![](/c3/1067783532.jpg)
出版社:高等教育出版社 ISBN:9787040291889 商品編碼:1067783532 品牌:文軒 出版時間:2010-06-01 代碼:68 作者:AlbertC.J.Luo,V.Afraimovi
"![](https://img10.360buyimg.com/imgzone/jfs/t1/102105/7/33921/65220/637ad2fbE3747b3ac/8e9da447b03cae40.jpg)
作 者:Albert C.J. Luo,V. Afraimovich 著作 定 價:68 出 版 社:高等教育出版社 出版日期:2010年06月01日 裝 幀:精裝 ISBN:9787040291889 《長距離相互作用、隨機及分數維動力學》編輯推薦:NonlinearPhysicalSciencefocusesontherecentadvancesoffundamentaltheoriesandprinciples,analyticalandsymbolicapproaches,aswellascomputationaltechniquesinnonlinearphysicalscienceandnonlinearmathematicswithengineeringapplications. ●1FractionalZaslavskyandHenonDiscreteMaps VasilyE.Tarasov 1.1Introduction 1.2Fractionalderivatives 1.2.1FractionalRiemann-Liouvillederivatives 1.2.2FractionalCaputoderivatives 1.2.3FractionalLiouvillederivatives 1.2.4Interpretationofequationswithfractionalderivatives. 1.2.5Discretemapswithmemory 1.3FractionalZaslavskymaps 1.3.1DiscreteChirikovandZaslavskymaps 1.3.2FractionaluniversalandZaslavskymap 1.3.3Kickeddampedrotatormap 1.3.4FractionalZaslavskymapfromfractionaldifferentialequations 1.4FractionalH6nonmap 1.4.1Henonmap 1.4.2FractionalHenonmap 1.5FractionalderivativeinthekickedtermandZaslavskymap 1.5.1Fractionalequationanddiscretemap 1.5.2Examples 1.6FractionalderivativeinthekickeddampedtermandgeneralizationsofZaslavskyandHenonmaps 1.6.1Fractionalequationanddiscretemap 1.6.2FractionalZaslavskyandHenonmaps 1.7Conclusion References
2Self-similarity,StochasticityandFractionality VladimirVUchaikin 2.1Introduction 2.1.1Tenyearsago 2.1.2Twokindsofmotion 2.1.3Dynamicself-similarity 2.1.4Stochasticself-similarity 2.1.5Self-similarityandstationarity 2.2FromBrownianmotiontoLevymotion 2.2.1Brownianmotion 2.2.2Self-similarBrownianmotioninnonstationarynonhomogeneousenvironment 2.2.3Stablelaws 2.2.4DiscretetimeLevymotion 2.2.5ContinuoustimeLevymotion 2.2.6FractionalequationsforcontinuoustimeLevymotion 2.3FractionalBrownianmotion 2.3.1DifferentialBrownianmotionprocess 2.3.2IntegralBrownianmotionprocess 2.3.3FractionalBrownianmotion 2.3.4FractionalGaussiannoises 2.3.5BarnesandAllanmodel 2.3.6FractionalLevymotion 2.4FractionalPoissonmotion 2.4.1Renewalprocesses 2.4.2Self-similarrenewalprocesses 2.4.3Threeformsoffractaldustgenerator 2.4.4ntharrivaltimedistribution 2.4.5FractionalPoissondistribution 2.5FractionalcompoundPoissonprocess 2.5.1CompoundPoissonprocess 2.5.2Levy-Poissonmotion 2.5.3FractionalcompoundPoissonmotion 2.5.4Alinkbetweensolutions 2.5.5FractionalgeneralizationoftheLevymotion Acknowledgments Appendix.Fractionaloperators References
3Long-rangeInteractionsandDilutedNetworks AntoniaCiani,DuccioFanelliandStefanoRuffo 3.1Long-rangeinteractions 3.1.1Lackofadditivity 3.1.2Equilibriumanomalies:Ensembleinequivalence,negativespecificheatandtemperaturejumps 3.1.3Non-equilibriumdynamicalproperties 3.1.4QuasiStationaryStates 3.1.5Physicalexamples 3.1.6Generalremarksandoutlook 3.2HamiltonianMeanFieldmodel:equilibriumandout-of-equilibriumfeatures 3.2.1Themodel 3.2.2Equilibriumstatisticalmechanics 3.2.3OntheemergenceofQuasiStationaryStates:Non- equilibriumdynamics 3.3IntroducingdilutionintheHamiltonianMeanFieldmodel 3.3.1HamiltonianMeanFieldmodelonadilutednetwork 3.3.2OnequilibriumsolutionofdilutedHamiltonianMeanField 3.3.3OnQuasiStationaryStatesinpresenceofdilution 3.3.4Phasetransition 3.4Conclusions Acknowledgments References
4MetastabilityandTransientsinBrainDynamics:ProblemsandRigorousResults ValentinS.Afraimovich,MehmetK. ezzinogluand MikhailI.Rabinovich 4.1Introduction:whatwediscussandwhynow 4.1.1Dynamicalmodelingofcognition 4.1.2Brainimaging 4.1.3Dynamicsofemotions 4.2Mentalmodes 4.2.1Statespace 4.2.2Functionalnetworks 4.2.3Emotion-cognitiontandem 4.2.4Dynamicalmodelofconsciousness 4.3Competition——robustnessandsensitivity 4.3.1Transientsversusattractorsinbrain 4.3.2Cognitivevariables 4.3.3Emotionalvariables 4.3.4Metastabilityanddynamicalprinciples 4.3.5Winnerlesscompetition——structuralstabilityoftransients 4.3.6Examples:competitivedynamicsinsensorysystems 4.3.7Stableheteroclinicchannels 4.4Basicecologicalmodel 4.4.1TheLotka-Volterrasystem 4.4.2Stressandhysteresis 4.4.3Moodandcognition 4.4.4Intermittentheteroclinicchannel 4.5Conclusion Acknowledgments Appendix1 Appendix2 References
5DynamicsofSolitonChains:FromSimpletoComplexandChaoticMotions KonstantinA.Gorshkov,LevA.OstrovskyandYuryA.Stepanyants 5.1Introduction 5.2Stablesolitonlatticesandahierarchyofenvelopesolitons 5.3ChainsofsolitonswithintheframeworkoftheGardnermodel 5.4Unstablesolitonlatticesandstochastisation 5.5Solitonstochastisationandstrongwaveturbulenceinaresonatorwithexternalsinusoidalpumping 5.6Chainsoftwo-dimensionalsolitonsinpositive-dispersionmedia 5.7Conclusion FewwordsinmemoryofGeorgeM.Zaslavsky References
6WhatisControlofTurbulenceinCrossedFields?-Don'tEvenThinkofEliminatingAllVortexes! DimitriVolchenkov 6.1Introduction 6.2Stochastictheoryofturbulenceincrossedfields:vortexesofallsizesdieout,butone 6.2.1Themethodofrenormalizationgroup 6.2.2Phenomenologyoffullydevelopedisotropicturbulence 6.2.3QuantumfieldtheoryformulationofstochasticNavier-Stokesturbulence 6.2.4AnalyticalpropertiesofFeynmandiagrams 6.2.5UltravioletrenormalizationandRG-equations 6.2.6WhatdotheRGrepresentationssum? 6.2.7Stochasticmagnetichydrodynamics 6.2.8Renormalizationgroupinmagnetichydrodynamics 6.2.9Criticaldimensionsinmagnetichydrodynamics 6.2.10Criticaldimensionsofcompositeoperatorsinmagnetichydrodynamics 6.2.11Operatorsofthecanonicaldimensiond=2 6.2.12Vectoroperatorsofthecanonicaldimensiond=3 6.2.13Instabilityinmagnetichydrodynamics 6.2.14Longlifetoeddiesofapreferablesize 6.3Insearchofloststability 6.3.1Phenomenologyoflong-rangeturbulenttransportinthescrape-offlayer(SOL)ofthermonuclearreactors 6.3.2Stochasticmodelsofturbulenttransportincross-fieldsystems 6.3.3Iterativesolutionsincrossedfields 6.3.4Functionalintegralformulationofcross-fieldturbulenttransport 6.3.5Large-scaleinstabilityofiterativesolutions 6.3.6Turbulencestabilizationbythepoloidalelectricdrift 6.3.7QualitativediscretetimemodelofanomaloustransportintheSOL 6.4Conclusion References
7EntropyandTransportinBilliards M.CourbageandS.M.SaberiFathi 7.1Introduction 7.2Entropy 7.2.1EntropyintheLorentzgas 7.2.2Somedynamicalpropertiesofthebarrierbilliardmodel 7.3Transport 7.3.1TransportinLorentzgas 7.3.2Transportinthebarrierbilliard 7.4Concludingremarks References Index 《長距離相互作用、隨機及分數維動力學》內容簡介:InmemoryofDr.GeorgeZaslavsky,Long-rangeInteractions,StochasticityandFractionalDynamicscovers'therecentdevelopmentsoflong-rangeinteraction,fractionaldynamics,braindynamicsandstochastictheoryofturbulence,eachchapterwaswrittenbyestablishedscientistsinthefield.ThebookisdedicatedtoDr.GeorgeZaslavsky,whowasoneofthreefoundersofthetheoryofHamiltonianchaos.Thebookdiscussesself-simil等 Albert C.J. Luo,V. Afraimovich 著作 編者:羅朝俊(墨西哥)阿弗萊諾維奇(ValentinAfraimovich)叢書主編:(瑞典)伊布拉基莫夫
Dr.AlbertC.J.LuoisaProfessoratSouthernIllinoisUniversityEdwardsville,USA. Dr.ValentinAfraimovichisaProiessoratSanLuisPotosiUniversity,Mexico. ![](https://img10.360buyimg.com/imgzone/jfs/t1/147514/7/5440/73116/5f34a3beE3ba58783/f5b2391383f5625c.jpg)
" |