overdamped Langevin Dynamics

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1

Hi all,

I want to used LAMMPS to perform the overdamped langevin dynamics, which eliminate the mass of particles and just use diffusion coefficient. Has anyone realized the method and added into LAMMPS. It is appreciated if you can share with me.

If not, I want to modify the fix NVE to realize it.
For Brownian Dynamics, the equations are intergrated with Euler formalism :

r(t+dt)=r(t)+dtF(t)/fric_coeff+ sqrt(2KbTdt/fric_coeff)* guss( )

This can be achieved in the class of initial_integrate( ) , It seems that the class of final_integrate ( ) is not necessary.
Is my unterstanding right in the framework of Velocity-Verlet method ( in verlet.cpp)?

Any suggestion is welcome

Thanks in advance

Wade

2

Dear Tian

    I don't think the feature you are describing has not been added to
LAMMPS yet. (Langevin-dynamics in the zero-mass limit, or,
equivalently, in the infinite-friction limit. It is sometimes called
"Brownian Dynamics".)

http://en.wikipedia.org/wiki/Brownian_dynamics

    If you want to add this feature to LAMMPS, that would be nice.

--- Summary ---

When I attempted to do this myself, but I ran into numerical
explosions and had to use small timesteps. I'm curious to know if by
now there are any good integration algorithms which avoid these issues
(other than using finite mass).

    Feel free to skip the rest of this long email.

Andrew

--- Details: why I use finite mass Langevin Dynamics ----

    I implemented this feature (zero-mass Brownian dynamics) in a
different MD program. However, in the end I decided not to use this
feature. Reducing the mass of each particle (to zero) results in much
faster, noiser motion. It causes causes particles to jump much
farther between timesteps (keeping the timestep fixed). Consequently
you have to use much smaller timesteps in order to prevent sudden
"jumps" in position which would cause numerical explosions. (This was
especially a problem using Lennard-Jones forces due to the 1/r^12
repulsion. Perhaps it's not a problem using harmonic forces.) I
suspect I'm not the only one who ran into this problem. Again, if
someone has a suggestion for a way around these kinds of problems,
please post it.

   So I found it much more computationally efficient to use ordinary,
finite-mass Langevin dynamics (for example, as implemented using "fix
langevin" http://lammps.sandia.gov/doc/fix_langevin.html). I would
choose the damping time (the "tdamp" parameter) according to the
timescales of interest. (This is equivalent to choosing the mass, if
viscocity of the solvent is and particle size is already determined.)
    For example, when I was running protein folding simulations,
movement of large domains of the protein were what mattered
physically, so I would set the damping time ("tdamp") similar to the
timescale of those kinds of motions. I did not care about what's
going on at shorter timescales than that.

   I liked this paper:
D. K. Klimov, D. Thirumalai, "Viscosity Dependence of Folding Rates of
Protein", Phys. Rev. Lett., 79, 317-320 (1997)

   My impression after reading that paper was if you increase the
friction coefficient (or equivalently reduce the mass) enough, then
the dynamics of protein folding are the same in that limit. (So you
don't have to go all the way to the zero-mass limit.)

   I could be wrong, but I haven't really met anybody who is
passionate enough about this topic to correct me yet.