# Crossover behaviors in branching annihilating attracting walk.

@article{Park2020CrossoverBI,
title={Crossover behaviors in branching annihilating attracting walk.},
author={Su-Chan Park},
journal={Physical review. E},
year={2020},
volume={101 5-1},
pages={
052103
}
}
• Su-Chan Park
• Published 9 February 2020
• Physics
• Physical review. E
We introduce branching annihilating attracting walk (BAAW) in one dimension. The attracting walk is implemented by a biased hopping in such a way that a particle prefers hopping to a nearest neighbor located on the side where the nearest particle is found within the range of attraction. We study the BAAW with four offspring by extensive Monte Carlo simulation. At first, we find the critical exponents of the BAAW with infinite range of attraction, which are different from those of the directed…
5 Citations

## Figures and Tables from this paper

Branching annihilating random walks with long-range attraction in one dimension.
This work introduces and numerically study the branching annihilating random walks with long-range attraction (BAWL) and shows by Monte Carlo simulations that branching bias with symmetric hopping exhibits the same critical behavior as the BAWL.
One-dimensional annihilating random walk with long-range interaction.
The survival probability and the mean spreading behaves in the long-time limit if there are only two particles in the beginning, and how the density decays to zero if all sites are occupied at the outset is studied.
Branching annihilating random walk with long-range repulsion: logarithmic scaling, reentrant phase transitions, and crossover behaviors
We study absorbing phase transitions in the one-dimensional branching annihilating random walk with long-range repulsion. The repulsion is implemented as hopping bias in such a way that a particle is
$A+ A \to \emptyset$ system in one dimension with particle motion determined by nearest neighbour distances: results for parallel updates
• Physics
• 2020
A one dimensional A+A → ∅ system where the direction of motion of the particles is determined by the position of the nearest neighours is studied. The particles move with a probability 0.5 + ǫ

## References

SHOWING 1-10 OF 26 REFERENCES
Branching and annihilating Lévy flights.
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2001
This work analyzes a system of particles undergoing the branching and annihilating reactions A-->(m+1)A and A+A-->Ø, with m even, to measure the exponents in both universality classes and examine their behavior as a function of sigma.
Crossovers from parity conserving to directed percolation universality.
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2008
The crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean-field method and the resulting models show a diversity within the DP universality class in one dimension.
Three different routes from the directed Ising to the directed percolation class.
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2008
The scaling nature of absorbing critical phenomena is well understood for the directed percolation (DP) and the directed Ising (DI) systems. However, a full analysis of the crossover behavior is
High-precision estimate of the critical exponents for the directed Ising universality class
AbstractWith extensive Monte Carlo simulations, we present high-precision estimates of the critical exponents of branching annihilating random walks with two offspring, a prototypical model of the
One-dimensional non-equilibrium kinetic Ising models with branching annihilating random walk
Non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest-neighbour spin exchanges at T= infinity are investigated numerically from the
Critical phenomena of nonequilibrium dynamical systems with two absorbing states
• Physics
• 1998
We study nonequilibrium dynamical models with two absorbing states: interacting monomer-dimer models, probabilistic cellular automata models, nonequilibrium kinetic Ising models. These models exhibit
Crossover from the pair contact process with diffusion to directed percolation.
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2006
Nontriviality of thePCPD crossover exponent strongly supports the non-DP nature of the PCPD critical scaling, which is further evidenced by the anomalous critical amplitude scaling near the PC PD point.
Critical decay exponent of the pair contact process with diffusion.
• Su-Chan Park
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2014
It is claimed that the discontinuity of the phase boundary cannot be consistent with the theoretical argument supporting the hypothesis that the PCPD should belong to the DP, and the strength of corrections to scaling is found using the recently introduced method.
Absorbing phase transitions of branching-annihilating random walks.
• Physics
Physical review letters
• 2003
The phase transitions to absorbing states of the branching-annihilating reaction-diffusion processes mA)-->(m+k)A, nA-->(n-l)A are studied systematically in one space dimension within a new family of models, providing the first evidence of universal scaling laws for pair and triplet processes.
Extinction, survival, and dynamical phase transition of branching annihilating random walk.
• Mathematics
Physical review letters
• 1992
Analysis of statistical properties of random walkers which disappear when they meet and make offsprings by a controllable rate and Universality classes are found to depend on the number of offsprins in space dimension less than 3.