Back to Departmental Colloquium: Spring 2000
Departmental Colloquium
Date: Wednesday, Feb 16, 2000
Time: 4:15PM
Location: JWB 335
Angela Stevens
Leipzig)
Title |
Stochastic interacting particle systems as models for selforganization in microbiology |
Abstract |
Selforganization in microbiology is not only interesting in itself but also serves as a model problem for questions in morphogenesis, e.g.“how do cells manage to cooperate and build higher organized structures.” Aggregation or selforganization of a species frequently involves movement towards or away from an external stimulus which sometimes is also modified. This behavior will be modeled by a self-attracting reinforced random walk. The random walk for a single particle can be formally approximated by a so-called chemotaxis equation which describes the dynamics of the particles probability distribution. To approximate the dynamics of many particles, their interaction has to be taken into account. Starting from a model where the dynamics of each particle is described by a stochastic differential equation which includes moderate interaction with the other particles, the chemotaxis equation can be rigorously derived as a model for the dynamics of the total population. For suitable parameters the solutions of the chemotaxis equation blowup in finite time which here reflects possible selforganization. |
Probability
Mathematical Biology
Differential Equations