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