By M. M. Woolfson
Computing device simulation is more and more utilized in physics and engineering to foretell the possible end result of experiments and to assist of their interpretation. this article for undergraduates illustrates the elemental concepts with a number of basic courses and difficulties drawn from a variety of disciplines.
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Extra resources for An introduction to computer simulation
26) enables concentrations at all points at time tj+1 to be found explicitly from the concentrations at time tj. We can illustrate this by considering the heat flow in a bar of length 1 m, well lagged except for the two ends, with a uniform cross-section, thermal conductivity 200Wm~ 1 K~ 1 , specific heat capacity 1000Jkg~ 1 K~ 1 and density 2700kgm~3. Initially the bar is at a uniform temperature of 300K but the two ends are maintained at temperatures of 300 K and 500 K respectively. The problem is to follow the sequence of temperature profiles in the bar to some steady-state condition.
The latter of these is the strategy used in the program POLYWALK (see p. xv) where up to four attempts are made to avoid a crossing, after which the trial is abandoned. 4 up to n = 32. Looking for the possibility that the rms distance may depend on some power of the number of steps, Fig. 11 shows the logarithm of the rms distance, as found by the program, plotted against log(w). 63 is shown in the final column. Although this relationship breaks down for larger values of n, we have found by numerical means a useful relationship as long as it is restricted to its range of validity.
It should be pointed out that the spikes and the rounding off are not directly connected. If the dissipation term is removed then the spikes will remain on the background of an otherwise constant eccentricity. 22 Models and simulation This particular simulation illustrates another feature of computational modelling. Although the explanation of the spikes is quite straightforward and easily understood, it may not have been obvious ab initio that such spikes would occur. A good simulation may well bring out new, unexpected and important features of the system under investigation.
An introduction to computer simulation by M. M. Woolfson