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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.
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.
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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