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Testing the Hard Disk Gas Model

The hard disk gas program was first tested through the examination of individual collisions. Sets of one to four molecules were collided with each other in a variety of ways, and the results were monitored to see if they agreed with expectations. After individual collisions were shown to behave properly, other tests were done to see if a gas of molecules obeyed the laws one would expect of a two dimensional gas.

In one test, the two chambers were set up with a tunnel between them, much like the situation where a demon would be used. No demon was active in this test. Instead, the molecules were allowed to move freely between the two chambers. All of the molecules were then placed in the left chamber, and the entropy of the system was measured at regular time intervals. As expected, the entropy increased with time as the system came to equilibrium, and remained relatively constant, with expected fluctuations, after a large number of time steps. (See Figure 7.)

Another property tested was the velocity distribution. As predicted by statistical mechanics, at equilibrium each distribution of each velocity component is a gaussian. (See Figures 8 and 9.).

Another property of the hard disk gas is that it is reversible. If the momenta of all of the molecules are negated, then the system should return to its earlier states. This is desirable because it shows that the second law is valid even when the underlying dynamics are reversible. The reversibility of this model of a hard disk gas is limited in practice, however. For a short number of collisions, the system may be returned to its original state by running the gas backwards. This is not the case over many time steps, because of the accumulation of round-off error in the computations.


next up previous
Next: Adding the Demon Up: The Computing Tunnel Demon Previous: The Hard Disk Gas

Eric H. Neilsen
Mon Jun 16 13:53:44 EDT 1997