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Transport in Transition Regimes

  • Conference proceedings
  • © 2004

Overview

Editors:
  1. Naoufel Ben Abdallah

    1. Laboratoire MIP, Université Paul Sabatier, France

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  2. Irene M. Gamba

    1. Department of Mathematics, University of Texas at Austin, Austin, USA

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  3. Christian Ringhofer

    1. Department of Mathematics, Arizona State University, Tempe, USA

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  4. Anton Arnold

    1. Angewandte Mathematik, Universität des Saarlandes, Saarbrucken, Germany

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  5. Robert T. Glassey

    1. Department of Mathematics, Indiana University, Bloomington, USA

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  6. Pierre Degond

    1. Laboratoire MIP, Université Paul Sabatier, France

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  7. C. David Levermore

    1. CSCAMM, University of Maryland, College Park, USA

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Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 135)

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About this book

IMA Volumes 135: Transport in Transition Regimes and 136: Dispersive Transport Equations and Multiscale Models focus on the modeling of processes for which transport is one of the most complicated components. This includes processes that involve a wide range of length scales over different spatio-temporal regions of the problem, ranging from the order of mean-free paths to many times this scale. Consequently, effective modeling techniques require different transport models in each region. The first issue is that of finding efficient simulations techniques, since a fully resolved kinetic simulation is often impractical. One therefore develops homogenization, stochastic, or moment based subgrid models. Another issue is to quantify the discrepancy between macroscopic models and the underlying kinetic description, especially when dispersive effects become macroscopic, for example due to quantum effects in semiconductors and superfluids. These two volumes address these questions in relation to a wide variety of application areas, such as semiconductors, plasmas, fluids, chemically reactive gases, etc.

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Table of contents (18 papers)

  1. Front Matter

    Pages i-x
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  2. BGK-Burnett Equations: A New Set of Second-Order Hydrodynamic Equations for Flows in Continuum-Transition Regime

    • Ramesh K. Agarwal
    Pages 1-35

  3. Steady States for Streater’s Energy-Transport Models of Self-Gravitating Particles

    • Piotr Biler, Jean Dolbeault, Maria J. Esteban, Peter A. Markowich, Tadeusz Nadzieja
    Pages 37-56

  4. Towards a Hybrid Monte Carlo Method for Rarefied Gas Dynamics

    • Russel E. Caflisch, Lorenzo Pareschi
    Pages 57-73

  5. Comparison of Monte Carlo and Deterministic Simulations of a Silicon Diode

    • Jose A. Carrillo, Irene M. Gamba, Orazio Muscato, Chi-Wang Shu
    Pages 75-84

  6. Discrete-Velocity Models for Numerical Simulations in Transitional Regime for Rarefied Flows and Radiative Transfer

    • Pierre Charrier, Bruno Dubroca, Luc Mieussens, Rodolphe Turpault
    Pages 85-101

  7. Some Recent Results on the Kinetic Theory of Phase Transitions

    • Jean-François Collet, Thierry Goudon, Sara Hariz, Frederic Poupaud, Alexis Vasseur
    Pages 103-120

  8. Fluids with Multivalued Internal Energy: The Anisotropic Case

    • P. Degond, M. Lemou, J. L. Lòpez
    Pages 121-136

  9. A Note on the Energy-Transport Limit of the Semiconductor Boltzmann Equation

    • Pierre Degond, C. David Levermore, Christian Schmeiser
    Pages 137-153

  10. Generalized Hydrodynamics and Irreversible Thermodynamics

    • Byung Chan Eu
    Pages 155-176

  11. A Steady-State Capturing Method for Hyperbolic Systems with Geometrical Source Terms

    • Shi Jin
    Pages 177-183

  12. Maximum Entropy Moment Problems and Extended Euler Equations

    • Michael Junk
    Pages 189-198

  13. Numerical Methods for Radiative Heat Transfer in Diffusive Regimes and Applications to Glass Manufacturing

    • Axel Klar, Guido Thömmes
    Pages 199-212

  14. Hydrodynamic Limits of the Boltzmann Equation

    • Nader Masmoudi
    Pages 217-230

  15. Sobolev Norm and Carrier Transport in Semiconductors

    • Orazio Muscato
    Pages 231-237

  16. The Evolution of a Gas in a Radiation Field from a Kinetic Point of View

    • A. Nouri
    Pages 241-248

  17. Hybrid Particle-Based Approach for the Simulation Of Semiconductor Devices: The Full-Band Cellular Automaton/Monte Carlo Method

    • Marco Saraniti, Shela J. Wigger, Stephen M. Goodnick
    Pages 249-264

  18. Some Remarks on the Equations of Burnett and Grad

    • Henning Struchtrup
    Pages 265-276

  19. Boundary Conditions and Boundary Layers for a Class of Linear Relaxation Systems in a Quarter Plane

    • Zhouping Xin, Wen-Qing Xu
    Pages 279-292

  20. Back Matter

    Pages 293-301
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Editors and Affiliations

  • Laboratoire MIP, Université Paul Sabatier, France

    Naoufel Ben Abdallah, Pierre Degond

  • Department of Mathematics, University of Texas at Austin, Austin, USA

    Irene M. Gamba

  • Department of Mathematics, Arizona State University, Tempe, USA

    Christian Ringhofer

  • Angewandte Mathematik, Universität des Saarlandes, Saarbrucken, Germany

    Anton Arnold

  • Department of Mathematics, Indiana University, Bloomington, USA

    Robert T. Glassey

  • CSCAMM, University of Maryland, College Park, USA

    C. David Levermore

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