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

Abstract

The scaling exponent and 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: 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.

Concentration for one and two-species one-dimensional reaction-diffusion systems

“…We denote the corresponding Hamiltonian with H ann. and introduce, as in [3,4,25], the parameter ∆ ′ defined by:…”

“…For small chains numerical data can be obtained with a high accuracy by using diagonalization techniques or simulations. The study of the finite-size scaling behavior (3.8) in the limit z → ∅ permits the determination of the particle concentration for infinite chains at very large times [25].…”

Identification of chlorophyll molecules in peripheral light harvesting complex LHC II

“…Calculations of the transient absorption spectrum were based on the one-dimensional annihilation (coagulation) model with periodic boundary conditions for nearest-neighbour type interactions [35,36]. To simulate the process of a real system the basic model was extended into the three-dimensional model with neighbour-neighbour type interactions.…”

“…The given model was successfully tested using the onedimensional string of the variable length under periodic boundary conditions [36].…”

Exactly solvable reaction diffusion models on a Bethe Lattice through the empty-interval method

“…Approximation methods are generally different in different dimensions, as for example the mean filed techniques, working good for high dimensions, generally do not give correct results for low-dimensional systems. A large fraction of analytical studies belong to low-dimensional (especially one-dimensional) systems, as solving low-dimensional systems should in principle be easier [1][2][3][4][5][6][7][8][9][10][11].…”