PROGRAM SUMMARY
Title of program:
GMIC++
Catalogue identifier:
ADRK
Ref. in CPC:
152(2003)208
Distribution format: zip file
Operating system: Windows NT/2000/XP, Cygwin, Linux Red Hat v8.0
High speed store required:
500K words
Number of lines in distributed program, including test data, etc:
4226
Keywords:
Grouping method, Master equation, Nucleation, Growth, Clusters,
Molecular physics, Chemical kinetics, Statistical physics,
Thermodynamics.
Programming language used: C++
Computer:
PC Pentium III .
Nature of physical problem:
A common approach to describe defect/adatom accumulation processes is by
using a system of master equations. For a good description, the number
of equations in the system is generally very large. As a result, their
numerical solution is very time consuming. This problem is less serious
at the early stage. However, as the process continues, the number of
master equations increases and the numerical difficulty becomes severe.
Method of solution:
To physically track the details of the accumulation process with
available computational resources, Kiritani [1] first proposed the group
method. Accordingly, the system of master equations is divided into
groups, keeping the first moments unchanged. Realizing the inadequacy
of the original grouping method, Golubov et al [2] proposed to preserve
also the second moment, which has been shown to provide an accurate
description of the defect/adatom accumulation processes, as originally
described by a large number of master equations.
Restrictions:
The method is valid for general defect/adatom accumulation processes,
which are describable by a set of master equations.
Typical running time:
It depends on energetics and the speed of the processes involved. As an
example, it takes 30 seconds on a Pentium III processor at 1GHz clock
frequency to track the vacancy clustering in nickel during one hour
ageing at 550oC, solving a system of up to 300 master equations.
References:
[1] M. Kiritani, J. Phys. Soc. Japan 37 (1974) 1532.
[2] S.I. Golubov, A.M. Ovcharenko, A.V. Barashev and B.N. Singh, Phil.
Mag. A 81 (2001) 643.