❗ Only fix bd and fix bd/baoab works. Do not use OMP versions.

README

This is the custom LAMMPS fix for overdamped langevin dynamics(Brownian dynamics). LAMMPS has fix langevin for langevin dynamics simulation. However the algorithm LAMMPS use to integrate langevin dynamics equation is Velocity-Verlet. This is not suiable for high friction(overdamped) simulation. Here are several files I modified from original fix_langevin.cpp and some other files to give LAMMPS a fix for overdamped langevin dynamics simulation. This fix is only suitable for high friction case since velocity is overdamped. The detailed physics for this fix can be viewed in derivation.pdf. For low friction, please use original fix langevin. As for what value is approriate for high and low friction, one should do experiments themsevles.

HOW TO USE

Build LAMMPS

1. Put fix_bd.cpp/fix_bd_baoab.cpp and their header files into src folder of LAMMPS.
2. Build LAMMPS.

Use it in input file

fix ID group-ID bd temperature damp seed

• ID, group-ID
• bd = style name of this fix command
• temperature = desired temperature of run (temperature units)
• damp = damping parameter (time units)
• seed = random number seed to use for white noise (positive integer)

Examples

fix 1 all bd 1.00 0.01 324231

IMPORTANT NOTES

• damp should be much smaller than one. This is to ensure the parameters are indeed for overdamped/high friction/low intertia regime. For instance, damp = 0.01 is sufficiently small for brownian dynamics simulation. damp = 100 is too large to use this fix. Instead, just use fix langevin for large value of damp constant.

Other Options

• fix bd/baoab: BAOAB algorithm for Brownian Dynamics simulation.
• fix bd/srk: SRK algorithm for Brownian Dynamics simulation. (DO NOT USE)
• fix bd/omp/fix bd/srk/omp/fix bd/baoab/omp: OMP version of Brownian Dynamics simulation. (DO NOT USE)

Reference

• Leimkuhler, Benedict, and Charles Matthews. "Rational construction of stochastic numerical methods for molecular sampling." Applied Mathematics Research eXpress 2013.1 (2012): 34-56.