Javier Bonet / University of Wales, Swansea
Richard D. Wood / University of Wales, Swansea

Nonlinear Continuum Mechanics for Finite Element Analysis
2nd Edition

Hardback (ISBN-13: 9780521838702)

Designing engineering components that make optimal use of materials requires consideration of the nonlinear characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through numerical formulation and simulation, and this requires an understanding of both the theoretical background and associated computer solution techniques. By presenting both nonlinear continuum analysis and associated finite element techniques under one roof, Bonet and Wood provide, in the new edition of this successful text, a complete, clear, and unified treatment of these important subjects. New chapters dealing with hyperelastic plastic behavior are included, and the authors have thoroughly updated the FLagSHyP program, freely accessible at www.flagshyp.com. Worked examples and exercises complete each chapter, making the text an essential resource for postgraduates studying nonlinear continuum mechanics. It is also ideal for those in industry requiring an appreciation of the way in which their computer simulation programs work.

* Second edition of well-received and successful graduate text on computational solid mechanics, updated and including two additional chapters dealing with large deformation elasto-plastic behaviour of truss analysis and solid continua * The authors present nonlinear continuum mechanics using finite element methods with updated software package * Suitable for post graduate teaching as well as for professionals needing a self-contained introduction

Contents

1. Introduction; 2. Mathematical preliminaries; 3. Analysis of three-dimensional truss structures; 4. Kinematics; 5. Stress and equilibrium; 6. Hyperelasticity; 7. Large elasto-plastic deformations; 8. Linearized equilibrium equations; 9. Discretization and solution; 10. Computer implementation; Bibliography. Index.

Reviews

' … a unified introduction - can be recommended to postgraduate students and to researchers from mechanical, aerospace and civil engineering areas.' Zentralblatt fur Mathematik und ihre Grenzgebiete

'The authors have succeeded in writing an excellent textbook - the book is absolutely recommended directly to students and scientists in the field of solid mechanics at universities.' K. Schweizerhof, ZAMM

A. A. Borovkov / Sobolev Institute of Mathematics, Novosibirsk
K. A. Borovkov / University of Melbourne

Asymptotic Analysis of Random Walks
Heavy-Tailed Distributions

Series: Encyclopedia of Mathematics and its Applications (No. 118)
Hardback (ISBN-13: 9780521881173)

This book is devoted to studying the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks, with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. Large deviation probabilities are of great interest in numerous applied areas, with typical examples being ruin probabilities in risk theory, error probabilities in mathematical statistics, and buffer overflow probabilities in queueing theory. The classical large deviations theory, developed for exponentially fast (or even faster) decaying at infinity distributions, mostly uses analytical methods. If the fast decay condition fails, which is the case in many important applied problems, then mostly direct probabilistic methods prove to be more efficient. This monograph presents a unified and systematic exposition of the large deviations theory for heavy-tailed random walks, based on a common approach, with a large number of new results.

* The first unified systematic exposition of the large deviations theory for heavy-tailed random walks * Computing the probabilities of these large deviations (rare events) is essential, in fields such as finance, networks and insurance; this books shows you how * Includes many never before published results on large deviations for random walks with non-identically distributed jumps

Contents

Introduction; 1. Preliminaries; 2. Random walks with jumps having no finite first moment; 3. Random walks with finite mean and infinite variance; 4. Random walks with jumps having finite variance; 5. Random walks with semiexponential jump distributions; 6. Random walks with exponentially decaying distributions; 7. Asymptotic properties of functions of distributions; 8. On the asymptotics of the first hitting times; 9. Large deviation theorems for sums of random vectors; 10. Large deviations in the space of trajectories; 11. Large deviations of sums of random variables of two types; 12. Non-identically distributed jumps with infinite second moments; 13. Non-identically distributed jumps with finite variances; 14. Random walks with dependent jumps; 15. Extension to processes with independent increments; 16. Extensions to generalised renewal processes; Bibliographic notes; Index of notations; Bibliography.

Michel Deza / Ecole Normale Superieure, Paris
Mathieu Dutour Sikiri* / Institut Rudjer Bo*kovi*, Zagreb

Geometry of Chemical Graphs
Polycycles and Two-faced Maps

Series: Encyclopedia of Mathematics and its Applications (No. 119)
Hardback (ISBN-13: 9780521873079)

Studying three new classes of plane graphs which generalise regular polyhedra together with the relevant background material this book discuses graphs with interesting applications in Chemistry and Crystallography. Polycycles (or clusters of cycles) are 2-connected plane graphs having unique combinatorial type of interior faces and the same degree q for interior vertices, while at most q for boundary vertices. Two-faced polyhedra are those, having at most two types of faces and the same degree of vertices. Topics covered include enumeration, symmetry, extremal properties, face-regularity, metric embedding as well as algorithmic problems and connection to links. After reading the introductory chapter, each chapter can be read independently from the others allowing researchers from other fields fast access to the relevant topics.

* The first book on the subject of polycycles; contains all relevant background material and mathematical tools for their study * Accessible to researchers and students in graph theory, discrete geometry, and combinatorics, as well as to those in more applied areas such as mathematical chemistry and crystallography * Programs for these results are available from the web page http://www.liga.ens.fr/~dutour/BOOK_Polycycles

Contents

Preface; 1. Introduction; 2. Two-faced maps; 3. Fullerenes as tilings of surfaces; 4. Polycycles; 5. Polycycles with given boundary; 6. Symmetries of polycycles; 7. Elementary polycycles; 8. Applications of elementary decompositions to (r, q)-polycycles; 9. Strictly face-regular spheres and tori; 10. Parabolic weakly face-regular spheres; 11. Generalities on 3-valent face-regular maps; 12. Spheres and tori, which are aRi; 13. Frank-Kasper spheres and tori; 14. Spheres and tori, which are bR1; 15. Spheres and tori, which are bR2; 16. Spheres and tori, which are bR3; 17. Spheres and tori, which are bR4; 18. Spheres and tori, which are bRj for j * 5; 19. Icosahedral fulleroids.

Ralf Meyer (University of Gottingen, Germany)

Local and Analytic Cyclic Homology

EMS Tracts in Mathematics Vol. 3
ISBN 978-3-03719-039-5
August 2007, 368 pages, hardcover, 17.0 cm x 24.0 cm.

Periodic cyclic homology is a homology theory for non-commutative algebras that plays a similar role in non-commutative geometry as de Rham cohomology for smooth manifolds. While it produces good results for algebras of smooth or polynomial functions, it fails for bigger algebras such as most Banach algebras or C*-algebras. Analytic and local cyclic homology are variants of periodic cyclic homology that work better for such algebras. In this book the author develops and compares these theories, emphasising their homological properties. This includes the excision theorem, invariance under passage to certain dense subalgebras, a Universal Coefficient Theorem that relates them to K-theory, and the Chern*Connes character for K-theory and K-homology.

The cyclic homology theories studied in this text require a good deal of functional analysis in bornological vector spaces, which is supplied in the first chapters. The focal points here are the relationship with inductive systems and the functional calculus in non-commutative bornological algebras.

The book is mainly intended for researchers and advanced graduate students interested in non-commutative geometry. Some chapters are more elementary and independent of the rest of the book, and will be of interest to researchers and students working in functional analysis and its applications.

Table of contents