lectures in theoretical biophysics - k. schulten , i. kosztin

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

2、in'sEquation......................32.2StochasticDierentialEquations.............................42.3HowtoDescribeNoise...................................52.4Itocalculus.........................................212.5Fokker-PlanckEquations..................................29

3、2.6StratonovichCalculus...................................312.7Appendix:NormalDistributionApproximation.....................342.7.1Stirling'sFormula.................................342.7.2BinomialDistribution...............................343EinsteinDiusionEquation373.1De

4、rivationandBoundaryConditions...........................373.2FreeDiusioninOne-dimensionalHalf-Space......................403.3FluorescenceMicrophotolysis...............................443.4FreeDiusionaroundaSphericalObject.........................483.5FreeDiusioninaFini

5、teDomain.............................573.6RotationalDiusion....................................604SmoluchowskiDiusionEquation634.1DerivationoftheSmoluchoswkiDiusionEquationforPotentialFields.......644.2One-DimensionalDiusoninaLinearPotential.....................674.2.1

6、Diusioninaninnitespace1=]1;1[..................674.2.2DiusioninaHalf-Space1=[0;1[.....................704.3DiusioninaOne-DimensionalHarmonicPotential...................745RandomNumbers795.1Randomness.........................................805.2RandomNumberGenerators.

7、..............................835.2.1HomogeneousDistribution.............................835.2.2GaussianDistribution...............................865.3MonteCarlointegration..................................88iiiCONTENTS6BrownianDynamics916.1DiscretizationofTime...........

8、........................916.2MonteCarloIntegrationofStochasticProcesses..................