Environmental Engineering Reference
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a very large body of simulation results already exists but for which extensive ex-
perimental information is just now becoming available. It is not an exaggeration
to say that interest in this field was created by simulations. Even more dramatic
examples are those of reactor meltdown or large-scale nuclear war: although we
want to know what the results of such events would be we do not want to carry out
experiments! There are also real physical systems, which are sufficiently complex
that they are not presently amenable to theoretical treatment. An example is the
problem of understanding the specific behavior of a system with many competing
interactions and which is undergoing a phase transition. A model Hamiltonian,
which is believed to contain all the essential features of the physics may be pro-
posed, and its properties may then be determined from simulations. If the simula-
tion (which now plays the role of theory) disagrees with experiment, then a new
Hamiltonian must be sought. An important advantage of the simulations is that
different physical effects, which are simultaneously present in real systems may
be isolated and through separate consideration by simulation may provide a much
better understanding.
1.3.1.2.5 THE ART OF RANDOM NUMBER GENERATION,
BACKGROUND
Monte Carlo methods are heavily dependent on the fast, efficient production
of streams of random numbers. Since physical processes, such as white noise
generation from electrical circuits, generally introduce new numbers much too
slowly to be effective with today's digital computers, random number sequences
are produced directly on the computer using software (the use of tables of ran-
dom numbers is also impractical because of the huge number of random numbers
now needed for most simulations and the slow access time to secondary storage
media). Since such algorithms are actually deterministic, the random number se-
quences, which are thus produced are only 'pseudorandom' and do indeed have
limitations, which need to be understood. Thus, in the Appendix of this review,
when we refer to Generation 'Random numbers' programs 1 and 2, Some nec-
essary background 'random numbers' it must be understood that we are really
speaking of 'pseudorandom'numbers (Appendix A).
These deterministic features are not always negative. For example, for testing
a program it is often useful to compare the results with a previous run made us-
ing exactly the same random numbers. The explosive growth in the use of Monte
Carlo simulations in diverse areas of physics has prompted extensive investiga-
tion of new methods and of the reliability of both old and new techniques. Monte
Carlo simulations are subject to both statistical and systematic errors from mul-
tiple sources, some of which are well understood. It has long been known that
poor quality random number generation can lead to systematic errors in Monte
Carlo simulation; in fact, early problems with popular generators led to the de-
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