Hello Alaa

responses below...

بسم الله الرحمن الرحيم

My questions are:

1.

See below

2. " Langevin dynamics allows controlling the temperature like a thermostat, thus approximating the canonical ensemble. "

Does you mean that for LD I must use fix langevin only which mean by default fix nvt and for BD I must use fix langevin along with fix nve?

No. If you are using LAMMPS, then use both "fix langevin" and "fix

nve" together. (Do not add "fix nvt")

3. can I run a simulation with no periodic BC and without any limit on the space in Lammps?

Yes

Keep in mind that if you are using "s" ("shrink wrapped") boundary

conditions and the distance between particles grows to be large,

LAMMPS may run out of memory when it attempts to build neighbor-lists,

due to the large box necessary to enclose your system.. If you are

simulating a single molecule (polymer) and you don't have any freely

diffusing objects in your simulation, then this should not be an

issue. If it is an issue, you can use the "neighbor" command to

increase the bin size and reduce memory usage.

LAMMPS Molecular Dynamics Simulator

(My chromosome folding simulations I use:

neighbor 30.0 bin

30.0 is much larger than the pairwise force cutoff distance I normally use)

1. Is this method in Lammps doing a BD as illustrated in Wikipedia ?

url: Brownian dynamics - Wikipedia

No.

"fix langevin" + "fix nve" together implement Langevin dynamics, not

Brownian dynamics.

Brownian dynamics is Langevin dynamics in the limit that the mass -> 0

(or, equivalently when the friction->infinity). As far as I am aware,

Brownian dynamics is not implemented in LAMMPS. (And for good reason,

in my opinion. See rant below.) Brownian dynamics is considered

reasonably accurate if you are interested in looking at the high

frequency (small timescale dynamics), because the frictional

coefficient of damping for water is so large that it can be

approximated as infinite (compared to the time it takes for anything

interesting to happen in the simulation).

However if you don't care about the high frequency dynamics of the

system... If you are only interested in events that occur on longer

timescales (for example, the time it takes for a protein to fold),

then it is much much more efficient to use Langevin dynamics (compared

to Brownian dynamics). The use of Brownian dynamics

If you are curious, there is a nice paper describing the effect of the

frictional damping rate on the dynamics of protein folding here:

If I remember correctly, they find that you can reduce the frictional

coefficient by a factor of 50 before it even starts to effect the

dynamics of protein folding. If you use run the simulation with 50x

less friction, this effectively increases the efficiency of your

simulation by a factor of 50 (because the rate of movement due to

diffusion is inversely proportional to the the friction). (Again,

increasing mass is equivalent to reducing friction in Langevin

dynamics. To make matters more confusing, this is equivalent to

-increasing- the "damp" parameter used with the fix langevin command

in LAMMPS, which corresponds to damping -time-, not rate.) As an

extreme example, I simulate chromosome folding, which takes vastly

longer more time than most proteins take to fold. To make this

process tractable, I reduce the friction so that the damping time is

on the order of (approximately) 1/10th of the time it takes for the

chromosome to fold (which is vastly, vastly smaller than the friction

of real water, but yet high enough that the DNA polymer still moves

diffusively at the long time scales I care about). Without doing

this, my simulations would never finish.

I remember wrote a simulation program which used true Brownian

dynamics. It was extremely slow and numerically unstable. Particles

moving in the zero-mass limit contain much more high frequency noise

in their movement than particles moving according to Langevin

dynamics, and the sudden jumps that occurred caused particles to bump

too far into each other and the simulation would explode (often).

Unless you really care about this noise, it is better to remove it by

running your simulations using Langevin dynamics with a large mass

value (small friction coefficient).

Hope this helps

Andrew

P.S. Don't be offended by this, but if it helps, here's a few

textbooks which describe Langevin dynamics in more detail:

Van Kampen "Stochastic Processes in Physics and Chemistry"

David Chandler "Introduction to Modern Statistical Mechanics"

Donald McQuarrie "Statistical Mechanics"

Among these books, the most concise explanation is either in Chandler

or Van Kampen. (Perhaps there are more modern books available by

now.)