J.L. Blue, ACMD
We are modeling crystal growth by two commonly used methods, Molecular Beam Epitaxial Growth and Chemical Vapor Deposition. In both methods, atoms impinge on a crystalline substrate, are adsorbed, and are then can move around on the surface.
We are doing a Monte Carlo method to do the simulation. The key to rapid
simulation is a search method we have developed to pick the right random item
from a non-ordered list. A straight-forward method is 
, where N is the
total number of items in the list. The formerly standard method was
; our method is 
. Last year Blue, Beichl, and Sullivan
produced a method which is 
. This year I developed a method which
is 
for most problems of interest. (If there are only L different
probabilities or rates in the N items, the time is 
.)
Our first efforts use a simple model of the physics involved; this year I expect to simulate a real growth process, the deposition of chromium on an iron substrate, in collaboration with the Physics Laboratory.