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10 papers · 2 filters
Numerical analysis of the master equation
Ronald Dickman
Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by severa…
Quasi-stationary distributions for stochastic processes with an absorbing state
Ronald Dickman, Ronaldo Vidigal
We study the long-time behavior of stochastic models with an absorbing state, conditioned on survival. For a large class of processes, in which saturation prevents unlimited growth…
Lattice Model for Approximate Self-Affine Soil Profiles
A. P. F. Atman, J. G. Vivas Miranda, A. Paz Gonzalez +1
A modeling of the soil structure and surface roughness by means of the concepts of the fractal growth is presented. Two parameters are used to control the model: the fragmentation…
Nonequilibrium Phase Transitions in Epidemics and Sandpiles
Ronald Dickman
Nonequilibrium phase transitions between an active and an absorbing state are found in models of populations, epidemics, autocatalysis, and chemical reactions on a surface. While a…
Growth Exponent in the Domany-Kinzel Cellular Automaton
A. P. F. Atman, J. G. Moreira
In a roughening process, the growth exponent describes how the roughness grows with the time : . We determine the exponent of a growth process generated b…
Scaling Exponents of Rough Surfaces Generated by the Domany-Kinzel Cellular Automaton
A. P. F. Atman, Ronald Dickman, J. G. Moreira
The critical behavior at the frozen/active transition in the Domany-Kinzel stochastic cellular automaton (DKCA) is studied {\it via} a surface growth process in (1+1) dimensions. A…