Encyclopedia Of Nonlinear Science

In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

Much mathematical modelling has involved the assumption that physical systems are approximately linear, leading to the construction of equations which, although relatively easy to solve, are unrealistic and overlook significant phenomena. Models assuming nonlinear systems, however, lead to theemergence of new structures that reflect reality much more closely. This second edition of Nonlinear Science, covers several important areas of nonlinear science, and places a strong emphasis on applications to realistic problems. It includes numerous new topics such as empirical results in molecular dynamics, solid-state physics, neuroscience, fluid dynamics, andbiophysics; numerous new exercises and solutions; updated sections on nerve impulse dynamics, quantum-theory of pump-probe measures, and local modes on lattices. With over 350 problems, including hints and solutions, this is an invaluable resource for graduate students and researchers in the appliedsciences, mathematics, biology, physics and engineering.This is the latest title in the Oxford Texts in Applied and Engineering Mathematics, which includes a range of texts from the undergraduate through to the graduate level. Most titles should be based on taught courses which explain the mathematical or computational techniques required for theresolution of fundamental applied problems. Other books in the series include: D. W. Jordan and P. Smith: Nonlinear ordinary differential equations: an introduction to dynamical systems 3rd Edition; I. J. Sobey: Introduction to interactive boundary layer theory; A. B. Tayler: Mathematical Models inApplied Mechanics (reissue); Ramdas Ram-Mohan: Finite Element and Boundary Element Applications in Quantum Mechanics; Lapeyre et al: Introduction to Monte-Carlo Methods for Transport and Diffusion Equations; Isaac Elishakoff and Yong Jin Ren: Finite Element Methods for Structures with LargeStochastic Variations

Written in Alwyn Scott’s inimitable style, one that readers will find both lucid and accessible, this masterwork elucidates the explosion of activity in nonlinear science in recent decades. The book explains the wide-ranging implications of nonlinear phenomena for future developments in many areas of modern science, including mathematics, physics, engineering, chemistry, biology, and neuroscience. Arguably as important as quantum theory, modern nonlinear science is essential for understanding the scientific developments of the twenty-first century.

Nonlinear science is by now a well established field of research at the interface of many traditional disciplines and draws on the theoretical concepts developed in physics and mathematics. The present volume gathers the contributions of leading scientists to give the state of the art in many areas strongly influenced by nonlinear research, such as superconduction, optics, lattice dynamics, biology and biomolecular dynamics. While this volume is primarily intended for researchers working in the field care, has been taken that it will also be of benefit to graduate students or nonexpert scientist wishing to familiarize themselves with the current status of research.

Problems and summaries after each chapter

Contributed articles.

Although chaos theory refers to the existence between seemingly random events, it has been gaining the attention of science, technology and managements fields. The shift from traditional procedures to the dynamics of chaos and complexity theory has resulted in a new element of complexity thinking, allowing for a greater capability for analyzing and understanding key business processes. Chaos and Complexity Theory for Management: Nonlinear Dynamics explores chaos and complexity theory and its relationship with the understanding of natural chaos in the business environment. Utilizing these theories aids in comprehending the development of businesses as a complex adaptive system.