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Dispersive Transport Equations and Multiscale Models

  • Conference proceedings
  • © 2004

Overview

Editors:
  1. Naoufel Ben Abdallah

    1. Laboratoire MIP, Université Paul Sabatier, Toulouse Cedex 4, France

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  2. Anton Arnold

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

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  3. Pierre Degond

    1. Laboratoire MIP, Université Paul Sabatier, Toulouse Cedex 4, France

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  4. Irene M. Gamba

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

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  5. Robert T. Glassey

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

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  6. C. David Levermore

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

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  7. Christian Ringhofer

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

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Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 136)

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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 wdie 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 (17 papers)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. On the Derivation of Nonlinear Schrödinger and Vlasov Equations

    • Claude Bardos, François Golse, Alex Gottlieb, Norbert J. Mauser
    Pages 1-23

  3. Taking on the Multiscale Challenge

    • Leonard J. Borucki
    Pages 25-35

  4. Nonresonant Smoothing for Coupled Wave + Transport Equations and the Vlasov-Maxwell System

    • François Bouchut, François Golse, Christophe Pallard
    Pages 37-50

  5. Integrated Multiscale Process Simulation in Microelectronics

    • Timothy S. Cale, Max O. Bloomfield, David F. Richards, Sofiane Soukane, Kenneth E. Jansent, John A. Tichy et al.
    Pages 51-76

  6. Constitutive Relations for Viscoleastic Fluid Models Derived from Kinetic Theory

    • P. Degond, M. Lemou, M. Picasso
    Pages 77-89

  7. Dispersive/Hyperbolic Hydrodynamic Models for Quantum Transport (In Semiconductor Devices)

    • Carl L. Gardner, Christian Ringhofer
    Pages 91-106

  8. A Review on Small Debye Length and Quasi-Neutral Limits in Macroscopic Models for Charged Fluids

    • Ingenuin Gasser
    Pages 107-119

  9. Global Solution of the Cauchy Problem for the Relativistic Vlasov-Poisson Equation with Cylindrically Symmetric Data

    • Robert T. Glassey, Jack Schaeffer
    Pages 121-132

  10. Mesoscopic Scale Modeling for Chemical Vapor Deposition in Semiconductor Manufacturing

    • Matthias K. Gobbert, Christian Ringhofer
    Pages 133-149

  11. Asymptotic Limits in Macroscopic Plasma Models

    • Ansgar Jüngel
    Pages 151-166

  12. A Landau-Zener Formula for Two-Scaled Wigner Measures

    • Clotilde Fermanian Kammerer, Patrick Gerard
    Pages 167-177

  13. Mesoscopic Modeling of Surface Processes

    • Markos A. Katsoulakis, Dionisios G. Vlachos
    Pages 179-198

  14. Homogenous and Heterogeneous Models for Silicon Oxidation

    • J.R. King
    Pages 199-217

  15. Feature-Scale to Wafer-Scale Modeling and Simulation of Physical Vapor Deposition

    • Peter L. O’Sullivan, Frieder H. Baumann, George H. Gilmer, Jacques Dalla Torre, Chan-Soo Shin, Ivan Petrov et al.
    Pages 219-236

  16. WKB Analysis in the Semiclassical Limit of a Discrete NLS System

    • Stephen P. Shipman
    Pages 237-258

  17. Bifurcation Analysis of Cylindrical Couette Flow with Evaporation and Condensation by the Boltzmann Equation

    • Yoshio Sone, Toshiyuki Doi
    Pages 259-279

  18. Magnetic Instability in a Collisionless Plasma

    • Walter A. Strauss
    Pages 281-286

  19. Back Matter

    Pages 287-295
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Editors and Affiliations

  • Laboratoire MIP, Université Paul Sabatier, Toulouse Cedex 4, France

    Naoufel Ben Abdallah, Pierre Degond

  • Angewandte Mathematik, Universität des Saarlandes, Saarbrucken, Germany

    Anton Arnold

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

    Irene M. Gamba

  • Department of Mathematics, Indiana University, Bloomington, USA

    Robert T. Glassey

  • CSCAMM, University of Maryland, College Park, USA

    C. David Levermore

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

    Christian Ringhofer

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