# brownian dynamics

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Hi Eric,

First let me thank you and sorry for posting this question to you …

I am simulating some particles using brownian dyanmics with water as a solvent using LAMMPS.

I assume this means that there is technically no water in the MD, that is interactions are carried out through potentials and a white noise force.

Let say, the particle mass (m) is 30 g/mole and radius (a) 0.5 nm. The water viscosity (eta) is 1.010^(-3) kg/(m.s). Avagadro number N = 6.02210^(23)

The damp parameter in fix langevin is equal to mass/(6pieta*a) by using Stokes law.

With the above parameters, damp = 5.3 fs. The temperature of the system is relaxed in a time span of damp (time units).

Which means the time step should be much smaller than the damp, 5.3 fs in this case.

Before going into things, physically, this model makes little sense without some details clarified, but I’ll leave them to you. Particles of 0.5 nm screams to me that treatment via the Langevin/Brownian motion(BM) model is not suitable. If you have a path to this treatment, ignore this comment I guess.

This don’t seem to be right for Brownian dynamics.

Why not? Beyond going into details of Brownian motion and Langevin type models, take a look at simpler systems, for example, a 2nd order deterministic linear system e.g. classical mass-spring-dashpot system. The time-scale to reach steady-state in this situation is on the order of a damping parameter. This means that the time-scale we integrate by should be lower than the time-scale given by (damping parameter)/mass.

I implore you to look at the classical solution for the velocity autocorrelation function in a Langevin equation, which governs how fast a system ‘forgets’ an initial condition (how fast your random temperature is achieved). You will find that the damping parameter you speak of shows up clearly in this situation. I won’t speak to correct evaluation, you might find it useful to test against some analytic solutions of Langevin eqns., which carry far more authority than myself.

I must be be missing something here, …

Is my damp parameter correctly evaluated ?

Thank you very much,