PHYSICAL MATHEMATICS SEMINAR
TITLE: PLANKTON PATCHINESS AND BROWNIAN BUGS
SPEAKER: WILLIAM R. YOUNG
University of California, San Diego
ABSTRACT:
We formulate and solve the simplest model of a planktonic species
reproducing and dispersing in a turbulent fluid. This Brownian bug model
is a population of independent, random-walking organisms, reproducing by
binary division, and dying at constant rates. Turbulence is modeled using
a random map, which produces a correlated displacement of neighboring
individuals. Despite the diffusion and advection, large aggregations
(patches) of bugs spontaneously develop from homogeneous initial
conditions. In this idealized model, clusters form because death can occur
anywhere, but birth is always adjacent to a living organism. In other words,
reproductive clustering overwhelms diffusion and creates non-Poisson
correlations between pairs (parent and progeny) of organisms. Because of its
simplicity and linearity, this Brownian bug process serves as a null hypothesis
for planktonic patchiness. The model is particularly useful because in several
cases exact solutions for the pair correlation can be obtained.
TUESDAY, NOVEMBER 18, 2003, 2:30 pm, Building 2, Room 338
Refreshments will be served at 3:30 PM in Room 2-349
Massachusetts Institute of Technology, Department of Mathematics, Cambridge, MA 02139