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Pattern Formation: An Introduction to Methods

模式形成

Cambridge University Press Rebecca Hoyle

ISBN：9780521520768，出版年：2006，中图分类号：O1 被引 537次

From the stripes of a zebra and the spots on a leopard's back to the ripples on a sandy beach or desert dune, regular patterns arise everywhere in nature. The appearance and evolution of these phenomena has been a focus of recent research activity across several disciplines. This book provides an introduction to the range of mathematical theory and methods used to analyse and explain these often intricate and beautiful patterns. Bringing together several different approaches, from group theoretic methods to envelope equations and theory of patterns in large-aspect ratio-systems, the book also provides insight behind the selection of one pattern over another. Suitable as an upper-undergraduate textbook for mathematics students or as a fascinating, engaging, and fully illustrated resource for readers in physics and biology, Rebecca Hoyle's book, using a non-partisan approach, unifies a range of techniques used by active researchers in this growing field

Mathematical theory Field (geography) Selection (linguistics) Cognitive science Range (mathematics) Pattern formation Focus (computing) Resource (project management)

Contemporary Accelerator Physics

当代加速器物理学

World Scientific Publishing Company Stephan Ivanov Tzenov

ISBN：9789812389008，出版年：2004，中图分类号：O4 被引 15次

This book adopts a non-traditional approach to accelerator theory. The exposition starts with the synchro-betatron formalism and continues with the linear and nonlinear theories of transverse betatron motion. Various methods of studying nonlinear dynamical systems (the canonical theory of perturbations and the methods of multiple scales and formal series) are explained through examples. The renormalization group approach to studying nonlinear (continuous and discrete) dynamical systems as applied to accelerators and storage rings is used throughout the book. The statistical description of charged particle beams (the Balescu-Lenard and Landau kinetic equations as well as the Vlasov equation) is dealt with in the second part of the book. The processes of pattern formation and formation of coherent structures (solitons) are also described.

Dynamical systems theory Accelerator physics Vlasov equation Nonlinear system Canonical theory Betatron Renormalization group Classical mechanics Statistical physics Pattern formation