Gregoire Allaire

Pierre Degond

Anton Arnold

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.

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

Quantum Transport

Ben Abdallah Naoufel

Irene M. Gamba

Robert T. Glassey

C. David Levermore

Christian Ringhofer

This volume focuses on modeling processes for which transport is one of the most complicated components, requiring different transport models in each region. The authors apply questions to a wide variety of application areas, such as semiconductors, plasmas, fluids, chemically reactive gases, etc.

Transport in Transition Regimes

Giovanni Russo

Lorenzo Pareschi

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. 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 works. Specific applications presented include plasma kinetic models, traffic flow models, granular media models, and coagulation-fragmentation problems. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.

Modeling and Computational Methods for Kinetic Equations

Grégoire Allaire

Nicola Bellomo

Eitan Tadmor

This volume collects ten surveys on the modeling, simulation, and applications of active particles using methods ranging from mathematical kinetic theory to nonequilibrium statistical mechanics. The contributing authors are leading experts working in this challenging field, and each of their chapters provides a review of the most recent results in their areas and looks ahead to future research directions. The approaches to studying active matter are presented here from many different perspectives, such as individual-based models, evolutionary games, Brownian motion, and continuum theories, as well as various combinations of these. Applications covered include biological network formation and network theory; opinion formation and social systems; control theory of sparse systems; theory and applications of mean field games; population learning; dynamics of flocking systems; vehicular traffic flow; and stochastic particles and mean field approximation. Mathematicians and other members of the scientific community interested in active matter and its many applications will find this volume to be a timely, authoritative, and valuable resource.

Advances in Theory, Models, and Applications

Active Particles, Volume 1

Pierre Degond

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