Random Numbers

Also in molecular dynamics simulations we need random numbers to generate, for example, a set of initial conditions for the velocities of particles. To this end we generate random numbers with a uniform distribution in the interval between zero and one and then transform these uniform random numbers to follow the Maxwell distribution. In a sense, the displacement of a particle or particles, may it be the result of the forces or by directly placing the particles, comes from the random numbers.

In this section we thus concern ourselves with probabilities, distributions and the generation of numbers that follow a given distribution. Our major interest focuses on the generation of numbers that are uniformly distributed and on some tests for their properties. It is of utmost importance to persuade oneself prior to a simulation that the random number generator which one will be using has the desired properties. Any defect making the random numbers 'non-random' effects the outcome of the simulation.

The sequence of numbers in a computer simulation used to make decisions or to generate new states are generated by a deterministic algorithm. This algorithm produces numbers, that in the common use of language appear chaotic. What is meant by this, is that they will appear to an outside observer as totally unpredictable, even though they were generated by an algorithm. This algorithm, given the initial state, always produces the same sequence of numbers any time we apply the algorithm. One is tempted to use a physical generator, for example exploiting the radioactive decay. We must note that such a generator relies on unproved assumptions while a mathematically constructed generator has precise properties, even though there may be some short-comings. Also, we want the numbers to be reproducible. This is important when we check out a program for errors. Further, the numbers generated from a physical process may not come at the needed rate.