Wed. August 13 at 2:00pm in the Conference Room

July 27, 2014 by Michael Grabchak
Categories: Spring 2022
Yuri Suhov,  University of Cambridge, Cambridge, UK
Title:  The Widom–Rowlinson model and the allelopathy phenomenon
Abstract: The Widom–Rowlinson (WR) model was proposed in early 1970s in Chemical Physics, to explain various phenomena at the molecular level.  There are several types of particles which repel one another when they belong to different types and have no influence upon each other if they belong to the same type (these assumptions can be made more general). This resembles an allelopathic phenomenon observed in biology where a given species prevents other species from occupying the space nearby by using a variety of means (poisoning soil or water, encouraging parasites harmful to other species but harmless to themselves, etc.). There is also a quantum version of the model.
The WR model became popular in various disciplines. An interesting question is about phase transitions: if the overall particle density is low, there is one equilibrium (Gibbs) distribution resembling Poisson. However, if the density is high, there may be one or several distributions where a particular type will dominate (occupy an overwhelming proportion of the space). This is determined by the collection of hard-core repulsion diameters. The talk will focus on new results on this question and emerging applications.