Biomathematics Seminar: Nonconstant diffusion constants, sticky walls and a dynamical transition: Fluctuation-driven birth-death dynamics
31 January 2012 14:00 in Department of Mathematical Sciences
Simple birth-death processes in which individuals of all species reproduce and die at the same rate display surprisingly rich diversity patterns despite the simplicity of their dynamics. From a statistical physics perspective, these models describe an ordering process that is entirely fluctuation driven. It is also a nonequilibrium dynamics: the noise does not satisfy a fluctuation-dissipation relation (the diffusion constant is not constant) and the possibility of extinction implies absorbing states (sticky walls). Together, these properties give rise to a curious dynamical phase transition in which the overall strength of the noise controls the universality class of the macroscopic ordering dynamics. Even more curiously, the conservation law that defines one of these universality classes is an emergent property of the nonequilibrium system, as opposed to something that is imposed from the outset.
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