Materials Science Study by Molecular Dynamics

** 1. Method**

When we study high-temperature plasmas and the microscopic

structure and functionality of condensed matters by computer

simulations, we use either classical molecular dynamics code

based on Newtonian dynamics, or the first principle code based

on quantum mechanics, depending on the scale and the process

to be studied. The former code can deal with the stellar motions

in the universe down to atomic motions in nanometer scales.

The latter code should be used for the study that includes atomic

processes where overlapping of atoms, hence that of electron

orbits, takes place.

The electrostatic forces are inverse-square forces like the

gravitational forces, which are long-range forces in nature. But,

one has to calculate them correctly also for short distances since

particle near-by collisions are frequent. Thus, we take summation

of the short-range part of the electrostatic forces over all the ion

combinations. This requires N*N calculations on each time step

of the simulation run, where N is the number of ions in the system.

If we integrate the equations for, at least, 100,000 steps and with

N= 1000, the total of 100 billion calculations are executed in the

run. Thus, we must use a fast computer for molecular dynamics

simulations.

In the classical molecular dynamics, the most time consuming

part of computation is the Ewald sum which takes into account

the periodicity of the charge distribution（typical in crystals).

However, the equations are rather simple. By contrast, the

first-principle molecular dynamics code solves the equation for

electron density, which requires large matrix diagonalization.

These procedures are rather complicated and even heavier in

computation than solving equations of motion.

**
2. PC Cluster Machines**

As explained above, molecular dynamics

simulations need very fast computers, and

only supercomputers could do the job

before. Now, the x86-based PC cluster

machines are replacing conventional

supercomputers bacuase of their capability

of handling large amount of computations.

Thus, if one can wisely parallelize the

molecular dynamics code, a Boewulf PC

cluster (parallel computer) is highly suited for

molecular dynamics simulations.

For these reasons, we constructed several

clusters based on Pentium III (1GHz), Xeon

(2.4GHz), Pentium 4 (3GHz) with MPICH.

We found later that using the low-latency

communication software GAMMA doubles

the computation power.

Recently we use Opteron 2.8 GHz clusters

with the SuSE Linux ES and the InfiniBand

MPI for inter-processor communications.

We are making good use of these cluster

machines in our current research of plasma

and condensed matters.

**Topics**

**
Boewulf PC cluster: How to make and use it** (summary)

First hand-made cluster with

Pentium III.

Dual Pentium III