## 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.