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Finite-size scaling studies of one-dimensional reaction-diffusion systems. Part II. Numerical methods

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Abstract

The scaling exponent and the scaling function for the 1D single-species coagulation model (A+A→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 of the concentration: Monte Carlo simulations and extrapolations of exact finite-lattice data. These methods are tested in a case where analytical results are available. To obtain reliable results from finite-size extrapolations, numerical data for lattices up to ten sites are sufficient.

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Krebs, K., Pfannmüller, M.P., Simon, H. et al. Finite-size scaling studies of one-dimensional reaction-diffusion systems. Part II. Numerical methods. J Stat Phys 78, 1471–1491 (1995). https://doi.org/10.1007/BF02180139

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Key Words

  • Reaction-diffusion systems
  • finite-size scaling
  • Monte Carlo simulations
  • nonequilibrium statistical mechanics
  • coagulation model