晶粒生长的蒙特卡罗模拟

20046MonteCarloMonteCarloMCMCMonteCarloMethodsimulationofthegraingrowthAbstract:Graingrowthexistsveryfrequentlyinthecondenseandamalgamationofmetaloralleys,processesofsinteringofpottery.Asitsposition,thecapabilityofthematerialsattributedirectlytothephenomena.Withthegreattopicofmaterialsengineering,however,duetorestrictionconditions,nomoreprogresshasachievedintheresearch.Nowadays,withtherapidprogressofcomputationalsimulationandtheimprovementoftheexactness.Besidesofthetraditionalexperimentandordinarytheoreticanalogy,computationalsimulationhasbeenregardastheothermethodtotheproblem.AllofthemodelsandmethodscanbedividedtoMonteCarloMethod(shortforMC)andImprovedMCMethod.KEYWORDSMonteCarloMethodgraingrowthcomputationalsimulation1233MCMC;LanguerreLanguerreMCMCMCQ-statepotts]2[Voronoi1,,:1,,F(R/R)P(Nc),R,R,Nc:nRKt=(1)(0)mmtRRBt=−=(2)1tKn1Hillert]3[n0.5n0.5t,RR0(0R),21m=1/nb(0)mmtRR=−2,,X=1-exp[-g(t)](3),X,g(t)g(t)=at2,:X=1-bexp(-atp)(4),bpp1.80.3,,21]4[Voronoi11Q,,1VoronoiVoronoiMC2MC()Q2(_1)ijMNssijEJδ=−∑(5),siiQ,sjisisjdelta,M,NEis10jsδ⎧=⎨≠⎩(6)(5),MC(6):(1)a1E(3)Q-1a2(21aa≠)E2(4)E(5)(7)Wexp(/)010BEKTEWE−∆∆⎧⎨∆≤⎩(7)E0;;E0,exp(-E/KBT),[0,1],exp(-E/KBT),,,2,NMonteCarloStepMCS,N,MCSTKWBe/,3MCPCMCQ-statepottsQ-statepotts1a1,aN1;21Qb,bN2;3N2=N1,b;,a;4,5VoronoinnMonteCarloStepQ-statepotts,1,Q-statepotts,2Q,,Q-statepotts,Q-statepotts:1a1,aN1;2bb≠abN2;3N2=N1,b;,a;4,5nnMonteCarloStepQ-statepotts1,2,Q-statepotts,MCPC1Voronoi2152552n),(iiYXn3150336400MCS3MCS014935250146360100141372150133395200126417250119441300112469350108486400102515450985365009455955092571600885972MC46450MCS5150MCS65084625S-t7R-t8RSR=(0)mmtRRBt=−=(0)mmtRR=−n=0.47m=1/nmatlab9(0)mmtRR=−t7S-t8R-t9(0)mmtRR=−t(MonteCarlo)[1],,MonteCarloI,1999,30(3)232235[2],,MonteCarloII,1999,30(3)[3][4]C,1998,35355[5],,[6],,,2001,20(1)61-66[7],,,,2000,17(2)