ROGER TEMAM / Universite de Poitiers
AND ALAIN MIRANVILLE / University of Indiana, Bloomington

Mathematical Modeling in Continuum Mechanics

Description: Continuum mechanics is widely taught to graduate students in applied mathematics, physics, and engineering, providing the basis for further study in fluid and solid mechanics. Presentations of the subject, however, vary greatly in their level of formalism, being either engineering and example oriented or mathematically over-sophisticated. Temam and Miranville provide a rigorous presentation of the underlying mathematics and physics of the problem, avoiding unnecessary use of function spaces. The authors then build on this base to present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics, including: viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This original text should be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level, whether in engineering, mathematics, physics, or the applied sciences.

Contents: Part I. Fundamental Concepts in Continuum Mechancis: 1. Describing the motion of a system: geometry and kinematics; 2. The fundamental law of dynamics; 3. The Cauchy stress-tensor. Applications; 4. Real and virtual powers; 5. Deformation tensor. Deformation rate tensor. Constitutive laws; 6. Energy equations. Shock equations; Part II. Physics of Fluids: 7. General properties of Newtonian fluids; 8. Flows of perfect fluids; 9. Viscous fluids and thermohydraulics; 10. Magnetohydrodynamics and inertial confi ement of plasmas; 11. Combustion; 12. Equations of the atmosphere and of the ocean; Part III. Solid Mechanics: 13. The general equations of linear elasticity; 14. Classical problems of elastostatics; 15. Energy theorems. Duality. Variational formulations; 16. Introduction to nonlinear constitutive laws and to homogenization; Part IV. Introduction to Wave Phenomena: 17. Linear wave equations in mechanics; 18. The soliton equation: the
Korteweg-de Vries equations; 19. The nonlinear Schrodinger equation; Appendix A.

ISBN, Binding, Price: 0521643627 Hardback
Approximate Publication date: 19 September 2000
2000 228 x 152 mm 344pp 40 line diagrams

VIKTOR DOTSENKO
Universitet Paris VI and Landau Institute for Theoretical Physics, Moscow

Introduction to the Replica Theory of Disordered Statistical Systems

Description: This book describes the statistical mechanics of classical spin systems with quenched disorder. The first part of the book covers the physics of spin-glass states using results obtained within the framework of the mean field theory of spin glasses. The technique of replica symmetry breaking is explained in detail, along with a discussion of the underlying physics. The second part is devoted to the theory of critical phenomena in the presence of weak quenched disorder. This includes a systematic derivation of the traditional
renormalization group theory, which is then used to obtain a new 'random' critical regime in disordered vector ferromagnets and in the two-dimensional Ising model. The third part of the book describes other types of disordered systems, relating to new results at the frontiers of modern research. The book is suitable for graduate students and researchers in the field of statistical mechanics of disordered systems.

Contents: Preface; 1. Introduction; Part I. Spin-Glass Systems: 2. Physics of the spin glass state; 2. The mean-field theory of spin glasses; 4. Physics of replica symmetry breaking; 5. Ultrametricity; 6. Experiments; Part II. Critical Phenomena and Quenched Disorder: 7. Scaling theory of the critical phenomena; 8. Critical behaviour in systems with disorder; 9. Spin glass effects in the critical phenomena; 10. Two dimensional Ising model with disorder; Part III. Other Types of Disordered Systems: 11. Ising systems with quenched random fields; 12. One dimensional directed polymers in random potentials; 13. Vector breaking of replica symmetry; 14. Conclusions; References.

ISBN, Binding, Price: 0521773407 Hardback
Approximate Publication date: 5 October 2000
Main Subject Category: Theoretical, mathematical physics
Series: Collection Alea-Saclay: Monographs and Texts in Statistical Physics
2000 247 x 174 mm 248pp 35 line diagrams

SHELDON M. ROSS
University of California, Berkeley

Topics in Discrete and Finite Mathematics

Description: Written for a broad audience of students in mathematics, computer science, operations research, statistics, and engineering, this textbook presents a short, lively survey of several fascinating non-calculus topics in modern applied mathematics. Coverage includes probability, mathematical finance, graphs, linear programming, statistics, computer science algorithms, and groups. A key feature is the abundance of interesting examples not normally found in standard finite mathematics courses, such as options pricing and arbitrage, tournaments, and counting formulas. The author assumes a level of mathematical sophistication at the beginning calculus level, that is, students should have had at least a course in pre-calculus, and the added sophistication attained from studying calculus would be useful.

Contents: 1. Preliminaries; 2. Combinatorial analysis; 3. Probability; 4. Mathematics of finance; 5. Graphs and trees; 6. Direct graphs; 7. Linear programming; 8. Sorting and searching; 9. Statistics; 10. Groups and permutations.

ISBN, Binding, Price: 052177571X Paperback
ISBN, Binding, Price: 0521772591 Hardback
Approximate Publication date: 8 October 2000
2000 228 x 152 mm 304pp 53 line diagrams 15 tables 230 exercises
Main Subject Category: Mathematics - Statistics, OR, Math Finance

EDITED BY B. SCAIFE
Trinity College, Dublin

Mathematical Papers of Sir William Rowan Hamilton vol.4

Description: This fourth and final volume of The Collected Papers of Sir William Rowan Hamilton (1805-1865) contains three previously unpublished and important manuscripts, namely Systems of Rays and two lengthy letters to de Morgan (on definite integrals) and Hart (on anharmonic coordinates). In addition the volume contains reprinted papers on geometry, analysis, astronomy, probability and finite differences, as well as a collection of papers on various topics. A cumulative index for all three volumes is provided, as well as a CD
containing all four volumes of the Collected Papers.

Contents: Part I. System of Rays, Part III: Part II. Letter to De Morgan, 15 February 1858, and 15 July 1858: Part III. Letter to Dr. Hart 1860: Part IV. Geometry:

ISBN, Binding, Price: 052159216X Hardback
Approximate Publication date: 5 October 2000
2000 276 x 219 mm 900pp 43 line diagrams 1 half-tone

Comparable titles: HAMILTON/Collected Papers of Sir William Rowan Hamilton, volume 3/1967/0521 051835

DANIEL BEN-AVRAHAM / Clarkson University
AND SHLOMO HAVLIN / Bar-Ilan University

Diffusion and Reactions in Fractals and Disordered Systems

Description: Fractal structures are found everywhere in nature, and as a consequence anomalous diffusion has far reaching implications in a host of phenomena. This book describes diffusion and transport in disordered media such as fractals, porous rocks and random resistor networks. Divided into four Parts, Part I contains material of general interest to statistical physics: fractals, percolation theory, regular random walks and diffusion, continuous time random walks and Levy walks and flights. Part II covers anomalous diffusion in fractals and disordered media, while Part III serves as an introduction to the kinetics of diffusion-limited reactions. Part IV discusses the problem of diffusion-limited coalescence in one dimension. This book will be of particular interest to researchers requiring a clear introduction to the field. It will also be of interest to graduate students studying in areas of physics, chemistry, and engineering.

Contents: Preface; Part I. Basic Concepts: 1. Fractals; 2. Percolation; 3. Random walks; 4. Beyond random walks; Part II. Anomalous Diffusion: 5. Diffusion; 6. Diffusion in percolation clusters; 7. Diffusion in loopless structures; 8. Disordered transition rates; 9. Biased anomalous diffusion; 10. Excluded volume interactions; Part III. Diffusion-Limited Reactions: 11. Classical models of reactions; 12. Trapping; 13. Simple reaction models; 14. Reaction-diffusion fronts; Part IV. Diffusion-Limited Coalescence: An Exactly Solvable Model:
15. Coalescence and the IPDF method; 16. Irreversible coalescence; 17. Reversible coalescence; 18. Complete representations of coalescence; 19. Finite reaction rates; Appendix A. Fractal dimension; Appendix B. Number of distinct sites visited by random walks; Appendix C. Exact enumeration; Appendix D. Long-range correlations.

ISBN, Binding, Price: 0521622786 Hardback
Approximate Publication date: 1 November 2000
Main Subject Category: Nonlinear science
2000 247 x 174 mm 288pp 100 line diagrams 128 exercises