Modeling of Collisions

Science & Math

Raviart, Pierre-Arnaud

Markowich, P.A.

Decoster, A.

Perthame, B.

Physics

Gauthier-Villars

Hardbound. This book is devoted to recent advances in the modeling of collisions. It contains a series of lectures delivered by a plasma physicist Alain Decoster and two applied mathematicians Peter Markowich and Benoît Perthame.The first part, by A. Decoster, recalls how the fluid equations of a collisional plasma are deduced from the Fokker-Planck description of a kinetic plasma. The transport equations thus obtained are known for a plasma with one kind of ions (Spitzer, Braginskii). The calculation is extended here to the case of several ionic species, including the different charge states of a single atomic species. The multifluid description of plasma interpenetration is also investigated.The second part, by B. Perthame, introduces to the mathematical theory of Boltzmann's equation. It derives the Boltzmann model as the Boltzmann-Grad limit of a system of particles. The fluid limit of the Boltzmann model is also considered.The third pa

Raviart, P. A.

<p>In the last two decades semiconductor device simulation has become a research area, which thrives on a cooperation of physicists, electrical engineers and mathe maticians. In this book the static semiconductor device problem is presented and analysed from an applied mathematician's point of view. I shall derive the device equations - as obtained for the first time by Van Roosbroeck in 1950 - from physical principles, present a mathematical analysis, discuss their numerical solu tion by discretisation techniques and report on selected device simulation runs. To me personally the most fascinating aspect of mathematical device analysis is that an interplay of abstract mathematics, perturbation theory, numerical analysis and device physics is prompting the design and development of new technology. I very much hope to convey to the reader the importance of applied mathematics for technological progress. Each chapter of this book is designed to be as selfcontained as possible, however, the mathematical analysis of the device problem requires tools which cannot be presented completely here. Those readers who are not interested in the mathemati cal methodology and rigor can extract the desired information by simply ignoring details and proofs of theorems. Also, at the beginning of each chapter I refer to textbooks which introduce the interested reader to the required mathematical concepts.</p>

The Stationary Semiconductor Device Equations (Computational Microelectronics)

Springer

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