基本説明
非線形科学の数学的バックグラウンドについて概観するレファレンス。生態学、生物系、化学反応、地球物理学、経済学、電気・電子工学、工学における振動問題、レーザー、光学、流体力学、固体力学など、多様な分野への応用も取り上げる。440項目をアルファベット順に収録。
Provides a useful overview of core mathematical background and applications of nonlinear science to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, and more. Entries- Common Examples in the Natural World; History of Nonlinear Science; Analytical and Computational Methods; Coherent Structures; Dynamial Systems; Mathematical Models; and more.
Full Description
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.
Contents
Selected Contents: Algorithmic complexity Ball lightning Biological evolution Boundary value problems Butterfly effect Cardiac arrhythmias and electrocardiogram Cellular automata Chaos vs. turbulence Controlling chaos Determinism Dynamical systems Emergence Fluid dynamics Fractals Game of life Laboratory models of nonlinear waves Monte-Carlo methods Multidimensional solitons Neural network models Nonequilibrium statistical mechanics Nonlinear optics Nonlinear Schrödinger equations Nonlinear toys Numerical methods Order from chaos Partial differential equations, nonlinear Period doubling Perturbation theory Population dynamics Quantum chaos Random matrix theory Reaction diffusion systems Sandpile model Spatio-temporal chaos Sine--Gordon (SG) equation Stochastic analyses of neural systems Symmetry groups Tacoma Narrows Bridge collapse Threshold phenomena Universality Vortex dominated flows Wave stability and instability