator, which conserve the particle number, momentum and energy integrals (sums) regardless of the coarseness of the velocity zoning. Such properties are usually desirable, but are especially useful, for example, when there are spatial regions and/or time intervals in which the plasma is cool, so that the collision operator acts rapidly and the velocity distribution is poorly resolved, yet it is crucial that gross conservation properties be respected in hydro-transport applications, such as in the LASNEX code. Some points are raised concerning spatial differencing and time integration.

  18. The continuous adjoint approach to the k-ω SST turbulence model with applications in shape optimization

    NASA Astrophysics Data System (ADS)

    Kavvadias, I. S.; Papoutsis-Kiachagias, E. M.; Dimitrakopoulos, G.; Giannakoglou, K. C.

    2015-11-01

    In this article, the gradient of aerodynamic objective functions with respect to design variables, in problems governed by the incompressible Navier-Stokes equations coupled with the k-ω SST turbulence model, is computed using the continuous adjoint method, for the first time. Shape optimization problems for minimizing drag, in external aerodynamics (flows around isolated airfoils), or viscous losses in internal aerodynamics (duct flows) are considered. Sensitivity derivatives computed with the proposed adjoint method are compared to those computed with finite differences or a continuous adjoint variant based on the frequently used assumption of frozen turbulence; the latter proves the need for differentiating the turbulence model. Geometries produced by optimization runs performed with sensitivities computed by the proposed method and the 'frozen turbulence' assumption are also compared to quantify the gain from formulating and solving the adjoint to the turbulence model equations.

  19. A massively parallel semi-Lagrangian algorithm for solving the transport equation

    SciTech Connect

    Manson, Russell; Wang, Dali

    2010-01-01

    The scalar transport equation underpins many models employed in science, engineering, technology and business. Application areas include, but are not restricted to, pollution transport, weather forecasting, video analysis and encoding (the optical flow equation), options and stock pricing (the Black-Scholes equation) and spatially explicit ecological models. Unfortunately finding numerical solutions to this equation which are fast and accurate is not trivial. Moreover, finding such numerical algorithms that can be implemented on high performance computer architectures efficiently is challenging. In this paper the authors describe a massively parallel algorithm for solving the advection portion of the transport equation. We present an approach here which is different to that used in most transport models and which we have tried and tested for various scenarios. The approach employs an intelligent domain decomposition based on the vector field of the system equations and thus automatically partitions the computational domain into algorithmically autonomous regions. The solution of a classic pure advection transport problem is shown to be conservative, monotonic and highly accurate at large time steps. Additionally we demonstrate that the algorithm is highly efficient for high performance computer architectures and thus offers a route towards massively parallel application.

  20. Analytical Theory of the Destruction Terms in Dissipation Rate Transport Equations

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert; Zhou, Ye

    1996-01-01

    Modeled dissipation rate transport equations are often derived by invoking various hypotheses to close correlations in the corresponding exact equations. D. C. Leslie suggested that these models might be derived instead from Kraichnan's wavenumber space integrals for inertial range transport power. This suggestion is applied to the destruction terms in the dissipation rate equations for incompressible turbulence, buoyant turbulence, rotating incompressible turbulence, and rotating buoyant turbulence. Model constants like C(epsilon 2) are expressed as integrals; convergence of these integrals implies the absence of Reynolds number dependence in the corresponding destruction term. The dependence of C(epsilon 2) on rotation rate emerges naturally; sensitization of the modeled dissipation rate equation to rotation is not required. A buoyancy related effect which is absent in the exact transport equation for temperature variance dissipation, but which sometimes improves computational predictions, also arises naturally. Both the presence of this effect and the appropriate time scale in the modeled transport equation depend on whether Bolgiano or Kolmogorov inertial range scaling applies. A simple application of these methods leads to a preliminary, dissipation rate equation for rotating buoyant turbulence.

  1. Least-squares finite element discretizations of neutron transport equations in 3 dimensions

    SciTech Connect

    Manteuffel, T.A; Ressel, K.J.; Starkes, G.

    1996-12-31

    The least-squares finite element framework to the neutron transport equation introduced in is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. Here we report on some practical aspects of this approach for neutron transport calculations in three space dimensions. The systems of partial differential equations resulting from a P{sub 1} and P{sub 2} approximation of the angular dependence are derived. In the diffusive limit, the system is essentially a Poisson equation for zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. We report on the numerical results obtained for the minimum of the least-squares functional augmented by an additional boundary term using trilinear finite elements on a uniform tesselation into cubes.

  2. Radiative or neutron transport modeling using a lattice Boltzmann equation framework

    NASA Astrophysics Data System (ADS)

    Bindra, H.; Patil, D. V.

    2012-07-01

    In this paper, the lattice Boltzmann equation (LBE)-based framework is used to obtain the solution for the linear radiative or neutron transport equation. The LBE framework is devised for the integrodifferential forms of these equations which arise due to the inclusion of the scattering terms. The interparticle collisions are neglected, hence omitting the nonlinear collision term. Furthermore, typical representative examples for one-dimensional or two-dimensional geometries and inclusion or exclusion of the scattering term (isotropic and anisotropic) in the Boltzmann transport equation are illustrated to prove the validity of the method. It has been shown that the solution from the LBE methodology is equivalent to the well-known Pn and Sn methods. This suggests that the LBE can potentially provide a more convenient and easy approach to solve the physical problems of neutron and radiation transport.

  3. Explicit solutions of the radiative transport equation in the P{sub 3} approximation

    SciTech Connect

    Liemert, André Kienle, Alwin

    2014-11-01

    Purpose: Explicit solutions of the monoenergetic radiative transport equation in the P{sub 3} approximation have been derived which can be evaluated with nearly the same computational effort as needed for solving the standard diffusion equation (DE). In detail, the authors considered the important case of a semi-infinite medium which is illuminated by a collimated beam of light. Methods: A combination of the classic spherical harmonics method and the recently developed method of rotated reference frames is used for solving the P{sub 3} equations in closed form. Results: The derived solutions are illustrated and compared to exact solutions of the radiative transport equation obtained via the Monte Carlo (MC) method as well as with other approximated analytical solutions. It is shown that for the considered cases which are relevant for biomedical optics applications, the P{sub 3} approximation is close to the exact solution of the radiative transport equation. Conclusions: The authors derived exact analytical solutions of the P{sub 3} equations under consideration of boundary conditions for defining a semi-infinite medium. The good agreement to Monte Carlo simulations in the investigated domains, for example, in the steady-state and time domains, as well as the short evaluation time needed suggests that the derived equations can replace the often applied solutions of the diffusion equation for the homogeneous semi-infinite medium.

  4. General analytic methods for solving coupled transport equations: From cosmology to beyond

    NASA Astrophysics Data System (ADS)

    White, G. A.

    2016-02-01

    We propose a general method to analytically solve transport equations during a phase transition without making approximations based on the assumption that any transport coefficient is large. Using a cosmic phase transition in the minimal supersymmetric standard model as a pedagogical example, we derive the solutions to a set of 3 transport equations derived under the assumption of supergauge equilibrium and the diffusion approximation. The result is then rederived efficiently using a technique we present involving a parametrized ansatz which turns the process of deriving a solution into an almost elementary problem. We then show how both the derivation and the parametrized ansatz technique can be generalized to solve an arbitrary number of transport equations. Finally we derive a perturbative series that relaxes the usual approximation that inactivates vacuum-expectation-value dependent relaxation and C P -violating source terms at the bubble wall and through the symmetric phase. Our analytical methods are able to reproduce a numerical calculation in the literature.

  5. Generalized parallel heat transport equations in collisional to weakly collisional plasmas

    SciTech Connect

    Zawaideh, E.; Kim, N.S.; Najmabadi, F.

    1988-11-01

    A new set of two-fluid heat transport equations that is valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates, a set of moment equations describing plasma energy transport along the field lines of a space- and time-dependent magnetic field is derived. No restrictions on the anisotropy of the ion distribution function or collisionality are imposed. In the highly collisional limit, these equations reduce to the classical heat conduction equation (e.g., Spitzer and Haerm or Braginskii), while in the weakly collisional limit, they describe a saturated heat flux (flux limited). Numerical examples comparing these equations with conventional heat transport equations show that in the limit where the ratio of the mean free path lambda to the scale length of the temperature gradient L/sub T/ approaches zero, there is no significant difference between the solutions of the new and conventional heat transport equations. As lambda/L/sub T/..-->..1, the conventional heat conduction equation contains a significantly larger error than (lambda/L/sub T/)/sup 2/. The error is found to be O(lambda/L)/sup 2/, where L is the smallest of the scale lengths of the gradient in the magnetic field, or the macroscopic plasma parameters (e.g., velocity scale length, temperature scale length, and density scale length). The accuracy of the flux-limited model depends significantly on the value of the flux limit parameter which, in general, is not known. The new set of equations shows that the flux-limited parameter is a function of the magnetic field and plasma parameter profiles.

  6. 2D/1D approximations to the 3D neutron transport equation. I: Theory

    SciTech Connect

    Kelley, B. W.; Larsen, E. W.

    2013-07-01

    A new class of '2D/1D' approximations is proposed for the 3D linear Boltzmann equation. These approximate equations preserve the exact transport physics in the radial directions x and y and diffusion physics in the axial direction z. Thus, the 2D/1D equations are more accurate approximations of the 3D Boltzmann equation than the conventional 3D diffusion equation. The 2D/1D equations can be systematically discretized, to yield accurate simulation methods for 3D reactor core problems. The resulting solutions will be more accurate than 3D diffusion solutions, and less expensive to generate than standard 3D transport solutions. In this paper, we (i) show that the simplest 2D/1D equation has certain desirable properties, (ii) systematically discretize this equation, and (iii) derive a stable iteration scheme for solving the discrete system of equations. In a companion paper [1], we give numerical results that confirm the theoretical predictions of accuracy and iterative stability. (authors)

  7. Molecular representation of molar domain (volume), evolution equations, and linear constitutive relations for volume transport.

    PubMed

    Eu, Byung Chan

    2008-09-01

    In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel. PMID:19044872

  8. Modeling ballistic effects in frequency-dependent transient thermal transport using diffusion equations

    NASA Astrophysics Data System (ADS)

    Maassen, Jesse; Lundstrom, Mark

    2016-03-01

    Understanding ballistic phonon transport effects in transient thermoreflectance experiments and explaining the observed deviations from classical theory remains a challenge. Diffusion equations are simple and computationally efficient but are widely believed to break down when the characteristic length scale is similar or less than the phonon mean-free-path. Building on our prior work, we demonstrate how well-known diffusion equations, namely, the hyperbolic heat equation and the Cattaneo equation, can be used to model ballistic phonon effects in frequency-dependent periodic steady-state thermal transport. Our analytical solutions are found to compare excellently to rigorous numerical results of the phonon Boltzmann transport equation. The correct physical boundary conditions can be different from those traditionally used and are paramount for accurately capturing ballistic effects. To illustrate the technique, we consider a simple model problem using two different, commonly used heating conditions. We demonstrate how this framework can easily handle detailed material properties, by considering the case of bulk silicon using a full phonon dispersion and mean-free-path distribution. This physically transparent approach provides clear insights into the nonequilibrium physics of quasi-ballistic phonon transport and its impact on thermal transport properties.

  9. Comparing the results of bed load transport equations to field measurements in an Alpine river

    NASA Astrophysics Data System (ADS)

    Rascher, E.; Baewert, H.; Schmidt, K.-H.; Morche, D.

    2012-04-01

    Transport processes play a decisive role in fluvial systems when sediment is carried from source to sink. In a mountain river reach the morphologic development is basically determined by the bed load transport. Attempts to observe bed load entrainment and movement directly in the field are often complicated through difficulties in spatial and temporal variability and a necessary field effort. For this reason the development of sediment transport equations has a long history. A variety of such formulae has appeared since the first "modern" equation of DU BOYS (1879) was presented. Each of them is based on one of the following approaches: shear stress, stream discharge, stochastic function for sediment movement or stream power. Many of these equations have been developed on the basis of flume data or field data sets from specific river reaches. Therefore a critical consideration of their application to other natural streams is essential. A lack of available field data is undoubtedly the cause for a deficiency of such testing. (GOMEZ & CHURCH 1989; HABERSACK & LARONNE 2002; MARTIN 2003) In this study a selection of sediment transport equations is tested against data sets of 50 field observations from the Partnach River, in the Reintal Valley, Germany, in the years 2008-2011. At the outlet of this alpine catchment the channel bed is characterized by a gradient of 2 % and a median grain size of 24 mm. Bed load samples were taken using the Helley-Smith sampler at flow rates ranging from 1.0 - 5.9 m3/s. According to these data evaluations performance and feasibility of transport equations for field applications are checked. Up to now the results between observed and calculated transport rates show a large scatter of more than several orders of magnitude. This underlines the statements from GOMEZ AND CHURCH (1989) that most equations under/over predict transport rates if the basic requirements (steady flow, equilibrium load), which are usually assumed, are not fulfilled.

  10. Adjoint-Based Sensitivity Maps for the Nearshore

    NASA Astrophysics Data System (ADS)

    Orzech, Mark; Veeramony, Jay; Ngodock, Hans

    2013-04-01

    The wave model SWAN (Booij et al., 1999) solves the spectral action balance equation to produce nearshore wave forecasts and climatologies. It is widely used by the coastal modeling community and is part of a variety of coupled ocean-wave-atmosphere model systems. A variational data assimilation system (Orzech et al., 2013) has recently been developed for SWAN and is presently being transitioned to operational use by the U.S. Naval Oceanographic Office. This system is built around a numerical adjoint to the fully nonlinear, nonstationary SWAN code. When provided with measured or artificial "observed" spectral wave data at a location of interest on a given nearshore bathymetry, the adjoint can compute the degree to which spectral energy levels at other locations are correlated with - or "sensitive" to - variations in the observed spectrum. Adjoint output may be used to construct a sensitivity map for the entire domain, tracking correlations of spectral energy throughout the grid. When access is denied to the actual locations of interest, sensitivity maps can be used to determine optimal alternate locations for data collection by identifying regions of greatest sensitivity in the mapped domain. The present study investigates the properties of adjoint-generated sensitivity maps for nearshore wave spectra. The adjoint and forward SWAN models are first used in an idealized test case at Duck, NC, USA, to demonstrate the system's effectiveness at optimizing forecasts of shallow water wave spectra for an inaccessible surf-zone location. Then a series of simulations is conducted for a variety of different initializing conditions, to examine the effects of seasonal changes in wave climate, errors in bathymetry, and variations in size and shape of the inaccessible region of interest. Model skill is quantified using two methods: (1) a more traditional correlation of observed and modeled spectral statistics such as significant wave height, and (2) a recently developed RMS

  11. Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation

    SciTech Connect

    Panta Pazos, Ruben; Biasotto Hauser, Eliete; Tullio de Vilhena, Marco

    2002-07-01

    In the last decade Vilhena and coworkers reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional S{sub N} equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTS{sub N} method, which consists in the application of the Laplace transform to the set of nodal S{sub N} equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of S{sub N} up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal S{sub N} equations for N up to 16 and we begin the convergence of the S{sub N} nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation. (authors)

  12. Coupled electron-photon radiation transport

    SciTech Connect

    Lorence, L.; Kensek, R.P.; Valdez, G.D.; Drumm, C.R.; Fan, W.C.; Powell, J.L.

    2000-01-17

    Massively-parallel computers allow detailed 3D radiation transport simulations to be performed to analyze the response of complex systems to radiation. This has been recently been demonstrated with the coupled electron-photon Monte Carlo code, ITS. To enable such calculations, the combinatorial geometry capability of ITS was improved. For greater geometrical flexibility, a version of ITS is under development that can track particles in CAD geometries. Deterministic radiation transport codes that utilize an unstructured spatial mesh are also being devised. For electron transport, the authors are investigating second-order forms of the transport equations which, when discretized, yield symmetric positive definite matrices. A novel parallelization strategy, simultaneously solving for spatial and angular unknowns, has been applied to the even- and odd-parity forms of the transport equation on a 2D unstructured spatial mesh. Another second-order form, the self-adjoint angular flux transport equation, also shows promise for electron transport.

  13. One-dimensional transport equation models for sound energy propagation in long spaces: theory.

    PubMed

    Jing, Yun; Larsen, Edward W; Xiang, Ning

    2010-04-01

    In this paper, a three-dimensional transport equation model is developed to describe the sound energy propagation in a long space. Then this model is reduced to a one-dimensional model by approximating the solution using the method of weighted residuals. The one-dimensional transport equation model directly describes the sound energy propagation in the "long" dimension and deals with the sound energy in the "short" dimensions by prescribed functions. Also, the one-dimensional model consists of a coupled set of N transport equations. Only N=1 and N=2 are discussed in this paper. For larger N, although the accuracy could be improved, the calculation time is expected to significantly increase, which diminishes the advantage of the model in terms of its computational efficiency. PMID:20370013

  14. Transport equations for low-energy solar particles in evolving interplanetary magnetic fields

    NASA Technical Reports Server (NTRS)

    Ng, C. K.

    1988-01-01

    Two new forms of a simplified Fokker-Planck equation are derived for the transport of low-energy solar energetic particles in an evolving interplanetary magnetic field, carried by a variable radial solar wind. An idealized solution suggests that the 'invariant' anisotropy direction reported by Allum et al. (1974) may be explained within the conventional theoretical framework. The equations may be used to relate studies of solar particle propagation to solar wind transients, and vice versa.

  15. Lorentz force correction to the Boltzmann radiation transport equation and its implications for Monte Carlo algorithms

    NASA Astrophysics Data System (ADS)

    Bouchard, Hugo; Bielajew, Alex

    2015-07-01

    To establish a theoretical framework for generalizing Monte Carlo transport algorithms by adding external electromagnetic fields to the Boltzmann radiation transport equation in a rigorous and consistent fashion. Using first principles, the Boltzmann radiation transport equation is modified by adding a term describing the variation of the particle distribution due to the Lorentz force. The implications of this new equation are evaluated by investigating the validity of Fano’s theorem. Additionally, Lewis’ approach to multiple scattering theory in infinite homogeneous media is redefined to account for the presence of external electromagnetic fields. The equation is modified and yields a description consistent with the deterministic laws of motion as well as probabilistic methods of solution. The time-independent Boltzmann radiation transport equation is generalized to account for the electromagnetic forces in an additional operator similar to the interaction term. Fano’s and Lewis’ approaches are stated in this new equation. Fano’s theorem is found not to apply in the presence of electromagnetic fields. Lewis’ theory for electron multiple scattering and moments, accounting for the coupling between the Lorentz force and multiple elastic scattering, is found. However, further investigation is required to develop useful algorithms for Monte Carlo and deterministic transport methods. To test the accuracy of Monte Carlo transport algorithms in the presence of electromagnetic fields, the Fano cavity test, as currently defined, cannot be applied. Therefore, new tests must be designed for this specific application. A multiple scattering theory that accurately couples the Lorentz force with elastic scattering could improve Monte Carlo efficiency. The present study proposes a new theoretical framework to develop such algorithms.

  16. Lorentz force correction to the Boltzmann radiation transport equation and its implications for Monte Carlo algorithms.

    PubMed

    Bouchard, Hugo; Bielajew, Alex

    2015-07-01

    To establish a theoretical framework for generalizing Monte Carlo transport algorithms by adding external electromagnetic fields to the Boltzmann radiation transport equation in a rigorous and consistent fashion. Using first principles, the Boltzmann radiation transport equation is modified by adding a term describing the variation of the particle distribution due to the Lorentz force. The implications of this new equation are evaluated by investigating the validity of Fano's theorem. Additionally, Lewis' approach to multiple scattering theory in infinite homogeneous media is redefined to account for the presence of external electromagnetic fields. The equation is modified and yields a description consistent with the deterministic laws of motion as well as probabilistic methods of solution. The time-independent Boltzmann radiation transport equation is generalized to account for the electromagnetic forces in an additional operator similar to the interaction term. Fano's and Lewis' approaches are stated in this new equation. Fano's theorem is found not to apply in the presence of electromagnetic fields. Lewis' theory for electron multiple scattering and moments, accounting for the coupling between the Lorentz force and multiple elastic scattering, is found. However, further investigation is required to develop useful algorithms for Monte Carlo and deterministic transport methods. To test the accuracy of Monte Carlo transport algorithms in the presence of electromagnetic fields, the Fano cavity test, as currently defined, cannot be applied. Therefore, new tests must be designed for this specific application. A multiple scattering theory that accurately couples the Lorentz force with elastic scattering could improve Monte Carlo efficiency. The present study proposes a new theoretical framework to develop such algorithms. PMID:26061045

  17. Efficient, Automated Monte Carlo Methods for Radiation Transport

    PubMed Central

    Kong, Rong; Ambrose, Martin; Spanier, Jerome

    2012-01-01

    Monte Carlo simulations provide an indispensible model for solving radiative transport problems, but their slow convergence inhibits their use as an everyday computational tool. In this paper, we present two new ideas for accelerating the convergence of Monte Carlo algorithms based upon an efficient algorithm that couples simulations of forward and adjoint transport equations. Forward random walks are first processed in stages, each using a fixed sample size, and information from stage k is used to alter the sampling and weighting procedure in stage k + 1. This produces rapid geometric convergence and accounts for dramatic gains in the efficiency of the forward computation. In case still greater accuracy is required in the forward solution, information from an adjoint simulation can be added to extend the geometric learning of the forward solution. The resulting new approach should find widespread use when fast, accurate simulations of the transport equation are needed. PMID:23226872

  18. Variance estimates for transport in stochastic media by means of the master equation

    SciTech Connect

    Pautz, S. D.; Franke, B. C.; Prinja, A. K.

    2013-07-01

    The master equation has been used to examine properties of transport in stochastic media. It has been shown previously that not only may the Levermore-Pomraning (LP) model be derived from the master equation for a description of ensemble-averaged transport quantities, but also that equations describing higher-order statistical moments may be obtained. We examine in greater detail the equations governing the second moments of the distribution of the angular fluxes, from which variances may be computed. We introduce a simple closure for these equations, as well as several models for estimating the variances of derived transport quantities. We revisit previous benchmarks for transport in stochastic media in order to examine the error of these new variance models. We find, not surprisingly, that the errors in these variance estimates are at least as large as the corresponding estimates of the average, and sometimes much larger. We also identify patterns in these variance estimates that may help guide the construction of more accurate models. (authors)

  19. Iterative solution of the multistream electron transport equation. I - Comparison with laboratory beam injection experiments

    NASA Technical Reports Server (NTRS)

    Porter, H. S.; Varosi, F.; Mayr, H. G.

    1987-01-01

    The Neumann iteration method presently used for solving the electron transport equation in which energy, attitude, and pitch angle are independent variables is fast, and can compute numerical point-response-function solutions of the electron transport equation. Because both the inelastic cross sections and angular elastic cross sections of the model are empirically based, the solutions obtained represent a test of compatibility between various sets of cross sections and energy deposition measurements. The use of a numerical quadrature based on analytic phase function forms yields accurate phase function integrals at low computational cost.

  20. Numerical Analysis of Quantum Transport Equation for Bose Gas in One Dimensional Optical Lattice

    NASA Astrophysics Data System (ADS)

    Kuwahara, Yukiro; Nakamura, Yusuke; Yamanaka, Yoshiya

    The quantum transport equation and the correction of the quasiparticle energy are derived by imposing the renormalization conditions on the improved time-dependent on-shell self-energy in nonequilibrium Thermo Field Dynamics. They are numerically analyzed for the one dimensional system of cold neutral atomic Bose gas confined by a combined harmonic and optical lattice potentials. The analysis indicates that the correction of the quaisparticle energy plays a crucial role in the thermal relaxation processes described by the quantum transport equation.

  1. Equations of state and transport properties of mixtures in the warm dense regime

    SciTech Connect

    Hou, Yong; Dai, Jiayu; Kang, Dongdong; Ma, Wen; Yuan, Jianmin

    2015-02-15

    We have performed average-atom molecular dynamics to simulate the CH and LiH mixtures in the warm dense regime, and obtained equations of state and the ionic transport properties. The electronic structures are calculated by using the modified average-atom model, which have included the broadening of energy levels, and the ion-ion pair potentials of mixtures are constructed based on the temperature-dependent density functional theory. The ionic transport properties, such as ionic diffusion and shear viscosity, are obtained through the ionic velocity correlation functions. The equations of state and transport properties for carbon, hydrogen and lithium, hydrogen mixtures in a wide region of density and temperature are calculated. Through our computing the average ionization degree, average ion-sphere diameter and transition properties in the mixture, it is shown that transport properties depend not only on the ionic mass but also on the average ionization degree.

  2. Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films

    NASA Astrophysics Data System (ADS)

    Chiloyan, Vazrik; Zeng, Lingping; Huberman, Samuel; Maznev, Alexei A.; Nelson, Keith A.; Chen, Gang

    2016-07-01

    The phonon Boltzmann transport equation (BTE) is widely utilized to study non-diffusive thermal transport. We find a solution of the BTE in the thin film transient thermal grating (TTG) experimental geometry by using a recently developed variational approach with a trial solution supplied by the Fourier heat conduction equation. We obtain an analytical expression for the thermal decay rate that shows excellent agreement with Monte Carlo simulations. We also obtain a closed form expression for the effective thermal conductivity that demonstrates the full material property and heat transfer geometry dependence, and recovers the limits of the one-dimensional TTG expression for very thick films and the Fuchs-Sondheimer expression for very large grating spacings. The results demonstrate the utility of the variational technique for analyzing non-diffusive phonon-mediated heat transport for nanostructures in multi-dimensional transport geometries, and will assist the probing of the mean free path distribution of materials via transient grating experiments.

  3. Un-collided-flux preconditioning for the first order transport equation

    SciTech Connect

    Rigley, M.; Koebbe, J.; Drumm, C.

    2013-07-01

    Two codes were tested for the first order neutron transport equation using finite element methods. The un-collided-flux solution is used as a preconditioner for each of these methods. These codes include a least squares finite element method and a discontinuous finite element method. The performance of each code is shown on problems in one and two dimensions. The un-collided-flux preconditioner shows good speedup on each of the given methods. The un-collided-flux preconditioner has been used on the second-order equation, and here we extend those results to the first order equation. (authors)

  4. Analytical Tests for Ray Effect Errors in Discrete Ordinate Methods for Solving the Neutron Transport Equation

    SciTech Connect

    Chang, B

    2004-03-22

    This paper contains three analytical solutions of transport problems which can be used to test ray-effect errors in the numerical solutions of the Boltzmann Transport Equation (BTE). We derived the first two solutions and the third was shown to us by M. Prasad. Since this paper is intended to be an internal LLNL report, no attempt was made to find the original derivations of the solutions in the literature in order to cite the authors for their work.

  5. Modeling scalar dissipation and scalar variance in large eddy simulation: Algebraic and transport equation closures

    NASA Astrophysics Data System (ADS)

    Knudsen, E.; Richardson, E. S.; Doran, E. M.; Pitsch, H.; Chen, J. H.

    2012-05-01

    Scalar dissipation rates and subfilter scalar variances are important modeling parameters in large eddy simulations (LES) of reacting flows. Currently available models capture the general behavior of these parameters, but these models do not always perform with the degree of accuracy that is needed for predictive LES. Here, two direct numerical simulations (DNS) are used to analyze LES dissipation rate and variance models, and to propose a new model for the dissipation rate that is based on a transport equation. The first DNS that is considered is a non-premixed auto-igniting C2H4 jet flame simulation originally performed by Yoo et al. [Proc. Combust. Inst. 33, 1619-1627 (2011)], 10.1016/j.proci.2010.06.147. A LES of this case is run using algebraic models for the dissipation rate and subfilter variance. It is shown that the algebraic models fail to adequately reproduce the DNS results. This motivates the introduction of a transport equation model for the LES dissipation rate. Closure of the equation is addressed by formulating a new adapted dynamic approach. This approach borrows dynamically computed information from LES quantities that, unlike the dissipation rate, do not reside on the smallest flow length scales. The adapted dynamic approach is analyzed by considering a second DNS of scalar mixing in homogeneous isotropic turbulence. Data from this second DNS are used to confirm that the adapted dynamic approach successfully closes the dissipation rate equation over a wide range of LES filter widths. The first reacting jet case is then returned to and used to test the LES transport equation models. The transport equation model for the dissipation rate is shown to be more accurate than its algebraic counterpoint, and the dissipation rate is eliminated as a source of error in the transported variance model.

  6. Exactly averaged stochastic equations for flow and transport in random media

    SciTech Connect

    Shvidler, Mark; Karasaki, Kenzi

    2001-11-30

    It is well known that exact averaging of the equations of flow and transport in random porous media are at present realized only for a small number of special, occasionally exotic, fields. On the other hand, the properties of approximate averaging methods are not yet fully understood. For example, the convergence behavior and the accuracy of truncated perturbation series are not well known. Furthermore, the calculation of the high-order perturbations is very complicated. These problems for a long time have stimulated attempts to find the answer for the question: Are there in existence some exact general and sufficiently universal forms of averaged equations? If the answer is positive, there arises the problem of the construction of these equations and analyzing them. There exist many publications related to these problems and oriented on different applications: hydrodynamics, flow and transport in porous media, theory of elasticity, acoustic and electromagnetic waves in random fields, etc. We present a method of finding some general forms of exactly averaged equations for flow and transport in random fields by using (1) an assumption of the existence of Green's functions for appropriate stochastic problems, (2 ) some general properties of the Green's functions, and (3) the some basic information about the random fields of the conductivity, porosity and flow velocity. We present some general forms of the exactly averaged non-local equations for the following cases. 1. Steady-state flow with sources in porous media with random conductivity. 2. Transient flow with sources in compressible media with random conductivity and porosity. 3. Non-reactive solute transport in random porous media. We discuss the problem of uniqueness and the properties of the non-local averaged equations, for the cases with some types of symmetry (isotropic, transversal isotropic, orthotropic) and we analyze the hypothesis of the structure of non-local equations in a general case of

  7. Receptivity in parallel flows: An adjoint approach

    NASA Technical Reports Server (NTRS)

    Hill, D. Christopher

    1993-01-01

    Linear receptivity studies in parallel flows are aimed at understanding how external forcing couples to the natural unstable motions which a flow can support. The vibrating ribbon problem models the original Schubauer and Skramstad boundary layer experiment and represents the classic boundary layer receptivity problem. The process by which disturbances are initiated in convectively-unstable jets and shear layers has also received attention. Gaster was the first to handle the boundary layer analysis with the recognition that spatial modes, rather than temporal modes, were relevant when studying convectively-unstable flows that are driven by a time-harmonic source. The amplitude of the least stable spatial mode, far downstream of the source, is related to the source strength by a coupling coefficient. The determination of this coefficient is at the heart of this type of linear receptivity study. The first objective of the present study was to determine whether the various wave number derivative factors, appearing in the coupling coefficients for linear receptivity problems, could be reexpressed in a simpler form involving adjoint eigensolutions. Secondly, it was hoped that the general nature of this simplification could be shown; indeed, a rather elegant characterization of the receptivity properties of spatial instabilities does emerge. The analysis is quite distinct from the usual Fourier-inversion procedures, although a detailed knowledge of the spectrum of the Orr-Sommerfeld equation is still required. Since the cylinder wake analysis proved very useful in addressing control considerations, the final objective was to provide a foundation upon which boundary layer control theory may be developed.

  8. Adjoint Techniques for Topology Optimization of Structures Under Damage Conditions

    NASA Technical Reports Server (NTRS)

    Akgun, Mehmet A.; Haftka, Raphael T.

    2000-01-01

    The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation (Haftka and Gurdal, 1992) in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers (Akgun et al., 1998a and 1999). It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages (Haftka et al., 1983). A common method for topology optimization is that of compliance minimization (Bendsoe, 1995) which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local

  9. Double-difference adjoint seismic tomography

    NASA Astrophysics Data System (ADS)

    Yuan, Yanhua O.; Simons, Frederik J.; Tromp, Jeroen

    2016-06-01

    We introduce a `double-difference' method for the inversion for seismic wavespeed structure based on adjoint tomography. Differences between seismic observations and model predictions at individual stations may arise from factors other than structural heterogeneity, such as errors in the assumed source-time function, inaccurate timings, and systematic uncertainties. To alleviate the corresponding nonuniqueness in the inverse problem, we construct differential measurements between stations, thereby reducing the influence of the source signature and systematic errors. We minimize the discrepancy between observations and simulations in terms of the differential measurements made on station pairs. We show how to implement the double-difference concept in adjoint tomography, both theoretically and in practice. We compare the sensitivities of absolute and differential measurements. The former provide absolute information on structure along the ray paths between stations and sources, whereas the latter explain relative (and thus higher-resolution) structural variations in areas close to the stations. Whereas in conventional tomography a measurement made on a single earthquake-station pair provides very limited structural information, in double-difference tomography one earthquake can actually resolve significant details of the structure. The double-difference methodology can be incorporated into the usual adjoint tomography workflow by simply pairing up all conventional measurements; the computational cost of the necessary adjoint simulations is largely unaffected. Rather than adding to the computational burden, the inversion of double-difference measurements merely modifies the construction of the adjoint sources for data assimilation.

  10. Exact analytical solutions for contaminant transport in rivers 1. The equilibrium advection-dispersion equation

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Analytical solutions of the advection-dispersion equation and related models are indispensable for predicting or analyzing contaminant transport processes in streams and rivers, as well as in other surface water bodies. Many useful analytical solutions originated in disciplines other than surface-w...

  11. Modeling Solute Transport in Soil Columns Using Advective-Dispersive Equation with Fractional Spatial Derivatives

    Technology Transfer Automated Retrieval System (TEKTRAN)

    It has been reported that this model cannot take into account several important features of solute movement through soil. Recently, a new model has been suggested that results in a solute transport equation with fractional spatial derivatives, or FADE. We have assembled a database on published solu...

  12. Parallel algorithms for 2-D cylindrical transport equations of Eigenvalue problem

    SciTech Connect

    Wei, J.; Yang, S.

    2013-07-01

    In this paper, aimed at the neutron transport equations of eigenvalue problem under 2-D cylindrical geometry on unstructured grid, the discrete scheme of Sn discrete ordinate and discontinuous finite is built, and the parallel computation for the scheme is realized on MPI systems. Numerical experiments indicate that the designed parallel algorithm can reach perfect speedup, it has good practicality and scalability. (authors)

  13. Moment-equation methods for calculating neoclassical transport coefficients in general toroidal plasmas

    SciTech Connect

    Sugama, H.; Nishimura, S.

    2008-04-15

    A detailed comparison is made between moment-equation methods presented by H. Sugama and S. Nishimura [Phys. Plasmas 9, 4637 (2002)] and by M. Taguchi [Phys. Fluids B 4, 3638 (1992)] for calculating neoclassical transport coefficients in general toroidal plasmas including nonsymmetric systems. It is shown that these methods can be derived from the drift kinetic equation with the same collision model used for correctly taking account of collisional momentum conservation. In both methods, the Laguerre polynomials of the energy variable are employed to expand the guiding-center distribution function and to obtain the moment equations, by which the radial neoclassical transport fluxes and the parallel flows are related to the thermodynamic forces. The methods are given here in the forms applicable for an arbitrary truncation number of the Laguerre-polynomial expansion so that their accuracies can be improved by increasing the truncation number. Differences between results from the two methods appear when the Laguerre-polynomial expansion is truncated up to a finite order because different weight functions are used in them to derive the moment equations. At each order of the truncation, the neoclassical transport coefficients obtained from the Sugama-Nishimura method show the Onsager symmetry and satisfy the ambipolar-diffusion condition intrinsically for symmetric systems. Also, numerical examples are given to show how the transport coefficients converge with the truncation number increased for the two methods.

  14. Coupling lattice Boltzmann and continuum equations for flow and reactive transport in porous media.

    SciTech Connect

    Coon, Ethan; Porter, Mark L.; Kang, Qinjun; Moulton, John D.; Lichtner, Peter C.

    2012-06-18

    In spatially and temporally localized instances, capturing sub-reservoir scale information is necessary. Capturing sub-reservoir scale information everywhere is neither necessary, nor computationally possible. The lattice Boltzmann Method for solving pore-scale systems. At the pore-scale, LBM provides an extremely scalable, efficient way of solving Navier-Stokes equations on complex geometries. Coupling pore-scale and continuum scale systems via domain decomposition. By leveraging the interpolations implied by pore-scale and continuum scale discretizations, overlapping Schwartz domain decomposition is used to ensure continuity of pressure and flux. This approach is demonstrated on a fractured medium, in which Navier-Stokes equations are solved within the fracture while Darcy's equation is solved away from the fracture Coupling reactive transport to pore-scale flow simulators allows hybrid approaches to be extended to solve multi-scale reactive transport.

  15. Benchmark solutions for the galactic ion transport equations: Energy and spatially dependent problems

    NASA Astrophysics Data System (ADS)

    Ganapol, Barry D.; Townsend, Lawrence W.; Wilson, John W.

    1989-03-01

    Nontrivial benchmark solutions are developed for the galactic ion transport (GIT) equations in the straight-ahead approximation. These equations are used to predict potential radiation hazards in the upper atmosphere and in space. Two levels of difficulty are considered: (1) energy independent, and (2) spatially independent. The analysis emphasizes analytical methods never before applied to the GIT equations. Most of the representations derived have been numerically implemented and compared to more approximate calculations. Accurate ion fluxes are obtained (3 to 5 digits) for nontrivial sources. For monoenergetic beams, both accurate doses and fluxes are found. The benchmarks presented are useful in assessing the accuracy of transport algorithms designed to accommodate more complex radiation protection problems. In addition, these solutions can provide fast and accurate assessments of relatively simple shield configurations.

  16. Exact PDF equations and closure approximations for advective-reactive transport

    SciTech Connect

    Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.; Karniadakis, George E.

    2013-06-01

    Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recently proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.

  17. Number-resolved master equation approach to quantum measurement and quantum transport

    NASA Astrophysics Data System (ADS)

    Li, Xin-Qi

    2016-08-01

    In addition to the well-known Landauer-Büttiker scattering theory and the nonequilibrium Green's function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number ( n)-resolved master equation ( n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.

  18. Benchmark solutions for the galactic ion transport equations: Energy and spatially dependent problems

    NASA Technical Reports Server (NTRS)

    Ganapol, Barry D.; Townsend, Lawrence W.; Wilson, John W.

    1989-01-01

    Nontrivial benchmark solutions are developed for the galactic ion transport (GIT) equations in the straight-ahead approximation. These equations are used to predict potential radiation hazards in the upper atmosphere and in space. Two levels of difficulty are considered: (1) energy independent, and (2) spatially independent. The analysis emphasizes analytical methods never before applied to the GIT equations. Most of the representations derived have been numerically implemented and compared to more approximate calculations. Accurate ion fluxes are obtained (3 to 5 digits) for nontrivial sources. For monoenergetic beams, both accurate doses and fluxes are found. The benchmarks presented are useful in assessing the accuracy of transport algorithms designed to accommodate more complex radiation protection problems. In addition, these solutions can provide fast and accurate assessments of relatively simple shield configurations.

  19. Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings

    SciTech Connect

    Jin, Shi; Xiu, Dongbin; Zhu, Xueyu

    2015-05-15

    In this paper we develop a set of stochastic numerical schemes for hyperbolic and transport equations with diffusive scalings and subject to random inputs. The schemes are asymptotic preserving (AP), in the sense that they preserve the diffusive limits of the equations in discrete setting, without requiring excessive refinement of the discretization. Our stochastic AP schemes are extensions of the well-developed deterministic AP schemes. To handle the random inputs, we employ generalized polynomial chaos (gPC) expansion and combine it with stochastic Galerkin procedure. We apply the gPC Galerkin scheme to a set of representative hyperbolic and transport equations and establish the AP property in the stochastic setting. We then provide several numerical examples to illustrate the accuracy and effectiveness of the stochastic AP schemes.

  20. An asymptotic-preserving Lagrangian algorithm for the time-dependent anisotropic heat transport equation

    SciTech Connect

    Chacon, Luis; del-Castillo-Negrete, Diego; Hauck, Cory D.

    2014-09-01

    We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while the second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X /X becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L2/X1L2 → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.

  1. Airfoil design using a coupled euler and integral boundary layer method with adjoint based sensitivities

    NASA Astrophysics Data System (ADS)

    Edwards, S.; Reuther, J.; Chattot, J. J.

    The objective of this paper is to present a control theory approach for the design of airfoils in the presence of viscous compressible flows. A coupled system of the integral boundary layer and the Euler equations is solved to provide rapid flow simulations. An adjoint approach consistent with the complete coupled state equations is employed to obtain the sensitivities needed to drive a numerical optimization algorithm. Design to a target pressure distribution is demonstrated on an RAE 2822 airfoil at transonic speeds.

  2. Deterministic proton transport solving a one dimensional Fokker-Planck equation

    SciTech Connect

    Marr, D.; Prael, R.; Adams, K.; Alcouffe, R.

    1997-10-01

    The transport of protons through matter is characterized by many interactions which cause small deflections and slight energy losses. The few which are catastrophic or cause large angle scattering can be viewed as extinction for many applications. The transport of protons at this level of approximation can be described by a Fokker Planck Equation. This equation is solved using a deterministic multigroup differencing scheme with a highly resolved set of discrete ordinates centered around the beam direction which is adequate to properly account for deflections and energy losses due to multiple Coulomb scattering. Comparisons with LAHET for a large variety of problems ranging from 800 MeV protons on a copper step wedge to 10 GeV protons on a sandwich of material are presented. The good agreement with the Monte Carlo code shows that the solution method is robust and useful for approximate solutions of selected proton transport problems.

  3. Multi-term approximation to the Boltzmann transport equation for electron energy distribution functions in nitrogen

    NASA Astrophysics Data System (ADS)

    Feng, Yue

    Plasma is currently a hot topic and it has many significant applications due to its composition of both positively and negatively charged particles. The energy distribution function is important in plasma science since it characterizes the ability of the plasma to affect chemical reactions, affect physical outcomes, and drive various applications. The Boltzmann Transport Equation is an important kinetic equation that provides an accurate basis for characterizing the distribution function---both in energy and space. This dissertation research proposes a multi-term approximation to solve the Boltzmann Transport Equation by treating the relaxation process using an expansion of the electron distribution function in Legendre polynomials. The elastic and 29 inelastic cross sections for electron collisions with nitrogen molecules (N2) and singly ionized nitrogen molecules ( N+2 ) have been used in this application of the Boltzmann Transport Equation. Different numerical methods have been considered to compare the results. The numerical methods discussed in this thesis are the implicit time-independent method, the time-dependent Euler method, the time-dependent Runge-Kutta method, and finally the implicit time-dependent relaxation method by generating the 4-way grid with a matrix solver. The results show that the implicit time-dependent relaxation method is the most accurate and stable method for obtaining reliable results. The results were observed to match with the published experimental data rather well.

  4. Averaging of Stochastic Equations for Flow and Transport in PorousMedia

    SciTech Connect

    Shvidler, Mark; Karasaki, Kenzi

    2005-01-07

    It is well known that at present exact averaging of theequations of flow and transport in random porous media have been realizedfor only a small number of special fields. Moreover, the approximateaveraging methods are not yet fully understood. For example, theconvergence behavior and the accuracy of truncated perturbation seriesare not well known; and in addition, the calculation of the high-orderperturbations is very complicated. These problems for a long time havestimulated attempts to find the answer for the question: Are there inexistence some exact general and sufficiently universal forms of averagedequations? If the answer is positive, there arises the problem of theconstruction of these equations and analyzing them. There are manypublications on different applications of this problem to various fields,including: Hydrodynamics, flow and transport in porous media, theory ofelasticity, acoustic and electromagnetic waves in random fields, etc.Here, we present a method of finding some general form of exactlyaveraged equations for flow and transport in random fields by using (1)some general properties of the Green s functions for appropriatestochastic problems, and (2) some basic information about the randomfields of the conductivity, porosity and flow velocity. We presentgeneral forms of exactly averaged non-local equations for the followingcases: (1) steady-state flow with sources in porous media with randomconductivity, (2) transient flow with sources in compressible media withrandom conductivity and porosity; and (3) Nonreactive solute transport inrandom porous media. We discuss the problem of uniqueness and theproperties of the non-local averaged equations for cases with some typeof symmetry (isotropic, transversal isotropic and orthotropic), and weanalyze the structure of the nonlocal equations in the general case ofstochastically homogeneous fields.

  5. Pseudospectral Methods of Solution of the Linear and Linearized Boltzmann Equations; Transport and Relaxation

    NASA Astrophysics Data System (ADS)

    Shizgal, Bernie D.

    2011-05-01

    The study of the solution of the linearized Boltzmann equation has a very long history arising from the classic work by Chapman and Cowling. For small departures from a Maxwellian, the nonlinear Boltzmann equation can be linearized and the transport coefficients calculated with the Chapman-Enskog approach. This procedure leads to a set of linear integral equations which are generally solved with the expansion of the departure from Maxwellian in Sonine polynomials. The method has been used successfully for many decades to compare experimental transport data in atomic gases with theory generally carried out for realistic atom-atom differential cross sections. There are alternate pseudospectral methods which involve the discretization of the distribution function on a discrete grid. This paper considers a pseudospectral method of solution of the linearized hard sphere Boltzmann equation for the viscosity in a simple gas. The relaxation of a small departure from a Maxwellian is also considered for the linear test particle problem with unit mass ratio which is compared with the relaxation for the linearized one component Boltzmann equation.

  6. Benchmark solutions for the galactic ion transport equations with spatial and energy coupling

    NASA Technical Reports Server (NTRS)

    Ganapol, Barry D.

    1988-01-01

    In order to anticipate future space shielding requirements, NASA has initiated an effort to formulate computational methods to simulate radiation effects in space. As part of the program, numerical transport algorithms have been developed for the deterministic Boltzman equation describing galactic cosmic ray (GCR) interactions with matter. It thus becomes necessary to assess the accuracy of proposed deterministic algorithms. For this reason, analytical benchmark solutions to mathematically tractable galactic cosmic ray equations have recently been obtained. Even though these problems involve simplifying assumptions of the associated physics, they still contain the essential features of the basic transport processes. The solutions obtained are features of the basic transport processes. The solutions obtained are compared to results from numerical algorithms in order to ensure proper coding and to provide a measure of the accuracy of the numerical methods used in the algorithm. For the first time, mathematical methods have been applied to the galactic ion transport (GIT) equations in the straight ahead approximation with constant nuclear properties. The approach utilizes a Laplace transforms inversion yielding a closed form benchmark solution which is also computationally efficient.

  7. Examining Tropical Cyclone - Kelvin Wave Interactions using Adjoint Diagnostics

    NASA Astrophysics Data System (ADS)

    Reynolds, C. A.; Doyle, J. D.; Hong, X.

    2015-12-01

    Adjoint-based tools can provide valuable insight into the mechanisms that influence the evolution and predictability of atmospheric phenomena, as they allow for the efficient and rigorous computation of forecast sensitivity to changes in the initial state. We apply adjoint-based tools from the non-hydrostatic Coupled Atmosphere/Ocean Mesoscale Prediction System (COAMPS) to explore the initial-state sensitivity and interactions between a tropical cyclone and atmospheric equatorial waves associated with the Madden Julian Oscillation (MJO) in the Indian Ocean during the DYNAMO field campaign. The development of Tropical Cyclone 5 (TC05) coincided with the passage of an equatorial Kelvin wave and westerly wind burst associated with an MJO that developed in the Indian Ocean in late November 2011, but it was unclear if and how one affected the other. COAMPS 24-h and 36-h adjoint sensitivities are analyzed for both TC05 and the equatorial waves to understand how the evolution of each system is sensitive to the other. The sensitivity of equatorial westerlies in the western Indian Ocean on 23 November shares characteristics with the classic Gill (1980) Rossby and Kelvin wave response to symmetric heating about the equator, including symmetric cyclonic circulations to the north and south of the westerlies, and enhanced heating in the area of convergence between the equatorial westerlies and easterlies. In addition, there is sensitivity in the Bay of Bengal associated with the cyclonic circulation that eventually develops into TC05. At the same time, the developing TC05 system shows strongest sensitivity to local wind and heating perturbations, but sensitivity to the equatorial westerlies is also clear. On 24 November, when the Kelvin wave is immediately south of the developing tropical cyclone, both phenomena are sensitive to each other. On 25 November TC05 no longer shows sensitivity to the Kelvin wave, while the Kelvin Wave still exhibits some weak sensitivity to TC05. In

  8. Solutions to bi-Maxwellian transport equations for the polar wind

    NASA Technical Reports Server (NTRS)

    Demars, H. G.; Schunk, R. W.

    1989-01-01

    In this study, polar wind solutions are obtained for a broad range of O(+) density, H(+) drift velocity, electron temperature and H(+) temperature boundary conditions. The bi-Maxwellian-based 16-moment set of transport equations is used, since this set is expected to be superior to Maxwellian-based equations in describing large temperature anisotropies and heat flows. The present solutions corroborate earlier results when similar boundary conditions are used. Also, for previously unexplored combinations of boundary conditions, the present solutions are often qualitatively different from any obtained before.

  9. Petrov-galerkin finite element method for solving the neutron transport equation

    SciTech Connect

    Greenbaum, A.; Ferguson, J.M.

    1986-05-01

    A finite element using different trial and test spaces in introduced for solving the neutron transport equation in spherical geometry. It is shown that the widely used discrete ordinates method can also be thought of as such a finite element technique, in which integrals appearing in the difference equations are replaced by one-point Gauss quadrature formulas (midpoint rule). Comparison of accuracy between the new method and the discrete ordinates method is discussed, and numerical examples are given to illustrate the greater accuracy of the new technique.

  10. Limitations of Adjoint-Based Optimization for Separated Flows

    NASA Astrophysics Data System (ADS)

    Otero, J. Javier; Sharma, Ati; Sandberg, Richard

    2015-11-01

    Cabin noise is generated by the transmission of turbulent pressure fluctuations through a vibrating panel and can lead to fatigue. In the present study, we model this problem by using DNS to simulate the flow separating off a backward facing step and interacting with a plate downstream of the step. An adjoint formulation of the full compressible Navier-Stokes equations with varying viscosity is used to calculate the optimal control required to minimize the fluid-structure-acoustic interaction with the plate. To achieve noise reduction, a cost function in wavenumber space is chosen to minimize the excitation of the lower structural modes of the structure. To ensure the validity of time-averaged cost functions, it is essential that the time horizon is long enough to be a representative sample of the statistical behaviour of the flow field. The results from the current study show how this scenario is not always feasible for separated flows, because the chaotic behaviour of turbulence surpasses the ability of adjoint-based methods to compute time-dependent sensitivities of the flow.

  11. Analytical solution of the advection-diffusion transport equation using a change-of-variable and integral transform technique

    Technology Transfer Automated Retrieval System (TEKTRAN)

    This paper presents a formal exact solution of the linear advection-diffusion transport equation with constant coefficients for both transient and steady-state regimes. A classical mathematical substitution transforms the original advection-diffusion equation into an exclusively diffusive equation. ...

  12. Electron and ion transport equations in computational weakly-ionized plasmadynamics

    SciTech Connect

    Parent, Bernard; Macheret, Sergey O.; Shneider, Mikhail N.

    2014-02-15

    A new set of ion and electron transport equations is proposed to simulate steady or unsteady quasi-neutral or non-neutral multicomponent weakly-ionized plasmas through the drift–diffusion approximation. The proposed set of equations is advantaged over the conventional one by being considerably less stiff in quasi-neutral regions because it can be integrated in conjunction with a potential equation based on Ohm's law rather than Gauss's law. The present approach is advantaged over previous attempts at recasting the system by being applicable to plasmas with several types of positive ions and negative ions and by not requiring changes to the boundary conditions. Several test cases of plasmas enclosed by dielectrics and of glow discharges between electrodes show that the proposed equations yield the same solution as the standard equations but require 10 to 100 times fewer iterations to reach convergence whenever a quasi-neutral region forms. Further, several grid convergence studies indicate that the present approach exhibits a higher resolution (and hence requires fewer nodes to reach a given level of accuracy) when ambipolar diffusion is present. Because the proposed equations are not intrinsically linked to specific discretization or integration schemes and exhibit substantial advantages with no apparent disadvantage, they are generally recommended as a substitute to the fluid models in which the electric field is obtained from Gauss's law as long as the plasma remains weakly-ionized and unmagnetized.

  13. TRANSPORT EQUATION FOR MHD TURBULENCE: APPLICATION TO PARTICLE ACCELERATION AT INTERPLANETARY SHOCKS

    SciTech Connect

    Sokolov, Igor V.; Gombosi, Tamas I.; Roussev, Ilia I.; Skender, Marina; Usmanov, Arcadi V. E-mail: tamas@umich.edu E-mail: Arcadi.Usmanov.1@gsfc.nasa.gov

    2009-05-01

    The aim of the present paper is to unify the various transport equations for turbulent waves that are used in different areas of space physics. Here, we mostly focus on the magnetohydrodynamic turbulence, in particular the Alfvenic turbulence. The applied methods, however, are general and can be extended to other forms of turbulence, for example the acoustic turbulence, or Langmuir plasma waves. With minor modifications, the derivations followed here can be extended for relativistic motions, thus making it possible to apply them to the wave transport in astrophysical objects with high plasma speeds (radiojets), or strong gravity (black hole surroundings)

  14. Exponentially-convergent Monte Carlo for the 1-D transport equation

    SciTech Connect

    Peterson, J. R.; Morel, J. E.; Ragusa, J. C.

    2013-07-01

    We define a new exponentially-convergent Monte Carlo method for solving the one-speed 1-D slab-geometry transport equation. This method is based upon the use of a linear discontinuous finite-element trial space in space and direction to represent the transport solution. A space-direction h-adaptive algorithm is employed to restore exponential convergence after stagnation occurs due to inadequate trial-space resolution. This methods uses jumps in the solution at cell interfaces as an error indicator. Computational results are presented demonstrating the efficacy of the new approach. (authors)

  15. Improved master equation approach to quantum transport: From Born to self-consistent Born approximation

    SciTech Connect

    Jin, Jinshuang; Li, Jun; Liu, Yu; Li, Xin-Qi; Yan, YiJing

    2014-06-28

    Beyond the second-order Born approximation, we propose an improved master equation approach to quantum transport under self-consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self-energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.

  16. Numerical solution of the time dependent neutron transport equation by the method of the characteristics

    SciTech Connect

    Talamo, Alberto

    2013-05-01

    This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps.

  17. Benchmark solutions for the galactic heavy-ion transport equations with energy and spatial coupling

    NASA Technical Reports Server (NTRS)

    Ganapol, Barry D.; Townsend, Lawrence W.; Lamkin, Stanley L.; Wilson, John W.

    1991-01-01

    Nontrivial benchmark solutions are developed for the galactic heavy ion transport equations in the straightahead approximation with energy and spatial coupling. Analytical representations of the ion fluxes are obtained for a variety of sources with the assumption that the nuclear interaction parameters are energy independent. The method utilizes an analytical LaPlace transform inversion to yield a closed form representation that is computationally efficient. The flux profiles are then used to predict ion dose profiles, which are important for shield design studies.

  18. Discontinuous Galerkin finite element method applied to the 1-D spherical neutron transport equation

    SciTech Connect

    Machorro, Eric . E-mail: machorro@amath.washington.edu

    2007-04-10

    Discontinuous Galerkin finite element methods are used to estimate solutions to the non-scattering 1-D spherical neutron transport equation. Various trial and test spaces are compared in the context of a few sample problems whose exact solution is known. Certain trial spaces avoid unphysical behaviors that seem to plague other methods. Comparisons with diamond differencing and simple corner-balancing are presented to highlight these improvements.

  19. Kinetic equations for hopping transport and spin relaxation in a random magnetic field

    NASA Astrophysics Data System (ADS)

    Shumilin, A. V.; Kabanov, V. V.

    2015-07-01

    We derive the kinetic equations for a hopping transport that take into account an electron spin and the possibility of double occupation. In the Ohmic regime, the equations are reduced to the generalized Miller-Abrahams resistor network. We apply these equations to the problem of the magnetic moment relaxation due to the interaction with the random hyperfine fields. It is shown that in a wide range of parameters the relaxation rate is governed by the hops with the similar rates as spin precession frequency. It is demonstrated that at the large time scale spin relaxation is nonexponential. We argue that the nonexponential relaxation of the magnetic moment is related to the spin of electrons in the slow-relaxing traps. Interestingly, the traps can significantly influence the spin relaxation in the infinite conducting cluster at large times.

  20. From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

    NASA Astrophysics Data System (ADS)

    Bodin, Jacques

    2015-03-01

    In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

  1. Derivation of the macroscopic solute transport equation for homogeneous, saturated, porous media

    SciTech Connect

    Chu, S.Y.; Sposito, G.

    1980-06-01

    The macroscopic transport equation for a conservative solute in a homogeneous, water-saturated porous medium is derived on the basis of a rigorous cumulant expansion applied to the equation of mass balance. The essential physical conept underlying the derivation is that of a local volume-averaged solute velocity which fluctuates on a time scale that is orders of magnitude smaller than its autocorrelation time scale, which, in turn, is much smaller than the time scale of interest in a typical solute transport experiment. This clear separation of the scales is illustrated with representative data on solute transport in homogeneous, water-saturated soils and is employed to justify the truncation of an exact cumulant expansion of the divergence of the volume-averaged solute mass flux density. With the cumulant expansion terminated at first order in the ratio of the solute velocity autocorrelation time to the macroscopic solute transport time interval, an expression for the macroscopic solute mass flux density is produced which is the same as Fick's law extended to porous media. 26 references.

  2. A transport equation for the scalar dissipation in reacting flows with variable density: First results

    NASA Astrophysics Data System (ADS)

    Mantel, T.

    1993-12-01

    Although the different regimes of premixed combustion are not well defined, most of the recent developments in turbulent combustion modeling are led in the so-called flamelet regime. The goal of these models is to give a realistic expression to the mean reaction rate (w). Several methods can be used to estimate (w). Bray and coworkers (Libby & Bray 1980, Bray 1985, Bray & Libby 1986) express the instantaneous reaction rate by means of a flamelet library and a frequency which describes the local interaction between the laminar flamelets and the turbulent flowfield. In another way, the mean reaction rate can be directly connected to the flame surface density (Sigma). This quantity can be given by the transport equation of the coherent flame model initially proposed by Marble & Broadwell 1977 and developed elsewhere. The mean reaction rate, (w), can also be estimated thanks to the evolution of an arbitrary scalar field G(x, t) = G(sub O) which represents the flame sheet. G(x, t) is obtained from the G-equation proposed by Williams 1985, Kerstein et al. 1988 and Peters 1993. Another possibility proposed in a recent study by Mantel & Borghi 1991, where a transport equation for the mean dissipation rate (epsilon(sub c)) of the progress variable c is used to determine (w). In their model, Mantel & Borghi 1991 considered a medium with constant density and constant diffusivity in the determination of the transport equation for (epsilon(sub c)). A comparison of different flamelet models made by Duclos et al. 1993 shows the realistic behavior of this model even in the case of constant density. Our objective in this present report is to present preliminary results on the study of this equation in the case of variable density and variable diffusivity. Assumptions of constant pressure and a Lewis number equal to unity allow us to significantly simplify the equation. A systematic order of magnitude analysis based on adequate scale relations is performed on each term of the

  3. A transport equation for the scalar dissipation in reacting flows with variable density: First results

    NASA Technical Reports Server (NTRS)

    Mantel, T.

    1993-01-01

    Although the different regimes of premixed combustion are not well defined, most of the recent developments in turbulent combustion modeling are led in the so-called flamelet regime. The goal of these models is to give a realistic expression to the mean reaction rate (w). Several methods can be used to estimate (w). Bray and coworkers (Libby & Bray 1980, Bray 1985, Bray & Libby 1986) express the instantaneous reaction rate by means of a flamelet library and a frequency which describes the local interaction between the laminar flamelets and the turbulent flowfield. In another way, the mean reaction rate can be directly connected to the flame surface density (Sigma). This quantity can be given by the transport equation of the coherent flame model initially proposed by Marble & Broadwell 1977 and developed elsewhere. The mean reaction rate, (w), can also be estimated thanks to the evolution of an arbitrary scalar field G(x, t) = G(sub O) which represents the flame sheet. G(x, t) is obtained from the G-equation proposed by Williams 1985, Kerstein et al. 1988 and Peters 1993. Another possibility proposed in a recent study by Mantel & Borghi 1991, where a transport equation for the mean dissipation rate (epsilon(sub c)) of the progress variable c is used to determine (w). In their model, Mantel & Borghi 1991 considered a medium with constant density and constant diffusivity in the determination of the transport equation for (epsilon(sub c)). A comparison of different flamelet models made by Duclos et al. 1993 shows the realistic behavior of this model even in the case of constant density. Our objective in this present report is to present preliminary results on the study of this equation in the case of variable density and variable diffusivity. Assumptions of constant pressure and a Lewis number equal to unity allow us to significantly simplify the equation. A systematic order of magnitude analysis based on adequate scale relations is performed on each term of the

  4. Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport

    SciTech Connect

    Litvinenko, Yuri E.; Effenberger, Frederic

    2014-12-01

    Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.

  5. Analytical Solutions of a Fractional Diffusion-advection Equation for Solar Cosmic-Ray Transport

    NASA Astrophysics Data System (ADS)

    Litvinenko, Yuri E.; Effenberger, Frederic

    2014-12-01

    Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.

  6. Adjoint sensitivity studies of loop current and eddy shedding in the Gulf of Mexico

    NASA Astrophysics Data System (ADS)

    Gopalakrishnan, Ganesh; Cornuelle, Bruce D.; Hoteit, Ibrahim

    2013-07-01

    Adjoint model sensitivity analyses were applied for the loop current (LC) and its eddy shedding in the Gulf of Mexico (GoM) using the MIT general circulation model (MITgcm). The circulation in the GoM is mainly driven by the energetic LC and subsequent LC eddy separation. In order to understand which ocean regions and features control the evolution of the LC, including anticyclonic warm-core eddy shedding in the GoM, forward and adjoint sensitivities with respect to previous model state and atmospheric forcing were computed using the MITgcm and its adjoint. Since the validity of the adjoint model sensitivities depends on the capability of the forward model to simulate the real LC system and the eddy shedding processes, a 5 year (2004-2008) forward model simulation was performed for the GoM using realistic atmospheric forcing, initial, and boundary conditions. This forward model simulation was compared to satellite measurements of sea-surface height (SSH) and sea-surface temperature (SST), and observed transport variability. Despite realistic mean state, standard deviations, and LC eddy shedding period, the simulated LC extension shows less variability and more regularity than the observations. However, the model is suitable for studying the LC system and can be utilized for examining the ocean influences leading to a simple, and hopefully generic LC eddy separation in the GoM. The adjoint sensitivities of the LC show influences from the Yucatan Channel (YC) flow and Loop Current Frontal Eddy (LCFE) on both LC extension and eddy separation, as suggested by earlier work. Some of the processes that control LC extension after eddy separation differ from those controlling eddy shedding, but include YC through-flow. The sensitivity remains stable for more than 30 days and moves generally upstream, entering the Caribbean Sea. The sensitivities of the LC for SST generally remain closer to the surface and move at speeds consistent with advection by the high-speed core of

  7. Using adjoint-based optimization to study wing flexibility in flapping flight

    NASA Astrophysics Data System (ADS)

    Wei, Mingjun; Xu, Min; Dong, Haibo

    2014-11-01

    In the study of flapping-wing flight of birds and insects, it is important to understand the impact of wing flexibility/deformation on aerodynamic performance. However, the large control space from the complexity of wing deformation and kinematics makes usual parametric study very difficult or sometimes impossible. Since the adjoint-based approach for sensitivity study and optimization strategy is a process with its cost independent of the number of input parameters, it becomes an attractive approach in our study. Traditionally, adjoint equation and sensitivity are derived in a fluid domain with fixed solid boundaries. Moving boundary is only allowed when its motion is not part of control effort. Otherwise, the derivation becomes either problematic or too complex to be feasible. Using non-cylindrical calculus to deal with boundary deformation solves this problem in a very simple and still mathematically rigorous manner. Thus, it allows to apply adjoint-based optimization in the study of flapping wing flexibility. We applied the ``improved'' adjoint-based method to study the flexibility of both two-dimensional and three-dimensional flapping wings, where the flapping trajectory and deformation are described by either model functions or real data from the flight of dragonflies. Supported by AFOSR.

  8. On the proper treatment of grid sensitivities in continuous adjoint methods for shape optimization

    NASA Astrophysics Data System (ADS)

    Kavvadias, I. S.; Papoutsis-Kiachagias, E. M.; Giannakoglou, K. C.

    2015-11-01

    The continuous adjoint method for shape optimization problems, in flows governed by the Navier-Stokes equations, can be formulated in two different ways, each of which leads to a different expression for the sensitivity derivatives of the objective function with respect to the control variables. The first formulation leads to an expression including only boundary integrals; it, thus, has low computational cost but, when used with coarse grids, its accuracy becomes questionable. The second formulation comprises a sum of boundary and field integrals; due to the field integrals, it has noticeably higher computational cost, obtaining though higher accuracy. In this paper, the equivalence of the two formulations is revisited from the mathematical and, particularly, the numerical point of view. Internal and external aerodynamics cases, in which the objective function is either the total pressure losses or the force exerted on a solid body, are examined and differences in the computed gradients are discussed. After identifying the reason behind these discrepancies, the adjoint formulation is enhanced by the adjoint to a (hypothetical) grid displacement model and the new approach is proved to reproduce the accuracy of the second adjoint formulation while maintaining the low cost of the first one.

  9. Aerodynamic Shape Optimization of Supersonic Aircraft Configurations via an Adjoint Formulation on Parallel Computers

    NASA Technical Reports Server (NTRS)

    Reuther, James; Alonso, Juan Jose; Rimlinger, Mark J.; Jameson, Antony

    1996-01-01

    This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods (13, 12, 44, 38). The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method (19, 20, 21, 23, 39, 25, 40, 41, 42, 43, 9) was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations (39, 25). In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that the basic methodology could be ported to distributed memory parallel computing architectures [241. In this paper, our concem will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.

  10. Aerodynamic Shape Optimization of Supersonic Aircraft Configurations via an Adjoint Formulation on Parallel Computers

    NASA Technical Reports Server (NTRS)

    Reuther, James; Alonso, Juan Jose; Rimlinger, Mark J.; Jameson, Antony

    1996-01-01

    This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations. In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that this basic methodology could be ported to distributed memory parallel computing architectures. In this paper, our concern will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.

  11. Sensitivity of temporal moments calculated by the adjoint-state method and joint inversing of head and tracer data

    NASA Astrophysics Data System (ADS)

    Cirpka, Olaf A.; Kitanidis, Peter K.

    Including tracer data into geostatistically based methods of inverse modeling is computationally very costly when all concentration measurements are used and the sensitivities of many observations are calculated by the direct differentiation approach. Harvey and Gorelick (Water Resour Res 1995;31(7):1615-26) have suggested the use of the first temporal moment instead of the complete concentration record at a point. We derive a computationally efficient adjoint-state method for the sensitivities of the temporal moments that require the solution of the steady-state flow equation and two steady-state transport equations for the forward problem and the same number of equations for each first-moment measurement. The efficiency of the method makes it feasible to evaluate the sensitivity matrix many times in large domains. We incorporate our approach for the calculation of sensitivities in the quasi-linear geostatistical method of inversing ("iterative cokriging"). The application to an artificial example of a tracer introduced into an injection well shows good convergence behavior when both head and first-moment data are used for inversing, whereas inversing of arrival times alone is less stable.

  12. Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory

    NASA Astrophysics Data System (ADS)

    Manuel, Cristina; Torres-Rincon, Juan M.

    2014-10-01

    We derive the relativistic chiral transport equation for massless fermions and antifermions by performing a semiclassical Foldy-Wouthuysen diagonalization of the quantum Dirac Hamiltonian. The Berry connection naturally emerges in the diagonalization process to modify the classical equations of motion of a fermion in an electromagnetic field. We also see that the fermion and antifermion dispersion relations are corrected at first order in the Planck constant by the Berry curvature, as previously derived by Son and Yamamoto for the particular case of vanishing temperature. Our approach does not require knowledge of the state of the system, and thus it can also be applied at high temperature. We provide support for our result by an alternative computation using an effective field theory for fermions and antifermions: the on-shell effective field theory. In this formalism, the off-shell fermionic modes are integrated out to generate an effective Lagrangian for the quasi-on-shell fermions/antifermions. The dispersion relation at leading order exactly matches the result from the semiclassical diagonalization. From the transport equation, we explicitly show how the axial and gauge anomalies are not modified at finite temperature and density despite the incorporation of the new dispersion relation into the distribution function.

  13. Taylor's hypothesis in turbulent channel flow considered using a transport equation analysis

    NASA Astrophysics Data System (ADS)

    Wallace, James; Geng, Chenhui; He, Guowei; Wang, Yinshan; Xu, Chunxiao

    2014-11-01

    A DNS of turbulent channel flow was carried out to examine Taylor's ``frozen turbulence'' hypothesis, i.e. the simple time-space transformation that allows (1 / Ū) ∂ / ∂ t to approximate streamwise derivatives, ∂ / ∂x , of velocity fluctuations. These terms in Taylor's hypothesis appear in the transport equation for instantaneous momentum for this flow. The additional terms, i.e. the additional convective acceleration and the pressure gradient and viscous force terms, act to diminish the validity of Taylor's hypothesis when they are relatively large compared to the Taylor's hypothesis terms and are not in balance. A similar analysis also has been applied to the transport equation for instantaneous vorticity. There the additional terms, namely the additional convective rates of change, the stretching/compression/rotation and the viscous diffusion of vorticity terms, similarly act to diminish the validity of Taylor's hypothesis when they also are relatively large compared to the terms in the hypothesis and are not in balance. Where in the channel flow this diminishment occurs, and to what degree, and which of the non-Taylor's hypothesis terms in the momentum and vorticity equations contribute most to this diminishment will be presented. Supported by National Natural Sci. Found. and the National Basic Res. Progr. of China and the Burgers Progr. for Fluid Dynamics.

  14. Application of adjoint Monte Carlo to accelerate simulations of mono-directional beams in treatment planning for Boron Neutron Capture Therapy

    SciTech Connect

    Nievaart, V. A.; Legrady, D.; Moss, R. L.; Kloosterman, J. L.; Hagen, T. H. J. J. van der; Dam, H. van

    2007-04-15

    This paper deals with the application of the adjoint transport theory in order to optimize Monte Carlo based radiotherapy treatment planning. The technique is applied to Boron Neutron Capture Therapy where most often mixed beams of neutrons and gammas are involved. In normal forward Monte Carlo simulations the particles start at a source and lose energy as they travel towards the region of interest, i.e., the designated point of detection. Conversely, with adjoint Monte Carlo simulations, the so-called adjoint particles start at the region of interest and gain energy as they travel towards the source where they are detected. In this respect, the particles travel backwards and the real source and real detector become the adjoint detector and adjoint source, respectively. At the adjoint detector, an adjoint function is obtained with which numerically the same result, e.g., dose or flux in the tumor, can be derived as with forward Monte Carlo. In many cases, the adjoint method is more efficient and by that is much quicker when, for example, the response in the tumor or organ at risk for many locations and orientations of the treatment beam around the patient is required. However, a problem occurs when the treatment beam is mono-directional as the probability of detecting adjoint Monte Carlo particles traversing the beam exit (detector plane in adjoint mode) in the negative direction of the incident beam is zero. This problem is addressed here and solved first with the use of next event estimators and second with the application of a Legendre expansion technique of the angular adjoint function. In the first approach, adjoint particles are tracked deterministically through a tube to a (adjoint) point detector far away from the geometric model. The adjoint particles will traverse the disk shaped entrance of this tube (the beam exit in the actual geometry) perpendicularly. This method is slow whenever many events are involved that are not contributing to the point

  15. 3D unstructured-mesh radiation transport codes

    SciTech Connect

    Morel, J.

    1997-12-31

    Three unstructured-mesh radiation transport codes are currently being developed at Los Alamos National Laboratory. The first code is ATTILA, which uses an unstructured tetrahedral mesh in conjunction with standard Sn (discrete-ordinates) angular discretization, standard multigroup energy discretization, and linear-discontinuous spatial differencing. ATTILA solves the standard first-order form of the transport equation using source iteration in conjunction with diffusion-synthetic acceleration of the within-group source iterations. DANTE is designed to run primarily on workstations. The second code is DANTE, which uses a hybrid finite-element mesh consisting of arbitrary combinations of hexahedra, wedges, pyramids, and tetrahedra. DANTE solves several second-order self-adjoint forms of the transport equation including the even-parity equation, the odd-parity equation, and a new equation called the self-adjoint angular flux equation. DANTE also offers three angular discretization options: $S{_}n$ (discrete-ordinates), $P{_}n$ (spherical harmonics), and $SP{_}n$ (simplified spherical harmonics). DANTE is designed to run primarily on massively parallel message-passing machines, such as the ASCI-Blue machines at LANL and LLNL. The third code is PERICLES, which uses the same hybrid finite-element mesh as DANTE, but solves the standard first-order form of the transport equation rather than a second-order self-adjoint form. DANTE uses a standard $S{_}n$ discretization in angle in conjunction with trilinear-discontinuous spatial differencing, and diffusion-synthetic acceleration of the within-group source iterations. PERICLES was initially designed to run on workstations, but a version for massively parallel message-passing machines will be built. The three codes will be described in detail and computational results will be presented.

  16. Temperature-dependent thermal conductivity in silicon nanostructured materials studied by the Boltzmann transport equation

    NASA Astrophysics Data System (ADS)

    Romano, Giuseppe; Esfarjani, Keivan; Strubbe, David A.; Broido, David; Kolpak, Alexie M.

    2016-01-01

    Nanostructured materials exhibit low thermal conductivity because of the additional scattering due to phonon-boundary interactions. As these interactions are highly sensitive to the mean free path (MFP) of phonons, MFP distributions in nanostructures can be dramatically distorted relative to bulk. Here we calculate the MFP distribution in periodic nanoporous Si for different temperatures, using the recently developed MFP-dependent Boltzmann transport equation. After analyzing the relative contribution of each phonon branch to thermal transport in nanoporous Si, we find that at room temperature optical phonons contribute 17 % to heat transport, compared to 5 % in bulk Si. Interestingly, we observe a constant thermal conductivity over the range 200 K transport of acoustic phonons with long intrinsic MFP and the temperature dependence of the heat capacity. Our findings, which are in qualitative agreement with the temperature trend of thermal conductivities measured in nanoporous Si-based systems, shed light on the origin of the reduction of thermal conductivity in nanostructured materials and demonstrate the necessity of multiscale heat transport engineering, in which the bulk material and geometry are optimized concurrently.

  17. Analytical solution of equations describing slow axonal transport based on the stop-and-go hypothesis

    NASA Astrophysics Data System (ADS)

    Kuznetsov, Andrey

    2011-06-01

    This paper presents an analytical solution for slow axonal transport in an axon. The governing equations for slow axonal transport are based on the stop-and-go hypothesis which assumes that organelles alternate between short periods of rapid movement on microtubules (MTs), short on-track pauses, and prolonged off-track pauses, when they temporarily disengage from MTs. The model includes six kinetic states for organelles: two for off-track organelles (anterograde and retrograde), two for running organelles, and two for pausing organelles. An analytical solution is obtained for a steady-state situation. To obtain the analytical solution, the governing equations are uncoupled by using a perturbation method. The solution is validated by comparing it with a high-accuracy numerical solution. Results are presented for neurofilaments (NFs), which are characterized by small diffusivity, and for tubulin oligomers, which are characterized by large diffusivity. The difference in transport modes between these two types of organelles in a short axon is discussed. A comparison between zero-order and first-order approximations makes it possible to obtain a physical insight into the effects of organelle reversals (when organelles change the type of a molecular motor they are attached to, an anterograde versus retrograde motor).

  18. Dual of QCD with one adjoint fermion

    SciTech Connect

    Mojaza, Matin; Nardecchia, Marco; Pica, Claudio; Sannino, Francesco

    2011-03-15

    We construct the magnetic dual of QCD with one adjoint Weyl fermion. The dual is a consistent solution of the 't Hooft anomaly matching conditions, allows for flavor decoupling, and remarkably constitutes the first nonsupersymmetric dual valid for any number of colors. The dual allows to bound the anomalous dimension of the Dirac fermion mass operator to be less than one in the conformal window.

  19. Coupling of Monte Carlo adjoint leakages with three-dimensional discrete ordinates forward fluences

    SciTech Connect

    Slater, C.O.; Lillie, R.A.; Johnson, J.O.; Simpson, D.B.

    1998-04-01

    A computer code, DRC3, has been developed for coupling Monte Carlo adjoint leakages with three-dimensional discrete ordinates forward fluences in order to solve a special category of geometrically-complex deep penetration shielding problems. The code extends the capabilities of earlier methods that coupled Monte Carlo adjoint leakages with two-dimensional discrete ordinates forward fluences. The problems involve the calculation of fluences and responses in a perturbation to an otherwise simple two- or three-dimensional radiation field. In general, the perturbation complicates the geometry such that it cannot be modeled exactly using any of the discrete ordinates geometry options and thus a direct discrete ordinates solution is not possible. Also, the calculation of radiation transport from the source to the perturbation involves deep penetration. One approach to solving such problems is to perform the calculations in three steps: (1) a forward discrete ordinates calculation, (2) a localized adjoint Monte Carlo calculation, and (3) a coupling of forward fluences from the first calculation with adjoint leakages from the second calculation to obtain the response of interest (fluence, dose, etc.). A description of this approach is presented along with results from test problems used to verify the method. The test problems that were selected could also be solved directly by the discrete ordinates method. The good agreement between the DRC3 results and the direct-solution results verify the correctness of DRC3.

  20. Analytic structure of two 1D-transport equations with nonlocal fluxes

    NASA Astrophysics Data System (ADS)

    Baker, Gregory R.; Li, Xiao; Morlet, Anne C.

    We replace the flux term in Burger's equation by two simple alternates that contain contributions depending globally on the solution. In one case, the term is in the form of a hyperbolic equation where the characteristic speed is nonlocal, and in the other the term is in conservation form. In both cases, the nonanalytic is due to the presence of the Hilbert transform. The equations have a loose analogy to the motion of vortex sheets. In particular, they both form singularities in finite time in the absence of viscous effects. Our motivation then is to study the influence of viscosity. In one case, viscosity does not prevent singularity formation. In the other, we can prove solutions exist for all time, and determine the likely weak solution as viscosity vanishes. An interesting aspect of our work is that singularity formation can be viewed as the motion of singularities in the complex physical plane that reach the real axis in finite time. In one case, the singularity is a pole and causes the solution to blow up when it reaches the real axis. In the other, numerical solutions and an asymptotic analysis suggest that the weak solution contains a square root singularity that reaches the real axis in finite time, and then propagates along it. We hope our results will spur further interest in the role of singularities in the complex spatial plane in solutions to transport equations.

  1. Adjoint problem in duct acoustics and its reciprocity to forward problem by the Time Domain Wave Packet method

    NASA Astrophysics Data System (ADS)

    Kocaogul, Ibrahim; Hu, Fang; Li, Xiaodong

    2014-03-01

    Radiation of acoustic waves at all frequencies can be obtained by Time Domain Wave Packet (TDWP) method in a single time domain computation. Other benefit of the TDWP method is that it makes possible the separation of acoustic and instability wave in the shear flow. The TDWP method is also particularly useful for computations in the ducted or waveguide environments where incident wave modes can be imposed cleanly without a potentially long transient period. The adjoint equations for the linearized Euler equations are formulated for the Cartesian coordinates. Analytical solution for adjoint equations is derived by using Green's function in 2D and 3D. The derivation of reciprocal relations is presented for closed and open ducts. The adjoint equations are then solved numerically in reversed time by the TDWP method. Reciprocal relation between the duct mode amplitudes and far field point sources in the presence of the exhaust shear flow is computed and confirmed numerically. Applications of the adjoint problem to closed and open ducts are also presented.

  2. The use of Galerkin finite-element methods to solve mass-transport equations

    USGS Publications Warehouse

    Grove, David B.

    1977-01-01

    The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

  3. Two-dimensional phase unwrapping using the transport of intensity equation.

    PubMed

    Pandey, Neeraj; Ghosh, Amitava; Khare, Kedar

    2016-03-20

    We report a method for two-dimensional phase unwrapping based on the transport of intensity equation (TIE). Given a wrapped phase profile, we generate an auxiliary complex field and propagate it to small distances to simulate two intensity images on closely spaced planes. Using the longitudinal intensity derivative of the auxiliary field as an input, the TIE is solved by employing the regularized Fourier-transform-based approach. The resultant phase profile is automatically in the unwrapped form, as it has been obtained as a solution of a partial differential equation rather than as an argument of a complex-valued function. Our simulations and experimental results suggest that this approach is fast and accurate and provides a simple and practical solution for routine phase unwrapping tasks in interferometry and digital holography. PMID:27140583

  4. Modeling Heat Conduction and Radiation Transport with the Diffusion Equation in NIF ALE-AMR

    SciTech Connect

    Fisher, A C; Bailey, D S; Kaiser, T B; Gunney, B N; Masters, N D; Koniges, A E; Eder, D C; Anderson, R W

    2009-10-06

    The ALE-AMR code developed for NIF is a multi-material hydro-code that models target assembly fragmentation in the aftermath of a shot. The combination of ALE (Arbitrary Lagrangian Eulerian) hydro with AMR (Adaptive Mesh Refinement) allows the code to model a wide range of physical conditions and spatial scales. The large range of temperatures encountered in the NIF target chamber can lead to significant fluxes of energy due to thermal conduction and radiative transport. These physical effects can be modeled approximately with the aid of the diffusion equation. We present a novel method for the solution of the diffusion equation on a composite mesh in order to capture these physical effects.

  5. Separation of electrostatic and magnetic phase shifts using a modified transport-of-intensity equation.

    PubMed

    Humphrey, E; Phatak, C; Petford-Long, A K; De Graef, M

    2014-04-01

    We introduce a new approach for the separation of the electrostatic and magnetic components of the electron wave phase shift, based on the transport-of-intensity equation (TIE) formalism. We derive two separate TIE-like equations, one for each of the phase shift components. We use experimental results on FeCoB and Permalloy patterned islands to illustrate how the magnetic and electrostatic longitudinal derivatives can be computed. The main advantage of this new approach is the fact that the differences in the power spectra of the two phase components (electrostatic phase shifts often have significant power in the higher frequencies) can be accommodated by the selection of two different Tikhonov regularization parameters for the two phase reconstructions. The extra computational demands of the method are more than compensated by the improved phase reconstruction results. PMID:24513573

  6. A coupling model of the radiative transport equation for calculating photon migration in biological tissue

    NASA Astrophysics Data System (ADS)

    Fujii, Hiroyuki; Okawa, Shinpei; Yamada, Yukio; Hoshi, Yoko; Watanabe, Masao

    2015-12-01

    Development of a physically accurate and computationally efficient photon migration model for turbid media is crucial for optical computed tomography such as diffuse optical tomography. For the development, this paper constructs a space-time coupling model of the radiative transport equation with the photon diffusion equation. In the coupling model, a space-time regime of the photon migration is divided into the ballistic and diffusive regimes with the interaction between the both regimes to improve the accuracy of the results and the efficiency of computation. The coupling model provides an accurate description of the photon migration in various turbid media in a wide range of the optical properties, and reduces computational loads when compared with those of full calculation of the RTE.

  7. Towards efficient backward-in-time adjoint computations using data compression techniques

    DOE PAGESBeta

    Cyr, E. C.; Shadid, J. N.; Wildey, T.

    2014-12-16

    In the context of a posteriori error estimation for nonlinear time-dependent partial differential equations, the state-of-the-practice is to use adjoint approaches which require the solution of a backward-in-time problem defined by a linearization of the forward problem. One of the major obstacles in the practical application of these approaches, we found, is the need to store, or recompute, the forward solution to define the adjoint problem and to evaluate the error representation. Our study considers the use of data compression techniques to approximate forward solutions employed in the backward-in-time integration. The development derives an error representation that accounts for themore » difference between the standard-approach and the compressed approximation of the forward solution. This representation is algorithmically similar to the standard representation and only requires the computation of the quantity of interest for the forward solution and the data-compressed reconstructed solution (i.e. scalar quantities that can be evaluated as the forward problem is integrated). This approach is then compared with existing techniques, such as checkpointing and time-averaged adjoints. Lastly, we provide numerical results indicating the potential efficiency of our approach on a transient diffusion–reaction equation and on the Navier–Stokes equations. These results demonstrate memory compression ratios up to 450×450× while maintaining reasonable accuracy in the error-estimates.« less

  8. Towards efficient backward-in-time adjoint computations using data compression techniques

    SciTech Connect

    Cyr, E. C.; Shadid, J. N.; Wildey, T.

    2014-12-16

    In the context of a posteriori error estimation for nonlinear time-dependent partial differential equations, the state-of-the-practice is to use adjoint approaches which require the solution of a backward-in-time problem defined by a linearization of the forward problem. One of the major obstacles in the practical application of these approaches, we found, is the need to store, or recompute, the forward solution to define the adjoint problem and to evaluate the error representation. Our study considers the use of data compression techniques to approximate forward solutions employed in the backward-in-time integration. The development derives an error representation that accounts for the difference between the standard-approach and the compressed approximation of the forward solution. This representation is algorithmically similar to the standard representation and only requires the computation of the quantity of interest for the forward solution and the data-compressed reconstructed solution (i.e. scalar quantities that can be evaluated as the forward problem is integrated). This approach is then compared with existing techniques, such as checkpointing and time-averaged adjoints. Lastly, we provide numerical results indicating the potential efficiency of our approach on a transient diffusion–reaction equation and on the Navier–Stokes equations. These results demonstrate memory compression ratios up to 450×450× while maintaining reasonable accuracy in the error-estimates.

  9. Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

    NASA Astrophysics Data System (ADS)

    Ancey, C.; Bohorquez, P.; Heyman, J.

    2015-12-01

    The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due

  10. Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

    NASA Astrophysics Data System (ADS)

    Al-Hashimi, M. H.; Salman, M.; Shalaby, A.; Wiese, U.-J.

    2013-10-01

    We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant.

  11. Phase retrieval by using the transport-of-intensity equation with Hilbert transform.

    PubMed

    Li, Wei-Shuo; Chen, Chun-Wei; Lin, Kuo-Feng; Chen, Hou-Ren; Tsai, Chih-Ya; Chen, Chyong-Hua; Hsieh, Wen-Feng

    2016-04-01

    Phase recovery by solving the transport-of-intensity equation (TIE) is a non-iterative and non-interferometric phase retrieval technique. From solving the TIE with conventional, one partial derivative and Hilbert transform methods for both the periodic and aperiodic samples, we demonstrate that the Hilbert transform method can provide the smoother phase images with edge enhancement and fine structures. Furthermore, compared with the images measured by optical and atomic force microscopy, the Hilbert transform method has the ability to quantitatively map out the phase images for both the periodic and aperiodic structures. PMID:27192301

  12. Unified description of equation of state and transport properties of nuclear matter

    SciTech Connect

    Benhar, Omar; Farina, Nicola; Valli, Marco; Fiorilla, Salvatore

    2008-10-13

    Correlated basis function perturbation theory and the formalism of cluster expansions have been recently employed to obtain an effective interaction from a state-of-the-art nucleon nucleon potential model. The approach based on the effective interaction allows for a consistent description of the nuclear matter ground state and nucleon-nucleon scattering in the nuclear medium. This paper reports the the results of numerical calculations of different properties of nuclear and neutron matter, including the equation of state and the shear viscosity and thermal conductivity transport coefficients, carried out using the effective interaction.

  13. Application of the transport of intensity equation to EUV multilayer defect analysis

    NASA Astrophysics Data System (ADS)

    Xu, Dongbo; Evanschitzky, Peter; Erdmann, Andreas

    2015-03-01

    This paper proposes a new method for the characterization of multilayer defects of EUV masks. The method uses measured or simulated EUV projection images at different focus positions. The Transport of Intensity Equation (TIE) is applied to retrieve the phase distribution of the reflected light in the vicinity of the defect. An Artificial Neural Network (ANN) is applied to correlate the optical properties of the intensity and recovered phase of the defect with the defect geometry parameters and to reconstruct the defect geometry parameters from though-focus-images of unknown defects.

  14. Gluon transport equation with effective mass and dynamical onset of Bose–Einstein condensation

    DOE PAGESBeta

    Blaizot, Jean-Paul; Jiang, Yin; Liao, Jinfeng

    2016-05-01

    In this paper we study the transport equation describing a dense system of gluons, in the small scattering angle approximation, taking into account medium-generated effective masses of the gluons. We focus on the case of overpopulated systems that are driven to Bose–Einstein condensation on their way to thermalization. Lastly, the presence of a mass modifies the dispersion relation of the gluon, as compared to the massless case, but it is shown that this does not change qualitatively the scaling behavior in the vicinity of the onset.

  15. Error analysis and correction in wavefront reconstruction from the transport-of-intensity equation

    PubMed Central

    Barbero, Sergio; Thibos, Larry N.

    2007-01-01

    Wavefront reconstruction from the transport-of-intensity equation (TIE) is a well-posed inverse problem given smooth signals and appropriate boundary conditions. However, in practice experimental errors lead to an ill-condition problem. A quantitative analysis of the effects of experimental errors is presented in simulations and experimental tests. The relative importance of numerical, misalignment, quantization, and photodetection errors are shown. It is proved that reduction of photodetection noise by wavelet filtering significantly improves the accuracy of wavefront reconstruction from simulated and experimental data. PMID:20052302

  16. Gluon transport equation with effective mass and dynamical onset of Bose-Einstein condensation

    NASA Astrophysics Data System (ADS)

    Blaizot, Jean-Paul; Jiang, Yin; Liao, Jinfeng

    2016-05-01

    We study the transport equation describing a dense system of gluons, in the small scattering angle approximation, taking into account medium-generated effective masses of the gluons. We focus on the case of overpopulated systems that are driven to Bose-Einstein condensation on their way to thermalization. The presence of a mass modifies the dispersion relation of the gluon, as compared to the massless case, but it is shown that this does not change qualitatively the scaling behavior in the vicinity of the onset.

  17. Variance-reduced particle simulation of the Boltzmann transport equation in the relaxation-time approximation.

    PubMed

    Radtke, Gregg A; Hadjiconstantinou, Nicolas G

    2009-05-01

    We present an efficient variance-reduced particle simulation technique for solving the linearized Boltzmann transport equation in the relaxation-time approximation used for phonon, electron, and radiative transport, as well as for kinetic gas flows. The variance reduction is achieved by simulating only the deviation from equilibrium. We show that in the limit of small deviation from equilibrium of interest here, the proposed formulation achieves low relative statistical uncertainty that is also independent of the magnitude of the deviation from equilibrium, in stark contrast to standard particle simulation methods. Our results demonstrate that a space-dependent equilibrium distribution improves the variance reduction achieved, especially in the collision-dominated regime where local equilibrium conditions prevail. We also show that by exploiting the physics of relaxation to equilibrium inherent in the relaxation-time approximation, a very simple collision algorithm with a clear physical interpretation can be formulated. PMID:19518597

  18. Theoretical analysis of integral neutron transport equation using collision probability method with quadratic flux approach

    SciTech Connect

    Shafii, Mohammad Ali Meidianti, Rahma Wildian, Fitriyani, Dian; Tongkukut, Seni H. J.; Arkundato, Artoto

    2014-09-30

    Theoretical analysis of integral neutron transport equation using collision probability (CP) method with quadratic flux approach has been carried out. In general, the solution of the neutron transport using the CP method is performed with the flat flux approach. In this research, the CP method is implemented in the cylindrical nuclear fuel cell with the spatial of mesh being conducted into non flat flux approach. It means that the neutron flux at any point in the nuclear fuel cell are considered different each other followed the distribution pattern of quadratic flux. The result is presented here in the form of quadratic flux that is better understanding of the real condition in the cell calculation and as a starting point to be applied in computational calculation.

  19. Simulating photon-transport in uniform media using the radiative transport equation: a study using the Neumann-series approach

    PubMed Central

    Jha, Abhinav K.; Kupinski, Matthew A.; Masumura, Takahiro; Clarkson, Eric; Maslov, Alexey V.; Barrett, Harrison H.

    2014-01-01

    We present the implementation, validation, and performance of a Neumann-series approach for simulating light propagation at optical wavelengths in uniform media using the radiative transport equation (RTE). The RTE is solved for an anisotropic-scattering medium in a spherical harmonic basis for a diffuse-optical-imaging setup. The main objectives of this paper are threefold: to present the theory behind the Neumann-series form for the RTE, to design and develop the mathematical methods and the software to implement the Neumann series for a diffuse-optical-imaging setup, and, finally, to perform an exhaustive study of the accuracy, practical limitations, and computational efficiency of the Neumann-series method. Through our results, we demonstrate that the Neumann-series approach can be used to model light propagation in uniform media with small geometries at optical wavelengths. PMID:23201893

  20. Representative equations for the thermodynamic and transport properties of fluids near the gas-liquid critical point

    NASA Technical Reports Server (NTRS)

    Sengers, J. V.; Basu, R. S.; Sengers, J. M. H. L.

    1981-01-01

    A survey is presented of representative equations for various thermophysical properties of fluids in the critical region. Representative equations for the transport properties are included. Semi-empirical modifications of the theoretically predicted asymtotic critical behavior that yield simple and practical representations of the fluid properties in the critical region are emphasized.

  1. Fokker-Planck equations for charged-particle transport with a discussion of some higher-order effects

    NASA Technical Reports Server (NTRS)

    Jokipii, J. R.

    1973-01-01

    A derivation of the Fokker-Planck equation, based on the central limit theorem, is presented which clearly illustrates the conditions for its validity. It is reiterated that previous use of the Fokker-Planck equation in cosmic-ray transport is correct. Higher-order effects associated with magnetic mirroring and field line random walk at low energies are discussed heuristically.

  2. An iterative KP1 method for solving the transport equation in 3D domains on unstructured grids

    NASA Astrophysics Data System (ADS)

    Kokonkov, N. I.; Nikolaeva, O. V.

    2015-10-01

    A two-step iterative KP1 method for solving systems of grid equations that approximate the integro-differential transport equation in 3D domains on unstructured grids using nodal SN methods is described. Results of testing the efficiency of the proposed method in solving benchmark problems of reactor protection on tetrahedral grids are presented.

  3. A Synchronous and Iterative Flux-Correction Formalism for Coupled Transport Equations

    NASA Astrophysics Data System (ADS)

    Schär, Christoph; Smolarkiewicz, Piotr K.

    1996-10-01

    Many problems of fluid dynamics involve the coupled transport of several, density-like, dependent variables (for instance, densities of mass and momenta in elastic flows). In this paper, a conservative and synchronous flux-corrected transport (FCT) formalism is developed which aims at a consistent transport of such variables. The technique differs from traditional FCT algorithms in two respects. First, the limiting of transportive fluxes of the primary variables (e.g., mass and momentum) does not derive from smooth estimates of the variables, but it derives from analytic constraints implied by the Lagrangian form of the governing continuity equations, which are imposed on the specific mixing ratios of the variables (e.g., velocity components). Second, the traditional FCT limiting based on sufficiency conditions is augmented by an iterative procedure which approaches the necessity requirements. This procedure can also be used in the framework of traditional FCT schemes, and a demonstration is provided that it can significantly reduce some of the pathological behaviors of FCT algorithms. Although the approach derived is applicable to the transport of arbitrary conserved quantities, it is particularly useful for the synchronous transport of mass and momenta in elastic flows, where it assures intrinsic stability of the algorithm regardless of the magnitude of the mass-density variable. This latter property becomes especially important in fluids with large density variations, or in models with a material "vertical" coordinate (e.g., geophysical hydrostatic stratified flows in isopycnic/isentropic coordinates), where material surfaces can collapse to zero-mass layers admitting, therefore, arbitrarily large local Courant numbers.

  4. Generalized uncertainty principle and self-adjoint operators

    SciTech Connect

    Balasubramanian, Venkat; Das, Saurya; Vagenas, Elias C.

    2015-09-15

    In this work we explore the self-adjointness of the GUP-modified momentum and Hamiltonian operators over different domains. In particular, we utilize the theorem by von-Neumann for symmetric operators in order to determine whether the momentum and Hamiltonian operators are self-adjoint or not, or they have self-adjoint extensions over the given domain. In addition, a simple example of the Hamiltonian operator describing a particle in a box is given. The solutions of the boundary conditions that describe the self-adjoint extensions of the specific Hamiltonian operator are obtained.

  5. Exact solutions to the interfacial surfactant transport equation on a droplet in a Stokes flow regime

    NASA Astrophysics Data System (ADS)

    Kallendorf, Christina; Fath, Anja; Oberlack, Martin; Wang, Yongqi

    2015-08-01

    In the research literature there exist very rare analytical solutions of the surfactant transport equation on an interface. In the present article, we derive sets of exact solutions to interfacial convection-diffusion equations which describe the interfacial transport of insoluble surfactants in a two-phase flow. The investigated model is based on a Stokes flow setting where a spherical shaped inner phase is dispersed in an outer phase. Under the assumption of the small capillary number, the deformation of the spherical phase interface is not taken into account. Neglecting the dependence of the surface tension on the interfacial surfactant concentration, hence neglecting the Marangoni effect, general exact solutions to the surfactant conservation law on the spherical surface with both convective and diffusive terms are provided by means of Heun's confluent function. For the steady case, it is shown that these solutions collapse to a simple exponential form. Furthermore, for the purely diffusive problem, exact solutions are constructed using Legendre polynomials. Such analytical solutions are very valuable as benchmark problems in numerical investigations.

  6. Application of the multigrid amplitude function method for time-dependent transport equation using MOC

    SciTech Connect

    Tsujita, K.; Endo, T.; Yamamoto, A.

    2013-07-01

    An efficient numerical method for time-dependent transport equation, the mutigrid amplitude function (MAF) method, is proposed. The method of characteristics (MOC) is being widely used for reactor analysis thanks to the advances of numerical algorithms and computer hardware. However, efficient kinetic calculation method for MOC is still desirable since it requires significant computation time. Various efficient numerical methods for solving the space-dependent kinetic equation, e.g., the improved quasi-static (IQS) and the frequency transform methods, have been developed so far mainly for diffusion calculation. These calculation methods are known as effective numerical methods and they offer a way for faster computation. However, they have not been applied to the kinetic calculation method using MOC as the authors' knowledge. Thus, the MAF method is applied to the kinetic calculation using MOC aiming to reduce computation time. The MAF method is a unified numerical framework of conventional kinetic calculation methods, e.g., the IQS, the frequency transform, and the theta methods. Although the MAF method is originally developed for the space-dependent kinetic calculation based on the diffusion theory, it is extended to transport theory in the present study. The accuracy and computational time are evaluated though the TWIGL benchmark problem. The calculation results show the effectiveness of the MAF method. (authors)

  7. Equations of the surface harmonics method for solving time-dependent neutron transport problems and their verification

    NASA Astrophysics Data System (ADS)

    Boyarinov, V. F.; Kondrushin, A. E.; Fomichenko, P. A.

    2013-12-01

    Time-dependent equations of the surface harmonics method (SHM) are obtained for planar one-dimensional geometry. The equations are verified by calculations of test problems from Benchmark Problem Book ANL-7416, and the capabilities and efficiency of applying the SHM for solving the time-dependent neutron transport equation in the diffusion approximation are demonstrated. The results of the work show that the implementation of the SHG for full-scale computations will make possible substantial progress in the efficient solution of time-dependent problems of neutron transport in nuclear reactors.

  8. CALIBRATION OF RICHARDS' AND CONVECTION--DISPERSION EQUATIONS TO FIELD-SCALE WATER FLOW AND SOLUTE TRANSPORT UNDER RAINFALL CONDITIONS

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Identification of flow and transport processes under natural boundary conditions in field soils is a complex task since most model parameters are not measurable at that scale. However, combining a numerical solution method of the governing flow and transport equations with an inverse optimization al...

  9. Analytical solutions of the one-dimensional advection-dispersion solute transport equation subject to time-dependent boundary conditions

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Analytical solutions of the advection-dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective-dispersive transport subj...

  10. An unstaggered constrained transport method for the 3D ideal magnetohydrodynamic equations

    NASA Astrophysics Data System (ADS)

    Helzel, Christiane; Rossmanith, James A.; Taetz, Bertram

    2011-05-01

    Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with nonlinear numerical instabilities. One approach for controlling the discrete divergence is through a so-called constrained transport method, which is based on first predicting a magnetic field through a standard finite volume solver, and then correcting this field through the appropriate use of a magnetic vector potential. In this work we develop a constrained transport method for the 3D ideal MHD equations that is based on a high-resolution wave propagation scheme. Our proposed scheme is the 3D extension of the 2D scheme developed by Rossmanith [J.A. Rossmanith, An unstaggered, high-resolution constrained transport method for magnetohydrodynamic flows, SIAM J. Sci. Comput. 28 (2006) 1766], and is based on the high-resolution wave propagation method of Langseth and LeVeque [J.O. Langseth, R.J. LeVeque, A wave propagation method for threedimensional hyperbolic conservation laws, J. Comput. Phys. 165 (2000) 126]. In particular, in our extension we take great care to maintain the three most important properties of the 2D scheme: (1) all quantities, including all components of the magnetic field and magnetic potential, are treated as cell-centered; (2) we develop a high-resolution wave propagation scheme for evolving the magnetic potential; and (3) we develop a wave limiting approach that is applied during the vector potential evolution, which controls unphysical oscillations in the magnetic field. One of the key numerical difficulties that is novel to 3D is that the transport equation that must be solved for the magnetic vector potential is only weakly hyperbolic. In presenting our numerical algorithm we describe how to numerically handle this problem of weak hyperbolicity, as well as how to choose an appropriate gauge condition. The

  11. Performance assessment of several equations of state and second virial coefficients in modified Enskog theory: Results for transport properties

    NASA Astrophysics Data System (ADS)

    Kiani, M.; Alavianmehr, M. M.; Otoofat, M.; Mohsenipour, A. A.; Ghatee, A.

    2015-11-01

    In this work, we identify a simple method for predicting transport properties of fluids over wide ranges of temperatures and pressure. In this respect, the capability of several equations of state (EOS) and second virial coefficient correlations to predict transport properties of fluids including carbon dioxide, methane and argon using modified Enskog theory (MET) is investigated. The transport properties in question are viscosity and thermal conductivity. The results indicate that the SRK EOS employed in the modified Enskog theory outperforms other equations of state. The average absolute deviation was found to be 12.2 and 18.5% for, respectively, the calculated thermal conductivity and viscosity using the MET.

  12. Efficient Construction of Discrete Adjoint Operators on Unstructured Grids Using Complex Variables

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.; Kleb, William L.

    2005-01-01

    A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.

  13. Efficient Construction of Discrete Adjoint Operators on Unstructured Grids by Using Complex Variables

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.; Kleb, William L.

    2005-01-01

    A methodology is developed and implemented to mitigate the lengthy software development cycle typically associated with constructing a discrete adjoint solver for aerodynamic simulations. The approach is based on a complex-variable formulation that enables straightforward differentiation of complicated real-valued functions. An automated scripting process is used to create the complex-variable form of the set of discrete equations. An efficient method for assembling the residual and cost function linearizations is developed. The accuracy of the implementation is verified through comparisons with a discrete direct method as well as a previously developed handcoded discrete adjoint approach. Comparisons are also shown for a large-scale configuration to establish the computational efficiency of the present scheme. To ultimately demonstrate the power of the approach, the implementation is extended to high temperature gas flows in chemical nonequilibrium. Finally, several fruitful research and development avenues enabled by the current work are suggested.

  14. Adjoint-based optimal control of an airfoil in gusting flows

    NASA Astrophysics Data System (ADS)

    Choi, Jeesoon; Colonius, Tim; California Institute of Technology Team

    2015-11-01

    In this study, we apply optimal control to an airfoil in gusting flow to investigate the possibility of extracting energy. The gradients of an objective function are obtained via the adjoint method and used to minimize the cost. The immersed boundary projection method is used for our forward solver, and the relevant adjoint equations are derived by the discrete-then-differentiate approach. Translational gusts are generated by a body force in the computational domain upstream to the body, and the method finds the optimal angles of the airfoil that exploits the greatest amount of energy. The influence of a vortex traversing an airfoil is also investigated and optimized to reduce the fluctuating lift.

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

    NASA Technical Reports Server (NTRS)

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

    2003-01-01

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

  16. Application of Adjoint Methodology to Supersonic Aircraft Design Using Reversed Equivalent Areas

    NASA Technical Reports Server (NTRS)

    Rallabhandi, Sriram K.

    2013-01-01

    This paper presents an approach to shape an aircraft to equivalent area based objectives using the discrete adjoint approach. Equivalent areas can be obtained either using reversed augmented Burgers equation or direct conversion of off-body pressures into equivalent area. Formal coupling with CFD allows computation of sensitivities of equivalent area objectives with respect to aircraft shape parameters. The exactness of the adjoint sensitivities is verified against derivatives obtained using the complex step approach. This methodology has the benefit of using designer-friendly equivalent areas in the shape design of low-boom aircraft. Shape optimization results with equivalent area cost functionals are discussed and further refined using ground loudness based objectives.

  17. Theoretical analysis and numerical experiments of variational adjoint approach for refractivity estimation

    NASA Astrophysics Data System (ADS)

    Zhao, Xiao-Feng; Huang, Si-Xun; Du, Hua-Dong

    2011-02-01

    This paper puts forward possibilities of refractive index profile retrieval using field measurements at an array of radio receivers in terms of variational adjoint approach. The derivation of the adjoint model begins with the parabolic wave equation for a smooth, perfectly conducting surface and horizontal polarization conditions. To deal with the ill-posed difficulties of the inversion, the regularization ideas are introduced into the establishment of the cost function. Based on steepest descent iterations, the optimal value of refractivity could be retrieved quickly at each point over height. Numerical experiments demonstrate that the method works well for low-distance signals, while it is not accurate enough for long-distance propagations. Through curve fitting processing, however, giving a good initial refractivity profile could generally improve the inversions.

  18. Transport Equations Resolution By N-BEE Anti-Dissipative Scheme In 2D Model Of Low Pressure Glow Discharge

    SciTech Connect

    Kraloua, B.; Hennad, A.

    2008-09-23

    The aim of this paper is to determine electric and physical properties by 2D modelling of glow discharge low pressure in continuous regime maintained by term constant source. This electric discharge is confined in reactor plan-parallel geometry. This reactor is filled by Argon monatomic gas. Our continuum model the order two is composed the first three moments the Boltzmann's equations coupled with Poisson's equation by self consistent method. These transport equations are discretized by the finite volumes method. The equations system is resolved by a new technique, it is about the N-BEE explicit scheme using the time splitting method.

  19. Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

    SciTech Connect

    Surya Mohan, P.; Tarvainen, Tanja; Schweiger, Martin; Pulkkinen, Aki; Arridge, Simon R.

    2011-08-10

    Highlights: {yields} We developed a variable order global basis scheme to solve light transport in 3D. {yields} Based on finite elements, the method can be applied to a wide class of geometries. {yields} It is computationally cheap when compared to the fixed order scheme. {yields} Comparisons with local basis method and other models demonstrate its accuracy. {yields} Addresses problems encountered n modeling of light transport in human brain. - Abstract: We propose the P{sub N} approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P{sub N} approximation is compared against Monte Carlo simulations and other state-of-the-art methods.

  20. Adjoint sensitivity analysis of an ultrawideband antenna

    SciTech Connect

    Stephanson, M B; White, D A

    2011-07-28

    The frequency domain finite element method using H(curl)-conforming finite elements is a robust technique for full-wave analysis of antennas. As computers become more powerful, it is becoming feasible to not only predict antenna performance, but also to compute sensitivity of antenna performance with respect to multiple parameters. This sensitivity information can then be used for optimization of the design or specification of manufacturing tolerances. In this paper we review the Adjoint Method for sensitivity calculation, and apply it to the problem of optimizing a Ultrawideband antenna.

  1. Improved Adjoint-Operator Learning For A Neural Network

    NASA Technical Reports Server (NTRS)

    Toomarian, Nikzad; Barhen, Jacob

    1995-01-01

    Improved method of adjoint-operator learning reduces amount of computation and associated computational memory needed to make electronic neural network learn temporally varying pattern (e.g., to recognize moving object in image) in real time. Method extension of method described in "Adjoint-Operator Learning for a Neural Network" (NPO-18352).

  2. Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

    SciTech Connect

    Al-Hashimi, M.H.; Salman, M.; Shalaby, A.; Wiese, U.-J.

    2013-10-15

    We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant. -- Highlights: •Self-adjoint extension theory and contact interactions. •Application of self-adjoint extensions to supersymmetry. •Contact interactions in finite volume with Robin boundary condition.

  3. libmpdata++ 0.1: a library of parallel MPDATA solvers for systems of generalised transport equations

    NASA Astrophysics Data System (ADS)

    Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.

    2014-11-01

    This paper accompanies first release of libmpdata++, a C++ library implementing the Multidimensional Positive-Definite Advection Transport Algorithm (MPDATA). The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include: homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.

  4. libmpdata++ 1.0: a library of parallel MPDATA solvers for systems of generalised transport equations

    NASA Astrophysics Data System (ADS)

    Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.

    2015-04-01

    This paper accompanies the first release of libmpdata++, a C++ library implementing the multi-dimensional positive-definite advection transport algorithm (MPDATA) on regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; a shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.

  5. Phase-space finite elements in a least-squares solution of the transport equation

    SciTech Connect

    Drumm, C.; Fan, W.; Pautz, S.

    2013-07-01

    The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshing tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)

  6. Adjoint sensitivity analysis of hydrodynamic stability in cyclonic flows

    NASA Astrophysics Data System (ADS)

    Guzman Inigo, Juan; Juniper, Matthew

    2015-11-01

    Cyclonic separators are used in a variety of industries to efficiently separate mixtures of fluid and solid phases by means of centrifugal forces and gravity. In certain circumstances, the vortex core of cyclonic flows is known to precess due to the instability of the flow, which leads to performance reductions. We aim to characterize the unsteadiness using linear stability analysis of the Reynolds Averaged Navier-Stokes (RANS) equations in a global framework. The system of equations, including the turbulence model, is linearised to obtain an eigenvalue problem. Unstable modes corresponding to the dynamics of the large structures of the turbulent flow are extracted. The analysis shows that the most unstable mode is a helical motion which develops around the axis of the flow. This result is in good agreement with LES and experimental analysis, suggesting the validity of the approach. Finally, an adjoint-based sensitivity analysis is performed to determine the regions of the flow that, when altered, have most influence on the frequency and growth-rate of the unstable eigenvalues.

  7. Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index

    SciTech Connect

    Lehtikangas, O.; Tarvainen, T.; Kim, A.D.; Arridge, S.R.

    2015-02-01

    The radiative transport equation can be used as a light transport model in a medium with scattering particles, such as biological tissues. In the radiative transport equation, the refractive index is assumed to be constant within the medium. However, in biomedical media, changes in the refractive index can occur between different tissue types. In this work, light propagation in a medium with piece-wise constant refractive index is considered. Light propagation in each sub-domain with a constant refractive index is modeled using the radiative transport equation and the equations are coupled using boundary conditions describing Fresnel reflection and refraction phenomena on the interfaces between the sub-domains. The resulting coupled system of radiative transport equations is numerically solved using a finite element method. The approach is tested with simulations. The results show that this coupled system describes light propagation accurately through comparison with the Monte Carlo method. It is also shown that neglecting the internal changes of the refractive index can lead to erroneous boundary measurements of scattered light.

  8. Effect of imposed boundary conditions on the accuracy of transport of intensity equation based solvers

    NASA Astrophysics Data System (ADS)

    Martinez-Carranza, J.; Falaggis, K.; Kozacki, T.; Kujawinska, Malgorzata

    2013-05-01

    The transport of intensity equation (TIE) describes the relation between the object phase and the intensity distribution in the Fresnel region and can be used as a non-interferometric technique to estimate the phase distribution of an object. A number of techniques have been developed to solve the TIE. In this work we focus on one popular class of Poisson solvers that are based on Fourier and the Multigrid techniques. The aim of this paper is to present an analysis of these types of TIE solvers taking into account the effect of the boundary condition, i.e. the Neumann Boundary Condition (NBC), the Dirichlet Boundary Condition (DBC), and the Periodic Boundary Condition (PBC). This analysis, which depends on the location of an object wave-front in the detector plane, aims to identify the advantages and disadvantage of these kinds of solvers and to provide the rules for choice of the best fitted boundary condition.

  9. An asymptotic-preserving scheme for the semiconductor Boltzmann equation toward the energy-transport limit

    NASA Astrophysics Data System (ADS)

    Hu, Jingwei; Wang, Li

    2015-01-01

    We design an asymptotic-preserving scheme for the semiconductor Boltzmann equation which leads to an energy-transport system for electron mass and energy as mean free path goes to zero. As opposed to the classical drift-diffusion limit where the stiff collisions are all in one scale, new difficulties arise in the two-scale stiff collision terms because the simple BGK penalization [15] fails to drive the solution to the correct limit. We propose to set up a spatially dependent threshold on the penalization of the stiffer collision operator such that the evolution of the solution resembles a Hilbert expansion at the continuous level. Formal asymptotic analysis and numerical results confirm the efficiency and accuracy of our scheme.

  10. Optical cryptosystem based on phase-truncated Fresnel diffraction and transport of intensity equation.

    PubMed

    Zhang, Chenggong; He, Wenqi; Wu, Jiachen; Peng, Xiang

    2015-04-01

    A novel optical cryptosystem based on phase-truncated Fresnel diffraction (PTFD) and transport of intensity equation (TIE) is proposed. By using the phase truncation technique, a phase-encoded plaintext could be encrypted into a real-valued noise-like intensity distribution by employing a random amplitude mask (RAM) and a random phase mask (RPM), which are regarded as two secret keys. For decryption, a generalized amplitude-phase retrieval (GAPR) algorithm combined with the TIE method are proposed to recover the plaintext with the help of two keys. Different from the current phase-truncated-based optical cryptosystems which need record the truncated phase as decryption keys, our scheme do not need the truncated phase because of the introducing of the TIE method. Moreover, the proposed scheme is expected to against existing attacks. A set of numerical simulation results show the feasibility and security of the proposed method. PMID:25968722

  11. Excited nuclear matter at Fermi energies: From transport properties to the equation of state

    NASA Astrophysics Data System (ADS)

    Lopez, O.; Durand, D.; Lehaut, G.

    2016-05-01

    Properties of excited nuclear matter are one of the main subject of investigation in Nuclear Physics. Indeed, the response of nuclear matter under extreme conditions encountered in heavy-ion induced reactions (large compression, thermal and collective excitations, isopin diffusion) around the Fermi energy is strongly needed when studying the nuclear equation of state and the underlying in-medium properties concerning the nuclear interaction. In this contribution, we will present some experimental results concerning the transport properties of nuclear matter, focusing specifically on the determination of in-medium quantities such as mean free pathes and nucleon-nucleon cross sections around the Fermi energy. We will see that, in this specific energy range, energy and isospin dissipations exhibit very peculiar features, such as the crossover between 1-body to 2-body dissipation regimes corresponding to the transition between the nuclear response from Mean-Field to the nucleonic response through the appearance of nucleon-nucleon collisions.

  12. Iterative feedback algorithm for phase retrieval based on transport of intensity equation

    NASA Astrophysics Data System (ADS)

    Liu, Kaifeng; Cheng, Hong; Zhang, Cheng; Shen, Chuan; Zhang, Fen; Wei, Sui

    2015-12-01

    In this paper, a novel phase retrieval algorithm is presented which combines the advantages of the Transport of Intensity Equation (TIE) method and the iteration method. TIE method is fast, but its precision is not high. Though the convergence rate of iteration method is slow, its result is more accurate. This algorithm consists of Iterative Angular Spectrum (IAS) method to utilize the physical constraints between the object and the spectral domain, and the relationship between the intensity and phase among the wave propagation. Firstly, the phase at the object plane is calculated from two intensity images by TIE. Then this result is treated as the initial phase of the IAS. Finally, the phase information at the object plane is acquired according the reversibility of the optical path. During the iteration process, the feedback mechanism is imposed on it that improve the convergence rate and the precision of phase retrieval and the simulation results are given.

  13. High throughput solution of Boltzmann transport equation: phonons, thermal conductivity and beyond

    NASA Astrophysics Data System (ADS)

    Plata, Jose; Nath, Pinku; Usanmaz, Demet; Toher, Cormac; Fornari, Marco; Buongiorno Nardelli, Marco; Curtarolo, Stefano

    Quantatively accurate predictions of the lattice thermal conductivity have important implications for key technologies ranging from thermoelectrics to thermal barrier coatings. Of the many approaches with varying computational costs and accuracy, which have been developed in the last years, the solution of the Boltzmann transport equation (BTE) is the only approach that guarantees accurate predictions of this property. We have implemented this methodology in the AFLOW high throughput materials science framework, which enables us to compute these anharmonic force constants and solve BTE to obtain the lattice thermal conductivity and related properties automatically in a single step. This technique can be combined with less expensive methodologies previously implemented in AFLOW to create an efficient and fast framework to accelerate the discovery of materials with interesting thermal properties.

  14. Silicon wafer microstructure imaging using InfraRed Transport of Intensity Equation

    NASA Astrophysics Data System (ADS)

    Li, Hongru; Feng, Guoying; Bourgade, Thomas; Zuo, Chao; Du, Yongzhao; Zhou, Shouhuan; Asundi, Anand

    2015-03-01

    A novel quantitative 3D imaging system of silicon microstructures using InfraRed Transport of Intensity Equation (IRTIE) is proposed in this paper. By recording the intensity at multiple planes and using FFT or DCT based TIE solver, fast and accurate phase retrieval for both uniform and non-uniform intensity distributions is proposed. Numerical simulation and experiments confirm the accuracy and reliability of the proposed method. The application of IR-TIE for inspection of micro-patterns in visibly opaque media using 1310 nm light source is demonstrated. For comparison, micro-patterns are also inspected by the contact scanning mode Taylor Hobson system. Quantitative agreement suggests the possibility of using IR-TIE for phase imaging of silicon wafers.

  15. Master equation approach to charge injection and transport in organic insulators

    NASA Astrophysics Data System (ADS)

    Freire, José A.; Voss, Grasiela

    2005-03-01

    We develop a master equation model of a disordered organic insulator sandwiched between metallic electrodes by treating as rate processes both the injection and the internal transport. We show how the master equation model allows for the inclusion of crucial correlation effects in the charge transport, particularly of the Pauli exclusion principle and of space-charge effects, besides, being dependent on just the microscopic form of the transfer rate between the localized electronic states, it allows for the investigation of different microscopic scenarios in the organic, such as polaronic hopping, correlated energy levels, interaction with image charge, etc. The model allows for a separate analysis of the injection and the recombination currents. We find that the disorder, besides increasing the injection current, eliminates the possibility of observation of a Fowler-Nordheim injection current at zero temperature, and that it does not alter the Schottky barrier size of the zero-field thermionic injection current from the value based on the energy difference between the electrode Fermi level and the highest occupied molecular orbital/lowest unoccupied molecular orbital levels in the organic, but it makes the Arrhenius temperature dependence appear at larger temperatures. We investigate how the I(V ) characteristics of a device is affected by the presence of correlations in the site energy distribution and by the form of the internal hopping rate, specifically the Miller-Abrahams rate and the Marcus or small-polaron rate. We show that the disorder does not modify significantly the eβ√E field dependence of the net current due to the Schottky barrier lowering caused by the attraction between the charge and its image in the electrode.

  16. A discrete ordinates approximation to the neutron transport equation applied to generalized geometries

    SciTech Connect

    DeHart, M.D.

    1992-12-01

    A method for applying the discrete ordinates method for solution of the neutron transport equation in arbitary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the traditional shape of a mesh element within a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. Using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. The present work makes no assumptions about the orientations or the number of sides in a given cell, and computes all geometric relationships between each set of sides in each cell for each discrete direction. A set of non-reentrant polygons can therefore be used to represent any given two dimensional space. Results for a number of test problems have been compared to solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN computer programs. Numerical results were obtained for problems ranging from simple one-dimensional geometry to complicated multidimensional configurations. These results have demonstrated the ability of the developed method to closely approximate complex geometrical configurations and to obtain accurate results for problems that are extremely difficult to model using traditional methods.

  17. Master equation approach to charge injection and transport in organic insulators.

    PubMed

    Freire, José A; Voss, Grasiela

    2005-03-22

    We develop a master equation model of a disordered organic insulator sandwiched between metallic electrodes by treating as rate processes both the injection and the internal transport. We show how the master equation model allows for the inclusion of crucial correlation effects in the charge transport, particularly of the Pauli exclusion principle and of space-charge effects, besides, being dependent on just the microscopic form of the transfer rate between the localized electronic states, it allows for the investigation of different microscopic scenarios in the organic, such as polaronic hopping, correlated energy levels, interaction with image charge, etc. The model allows for a separate analysis of the injection and the recombination currents. We find that the disorder, besides increasing the injection current, eliminates the possibility of observation of a Fowler-Nordheim injection current at zero temperature, and that it does not alter the Schottky barrier size of the zero-field thermionic injection current from the value based on the energy difference between the electrode Fermi level and the highest occupied molecular orbital/lowest unoccupied molecular orbital levels in the organic, but it makes the Arrhenius temperature dependence appear at larger temperatures. We investigate how the I(V) characteristics of a device is affected by the presence of correlations in the site energy distribution and by the form of the internal hopping rate, specifically the Miller-Abrahams rate and the Marcus or small-polaron rate. We show that the disorder does not modify significantly the ebeta square root E field dependence of the net current due to the Schottky barrier lowering caused by the attraction between the charge and its image in the electrode. PMID:15836407

  18. Toward a Comprehensive Carbon Budget for North America: Potential Applications of Adjoint Methods with Diverse Datasets

    NASA Technical Reports Server (NTRS)

    Andrews, A.

    2002-01-01

    A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future COS levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an "inverse problem," where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from long-term surface monitoring stations with data from intensive field campaigns and with proposed future satellite observations. A major advantage of the adjoint approach is that meteorological and surface data, as well as data for other atmospheric constituents and pollutants can be efficiently included in addition to observations of CO2 mixing ratios. This presentation will provide an overview of potentially useful datasets for carbon cycle research in general with an emphasis on planning for the North American Carbon Project. Areas of overlap with ongoing and proposed work on air quality/air pollution issues will be highlighted.

  19. Source attribution of particulate matter pollution over North China with the adjoint method

    NASA Astrophysics Data System (ADS)

    Zhang, Lin; Liu, Licheng; Zhao, Yuanhong; Gong, Sunling; Zhang, Xiaoye; Henze, Daven K.; Capps, Shannon L.; Fu, Tzung-May; Zhang, Qiang; Wang, Yuxuan

    2015-08-01

    We quantify the source contributions to surface PM2.5 (fine particulate matter) pollution over North China from January 2013 to 2015 using the GEOS-Chem chemical transport model and its adjoint with improved model horizontal resolution (1/4° × 5/16°) and aqueous-phase chemistry for sulfate production. The adjoint method attributes the PM2.5 pollution to emissions from different source sectors and chemical species at the model resolution. Wintertime surface PM2.5 over Beijing is contributed by emissions of organic carbon (27% of the total source contribution), anthropogenic fine dust (27%), and SO2 (14%), which are mainly from residential and industrial sources, followed by NH3 (13%) primarily from agricultural activities. About half of the Beijing pollution originates from sources outside of the city municipality. Adjoint analyses for other cities in North China all show significant regional pollution transport, supporting a joint regional control policy for effectively mitigating the PM2.5 air pollution.

  20. Linearized model collision operators for multiple ion species plasmas and gyrokinetic entropy balance equations

    SciTech Connect

    Sugama, H.; Watanabe, T.-H.; Nunami, M.

    2009-11-15

    Linearized model collision operators for multiple ion species plasmas are presented that conserve particles, momentum, and energy and satisfy adjointness relations and Boltzmann's H-theorem even for collisions between different particle species with unequal temperatures. The model collision operators are also written in the gyrophase-averaged form that can be applied to the gyrokinetic equation. Balance equations for the turbulent entropy density, the energy of electromagnetic fluctuations, the turbulent transport fluxes of particle and heat, and the collisional dissipation are derived from the gyrokinetic equation including the collision term and Maxwell equations. It is shown that, in the steady turbulence, the entropy produced by the turbulent transport fluxes is dissipated in part by collisions in the nonzonal-mode region and in part by those in the zonal-mode region after the nonlinear entropy transfer from nonzonal to zonal modes.

  1. High Order Finite Volume Nonlinear Schemes for the Boltzmann Transport Equation

    SciTech Connect

    Bihari, B L; Brown, P N

    2005-03-29

    The authors apply the nonlinear WENO (Weighted Essentially Nonoscillatory) scheme to the spatial discretization of the Boltzmann Transport Equation modeling linear particle transport. The method is a finite volume scheme which ensures not only conservation, but also provides for a more natural handling of boundary conditions, material properties and source terms, as well as an easier parallel implementation and post processing. It is nonlinear in the sense that the stencil depends on the solution at each time step or iteration level. By biasing the gradient calculation towards the stencil with smaller derivatives, the scheme eliminates the Gibb's phenomenon with oscillations of size O(1) and reduces them to O(h{sup r}), where h is the mesh size and r is the order of accuracy. The current implementation is three-dimensional, generalized for unequally spaced meshes, fully parallelized, and up to fifth order accurate (WENO5) in space. For unsteady problems, the resulting nonlinear spatial discretization yields a set of ODE's in time, which in turn is solved via high order implicit time-stepping with error control. For the steady-state case, they need to solve the non-linear system, typically by Newton-Krylov iterations. There are several numerical examples presented to demonstrate the accuracy, non-oscillatory nature and efficiency of these high order methods, in comparison with other fixed-stencil schemes.

  2. New insights into self-heating in double-gate transistors by solving Boltzmann transport equations

    SciTech Connect

    Thu Trang Nghiêm, T.; Saint-Martin, J.; Dollfus, P.

    2014-08-21

    Electro-thermal effects become one of the most critical issues for continuing the downscaling of electron devices. To study this problem, a new efficient self-consistent electron-phonon transport model has been developed. Our model of phonon Boltzmann transport equation (pBTE) includes the decay of optical phonons into acoustic modes and a generation term given by electron-Monte Carlo simulation. The solution of pBTE uses an analytic phonon dispersion and the relaxation time approximation for acoustic and optical phonons. This coupled simulation is applied to investigate the self-heating effects in a 20 nm-long double gate MOSFET. The temperature profile per mode and the comparison between Fourier temperature and the effective temperature are discussed. Some significant differences occur mainly in the hot spot region. It is shown that under the influence of self-heating effects, the potential profile is modified and both the drain current and the electron ballisticity are reduced because of enhanced electron-phonon scattering rates.

  3. First-principles calculation method for electron transport based on the grid Lippmann-Schwinger equation.

    PubMed

    Egami, Yoshiyuki; Iwase, Shigeru; Tsukamoto, Shigeru; Ono, Tomoya; Hirose, Kikuji

    2015-09-01

    We develop a first-principles electron-transport simulator based on the Lippmann-Schwinger (LS) equation within the framework of the real-space finite-difference scheme. In our fully real-space-based LS (grid LS) method, the ratio expression technique for the scattering wave functions and the Green's function elements of the reference system is employed to avoid numerical collapse. Furthermore, we present analytical expressions and/or prominent calculation procedures for the retarded Green's function, which are utilized in the grid LS approach. In order to demonstrate the performance of the grid LS method, we simulate the electron-transport properties of the semiconductor-oxide interfaces sandwiched between semi-infinite jellium electrodes. The results confirm that the leakage current through the (001)Si-SiO_{2} model becomes much larger when the dangling-bond state is induced by a defect in the oxygen layer, while that through the (001)Ge-GeO_{2} model is insensitive to the dangling bond state. PMID:26465580

  4. First-principles calculation method for electron transport based on the grid Lippmann-Schwinger equation

    NASA Astrophysics Data System (ADS)

    Egami, Yoshiyuki; Iwase, Shigeru; Tsukamoto, Shigeru; Ono, Tomoya; Hirose, Kikuji

    2015-09-01

    We develop a first-principles electron-transport simulator based on the Lippmann-Schwinger (LS) equation within the framework of the real-space finite-difference scheme. In our fully real-space-based LS (grid LS) method, the ratio expression technique for the scattering wave functions and the Green's function elements of the reference system is employed to avoid numerical collapse. Furthermore, we present analytical expressions and/or prominent calculation procedures for the retarded Green's function, which are utilized in the grid LS approach. In order to demonstrate the performance of the grid LS method, we simulate the electron-transport properties of the semiconductor-oxide interfaces sandwiched between semi-infinite jellium electrodes. The results confirm that the leakage current through the (001 )Si -SiO2 model becomes much larger when the dangling-bond state is induced by a defect in the oxygen layer, while that through the (001 )Ge -GeO2 model is insensitive to the dangling bond state.

  5. Real-time quantitative phase imaging based on transport of intensity equation with dual simultaneously recorded field of view.

    PubMed

    Tian, Xiaolin; Yu, Wei; Meng, Xin; Sun, Aihui; Xue, Liang; Liu, Cheng; Wang, Shouyu

    2016-04-01

    Since quantitative phase distribution reflects both cellular shapes and conditions from another view, compared to traditional intensity observation, different quantitative phase microscopic methods are proposed for cellular detections. However, the transport of intensity equation-based approach not only presents phase, but also intensity, which attracts much attention. While classical transport of intensity equation needs multi-focal images which often cannot realize simultaneous phase measurement, in this Letter, to break through the limitation, a real-time quantitative phase imaging method using transport of intensity equation is proposed. Two identical CCD cameras are set at the binocular tubes to capture the same field of view but at different focal planes. With a double-frame algorithm assuming that the on-focal image is the average of over- and under-focal information, the proposed method is capable of calculating quantitative phase distributions of samples accurately and simultaneously indicating its potentialities in cellular real-time monitoring. PMID:27192253

  6. Second order time evolution of the multigroup diffusion and P{sub 1} equations for radiation transport

    SciTech Connect

    Olson, Gordon L.

    2011-08-20

    Highlights: {yields} An existing multigroup transport algorithm is extended to be second-order in time. {yields} A new algorithm is presented that does not require a grey acceleration solution. {yields} The two algorithms are tested with 2D, multi-material problems. {yields} The two algorithms have comparable computational requirements. - Abstract: An existing solution method for solving the multigroup radiation equations, linear multifrequency-grey acceleration, is here extended to be second order in time. This method works for simple diffusion and for flux-limited diffusion, with or without material conduction. A new method is developed that does not require the solution of an averaged grey transport equation. It is effective solving both the diffusion and P{sub 1} forms of the transport equation. Two dimensional, multi-material test problems are used to compare the solution methods.

  7. Interfacial area transport equation for bubbly to cap-bubbly transition flows

    NASA Astrophysics Data System (ADS)

    Worosz, Theodore S.

    To fully realize the benefit of the two-group interfacial area transport equation (IATE) as a constitutive model for the interfacial area concentration in the two-fluid model, it is imperative that models be developed to dynamically transition from one-group to two-group flows. With this in mind, the two-group IATE is derived in detail to establish new expansion source terms that correctly account for the effects of intergroup bubble transport. In addition to this theoretical effort, the state-of-the-art four-sensor conductivity probe is used to establish a reliable experimental database of local two-phase flow parameters to characterize one-group to two-group transition flows and to support model development. The experiments are performed in verticalupward air-water two-phase flow in a 5.08cm pipe. Additionally, the local conductivity probe is improved through systematic studies into: 1) signal "ghosting" electrical interference among probe sensors, 2) sampling frequency sensitivity, 3) measurement duration sensitivity, and 4) probe sensor orientation. Wake-dominated bubble transport characterizes the transition from onegroup to two-group flows. Therefore, the necessary intergroup and intragroup wake entrainment source terms that are required for two-group interfacial area transport in transition flows are developed. Furthermore, an approach is developed to initiate the shearing-off source and reduce the one-group interaction mechanisms as an established two-group flow develops. The new interfacial area transport model for one-group to two-group transition flows is evaluated against the experimental database. The model accurately captures the exchange of void fraction and interfacial area concentration between group-I and group-II in transition flows. Overall, the group-I void fraction and interfacial area concentration are predicted within +/-6% and +/-4%, respectively, of the experimental data. The group-II void fraction and interfacial area concentration are

  8. TH-E-BRE-02: A Forward Scattering Approximation to Dose Calculation Using the Linear Boltzmann Transport Equation

    SciTech Connect

    Catt, B; Snyder, M

    2014-06-15

    Purpose: To investigate the use of the linear Boltzmann transport equation as a dose calculation tool which can account for interface effects, while still having faster computation times than Monte Carlo methods. In particular, we introduce a forward scattering approximation, in hopes of improving calculation time without a significant hindrance to accuracy. Methods: Two coupled Boltzmann transport equations were constructed, one representing the fluence of photons within the medium, and the other, the fluence of electrons. We neglect the scattering term within the electron transport equation, resulting in an extreme forward scattering approximation to reduce computational complexity. These equations were then solved using a numerical technique for solving partial differential equations, known as a finite difference scheme, where the fluence at each discrete point in space is calculated based on the fluence at the previous point in the particle's path. Using this scheme, it is possible to develop a solution to the Boltzmann transport equations by beginning with boundary conditions and iterating across the entire medium. The fluence of electrons can then be used to find the dose at any point within the medium. Results: Comparisons with Monte Carlo simulations indicate that even simplistic techniques for solving the linear Boltzmann transport equation yield expected interface effects, which many popular dose calculation algorithms are not capable of predicting. Implementation of a forward scattering approximation does not appear to drastically reduce the accuracy of this algorithm. Conclusion: Optimized implementations of this algorithm have been shown to be very accurate when compared with Monte Carlo simulations, even in build up regions where many models fail. Use of a forward scattering approximation could potentially give a reasonably accurate dose distribution in a shorter amount of time for situations where a completely accurate dose distribution is not

  9. A Novel Algorithm for Solving the Multidimensional Neutron Transport Equation on Massively Parallel Architectures

    SciTech Connect

    Azmy, Yousry

    2014-06-10

    We employ the Integral Transport Matrix Method (ITMM) as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells' fluxes and between the cells' and boundary surfaces' fluxes. The main goals of this work are to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and parallel performance of the developed methods with increasing number of processes, P. The fastest observed parallel solution method, Parallel Gauss-Seidel (PGS), was used in a weak scaling comparison with the PARTISN transport code, which uses the source iteration (SI) scheme parallelized with the Koch-baker-Alcouffe (KBA) method. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method- even without acceleration/preconditioning-is completitive for optically thick problems as P is increased to the tens of thousands range. For the most optically thick cells tested, PGS reduced execution time by an approximate factor of three for problems with more than 130 million computational cells on P = 32,768. Moreover, the SI-DSA execution times's trend rises generally more steeply with increasing P than the PGS trend. Furthermore, the PGS method outperforms SI for the periodic heterogeneous layers (PHL) configuration problems. The PGS method outperforms SI and SI-DSA on as few as P = 16 for PHL problems and reduces execution time by a factor of ten or more for all problems considered with more than 2 million computational cells on P = 4.096.

  10. On the forward-backward-in-time approach for Monte Carlo solution of Parker's transport equation: One-dimensional case

    NASA Astrophysics Data System (ADS)

    Bobik, P.; Boschini, M. J.; Della Torre, S.; Gervasi, M.; Grandi, D.; La Vacca, G.; Pensotti, S.; Putis, M.; Rancoita, P. G.; Rozza, D.; Tacconi, M.; Zannoni, M.

    2016-05-01

    The cosmic rays propagation inside the heliosphere is well described by a transport equation introduced by Parker in 1965. To solve this equation, several approaches were followed in the past. Recently, a Monte Carlo approach became widely used in force of its advantages with respect to other numerical methods. In this approach the transport equation is associated to a fully equivalent set of stochastic differential equations (SDE). This set is used to describe the stochastic path of quasi-particle from a source, e.g., the interstellar space, to a specific target, e.g., a detector at Earth. We present a comparison of forward-in-time and backward-in-time methods to solve the cosmic rays transport equation in the heliosphere. The Parker equation and the related set of SDE in the several formulations are treated in this paper. For the sake of clarity, this work is focused on the one-dimensional solutions. Results were compared with an alternative numerical solution, namely, Crank-Nicolson method, specifically developed for the case under study. The methods presented are fully consistent each others for energy greater than 400 MeV. The comparison between stochastic integrations and Crank-Nicolson allows us to estimate the systematic uncertainties of Monte Carlo methods. The forward-in-time stochastic integrations method showed a systematic uncertainty <5%, while backward-in-time stochastic integrations method showed a systematic uncertainty <1% in the studied energy range.

  11. Adjoint-based error estimation and mesh adaptation for the correction procedure via reconstruction method

    NASA Astrophysics Data System (ADS)

    Shi, Lei; Wang, Z. J.

    2015-08-01

    Adjoint-based mesh adaptive methods are capable of distributing computational resources to areas which are important for predicting an engineering output. In this paper, we develop an adjoint-based h-adaptation approach based on the high-order correction procedure via reconstruction formulation (CPR) to minimize the output or functional error. A dual-consistent CPR formulation of hyperbolic conservation laws is developed and its dual consistency is analyzed. Super-convergent functional and error estimate for the output with the CPR method are obtained. Factors affecting the dual consistency, such as the solution point distribution, correction functions, boundary conditions and the discretization approach for the non-linear flux divergence term, are studied. The presented method is then used to perform simulations for the 2D Euler and Navier-Stokes equations with mesh adaptation driven by the adjoint-based error estimate. Several numerical examples demonstrate the ability of the presented method to dramatically reduce the computational cost comparing with uniform grid refinement.

  12. Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry

    NASA Technical Reports Server (NTRS)

    Nemec, Marian; Aftosmis, Michael J.

    2006-01-01

    A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design

  13. Stochastic dynamics from the fractional Fokker-Planck-Kolmogorov equation: Large-scale behavior of the turbulent transport coefficient

    NASA Astrophysics Data System (ADS)

    Milovanov, Alexander V.

    2001-04-01

    The formulation of the fractional Fokker-Planck-Kolmogorov (FPK) equation [Physica D 76, 110 (1994)] has led to important advances in the description of the stochastic dynamics of Hamiltonian systems. Here, the long-time behavior of the basic transport processes obeying the fractional FPK equation is analyzed. A derivation of the large-scale turbulent transport coefficient for a Hamiltonian system with 112 degrees of freedom is proposed in connection with the fractal structure of the particle chaotic trajectories. The principal transport regimes (i.e., a diffusion-type process, ballistic motion, subdiffusion in the limit of the frozen Hamiltonian, and behavior associated with self-organized criticality) are obtained as partial cases of the generalized transport law. A comparison with recent numerical and experimental studies is given.

  14. Stochastic dynamics from the fractional Fokker-Planck-Kolmogorov equation: large-scale behavior of the turbulent transport coefficient.

    PubMed

    Milovanov, A V

    2001-04-01

    The formulation of the fractional Fokker-Planck-Kolmogorov (FPK) equation [Physica D 76, 110 (1994)] has led to important advances in the description of the stochastic dynamics of Hamiltonian systems. Here, the long-time behavior of the basic transport processes obeying the fractional FPK equation is analyzed. A derivation of the large-scale turbulent transport coefficient for a Hamiltonian system with 11 / 2 degrees of freedom is proposed in connection with the fractal structure of the particle chaotic trajectories. The principal transport regimes (i.e., a diffusion-type process, ballistic motion, subdiffusion in the limit of the frozen Hamiltonian, and behavior associated with self-organized criticality) are obtained as partial cases of the generalized transport law. A comparison with recent numerical and experimental studies is given. PMID:11308983

  15. Development of an adjoint model of GRAPES-CUACE and its application in tracking influential haze source areas in north China

    NASA Astrophysics Data System (ADS)

    An, Xing Qin; Xian Zhai, Shi; Jin, Min; Gong, Sunling; Wang, Yu

    2016-06-01

    The aerosol adjoint module of the atmospheric chemical modeling system GRAPES-CUACE (Global-Regional Assimilation and Prediction System coupled with the CMA Unified Atmospheric Chemistry Environment) is constructed based on the adjoint theory. This includes the development and validation of the tangent linear and the adjoint models of the three parts involved in the GRAPES-CUACE aerosol module: CAM (Canadian Aerosol Module), interface programs that connect GRAPES and CUACE, and the aerosol transport processes that are embedded in GRAPES. Meanwhile, strict mathematical validation schemes for the tangent linear and the adjoint models are implemented for all input variables. After each part of the module and the assembled tangent linear and adjoint models is verified, the adjoint model of the GRAPES-CUACE aerosol is developed and used in a black carbon (BC) receptor-source sensitivity analysis to track influential haze source areas in north China. The sensitivity of the average BC concentration over Beijing at the highest concentration time point (referred to as the Objective Function) is calculated with respect to the BC amount emitted over the Beijing-Tianjin-Hebei region. Four types of regions are selected based on the administrative division or the sensitivity coefficient distribution. The adjoint sensitivity results are then used to quantify the effect of reducing the emission sources at different time intervals over different regions. It is indicated that the more influential regions (with relatively larger sensitivity coefficients) do not necessarily correspond to the administrative regions. Instead, the influence per unit area of the sensitivity selected regions is greater. Therefore, controlling the most influential regions during critical time intervals based on the results of the adjoint sensitivity analysis is much more efficient than controlling administrative regions during an experimental time period.

  16. Adjoint tomography of the southern California crust.

    PubMed

    Tape, Carl; Liu, Qinya; Maggi, Alessia; Tromp, Jeroen

    2009-08-21

    Using an inversion strategy based on adjoint methods, we developed a three-dimensional seismological model of the southern California crust. The resulting model involved 16 tomographic iterations, which required 6800 wavefield simulations and a total of 0.8 million central processing unit hours. The new crustal model reveals strong heterogeneity, including local changes of +/-30% with respect to the initial three-dimensional model provided by the Southern California Earthquake Center. The model illuminates shallow features such as sedimentary basins and compositional contrasts across faults. It also reveals crustal features at depth that aid in the tectonic reconstruction of southern California, such as subduction-captured oceanic crustal fragments. The new model enables more realistic and accurate assessments of seismic hazard. PMID:19696349

  17. Adjoints and Low-rank Covariance Representation

    NASA Technical Reports Server (NTRS)

    Tippett, Michael K.; Cohn, Stephen E.

    2000-01-01

    Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.

  18. Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation

    NASA Technical Reports Server (NTRS)

    Reuther, James; Jameson, Antony; Farmer, James; Martinelli, Luigi; Saunders, David

    1996-01-01

    This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods (13, 12, 43, 38). In our earlier studies (19, 20, 22, 23, 39, 25, 40, 41, 42) it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations (39, 25). In our most recent works (40, 42) the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet.

  19. GPU-accelerated adjoint algorithmic differentiation

    NASA Astrophysics Data System (ADS)

    Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe

    2016-03-01

    Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the "tape". Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography.

  20. GPU-Accelerated Adjoint Algorithmic Differentiation

    PubMed Central

    Gremse, Felix; Höfter, Andreas; Razik, Lukas; Kiessling, Fabian; Naumann, Uwe

    2015-01-01

    Many scientific problems such as classifier training or medical image reconstruction can be expressed as minimization of differentiable real-valued cost functions and solved with iterative gradient-based methods. Adjoint algorithmic differentiation (AAD) enables automated computation of gradients of such cost functions implemented as computer programs. To backpropagate adjoint derivatives, excessive memory is potentially required to store the intermediate partial derivatives on a dedicated data structure, referred to as the “tape”. Parallelization is difficult because threads need to synchronize their accesses during taping and backpropagation. This situation is aggravated for many-core architectures, such as Graphics Processing Units (GPUs), because of the large number of light-weight threads and the limited memory size in general as well as per thread. We show how these limitations can be mediated if the cost function is expressed using GPU-accelerated vector and matrix operations which are recognized as intrinsic functions by our AAD software. We compare this approach with naive and vectorized implementations for CPUs. We use four increasingly complex cost functions to evaluate the performance with respect to memory consumption and gradient computation times. Using vectorization, CPU and GPU memory consumption could be substantially reduced compared to the naive reference implementation, in some cases even by an order of complexity. The vectorization allowed usage of optimized parallel libraries during forward and reverse passes which resulted in high speedups for the vectorized CPU version compared to the naive reference implementation. The GPU version achieved an additional speedup of 7.5 ± 4.4, showing that the processing power of GPUs can be utilized for AAD using this concept. Furthermore, we show how this software can be systematically extended for more complex problems such as nonlinear absorption reconstruction for fluorescence-mediated tomography

  1. The piecewise linear discontinuous finite element method applied to the RZ and XYZ transport equations

    NASA Astrophysics Data System (ADS)

    Bailey, Teresa S.

    In this dissertation we discuss the development, implementation, analysis and testing of the Piecewise Linear Discontinuous Finite Element Method (PWLD) applied to the particle transport equation in two-dimensional cylindrical (RZ) and three-dimensional Cartesian (XYZ) geometries. We have designed this method to be applicable to radiative-transfer problems in radiation-hydrodynamics systems for arbitrary polygonal and polyhedral meshes. For RZ geometry, we have implemented this method in the Capsaicin radiative-transfer code being developed at Los Alamos National Laboratory. In XYZ geometry, we have implemented the method in the Parallel Deterministic Transport code being developed at Texas A&M University. We discuss the importance of the thick diffusion limit for radiative-transfer problems, and perform a thick diffusion-limit analysis on our discretized system for both geometries. This analysis predicts that the PWLD method will perform well in this limit for many problems of physical interest with arbitrary polygonal and polyhedral cells. Finally, we run a series of test problems to determine some useful properties of the method and verify the results of our thick diffusion limit analysis. Finally, we test our method on a variety of test problems and show that it compares favorably to existing methods. With these test problems, we also show that our method performs well in the thick diffusion limit as predicted by our analysis. Based on PWLD's solid finite-element foundation, the desirable properties it shows under analysis, and the excellent performance it demonstrates on test problems even with highly distorted spatial grids, we conclude that it is an excellent candidate for radiative-transfer problems that need a robust method that performs well in thick diffusive problems or on distorted grids.

  2. A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report

    SciTech Connect

    Filippone, W.L.; Baker, R.S.

    1990-12-31

    The neutron transport equation is solved by a hybrid method that iteratively couples regions where deterministic (S{sub N}) and stochastic (Monte Carlo) methods are applied. Unlike previous hybrid methods, the Monte Carlo and S{sub N} regions are fully coupled in the sense that no assumption is made about geometrical separation or decoupling. The hybrid method provides a new means of solving problems involving both optically thick and optically thin regions that neither Monte Carlo nor S{sub N} is well suited for by themselves. The fully coupled Monte Carlo/S{sub N} technique consists of defining spatial and/or energy regions of a problem in which either a Monte Carlo calculation or an S{sub N} calculation is to be performed. The Monte Carlo region may comprise the entire spatial region for selected energy groups, or may consist of a rectangular area that is either completely or partially embedded in an arbitrary S{sub N} region. The Monte Carlo and S{sub N} regions are then connected through the common angular boundary fluxes, which are determined iteratively using the response matrix technique, and volumetric sources. The hybrid method has been implemented in the S{sub N} code TWODANT by adding special-purpose Monte Carlo subroutines to calculate the response matrices and volumetric sources, and linkage subrountines to carry out the interface flux iterations. The common angular boundary fluxes are included in the S{sub N} code as interior boundary sources, leaving the logic for the solution of the transport flux unchanged, while, with minor modifications, the diffusion synthetic accelerator remains effective in accelerating S{sub N} calculations. The special-purpose Monte Carlo routines used are essentially analog, with few variance reduction techniques employed. However, the routines have been successfully vectorized, with approximately a factor of five increase in speed over the non-vectorized version.

  3. Improved Hybrid Monte Carlo/n-Moment Transport Equations Model for the Polar Wind

    NASA Astrophysics Data System (ADS)

    Barakat, A. R.; Ji, J.; Schunk, R. W.

    2013-12-01

    In many space plasma problems (e.g. terrestrial polar wind, solar wind, etc.), the plasma gradually evolves from dense collision-dominated into rarified collisionless conditions. For decades, numerous attempts were made in order to address this type of problem using simulations based on one of two approaches. These approaches are: (1) the (fluid-like) Generalized Transport Equations, GTE, and (2) the particle-based Monte Carlo (MC) techniques. In contrast to the computationally intensive MC, the GTE approach can be considerably more efficient but its validity is questionable outside the collision-dominated region depending on the number of transport parameters considered. There have been several attempts to develop hybrid models that combine the strengths of both approaches. In particular, low-order GTE formulations were applied within the collision-dominated region, while an MC simulation was applied within the collisionless region and in the collisional-to-collisionless transition region. However, attention must be paid to assuring the consistency of the two approaches in the region where they are matched. Contrary to all previous studies, our model pays special attention to the ';matching' issue, and hence eliminates the discontinuities/inaccuracies associated with mismatching. As an example, we applied our technique to the Coulomb-Milne problem because of its relevance to the problem of space plasma flow from high- to low-density regions. We will compare the velocity distribution function and its moments (density, flow velocity, temperature, etc.) from the following models: (1) the pure MC model, (2) our hybrid model, and (3) previously published hybrid models. We will also consider a wide range of the test-to-background mass ratio.

  4. Phase-coherent quantum transport in silicon nanowires based on Wigner transport equation: Comparison with the nonequilibrium-Green-function formalism

    NASA Astrophysics Data System (ADS)

    Barraud, Sylvain

    2009-09-01

    Various theoretical formulations are proposed for investigating the carrier transport in nanoscale electronic devices. In this paper, a discrete formulation of the Wigner transport equation (WTE) for the self-consistent simulation of phase-coherent quantum transport in silicon nanowire metal-oxide-semiconductor field-effect transistor (MOSFET) devices is presented. The device is simulated using an effective-mass Hamiltonian within the mode-space approximation. The numerical scheme proposed in this work solves self-consistently three dimensional Poisson's equation, two dimensional Schrödinger's equation in each cross-sectional plane of the nanowire, and the steady-state one dimensional WTE for each conduction mode to handle the quantum transport along the channel. Details on numerical implementation of the Wigner function method are given, and the results are compared with those of the nonequilibrium Green's function (NEGF) method in the ballistic limit. The calculations of current-voltage electrical characteristics of surround-gated silicon nanowires are performed using both NEGF and WTE formulations. The good agreement observed between these approaches means that a direct solution of the WTE is an accurate simulation method for modeling the ballistic quantum transport in silicon nanowire MOSFETs.

  5. The advective-dispersive equation with spatial fractional derivatives as a model for tracer transport in structured soil

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The classical model to describe solute transport in soil is based on the advective-dispersive equation where Fick’s law is used to explain dispersion. From the microscopic point of view this is equivalent to consider that the motion of the particles of solute may be simulated by the Brownian motion....

  6. COMPARING THE FRACTIONAL AND THE CLASSICAL SOLUTE TRANSPORT EQUATIONS WITH DATA ON SOLUTE BREAKTHROUGH IN SOIL COLUMNS

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Solute transport in soils and sediments is commonly simulated with the parabolic advective-dispersive equation, or ADE. In the last decades, it has been reported that this model cannot take in account several important features of solute movement through soil. Recently, a new model base on the assu...

  7. Conservation laws of inviscid Burgers equation with nonlinear damping

    NASA Astrophysics Data System (ADS)

    Abdulwahhab, Muhammad Alim

    2014-06-01

    In this paper, the new conservation theorem presented in Ibragimov (2007) [14] is used to find conservation laws of the inviscid Burgers equation with nonlinear damping ut+g(u)ux+λh(u)=0. We show that this equation is both quasi self-adjoint and self-adjoint, and use these concepts to simplify conserved quantities for various choices of g(u) and h(u).

  8. Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations

    NASA Astrophysics Data System (ADS)

    Chu, Michael; Vishwanath, Karthik; Klose, Alexander D.; Dehghani, Hamid

    2009-04-01

    The accuracy of the commonly used diffusion approximation as used in diffuse optical tomography is known to be limited in cases involving strong absorption and in these situations a higher ordered approximation is necessary. In this study, a light transport model has been developed based upon the three-dimensional frequency-domain simplified spherical harmonics (SPN) approximation for orders up to N = 7. The SPN data are tested against a semi-infinite multi-layered Monte Carlo model. It has been shown that the SPN approximation for higher orders (N >1) provides an increase in accuracy over the diffusion equation specifically near sources and at boundaries of regions with increased optical absorption. It is demonstrated that the error of fluence calculated near the sources between the diffusion approximation and the SPN model (N = 7) can be as large as 60%, therefore limiting the use of the diffusion approximation for small animal imaging and in situations where optical changes near sources are critical for tomographic reconstructions.

  9. Optimum plane selection for transport-of-intensity-equation-based solvers.

    PubMed

    Martinez-Carranza, J; Falaggis, K; Kozacki, T

    2014-10-20

    Deterministic single beam phase retrieval techniques based on the transport of intensity equation (TIE) use the axial intensity derivative obtained from a series of intensities recorded along the propagation axis as an input to the TIE-based solver. The common belief is that, when reducing the error present in the axial intensity derivative, there will be minimal error in the retrieved phase. Thus, reported optimization schemes of measurement condition focuses on the minimization of error in the axial intensity derivative. As it is shown in this contribution, this assumption is not correct and leads to underestimating the value of plane separation, which increases the phase retrieval errors and sensitivity to noise of the TIE-based measurement system. Therefore, in this paper, a detailed analysis that shows the existence of an optimal separation that minimizes the error in the retrieved phase for a given TIE-based solver is carried out. The developed model is used to derive analytical expressions that provide an optimal plane separation for a given number of planes and level of noise for the case of equidistant plane separation. The obtained results are derived for the widely used Fourier-transform-based TIE solver, but it is shown that they can also be applied to multigrid-based techniques. PMID:25402794

  10. Non-dispersive carrier transport in molecularly doped polymers and the convection-diffusion equation

    NASA Astrophysics Data System (ADS)

    Tyutnev, A. P.; Parris, P. E.; Saenko, V. S.

    2015-08-01

    We reinvestigate the applicability of the concept of trap-free carrier transport in molecularly doped polymers and the possibility of realistically describing time-of-flight (TOF) current transients in these materials using the classical convection-diffusion equation (CDE). The problem is treated as rigorously as possible using boundary conditions appropriate to conventional time of flight experiments. Two types of pulsed carrier generation are considered. In addition to the traditional case of surface excitation, we also consider the case where carrier generation is spatially uniform. In our analysis, the front electrode is treated as a reflecting boundary, while the counter electrode is assumed to act either as a neutral contact (not disturbing the current flow) or as an absorbing boundary at which the carrier concentration vanishes. As expected, at low fields transient currents exhibit unusual behavior, as diffusion currents overwhelm drift currents to such an extent that it becomes impossible to determine transit times (and hence, carrier mobilities). At high fields, computed transients are more like those typically observed, with well-defined plateaus and sharp transit times. Careful analysis, however, reveals that the non-dispersive picture, and predictions of the CDE contradict both experiment and existing disorder-based theories in important ways, and that the CDE should be applied rather cautiously, and even then only for engineering purposes.

  11. Universal limiter for transient interpolation modeling of the advective transport equations: The ULTIMATE conservative difference scheme

    NASA Technical Reports Server (NTRS)

    Leonard, B. P.

    1988-01-01

    A fresh approach is taken to the embarrassingly difficult problem of adequately modeling simple pure advection. An explicit conservative control-volume formation makes use of a universal limiter for transient interpolation modeling of the advective transport equations. This ULTIMATE conservative difference scheme is applied to unsteady, one-dimensional scalar pure advection at constant velocity, using three critical test profiles: an isolated sine-squared wave, a discontinuous step, and a semi-ellipse. The goal, of course, is to devise a single robust scheme which achieves sharp monotonic resolution of the step without corrupting the other profiles. The semi-ellipse is particularly challenging because of its combination of sudden and gradual changes in gradient. The ULTIMATE strategy can be applied to explicit conservation schemes of any order of accuracy. Second-order schemes are unsatisfactory, showing steepening and clipping typical of currently popular so-called high resolution shock-capturing of TVD schemes. The ULTIMATE third-order upwind scheme is highly satisfactory for most flows of practical importance. Higher order methods give predictably better step resolution, although even-order schemes generate a (monotonic) waviness in the difficult semi-ellipse simulation. Little is to be gained above ULTIMATE fifth-order upwinding which gives results close to the ultimate for which one might hope.

  12. A space-angle DGFEM approach for the Boltzmann radiation transport equation with local angular refinement

    NASA Astrophysics Data System (ADS)

    Kópházi, József; Lathouwers, Danny

    2015-09-01

    In this paper a new method for the discretization of the radiation transport equation is presented, based on a discontinuous Galerkin method in space and angle that allows for local refinement in angle where any spatial element can support its own angular discretization. To cope with the discontinuous spatial nature of the solution, a generalized Riemann procedure is required to distinguish between incoming and outgoing contributions of the numerical fluxes. A new consistent framework is introduced that is based on the solution of a generalized eigenvalue problem. The resulting numerical fluxes for the various possible cases where neighboring elements have an equal, higher or lower level of refinement in angle are derived based on tensor algebra and the resulting expressions have a very clear physical interpretation. The choice of discontinuous trial functions not only has the advantage of easing local refinement, it also facilitates the use of efficient sweep-based solvers due to decoupling of unknowns on a large scale thereby approaching the efficiency of discrete ordinates methods with local angular resolution. The approach is illustrated by a series of numerical experiments. Results show high orders of convergence for the scalar flux on angular refinement. The generalized Riemann upwinding procedure leads to stable and consistent solutions. Further the sweep-based solver performs well when used as a preconditioner for a Krylov method.

  13. New Techniques for Simulation of Ion Implantation by Numerical Integration of Boltzmann Transport Equation

    NASA Astrophysics Data System (ADS)

    Wang, Shyh-Wei; Guo, Shuang-Fa

    1998-01-01

    New techniques for more accurate and efficient simulation of ion implantations by a stepwise numerical integration of the Boltzmann transport equation (BTE) have been developed in this work. Instead of using uniform energy grid, a non-uniform grid is employed to construct the momentum distribution matrix. A more accurate simulation result is obtained for heavy ions implanted into silicon. In the same time, rather than utilizing the conventional Lindhard, Nielsen and Schoitt (LNS) approximation, an exact evaluation of the integrals involving the nuclear differential scattering cross-section (dσn=2πp dp) is proposed. The impact parameter p as a function of ion energy E and scattering angle φ is obtained by solving the magic formula iteratively and an interpolation techniques is devised during the simulation process. The simulation time using exact evaluation is about 3.5 times faster than that using the Littmark and Ziegler (LZ) spline fitted cross-section function for phosphorus implantation into silicon.

  14. Non-Markovian Effects in the Lindblad Master Equation Approach to Electronic Transport

    NASA Astrophysics Data System (ADS)

    Ribeiro, P.; Vieira, V. R.

    Non-equilibrium processes in open quantum systems can be generically described within the framework of the Lindblad master equation i.e. without a memory kernel. This statement holds even for processes where information can flow-back from the environment to the system. This rather contra-intuitive fact lead to define a process as non Markovian if, during the time evolution of two different initial states of the system, their distinguishability increases, reflecting a back-flow of information from the environment to the system. However, for non Markovian dynamics, the set of conditions to ensure the positivity of the density matrix for all times is not known, making difficult the explicit construction of non Markovian Lindblad operators. Using the Keldysh non equilibrium Green's functions, we explicitly solve a generic quadratic model of electrons coupled at t = 0 to a set of wide-band baths characterized by temperature and chemical potential. We identify the equivalent Lindblad operators describing the evolution of the density matrix and show that the resulting dynamical process is generically non Markovian. We further discuss the cases in which Markovian dynamics is recovered. We apply our approach to a simple model for electronic transport thought a one dimensional wire coupled at t = 0 to wide-band metallic leads, and to a XY spin chain attached to two contacts.

  15. Phase retrieval in arbitrarily shaped aperture with the transport-of-intensity equation

    NASA Astrophysics Data System (ADS)

    Huang, Lei; Zuo, Chao; Idir, Mourad; Qu, Weijuan; Asundi, Anand

    2015-03-01

    Phase is not easy to detect directly as intensity, but sometimes it contains the really desired information. The transport-of-intensity equation (TIE) is a powerful tool to retrieve the phase from the intensity. However, by considering the boundary energy exchange and the whole energy conversation in the field of view, the current popular Fast Fourier transform (FFT) based TIE solver can only retrieve the phase under homogeneous Neumann boundary condition. For many applications, the boundary condition could be more complex and general. A novel TIE phase retrieval method is proposed to deal with an optical field under a general boundary condition. In this method, an arbitrarily-shape hard aperture is added in the optical field. In our method, the TIE is solved by using iterative discrete cosine transforms (DCT) method, which contains a phase compensation mechanism to improve the retrieval results. The proposed method is verified in simulation with an arbitrary phase, an arbitrarily-shaped aperture, and non-uniform intensity distribution. Experiment is also carried out to check its feasibility and the method proposed in this work is very easy and straightforward to use in a practical measurement as a flexible phase retrieval tool.

  16. A space–angle DGFEM approach for the Boltzmann radiation transport equation with local angular refinement

    SciTech Connect

    Kópházi, József Lathouwers, Danny

    2015-09-15

    In this paper a new method for the discretization of the radiation transport equation is presented, based on a discontinuous Galerkin method in space and angle that allows for local refinement in angle where any spatial element can support its own angular discretization. To cope with the discontinuous spatial nature of the solution, a generalized Riemann procedure is required to distinguish between incoming and outgoing contributions of the numerical fluxes. A new consistent framework is introduced that is based on the solution of a generalized eigenvalue problem. The resulting numerical fluxes for the various possible cases where neighboring elements have an equal, higher or lower level of refinement in angle are derived based on tensor algebra and the resulting expressions have a very clear physical interpretation. The choice of discontinuous trial functions not only has the advantage of easing local refinement, it also facilitates the use of efficient sweep-based solvers due to decoupling of unknowns on a large scale thereby approaching the efficiency of discrete ordinates methods with local angular resolution. The approach is illustrated by a series of numerical experiments. Results show high orders of convergence for the scalar flux on angular refinement. The generalized Riemann upwinding procedure leads to stable and consistent solutions. Further the sweep-based solver performs well when used as a preconditioner for a Krylov method.

  17. An inexact Newton method for fully-coupled solution of the Navier-Stokes equations with heat and mass transport

    SciTech Connect

    Shadid, J.N.; Tuminaro, R.S.; Walker, H.F.

    1997-02-01

    The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.

  18. Solution of the within-group multidimensional discrete ordinates transport equations on massively parallel architectures

    NASA Astrophysics Data System (ADS)

    Zerr, Robert Joseph

    2011-12-01

    The integral transport matrix method (ITMM) has been used as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells and between the cells and boundary surfaces. The main goals of this work were to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and performance of the developed methods for increasing number of processes. This project compares the effectiveness of the ITMM with the SI scheme parallelized with the Koch-Baker-Alcouffe (KBA) method. The primary parallel solution method involves a decomposition of the domain into smaller spatial sub-domains, each with their own transport matrices, and coupled together via interface boundary angular fluxes. Each sub-domain has its own set of ITMM operators and represents an independent transport problem. Multiple iterative parallel solution methods have investigated, including parallel block Jacobi (PBJ), parallel red/black Gauss-Seidel (PGS), and parallel GMRES (PGMRES). The fastest observed parallel solution method, PGS, was used in a weak scaling comparison with the PARTISN code. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method without acceleration/preconditioning is not competitive for any problem parameters considered. The best comparisons occur for problems that are difficult for SI DSA, namely highly scattering and optically thick. SI DSA execution time curves are generally steeper than the PGS ones. However, until further testing is performed it cannot be concluded that SI DSA does not outperform the ITMM with PGS even on several thousand or tens of

  19. A Hybrid FE-FV Discontinuous Method to Solve Flow and Transport Equations in Heterogeneous Porous Media

    NASA Astrophysics Data System (ADS)

    Nick, H. M.; Matthai, S. K.

    2009-05-01

    In heterogeneous porous media material discontinuities affect single phase flow as well as multiphase flow. The finite-element method allows to represent such boundaries using piecewise constant or linear material property variations from finite element to element. However, when a node-centered complementary finite volume method is used to model transport across these material interfaces, this discretization can not represent jump discontinuities in concentration or saturation. To overcome this dilemma there are two options, one can either enrich the nodes at the interfaces by additional degrees of freedom or explode the model along the interfaces. This technique, is another way of resolving this problem. Interface nodes are multiplicated so that they match in number the material domains which they join. Here, we use this latter approach, developing an IMPES transport model that can evolve discontinuities at material interfaces in a heterogeneous porous medium. To achieve pressure continuity across the exploded material interfaces, we implement a new implicit algorithm. For the transport equation, we develop a higher-order-accurate scheme which captures jump discontinuity of the transport variable. We use operator-splitting to solve the transport equation after the pressure equation, with the finite volume method, modeling diffusion implicitly employing the finite element method. We verify the new method by a comparison between its results and those of the continuous one. The main advantage of the discontinuous scheme is the resolution of the effects of the material discontinuities. The first order discretization dependency is removed.

  20. Sensitivity of Lumped Constraints Using the Adjoint Method

    NASA Technical Reports Server (NTRS)

    Akgun, Mehmet A.; Haftka, Raphael T.; Wu, K. Chauncey; Walsh, Joanne L.

    1999-01-01

    Adjoint sensitivity calculation of stress, buckling and displacement constraints may be much less expensive than direct sensitivity calculation when the number of load cases is large. Adjoint stress and displacement sensitivities are available in the literature. Expressions for local buckling sensitivity of isotropic plate elements are derived in this study. Computational efficiency of the adjoint method is sensitive to the number of constraints and, therefore, the method benefits from constraint lumping. A continuum version of the Kreisselmeier-Steinhauser (KS) function is chosen to lump constraints. The adjoint and direct methods are compared for three examples: a truss structure, a simple HSCT wing model, and a large HSCT model. These sensitivity derivatives are then used in optimization.

  1. Application of variational principles and adjoint integrating factors for constructing numerical GFD models

    NASA Astrophysics Data System (ADS)

    Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey

    2015-04-01

    The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each

  2. Pricing of American style options with an adjoint process correction method

    NASA Astrophysics Data System (ADS)

    Jaekel, Uwe

    2005-07-01

    Pricing of American options is a more complicated problem than pricing of European options. In this work a formula is derived that allows the computation of the early exercise premium, i.e. the price difference between these two option types in terms of an adjoint process evolving in the reversed time direction of the original process determining the evolution of the European price. We show how this equation can be utilised to improve option price estimates from numerical schemes like finite difference or Monte Carlo methods.

  3. Surface wave sensitivity: mode summation versus adjoint SEM

    NASA Astrophysics Data System (ADS)

    Zhou, Ying; Liu, Qinya; Tromp, Jeroen

    2011-12-01

    We compare finite-frequency phase and amplitude sensitivity kernels calculated based on frequency-domain surface wave mode summation and a time-domain adjoint method. The adjoint calculations involve a forward wavefield generated by an earthquake and an adjoint wavefield generated at a seismic receiver. We determine adjoint sources corresponding to frequency-dependent phase and amplitude measurements made using a multitaper technique, which may be applied to any single-taper measurement, including box car windowing. We calculate phase and amplitude sensitivity kernels using an adjoint method based on wave propagation simulations using a spectral element method (SEM). Sensitivity kernels calculated using the adjoint SEM are in good agreement with kernels calculated based on mode summation. In general, the adjoint SEM is more computationally expensive than mode summation in global studies. The advantage of the adjoint SEM lies in the calculation of sensitivity kernels in 3-D earth models. We compare surface wave sensitivity kernels computed in 1-D and 3-D reference earth models and show that (1) lateral wave speed heterogeneities may affect the geometry and amplitude of surface wave sensitivity; (2) sensitivity kernels of long-period surface waves calculated in 1-D model PREM and 3-D models S20RTS+CRUST2.0 and FFSW1+CRUST2.0 do not show significant differences, indicating that the use of a 1-D reference model is adequate in global inversions of long-period surface waves (periods of 50 s and longer); and (3) the differences become significant for short-period Love waves when mode coupling is sensitive to large differences in reference crustal structure. Finally, we show that sensitivity kernels in anelastic earth models may be calculated in purely elastic earth models provided physical dispersion is properly accounted for.

  4. Transport Equations for CAD Modeling of Al(x)Ga(1-x)N/GaN HEMTs

    NASA Technical Reports Server (NTRS)

    Freeman, Jon C.

    2003-01-01

    BEMTs formed from Al(x)Ga(1-x)N/GaN heterostructures are being investigated for high RF power and efficiency around the world by many groups, both academic and industrial. In these devices, the 2DEG formation is dominated by both spontaneous and piezoelectric polarization fields, with each component having nearly the same order of magnitude. The piezoelectric portion is induced by the mechanical strain in the structure, and to analyze these devices, one must incorporate the stress/strain relationships, along with the standard semiconductor transport equations. These equations for Wurtzite GaN are not easily found in the open literature, hence this paper summarizes them, along with the constitutive equations for piezoelectric materials. The equations are cast into the format for the Wurtzite crystal class, which is the most common way GaN is grown epitaxially.

  5. Universal Racah matrices and adjoint knot polynomials: Arborescent knots

    NASA Astrophysics Data System (ADS)

    Mironov, A.; Morozov, A.

    2016-04-01

    By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SUN) and Kauffman (SON) polynomials. For E8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6 × 6 case. The adjoint polynomials do not distinguish between mutants and therefore are not very efficient in knot theory, however, universal polynomials in higher representations can probably be better in this respect.

  6. Green's formula and variational principles for cosmic-ray transport with application to rotating and shearing flows

    NASA Technical Reports Server (NTRS)

    Webb, G. M.; Jokipii, J. R.; Morfill, G. E.

    1994-01-01

    Green's theorem and Green's formula for the diffusive cosmic-ray transport equation in relativistic flows are derived. Green's formula gives the solution of the transport equation in terms of the Green's function of the adjoint transport equation, and in terms of distributed sources throughout the region R of interest, plus terms involving the particle intensity and streaming on the boundary. The adjoint transport equation describes the time-reversed particle transport. An Euler-Lagrange variational principle is then obtained for both the mean scattering frame distribution function f, and its adjoint f(dagger). Variations of the variational functional with respect to f(dagger) yield the transport equation, whereas variations of f yield the adjoint transport equation. The variational principle, when combined with Noether's theorem, yields the conservation law associated with Green's theorem. An investigation of the transport equation for steady, azimuthal, rotating flows suggests the introduction of a new independent variable H to replace the comoving frame momentum variable p'. For the case of rigid rotating flows, H is conserved and is shown to be analogous to the Hamiltonian for a bead on a rigidly rotating wire. The variable H corresponds to a balance between the centrifugal force and the particle inertia in the rotating frame. The physical interpretation of H includes a discussion of nonrelativistic and special relativistic rotating flows as well as the cases of aziuthal, differentially rotating flows about Schwarzs-child and Kerr black holes. Green's formula is then applied to the problem of the acceleration of ultra-high-energy cosmic rays by galactic rotation. The model for galactic rotation assumes an angular velocity law Omega = Omega(sub 0)(omega(sub 0)/omega), where omega denotes radial distance from the axis of rotation. Green's functions for the galactic rotation problem are used to investigate the spectrum of accelerated particles arising from

  7. Green's formula and variational principles for cosmic-ray transport with application to rotating and shearing flows

    NASA Astrophysics Data System (ADS)

    Webb, G. M.; Jokipii, J. R.; Morfill, G. E.

    1994-03-01

    Green's theorem and Green's formula for the diffusive cosmic-ray transport equation in relativistic flows are derived. Green's formula gives the solution of the transport equation in terms of the Green's function of the adjoint transport equation, and in terms of distributed sources throughout the region R of interest, plus terms involving the particle intensity and streaming on the boundary. The adjoint transport equation describes the time-reversed particle transport. An Euler-Lagrange variational principle is then obtained for both the mean scattering frame distribution function f, and its adjoint f(dagger). Variations of the variational functional with respect to f(dagger) yield the transport equation, whereas variations of f yield the adjoint transport equation. The variational principle, when combined with Noether's theorem, yields the conservation law associated with Green's theorem. An investigation of the transport equation for steady, azimuthal, rotating flows suggests the introduction of a new independent variable H to replace the comoving frame momentum variable p'. For the case of rigid rotating flows, H is conserved and is shown to be analogous to the Hamiltonian for a bead on a rigidly rotating wire. The variable H corresponds to a balance between the centrifugal force and the particle inertia in the rotating frame. The physical interpretation of H includes a discussion of nonrelativistic and special relativistic rotating flows as well as the cases of azimuthal, differentially rotating flows about Schwarzs-child and Kerr black holes. Green's formula is then applied to the problem of the acceleration of ultra-high-energy cosmic rays by galactic rotation. The model for galactic rotation assumes an angular velocity law Omega = Omega0(omega0/omega), where omega denotes radial distance from the axis of rotation. Green's functions for the galactic rotation problem are used to investigate the spectrum of accelerated particles arising from monoenergetic and

  8. Two-group interfacial area transport equation in large diameter pipes

    NASA Astrophysics Data System (ADS)

    Smith, Todd Ryan

    2002-01-01

    The closure relations for the two-group interfacial area transport equation (LATE) by which the changes of interfacial area concentration can be dynamically modeled are set forth in this thesis for the case of large diameter pipes. In the two-group formulation, the sources and sink terms are established by mechanistic modeling of the intra-group and inter-group transport of the bubbles based on five major bubble interaction mechanisms. These mechanisms are bubble coalescence as a result of random collision, RC, wake entrainment, WE, bubble break-up due to turbulent impact, TI, small bubble shearing-off of large bubbles, SO, and bubble break-up due to surface instability for large bubbles, SI. The models developed are supported by experiments using a four-sensor conductivity probe in large diameter test sections, 10.16 cm and 15.24 cm in diameter. A total of 31 different flow conditions under atmospheric pressure are examined in the bubbly to churn-turbulent flow regimes. The local flow parameters measured by the multi-sensor conductivity probe include the local time-averaged void fraction, interfacial area concentration, bubble Sauter mean diameter, interfacial velocity, and interface frequency for the two groups of bubbles. The model is evaluated against the extensive database and good agreement is obtained between the model predictions and the experimental data. The average error based on the total interfacial area concentration is around 7.0% for interfacial area concentration in both test sections. Recirculation in the large pipes is given special treatment in the measurement analysis. Using upwards and downwards facing probes, information on the missing bubble signals is obtained which is used to correct the local data by either the Effective Bubble Number or Intrusiveness Factor Method. The correction to void fraction is found to be about a 12% increase in the local area averaged value, while interfacial area concentration may increase upwards of 60% in the

  9. Equation of state and transport property measurements of warm dense matter.

    SciTech Connect

    Knudson, Marcus D.; Desjarlais, Michael Paul

    2009-10-01

    Location of the liquid-vapor critical point (c.p.) is one of the key features of equation of state models used in simulating high energy density physics and pulsed power experiments. For example, material behavior in the location of the vapor dome is critical in determining how and when coronal plasmas form in expanding wires. Transport properties, such as conductivity and opacity, can vary an order of magnitude depending on whether the state of the material is inside or outside of the vapor dome. Due to the difficulty in experimentally producing states near the vapor dome, for all but a few materials, such as Cesium and Mercury, the uncertainty in the location of the c.p. is of order 100%. These states of interest can be produced on Z through high-velocity shock and release experiments. For example, it is estimated that release adiabats from {approx}1000 GPa in aluminum would skirt the vapor dome allowing estimates of the c.p. to be made. This is within the reach of Z experiments (flyer plate velocity of {approx}30 km/s). Recent high-fidelity EOS models and hydrocode simulations suggest that the dynamic two-phase flow behavior observed in initial scoping experiments can be reproduced, providing a link between theory and experiment. Experimental identification of the c.p. in aluminum would represent the first measurement of its kind in a dynamic experiment. Furthermore, once the c.p. has been experimentally determined it should be possible to probe the electrical conductivity, opacity, reflectivity, etc. of the material near the vapor dome, using a variety of diagnostics. We propose a combined experimental and theoretical investigation with the initial emphasis on aluminum.

  10. Supersonic wing and wing-body shape optimization using an adjoint formulation

    NASA Technical Reports Server (NTRS)

    Reuther, James; Jameson, Antony

    1995-01-01

    This paper describes the implementation of optimization techniques based on control theory for wing and wing-body design of supersonic configurations. The work represents an extension of our earlier research in which control theory is used to devise a design procedure that significantly reduces the computational cost by employing an adjoint equation. In previous studies it was shown that control theory could be used toeviseransonic design methods for airfoils and wings in which the shape and the surrounding body-fitted mesh are both generated analytically, and the control is the mapping function. The method has also been implemented for both transonic potential flows and transonic flows governed by the Euler equations using an alternative formulation which employs numerically generated grids, so that it can treat more general configurations. Here results are presented for three-dimensional design cases subject to supersonic flows governed by the Euler equation.

  11. Baryogenesis via leptogenesis in adjoint SU(5)

    SciTech Connect

    Blanchet, Steve; Fileviez Perez, Pavel E-mail: fileviez@physics.wisc.edu

    2008-08-15

    The possibility of explaining the baryon asymmetry in the Universe through the leptogenesis mechanism in the context of adjoint SU(5) is investigated. In this model neutrino masses are generated through the type I and type III seesaw mechanisms, and the field responsible for the type III seesaw, called {rho}{sub 3}, generates the B-L asymmetry needed to satisfy the observed value of the baryon asymmetry in the Universe. We find that the CP asymmetry originates only from the vertex correction, since the self-energy contribution is not present. When neutrino masses have a normal hierarchy, successful leptogenesis is possible for 10{sup 11} GeV{approx}

  12. Quantum transport simulations of graphene nanoribbon devices using Dirac equation calibrated with tight-binding π-bond model

    PubMed Central

    2012-01-01

    We present an efficient approach to study the carrier transport in graphene nanoribbon (GNR) devices using the non-equilibrium Green's function approach (NEGF) based on the Dirac equation calibrated to the tight-binding π-bond model for graphene. The approach has the advantage of the computational efficiency of the Dirac equation and still captures sufficient quantitative details of the bandstructure from the tight-binding π-bond model for graphene. We demonstrate how the exact self-energies due to the leads can be calculated in the NEGF-Dirac model. We apply our approach to GNR systems of different widths subjecting to different potential profiles to characterize their device physics. Specifically, the validity and accuracy of our approach will be demonstrated by benchmarking the density of states and transmissions characteristics with that of the more expensive transport calculations for the tight-binding π-bond model. PMID:22325480

  13. Quantum transport simulations of graphene nanoribbon devices using Dirac equation calibrated with tight-binding π-bond model.

    PubMed

    Chin, Sai-Kong; Lam, Kai-Tak; Seah, Dawei; Liang, Gengchiau

    2012-01-01

    We present an efficient approach to study the carrier transport in graphene nanoribbon (GNR) devices using the non-equilibrium Green's function approach (NEGF) based on the Dirac equation calibrated to the tight-binding π-bond model for graphene. The approach has the advantage of the computational efficiency of the Dirac equation and still captures sufficient quantitative details of the bandstructure from the tight-binding π-bond model for graphene. We demonstrate how the exact self-energies due to the leads can be calculated in the NEGF-Dirac model. We apply our approach to GNR systems of different widths subjecting to different potential profiles to characterize their device physics. Specifically, the validity and accuracy of our approach will be demonstrated by benchmarking the density of states and transmissions characteristics with that of the more expensive transport calculations for the tight-binding π-bond model. PMID:22325480

  14. Solution of the within-group multidimensional discrete ordinates transport equations on massively parallel architectures

    NASA Astrophysics Data System (ADS)

    Zerr, Robert Joseph

    2011-12-01

    The integral transport matrix method (ITMM) has been used as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells and between the cells and boundary surfaces. The main goals of this work were to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and performance of the developed methods for increasing number of processes. This project compares the effectiveness of the ITMM with the SI scheme parallelized with the Koch-Baker-Alcouffe (KBA) method. The primary parallel solution method involves a decomposition of the domain into smaller spatial sub-domains, each with their own transport matrices, and coupled together via interface boundary angular fluxes. Each sub-domain has its own set of ITMM operators and represents an independent transport problem. Multiple iterative parallel solution methods have investigated, including parallel block Jacobi (PBJ), parallel red/black Gauss-Seidel (PGS), and parallel GMRES (PGMRES). The fastest observed parallel solution method, PGS, was used in a weak scaling comparison with the PARTISN code. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method without acceleration/preconditioning is not competitive for any problem parameters considered. The best comparisons occur for problems that are difficult for SI DSA, namely highly scattering and optically thick. SI DSA execution time curves are generally steeper than the PGS ones. However, until further testing is performed it cannot be concluded that SI DSA does not outperform the ITMM with PGS even on several thousand or tens of

  15. Determination of transport wind speed in the gaussian plume diffusion equation for low-lying point sources

    NASA Astrophysics Data System (ADS)

    Wang, I. T.

    A general method for determining the effective transport wind speed, overlineu, in the Gaussian plume equation is discussed. Physical arguments are given for using the generalized overlineu instead of the often adopted release-level wind speed with the plume diffusion equation. Simple analytical expressions for overlineu applicable to low-level point releases and a wide range of atmospheric conditions are developed. A non-linear plume kinematic equation is derived using these expressions. Crosswind-integrated SF 6 concentration data from the 1983 PNL tracer experiment are used to evaluate the proposed analytical procedures along with the usual approach of using the release-level wind speed. Results of the evaluation are briefly discussed.

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

    SciTech Connect

    Thompson, K.G.

    2000-11-01

    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

  17. Implementation of the interfacial area transport equation in trace for boiling two-phase flows

    NASA Astrophysics Data System (ADS)

    Bernard, Matthew S.

    Correctly predicting the interfacial area concentration (a i) is vital to the overall accuracy of the two-fluid model because ai describes the amount of surface area that exists between the two-phases, and is therefore directly related to interfacial mass, momentum and energy transfer. The conventional method for specifying ai in the two-fluid model is through flow regime-based empirical correlations coupled with regime transition criteria. However, a more physically consistent approach to predicting ai is through the interfacial area transport equation (IATE), which can address the deficiencies of the flow regime-based approach. Some previous studies have been performed to demonstrate the feasibility of IATE in developmental versions of the nuclear reactor systems analysis code, TRACE. However, a full TRACE version capable of predicting boiling two-phase flows with the IATE has not been established. Therefore, the current work develops a version of TRACE that is capable of predicting boiling two-phase flows using the IATE. The development is carried out in stages. First, a version of TRACE which employs the two-group IATE for adiabatic, vertical upward, air-water conditions is developed. An in-depth assessment on the existing experimental database is performed to select reliable experimental data for code assessment. Then, the implementation is assessed against the qualified air-water two-phase flow experimental data. Good agreement is observed between the experimental data for ai and the TRACE code with an average error of +/-9% for all conditions. Following the initial development, one-group IATE models for vertical downward and horizontal two-phase flows are implemented and assessed against qualified data. Finally, IATE models capable of predicting subcooled boiling two-phase flows are implemented. An assessment of the models shows that TRACE is capable of generating ai in subcooled boiling two-phase flows with the IATE and that heat transfer effects dominate

  18. A Reynolds-averaged turbulence modeling approach using three transport equations for the turbulent viscosity, kinetic energy, and dissipation rate

    NASA Astrophysics Data System (ADS)

    Yoshizawa, Akira; Abe, Hiroyuki; Matsuo, Yuichi; Fujiwara, Hitoshi; Mizobuchi, Yasuhiro

    2012-07-01

    A Reynolds-averaged approach to turbulent shear flows is sought with resort to a three-equation method. Its novelty is the introduction of a turbulent-viscosity transport equation through the transport equation for the Reynolds stress in addition to those for the turbulent kinetic energy and the dissipation rate. The latter two equations are used for evaluating the dimensional coefficients in the former. The aim of this model is to enhance the capability to cope with nonstationary and advection effects in various turbulent flows. The adaptability to them is confirmed through the application to homogeneous-shear and supersonic free-shear flows. In particular, the reasonable prediction is obtained in the latter where the growth rate of the shear layer is suppressed with the increase in the convective Mach number. The present model is also applied to a three-dimensional flow past a wing tip as an instance of complex aeronautical flows, and the excessive diffusion of the trailing vortices is shown to be suppressed. The turbulent-viscosity representation for the Reynolds stress is systematically supplemented with nonlinear effects of mean-velocity gradient tensors, and its adequacy is verified in a channel flow.

  19. A user's manual for MASH 1. 0: A Monte Carlo Adjoint Shielding Code System

    SciTech Connect

    Johnson, J.O.

    1992-03-01

    The Monte Carlo Adjoint Shielding Code System, MASH, calculates neutron and gamma-ray environments and radiation protection factors for armored military vehicles, structures, trenches, and other shielding configurations by coupling a forward discrete ordinates air-over-ground transport calculation with an adjoint Monte Carlo treatment of the shielding geometry. Efficiency and optimum use of computer time are emphasized. The code system include the GRTUNCL and DORT codes for air-over-ground transport calculations, the MORSE code with the GIFT5 combinatorial geometry package for adjoint shielding calculations, and several peripheral codes that perform the required data preparations, transformations, and coupling functions. MASH is the successor to the Vehicle Code System (VCS) initially developed at Oak Ridge National Laboratory (ORNL). The discrete ordinates calculation determines the fluence on a coupling surface surrounding the shielding geometry due to an external neutron/gamma-ray source. The Monte Carlo calculation determines the effectiveness of the fluence at that surface in causing a response in a detector within the shielding geometry, i.e., the dose importance'' of the coupling surface fluence. A coupling code folds the fluence together with the dose importance, giving the desired dose response. The coupling code can determine the dose response a a function of the shielding geometry orientation relative to the source, distance from the source, and energy response of the detector. This user's manual includes a short description of each code, the input required to execute the code along with some helpful input data notes, and a representative sample problem (input data and selected output edits) for each code.

  20. Adjoint tomography of the Middle East

    NASA Astrophysics Data System (ADS)

    Peter, D. B.; Savage, B.; Rodgers, A. J.; Tromp, J.

    2010-12-01

    Improvements in nuclear explosion monitoring require refined seismic models of the target region. In our study, we focus on the Middle East, spanning a region from Turkey to the west and West India to the east. This area represents a complex geologic and tectonic setting with sparse seismic data coverage. This has lead to diverging interpretations of crustal and underlying upper-mantle structure by different research groups, complicating seismic monitoring of the Middle East at regional distances. We evaluated an initial 3D seismic model of this region by computing full waveforms for several regional earthquakes by a spectral-element method. We measure traveltime and multitaper phase shifts between observed broadband data and synthetic seismograms for distinct seismic phases within selected time windows using a recently developed automated measurement algorithm. Based on the remaining misfits, we setup an iterative inversion procedure for a fully numerical 3D seismic tomography approach. In order to improve the initial 3D seismic model, the sensitivity to seismic structure of the traveltime and multitaper phase measurements for all available seismic network recordings is computed. As this represents a computationally very intensive task, we take advantage of a fully numerical adjoint approach by using the efficient software package SPECFEM3D_GLOBE on a dedicated cluster. We show examples of such sensitivity kernels for different seismic events and use them in a steepest descent approach to update the 3D seismic model, starting at longer periods between 60 s and up to 200 s and moving towards shorter periods of 11 s. We highlight various improvements in the initial seismic structure during the iterations in order to better fit regional seismic waveforms in the Middle East.

  1. Adjoint tomography of the Middle East

    NASA Astrophysics Data System (ADS)

    Peter, D. B.; Savage, B.; Rodgers, A.; Morency, C.; Tromp, J.

    2011-12-01

    Improvements in nuclear explosion monitoring require refined seismic models of the target region. In our study, we focus on the Middle East, spanning a region from Turkey to the west and West India to the east. This area represents a complex geologic and tectonic setting with sparse seismic data coverage. This has lead to diverging interpretations of crustal and underlying upper-mantle structure by different research groups, complicating seismic monitoring of the Middle East at regional distances. We evaluated an initial 3D seismic model of this region by computing full waveforms for several regional earthquakes based on a spectral-element method. We measure traveltime and multitaper phase differences between observed broadband data and synthetic seismograms for distinct seismic phases within selected time windows using a recently developed automated measurement algorithm. Based on the remaining misfits, we setup an iterative inversion procedure for a fully numerical 3D seismic tomography approach. In order to improve the initial 3D seismic model, sensitivity to seismic structures of traveltime and multitaper phase measurements for all available seismic network recordings is computed. As this represents a computationally very intensive task, we take advantage of a fully numerical adjoint approach by using the efficient software package SPECFEM3D_GLOBE on a dedicated cluster. We show examples of such sensitivity kernels for different seismic events. All these `event kernels' are then summed, smoothed and further used in a preconditioned conjugate-gradient approach. Thus we iteratively update the 3D seismic model, starting at longer periods between 60~s and up to 150~s and moving towards shorter periods of 11~s. We highlight various improvements in the initial seismic structure during the iterations in order to better fit regional seismic waveforms in the Middle East.

  2. A one-equation turbulence transport model for high Reynolds number wall-bounded flows

    NASA Technical Reports Server (NTRS)

    Baldwin, Barrett S.; Barth, Timothy J.

    1990-01-01

    A one-equation turbulence model that avoids the need for an algebraic length scale is derived from a simplified form of the standard k-epsilon model equations. After calibration based on well established properties of the flow over a flat plate, predictions of several other flows are compared with experiment. The preliminary results presented indicate that the model has predictive and numerical properties of sufficient interest to merit further investigation and refinement. The one-equation model is also analyzed numerically and robust solution methods are presented.

  3. A one-equation turbulence transport model for high Reynolds number wall-bounded flows

    NASA Technical Reports Server (NTRS)

    Baldwin, Barrett S.; Barth, Timothy J.

    1991-01-01

    A one-equation turbulence model that avoids the need for an algebraic length scale is derived from a simplified form of the standard-k-epsilon model equations. After calibration based on well established properties of the flow over a flat plate, predictions of several other flows are compared with experiment. The preliminary results presented indicate that the model has predictive and numerical properties of sufficient interest to merit further investigation and refinement. The one-equation model is also analyzed numerically and robust solution methods are presented.

  4. Adjoint free four-dimensional variational data assimilation for a storm surge model of the German North Sea

    NASA Astrophysics Data System (ADS)

    Zheng, Xiangyang; Mayerle, Roberto; Xing, Qianguo; Fernández Jaramillo, José Manuel

    2016-08-01

    In this paper, a data assimilation scheme based on the adjoint free Four-Dimensional Variational(4DVar) method is applied to an existing storm surge model of the German North Sea. To avoid the need of an adjoint model, an ensemble-like method to explicitly represent the linear tangent equation is adopted. Results of twin experiments have shown that the method is able to recover the contaminated low dimension model parameters to their true values. The data assimilation scheme was applied to a severe storm surge event which occurred in the North Sea in December 5, 2013. By adjusting wind drag coefficient, the predictive ability of the model increased significantly. Preliminary experiments have shown that an increase in the predictive ability is attained by narrowing the data assimilation time window.

  5. Adjoint free four-dimensional variational data assimilation for a storm surge model of the German North Sea

    NASA Astrophysics Data System (ADS)

    Zheng, Xiangyang; Mayerle, Roberto; Xing, Qianguo; Fernández Jaramillo, José Manuel

    2016-06-01

    In this paper, a data assimilation scheme based on the adjoint free Four-Dimensional Variational(4DVar) method is applied to an existing storm surge model of the German North Sea. To avoid the need of an adjoint model, an ensemble-like method to explicitly represent the linear tangent equation is adopted. Results of twin experiments have shown that the method is able to recover the contaminated low dimension model parameters to their true values. The data assimilation scheme was applied to a severe storm surge event which occurred in the North Sea in December 5, 2013. By adjusting wind drag coefficient, the predictive ability of the model increased significantly. Preliminary experiments have shown that an increase in the predictive ability is attained by narrowing the data assimilation time window.

  6. Sensitivity Analysis of Differential-Algebraic Equations and Partial Differential Equations

    SciTech Connect

    Petzold, L; Cao, Y; Li, S; Serban, R

    2005-08-09

    Sensitivity analysis generates essential information for model development, design optimization, parameter estimation, optimal control, model reduction and experimental design. In this paper we describe the forward and adjoint methods for sensitivity analysis, and outline some of our recent work on theory, algorithms and software for sensitivity analysis of differential-algebraic equation (DAE) and time-dependent partial differential equation (PDE) systems.

  7. Parameter scaling to produce different charged-particle beam-transport systems having identical equations of motion

    SciTech Connect

    Wadlinger, E.A.

    1988-04-01

    Designs are freuently required for charged-particle optics channels to transport space-charge (Coulomb) force-dominated beams for use with accelerators under design or construction. It is often desirable to experimentally test a design using an existing accelerator having different parameters from the one under consideration. This paper shows how to scale a charged-particle transport design to make a model experiment for testing the design with an existing accelerator. Sometimes, with the proper choice of accelerator, the model experimetn can be much less expensive than the target device. By scaling variables (beam current and emittance, magnetic fields, etc.) in a way that produces certain invariant quantities, we obtain identical equations of motion for different charged-particle beam channels transporting different beams. The scaling relations take a transport channel design for one application having a given time structure (for instance, the time structure determiend by the radio frequency of a beam bunching cavity), beam energy, current, etc., and determine an equivalent transport channel design for another device with different parameters. Therefore, we can predict particle and beam behavior in one situation by knowing it in another. Even growth in emittance will be modeled correctly in spite of the fact that the devices transport beams with different time structure, energy, and currents. 2 refs., 1 fig., 1 tab.

  8. 3D Multigroup Sn Neutron Transport Code

    2001-02-14

    ATTILA is a 3D multigroup transport code with arbitrary order ansotropic scatter. The transport equation is solved in first order form using a tri-linear discontinuous spatial differencing on an arbitrary tetrahedral mesh. The overall solution technique is source iteration with DSA acceleration of the scattering source. Anisotropic boundary and internal sources may be entered in the form of spherical harmonics moments. Alpha and k eigenvalue problems are allowed, as well as fixed source problems. Forwardmore » and adjoint solutions are available. Reflective, vacumn, and source boundary conditions are available. ATTILA can perform charged particle transport calculations using slowing down (CSD) terms. ATTILA can also be used to peform infra-red steady-state calculations for radiative transfer purposes.« less

  9. 3D Multigroup Sn Neutron Transport Code

    SciTech Connect

    McGee, John; Wareing, Todd; Pautz, Shawn

    2001-02-14

    ATTILA is a 3D multigroup transport code with arbitrary order ansotropic scatter. The transport equation is solved in first order form using a tri-linear discontinuous spatial differencing on an arbitrary tetrahedral mesh. The overall solution technique is source iteration with DSA acceleration of the scattering source. Anisotropic boundary and internal sources may be entered in the form of spherical harmonics moments. Alpha and k eigenvalue problems are allowed, as well as fixed source problems. Forward and adjoint solutions are available. Reflective, vacumn, and source boundary conditions are available. ATTILA can perform charged particle transport calculations using slowing down (CSD) terms. ATTILA can also be used to peform infra-red steady-state calculations for radiative transfer purposes.

  10. Adjoint sensitivity analysis of plasmonic structures using the FDTD method.

    PubMed

    Zhang, Yu; Ahmed, Osman S; Bakr, Mohamed H

    2014-05-15

    We present an adjoint variable method for estimating the sensitivities of arbitrary responses with respect to the parameters of dispersive discontinuities in nanoplasmonic devices. Our theory is formulated in terms of the electric field components at the vicinity of perturbed discontinuities. The adjoint sensitivities are computed using at most one extra finite-difference time-domain (FDTD) simulation regardless of the number of parameters. Our approach is illustrated through the sensitivity analysis of an add-drop coupler consisting of a square ring resonator between two parallel waveguides. The computed adjoint sensitivities of the scattering parameters are compared with those obtained using the accurate but computationally expensive central finite difference approach. PMID:24978258

  11. Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers

    NASA Technical Reports Server (NTRS)

    Reuther, James; Jameson, Antony; Alonso, Juan Jose; Rimlinger, Mark J.; Saunders, David

    1997-01-01

    An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat

  12. Source attribution of PM2.5 pollution over North China using the adjoint method

    NASA Astrophysics Data System (ADS)

    Zhang, L.; Liu, L.; Zhao, Y.; Gong, S.; Henze, D. K.

    2014-12-01

    Conventional methods for source attribution of air pollution are based on measurement statistics (such as Positive Matrix Factorization) or sensitivity simulations with a chemical transport model (CTM). These methods generally ignore the nonlinear chemistry associated with the pollution formation or require unaffordable computational time. Here we use the adjoint of GEOS-Chem CTM at 0.25x0.3125 degree resolution to examine the sources contributing to the PM2.5 pollution over North China in winter 2013. We improved the model sulfate simulation by implementing the aqueous-phase oxidation of S(IV) by nitrogen dioxide. The adjoint results provide detailed source information at the model underlying grid resolution including source types and sectors. We show that PM2.5 pollution over Beijing and Baoding (Hebei) in winter was largely contributed by the large-scale residential and industrial burnings, and ammonia (NH3) emissions from agriculture activities. Nearly half of pollution was transported from outside of the city domains, and accumulated over 2-3 days. We also show under the current emission conditions, the PM2.5 concentrations over North China are more sensitive to NH3 emissions than NOx and SO2 emissions.

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

    NASA Astrophysics Data System (ADS)

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

    2014-09-01

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

  14. Implementation of the LAX-Wendroff Method in Cobra-TF for Solving Two-Phase Flow Transport Equations

    SciTech Connect

    Salko, Robert K; Wang, Dean; Ren, Kangyu

    2016-01-01

    COBRA-TF (Coolant Boiling in Rod Arrays Two Fluid), or CTF, is a subchannel code used to conduct the reactor core thermal hydraulic (T/H) solution in both standalone and coupled multi-physics applications. CTF applies the first-order upwind spatial discretization scheme for solving two-phase flow conservation equations. In this work, the second-order Lax-Wendroff (L-W) scheme has been implemented in CTF to solve the two-phase flow transport equations to improve numerical accuracy in both temporal and spatial discretization. To avoid the oscillation issue, a non-linear flux limiter VA (Van Albada) is employed for the convective terms in the transport equations. Assessments have been carried out to evaluate the performance and stability of the implemented second-order L-W scheme. It has been found that the L-W scheme performs better than the upwind scheme for the single-phase and two-phase flow problems in terms of numerical accuracy and computational efficiency.

  15. Predictions of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions Using an Intermittency Transport Equation

    NASA Technical Reports Server (NTRS)

    Suzen, Y. B.; Huang, P. G.; Hultgren, Lennart S.; Ashpis, David E.

    2003-01-01

    A new transport equation for the intermittency factor was proposed to predict separated and transitional boundary layers under low-pressure turbine airfoil conditions. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, t , with the intermittency factor, y. Turbulent quantities are predicted by using Menter s two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model, which not only can reproduce the experimentally observed streamwise variation of the intermittency in the transition zone, but also can provide a realistic cross-stream variation of the intermittency profile. In this paper, the intermittency model is used to predict a recent separated and transitional boundary layer experiment under low pressure turbine airfoil conditions. The experiment provides detailed measurements of velocity, turbulent kinetic energy and intermittency profiles for a number of Reynolds numbers and freestream turbulent intensity conditions and is suitable for validation purposes. Detailed comparisons of computational results with experimental data are presented and good agreements between the experiments and predictions are obtained.

  16. Predictions of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions Using an Intermittency Transport Equation

    NASA Technical Reports Server (NTRS)

    Suzen, Y. Bora; Huang, P. G.; Hultgren, Lennart S.; Ashpis, David E.

    2001-01-01

    A new transport equation for the intermittency factor was proposed to predict separated and transitional boundary layers under low-pressure turbine airfoil conditions. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, mu(sub t), with the intermittency factor, gamma. Turbulent quantities are predicted by using Menter's two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model, which not only can reproduce the experimentally observed streamwise variation of the intermittency in the transition zone, but also can provide a realistic cross-stream variation of the intermittency profile. In this paper, the intermittency model is used to predict a recent separated and transitional boundary layer experiment under low pressure turbine airfoil conditions. The experiment provides detailed measurements of velocity, turbulent kinetic energy and intermittency profiles for a number of Reynolds numbers and freestream turbulent intensity conditions and is suitable for validation purposes. Detailed comparisons of computational results with experimental data are presented and good agreements between the experiments and predictions are obtained.

  17. Transport solutions of the Lamé equations and shock elastic waves

    NASA Astrophysics Data System (ADS)

    Alexeyeva, L. A.; Kaishybaeva, G. K.

    2016-07-01

    The Lamé system describing the dynamics of an isotropic elastic medium affected by a steady transport load moving at subsonic, transonic, or supersonic speed is considered. Its fundamental and generalized solutions in a moving frame of reference tied to the transport load are analyzed. Shock waves arising in the medium at supersonic speeds are studied. Conditions on the jump in the stress, displacement rate, and energy across the shock front are obtained using distribution theory. Numerical results concerning the dynamics of an elastic medium influenced by concentrated transport loads moving at sub-, tran- and supersonic speeds are presented.

  18. An Adjoint-Based Analysis of the Sampling Footprints of Tall Tower, Aircraft and Potential Future Lidar Observations of CO2

    NASA Technical Reports Server (NTRS)

    Andrews, Arlyn; Kawa, Randy; Zhu, Zhengxin; Burris, John; Abshire, Jim

    2004-01-01

    A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future CO2 levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an 'inverse problem', where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from longterm surface and aircraft monitoring stations with data from intensive field campaigns and with proposed future satellite observations. We have recently developed an adjoint for the GSFC 3-D Parameterized Chemistry and Transport Model (PCTM). Here, we will present results from a PCTM Adjoint study comparing the sampling footprints of tall tower, aircraft and potential future lidar observations of CO2. The vertical resolution and extent of the profiles and the observation frequency will be considered for several sites in North America.

  19. Role of non-ideality for the ion transport in porous media: Derivation of the macroscopic equations using upscaling

    NASA Astrophysics Data System (ADS)

    Allaire, Grégoire; Brizzi, Robert; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey

    2014-07-01

    This paper is devoted to the homogenization (or upscaling) of a system of partial differential equations describing the non-ideal transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid porous medium. Realistic non-ideal effects are taken into account by an approach based on the mean spherical approximation (MSA) model which takes into account finite size ions and screening effects. We first consider equilibrium solutions in the absence of external forces. In such a case, the velocity and diffusive fluxes vanish and the equilibrium electrostatic potential is the solution of a variant of the Poisson-Boltzmann equation coupled with algebraic equations. Contrary to the ideal case, this nonlinear equation has no monotone structure. However, based on invariant region estimates for the Poisson-Boltzmann equation and for small characteristic value of the solute packing fraction, we prove existence of at least one solution. To our knowledge this existence result is new at this level of generality. When the motion is governed by a small static electric field and a small hydrodynamic force, we generalize O'Brien's argument to deduce a linearized model. Our second main result is the rigorous homogenization of these linearized equations and the proof that the effective tensor satisfies Onsager properties, namely is symmetric positive definite. We eventually make numerical comparisons with the ideal case. Our numerical results show that the MSA model confirms qualitatively the conclusions obtained using the ideal model but there are quantitative differences arising that can be important at high charge or high concentrations.

  20. Fokker-Planck equations for charged-particle transport in random fields.

    NASA Technical Reports Server (NTRS)

    Jokipii, J. R.

    1972-01-01

    The Fokker-Planck equations for charged-particle dynamics are rederived, extending somewhat the elegant discussion of Hasselmann and Wibberenz. It is shown that the usual results are obtae and the conclusions in many cases are correct over a very broad range in energy. In particular, the rate for pitch-angle scattering may be accurately given down to energies much lower than previously thought. Recent claims that these Fokker-Planck equations are in general incorrect are thus shown to be in error.

  1. The nature and role of advection in advection-diffusion equations used for modelling bed load transport

    NASA Astrophysics Data System (ADS)

    Ancey, Christophe; Bohorquez, Patricio; Heyman, Joris

    2016-04-01

    The advection-diffusion equation arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Stochastic models can also be used to derive this equation, with the significant advantage that they provide information on the statistical properties of particle activity. Stochastic models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. We develop an approach based on birth-death Markov processes, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received little attention. We show that particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

  2. Higher-order approximation of contaminant transport equation for turbulent channel flows based on centre manifolds and its numerical solution

    NASA Astrophysics Data System (ADS)

    Ngo-Cong, D.; Mohammed, F. J.; Strunin, D. V.; Skvortsov, A. T.; Mai-Duy, N.; Tran-Cong, T.

    2015-06-01

    The contaminant transport process governed by the advection-diffusion equation plays an important role in modelling industrial and environmental flows. In this article, our aim is to accurately reduce the 2-D advection-diffusion equation governing the dispersion of a contaminant in a turbulent open channel flow to its 1-D approximation. The 1-D model helps to quickly estimate the horizontal size of contaminant clouds based on the values of the model coefficients. We derive these coefficients analytically and investigate numerically the model convergence. The derivation is based on the centre manifold theory to obtain successively more accurate approximations in a consistent manner. Two types of the average velocity profile are considered: the classical logarithmic profile and the power profile. We further develop the one-dimensional integrated radial basis function network method as a numerical approach to obtain the numerical solutions to both the original 2-D equation and the approximate 1-D equations. We compare the solutions of the original models with their centre-manifold approximations at very large Reynolds numbers. The numerical results obtained from the approximate 1-D models are in good agreement with those of the original 2-D model for both the logarithmic and power velocity profiles.

  3. Alternative(s) to fractional-diffusion equations in bedload-transport models

    NASA Astrophysics Data System (ADS)

    Ancey, Christophe; Mettra, François; Mettraux, Valentin

    2010-05-01

    The idea of stochastic sediment transport models emerged in the 1930s, notably with the doctoral work of Hans A. Einstein (1936). Einstein's seminal work gave impulse to several stochastic models, which usually led to thin-tailed or bounded distributions for the particle-transport rate. Experimental observations together with field surveys suggest that particle-transport rate exhibits frequent and large fluctuations, in particular at low flow rates (i.e., when the bottom shear just exceeds the threshold of incipient motion), which cannot be described using classic distributions used so far for modelling bedload transport (e.g., Hamamori's distribution). The existence of these large and frequent fluctuations could offer a wide field of applications to fractional-derivative theory. Alternative approaches exist as well: in this talk, we explore the potentialities of a birth-death Markov model to model sediment transport within a fixed volume of control. Under steady-uniform-flow conditions, the model predicts that the number of moving particles inside the control volume follows a negative binomial distribution. Although this probability distribution does not enter the family of heavy-tailed distributions, it may give rise to large and frequent fluctuations. We investigate the consequences of these fluctuations on bed dynamics, more especially on the features (growth rate and probability distribution) of nascent bedforms that develop on initially planar beds as a result of intermittent bedload transport.

  4. Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

    NASA Technical Reports Server (NTRS)

    Nemec, Marian; Aftosmis,Michael J.

    2006-01-01

    Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach

  5. Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

    NASA Technical Reports Server (NTRS)

    Tucker, Paul G.; Rumsey, Christopher L.; Bartels, Robert E.; Biedron, Robert T.

    2003-01-01

    Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson s Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

  6. Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

    NASA Technical Reports Server (NTRS)

    Tucker, Paul G.; Rumsey, Christopher L.; Bartels, Robert E.; Biedron, Robert T.

    2003-01-01

    Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson's Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

  7. Generalized semi-analytical solutions to multispecies transport equation coupled with sequential first-order reaction network with spatially or temporally variable transport and decay coefficients

    NASA Astrophysics Data System (ADS)

    Suk, Heejun

    2016-08-01

    This paper presents a semi-analytical procedure for solving coupled the multispecies reactive solute transport equations, with a sequential first-order reaction network on spatially or temporally varying flow velocities and dispersion coefficients involving distinct retardation factors. This proposed approach was developed to overcome the limitation reported by Suk (2013) regarding the identical retardation values for all reactive species, while maintaining the extensive capability of the previous Suk method involving spatially variable or temporally variable coefficients of transport, general initial conditions, and arbitrary temporal variable inlet concentration. The proposed approach sequentially calculates the concentration distributions of each species by employing only the generalized integral transform technique (GITT). Because the proposed solutions for each species' concentration distributions have separable forms in space and time, the solution for subsequent species (daughter species) can be obtained using only the GITT without the decomposition by change-of-variables method imposing the limitation of identical retardation values for all the reactive species by directly substituting solutions for the preceding species (parent species) into the transport equation of subsequent species (daughter species). The proposed solutions were compared with previously published analytical solutions or numerical solutions of the numerical code of the Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) in three verification examples. In these examples, the proposed solutions were well matched with previous analytical solutions and the numerical solutions obtained by 2DFATMIC model. A hypothetical single-well push-pull test example and a scale-dependent dispersion example were designed to demonstrate the practical application of the proposed solution to a real field problem.

  8. Ocean acoustic tomography from different receiver geometries using the adjoint method.

    PubMed

    Zhao, Xiaofeng; Wang, Dongxiao

    2015-12-01

    In this paper, an ocean acoustic tomography inversion using the adjoint method in a shallow water environment is presented. The propagation model used is an implicit Crank-Nicolson finite difference parabolic equation solver with a non-local boundary condition. Unlike previous matched-field processing works using the complex pressure fields as the observations, here, the observed signals are the transmission losses. Based on the code tests of the tangent linear model, the adjoint model, and the gradient, the optimization problem is solved by a gradient-based minimization algorithm. The inversions are performed in numerical simulations for two geometries: one in which hydrophones are sparsely distributed in the horizontal direction, and another in which the hydrophones are distributed vertically. The spacing in both cases is well beyond the half-wavelength threshold at which beamforming could be used. To deal with the ill-posedness of the inverse problem, a linear differential regularization operator of the sound-speed profile is used to smooth the inversion results. The L-curve criterion is adopted to select the regularization parameter, and the optimal value can be easily determined at the elbow of the logarithms of the residual norm of the measured-predicted fields and the norm of the penalty function. PMID:26723329

  9. Solid oxide fuel cell simulation and design optimization with numerical adjoint techniques

    NASA Astrophysics Data System (ADS)

    Elliott, Louie C.

    This dissertation reports on the application of numerical optimization techniques as applied to fuel cell simulation and design. Due to the "multi-physics" inherent in a fuel cell, which results in a highly coupled and non-linear behavior, an experimental program to analyze and improve the performance of fuel cells is extremely difficult. This program applies new optimization techniques with computational methods from the field of aerospace engineering to the fuel cell design problem. After an overview of fuel cell history, importance, and classification, a mathematical model of solid oxide fuel cells (SOFC) is presented. The governing equations are discretized and solved with computational fluid dynamics (CFD) techniques including unstructured meshes, non-linear solution methods, numerical derivatives with complex variables, and sensitivity analysis with adjoint methods. Following the validation of the fuel cell model in 2-D and 3-D, the results of the sensitivity analysis are presented. The sensitivity derivative for a cost function with respect to a design variable is found with three increasingly sophisticated techniques: finite difference, direct differentiation, and adjoint. A design cycle is performed using a simple optimization method to improve the value of the implemented cost function. The results from this program could improve fuel cell performance and lessen the world's dependence on fossil fuels.

  10. Adjoint Optimization of Multistage Axial Compressor Blades with Static Pressure Constraint at Blade Row Interface

    NASA Astrophysics Data System (ADS)

    Yu, Jia; Ji, Lucheng; Li, Weiwei; Yi, Weilin

    2016-06-01

    Adjoint method is an important tool for design refinement of multistage compressors. However, the radial static pressure distribution deviates during the optimization procedure and deteriorates the overall performance, producing final designs that are not well suited for realistic engineering applications. In previous development work on multistage turbomachinery blade optimization using adjoint method and thin shear-layer N-S equations, the entropy production is selected as the objective function with given mass flow rate and total pressure ratio as imposed constraints. The radial static pressure distribution at the interfaces between rows is introduced as a new constraint in the present paper. The approach is applied to the redesign of a five-stage axial compressor, and the results obtained with and without the constraint on the radial static pressure distribution at the interfaces between rows are discussed in detail. The results show that the redesign without the radial static pressure distribution constraint (RSPDC) gives an optimal solution that shows deviations on radial static pressure distribution, especially at rotor exit tip region. On the other hand, the redesign with the RSPDC successfully keeps the radial static pressure distribution at the interfaces between rows and make sure that the optimization results are applicable in a practical engineering design.

  11. Generalized linear Boltzmann equation, describing non-classical particle transport, and related asymptotic solutions for small mean free paths

    NASA Astrophysics Data System (ADS)

    Rukolaine, Sergey A.

    2016-05-01

    In classical kinetic models a particle free path distribution is exponential, but this is more likely to be an exception than a rule. In this paper we derive a generalized linear Boltzmann equation (GLBE) for a general free path distribution in the framework of Alt's model. In the case that the free path distribution has at least first and second finite moments we construct an asymptotic solution to the initial value problem for the GLBE for small mean free paths. In the special case of the one-speed transport problem the asymptotic solution results in a diffusion approximation to the GLBE.

  12. A Piecewise Linear Discontinuous Finite Element Spatial Discretization of the Transport Equation in 2D Cylindrical Geometry

    SciTech Connect

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

    2008-10-01

    We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional cylindrical (RZ) geometry for arbitrary polygonal meshes. This discretization is a discontinuous finite element method that utilizes the piecewise linear basis functions developed by Stone and Adams. We describe an asymptotic analysis that shows this method to be accurate for many problems in the thick diffusion limit on arbitrary polygons, allowing this method to be applied to radiative transfer problems with these types of meshes. We also present numerical results for multiple problems on quadrilateral grids and compare these results to the well-known bi-linear discontinuous finite element method.

  13. Comparison of solutions to bi-Maxwellian and Maxwellian transport equations for subsonic flows. [in terrestrial ionosphere

    NASA Technical Reports Server (NTRS)

    Demars, H. G.; Schunk, R. W.

    1987-01-01

    Conditions corresponding to the steady state subsonic flow of a fully ionized electron-proton plasma in the terrestrial ionosphere are presently characterized by systematically comparing the solutions to the bi-Maxwellian-based 16-moment and Maxwellian-based 13-moment transport equations. The former can account for large temperature anisotropies and the flow of both parallel and perpendicular thermal energy, while the latter account for small temperature anisotropies and only a total heat flow. The comparison is conducted for 2000-10,000 K lower boundary temperatures and 1-4-K/km temperature gradients, over the 1500-13,000-km altitude range.

  14. Numerical modeling of photon migration in the cerebral cortex of the living rat using the radiative transport equation

    NASA Astrophysics Data System (ADS)

    Fujii, Hiroyuki; Okawa, Shinpei; Nadamoto, Ken; Okada, Eiji; Yamada, Yukio; Hoshi, Yoko; Watanabe, Masao

    2015-03-01

    Accurate modeling and efficient calculation of photon migration in biological tissues is requested for determination of the optical properties of living tissues by in vivo experiments. This study develops a calculation scheme of photon migration for determination of the optical properties of the rat cerebral cortex (ca 0.2 cm thick) based on the three-dimensional time-dependent radiative transport equation assuming a homogeneous object. It is shown that the time-resolved profiles calculated by the developed scheme agree with the profiles measured by in vivo experiments using near infrared light. Also, an efficient calculation method is tested using the delta-Eddington approximation of the scattering phase function.

  15. Transport equation in the problem of the distribution function of nanoparticles in a colloidal solution exposed to laser pulses

    NASA Astrophysics Data System (ADS)

    Kirichenko, N. A.; Shcherbina, M. E.; Serkov, A. A.; Rakov, I. I.

    2015-12-01

    The behaviour of a colloidal solution of gold nanoparticles irradiated by a repetitively pulsed laser with a pulse duration of a few nanoseconds is investigated theoretically and experimentally. A mathematical model is constructed, which allows the behaviour of the nanoparticle distribution function to be described. The model is based on the transport equation in the 'space' of particle sizes. The proposed model allows for a relatively simple study and makes it possible to establish some common patterns in the behaviour of an ensemble of nanoparticles under various conditions. The results obtained are in satisfactory agreement with the available experimental data.

  16. Gliders Measure Western Boundary Current Transport from the South Pacific to the Equator

    NASA Astrophysics Data System (ADS)

    Davis, R. E.; Kessler, W. S.; Sherman, J. T.

    2011-12-01

    Since 2007, the Consortium on the Ocean's Role in Climate (CORC) has used repeated glider transects across the southern Solomon Sea to measure the previously nearly unsampled mass and heat transport from the South Pacific to the equatorial zone. Mean transport is dominated by the New Guinea Coastal Undercurrent (NGCUC). This low-latitude western boundary current is a major element of the shallow meridional overturning circulation, returning water from the subtropical South Pacific to the Equatorial Undercurrent (EUC) where it upwells. We find the mean NGCUC to be a jet less than 100 km wide, centered near 300 m depth, with equatorward velocities reaching 35 cm/s and salinity anomalies on isopycnals up to 0.05. Weaker poleward flow is found near the surface in the eastern basin. Equatorward transport above 700 m is typically 20 Sv, but nearly vanished during two La Niñas and reached 25 Sv during an El Niño. Within these events the seasonal cycle cannot yet be defined. Transport variability is strongest outside the boundary current and appears to consist of two independently moving layers with a boundary near 250 m. ENSO variability is predominantly in the upper layer. The relation of Solomon Sea mass and heat transport with ENSO indicators will be discussed The ability to initiate and maintain measurements that support such quantitative analyses with a small effort in a remote site far from research institutions demonstrates that gliders can be a productive part of the global ocean observing system.

  17. Transport properties and equation of state for HCNO mixtures in and beyond the warm dense matter regime

    SciTech Connect

    Ticknor, Christopher; Collins, Lee A.; Kress, Joel D.

    2015-08-04

    We present simulations of a four component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5–200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. In addition, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based on the Coulomb coupling parameter and one-component plasmas.

  18. Transport properties and equation of state for HCNO mixtures in and beyond the warm dense matter regime

    DOE PAGESBeta

    Ticknor, Christopher; Collins, Lee A.; Kress, Joel D.

    2015-08-04

    We present simulations of a four component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5–200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. In addition, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based onmore » the Coulomb coupling parameter and one-component plasmas.« less

  19. Assimilating Remote Ammonia Observations with a Refined Aerosol Thermodynamics Adjoint"

    EPA Science Inventory

    Ammonia emissions parameters in North America can be refined in order to improve the evaluation of modeled concentrations against observations. Here, we seek to do so by developing and applying the GEOS-Chem adjoint nested over North America to conductassimilation of observations...

  20. Reconstruction of ocean circulation from sparse data using the adjoint method: LGM and the present

    NASA Astrophysics Data System (ADS)

    Kurahashi-Nakamura, T.; Losch, M. J.; Paul, A.; Mulitza, S.; Schulz, M.

    2010-12-01

    Understanding the behavior of the Earth's climate system under different conditions in the past is the basis for more robust projections of future climate. It is thought that the ocean circulation plays a very important role in the climate system, because it can greatly affect climate by dynamic-thermodynamic (as a medium of heat transport) and biogeochemical processes (by affecting the global carbon cycle). In this context, studying the period of the Last Glacial Maximum (LGM) is particularly promising, as it represents a climate state that is very different from today. Furthermore the LGM, compared to other paleoperiods, is characterized by a relatively good paleo-data coverage. Unfortunately, the ocean circulation during the LGM is still uncertain, with a range of climate models estimating both a stronger and a weaker formation rate of North Atlantic Deep Water (NADW) as compared to the present rate. Here, we present a project aiming at reducing this uncertainty by combining proxy data with a numerical ocean model using variational techniques. Our approach, the so-called adjoint method, employs a quadratic cost function of model-data differences weighted by their prior error estimates. We seek an optimal state estimate at the global minimum of the cost function by varying the independent control variables such as initial conditions (e.g. temperature), boundary conditions (e.g. surface winds, heat flux), or internal parameters (e.g. vertical diffusivity). The adjoint or dual model computes the gradient of the cost function with respect to these control variables and thus provides the information required by gradient descent algorithms. The gradients themselves provide valuable information about the sensitivity of the system to perturbations in the control variables. We use the Massachusetts Institute of Technology ocean general circulation model (MITgcm) with a cubed-sphere grid system that avoids converging grid lines and pole singularities. This model code is

  1. Discontinuous Galerkin discretization of the Reynolds-averaged Navier-Stokes equations with the shear-stress transport model

    NASA Astrophysics Data System (ADS)

    Schoenawa, Stefan; Hartmann, Ralf

    2014-04-01

    In this article we consider the development of Discontinuous Galerkin (DG) methods for the numerical approximation of the Reynolds-averaged Navier-Stokes (RANS) equations with the shear-stress transport (SST) model by Menter. This turbulence model is based on a blending of the Wilcox k-ω model used near the wall and the k-ɛ model used in the rest of the domain where the blending functions depend on the distance to the nearest wall. For the computation of the distance of each quadrature point in the domain to the nearest of the curved, piecewise polynomial wall boundaries, we propose a stabilized continuous finite element (FE) discretization of the eikonal equation. Furthermore, we propose a new wall boundary condition for the dissipation rate ω based on the projection of the analytic near-wall behavior of ω onto the discrete ansatz space of the DG discretization. Finally, we introduce an artificial viscosity to the discretization of the turbulence kinetic energy (k-)equation to suppress oscillations of k near the underresolved boundary layer edge. The wall distance computation based on the continuous FE discretization of the eikonal equation is demonstrated for an internal and three external/aerodynamic flow geometries including a three-element high-lift configuration. The DG discretization of the RANS equations with the SST model is demonstrated for turbulent flows past a flat plate and the RAE2822 airfoil (Cases 9 and 10). The results are compared to the underlying k-ω model and experimental data.

  2. Heat flux solutions of the 13-moment approximation transport equations in a multispecies gas

    SciTech Connect

    Jian Wu; Taieb, C.

    1993-09-01

    The authors study steady state heat flux equations by means of the 13-moment approximation for situations applicable to aeronomy and space plasmas. They compare their results with Fourier`s law applied to similar problems, to test validity conditions for it. They look at the flux of oxygen and hydrogen ions in the high-latitude ionosphere, and compare calculations with observations from EISCAT radar measurements. These plasma components are observed to have strongly non-Maxwellian distributions.

  3. A solution of the monoenergetic neutral particle transport equation for adjacent half-spaces with anisotropic scattering

    NASA Astrophysics Data System (ADS)

    Ganapol, B. D.; Mostacci, D.; Previti, A.

    2016-07-01

    We present highly accurate solutions to the neutral particle transport equation in a half-space. While our initial motivation was in response to a recently published solution based on Chandrasekhar's H-function, the presentation to follow has taken on a more comprehensive tone. The solution by H-functions certainly did achieved high accuracy but was limited to isotropic scattering and emission from spatially uniform and linear sources. Moreover, the overly complicated nature of the H-function approach strongly suggests that its extension to anisotropic scattering and general sources is not at all practical. For this reason, an all encompassing theory for the determination of highly precise benchmarks, including anisotropic scattering for a variety of spatial source distributions, is presented for particle transport in a half-space. We illustrate the approach via a collection of cases including tables of 7-place flux benchmarks to guide transport methods developers. The solution presented can be applied to a considerable number of one and two half-space transport problems with variable sources and represents a state-of-the-art benchmark solution.

  4. Effective ionization coefficients and transport parameters in binary and ultradilute SF6-Ar mixtures using Boltzmann equation analysis

    NASA Astrophysics Data System (ADS)

    Cekmen, Z. C.; Dincer, M. S.

    2009-07-01

    The effective ionization coefficients and transport parameters such as electron mean energy drift velocity and transverse diffusion coefficient in binary and ultradilute SF6-Ar gas mixtures have been calculated for density reduced electric field strength E/N values from 10 to 400 Td. These calculations have been performed by using the two-term spherical harmonic expansion to obtain the numerical solution of the Boltzmann transport equation based on the finite element method under steady-state Townsend condition. In order to confirm the model and code developed in this study, the Reid ramp model has been used as a benchmark test and then effective ionization coefficients and transport parameters have been evaluated for SF6 contents of 1%, 10%, 25%, 50%, 70% and 100% in the binary mixture. Finally SF6 contents in the ultradilute mixtures of 0.1%, 0.3%, 0.5% and 0.7% are taken into account with the evaluated effective ionizations and transport parameters of electron mean energy, drift velocity and transverse diffusion coefficients.

  5. Sources and processes contributing to nitrogen deposition: an adjoint model analysis applied to biodiversity hotspots worldwide.

    PubMed

    Paulot, Fabien; Jacob, Daniel J; Henze, Daven K

    2013-04-01

    Anthropogenic enrichment of reactive nitrogen (Nr) deposition is an ecological concern. We use the adjoint of a global 3-D chemical transport model (GEOS-Chem) to identify the sources and processes that control Nr deposition to an ensemble of biodiversity hotspots worldwide and two U.S. national parks (Cuyahoga and Rocky Mountain). We find that anthropogenic sources dominate deposition at all continental sites and are mainly regional (less than 1000 km) in origin. In Hawaii, Nr supply is controlled by oceanic emissions of ammonia (50%) and anthropogenic sources (50%), with important contributions from Asia and North America. Nr deposition is also sensitive in complicated ways to emissions of SO2, which affect Nr gas-aerosol partitioning, and of volatile organic compounds (VOCs), which affect oxidant concentrations and produce organic nitrate reservoirs. For example, VOC emissions generally inhibit deposition of locally emitted NOx but significantly increase Nr deposition downwind. However, in polluted boreal regions, anthropogenic VOC emissions can promote Nr deposition in winter. Uncertainties in chemical rate constants for OH + NO2 and NO2 hydrolysis also complicate the determination of source-receptor relationships for polluted sites in winter. Application of our adjoint sensitivities to the representative concentration pathways (RCPs) scenarios for 2010-2050 indicates that future decreases in Nr deposition due to NOx emission controls will be offset by concurrent increases in ammonia emissions from agriculture. PMID:23458244

  6. Seeking Energy System Pathways to Reduce Ozone Damage to Ecosystems through Adjoint-based Sensitivity Analysis

    NASA Astrophysics Data System (ADS)

    Capps, S. L.; Pinder, R. W.; Loughlin, D. H.; Bash, J. O.; Turner, M. D.; Henze, D. K.; Percell, P.; Zhao, S.; Russell, M. G.; Hakami, A.

    2014-12-01

    Tropospheric ozone (O3) affects the productivity of ecosystems in addition to degrading human health. Concentrations of this pollutant are significantly influenced by precursor gas emissions, many of which emanate from energy production and use processes. Energy system optimization models could inform policy decisions that are intended to reduce these harmful effects if the contribution of precursor gas emissions to human health and ecosystem degradation could be elucidated. Nevertheless, determining the degree to which precursor gas emissions harm ecosystems and human health is challenging because of the photochemical production of ozone and the distinct mechanisms by which ozone causes harm to different crops, tree species, and humans. Here, the adjoint of a regional chemical transport model is employed to efficiently calculate the relative influences of ozone precursor gas emissions on ecosystem and human health degradation, which informs an energy system optimization. Specifically, for the summer of 2007 the Community Multiscale Air Quality (CMAQ) model adjoint is used to calculate the location- and sector-specific influences of precursor gas emissions on potential productivity losses for the major crops and sensitive tree species as well as human mortality attributable to chronic ozone exposure in the continental U.S. The atmospheric concentrations are evaluated with 12-km horizontal resolution with crop production and timber biomass data gridded similarly. These location-specific factors inform the energy production and use technologies selected in the MARKet ALlocation (MARKAL) model.

  7. Symmetries and nonlocal conservation laws of the general magma equation

    NASA Astrophysics Data System (ADS)

    Khamitova, Raisa

    2009-11-01

    In this paper the general magma equation modelling a melt flow in the Earth's mantle is discussed. Applying the new theorem on nonlocal conservation laws [Ibragimov NH. A new conservation theorem. J Math Anal Appl 2007;333(1):311-28] and using the symmetries of the model equation nonlocal conservation laws are computed. In accordance with Ibragimov [Ibragimov NH. Quasi-self-adjoint differential equations. Preprint in Archives of ALGA, vol. 4, BTH, Karlskrona, Sweden: Alga Publications; 2007. p. 55-60, ISSN: 1652-4934] it is shown that the general magma equation is quasi-self-adjoint for arbitrary m and n and self-adjoint for n = -m. These important properties are used for deriving local conservation laws.

  8. Adaptive mesh refinement and adjoint methods in geophysics simulations

    NASA Astrophysics Data System (ADS)

    Burstedde, Carsten

    2013-04-01

    required by human intervention and analysis. Specifying an objective functional that quantifies the misfit between the simulation outcome and known constraints and then minimizing it through numerical optimization can serve as an automated technique for parameter identification. As suggested by the similarity in formulation, the numerical algorithm is closely related to the one used for goal-oriented error estimation. One common point is that the so-called adjoint equation needs to be solved numerically. We will outline the derivation and implementation of these methods and discuss some of their pros and cons, supported by numerical results.

  9. Steady state and modulated heat conduction in layered systems predicted by the analytical solution of the phonon Boltzmann transport equation

    NASA Astrophysics Data System (ADS)

    Ordonez-Miranda, Jose; Yang, Ronggui; Volz, Sebastian; Alvarado-Gil, J. J.

    2015-08-01

    Based on the phonon Boltzmann transport equation under the relaxation time approximation, analytical expressions for the temperature profiles of both the steady state and modulated heat conduction inside a thin film deposited on a substrate are derived and analyzed. It is shown that these components of the temperature depend strongly on the ratio between the film thickness and the average phonon mean free path (MFP), and they exhibit the diffusive behavior as predicted by the Fourier's law of heat conduction when this ratio is much larger than unity. In contrast, in the ballistic regime when this ratio is comparable to or smaller than unity, the steady-state temperature tends to be independent of position, while the amplitude and the phase of the modulated temperature appear to be lower than those determined by the Fourier's law. Furthermore, we derive an invariant of heat conduction and a simple formula for the cross-plane thermal conductivity of dielectric thin films, which could be a useful guide for understanding and optimizing the thermal performance of the layered systems. This work represents the Boltzmann transport equation-based extension of the Rosencwaig and Gersho work [J. Appl. Phys. 47, 64 (1976)], which is based on the Fourier's law and has widely been used as the theoretical framework for the development of photoacoustic and photothermal techniques. This work might shed some light on developing a theoretical basis for the determination of the phonon MFP and relaxation time using ultrafast laser-based transient heating techniques.

  10. An upscaled two-equation model of transport in porous media through unsteady-state closure of volume averaged formulations

    NASA Astrophysics Data System (ADS)

    Chaynikov, S.; Porta, G.; Riva, M.; Guadagnini, A.

    2012-04-01

    We focus on a theoretical analysis of nonreactive solute transport in porous media through the volume averaging technique. Darcy-scale transport models based on continuum formulations typically include large scale dispersive processes which are embedded in a pore-scale advection diffusion equation through a Fickian analogy. This formulation has been extensively questioned in the literature due to its inability to depict observed solute breakthrough curves in diverse settings, ranging from the laboratory to the field scales. The heterogeneity of the pore-scale velocity field is one of the key sources of uncertainties giving rise to anomalous (non-Fickian) dispersion in macro-scale porous systems. Some of the models which are employed to interpret observed non-Fickian solute behavior make use of a continuum formulation of the porous system which assumes a two-region description and includes a bimodal velocity distribution. A first class of these models comprises the so-called ''mobile-immobile'' conceptualization, where convective and dispersive transport mechanisms are considered to dominate within a high velocity region (mobile zone), while convective effects are neglected in a low velocity region (immobile zone). The mass exchange between these two regions is assumed to be controlled by a diffusive process and is macroscopically described by a first-order kinetic. An extension of these ideas is the two equation ''mobile-mobile'' model, where both transport mechanisms are taken into account in each region and a first-order mass exchange between regions is employed. Here, we provide an analytical derivation of two region "mobile-mobile" meso-scale models through a rigorous upscaling of the pore-scale advection diffusion equation. Among the available upscaling methodologies, we employ the Volume Averaging technique. In this approach, the heterogeneous porous medium is supposed to be pseudo-periodic, and can be represented through a (spatially) periodic unit cell

  11. Improved forward wave propagation and adjoint-based sensitivity kernel calculations using a numerically stable finite-element PML

    NASA Astrophysics Data System (ADS)

    Xie, Zhinan; Komatitsch, Dimitri; Martin, Roland; Matzen, René

    2014-09-01

    In recent years, the application of time-domain adjoint methods to improve large, complex underground tomographic models at the regional scale has led to new challenges for the numerical simulation of forward or adjoint elastic wave propagation problems. An important challenge is to design an efficient infinite-domain truncation method suitable for accurately truncating an infinite domain governed by the second-order elastic wave equation written in displacement and computed based on a finite-element (FE) method. In this paper, we make several steps towards this goal. First, we make the 2-D convolution formulation of the complex-frequency-shifted unsplit-field perfectly matched layer (CFS-UPML) derived in previous work more flexible by providing a new treatment to analytically remove singular parameters in the formulation. We also extend this new formulation to 3-D. Furthermore, we derive the auxiliary differential equation (ADE) form of CFS-UPML, which allows for extension to higher order time schemes and is easier to implement. Secondly, we rigorously derive the CFS-UPML formulation for time-domain adjoint elastic wave problems, which to our knowledge has never been done before. Thirdly, in the case of classical low-order FE methods, we show numerically that we achieve long-time stability for both forward and adjoint problems both for the convolution and the ADE formulations. In the case of higher order Legendre spectral-element methods, we show that weak numerical instabilities can appear in both formulations, in particular if very small mesh elements are present inside the absorbing layer, but we explain how these instabilities can be delayed as much as needed by using a stretching factor to reach numerical stability in practice for applications. Fourthly, in the case of adjoint problems with perfectly matched absorbing layers we introduce a computationally efficient boundary storage strategy by saving information along the interface between the CFS-UPML and

  12. Evolution of the ultra high energy cosmic ray spectrum by transport equation

    SciTech Connect

    Hill, C.T.; Schramm, D.N.

    1983-04-01

    Ultra-high energy proton primaries interacting with the 3/sup 0/K photon background are treated as a transport phenomenon. Baryon number is explicitly conserved and the evolved spectrum develops a bump at a scale of order 5x10/sup 19/ eV, below the cutoff, due to the pile-up of energy degraded protons. This may correspond in part to the observed ankle structure in the CR spectrum.

  13. High-resolution mapping of sources contributing to urban air pollution using adjoint sensitivity analysis: benzene and diesel black carbon.

    PubMed

    Bastien, Lucas A J; McDonald, Brian C; Brown, Nancy J; Harley, Robert A

    2015-06-16

    The adjoint of the Community Multiscale Air Quality (CMAQ) model at 1 km horizontal resolution is used to map emissions that contribute to ambient concentrations of benzene and diesel black carbon (BC) in the San Francisco Bay area. Model responses of interest include population-weighted average concentrations for three highly polluted receptor areas and the entire air basin. We consider both summer (July) and winter (December) conditions. We introduce a novel approach to evaluate adjoint sensitivity calculations that complements existing methods. Adjoint sensitivities to emissions are found to be accurate to within a few percent, except at some locations associated with large sensitivities to emissions. Sensitivity of model responses to emissions is larger in winter, reflecting weaker atmospheric transport and mixing. The contribution of sources located within each receptor area to the same receptor's air pollution burden increases from 38-74% in summer to 56-85% in winter. The contribution of local sources is higher for diesel BC (62-85%) than for benzene (38-71%), reflecting the difference in these pollutants' atmospheric lifetimes. Morning (6-9am) and afternoon (4-7 pm) commuting-related emissions dominate region-wide benzene levels in winter (14 and 25% of the total response, respectively). In contrast, afternoon rush hour emissions do not contribute significantly in summer. Similar morning and afternoon peaks in sensitivity to emissions are observed for the BC response; these peaks are shifted toward midday because most diesel truck traffic occurs during off-peak hours. PMID:26001097

  14. Investigating troposhpere-stratosphere coupling during the southern hemisphere sudden stratospheric warming using an adjoint model.

    NASA Astrophysics Data System (ADS)

    Holdaway, D.; Coy, L.

    2015-12-01

    In September 2002 a major sudden stratospheric warming (SSW) occurred in the southern hemisphere. Although numerous SSWs have been observed in the northern hemisphere, this remains the only recorded major SSW in the southern hemisphere. Much debate has focused on this unique event and the causes, even resulting in a special issue of the Journal of Atmospheric Science. In this work we use the adjoint of NASA's Goddard Earth Observing System version 5 (GEOS-5) to investigate sensitivity to initial conditions during the onset of the 2002 SSW. The adjoint model provides a framework for propagating gradients with respect to the model state backwards in time. As such it is used to reveal aspects of the model initial conditions that have the biggest impact on the temperature in the stratosphere during the warming. The adjoint model reveals a large sensitivity over the southern Atlantic ocean and in the troposphere. This reinforces previous studies that attributed the SSW to a blocking ridge in this region. By converting sensitivity to perturbations it is shown that relatively small localized tropospheric perturbations to winds and temperature can be transported to the stratosphere and have a large impact on the SSW.

  15. Adjoint Method and Predictive Control for 1-D Flow in NASA Ames 11-Foot Transonic Wind Tunnel

    NASA Technical Reports Server (NTRS)

    Nguyen, Nhan; Ardema, Mark

    2006-01-01

    This paper describes a modeling method and a new optimal control approach to investigate a Mach number control problem for the NASA Ames 11-Foot Transonic Wind Tunnel. The flow in the wind tunnel is modeled by the 1-D unsteady Euler equations whose boundary conditions prescribe a controlling action by a compressor. The boundary control inputs to the compressor are in turn controlled by a drive motor system and an inlet guide vane system whose dynamics are modeled by ordinary differential equations. The resulting Euler equations are thus coupled to the ordinary differential equations via the boundary conditions. Optimality conditions are established by an adjoint method and are used to develop a model predictive linear-quadratic optimal control for regulating the Mach number due to a test model disturbance during a continuous pitch

  16. Estimates of black carbon emissions in the western United States using the GEOS-Chem adjoint model

    NASA Astrophysics Data System (ADS)

    Mao, Y. H.; Li, Q. B.; Henze, D. K.; Jiang, Z.; Jones, D. B. A.; Kopacz, M.; He, C.; Qi, L.; Gao, M.; Hao, W.-M.; Liou, K.-N.

    2015-07-01

    We estimate black carbon (BC) emissions in the western United States for July-September 2006 by inverting surface BC concentrations from the Interagency Monitoring of Protected Visual Environments (IMPROVE) network using a global chemical transport model (GEOS-Chem) and its adjoint. Our best estimate of the BC emissions is 49.9 Gg at 2° × 2.5° (a factor of 2.1 increase) and 47.3 Gg at 0.5° × 0.667° (1.9 times increase). Model results now capture the observed major fire episodes with substantial bias reductions ( 35 % at 2° × 2.5° and 15 % at 0.5° × 0.667°). The emissions are 20-50 % larger than those from our earlier analytical inversions (Mao et al., 2014). The discrepancy is especially drastic in the partitioning of anthropogenic versus biomass burning emissions. The August biomass burning BC emissions are 4.6-6.5 Gg and anthropogenic BC emissions 8.6-12.8 Gg, varying with the model resolution, error specifications, and subsets of observations used. On average both anthropogenic and biomass burning emissions in the adjoint inversions increase 2-fold relative to the respective {a priori} emissions, in distinct contrast to the halving of the anthropogenic and tripling of the biomass burning emissions in the analytical inversions. We attribute these discrepancies to the inability of the adjoint inversion system, with limited spatiotemporal coverage of the IMPROVE observations, to effectively distinguish collocated anthropogenic and biomass burning emissions on model grid scales. This calls for concurrent measurements of other tracers of biomass burning and fossil fuel combustion (e.g., carbon monoxide and carbon isotopes). We find that the adjoint inversion system as is has sufficient information content to constrain the total emissions of BC on the model grid scales.

  17. Stochastic modeling in sediment dynamics: Exner equation for planar bed incipient bed load transport conditions

    NASA Astrophysics Data System (ADS)

    Ancey, Christophe

    2010-06-01

    Even under flow equilibrium conditions, river bed topography continuously evolves with time, producing trains of irregular bed forms. The idea has recently emerged that the variability in the bed form geometry results from some randomness in sediment flux. In this paper, we address this issue by using the Exner equation and a population exchange model derived in an earlier paper. In this model, particle entrainment and deposition are idealized as population exchanges between the stream and the bed, which makes it possible to use birth-death Markov process theory to track the number of moving grains. The paper focuses on nascent bed forms on initially planar beds, a situation in which the coupling between the stream and bed is weak. In a steady state, the number of moving particles follows a negative binomial distribution. Although this probability distribution does not enter the family of heavy-tailed distributions, it may give rise to large and frequent fluctuations because the standard deviation can be much larger than the mean, a feature that is not accounted for with classic probability laws (e.g., Hamamori's law) used so far for describing bed load fluctuations. In the large-system limit, the master equation of the birth-death Markov process can be transformed into a Fokker-Planck equation. This transformation is used here to show that the number of moving particles can be described as an Ornstein-Uhlenbeck process. An important consequence is that in the long term, the number of moving particles follows a Gaussian distribution. Laboratory experiments show that this approximation is correct when the mean number per unit length of stream, ?/L, is sufficiently large (typically two particles per centimeter in our experiments). The particle number fluctuations give rise to bed elevation fluctuations, whose spectrum falls off like ω-2 in the high-frequency regime (with ω the angular frequency) and variance grows linearly with time. These features are in agreement

  18. High speed transport cruise drag. [scaling laws using Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Roberts, Leonard

    1992-01-01

    This report provides scaling laws for the cruise aerodynamics of high speed transport wings based on the results of Navier-Stokes computations. Expressions for the various drag components are found, together with the corresponding values (L/D)(sub m) for various values of the geometric parameter s/l which allow for simple optimization of the wing configurations with respect to the span. It is found that linear theory expressions can be used for this purpose provided the coefficients of these experiments for C(sub D) and (L/D)(sub m) are available using Navier-Stokes results.

  19. Parallel multigrid solver of radiative transfer equation for photon transport via graphics processing unit.

    PubMed

    Gao, Hao; Phan, Lan; Lin, Yuting

    2012-09-01

    A graphics processing unit-based parallel multigrid solver for a radiative transfer equation with vacuum boundary condition or reflection boundary condition is presented for heterogeneous media with complex geometry based on two-dimensional triangular meshes or three-dimensional tetrahedral meshes. The computational complexity of this parallel solver is linearly proportional to the degrees of freedom in both angular and spatial variables, while the full multigrid method is utilized to minimize the number of iterations. The overall gain of speed is roughly 30 to 300 fold with respect to our prior multigrid solver, which depends on the underlying regime and the parallelization. The numerical validations are presented with the MATLAB codes at https://sites.google.com/site/rtefastsolver/. PMID:23085905

  20. Appearances of pseudo-bosons from Black-Scholes equation

    NASA Astrophysics Data System (ADS)

    Bagarello, F.

    2016-04-01

    It is a well known fact that the Black-Scholes equation admits an alternative representation as a Schrödinger equation expressed in terms of a non-self-adjoint Hamiltonian. We show how pseudo-bosons, linear or not, naturally arise in this context, and how they can be used in the computation of the pricing kernel.

  1. Orbit-averaged drift kinetic equation for the study of alpha-particle transport in tokamaks

    SciTech Connect

    Sager, G.T.; Miley, G.H. . Fusion Studies Lab.); Burrell, K.H. )

    1990-11-01

    Neoclassical transport of minority suprathermal alpha particles is investigated. This paper departs from previous investigations in that (a) the banana-width ordering parameter {rho}{sub {theta}}/L is not formally restricted to be a small parameter and (b) a linearized collision operator that retains the effects of pitch-angle scattering, electron and ion drag, and speed diffusion is used. A step model approximation for the large-aspect-ratio, circular-cross-section tokamak magnetic field is adopted to simplify the orbit-averaging procedure. Assuming that the suprathermal alphas are in the banana regime, an asymptotic expansion in {tau}{sub B}/{tau}{sub S} {much lt} l is carried out.

  2. Examination of Observation Impacts derived from OSEs and Adjoint Models

    NASA Technical Reports Server (NTRS)

    Gelaro, Ronald

    2008-01-01

    With the adjoint of a data assimilation system, the impact of any or all assimilated observations on measures of forecast skill can be estimated accurately and efficiently. The approach allows aggregation of results in terms of individual data types, channels or locations, all computed simultaneously. In this study, adjoint-based estimates of observation impact are compared with results from standard observing system experiments (OSEs) in the NASA Goddard Earth Observing System Model, Version 5 (GEOS-5) GEOS-5 system. The two approaches are shown to provide unique, but complimentary, information. Used together, they reveal both redundancies and dependencies between observing system impacts as observations are added or removed. Understanding these dependencies poses a major challenge for optimizing the use of the current observational network and defining requirements for future observing systems.

  3. On improving storm surge forecasting using an adjoint optimal technique

    NASA Astrophysics Data System (ADS)

    Li, Yineng; Peng, Shiqiu; Yan, Jing; Xie, Lian

    2013-12-01

    A three-dimensional ocean model and its adjoint model are used to simultaneously optimize the initial conditions (IC) and the wind stress drag coefficient (Cd) for improving storm surge forecasting. To demonstrate the effect of this proposed method, a number of identical twin experiments (ITEs) with a prescription of different error sources and two real data assimilation experiments are performed. Results from both the idealized and real data assimilation experiments show that adjusting IC and Cd simultaneously can achieve much more improvements in storm surge forecasting than adjusting IC or Cd only. A diagnosis on the dynamical balance indicates that adjusting IC only may introduce unrealistic oscillations out of the assimilation window, which can be suppressed by the adjustment of the wind stress when simultaneously adjusting IC and Cd. Therefore, it is recommended to simultaneously adjust IC and Cd to improve storm surge forecasting using an adjoint technique.

  4. Transport in simple networks described by an integrable discrete nonlinear Schrödinger equation.

    PubMed

    Nakamura, K; Sobirov, Z A; Matrasulov, D U; Sawada, S

    2011-08-01

    We elucidate the case in which the Ablowitz-Ladik (AL)-type discrete nonlinear Schrödinger equation (NLSE) on simple networks (e.g., star graphs and tree graphs) becomes completely integrable just as in the case of a simple one-dimensional (1D) discrete chain. The strength of cubic nonlinearity is different from bond to bond, and networks are assumed to have at least two semi-infinite bonds with one of them working as an incoming bond. The present work is a nontrivial extension of our preceding one [Sobirov et al., Phys. Rev. E 81, 066602 (2010)] on the continuum NLSE to the discrete case. We find (1) the solution on each bond is a part of the universal (bond-independent) AL soliton solution on the 1D discrete chain, but it is multiplied by the inverse of the square root of bond-dependent nonlinearity; (2) nonlinearities at individual bonds around each vertex must satisfy a sum rule; and (3) under findings 1 and 2, there exist an infinite number of constants of motion. As a practical issue, with the use of an AL soliton injected through the incoming bond, we obtain transmission probabilities inversely proportional to the strength of nonlinearity on the outgoing bonds. PMID:21929130

  5. Fast linear solver for radiative transport equation with multiple right hand sides in diffuse optical tomography

    NASA Astrophysics Data System (ADS)

    Jia, Jingfei; Kim, Hyun K.; Hielscher, Andreas H.

    2015-12-01

    It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta-Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5-3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners.

  6. Equation of state and transport properties of warm dense helium via quantum molecular dynamics simulations

    NASA Astrophysics Data System (ADS)

    Li, Zhi-Guo; Cheng, Yan; Chen, Qi-Feng; Chen, Xiang-Rong

    2016-05-01

    The equation of state, self-diffusion, and viscosity coefficients of helium have been investigated by quantum molecular dynamics (QMD) simulations in the warm dense matter regime. Our simulations are validated through the comparison with the reliable experimental data. The calculated principal and reshock Hugoniots of liquid helium are in good agreement with the gas-gun data. On this basis, we revisit the issue for helium, i.e., the possibility of the instabilities predicted by chemical models at around 2000 GPa and 10 g/cm3 along the pressure isotherms of 6309, 15 849, and 31 623 K. Our calculations show no indications of instability in this pressure-temperature region, which reconfirm the predictions of previous QMD simulations. The self-diffusion and viscosity coefficients of warm dense helium have been systematically investigated by the QMD simulations. We carefully test the finite-size effects and convergences of statistics, and obtain numerically converged self-diffusion and viscosity coefficients by using the Kubo-Green formulas. The present results have been used to evaluate the existing one component plasma models. Finally, the validation of the Stokes-Einstein relationship for helium in the warm dense regime is discussed.

  7. Fast Solutions of Maxwell's Equation for High Resolution Electromagnetic Imaging of Transport Pathways

    SciTech Connect

    DAY,DAVID M.; NEWMAN,GREGORY A.

    1999-10-01

    A fast precondition technique has been developed which accelerates the finite difference solutions of the 3D Maxwell's equations for geophysical modeling. The technique splits the electric field into its curl free and divergence free projections, and allows for the construction of an inverse operator. Test examples show an order of magnitude speed up compared with a simple Jacobi preconditioner. Using this preconditioner a low frequency Neumann series expansion is developed and used to compute responses at multiple frequencies very efficiently. Simulations requiring responses at multiple frequencies, show that the Neumann series is faster than the preconditioned solution, which must compute solutions at each discrete frequency. A Neumann series expansion has also been developed in the high frequency limit along with spectral Lanczos methods in both the high and low frequency cases for simulating multiple frequency responses with maximum efficiency. The research described in this report was to have been carried out over a two-year period. Because of communication difficulties, the project was funded for first year only. Thus the contents of this report are incomplete with respect to the original project objectives.

  8. Gradient flipping algorithm: introducing non-convex constraints in wavefront reconstructions with the transport of intensity equation.

    PubMed

    Parvizi, A; Van den Broek, W; Koch, C T

    2016-04-18

    The transport of intensity equation (TIE) is widely applied for recovering wave fronts from an intensity measurement and a measurement of its variation along the direction of propagation. In order to get around the problem of non-uniqueness and ill-conditionedness of the solution of the TIE in the very common case of unspecified boundary conditions or noisy data, additional constraints to the solution are necessary. Although from a numerical optimization point of view, convex constraint as imposed to by total variation minimization is preferable, we will show that in many cases non-convex constraints are necessary to overcome the low-frequency artifacts so typical for convex constraints. We will provide simulated and experimental examples that demonstrate the superiority of solutions to the TIE obtained by our recently introduced gradient flipping algorithm over a total variation constrained solution. PMID:27137272

  9. Series integration of the diaphragm cell transport equation when the diffusion coefficient is a function of concentration

    NASA Technical Reports Server (NTRS)

    Cain, Judith B.; Baird, James K.

    1992-01-01

    An integral of the form, t = B0 + BL ln(Delta-c) + B1(Delta-c) + B2(Delta-c)-squared + ..., where t is the time and Delta-c is the concentration difference across the frit, is derived in the case of the diaphragm cell transport equation where the interdiffusion coefficient is a function of concentration. The coefficient, B0, is a constant of the integration, while the coefficients, BL, B1, B2,..., depend in general upon the constant, the compartment volumes, and the interdiffusion coefficient and various of its concentration derivatives evaluated at the mean concentration for the cell. Explicit formulas for BL, B1, B2,... are given.

  10. Fully automated, high speed, tomographic phase object reconstruction using the transport of intensity equation in transmission and reflection configurations.

    PubMed

    Nguyen, Thanh; Nehmetallah, George; Tran, Dat; Darudi, Ahmad; Soltani, Peyman

    2015-12-10

    While traditional transport of intensity equation (TIE) based phase retrieval of a phase object is performed through axial translation of the CCD, in this work a tunable lens TIE is employed in both transmission and reflection configurations. These configurations are extended to a 360° tomographic 3D reconstruction through multiple illuminations from different angles by a custom fabricated rotating assembly of the phase object. Synchronization circuitry is developed to control the CCD camera and the Arduino board, which in its turn controls the tunable lens and the stepper motor to automate the tomographic reconstruction process. Finally, a MATLAB based user friendly graphical user interface is developed to control the whole system and perform tomographic reconstruction using both multiplicative and inverse radon based techniques. PMID:26836869

  11. Phase retrieval with the transport-of-intensity equation in an arbitrarily-shaped aperture by iterative discrete cosine transforms

    DOE PAGESBeta

    Huang, Lei; Zuo, Chao; Idir, Mourad; Qu, Weijuan; Asundi, Anand

    2015-04-21

    A novel transport-of-intensity equation (TIE) based phase retrieval method is proposed with putting an arbitrarily-shaped aperture into the optical wavefield. In this arbitrarily-shaped aperture, the TIE can be solved under non-uniform illuminations and even non-homogeneous boundary conditions by iterative discrete cosine transforms with a phase compensation mechanism. Simulation with arbitrary phase, arbitrary aperture shape, and non-uniform intensity distribution verifies the effective compensation and high accuracy of the proposed method. Experiment is also carried out to check the feasibility of the proposed method in real measurement. Comparing to the existing methods, the proposed method is applicable for any types of phasemore » distribution under non-uniform illumination and non-homogeneous boundary conditions within an arbitrarily-shaped aperture, which enables the technique of TIE with hard aperture become a more flexible phase retrieval tool in practical measurements.« less

  12. Phase retrieval with the transport-of-intensity equation in an arbitrarily-shaped aperture by iterative discrete cosine transforms

    SciTech Connect

    Huang, Lei; Zuo, Chao; Idir, Mourad; Qu, Weijuan; Asundi, Anand

    2015-04-21

    A novel transport-of-intensity equation (TIE) based phase retrieval method is proposed with putting an arbitrarily-shaped aperture into the optical wavefield. In this arbitrarily-shaped aperture, the TIE can be solved under non-uniform illuminations and even non-homogeneous boundary conditions by iterative discrete cosine transforms with a phase compensation mechanism. Simulation with arbitrary phase, arbitrary aperture shape, and non-uniform intensity distribution verifies the effective compensation and high accuracy of the proposed method. Experiment is also carried out to check the feasibility of the proposed method in real measurement. Comparing to the existing methods, the proposed method is applicable for any types of phase distribution under non-uniform illumination and non-homogeneous boundary conditions within an arbitrarily-shaped aperture, which enables the technique of TIE with hard aperture become a more flexible phase retrieval tool in practical measurements.

  13. Seismic Window Selection and Misfit Measurements for Global Adjoint Tomography

    NASA Astrophysics Data System (ADS)

    Lei, W.; Bozdag, E.; Lefebvre, M.; Podhorszki, N.; Smith, J. A.; Tromp, J.

    2013-12-01

    Global Adjoint Tomography requires fast parallel processing of large datasets. After obtaing the preprocessed observed and synthetic seismograms, we use the open source software packages FLEXWIN (Maggi et al. 2007) to select time windows and MEASURE_ADJ to make measurements. These measurements define adjoint sources for data assimilation. Previous versions of these tools work on a pair of SAC files---observed and synthetic seismic data for the same component and station, and loop over all seismic records associated with one earthquake. Given the large number of stations and earthquakes, the frequent read and write operations create severe I/O bottlenecks on modern computing platforms. We present new versions of these tools utilizing a new seismic data format, namely the Adaptive Seismic Data Format(ASDF). This new format shows superior scalability for applications on high-performance computers and accommodates various types of data, including earthquake, industry and seismic interferometry datasets. ASDF also provides user-friendly APIs, which can be easily integrated into the adjoint tomography workflow and combined with other data processing tools. In addition to solving the I/O bottleneck, we are making several improvements to these tools. For example, FLEXWIN is tuned to select windows for different types of earthquakes. To capture their distinct features, we categorize earthquakes by their depths and frequency bands. Moreover, instead of only picking phases between the first P arrival and the surface-wave arrivals, our aim is to select and assimilate many other later prominent phases in adjoint tomography. For example, in the body-wave band (17 s - 60 s), we include SKS, sSKS and their multiple, while in the surface-wave band (60 s - 120 s) we incorporate major-arc surface waves.

  14. Adjoint calculations for multiple scattering of Compton and Rayleigh effects

    NASA Astrophysics Data System (ADS)

    Fernández, J. E.; Sumini, M.

    1992-08-01

    As is well known, the experimental determination of the Compton profile requires a particular geometry with a scattering angle close to π. That situation involves a narrow multiple-scattering spectrum that overlaps the Compton peak, making it difficult to analyze the different contributions to the profile. We show how the solution of the adjoint problem can help in devising more useful experimental configurations, giving, through its classical "importance" meaning, a formally clear picture of the whole problem.

  15. Forward and adjoint sensitivity computation of chaotic dynamical systems

    SciTech Connect

    Wang, Qiqi

    2013-02-15

    This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged “statistical” quantities to infinitesimal perturbations of the system parameters. The algorithms are demonstrated on the Lorenz attractor. We show that sensitivity derivatives of statistical quantities can be accurately estimated using a single, short trajectory (over a time interval of 20) on the Lorenz attractor.

  16. A comparison of adjoint and data-centric verification techniques.

    SciTech Connect

    Wildey, Timothy Michael; Cyr, Eric Christopher; Shadid, John Nicolas; Pawlowski, Roger Patrick; Smith, Thomas Michael

    2013-03-01

    This document summarizes the results from a level 3 milestone study within the CASL VUQ effort. We compare the adjoint-based a posteriori error estimation approach with a recent variant of a data-centric verification technique. We provide a brief overview of each technique and then we discuss their relative advantages and disadvantages. We use Drekar::CFD to produce numerical results for steady-state Navier Stokes and SARANS approximations. 3

  17. Monopole condensation in two-flavor adjoint QCD

    SciTech Connect

    Cossu, Guido; D'Elia, Massimo; Di Giacomo, Adriano; Lacagnina, Giuseppe; Pica, Claudio

    2008-04-01

    In QCD with adjoint fermions, the deconfining transition takes place at a lower temperature than the chiral transition. We study the two transitions by use of the Polyakov loop, the monopole order parameter, and the chiral condensate. The deconfining transition is first order, the chiral is a crossover. The order parameters for confinement are not affected by the chiral transition. We conclude that the degrees of freedom relevant to confinement are different from those describing chiral symmetry.

  18. Comparison of adjoint and analytical Bayesian inversion methods for constraining Asian sources of carbon monoxide using satellite (MOPITT) measurements of CO columns

    NASA Astrophysics Data System (ADS)

    Kopacz, Monika; Jacob, Daniel J.; Henze, Daven K.; Heald, Colette L.; Streets, David G.; Zhang, Qiang

    2008-04-01

    We apply the adjoint of an atmospheric chemical transport model (GEOS-Chem CTM) to constrain Asian sources of carbon monoxide (CO) with 2° × 2.5° spatial resolution using Measurement of Pollution in the Troposphere (MOPITT) satellite observations of CO columns in February-April 2001. Results are compared to the more common analytical method for solving the same Bayesian inverse problem and applied to the same data set. The analytical method is more exact but because of computational limitations it can only constrain emissions over coarse regions. We find that the correction factors to the a priori CO emission inventory from the adjoint inversion are consistent with those of the analytical inversion when averaged over the large regions of the latter. Unlike the analytical solution, the adjoint correction factors are not subject to compensating errors between adjacent regions (error anticorrelation). The adjoint solution also reveals fine-scale variability that the analytical inversion cannot resolve. For example, India shows both large emissions underestimates in the densely populated Ganges Valley and large overestimates in the eastern part of the country where springtime emissions are dominated by biomass burning. Correction factors to Chinese emissions are largest in central and eastern China, consistent with a recent bottom-up inventory though there are disagreements in the fine structure. Correction factors for biomass burning are consistent with a recent bottom-up inventory based on MODIS satellite fire data.

  19. Spectral monodromy of non-self-adjoint operators

    NASA Astrophysics Data System (ADS)

    Phan, Quang Sang

    2014-01-01

    In the present paper, we build a combinatorial invariant, called the "spectral monodromy" from the spectrum of a single (non-self-adjoint) h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from the quantum monodromy defined for the joint spectrum of an integrable system of n commuting self-adjoint h-pseudodifferential operators, given by S. Vu Ngoc ["Quantum monodromy in integrable systems," Commun. Math. Phys. 203(2), 465-479 (1999)]. The first simple case that we treat in this work is a normal operator. In this case, the discrete spectrum can be identified with the joint spectrum of an integrable quantum system. The second more complex case we propose is a small perturbation of a self-adjoint operator with a classical integrability property. We show that the discrete spectrum (in a small band around the real axis) also has a combinatorial monodromy. The main difficulty in this case is that we do not know the description of the spectrum everywhere, but only in a Cantor type set. In addition, we also show that the corresponding monodromy can be identified with the classical monodromy, defined by J. Duistermaat ["On global action-angle coordinates," Commun. Pure Appl. Math. 33(6), 687-706 (1980)].

  20. Adjoint-based sensitivity analysis for reactor-safety applications

    SciTech Connect

    Parks, C.V.

    1985-01-01

    The application and usefulness of an adjoint-based methodology for performing sensitivity analysis on reactor safety computer codes is investigated. The adjoint-based methodology, referred to as differential sensitivity theory (DST), provides first-order derivatives of the calculated quantities of interest (responses) with respect to the input parameters. The basic theoretical development of DST is presented along with the needed general extensions for consideration of model discontinuities and a variety of useful response definitions. A simple analytic problem is used to highlight the general DST procedures. Finally, DST procedures presented in this work are applied to two highly nonlinear reactor accident analysis codes: (1) FASTGAS, a relatively small code for analysis of loss-of-decay-heat-removal accident in a gas-cooled fast reactor, and (2) an existing code called VENUS-II which is typically employed for analyzing the core disassembly phase of a hypothetical fast reactor accident. The two codes are different both in terms of complexity and in terms of the facets of DST which can be illustrated. Sensitivity results from the adjoint codes ADJGAS and VENUS-ADJ are verified with direct recalculations using perturbed input parameters. The effectiveness of the DST results for parameter ranking, prediction of response changes, and uncertainty analysis are illustrated. The conclusion drawn from this study is that DST is a viable, cost-effective methodology for accurate sensitivity analysis.

  1. ANISORROPIA: the adjoint of the aerosol thermodynamic model ISORROPIA

    NASA Astrophysics Data System (ADS)

    Capps, S. L.; Henze, D. K.; Hakami, A.; Russell, A. G.; Nenes, A.

    2012-01-01

    We present the development of ANISORROPIA, the discrete adjoint of the ISORROPIA thermodynamic equilibrium model that treats the Na+-SO42-- HSO4--NH4+ -NO3--Cl--H2O aerosol system, and we demonstrate its sensitivity analysis capabilities. ANISORROPIA calculates sensitivities of an inorganic species in aerosol or gas phase with respect to the total concentrations of each species present with less than a two-fold increase in computational time over the concentration calculations. Due to the highly nonlinear and discontinuous solution surface of ISORROPIA, evaluation of the adjoint required a new, complex-variable version of the model, which determines first-order sensitivities with machine precision and avoids cancellation errors arising from finite difference calculations. The adjoint is verified over an atmospherically relevant range of concentrations, temperature, and relative humidity. We apply ANISORROPIA to recent field campaign results from Atlanta, GA, USA, and Mexico City, Mexico, to characterize the inorganic aerosol sensitivities of these distinct urban air masses. The variability in the relationship between fine mode inorganic aerosol mass and precursor concentrations shown has important implications for air quality and climate.

  2. Self-adjoint time operators and invariant subspaces

    NASA Astrophysics Data System (ADS)

    Gómez, Fernando

    2008-02-01

    The question of existence of self-adjoint time operators for unitary evolutions in classical and quantum mechanics is revisited on the basis of Halmos-Helson theory of invariant subspaces, Sz.-Nagy-Foiaş dilation theory and Misra-Prigogine-Courbage theory of irreversibility. It is shown that the existence of self-adjoint time operators is equivalent to the intertwining property of the evolution plus the existence of simply invariant subspaces or rigid operator-valued functions for its Sz.-Nagy-Foiaş functional model. Similar equivalent conditions are given in terms of intrinsic randomness in the context of statistical mechanics. The rest of the contents are mainly a unifying review of the subject scattered throughout an unconnected literature. A well-known extensive set of equivalent conditions is derived from the above results; such conditions are written in terms of Schrrdinger couples, the Weyl commutation relation, incoming and outgoing subspaces, innovation processes, Lax-Phillips scattering, translation and spectral representations, and spectral properties. Also the natural procedure dealing with symmetric time operators in standard quantum mechanics involving their self-adjoint extensions is illustrated by considering the quantum Aharonov-Bohm time-of-arrival operator.

  3. Spectral monodromy of non-self-adjoint operators

    SciTech Connect

    Phan, Quang Sang

    2014-01-15

    In the present paper, we build a combinatorial invariant, called the “spectral monodromy” from the spectrum of a single (non-self-adjoint) h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from the quantum monodromy defined for the joint spectrum of an integrable system of n commuting self-adjoint h-pseudodifferential operators, given by S. Vu Ngoc [“Quantum monodromy in integrable systems,” Commun. Math. Phys. 203(2), 465–479 (1999)]. The first simple case that we treat in this work is a normal operator. In this case, the discrete spectrum can be identified with the joint spectrum of an integrable quantum system. The second more complex case we propose is a small perturbation of a self-adjoint operator with a classical integrability property. We show that the discrete spectrum (in a small band around the real axis) also has a combinatorial monodromy. The main difficulty in this case is that we do not know the description of the spectrum everywhere, but only in a Cantor type set. In addition, we also show that the corresponding monodromy can be identified with the classical monodromy, defined by J. Duistermaat [“On global action-angle coordinates,” Commun. Pure Appl. Math. 33(6), 687–706 (1980)].

  4. Time-dependent quantum transport through an interacting quantum dot beyond sequential tunneling: second-order quantum rate equations

    NASA Astrophysics Data System (ADS)

    Dong, B.; Ding, G. H.; Lei, X. L.

    2015-05-01

    A general theoretical formulation for the effect of a strong on-site Coulomb interaction on the time-dependent electron transport through a quantum dot under the influence of arbitrary time-varying bias voltages and/or external fields is presented, based on slave bosons and the Keldysh nonequilibrium Green's function (GF) techniques. To avoid the difficulties of computing double-time GFs, we generalize the propagation scheme recently developed by Croy and Saalmann to combine the auxiliary-mode expansion with the celebrated Lacroix's decoupling approximation in dealing with the second-order correlated GFs and then establish a closed set of coupled equations of motion, called second-order quantum rate equations (SOQREs), for an exact description of transient dynamics of electron correlated tunneling. We verify that the stationary solution of our SOQREs is able to correctly describe the Kondo effect on a qualitative level. Moreover, a comparison with other methods, such as the second-order von Neumann approach and Hubbard-I approximation, is performed. As illustrations, we investigate the transient current behaviors in response to a step voltage pulse and a harmonic driving voltage, and linear admittance as well, in the cotunneling regime.

  5. Minimising the error in eigenvalue calculations involving the Boltzmann transport equation using goal-based adaptivity on unstructured meshes

    SciTech Connect

    Goffin, Mark A.; Baker, Christopher M.J.; Buchan, Andrew G.; Pain, Christopher C.; Eaton, Matthew D.; Smith, Paul N.

    2013-06-01

    This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, k{sub eff}, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for k{sub eff} with directional dependence. General error estimators are derived for any given functional of the flux and applied to k{sub eff} to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The k{sub eff} goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained.

  6. Boundary-artifact-free phase retrieval with the transport of intensity equation: fast solution with use of discrete cosine transform.

    PubMed

    Zuo, Chao; Chen, Qian; Asundi, Anand

    2014-04-21

    The transport of intensity equation (TIE) is a two-dimensional second order elliptic partial differential equation that must be solved under appropriate boundary conditions. However, the boundary conditions are difficult to obtain in practice. The fast Fourier transform (FFT) based TIE solutions are widely adopted for its speed and simplicity. However, it implies periodic boundary conditions, which lead to significant boundary artifacts when the imposed assumption is violated. In this work, TIE phase retrieval is considered as an inhomogeneous Neumann boundary value problem with the boundary values experimentally measurable around a hard-edged aperture, without any assumption or prior knowledge about the test object and the setup. The analytic integral solution via Green's function is given, as well as a fast numerical implementation for a rectangular region using the discrete cosine transform. This approach is applicable for the case of non-uniform intensity distribution with no extra effort to extract the boundary values from the intensity derivative signals. Its efficiency and robustness have been verified by several numerical simulations even when the objects are complex and the intensity measurements are noisy. This method promises to be an effective fast TIE solver for quantitative phase imaging applications. PMID:24787811

  7. Neoclassical electron and ion transport in toroidally rotating plasmas

    SciTech Connect

    Sugama, H.; Horton, W.

    1997-06-01

    Neoclassical transport processes of electrons and ions are investigated in detail for toroidally rotating axisymmetric plasmas with large flow velocities on the order of the ion thermal speed. The Onsager relations for the flow-dependent neoclassical transport coefficients are derived from the symmetry properties of the drift kinetic equation with the self-adjoint collision operator. The complete neoclassical transport matrix with the Onsager symmetry is obtained for the rotating plasma consisting of electrons and single-species ions in the Pfirsch{endash}Schl{umlt u}ter and banana regimes. It is found that the inward banana fluxes of particles and toroidal momentum are driven by the parallel electric field, which are phenomena coupled through the Onsager symmetric off-diagonal coefficients to the parallel currents caused by the radial thermodynamic forces conjugate to the inward fluxes, respectively. {copyright} {ital 1997 American Institute of Physics.}

  8. Electrical transport limited by electron-phonon coupling from Boltzmann transport equation: An ab initio study of Si, Al, and MoS2

    NASA Astrophysics Data System (ADS)

    Li, Wu

    2015-08-01

    We demonstrate the ab initio electrical transport calculation limited by electron-phonon coupling by using the full solution of the Boltzmann transport equation (BTE), which applies equally to metals and semiconductors. Numerical issues are emphasized in this work. We show that the simple linear interpolation of the electron-phonon coupling matrix elements from a relatively coarse grid to an extremely fine grid can ease the calculational burden, which makes the calculation feasible in practice. For the Brillouin zone (BZ) integration of the transition probabilities involving one δ function, the Gaussian smearing method with a physical choice of locally adaptive broadening parameters is employed. We validate the calculation in the cases of n -type Si and Al. The calculated conductivity and mobility are in good agreement with experiments. In the metal case we also demonstrate that the Gaussian smearing method with locally adaptive broadening parameters works excellently for the BZ integration with double δ functions involved in the Eliashberg spectral function and its transport variant. The simpler implementation is the advantage of the Gaussian smearing method over the tetrahedron method. The accuracy of the relaxation time approximation and the approximation made by Allen [Phys. Rev. B 17, 3725 (1978), 10.1103/PhysRevB.17.3725] has been examined by comparing with the exact solution of BTE. We also apply our method to n -type monolayer MoS2, for which a mobility of 150 cm2 v-1 s-1 is obtained at room temperature. Moreover, the mean free paths are less than 9 nm, indicating that in the presence of grain boundaries the mobilities should not be effectively affected if the grain boundary size is tens of nanometers or larger. The ab initio approach demonstrated in this paper can be directly applied to other materials without the need for any a priori knowledge about the electron-phonon scattering processes, and can be straightforwardly extended to study cases with

  9. A User's Manual for MASH V1.5 - A Monte Carlo Adjoint Shielding Code System

    SciTech Connect

    C. O. Slater; J. M. Barnes; J. O. Johnson; J.D. Drischler

    1998-10-01

    The Monte Carlo ~djoint ~ielding Code System, MASH, calculates neutron and gamma- ray environments and radiation protection factors for armored military vehicles, structures, trenches, and other shielding configurations by coupling a forward discrete ordinates air- over-ground transport calculation with an adjoint Monte Carlo treatment of the shielding geometry. Efficiency and optimum use of computer time are emphasized. The code system includes the GRTUNCL and DORT codes for air-over-ground transport calculations, the MORSE code with the GIFT5 combinatorial geometry package for adjoint shielding calculations, and several peripheral codes that perform the required data preparations, transformations, and coupling functions. The current version, MASH v 1.5, is the successor to the original MASH v 1.0 code system initially developed at Oak Ridge National Laboratory (ORNL). The discrete ordinates calculation determines the fluence on a coupling surface surrounding the shielding geometry due to an external neutron/gamma-ray source. The Monte Carlo calculation determines the effectiveness of the fluence at that surface in causing a response in a detector within the shielding geometry, i.e., the "dose importance" of the coupling surface fluence. A coupling code folds the fluence together with the dose importance, giving the desired dose response. The coupling code can determine the dose response as a function of the shielding geometry orientation relative to the source, distance from the source, and energy response of the detector. This user's manual includes a short description of each code, the input required to execute the code along with some helpful input data notes, and a representative sample problem.

  10. Multigroup discrete ordinates solution of Boltzmann-Fokker-Planck equations and cross section library development of ion transport

    SciTech Connect

    Prinja, A.K.

    1995-08-01

    We have developed and successfully implemented a two-dimensional bilinear discontinuous in space and time, used in conjunction with the S{sub N} angular approximation, to numerically solve the time dependent, one-dimensional, one-speed, slab geometry, (ion) transport equation. Numerical results and comparison with analytical solutions have shown that the bilinear-discontinuous (BLD) scheme is third-order accurate in the space ad time dimensions independently. Comparison of the BLD results with diamond-difference methods indicate that the BLD method is both quantitavely and qualitatively superior to the DD scheme. We note that the form of the transport operator is such that these conclusions carry over to energy dependent problems that include the constant-slowing-down-approximation term, and to multiple space dimensions or combinations thereof. An optimized marching or inversion scheme or a parallel algorithm should be investigated to determine if the increased accuracy can compensate for the extra overhead required for a BLD solution, and then could be compared to other discretization methods such as nodal or characteristic schemes.

  11. Differential form of the Skornyakov-Ter-Martirosyan Equations

    NASA Astrophysics Data System (ADS)

    Pen'Kov, F. M.; Sandhas, W.

    2005-12-01

    The Skornyakov-Ter-Martirosyan three-boson integral equations in momentum space are transformed into differential equations. This allows us to take into account quite directly the Danilov condition providing self-adjointness of the underlying three-body Hamiltonian with zero-range pair interactions. For the helium trimer the numerical solutions of the resulting differential equations are compared with those of the Faddeev-type AGS equations.

  12. Differential form of the Skornyakov-Ter-Martirosyan Equations

    SciTech Connect

    Pen'kov, F. M.; Sandhas, W.

    2005-12-15

    The Skornyakov-Ter-Martirosyan three-boson integral equations in momentum space are transformed into differential equations. This allows us to take into account quite directly the Danilov condition providing self-adjointness of the underlying three-body Hamiltonian with zero-range pair interactions. For the helium trimer the numerical solutions of the resulting differential equations are compared with those of the Faddeev-type AGS equations.

  13. Efficient yet accurate solution of the linear transport equation in the presence of internal sources - The exponential-linear-in-depth approximation

    NASA Technical Reports Server (NTRS)

    Kylling, Arve; Stamnes, Knut

    1992-01-01

    The present solutions to the linear transport equation pertain to monoenergetic particles' interaction with a multiple scattering/absorbing layered medium with a general anisotropic internal source term. Attention is given to a novel exponential-linear approximation to the internal source, as a function of scattering depth, which furnishes an at-once efficient and accurate solution to the linear transport equation through its reduction of the spatial mesh size. The great superiority of the proposed method is demonstrated by the numerical results obtained in the illustrative cases of (1) an embedded thermal source and (2) a rapidly varying beam pseudosource.

  14. Seismic Imaging of VTI, HTI and TTI based on Adjoint Methods

    NASA Astrophysics Data System (ADS)

    Rusmanugroho, H.; Tromp, J.

    2014-12-01

    Recent studies show that isotropic seismic imaging based on adjoint method reduces low-frequency artifact caused by diving waves, which commonly occur in two-wave wave-equation migration, such as Reverse Time Migration (RTM). Here, we derive new expressions of sensitivity kernels for Vertical Transverse Isotropy (VTI) using the Thomsen parameters (ɛ, δ, γ) plus the P-, and S-wave speeds (α, β) as well as via the Chen & Tromp (GJI 2005) parameters (A, C, N, L, F). For Horizontal Transverse Isotropy (HTI), these parameters depend on an azimuthal angle φ, where the tilt angle θ is equivalent to 90°, and for Tilted Transverse Isotropy (TTI), these parameters depend on both the azimuth and tilt angles. We calculate sensitivity kernels for each of these two approaches. Individual kernels ("images") are numerically constructed based on the interaction between the regular and adjoint wavefields in smoothed models which are in practice estimated through Full-Waveform Inversion (FWI). The final image is obtained as a result of summing all shots, which are well distributed to sample the target model properly. The impedance kernel, which is a sum of sensitivity kernels of density and the Thomsen or Chen & Tromp parameters, looks crisp and promising for seismic imaging. The other kernels suffer from low-frequency artifacts, similar to traditional seismic imaging conditions. However, all sensitivity kernels are important for estimating the gradient of the misfit function, which, in combination with a standard gradient-based inversion algorithm, is used to minimize the objective function in FWI.

  15. Spectral-Element Simulations of Wave Propagation in Porous Media: Finite-Frequency Sensitivity Kernels Based Upon Adjoint Methods

    NASA Astrophysics Data System (ADS)

    Morency, C.; Tromp, J.

    2008-12-01

    successfully performed. We present finite-frequency sensitivity kernels for wave propagation in porous media based upon adjoint methods. We first show that the adjoint equations in porous media are similar to the regular Biot equations upon defining an appropriate adjoint source. Then we present finite-frequency kernels for seismic phases in porous media (e.g., fast P, slow P, and S). These kernels illustrate the sensitivity of seismic observables to structural parameters and form the basis of tomographic inversions. Finally, we show an application of this imaging technique related to the detection of buried landmines and unexploded ordnance (UXO) in porous environments.

  16. Finite difference numerical method for the superlattice Boltzmann transport equation and case comparison of CPU(C) and GPU(CUDA) implementations

    SciTech Connect

    Priimak, Dmitri

    2014-12-01

    We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques.

  17. A user`s manual for MASH 1.0: A Monte Carlo Adjoint Shielding Code System

    SciTech Connect

    Johnson, J.O.

    1992-03-01

    The Monte Carlo Adjoint Shielding Code System, MASH, calculates neutron and gamma-ray environments and radiation protection factors for armored military vehicles, structures, trenches, and other shielding configurations by coupling a forward discrete ordinates air-over-ground transport calculation with an adjoint Monte Carlo treatment of the shielding geometry. Efficiency and optimum use of computer time are emphasized. The code system include the GRTUNCL and DORT codes for air-over-ground transport calculations, the MORSE code with the GIFT5 combinatorial geometry package for adjoint shielding calculations, and several peripheral codes that perform the required data preparations, transformations, and coupling functions. MASH is the successor to the Vehicle Code System (VCS) initially developed at Oak Ridge National Laboratory (ORNL). The discrete ordinates calculation determines the fluence on a coupling surface surrounding the shielding geometry due to an external neutron/gamma-ray source. The Monte Carlo calculation determines the effectiveness of the fluence at that surface in causing a response in a detector within the shielding geometry, i.e., the ``dose importance`` of the coupling surface fluence. A coupling code folds the fluence together with the dose importance, giving the desired dose response. The coupling code can determine the dose response a a function of the shielding geometry orientation relative to the source, distance from the source, and energy response of the detector. This user`s manual includes a short description of each code, the input required to execute the code along with some helpful input data notes, and a representative sample problem (input data and selected output edits) for each code.

  18. A cell-local finite difference discretization of the low-order quasidiffusion equations for neutral particle transport on unstructured quadrilateral meshes

    SciTech Connect

    Wieselquist, William A.; Anistratov, Dmitriy Y.; Morel, Jim E.

    2014-09-15

    We present a quasidiffusion (QD) method for solving neutral particle transport problems in Cartesian XY geometry on unstructured quadrilateral meshes, including local refinement capability. Neutral particle transport problems are central to many applications including nuclear reactor design, radiation safety, astrophysics, medical imaging, radiotherapy, nuclear fuel transport/storage, shielding design, and oil well-logging. The primary development is a new discretization of the low-order QD (LOQD) equations based on cell-local finite differences. The accuracy of the LOQD equations depends on proper calculation of special non-linear QD (Eddington) factors from a transport solution. In order to completely define the new QD method, a proper discretization of the transport problem is also presented. The transport equation is discretized by a conservative method of short characteristics with a novel linear approximation of the scattering source term and monotonic, parabolic representation of the angular flux on incoming faces. Analytic and numerical tests are used to test the accuracy and spatial convergence of the non-linear method. All tests exhibit O(h{sup 2}) convergence of the scalar flux on orthogonal, random, and multi-level meshes.

  19. Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations

    NASA Astrophysics Data System (ADS)

    Bouzat, Sebastián

    2016-01-01

    One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models.

  20. Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations.

    PubMed

    Bouzat, Sebastián

    2016-01-01

    One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models. PMID:26871095