# Reaction-controlled diffusion: Monte Carlo simulations.

@article{Reid2003ReactioncontrolledDM,
title={Reaction-controlled diffusion: Monte Carlo simulations.},
author={Beth A. Reid and Uwe Claus T{\"a}uber and Jason Cory Brunson},
journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
year={2003},
volume={68 4 Pt 2},
pages={
046121
}
}
• Published 1 March 2003
• Physics
• Physical review. E, Statistical, nonlinear, and soft matter physics
We study the coupled two-species nonequilibrium reaction-controlled diffusion model introduced by Trimper et al. [Phys. Rev. E 62, 6071 (2000)] by means of detailed Monte Carlo simulations in one and two dimensions. Particles of type A may independently hop to an adjacent lattice site, provided it is occupied by at least one B particle. The B particle species undergoes diffusion-limited reactions. In an active state with nonzero, essentially homogeneous B particle saturation density, the A…
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## References

SHOWING 1-10 OF 22 REFERENCES
Reaction-controlled diffusion
• Physics
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
• 2000
The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation because of the combination of B decay and activated A hopping processes, which gives rise to anomalous diffusion.
Renormalization group study of theA+B→⊘ diffusion-limited reaction
• Physics
• 1994
AbstractTheA+B→⊘ diffusion-limited reaction, with equal initial densitiesa(0)=b(0)=n0, is studied by means of a field-theoretic renormalization group formulation of the problem. For dimensiond>2 an
Theory of Branching and Annihilating Random Walks.
• Physics
Physical review letters
• 1996
A new universality class has been observed in d = 1 for even values of m, when the number of particles is locally conserved modulo 2, and another issue which clearly requires theoretical explanation is the occurrence of a transition at a finite value of σm.
On the nonequilibrium phase transition in reaction-diffusion systems with an absorbing stationary state
It is pointed out that chemical reactions which show an absorbing stationary state in the master-equation approach (e.g. Schlögl's first reaction) exhibit nevertheless a second order phase transition
Field Theory of Branching and Annihilating Random Walks
• Physics
• 1997
We develop a systematic analytic approach to the problem of branching and annihilating random walks, equivalent to the diffusion-limited reaction processes 2A → ∅ and A → (m + 1) A, where m ≥ 1.
Renormalization group calculation for the reaction kA + 0
The diffusion-controlled reaction kA + M is known IO be strongly dependent on Ruchlations in dimensions d < d. = 2/(k - 1). We develop a field-theoretic renormalization group approach to this system
Non-equilibrium critical phenomena and phase transitions into absorbing states
This review addresses recent developments in non-equilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed
Method to estimate critical exponents using numerical studies
• Physics
• 2002
A novel method to estimate the critical point and critical exponents of physical models from numerical studies is presented. The method utilizes linear approximation to compute the values of the
Fractals and Disordered Systems
• Physics
• 1991
1 Fractals and Multifractals: The Interplay of Physics and Geometry (With 30 Figures).- 1.1 Introduction.- 1.2 Nonrandom Fractals.- 1.3 Random Fractals: The Unbiased Random Walk.- 1.4 The Concept of
On phase transitions in Schlögl's second model
AbstractWe study Schlögl's second model, characterized by chemical reactions \begin{array}{*{20}c} {2X\underset{{k_2 }}{\overset{{k_1 }}{\longleftrightarrow}}3X,} & {X\underset{{k_4