Kategoria BISAC: Science >> Physics - Mathematical & Computational

Stochastic differential equations play an increasingly important role in modeling the dynamics of a large variety of systems in the natural sciences, and in technological applications. This book is aimed at advanced undergraduate and graduate students, and researchers in mathematics, physics, the natural sciences, and engineering. It presents a new constructive approach to the quantitative description of solutions to systems of stochastic differential equations evolving on well-separated timescales. The method, which combines techniques from stochastic analysis and singular perturbation...

From the reviews: "This attractive book provides an account of the theory of special relativity from a geometrical viewpoint, explaining the unification and insights that are given by such a treatment. ...] Can be read with profit by all who have taken a first course in relativity physics." ASLIB Book Guide

Stochastic geometry is a relatively new branch of mathematics. Although its predecessors such as geometric probability date back to the 18th century, the formal concept of a random set was developed in the beginning of the 1970s. Theory of Random Sets presents a state of the art treatment of the modern theory, but it does not neglect to recall and build on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference of the 1990s.

The book is entirely...

The analysis and simulation of multifield problems have recently become one of the most actual and vivid areas of research. Although the individual subproblems of complex technical and physical phenomena often are understood separately, their interaction and coupling create not only new difficulties but also a complete new level and quality of interacting coupled field problems. Presented by leading experts this book includes recent results in these fields from the International Conference on Multifield Problems, April 8-10, 2002 at the University of Stuttgart, Germany.

The main theme of this book is semiclassical methods for systems with spin, in particular methods involving trace formulae and torus quantisation and their applications in the theory of quantum chaos, e.g. the characterisation of spectral correlations. The theoretical tools developed here not only have immediate applications in the theory of quantum chaos - which is the second focus of the book - but also in atomic and mesoscopic physics. Thus the intuitive understanding of semiclassical spin dynamics will also be helpful in emerging subjects like spintronics and quantum computation.

The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be complemented by a companion book dedicated to discrete integrable systems. Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.

The book covers topics in the theory of algebraic transformation groups and algebraic varieties which are very much at the frontier of mathematical research.

Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. In fact, optical systems (geometric or wave) have an even richer symmetry structure than mechanical ones (classical or quantum). The symmetries underlying the geometric model of light are based on the symplectic group. Geometric Optics on Phase Space develops both geometric optics and group theory from first principles in their Hamiltonian formulation on phase space. This treatise provides the mathematical background and also collects a host of useful methods...

This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and Painleve analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas,...