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This simulation has been plagued by quite a number of numerical problems. It has been somewhat fortunate that many of the errors have been errors that tended to increase the total energy of the system in a non-physical way. This makes these errors rather easy to detect.
Monitoring the reasons that the step size has changed shows that the numerical integration correction of the step size is rarely invoked to reduce the step size. Rather, an imminent pairing change or a close, high velocity encounter tends to keep the step size small most of the time.
The only way the step size can increase is by the recommendation of the numerical integration. Typically, it has been seen that this recommendation is offers an increase of a factor of four, the maximum allowed increase. It is probably worth allowing the maximum step size to be much larger than the current default value of 10000. The risk with large step sizes is that two or more pairing changes may be missed - with the final state being the same as the first. The intermediate pairing changes would likely have resulted in a change to the motion of the centre of mass. (Either translational or rotational)
As the number of particles goes up, the simulation speed will likely be reduced. A higher number of particles means a higher occurance of pairing changes and close approaches. Allowing each particle to have its own step size would allow computation to be focused on the particles that need it. The particles, however, will have to be synchronized at many points in order to do the pairing.
On a very tightly coupled multiprocessing system (a Transputer for instance), it might be possible to allow each particle to have its own step size, and have an overseer processor that did the pairing change calculations. If a change was detected, the calculation would be restarted just before the pairing change.
It should be clear that this depends on a working pairing algorithm. A very different description of the Hungarian algorithm has very recently been found in , and it seems to have a much more straight-forward description. This algorithm is being implemented, but has not yet been debugged.
This does not solve the baryonic (three quark) problem. In the baryonic case, it is likely that the cost of forming flux tubes completely overwhelms the cost of actually doing the numerical integration.