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Peter Grassberger

As seen in: Physical Review B
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Articles by Peter Grassberger

Aftermath epidemics: Percolation on the sites visited by generalized random walks

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By Peter Grassberger, FZ Jülich, Mohadeseh Feshanjerdi, Amir Ali Masoudi
| Physical Review B
We study percolation on the sites of a finite lattice visited by a generalized random walk of finite length with periodic boundary conditions. More precisely, consider Levy flights and walks with finite jumps of length >1 [like Knight's move random walks (RWs) in two dimensions and generalized Knight's move RWs in 3D]. In these walks, the visited sites do not form (as in ordinary RWs) a single connected cluster, and thus percolation on them is nontrivial.
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Many universality classes in an interface model restricted to non-negative heights

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By Peter Grassberger, FZ Jülich, Deepak Dhar, P. K. Mohanty
| Physical Review B
Abstract We present a simple one-dimensional stochastic model with three control parameters and a surprisingly rich zoo of phase transitions. At each (discrete) site x and time t, an integer n(x,t) satisfies a linear interface equation with added random noise. Depending on the control parameters, this noise may or may not satisfy the detailed balance condition, so that the growing interfaces are in the Edwards-Wilkinson or in the Kardar-Parisi-Zhang universality class.
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Phase transitions in cooperative coinfections: Simulation results for networks and lattices

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By Li Chen, Peter Grassberger, Fakhteh Ghanbarnejad, Weiran Cai
| Physical Review B
We study the spreading of two mutually cooperative diseases on different network topologies, and with two microscopic realizations, both of which are stochastic versions of a susceptible-infected-removed type model studied by us recently in mean field approximation. There it had been found that cooperativity can lead to first order transitions from spreading to extinction.
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