V.V. Aristov
Computing Center of the Russian Academy of
Sciences, Moscow,
Russia
Direct Methods for Solving the Boltzmann
Equation
and Study of Nonequilibrium Flow
FLUID MECHANICS AND ITS APPLICATIONS Volume
60
The outstanding points of our book consist
of investigations into
the possibility of the numerical schemes
of the direct method for
solving the Boltzmann equation. Both deterministic
and Monte
Carlo procedures are considered to evaluate
the collision
integrals. The main mathematical tool is
the conservative
splitting method on the basis of which, a
set of classical and
new problems are solved to study nonequilibrium
gas flows. This
monograph differs from other books in the
same field, because,
for example the book by G.A. Bird is concerned
with the approach
of simulation of rarefied gas flows and the
book by C. Cercignani
deals with the classical kinetic theory issues
and describes
mainly the analytical and engineering methods
for solving the
Boltzmann equation. Our book is the first
(as we know) monograph
which is devoted to the numerical direct
solving of the Boltzmann
equation. The intended level of readership
are graduate and
postgraduate students and researches. This
book can be used by
the target groups as the mathematical apparatus
to numerical
study of complex problems of nonequilibrium
gas flows.
Contents
Preface. Introduction. 1. The Boltzmann Equation
as a Physical
and Mathematical Model. 2. Survey of Mathematical
Approaches to
Solving the Boltzmann Equation. 3. Main Features
of the Direct
Numerical Approaches. 4. Deterministic (Regular)
Method for
Solving the Boltzmann Equation. 5. Construction
of Conservative
Scheme for the Kinetic Equation. 6. Parallel
Algorithms for the
Kinetic Equation. 7. Application of the Conservative
Splitting
Method for Investigating Near Continuum Gas
Flows. 8. Study of
Uniform Relaxation in Kinetic Gas Theory.
9. Nonuniform
Relaxation Problem as a Basic Model for Description
of Open
Systems. 10. One-Dimensional Kinetic Problems.
11. Multi-Dimensional
Problems. Study of Free Jet Flows. 12. The
Boltzmann Equation and
the Description of Unstable Flows. 13. Solutions
of Some Multi-Dimensional
Problems. 14. Special Hypersonic Flows and
Flows with Very High
Temperatures.
Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6831-2
January 2001, 312 pp.
T. Kambe / University of Tokyo, Japan
T. Nakano / Chuo University, Japan
T. Miyauchi / Tokyo Institute of Technology,
Japan
IUTAM Symposium on Geometry and Statistics
of Turbulence
Held at the Shonan Int'l. Village Center,
Hayama (Kanagawa-ken), Japan, November 1-5,
1999
FLUID MECHANICS AND ITS APPLICATIONS Volume
59
This book is new because emphasis is placed
on the aspect that
the statistical laws in turbulence are not
disconnected with the
coherent structures distributing randomly
in space and forming/decaying
spontaneously in time, and that the anomalous
scaling laws of a
passive scalar in turbulence are captured
from the first
principle. Existence of such coherences in
the stochastic
processes of turbulence leads to the intermittency
and also non-Gaussian
statistics. Details of the geometrical structures
are
investigated how they are described in terms
of vortices of shear
layers.
The current state of the art is presented
in this book for
graduate- and advanced-level students, by
scientists working in
the frontier of diverse areas of turbulence
study theoretically,
computationally, and experimentally, centered
at the subject
Structure and Statistics.
Contents
Preface. A. General and Mathematical. B.
Coherent Structures,
Intermittency, and Cascade. C. Probability
Density Functions and
Structure Functions. D. Passive Scalar Advections.
E. Vortices,
Vorticity, and Strain Dynamics. F. Large
Scale Motions, LES, and
Closure. G. Thermal Turbulence, and Stratified
and Rotating
Turbulence. H. Transition Mechanisms. I.
Modulation of Turbulence.
J. Pipe-Flow and Channel-Flow Turbulence.
K. Boundary Layers and
Near-Wall Turbulence. Participant List. Index.
Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6711-1
January 2001, 416 pp.
Saul I. Gass / University of Maryland, College Park, USA
Carl M. Harris / George Mason University,
Fairfax, VA, USA
Encyclopedia of Operations Research and Management
Science
Centennial Edition
The goal of the Encyclopedia of Operations
Research and
Management Science is to provide decision
makers and problem
solvers in business, industry, government
and academia with a
comprehensive overview of the wide range
of ideas, methodologies,
and synergistic forces that combine to form
the pre-eminent
decision-aiding fields of operations research
and management
science (OR/MS). The Second Edition is a
further extension of
this goal - which through addressing and
solving a wide range of
problems - OR/MS methodologies continue to
flourish and grow.
This is a field that is used extensively
throughout the applied
sciences, and, because of this, the new edition
has added topics
in the following areas:
Analytic Network Process;
Call Centers;
Certainty Equivalence;
Comb. Optimization by Simulated CE;
Computational Organization;
Constraint Programming;
Data Mining;
Degeneracy Graphs;
Economic Order Q Extensions;
Educational Issues in B-Schools;
Electronic Commerce;
Financial Markets;
Global Climate Change;
Hidden Markov Models;
History of Early British OR;
Implementation for Public Sector;
Info Tech Benefits;
Interactive Multi-Objective Math. Programming;
Knapsacks with Nonlinearities;
Little's Law in Distribution Form;
Military Ops Other than War;
Multivariate Quality Control;
Perturbation Analysis;
Simulation Metamodeling;
Simulation Optimization;
Supply Chain Management;
Theory of Constraints;
Timetabling.
The intended audience of the Encyclopedia
of Operations Research
and Management Science is technically diverse
and wide; it
includes anyone concerned with the science,
techniques, and ideas
of how one makes decisions. As this audience
encompasses many
professions, educational backgrounds and
skills, we were
attentive to the form, format and scope of
the articles. Thus,
the articles are designed to serve as initial
sources of
information for all such readers, with special
emphasis on the
needs of students. Each article provides
a background or history
of the topic, describes relevant applications,
overviews present
and future trends, and lists seminal and
current references. To
allow for variety in exposition, the authors
were instructed to
present their material from both research
and applied
perspectives.
The Encyclopedia has been organized into
specific topics that
collectively encompass the foundations, applications,
and
emerging elements of this ever-changing field.
We also wanted to
establish the close associations that OR/MS
has maintained with
other scientific endeavors, with special
emphasis on its
symbiotic relationships to computer science,
information
processing, and mathematics. Based on our
broad view of OR/MS, we
commissioned 228 major expository articles
and complemented them
by numerous entries: descriptions, discussions,
definitions, and
abbreviations. The connections between topics
are highlighted by
an entry's final `See' statement, as appropriate.
Each topical
article provides a background or history
of the topic, describes
relevant applications, overviews present
and future trends, and
lists seminal and current references. Of
significant importance
is that each contributed topic has been authored
by a leading
authoritative researcher on that particular
topic.
Kluwer Academic Publishers, Boston
Hardbound, ISBN 0-7923-7827-X
February 2001, 960 pp.
edited by
Luigi Accardi / Hui-Hsiung Kuo /Nobuaki Obata
/ Kimiaki Saito / Si Si / Ludwig Streit
Recent Developments in Infinite-Dimensional
Analysis & Quantum Probability
Papers in honour of Takeyuki Hida's 70th
birthday
Reprinted from ACTA APPLICANDAE MATHEMATICA,
63:1-3
Recent Developments in Infinite-Dimensional
Analysis and Quantum
Probability is dedicated to Professor Takeyuki
Hida on the
occasion of his 70th birthday. The book is
more than a collection
of articles. In fact, in it the reader will
find a consistent
editorial work, devoted to attempting to
obtain a unitary picture
from the different contributions and to give
a comprehensive
account of important recent developments
in contemporary white
noise analysis and some of its applications.
For this reason, not
only the latest results, but also motivations,
explanations and
connections with previous work have been
included.
The wealth of applications, from number theory
to signal
processing, from optimal filtering to information
theory, from
the statistics of stationary flows to quantum
cable equations,
show the power of white noise analysis as
a tool. Beyond these,
the authors emphasize its connections with
practically all
branches of contemporary probability, including
stochastic
geometry, the structure theory of stationary
Gaussian processes,
Neumann boundary value problems, and large
deviations.
Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-7016-3
April 2001, 472 pp.
edited by
Yoshiaki Maeda ,Tatsuya Tate ,Hitoshi Moriyoshi
/Keio University,
Hideki Omori / Science University of Tokyo,Satoshi
Watamura /
Tohoku University,
Daniel Sternheimer / CNRS and Universite'
de Bourgogne, Dijon,
France
Noncommutative Differential Geometry and
Its Applications to
Physics
Proceedings of the Workshop at Shonan, Japan,
June 1999
MATHEMATICAL PHYSICS STUDIES Volume 23
Noncommutative differential geometry is a
new approach to
classical geometry. It was originally used
by Fields Medalist A.
Connes in the theory of foliations, where
it led to striking
extensions of Atiyah-Singer index theory.
It also may be
applicable to hitherto unsolved geometric
phenomena and physical
experiments.
However, noncommutative differential geometry
was not well
understood even among mathematicians. Therefore,
an international
symposium on commutative differential geometry
and its
applications to physics was held in Japan,
in July 1999. Topics
covered included: deformation problems, Poisson
groupoids, operad
theory, quantization problems, and D-branes.
The meeting was
attended by both mathematicians and physicists,
which resulted in
interesting discussions. This volume contains
the refereed
proceedings of this symposium.
Providing a state of the art overview of
research in these
topics, this book is suitable as a source
book for a seminar in
noncommutative geometry and physics.
Audience: This volume will be of interest
to researchers and
postgraduate students whose work involves
quantum mechanics,
quantum field theory, integral transforms,
operational calculus,
and global analysis on manifolds.
Contents and Contributors
Preface. Methods of Equivariant Quantization;
C. Dubal, et al.
Application of Noncommutative Differential
Geometry on Lattice to
Anomaly Analysis in Abelian Lattice Gauge
Theory; T. Fujiwara, et
al. Geometrical Structures on Noncommutative
Spaces; O. Grandjean.
A Relation Between Commutative and Noncommutative
Descriptions of
D-Branes; N. Ishibashi. Intersection Numbers
on the Moduli Spaces
of Stable Maps in Genus 0; A. Kabanov, T.
Kimura. D-Brane Actions
on Ka"hler Manifolds; A. Kato. On the
Projective
Classification of the Modules of Differential
Operators on m; P.B.A.
Lecomte. An Interpretation of Schouten-Nijenhuis
Bracket; K.
Mikami. Remarks on the Characteristic Classes
Associated with the
Group of Fourier Integral Operators; N. Miyazaki.
C★-Algebraic
Deformation and Index Theory; T. Natsume.
Singular Systems of
Exponential Functions; H. Omori, et al. Determinants
of Elliptic
Boundary Problems in Quantum Field Theory;
S.G. Scott, et al. On
Geometry of Non-Abelian Duality; P. Severa.
Weyl Calculus and
Wigner Transform on the Poincare' Disk; T.
Tate. Lectures on
Graded Differential Algebras and Noncommutative
Geometry; M.
Dubois-Violette.
Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6930-0
April 2001, 320 pp.
Radu Miron / Faculty of Mathematics, University Al.I. Cuza, Iasi, Romania
Dragos Hrimiuc / University of Alberta, Edmonton,
Canada
Hideo Shimada / Hokkaido Tokai University,
Sapporo, Japan
Sorin V. Sabau / Tokyo Metropolitan University,
Japan
The Geometry of Hamilton and Lagrange Spaces
FUNDAMENTAL THEORIES OF PHYSICS Volume 118
This monograph presents for the first time
the foundations of
Hamilton Geometry. The concept of Hamilton
Space, introduced by
the first author and investigated by the
authors, opens a new
domain in differential geometry with large
applications in
mechanics, physics, optimal control, etc.
The book consists of thirteen chapters. The
first three chapters
present the topics of the tangent bundle
geometry, Finsler and
Lagrange spaces.
Chapters 4-7 are devoted to the construction
of geometry of
Hamilton spaces and the duality between these
spaces and Lagrange
spaces. The dual of a Finsler space is a
Cartan space. Even this
notion is completely new, its geometry has
the same symmetry and
beauty as that of Finsler spaces.
Chapter 8 deals with symplectic transformations
of cotangent
bundle. The last five chapters present, for
the first time, the
geometrical theory and applications of Higher-Order
Hamilton
spaces. In particular, the case of order
two is presented in
detail.
Audience: mathematicians, geometers, physicists,
and mechanicians.
This volume can also be recommended as a
supplementary graduate
text.
Contents
Preface. 1. The geometry of tangent bundle.
2. Finsler spaces. 3.
Lagrange spaces. 4. The geometry of cotangent
bundle. 5. Hamilton
spaces. 6. Cartan spaces. 7. The duality
between Lagrange and
Hamilton spaces. 8. Symplectic transformations
of the
differential geometry of T★ M.
9. The dual bundle of a
k-osculator bundle. 10. Linear connections
on the manifold
T★2M. 11. Generalized Hamilton
spaces of order 2. 12.
Hamilton spaces of order 2. 13. Cartan spaces
of order 2.
Bibliography. Index.
Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6926-2
May 2001, 356 pp.