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long-range interactions, stochasticity 科技综合 albert c.j. luo，v. a

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作者albert c.j. luo，v. a

出版社高等教育出版社

ISBN9787040291889

出版时间2010-06

版次1

装帧平装

开本16

页数311页

定价68元

货号xhwx_1200127458

上书时间2024-11-12

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长距离相互作用、及分数维动力学编辑：nonlinearphyicalciencefocueontherecentadvanceoffundamentaltheorieandprincipleanalyticalandymbolicapproacheawellaputationaltechniqueinnonlinearphyicalcienceandnonlinearmathematicwithengineeringapplication.

目录：

1fractionalzaslavskyandhenondiscretema
vasilye.tarasov
1.1introduction
1.2fractionalderivatives
1.2.1fractionalriemann-liouvillederivatives
1.2.2fractionalcaputoderivatives
1.2.3fractionalliouvillederivatives
1.2.4interpretationofequationswithfractionalderivatives.
1.2.5discretemawithmemory
1.3fractionalzaslavskyma
1.3.1discretechirikovandzaslavskyma
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
1.6fractionalderivativeinthekickeddampedtermandgeneralizationsofzaslavskyandhenonma
1.6.1fractionalequationanddiscretemap
1.6.2fractionalzaslavskyandhenonma
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
2.5fractionalpoundpoissonprocess
2.5.1poundpoissonprocess
2.5.2levy-poissonmotion
2.5.3fractionalpoundpoissonmotion
2.5.4alinkbetweensolutions
2.5.5fractionalgeneralizationofthelevymotion
acknowledgments
appendix.fractionaloperators
references

3long-rangeinteractionsanddilutedworks
antoniaciani,ducciofanelliandstefanoruffo
3.1long-rangeinteractions
3.1.1lackofadditivity
3.1.2equilibriumanomalies:ensembleinequivalence,specificheatandtemperaturejum
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
3.3.1hamiltonianmeanfieldmodelonadilutedwork
3.3.2onequilibriumsolutionofdilutedhamiltonianmeanfield
3.3.3onquasistationarystatesinpresenceofdilution
3.3.4phasetransition
3.4conclusions
acknowledgments
references

4metastabilityandtransientsinbraindynamics:problemsandrigorousresults
valentins.afraimovich,mehmetk.muezzinogluand
mikhaili.rabinovich
4.1introduction:whatwediscussandwhynow
4.1.1dynamicalmodelingofcognition
4.1.2brainimaging
4.1.3dynamicsofemotions
4.2mentalmodes
4.2.1statespace
4.2.2functionalworks
4.2.3emotion-cognitiontandem
4.2.4dynamicalmodelofconsciousness
4.3petition——robustnessandsensitivity
4.3.1transientsversusattractorsinbrain
4.3.2cognitivevariables
4.3.3emotionalvariables
4.3.4metastabilityanddynamicalprinciples
4.3.5winnerlesspetition——structuralstabilityoftransients
4.3.6examples:petitivedynamicsinsensorysystems
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:fromsimpletoplexandchaoticmotions
konstantina.gorshkov,leva.ostrovskyandyurya.stepanyants
5.1introduction
5.2stablesolitonlatticesandahierarchyofenvelopesolitons
5.3chainsofsolitonswithintheframeworkofthegardnermodel
5.4unstablesolitonlatticesandstochastisation
5.5solitonstochastisationandstrongwaveturbulenceinaresonatorwithexternalsinusoidalpumping
5.6chainsoftwo-dimensionalsolitonsinitive-dispersionmedia
5.7conclusion
fewwordsinmemoryofgeorgem.zaslavsky
references

6whatiscontrolofturbulenceincrossedfields?-donteventhinkofeliminatingallvortexes!
dimitrivolchenkov
6.1introduction
6.2stochastictheoryofturbulenceincrossedfields:vortexesofallsizesdieout,butone
6.2.1themethodofrenormalizationgroup
6.2.2phenomenologyoffullydevelopedisotropicturbulence
6.2.3quantumfieldtheoryformulationofstochastiavier-stokesturbulence
6.2.4analyticalpropertiesoffeynmandiagrams
6.2.5ultravioletrenormalizationandrg-equations
6.2.6whatdothergrepresentationssum?
6.2.7stochasticmagichydrodynamics
6.2.8renormalizationgroupinmagichydrodynamics
6.2.9criticaldimensionsinmagichydrodynamics
6.2.10criticaldimensionsofiteoperatorsinmagichydrodynamics
6.2.11operatorsofthecanonicaldimensiond=2
6.2.12vectoroperatorsofthecanonicaldimensiond=3
6.2.13instabilityinmagichydrodynamics
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
7.4concluremarks
references
index

内容简介：

in memory of dr. george zalavky longrange interaction tochaticity and fractional dynamic cover the recent development of longrange interaction fractional dynamic brain dynamic and tochatic theory of turbulence each chapter wa written by etablihed cientit in the field. the book i dedicated to dr. george zalavky who wa one of three founder of the theory of hamiltonian chao. the book dicue elfimilarity and tochaticity and fractionality for dicrete and continuou dynamical ytem a well a longrange interaction and diluted work. a prehenive theory for brain dynamic i alo preented. in addition the plety and tochaticity for oliton chain and turbulence are addreed.
the book i intended for reearcher in the field of nonlinear dynamic in mathematic phyic and engineering.
dr. albert c.j. luo i a profeor at outhern illinoi univerity edwardville ua. dr. valentin afraimovich i a profeor at an lui potoi univerity meco.
本书介绍了连续及离散动力系统的自相似、及分数维。

作者简介：

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.luoiaprofeoratouthernillinoiuniverityedwardvilleua.dr.valentinafraimovichiaproieoratanluipotoiuniveritymeco.