Pierre Degond's Books

Quantum Transport

Modelling, Analysis and Asymptotics - Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 11–16, 2006

By: Gregoire Allaire,Anton Arnold,Pierre Degond,Thomas Y. Hou

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Quantum Transport

Modelling, Analysis and Asymptotics - Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 11–16, 2006

By: Gregoire Allaire,Anton Arnold,Pierre Degond,Thomas Y. Hou

In this volume, a result of The CIME Summer School held in Cetraro, Italy, in 2006, four leading specialists present different aspects of quantum transport modeling. It provides an excellent basis for researchers in this field.

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Page Count

272

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540795731

ISBN 13

9783540795735

Numerical Approximation of Hyperbolic Systems of Conservation Laws

By: Edwige Godlewski,Pierre-Arnaud Raviart

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Numerical Approximation of Hyperbolic Systems of Conservation Laws

By: Edwige Godlewski,Pierre-Arnaud Raviart

This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors. Since the earlier work concentrated on the mathematical theory of multidimensional scalar conservation laws, this book will focus on systems and the theoretical aspects which are needed in the applications, such as the solution of the Riemann problem and further insights into more sophisticated problems, with special attention to the system of gas dynamics. This new edition includes more examples such as MHD and shallow water, with an insight on multiphase flows. Additionally, the text includes source terms and well-balanced/asymptotic preserving schemes, introducing relaxation schemes and addressing problems related to resonance and discontinuous fluxes while adding details on the low Mach number situation.

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Page Count

846

Publisher

Springer Nature

Published Date

ISBN 10

1071613448

ISBN 13

9781071613443

Mean Field Games

Cetraro, Italy 2019

By: Yves Achdou,Pierre Cardaliaguet,François Delarue,Alessio Porretta,Filippo Santambrogio

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Mean Field Games

Cetraro, Italy 2019

By: Yves Achdou,Pierre Cardaliaguet,François Delarue,Alessio Porretta,Filippo Santambrogio

This volume provides an introduction to the theory of Mean Field Games, suggested by J.-M. Lasry and P.-L. Lions in 2006 as a mean-field model for Nash equilibria in the strategic interaction of a large number of agents. Besides giving an accessible presentation of the main features of mean-field game theory, the volume offers an overview of recent developments which explore several important directions: from partial differential equations to stochastic analysis, from the calculus of variations to modeling and aspects related to numerical methods. Arising from the CIME Summer School "Mean Field Games" held in Cetraro in 2019, this book collects together lecture notes prepared by Y. Achdou (with M. Laurière), P. Cardaliaguet, F. Delarue, A. Porretta and F. Santambrogio. These notes will be valuable for researchers and advanced graduate students who wish to approach this theory and explore its connections with several different fields in mathematics.

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316

Publisher

Springer Nature

Published Date

ISBN 10

3030598373

ISBN 13

9783030598372

Paris-Princeton Lectures on Mathematical Finance 2010

By: Areski Cousin,Stéphane Crépey,Olivier Guéant,David Hobson,Monique Jeanblanc,Jean-Michel Lasry,Jean-Paul Laurent,Pierre-Louis Lions,Peter Tankov

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Paris-Princeton Lectures on Mathematical Finance 2010

By: Areski Cousin,Stéphane Crépey,Olivier Guéant,David Hobson,Monique Jeanblanc,Jean-Michel Lasry,Jean-Paul Laurent,Pierre-Louis Lions,Peter Tankov

The Paris-Princeton Lectures in Financial Mathematics, of which this is the fourth volume, publish cutting-edge research in self-contained, expository articles from outstanding specialists - established or on the rise! The aim is to produce a series of articles that can serve as an introductory reference source for research in the field. The articles are the result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with five articles by: 1. Areski Cousin, Monique Jeanblanc and Jean-Paul Laurent, 2. Stéphane Crépey, 3. Olivier Guéant, Jean-Michel Lasry and Pierre-Louis Lions, 4. David Hobson and 5. Peter Tankov.

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374

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642146597

ISBN 13

9783642146596

Modeling and Computational Methods for Kinetic Equations

By: Pierre Degond,Lorenzo Pareschi,Giovanni Russo

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Modeling and Computational Methods for Kinetic Equations

By: Pierre Degond,Lorenzo Pareschi,Giovanni Russo

In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. New applications in traffic flow engineering, granular media modeling, and polymer and phase transition physics have resulted in new numerical algorithms which depart from traditional stochastic Monte--Carlo methods. This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused theoretical or applied works. The book is divided into two parts. Part I is devoted to the most fundamental kinetic model: the Boltzmann equation of rarefied gas dynamics. Additionally, widely used numerical methods for the discretization of the Boltzmann equation are reviewed: the Monte--Carlo method, spectral methods, and finite-difference methods. Part II considers specific applications: plasma kinetic modeling using the Landau--Fokker--Planck equations, traffic flow modeling, granular media modeling, quantum kinetic modeling, and coagulation-fragmentation problems. Modeling and Computational Methods of Kinetic Equations will be accessible to readers working in different communities where kinetic theory is important: graduate students, researchers and practitioners in mathematical physics, applied mathematics, and various branches of engineering. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.

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Page Count

372

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817632549

ISBN 13

9780817632540

Quantum Transport

Modelling, Analysis and Asymptotics - Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 11–16, 2006

By: Gregoire Allaire,Anton Arnold,Pierre Degond,Thomas Y. Hou

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Quantum Transport

Modelling, Analysis and Asymptotics - Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 11–16, 2006

By: Gregoire Allaire,Anton Arnold,Pierre Degond,Thomas Y. Hou

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Page Count

260

Publisher

Springer

Published Date

ISBN 10

3540872566

ISBN 13

9783540872566

Book's by Pierre Degond

Quantum Transport

Quantum Transport

Numerical Approximation of Hyperbolic Systems of Conservation Laws

Numerical Approximation of Hyperbolic Systems of Conservation Laws

Mean Field Games

Mean Field Games

Paris-Princeton Lectures on Mathematical Finance 2010

Paris-Princeton Lectures on Mathematical Finance 2010

Modeling and Computational Methods for Kinetic Equations

Modeling and Computational Methods for Kinetic Equations

Quantum Transport

Quantum Transport

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