2016-08-31-DPD-粗粒&耗散粒子动力学

耗散粒子动力学方法无网格与粒子类方法高级讲习班刘谋斌[e-mail]北京大学工学院2016-8-31@北京基本内容粗粒化DPD基本方法DPD数值模拟DPD应用DPD-Openissues2/661粗粒化—时空尺度的多样性3/66smAtomisticmodelsClassicMD,AbinitioMD,KineticMC...MesoscopicmodelsDPDLBM...ContinuummodelsFEMFDM/FVMSPH...Liu&Liu,WSPC,2015.Nano-scale:characteristiclength~10-9-10-7m,characteristictimes~10-14-10-10sMicro-scale:characteristiclength~10-8-10-6m,characteristictimes~10-11–10-8sMeso-scale:characteristiclength~10-7-10-4m,Characteristictimes~10-9-10-3s.Macro-scale:characteristiclength≥10-3m,characteristictimes≥10-3s时空尺度(Time-andlength-scale)4/66时空尺度(Time-andlength-scale)•TimescaleThemaximumtimestepofintegrationinMDsimulationisdefinedbythefastestmotioninthesystem.Usingmoderncomputersitispossibletocalculate106–108timesteps.Thereforewecanonlysimulateprocessesthatoccurwithin1–100ns.•LengthscaleThesizeofthecomputationalcellislimitedbythenumberofatomsthatcanbeincludedinthesimulation,typically104–109.Thiscorrespondstothesizeofthecomputationalcellontheorderof10–100nm.1粗粒化—MD模拟的局限性5/66为什么MD时空尺度小？•Lookattypicalscalesofcarbon-basedmolecules:length1Å,mass12amu,springconstantk=20eV/Å2,theassociatedtimescaleis2714-19-10212.01.6610kg26.2810sec201.610J/(10m)mTkπ−−××==≈××Weusetheunitsconversionfactors:1eV=1.6x10-19joule1amu=1.66x10-27kg1Å=10-10meter1millisec=10-3sec1μs=10-6sec1nanosec=10-9sec1picosec=10-12sec1femtosec=10-15sec1粗粒化—MD模拟的局限性6/66如何扩展MD时空尺度？•InordertoincreaseTDecreasetheinteractionstrengthk,wemaketheinteractionsofter,Increasemassm,insteadofsimulatingasingleatom,wesimulatealumpofthem.2mTkπ=1粗粒化—MD模拟的局限性7/66如何扩展MD时空尺度?-CG1粗粒化—粗粒化概念Coarsegraining(CG):groupingthingstogetherandtreatingthemasoneobjectn-Alkane(烷烃)UnitedatommodelQuantumMDClassicalMDByusingCG,sometrivial(molecular)detailsareignored,whilethemainfeaturesofconcernedphysicscanbeeffectivelyobtained!8/66GeneralprocedureofCG1粗粒化—基本步骤1.definingthegoalanddeterminingthedegreeofcoarse-graining,2.mappingatomisticmodeltocoarse-grainedmodel,3.interactionbetweenthecoarse-grainedparticles,4.reproducingtargetfunctionsbythecoarse-grainedmodel,5.optimizingparameters/functionsinthecoarse-grainedmodel,6.conductingcoarse-grainedsimulations.9/66ThebenefitofCG1粗粒化—优势PNCOCAll-atommodel118atomsCoarse-grainedmodel10sitesllcCPUpertimestepatleast10timesless(orevenbetter)Amodeloflipidmax~BmtlkT∆Maximumtime-stepkTmltcc~max∆10/66介观尺度(mesoscale)1粗粒化—介观尺度Mesoscalesimulation:extremecoarsegrainingtotreatthingsonthemesoscopicscale(Thescale100nmwhichishugebyatomicstandardsbutwherefluctuationsarestillrelevant)longpolymer100nm11/66介观尺度(mesoscale)–BridgeGap1粗粒化—介观尺度12/66介观尺度(mesoscale)-Approaches1粗粒化—介观尺度13/66介观尺度(mesoscale)-Methods1粗粒化—介观尺度14/662DPD基本方法—Coarse-graining15/662DPD基本方法—Coarse-graining16/662DPD基本方法—Hydrodynamics17/662DPD基本方法—DPDdevelopment18/662DPD基本方法—控制方程,intextiiiiiidddtdt===+rvvfffintCDRiijijijijjiji≠≠==++∑∑fFFFF19/662DPD基本方法—保守力20/662DPD基本方法—保守力21/662DPD基本方法—耗散力+随机力22/662DPD基本方法—耗散力+随机力•Dissipative(friction)forcesreducetherelativevelocityofthepairofparticlesRandomforcescompensateforeliminateddegreesoffreedom•DissipativeandrandomforcesformDPDthermostat•Themagnitudeofdissipativeandrandomforcesaredefinedbyfluctuationdissipationtheorem23/662DPD基本方法—振荡-耗散理论()()2(1)0sDRcccrrrrwrwrrr−==≥()()2DRwrwr=2B2kTσγ=24/662DPD基本方法—软球+热浴DPDasSoftParticlesandaThermostat！Withouttherandomanddissipativeforce,thiswouldsimplybemoleculardynamicswithasoftrepulsivepotential.Withthedissipativeandrandomforcesthesystemhasacanonicaldistribution,sotheyactasathermostat.Thesetwopartsofthemethodarequiteseparatebutthethermostathasanumberofnicefeatures.LocalConservesMomentumGallileanInvariant25/662DPD基本方法—能力CapabilitiesofDPD26/662DPD基本方法—vsMDComparisonofDPDwithMD27/663DPD数值模拟—ProcedureDefineinitialpositionsandvelocitiesCalculateforcesatcurrenttimentintCDRiijijijijjiji≠≠==++∑∑fFFFFintextiii=+ffft∆111()()()()nnininininttttttt+++=+∆→→rrvvEvaluatedesiredphysicalquantitiesandwritetrajectorydataIstn+1tmax?CompletetheDPDsimulationSavefinaldataSolveequationsofmotionforallparticlesoverashorttime边界条件（boundaryconditions）1.初始化(initialization)位置、速度（position&velocity）粒子搜索链表（neighboringcells）2.平衡化(equilibration)力场/作用势（forcefield）3.产生数据(production)4.数据分析(analysis)温度控制（temperaturecontrol）时间积分（timeintegration）统计力学关系式28/66IntegratingtheequationsofmotionHowtosolvetheDPDequationsofmotionisitselfsomethingofanissue.Thenicepropertyofmoleculardynamicstypealgorithms(e.g.satisfyingdetailedbalance)arelostbecauseofthevelocitydependentdissipativeforce.Thisisparticularlytrueintheparametricallycorrectregime.Whyisthisimportant?•Anyofthesealgorithmsareokayifthetime-stepissmallenough•Thelongeratime-stepyoucanuse,thelesscomputationaltimeyoursimulationsneedHowlongatimestepcanIuse?•Bewaretocheckmorethanthatthetemperatureiscorrect•Theradialdistributionfunctionisamoresensitivetest.Thetemperaturecanbeokaywhileotherequilibriumpropertiesareseverelyinaccurate.L-J.Chen,Z-YLu,H-Jian,Z-Li,andC-CSun,J.Chem.Phys.122,104907(2005)3DPD数值模拟—Timeintegration29/66P.EspanolandP.B.Warren,Europhys.Lett.30,191,(1995).Euler-typealgori