This applet demonstrates an incorrectly programmed molecular dynamics simulation of hard particles. Start the simulation with the current settings. If you wait long enough you will notice that some collisions are missed by the integration algorithm, and occasionally disks pass through each other without colliding. The problem becomes acute at low density, which you can obtain by reducing the number of disks with the slider. Lower the temperature to slow down the motion.
The problem is with the periodic boundaries. Collisions are examined only with the nearest image of any given particle. A may particle in fact be on a collision course with the second nearest (or yet more distant) image of another particle, while be moving away from the nearest image. If the particle suffers no collisions in the interim (a situation more likely at low density), the two particles may end up passing through each other, with their collision never detected.The situation is easily remedied by automatically updating the collision list of each particle after it travels some distance without experiencing any collision. Alternatively, the collision list could be updated after a particle passes through one of the periodic boundaries of the system.
Note that the system displayed here presents eight periodic images of the central simulation cell.