Quasi-hydrodynamic Semiconductor Equations
Quasi-hydrodynamic Semiconductor Equations

Author: Ansgar Jüngel

Publisher: Birkhäuser

Published: 2011-04-27

Total Pages: 301

ISBN-13: 303488334X

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This book presents a hierarchy of macroscopic models for semiconductor devices, studying three classes of models in detail: isentropic drift-diffusion equations, energy-transport models, and quantum hydrodynamic equations. The derivation of each, including physical discussions, is shown. Numerical simulations for modern semiconductor devices are performed, showing the particular features of each. The author develops modern analytical techniques, such as positive solution methods, local energy methods for free-boundary problems and entropy methods.

Quasi-hydrodynamic Semiconductor Equations
Quasi-hydrodynamic Semiconductor Equations

Author: Ansgar Jüngel

Publisher: Springer Science & Business Media

Published: 2001-02-01

Total Pages: 314

ISBN-13: 9783764363499

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This book presents a hierarchy of macroscopic models for semiconductor devices, studying three classes of models in detail: isentropic drift-diffusion equations, energy-transport models, and quantum hydrodynamic equations. The derivation of each, including physical discussions, is shown. Numerical simulations for modern semiconductor devices are performed, showing the particular features of each. The author develops modern analytical techniques, such as positive solution methods, local energy methods for free-boundary problems and entropy methods.

Dispersive Transport Equations and Multiscale Models
Dispersive Transport Equations and Multiscale Models

Author: Ben Abdallah Naoufel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 297

ISBN-13: 1441989358

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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.

Transport Equations for Semiconductors
Transport Equations for Semiconductors

Author: Ansgar Jüngel

Publisher: Springer Science & Business Media

Published: 2009-03-17

Total Pages: 326

ISBN-13: 3540895256

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This volume presents a systematic and mathematically accurate description and derivation of transport equations in solid state physics, in particular semiconductor devices.

Partial Differential Equations and Spectral Theory
Partial Differential Equations and Spectral Theory

Author: Michael Demuth

Publisher: Springer Science & Business Media

Published: 2011-02-01

Total Pages: 351

ISBN-13: 303480024X

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This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original contributions from the authors. They are written in a clear expository style that makes them accessible to a broader audience. The articles contain a detailed introduction and discuss recent progress, provide additional motivation, and develop the necessary tools. Moreover, the authors share their views on future developments, hypotheses, and unsolved problems.

Some Problems on Nonlinear Hyperbolic Equations and Applications
Some Problems on Nonlinear Hyperbolic Equations and Applications

Author: Yuejun Peng

Publisher: World Scientific

Published: 2010

Total Pages: 464

ISBN-13: 9814322881

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This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.

More Progresses In Analysis - Proceedings Of The 5th International Isaac Congress
More Progresses In Analysis - Proceedings Of The 5th International Isaac Congress

Author: Heinrich G W Begehr

Publisher: World Scientific

Published: 2009-05-12

Total Pages: 1497

ISBN-13: 9814469688

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International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors.The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O Besov, V Burenkov and R P Gilbert on the occasion of their anniversaries.

More Progresses in Analysis
More Progresses in Analysis

Author: Heinrich G. W. Begehr

Publisher: World Scientific

Published: 2009

Total Pages: 1497

ISBN-13: 9812835628

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International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors. The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O Besov, V Burenkov and R P Gilbert on the occasion of their anniversaries.

Scientific Computing in Electrical Engineering
Scientific Computing in Electrical Engineering

Author: Angelo Marcello Anile

Publisher: Springer Science & Business Media

Published: 2007-01-10

Total Pages: 460

ISBN-13: 3540328629

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This book is a collection of papers presented at the last Scientific Computing in Electrical Engineering (SCEE) Conference, held in Sicily, in 2004. The series of SCEE conferences aims at addressing mathematical problems which have a relevancy to industry. The areas covered at SCEE-2004 were: Electromagnetism, Circuit Simulation, Coupled Problems and General mathematical and computational methods.

Applied Analysis: Mathematics For Science, Technology, Engineering (Third Edition)
Applied Analysis: Mathematics For Science, Technology, Engineering (Third Edition)

Author: Takashi Suzuki

Publisher: World Scientific

Published: 2022-04-28

Total Pages: 688

ISBN-13: 981125737X

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This book is to be a new edition of Applied Analysis. Several fundamental materials of applied and theoretical sciences are added, which are needed by the current society, as well as recent developments in pure and applied mathematics. New materials in the basic level are the mathematical modelling using ODEs in applied sciences, elements in Riemann geometry in accordance with tensor analysis used in continuum mechanics, combining engineering and modern mathematics, detailed description of optimization, and real analysis used in the recent study of PDEs. Those in the advance level are the integration of ODEs, inverse Strum Liouville problems, interface vanishing of the Maxwell system, method of gradient inequality, diffusion geometry, mathematical oncology. Several descriptions on the analysis of Smoluchowski-Poisson equation in two space dimension are corrected and extended, to ensure quantized blowup mechanism of this model, particularly, the residual vanishing both in blowup solution in finite time with possible collision of sub-collapses and blowup solutions in infinite time without it.