《Simulations Moléculaires》 Cours04VIII

Some examples of application

Some examples of application

How to analyse the errors of simulation results? Systematic errors. Possible sources poor equilibration, bad random number generator .system size effect Practical method for detecting systematic errors . longer simulation, different initial configurations test random number generator, use different generators asimulation with larger systems

How to analyse the errors of simulation results? Systematic errors: Possible sources: •poor equilibration; •bad random number generator; •system size effect. Practical method for detecting systematic errors: •longer simulation, different initial configurations; •test random number generator, use different generators; •simulation with larger systems

Statistical errors Statistical errors can be reduced by longer simulations but can not be eliminated completely Practical method for estimating statistical errors -block average method Let run be the mean value of a property a calculated from a sample of size N, i.e ,A Separate n into n blocks, each of the size Nb=N/n and calculate the block average N i=1 ar a214(4 o gives an estimation of the statistical error

Statistical errors: Statistical errors can be reduced by longer simulations but can not be eliminated completely. Practical method for estimating statistical errors - block average method: Let run be the mean value of a property A calculated from a sample of size N, i.e., = = N i run N Ai A 1 1 Separate N into n blocks, each of the size Nb=N/n and calculate the block average, = = N A b i i b b A N 1 1 and ( ) = = − n b b run A A n 1 2 2 1   gives an estimation of the statistical error

Example I Diffusion-controlled reactions Reference W. Dong, F Baros and J.C. Andre, J. Chem. Phys. 91, 4643 (1989) Diffusion-controlled reactions. I Molecular dynamics simulations of a noncontinuum mode Example 2 Fluid diffusion through a porous solid Reference W. Dong and H Luo, Phys. Rev. E52, 801, (1995 Fluid diffusion through a porous solid Nonequilibrium molecular- dynamics simulations

Example 1: Diffusion-controlled reactions Reference: W. Dong, F. Baros and J.C. André, J. Chem. Phys. 91, 4643, (1989). Diffusion-controlled reactions. I. Molecular dynamics simulations of a noncontinuum model. Example 2: Fluid diffusion through a porous solid Reference: W. Dong and H. Luo, Phys. Rev. E 52, 801, (1995). Fluid diffusion through a porous solid: Nonequilibrium molecular￾dynamics simulations