Simulated Random Sequential Filling of Space by Non-Touching Uniform Spheres.
Final rept. May 73-Dec 74,
MINNESOTA UNIV MINNEAPOLIS DEPT OF PHYSICS
Pagination or Media Count:
A computer method study of filling space with uniform size, non-touching spheres in a random sequential fashion until saturation prevents adding additional spheres. A saturation value of .710 sphere centersunit volume corresponding to a packing fraction of .372 is deduced after attempts to analyze the probability of voids remaining in the distribution. An empirical expression is developed for the probability of accommodating a sphere on the Xth random attempt which appears valid for large X. Nearest neighbor distributions are determined for the first twelve neighbors and average distances for the first thirty neighbors. Radial densities are compared with previous work by Scott, Finney, and Tory showing maxima and minimia. Evidence indicates a slight tendency for shells of approximately eight neighbors to form about any given sphere. Nearest neighbor pairs defined as adjacent spheres which are each others nearest neighbor are counted as accounting for approximately a half of the sphere population. A study of neighbors of any given sphere with which the given sphere could collide head-on if in straight line motion yields an overall average of approximately five such neighbors per sphere. Probability data is given for head-on neighbors.
- Statistics and Probability