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1、AginginBlinkingQuantumDots:RenewalorSlowModulation?P.ParadisiInstituteofAtmosphericSciencesandClimate(CNR),LecceUnitS.BiancoCenterforNonlinearSciences,UniversityofNorthTexasP.Grigolini,InstituteofChemicalandPhysicalProcesses(CNR),PisaCenterforNonlinearSciences,UniversityofNorthTexasDepartmentofPh
2、ysics,PisaUniversityOutlineRenewalprocessesanexample:theMannevilleMapRenewalAgingHowcanweevaluatetheamountofRenewalAginginatimeseries?RenewalAginginModulationprocessesApplicationtoBlinkingQuantumDots:renewalorslowmodulation?RenewalProcessesStochasticprocesswith:-recurrent(critical)eventsassociate
3、dwithsomepatternofthesystemvariables-WaitingTimes(WTs)aremutuallyindependentrandomvariables-WT=timeintervalbetweentwocriticaleventsD.R.Cox,RenewalTheory,ChapmanandHall,London(1962)Poissonprocesses:exponentialdistributionofWTsInterestingcase:power-lawtailinthedistributionofWTs(Non-Poissonrenewalpr
4、ocesses)Example:MannevilleMapModelforTurbulenceIntermittency:alternanceofLaminarRegionsandChaoticBurstsLaminarRegionswithlongResidence(Exit)TimesWaitingTimesShortandIntenseBurstshavetheeffectoferasingmemoryrandomcriticaleventP.Manneville,J.Physique41,1235(1980)RenewalAgingManneville-typestochasti
5、cmodel(z>1)Criticalevent:Exitfromy=1WT=ExitTimeRandombackinjection,uniformin[0,1]ParetodistributionofWTsP.Allegrinietal.,Phys.Rev.E68,056123(2003)Liouvilleequationforthetimeevolutionoftheprobabilitydistribution:Afteracriticalevent,thesystemrestartsfromanewrandominitialcondition(uniformdistributio
6、n).P.Allegrinietal.,Phys.Rev.E68,056123(2003)AginginRenewalProcessesisrelatedtothetimeevolutionofp(y,t)StartingobservationattimetaimpliesobservinganagedWTstatisticsPossibilityofusingthispropertyasanindicatorof“RenewalAging”ImportantFactsPoissonprocesseshavezerorenewalagingNon-zeroRenewalagingforN
7、on-PoissonrenewalprocessesDependenceonthedistributionofWTsApproximateanalyticalresultsavailableforPareto(power-law)distributionofWTsDescriptionofthemethodDefinitionofcriticaleventsinthetimeseriesWTssequenceWTsarecorrel
