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Optimal disorder for segregation in annealed small worlds

Santiago Gil·Damian H. Zanette
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Abstract

We study a model for microscopic segregation in a homogeneous system of particles moving on a one-dimensional lattice. Particles tend to separate from each other, and evolution ceases when at least one empty site is found between any two particles. Motion is a mixture of diffusion to nearest-neighbour sites and long-range jumps, known as annealed small-world propagation. The long-range jump probability plays the role of the small-world disorder. We show that there is an optimal value of this probability, for which the segregation process is fastest. Moreover, above a critical probability, the time needed to reach a fully segregated state diverges for asymptotically large systems. These special values of the long-range jump probability depend crucially on the particle density. Our system is a novel example of the rare dynamical processes with critical behaviour at a finite value of the small-world disorder.

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Santiago Gil, Damian H. Zanette. 2005-04-11. Optimal disorder for segregation in annealed small worlds. https://doi.org/10.1140/epjb%2Fe2005-00319-8

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