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1、30May1997CHEMICALPHYSICSLETTERSELSEVIERChemicalPhysicsLetters270(1997)476-483ElectrostaticsbyBrowniandynamics:solvingthePoissonequationneardielectricinterfacesVeacheslavZaloj1,NoamAgmonTheFritzHaberResearchCenter,DepartmentofPhysicalChemistry,TheHebrewUniversity,Jerusalem91904,IsraelRec
2、eived26December1996;infinalform31March1997AbstractTheisomorphismbetweenelectrostaticsanddiffusionisdiscussedandutilizedtodevelopaBrowniandynamicsalgorithmforsolvingthePoissonequationneardielectricinterfaces.Theelectrostaticpotentialbehavesasifcarriedbynoninteracting,randomlymovingpseudo
3、-pa~cleswhoseresidencetimeinagivenregionofspaceisproportionaltotheelectrostaticpotentialthere.Byapplyingrandomnumbersfromtheexactsolutionfordiffusionnearaplanardiscontinuity,theBrownianmotionoftheseparticlescanbepropagatedforlargetimesteps,independentofspatialgridsorartificialboundaryco
4、nditions.TheapplicabilityoftheBrownianalgorithmisdemonstratedinsimpleillustrativecalculations.?1997ElsevierScienceB.V.1.IntroductionThemostpopularprocedureforsolvingtheseequa-tionsistheFiniteDifferenceMethod(FDM)[6-12].ElectrostaticinteractionsplayamajorroleinWhilerapidconvergencetechni
5、queshavebeendevel-determiningtheshapeandfunctionofbiologi-oped,theyarerestrictedbytheinherentmappingofcalmacromolecules(proteins,nucleicacids)andthecontinuumproblemontoafinitegrid.Thisrestric-lipidmembranes[1,2].Continuummodelsofbio-tionhasseveralconsequences.First,boundarycondi-electro
6、statics[3-5]treattheorganicresiduesasationsfortheelectrostaticpotentialonthesurfaceoflow-dielectricmediumembeddedinahigh-dielectricthesimulationgridhavetobedefined.Simpleguessessolvent(water).Electrostaticpotentialsneardielec-forboundaryconditionsmightbezeroorCoulombpo-tricinterfacesdev
7、iatesubstantiallyfromCoulomb'stentials.Thisrequiresmakingthegridboxsufficientlylaw.Withintheframeworkofcontinuumelectro-largesothattheelectrostaticpotentialindeedassumesstatics,anaccuratedescriptionrequiresanumericaltheseasymptoticformsonitssurface.Byenlargingsolutionofthe(line
