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 moleculardynamics simulations