BASIC CONCEPTS AND AN OVERVIEW - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 119

scales of time and length) must be developed. Coarse-graining techniques can be
used to clarify features of the results, which are not immediately obvious from
inspection of columns of numbers. 'Windows' of various sizes can be used to scan
the system looking for patterns, which develop in both space and time; and the
development of such methods may well profit from interaction with computer sci-
ence. Clearly improved computer performance is moving swiftly in the direction
of parallel computing. Because of the inherent complexity of message passing,
it is likely that we shall see the development of hybrid computers in which large
arrays of symmetric (shared memory) multiprocessors appear. (Until much higher
speeds are achieved on the Internet, it is unlikely that non-local assemblies of
machines will prove useful for the majority of Monte Carlo simulations.) We must
continue to examine the algorithms and codes, which are used for Monte Carlo
simulations to insure that they remain well suited to the available computational
resources. We strongly believe that the utility of Monte Carlo simulations will
continue to grow quite rapidly, but the directions may not always be predictable.
We hope that the material in this topic will prove useful to the reader who wanders
into unfamiliar scientific territory and must be able to create new tools instead of
merely copying those that can be found in many places in the literature.
1.3.1.1 RANGE OF PROBLEMS CAN WE SOLVE WITH MONTE
CARLO SIMULATION
The range of different physical phenomena, which can be explored using Monte
Carlo methods, is exceedingly broad. Models, which either naturally or through
approximation can be discretized, can be considered. The motion of individual
atoms may be examined directly; for example, in a binary (AB) metallic alloy
where one is interested in the diffusion or un mixing kinetics (if the alloy was
prepared in a thermodynamically unstable state) the random hopping of atoms to
neighboring sites can be modeled directly. This problem is complicated because
the jump rates of the different atoms depend on the locally differing environment.
Equilibrium properties of systems of interacting atoms have been extensively
studied as have a wide range of models for simple and complex fluids, magnetic
materials, metallic alloys, adsorbed surface layers, etc. More recently polymer
models have been studied with increasing frequency; note that the simplest model
of a flexible polymer is a random walk, an object that is well suited for Monte
Carlo simulation. Furthermore, some of the most significant advances in under-
standing the theory of elementary particles have been made using Monte Carlo
simulations of lattice gauge models [131].
1.3.1.2 THE PROBLEMS OF MONTE CARLO SIMULATION
1.3.1.2.1. LIMITED COMPUTER TIME AND MEMORY
Because of limits on computer speed there are some problems, which are inher-
ently not suited to computer simulation, at this time. A simulation, which requires
years of CPU time on whatever machine is available, is simply impractical. Simi-