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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.
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.
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.
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.
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.
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 m
This volume compiles eight recent surveys that present
state-of-the-art results in the field of active matter at different
scales, modeled by agent-based, kinetic, and hydrodynamic
descriptions. Following the previously published volume, these
chapters were written by leading experts in the field and
accurately reflect the diversity of subject matter in theory and
applications. Several mathematical tools are employed throughout
the volume, including analysis of nonlinear PDEs, network theory,
mean field approximations, control theory, and flocking analysis.
The book also covers a wide range of applications, including:
Biological network formation Social systems Control theory of
sparse systems Dynamics of swarming and flocking systems Stochastic
particles and mean field approximations 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.
Downscaling of semiconductor devices, which is now reaching the
nanometer scale, makes it mandatory for us to understand the
quantum phenomena -
volvedinchargetransport.Indeed,fornanoscaledevices,thequantumnature
of electrons cannot be neglected. In fact, it underlies the
operation of an increasing number of devices. Unlike classical
transport, the intuition of the
physicistandtheengineerisbecominginsu?cientforpredictingthenatureof
device operation in the quantum context-the need for su?ciently
accurate and numerically tractable models represents an outstanding
challenge in which applied mathematics can play an important role.
TheCIMESession"QuantumTransport:Modelling,AnalysisandAsy- totics",
which took place in Cetraro (Cosenza), Italy, from September 11 to
September 16, 2006, was intended both to present an overview of
up-to-date mathematical problems in this ?eld and to provide the
audience with te- niques borrowed from other ?elds of application.
It was attended by about 50 scientists and researchers, coming from
d- ferent countries. The list of participants is included at the
end of this book. The school was structured into four courses: ' *
Gr' egoire Allaire (Ecole Polytechnique, Palaiseau, France)
Periodic - mogeneization and E?ective MassTheorems for theSchr.
odinger Equation. * AntonArnold(TechnischeUniversit.
at,Vienna)MathematicalProperties of Quantum Evolution Equations. *
Pierre Degond (Universit' e Paul Sabatier and CNRS, Toulouse,
France) Quantum Hydrodynamic and Di?usion Models Derived from the
Entropy Principle. * Thomas Yizhao Hou (Caltech, Los Angeles, USA)
Multiscale Com- tations for Flow and Transport in Heterogeneous
Media. This book contains the texts of the four series of lectures
presented at the Summer School. Here follows a brief description of
the subjects of these courses.
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