lectures in theoretical biophysics - schulten

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1、LecturesinTheoreticalBiophysicsK.SchultenandI.KosztinDepartmentofPhysicsandBeckmanInstituteUniversityofIllinoisatUrbana–Champaign405N.MathewsStreet,Urbana,IL61801USA(April23,2000)Contents1Introduction12DynamicsundertheIn uenceofStochasticForces32.1Newton'sEquationa

2、ndLangevin'sEquation......................32.2StochasticDierentialEquations.............................42.3HowtoDescribeNoise...................................52.4Itocalculus.........................................212.5Fokker-PlanckEquations....................

3、..............292.6StratonovichCalculus...................................312.7Appendix:NormalDistributionApproximation.....................342.7.1Stirling'sFormula.................................342.7.2BinomialDistribution...............................343Einstei

4、nDiusionEquation373.1DerivationandBoundaryConditions...........................373.2FreeDiusioninOne-dimensionalHalf-Space......................403.3FluorescenceMicrophotolysis...............................443.4FreeDiusionaroundaSphericalObject.................

5、........483.5FreeDiusioninaFiniteDomain.............................573.6RotationalDiusion....................................604SmoluchowskiDiusionEquation634.1DerivationoftheSmoluchoswkiDiusionEquationforPotentialFields.......644.2One-DimensionalDiusoninaLin

6、earPotential.....................674.2.1Diusioninaninnitespace1=]1;1[..................674.2.2DiusioninaHalf-Space1=[0;1[.....................704.3DiusioninaOne-DimensionalHarmonicPotential...................745RandomNumbers795.1Randomness.....................

7、....................805.2RandomNumberGenerators...............................835.2.1HomogeneousDistribution.............................835.2.2GaussianDistribution...............................865.3MonteCarlointegration..................................88iiiCONTE

8、NTS6BrownianDynamics916.1DiscretizationofTime...................................916.2MonteCarloIntegrationofStochasticProcesses..................