211 research outputs found
Fractal rain distributions and chaotic advection
Localized rain events have been found to follow power-law distributions over
several decades, suggesting parallels between precipitation and seismic
activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws can be
generated by treating raindrops as passive tracers advected by the velocity
field of a two-dimensional system of point vortices [R. Dickman, PRL 90, 108701
(2003)]. Here I review observational and theoretical aspects of fractal rain
distributions and chaotic advection, and present new results on tracer
distributions in the vortex model.Comment: 16 pages; 8 figures (high resolution versions of figures 1-3
available on request
Path Integrals and Perturbation Theory for Stochastic Processes
We review and extend the formalism introduced by Peliti, that maps a Markov
process to a path-integral representation. After developing the mapping, we
apply it to some illustrative examples: the simple decay process, the
birth-and-death process, and the Malthus-Verhulst process. In the first two
cases we show how to obtain the exact probability generating function using the
path integral. We show how to implement a diagrammatic perturbation theory for
processes that do not admit an exact solution. Analysis of a set of coupled
Malthus-Verhulst processes on a lattice leads, in the continuum limit, to a
field theory for directed percolation and allied models.Comment: 33 pages, 6 figure
Critical Behavior of the Widom-Rowlinson Lattice Model
We report extensive Monte Carlo simulations of the Widom-Rowlinson lattice
model in two and three dimensions. Our results yield precise values for the
critical activities and densities, and clearly place the critical behavior in
the Ising universality class.Comment: 6 pages, LaTeX, 5 figures available upon reques
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