Colloquium
3:00 p.m., Friday (September 16, 2005)
Math Annex 1100
Alexander Holroyd
UBC
The Bootstrap Percolation Cellular Automaton  a case study in Theory versus Experiment
See
http://www.math.ubc.ca/~holroyd/boot/ for a picture.
Cellular automata arise naturally in the study of physical systems,
and exhibit a seemingly limitless range of intriguing behaviour. Such
models lend themselves naturally to computer simulation, but rigorous
analysis can be notoriously difficult, and can yield highly unexpected
results.
Bootstrap percolation is a very simple model for nucleation and growth
which turns out to hold many surprises. Sites in a square grid are
initially declared ``infected" independently with some fixed
probability. Subsequently, healthy sites become infected if they have
at least two infected neighbours, while infected sites remain infected
forever. The model undergoes a phase transition at a certain
threshold whose asymptotic
value differs from numerical predictions by more than a factor of two!
This discrepancy points to a previously unsuspected phenomenon called
``crossover", and leads to further intriguing questions.
Refreshments will be served at 2:45 p.m. (MATX 1115, Faculty Lounge).
