Environmental Engineering Reference
In-Depth Information
velopment of improved methods for producing pseudorandom numbers. As we
shall show in the following discussion both the testing as well as the generation
of random numbers remain important problems that have not been fully solved.
In general, the random number sequences, which are needed, should be uniform,
uncorrelated, and of extremely long period, that is, do not repeat over quite long
intervals. In the following subsections we shall discuss several different kinds of
generators. The reason for this is that it is now clear that for optimum performance
and accuracy, the random number generator needs to be matched to the algorithm
and computer. Indeed, the resolution of Monten Carlo studies has now advanced
to the point where no generator can be considered to be completely 'safe' for use
with a new simulation algorithm on a new problem. The practitioner is now faced
anew with the challenge of testing the random number generator for each high-
resolution application, and we shall review some of the 'tests' later in this section.
The generators, which are discussed in the next subsections produce a sequence
of random integers. One important topic, which we shall not consider here is
the question of the implementation of random number generators on massively
parallel computers. In such cases one must be certain that the random number se-
quences on all processors are distinct and uncorrelated. As the number of proces-
sors available to single users increases, this question must surely be addressed, but
we feel that at the present time this is a rather specialized topic and we shall not
consider it further. This method for generation of random walk numbers includ-
ing: Congruential method, Mixed congruential methods, Shift register algorithms,
Lagged Fibonacci generators, Tests for quality, non-uniform distributions.
1.3.2 MOLECULAR DYNAMICS SIMULATION AND ITS AIMS
Simulations as a bridge between microscopic and macroscopic, theory and ex-
periment. We carry out computer simulations in the hope of understanding the
properties of assemblies of molecules in terms of their structure and the micro-
scopic interactions between them. This serves as a complement to conventional
experiments, enabling us to learn something new, something that cannot be found
out in other ways. In this review we shall concentrate on MD. The obvious ad-
vantage of MD over MC is that it gives a route to dynamical properties of the
system: transport coefficients, time-dependent responses to perturbations, rheo-
logical properties and spectra. Computer simulations act as a bridge between mi-
croscopic length and timescales and the macroscopic world of the laboratory: we
provide a guess at the interactions between molecules, and obtain 'exact' predic-
tions of bulk properties. The predictions are 'exact' in the sense that they can be
made as accurate as we like, subject to the limitations imposed by our computer
budget. At the same time, the hidden detail behind bulk measurements can be
revealed. An example is the link between the diffusion coefficient and velocity
autocorrelation function (the former easy to measure experimentally, the latter
much harder). Simulations act as a bridge in another sense: between theory and
Search WWH ::
Custom Search