Soft Spheres in a Box

In 1996, I performed some experiments simulating the dynamics of "soft spheres" in a box. Each sphere is given a random initial velocity, and initial position within the box. A repulsive potential of 1/(r^12) is used to simulate rigid walls, and "hard/soft" spheres. Since the potential contains only pairwise interactions, it scales quadratically with the number of spheres. This model problem was select to see if a time-reversible variable stepsize algorithm could be applied to simple problems in molecular dynamics. I applied a second-order time-reversible variable-stepsize integrator, better known as Adaptive Verlet*.

* W. Huang and B. Leimkuhler, The Adaptive Verlet Method, SIAM J. Sci. Comput. 18 , 239--256 (1997).

Here is a movie showing the dynamics over a relatively long time-interval.

Here are some results in the form of graphs (click to enlarge):

Energy Error

Variation in Step

K.E. and P.E.