Molecular Dynamics (1)
Molecular Dynamics (1)
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 Crystal initial configuration e. g, fcc crystal Advantage: avoiding overlaps easy to generate Drawbacks: not liquid-like Use: suitable for all type of MC and MD
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. - Crystal initial configuration: e.g., fcc crystal Advantage: avoiding overlaps, easy to generate. Drawbacks: not liquid-like Use: suitable for all type of MC and MD
Initial velo cities Maxwell-Boltzmann distribution 3)12na 2k Uniform distribution Each velocity components drawn from a uniform distribution in a range (-v max, maX Constraint nv
Initial velocities: Maxwell-Boltzmann distribution: ) 2 exp( 2 ( ) 2 k T k T f m mv v i i i x i x = − Uniform distribution: Each velocity components drawn from a uniform distribution in a range (-vmax, vmax). Constraint: 0 1 = = = N i mivi P
Exercise 1)Write a program for generating an initial configuration with the particles places on a fcc lattice 2)Write a program for generating initial velocities from an uniform distribution in the range(-Vmax, Vmax)(vmax =5) with the constraint that the total initial velocity is zero
Exercise 1) Write a program for generating an initial configuration with the particles places on a fcc lattice. 2) Write a program for generating initial velocities from an uniform distribution in the range (-vmax, vmax) (vmax=5) with the constraint that the total initial velocity is zero
Equilibration Monitoring the equilibration of system with several observables e. g, internal energy, pressure etc A The production run should not start before the system reaches the targeted equilibrium state!
Equilibration Monitoring the equilibration of system with several observables, e.g., internal energy, pressure etc.. A t The production run should not start before the system reaches the targeted equilibrium state!