简介:AccordingtoLorenz,chaoticdynamicsystemshavesensitivedependenceoninitialconditions(SDIC),i.e.,thebutterfly-effect:atinydifferenceoninitialconditionsmightleadtohugedifferenceofcomputer-generatedsimulationsafteralongtime.Thus,computer-generatedchaoticresultsgivenbytraditionalalgorithmsindoubleprecisionareakindofmixtureof'true'(convergent)solutionandnumericalnoisesatthesamelevel.Today,thisdefectcanbeovercomebymeansofthe'cleannumericalsimulation'(CNS)withnegligiblenumericalnoisesinalongenoughintervaloftime.TheCNSisbasedontheTaylorseriesmethodathighenoughorderanddatainthemultipleprecisionwithlargeenoughnumberofdigits,plusaconvergencecheckusinganadditionalsimulationwithevensmallernumericalnoises.Intheory,convergent(reliable)chaoticsolutionscanbeobtainedinanarbitrarylong(butfinite)intervaloftimebymeansoftheCNS.TheCNScanreducenumericalnoisestosuchalevelevenmuchsmallerthanmicro-leveluncertaintyofphysicalquantitiesthatpropagationofthesephysicalmicro-leveluncertaintiescanbepreciselyinvestigated.Inthispaper,webrieflyintroducethebasicideasoftheCNS,anditsapplicationsinlong-termreliablesimulationsofLorenzequation,three-bodyproblemandRayleigh-Bénardturbulentflows.UsingtheCNS,itisfoundthatachaoticthree-bodysystemwithsymmetrymightdisruptwithoutanyexternaldisturbance,say,itssymmetry-breakingandsystem-disruptionare'self-excited',i.e.,out-of-nothing.Inaddition,bymeansoftheCNS,wecanprovidearigoroustheoreticalevidencethatthemicro-levelthermalfluctuationistheoriginofmacroscopicrandomnessofturbulentflows.Naturally,muchmoreprecisethantraditionalalgorithmsindoubleprecision,theCNScanprovideusanewwaytomoreaccuratelyinvestigatechaoticdynamicsystems.
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简介:自1912年至今,美国拆坝历史已有百年之久,期间拆坝共计1108座。从拆坝数量、分布范围、坝高和坝龄等多个角度对这些闸坝的资料进行分析比较,得出不同年代美国的拆坝特点:1980年以前拆坝数量少,分布范围较小,但闸坝的负面影响及拆坝必要性开始被人们所认识;20世纪80年代以后拆坝数量和范匍逐渐扩大,坝高仍小于20m,拆坝原因以生态修复为主,且更加关注闸坝安全问题;20世纪90年代拆坝数量继续扩大.拆坝高度实现突破,编制完成《大坝及水电设施退役导则》;21世纪,拆坝数量、高度和长度都打破以往记录.被拆闸坝以混凝土坝为主且绝大多数超过了使用寿命。同时,分析表明,闸坝的拆除与当时的社会经济状况有着密不可分的联系。