Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCrossover from directed percolation to compact directed percolation
142
0
0.0
(
0
)
Added by
Jose Fernando Mendes
Publication date
1996
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We study critical spreading in a surface-modified directed percolation model in which the left- and right-most sites have different occupation probabilities than in the bulk. As we vary the probability for growth at an edge, the critical exponents switch from the compact directed percolation class to ordinary directed percolation. We conclude that the nonuniversality observed in models with multiple absorbing configurations cannot be explained as a simple surface effect.
rate research
Read More
These lectures provide an introduction to the directed percolation and directed animals problems, from a physicists point of view. The probabilistic cellular automaton formulation of directed percolation is introduced. The planar duality of the diode-resistor-insulator percolation problem in two dimensions, and relation of the directed percolation to undirected first passage percolation problem are described. Equivalence of the $d$-dimensional directed animals problem to $(d-1)$-dimensional Yang-Lee edge-singularity problem is established. Self-organized critical formulation of the percolation problem, which does not involve any fine-tuning of coupling constants to get critical behavior is briefly discussed.
A simple one-dimensional microscopic model of the depinning transition of an interface from an attractive hard wall is introduced and investigated. Upon varying a control parameter, the critical behaviour observed along the transition line changes from a directed-percolation to a multiplicative-noise type. Numerical simulations allow for a quantitative study of the multicritical point separating the two regions, Mean-field arguments and the mapping on a yet simpler model provide some further insight on the overall scenario.
The self-consistent probabilistic approach has proven itself powerful in studying the percolation behavior of interdependent or multiplex networks without tracking the percolation process through each cascading step. In order to understand how directed dependency links impact criticality, we employ this approach to study the percolation properties of networks with both undirected connectivity links and directed dependency links. We find that when a random network with a given degree distribution undergoes a second-order phase transition, the critical point and the unstable regime surrounding the second-order phase transition regime are determined by the proportion of nodes that do not depend on any other nodes. Moreover, we also find that the triple point and the boundary between first- and second-order transitions are determined by the proportion of nodes that depend on no more than one node. This implies that it is maybe general for multiplex network systems, some important properties of phase transitions can be determined only by a few parameters. We illustrate our findings using Erdos-Renyi (ER) networks.
We study a hierarchy of directed percolation (DP) processes for particle species A, B, ..., unidirectionally coupled via the reactions A -> B, ... When the DP critical points at all levels coincide, multicritical behavior emerges, with density exponents beta^{(k)} which are markedly reduced at each hierarchy level k >= 2. We compute the fluctuation corrections to beta^{(2)} to O(epsilon = 4-d) using field-theoretic renormalization group techniques. Monte Carlo simulations are employed to determine the new exponents in dimensions d <= 3.
We introduce a stochastic sandpile model where finite drive and dissipation are coupled to the activity field. The absorbing phase transition here, as expected, belongs to the directed percolation (DP) universality class. We focus on the small drive and dissipation limit, i.e. the so-called self-organised critical (SOC) regime and show that the system exhibits a crossover from ordinary DP scaling to a dissipation-controlled scaling which is independent of the underlying dynamics or spatial dimension. The new scaling regime continues all the way to the zero bulk drive limit suggesting that the corresponding SOC behaviour is only DP, modified by the dissipation-controlled scaling. We demonstrate this for the continuous and discrete Manna model driven by noise and bulk dissipation.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
