Privman V., Doering C.R., Frisch H.L.
Crossover from Rate-Equation to Diffusion-Controlled Kinetics in Two-Particle Coagulation
(29K, TeX (plain))

ABSTRACT.  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.