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长距离相互作用、随机及分数维动力学

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作者本书编写组

出版社高等教育出版社

ISBN9787040291889

出版时间2010-06

版次1

装帧精装

开本16开

纸张胶版纸

页数308页

字数99999千字

定价68元

上书时间2024-05-25

纵列風

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商品描述: 基本信息
书名:长距离相互作用、随机及分数维动力学
定价：68元
作者:本书编写组
出版社：高等教育出版社
出版日期：2010-06-01
ISBN：9787040291889
字数：360000
页码：308
版次：1
装帧：精装
开本：12开
商品重量：
编辑推荐
《长距离相互作用、随机及分数维动力学》编辑推荐：NonlinearPhysicalSciencefocusesontherecentadvancesoffundamentaltheoriesandprinciples,analyticalandsymbolicapproaches,aswellascomputationaltechniquesinnonlinearphysicalscienceandnonlinearmathematicswithengineeringapplications.
内容提要
In memory of Dr. George Zaslavsky, Long-range Interactions, Stochasticity and Fractional Dynamics covers'the recent developments of long-range interaction, fractional dynamics, brain dynamics and stochastic theory of turbulence, each chapter was written by established scientists in the field. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. The book discusses self-similarity and stochasticity and fractionality for discrete and continuous dynamical systems, as well as long-range interactions and diluted networks. A comprehensive theory for brain dynamics is also presented. In addition, the complexity and stochasticity for soliton chains and turbulence are addressed. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering.
目录
1 Fractional Zaslavsky and Henon Discrete Maps Vasily E. Tarasov 1.1 Introduction 1.2 Fractional derivatives 1.2.1 Fractional Riemann-Liouville derivatives 1.2.2 Fractional Caputo derivatives 1.2.3 Fractional Liouville derivatives 1.2.4 Interpretation of equations with fractional derivatives. 1.2.5 Discrete maps with memory 1.3 Fractional Zaslavsky maps 1.3.1 Discrete Chirikov and Zaslavsky maps 1.3.2 Fractional universal and Zaslavsky map 1.3.3 Kicked damped rotator map 1.3.4 Fractional Zaslavsky map from fractional differential equations 1.4 Fractional H6non map 1.4.1 Henon map 1.4.2 Fractional Henon map 1.5 Fractional derivative in the kicked term and Zaslavsky map 1.5.1 Fractional equation and discrete map 1.5.2 Examples 1.6 Fractional derivative in the kicked damped term and generalizations of Zaslavsky and Henon maps 1.6.1 Fractional equation and discrete map 1.6.2 Fractional Zaslavsky and Henon maps 1.7 Conclusion References2 Self-similarity, Stochasticity and Fractionality Vladimir V Uchaikin 2.1 Introduction 2.1.1 Ten years ago 2.1.2 Two kinds of motion 2.1.3 Dynamic self-similarity 2.1.4 Stochastic self-similarity 2.1.5 Self-similarity and stationarity 2.2 From Brownian motion to Levy motion 2.2.1 Brownian motion 2.2.2 Self-similar Brownian motion in nonstationary nonhomogeneous environment 2.2.3 Stable laws 2.2.4 Discrete time Levy motion 2.2.5 Continuous time Levy motion 2.2.6 Fractional equations for continuous time Levy motion 2.3 Fractional Brownian motion 2.3.1 Differential Brownian motion process 2.3.2 Integral Brownian motion process 2.3.3 Fractional Brownian motion 2.3.4 Fractional Gaussian noises 2.3.5 Barnes and Allan model 2.3.6 Fractional Levy motion 2.4 Fractional Poisson motion 2.4.1 Renewal processes 2.4.2 Self-similar renewal processes 2.4.3 Three forms of fractal dust generator 2.4.4 nth arrival time distribution 2.4.5 Fractional Poisson distribution 2.5 Fractional compound Poisson process 2.5.1 Compound Poisson process 2.5.2 Levy-Poisson motion 2.5.3 Fractional compound Poisson motion 2.5.4 A link between solutions 2.5.5 Fractional generalization of the Levy motion Acknowledgments Appendix. Fractional operators References3 Long-range Interactions and Diluted Networks Antonia Ciani, Duccio Fanelli and Stefano Ruffo 3.1 Long-range interactions 3.1.1 Lack of additivity 3.1.2 Equilibrium anomalies: Ensemble inequivalence, specific heat and temperature jumps 3.1.3 Non-equilibrium dynamical properties 3.1.4 Quasi Stationary States 3.1.5 Physical examples 3.1.6 General remarks and outlook 3.2 Hamiltonian Mean Field model: equilibrium and out-of- equilibrium features 3.2.1 The model 3.2.2 Equilibrium statistical mechanics 3.2.3 On the emergence of Quasi Stationary States: Non- equilibrium dynamics 3.3 Introducing dilution in the Hamiltonian Mean Field model 3.3.1 Hamiltonian Mean Field model on a diluted network 3.3.2 On equilibrium solution of diluted Hamiltonian Mean Field 3.3.3 On Quasi Stationary States in presence of dilution 3.3.4 Phase transition 3.4 Conclusions Acknowledgments References4 Metastability and Transients in Brain Dynamics: Problems and Rigorous Results Valentin S. Afraimovich, Mehmet K. Muezzinoglu and Mikhail I. Rabinovich 4.1 Introduction: what we discuss and why now 4.1.1 Dynamical modeling of cognition 4.1.2 Brain imaging 4.1.3 Dynamics of emotions 4.2 Mental modes 4.2.1 State space 4.2.2 Functional networks 4.2.3 Emotion-cognition tandem 4.2.4 Dynamical model of consciousness 4.3 Competition--robustness and sensitivity 4.3.1 Transients versus attractors in brain 4.3.2 Cognitive variables 4.3.3 Emotional variables 4.3.4 Metastability and dynamical principles 4.3.5 Winnerless competition--structural stability of transients 4.3.6 Examples: competitive dynamics in sensory systems 4.3.7 Stable heteroclinic channels 4.4 Basic ecological model 4.4.1 The Lotka-Volterra system 4.4.2 Stress and hysteresis 4.4.3 Mood and cognition 4.4.4 Intermittent heteroclinic channel 4.5 Conclusion Acknowledgments Appendix 1 Appendix 2 References5 Dynamics of Soliton Chains: From Simple to Complex and Chaotic Motions Konstantin A. Gorshkov, Lev A. Ostrovsky and Yury A. Stepanyants 5.1 Introduction 5.2 Stable soliton lattices and a hierarchy of envelope solitons 5.3 Chains of solitons within the framework of the Gardner model 5.4 Unstable soliton lattices and stochastisation 5.5 Soliton stochastisation and strong wave turbulence in a resonator with external sinusoidal pumping 5.6 Chains of two-dimensional solitons in positive-dispersion media 5.7 Conclusion Few words in memory of George M. Zaslavsky References6 What is Control of Turbulence in Crossed Fields?-Don't Even Think of Eliminating All Vortexes! Dimitri Volchenkov 6.1 Introduction 6.2 Stochastic theory of turbulence in crossed fields: vortexes of all sizes die out, but one 6.2.1 The method of renormalization group 6.2.2 Phenomenology of fully developed isotropic turbulence 6.2.3 Quantum field theory formulation of stochastic Navier-Stokes turbulence 6.2.4 Analytical properties of Feynman diagrams 6.2.5 Ultraviolet renormalization and RG-equations 6.2.6 What do the RG representations sum? 6.2.7 Stochastic magnetic hydrodynamics 6.2.8 Renormalization group in magnetic hydrodynamics 6.2.9 Critical dimensions in magnetic hydrodynamics 6.2.10 Critical dimensions of composite operators in magnetic hydrodynamics 6.2.11 Operators of the canonical dimension d = 2 6.2.12 Vector operators of the canonical dimension d = 3 6.2.13 Instability in magnetic hydrodynamics 6.2.14 Long life to eddies of a preferable size 6.3 In search of lost stability 6.3.1 Phenomenology of long-range turbulent transport in the scrape-off layer (SOL) of thermonuclear reactors 6.3.2 Stochastic models of turbulent transport in cross-field systems 6.3.3 Iterative solutions in crossed fields 6.3.4 Functional integral formulation of cross-field turbulent transport 6.3.5 Large-scale instability of iterative solutions 6.3.6 Turbulence stabilization by the poloidal electric drift 6.3.7 Qualitative discrete time model of anomalous transport in the SOL 6.4 Conclusion References7 Entropy and Transport in Billiards M. Courbage and S.M. Saberi Fathi 7.1 Introduction 7.2 Entropy 7.2.1 Entropy in the Lorentz gas 7.2.2 Some dynamical properties of the barrier billiard model 7.3 Transport 7.3.1 Transport in Lorentz gas 7.3.2 Transport in the barrier billiard 7.4 Concluding remarks ReferencesIndex
作者介绍
编者：罗朝俊（墨西哥）阿弗莱诺维奇（ValentinAfraimovich）丛书主编：（瑞典）伊布拉基莫夫Dr.AlbertC.J.LuoisaProfessoratSouthernIllinoisUniversityEdwardsville,USA.Dr.ValentinAfraimovichisaProiessoratSanLuisPotosiUniversity,Meco.
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长距离相互作用、随机及分数维动力学

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