How to analyse the errors of simulation results? Sustematic 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

一、格林-巴利综合征(GBS) 二、急性感染性多发性神经根神经炎 三、主要临床特征:进行性对称性弛缓性瘫痪 四、发病率:1.6/10万人口 五、当前我国和多数国家最常见的急性周围神经病 六、病程自限,严重者死于呼吸肌麻痹

Application of MR2T2 algorithm in statistical mechanics Canonical ensemble: Distribution function: p(rN)=exp(-E(rN)/KT)/Q Q= JdrN exp(-E(rN)/kT) Different states of the Markov chain: In the application of Metropolis algorithm to a simulation of molecular system, the states of the Markov chain correspond to different configurations of the molecular system

What is a Monte Carlo simulation? Monte Carlo simulation is numerical method based on the extensive use of random numbers for solving different problems. Remark: Monte Carlo simulation can be used tostudy not only stochastic problems (e.g., diffusion) but also non stochastic ones (Monte Carlo

How to start up? Initial configuration: Criteria for choosing initial configuration: quick relaxation to the equilibrium state. Random initial configuration: Advantage: liquid-like, easy to generate. Drawback: substantial overlaps at high densities. Use: Monte-Carlo for systems without hard-core interactions. Not suitable for hard-core interactions and MD at high densities

Why one needs statistics for describing physical phenomena? Any measurable macroscopic property is an average over a very huge number of microscopic configurations. Time scale of thermal fluctuations and basic relaxations~fs(femto second, 10-15 second). During the time interval necessary for realizing a measurement, a macroscopic system undergoes the change of its microscopic configuration for many many times!

Plan .Introduction Brief recall of statistical mechanics and thermodynamics .Molecular dynamics method (MD) .Monte Carlo method (MC) .Illustration of a few applications of MD and MC in the research works carried out in our laboratory .Tutorials on MD and MC