Finite-Size Scaling Studies of Reaction-Diffusion Systems Part III: Numerical Methods

Abstract

The scaling exponent and scaling function for the 1D single species coagulation model $(A+A\to A)$ are shown to be universal, i.e. they are not influenced by the value of the coagulation rate. They are independent of the initial conditions as well. Two different numerical methods are used to compute the scaling properties: Monte Carlo simulations and extrapolations of exact finite lattice data. These methods are tested in a case where analytical results are available. It is shown that Monte Carlo simulations can be used to compute even the correction terms. To obtain reliable results from finite-size extrapolations exact numerical data for lattices up to ten sites are sufficient.

19 pages, LaTeX, 5 figures uuencoded, BONN HE-94-02

References in corpus (3)

• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• Fast-diffusion mean-field theory for k-body reactions in one dimension
• Crossover from Rate-Equation to Diffusion-Controlled Kinetics in Two-Particle Coagulation

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• Universality properties of the stationary states in the one-dimensional coagulation-diffusion model with external particle input
• Solution of classical stochastic one dimensional many-body systems
• Diffusion-Limited Coalescence and Annihilation in Random Media
• Inhomogeneous Steady States of Diffusion-Limited Coalescence, A+A<-->A
• Diffusion-Limited Coalescence, A+A<-->A, with a Trap
• Finite-size scaling in the ageing dynamics of the $1D$ Glauber-Ising model
• Large-Scale Simulations of Diffusion-Limited n-Species Annihilation
• Reply on the Comment cond-mat/0008209 about "Solution of Classical Stochastic One-Dimensional Many-Body Systems"
• Crossover properties of a one-dimensional reaction-diffusion process with a transport current
• Avalanches in the Raise and Peel model in the presence of a wall
• Exact solution of the Glauber-Ising model on the finite-length semi-open chain