Andrew Majda / New York University
Xiaoming Wang / Florida State University and Iowa State University

Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows

Hardback (ISBN-13: 9780521834414 | ISBN-10: 0521834414)
Publication is planned for May 2006 | 564 pages | 247 x 174 mm

The general area of geophysical fluid mechanics is truly interdisciplinary. Now ideas from statistical physics are being applied in novel ways to inhomogeneous complex systems such as atmospheres and oceans. In this book, the basic ideas of geophysics, probability theory, information theory, nonlinear dynamics and equilibrium statistical mechanics are introduced and applied to large time-selective decay, the effect of large scale forcing, nonlinear stability, fluid flow on a sphere and Jupiter's Great Red Spot. The book is the first to adopt this approach and it contains many recent ideas and results. Its audience ranges from graduate students and researchers in both applied mathematics and the geophysical sciences. It illustrates the richness of the interplay of mathematical analysis, qualitative models and numerical simulations which combine in the emerging area of computational science.

* First book combining nonlinear dynamical and statistical approaches at elementary level
* Only basic prerequisites; many topics introduced through examples as and when required
* Many applications to geophysics including Great Red Spot of Jupiter

Contents

1. Barotropic geophysical flows and two-dimensional fluid flows: an elementary introduction; 2. The Response to large scale forcing; 3. The selective decay principle for basic geophysical flows; 4. Nonlinear stability of steady geophysical flows; 5. Topographic mean-flow interaction, nonlinear instability, and chaotic dynamics; 6. Introduction to empirical statistical theory; 7. Equilibrium statistical mechanics for systems of ordinary differential equations; 8. Statistical mechanics for the truncated quasi-geostrophic equations; 9. Empirical statistical theories for most probable states; 10. Assessing the potential applicability of equilibrium statistical theories for geophysical flows: an overview; 11. Predictions and comparison of equilibrium statistical theories; 12. Equilibrium statistical theories and dynamical modeling of flows with forcing and dissipation; 13. Predicting the jets and spots on Jupiter by equilibrium statistical mechanics; 14. Statistically relevant and irrelevant conserved quantities for truncated quasi-geostrophic flow and the Burger Hopf model; 15. A mathematical framework for quantifying predictability utilizing relative entropy; 16. Barotropic quasi-geostrophic equations on the sphere; Bibliography; Index.

Robert Messer / Albion College, Michigan
Philip Straffin / Beloit College, Wisconsin

Topology Now !

Series: Classroom Resource Material
Hardback (ISBN-13: 9780883857441 | ISBN-10: 0883857448)
Publication is planned for May 2006 | 250 pages | 253 x 177 mm

Courses: Introduction to topology, topology

Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors have written this textbook to make the material accessible to undergraduate students without requiring extensive prerequisites in upper-level mathematics. The approach is to cultivate the intuitive ideas of continuity, convergence, and connectedness so students can quickly delve into knot theory, the topology of surfaces and three-dimensional manifolds, fixed points and elementary homotopy theory. The fundamental concepts of point-set topology appear at the end of the book when students can see how this level of abstraction provides a sound logical basis for the geometrical ideas that have come before. This organization exposes students to the exciting world of topology now(!) rather than later. Students using this textbook should have some exposure to the geometry of objects in higher-dimensional Euclidean spaces together with an appreciation of precise mathematical definitions and proofs.

* Develops intuitive geometric ideas before moving on to axiomatic topological ideas
* The approach allows students rapid access to the exciting geometric ideas of topology
* The well written text is supplemented by many instructive diagrams, exercises and worked examples

Contents

Preface; Acknowledgments; 1. Deformations; 2. Knots and links; 3. Surfaces; 4. Three-dimensional manifolds; 5. Fixed points; 6. The fundamental group; 7. Metric and topological spaces; Index.

Ivo Sachs / Ludwig-Maximilians-Universitat Munchen
Siddartha Sen / Trinity College, Dublin
James Sexton / Trinity College, Dublin

Elements of Statistical Mechanics
With an Introduction to Quantum Field Theory and Numerical Simulation

Hardback (ISBN-13: 9780521841986 | ISBN-10: 0521841984)
Publication is planned for May 2006 | 346 pages | 247 x 174 mm

Courses: Statistical Mechanics Statistical Physics Thermodynamics
Levels: ADVANCED UNDERGRADUATE AND GRADUATE

This textbook provides a concise introduction to the key concepts and tools of modern statistical mechanics. It also covers advanced topics such as non-relativistic quantum field theory and numerical methods. After introducing classical analytical techniques, such as cluster expansion and Landau theory, the authors present important numerical methods with applications to magnetic systems, Lennard-Jones fluids and biophysics. Quantum statistical mechanics is discussed in detail and applied to Bose-Einstein condensation and topics in astrophysics and cosmology. In order to describe emergent phenomena in interacting quantum systems, canonical non-relativistic quantum field theory is introduced and then reformulated in terms of Feynman integrals. Combining the authors' many years' experience of teaching courses in this area, this textbook is ideal for advanced undergraduate and graduate students in physics, chemistry and mathematics.

* Analytical and numerical techniques in one text, including sample codes and solved problems on the web at www.cambridge.org/0521841984
* Covers a wide range of applications including magnetic systems, turbulence astrophysics, and biology
* Contains a concise introduction to Markov processes and molecular dynamics

Contents

1. The problem; 2. Statistical mechanics; 3. Variations of a theme; 4. Handling interactions; 5. Monte Carlo integration; 6. Numerical molecular dynamics; 7. Quantum statistical mechanics; 8. Astrophysics; 9. Non-relativistic quantum field theory; 10. Superfluidity; 11. Path integrals; 12. A second look; 13. Phase transitions and the renormalization group.

Andrew Whitaker / The Queen's University of Belfast

Einstein, Bohr and the Quantum Dilemma, 2nd Edition
From Quantum Theory to Quantum Information

Paperback (ISBN-13: 9780521671026 | ISBN-10: 0521671027)
Not yet published - available from May 2006

Quantum theory, the most successful physical theory of all time, provoked intense debate between the twentieth century's two greatest physicists, Niels Bohr and Albert Einstein. Quantum information theory has emerged from intensive study of the structure and interpretation of quantum theory to become one of the fastest growing areas of twenty-first century science. This second edition has been extensively revised and updated to cover recent developments, including the findings of papers published since the well-received first edition. A substantial new chapter is devoted to the development and structure of quantum information theory. Developments in the experimental and theoretical study of Bell's Theorem are also covered in detail, and the accounts of ongoing work have been brought up to date. A fascinating account of the development of quantum theory, this book will appeal to anyone with an interest in the fundamental questions of physics, its philosophy and its history.

* Straightforward account of the work of Bohr, Einstein and Bell which elucidated the nature of quantum theory
* Updated to include a readable account of quantum information theory
* Contains very little mathematics

Contents

1. Bohr and Einstein: Einstein and Bohr; 2. The peace before the quantum; 3. A glance at relativity; 4. The slow rise of the quantum; 5. Bohr: what does it all mean?; 6. Einstein’s negative views; 7. Bohm, Bell and experimental philosophy; 8. A round-up of recent developments; 9. Quantum information theory - an introduction; 10. Bohr or Einstein?; References; Bibliography.

Reviews

From reviews of the first edition: ‘This book is a potential block-buster. Written in a nice style, structured like a popular lecture, its language is lucid and the contents well selected … it has the most thorough coverage and clear explanation of classical physics that I have read for a long time … It has additonally the advantages of being well-researched, with the latest available material … and written by a first rate physicist with excellent communication skills.’ Samar Jha, The Statesman

‘Whitaker’s book is admirably clear and deceptively simple: he has a real knack of describing difficult ideas in an accessible form. He is up-to-date, never descends to the facile level so often adopted by writers of introductory books, and what’s more, has provided a thorough bibliography so that the really interested reader can find the original treatment. I recommend this book not only for students but for anyone with an interest in fundamental issues in physics.’ P. L. Knight, Journal of Modern Optics

‘I most strongly recommend this book to anyone - lay person, student and professional alike - interested in the foundations of our candidate for the fundamental theory of physics (quantum mechanics).’ James T. Cushing, The Times Higher Education Supplement