Reaction-controlled diffusion: Monte Carlo simulations.

  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},
  volume={68 4 Pt 2},
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… 
Path integrals for stochastic hybrid reaction-diffusion processes
We construct a functional path integral for a stochastic hybrid reaction-diffusion (RD) equation, in which the reaction term depends on the discrete state of a randomly switching environment. We
Diffusion rate determines balance between extinction and proliferation in birth-death processes.
It is shown that for a large class of models, the reactant density is maximal at intermediate diffusion rates and low or zero at either very high or very low diffusion rates.
Predator-prey dynamics in a uniform medium lead to directed percolation and wave-train propagation.
It is shown that when the prey perturbation extinction probability is high, the loss of synchronization between the prey densities in different regions in space leads to two possible dynamic regimes: a directed percolation regime based on the balance between regions escaping the absorbing state and regions absorbed into it, and wave trains representing the transition of the entire space to the mean-field stable positive fixed point.
Monitoring Lévy-process crossovers
Monitoring L\'evy-Process Crossovers
The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among
Mittag–Leffler Memory Kernel in Lévy Flights
In this article, we make a detailed study of some mathematical aspects associated with a generalized Lévy process using fractional diffusion equation with Mittag–Leffler kernel in the context of


Reaction-controlled diffusion
  • Trimper, Tauber, Schutz
  • 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
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.
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
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
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
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