Physics – Condensed Matter
Scientific paper
1993-03-06
Phys. Rev. E 48, 846-851 (1993)
Physics
Condensed Matter
21 pages, plain TeX
Scientific paper
10.1103/PhysRevE.48.846
We develop an analytical diffusion-equation-type approximation scheme for the one-dimensional coagulation reaction A+A->A with partial reaction probability on particle encounters which are otherwise hard-core. The new approximation describes the crossover from the mean-field rate-equation behavior at short times to the universal, fluctuation-dominated behavior at large times. The approximation becomes quantitatively accurate when the system is initially close to the continuum behavior, i.e., for small initial density and fast reaction. For large initial density and slow reaction, lattice effects are nonnegligible for an extended initial time interval. In such cases our approximation provides the correct description of the initial mean-field as well as the asymptotic large-time, fluctuation-dominated behavior. However, the intermediate-time crossover between the two regimes is described only semiquantitatively.
Doering Charles R.
Frisch Harry L.
Privman Vladimir
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