 9359 Privman V., Doering C.R., Frisch H.L.
 Crossover from RateEquation to DiffusionControlled Kinetics in TwoParticle Coagulation
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Mar 6, 93

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Abstract. We develop an analytical diffusionequationtype approximation
scheme for the onedimensional coagulation reaction A+A>A
with partial reaction probability on particle encounters which are
otherwise hardcore. The new approximation describes the crossover
from the meanfield rateequation behavior at short times to the
universal, fluctuationdominated 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
meanfield as well as the asymptotic largetime,
fluctuationdominated behavior. However, the intermediatetime
crossover between the two regimes is described only
semiquantitatively.
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