Mathematical Models in Natural Science and Engineering

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W. Hollik, R. Rückl, J. Wess (eds

Although the Standard Model of strong and electroweak interactions describesparticle physics phenomena up to the vector boson mass scale very well, it is in general believed that it is not the ultimate theory. The aim of this series of seminars was to initiate discussions between field theorists and phenomenologically oriented high energy physicists on the observable consequenses of the concept of SUSY. The subjects covered by the individual contributions include an introduction to the basic features of SUSY models, in particular the minimal supersymmetric Standard Model, followed by discussions of the theoretical predictions and experimental findings on the particle content and mass spectra, cosmological consequenses, indirect manifestations through quantum effects, radiative corrections in the supersymmetric Higgs sector, and the concept of dynamical electroweak symmetry breaking in the context ofSUSY. These topics are treated at a level appropriate for advanced students.However, the book should also be useful for teachers and researchers.

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E.N. Economou

The main part of this book is devoted to the simplest kind of Green's functions, namely the solutions of linear differential equations with a -function source. It is shown that these familiar Green's functions are a powerful tool for obtaining relatively simple and general solutions of basic problems such as scattering and boundlevel information. The bound-level treatment gives a clear physical understanding of "difficult" questions such as superconductivity, the Kondo effect, and, to a lesser degree, disorder-induced localization. The more advanced subject of many-body Green's functions is presented in the last part of the book.

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Michel Remoissenet

Written for an interdisciplinary readership of physicists, engineers, and chemists, this book is a practical guide to the fascinating world of solitons. These waves of large amplitude propagate over long distances without dispersing and therefore show one of the most striking aspects of nonlinearity. The author addresses students, practitioners, and researchers, approaching the subject from the standpoint of applications in optics, hydrodynamics, and electrical and chemical engineering. The book also encourages the readers to perform their own experiments. Since the printing of the second edition of this book, there has been a large growth in the literature on nonlinear waves and so has the wide applicability of the subject to the physical, chemical and biological sciences. Accordingly, this third edition has been thoroughly revised. Some of the topics are brought up to date with pertinent references. Furthermore, the book now includes a completely new chapter on solitary waves in diffuse systems.

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Susanne Pfalzner, Paul Gibbon

Studying the dynamics of a large number of particles interacting through long-range forces, commonly referred to as the N-body problem, is a central aspect of many different branches of physics. In recent years, significant advances have been made in the development of fast N-body algorithms to deal efficiently with such complex problems. This book is the first to give a thorough introduction to these so-called tree methods, setting out the basic principles and giving many practical examples of their use. After a description of the key features of the hierarchical tree method, a variety of general N-body techniques are presented. Open boundary problems are then discussed, as well as the optimization of tree codes, periodic boundary problems, and the fast multipole method. No prior specialist knowledge is assumed, and the techniques are illustrated throughout with reference to a broad range of applications. The book will be of great interest to graduate students and researchers working on the modelling of systems in astrophysics, plasma physics, nuclear and particle physics, condensed-matter physics, and materials science.