Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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MPI Kolloquium

Wednesday, 13.11.2013 15:15 s.t.

Cooperative first order percolation transitions: From HIV to the random field Ising model

by Prof. Dr. Peter Grassberger
from Department of Physics and Astronomy, University of Calgary (Canada)

Contact person: Jan Nagler

Location

Ludwig Prandtl lecture hall

Abstract

Normally, the percolation transition is continuous ("second order"). Recently, discontinuous ("first order") percolation transitions have stirred much interest. In this talk, I will discuss first order percolation transitions -- and the second-to-first order transition at "tricritical" points -- that arise from two different types of cooperativity. Maybe the most important application of percolation is to epidemic processes -- including "non-biological" epidemics like the spreading of "agents" like rumors, fads, water in sandstone, magnetic moments in disordered magnets, and computer viruses. In such spreading processes, infected victims can "cooperate" when two infected neighbors are more successful in propagating the agent than each one would be by itself. On the other hand, if there is more than one type of agents, they can also cooperate -- like the spreading of HIV with that of tuberculosis, hepatitis, or malaria. Both types of cooperativity can lead to first order transitions, if they are strong enough. But details are very different. In the talk I will discuss several approaches to treat these problems, inclusing simulations, mean field (chemical rate) equations, renormalization group methods, and "cavity" methods using generating functions.

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