Diffusion-Limited Binary Reactions: The Hierarchy of Nonclassical Regimes for Correlated Initial Conditions

Abstract

We predict hierarchies of kinetic regimes and crossover conditions for elementary A + A -0 and A + B -0 batch reactions from a nonclassical reaction4iffusion formalism that includes spatial fluctuations. This paper addresses the case of a spatially correlated initial distribution of reactants; random initial conditions have been discussed in another paper. The hierarchies of kinetic regimes are even richer than those found for random initial conditions, with the particular hierarchy determined by the tightness of the initial correlations. In most cases there is one regime (which we call a "burst") where the decay of the densities in the A + B reaction is even faster than in the A + A reaction. We confirm our predictions via detailed numerical simulations.

Voltage Rectification in a Driven Asymmetric SQUID

“…In particular, an initial distribution that is more homogeneous or mixed than a random one is expected to lead to behavior closer to classical; conversely, an initial distribution in which fluctuations are more prominent is expected to lead to greater deviations from the law of mass action. Our work expands on previous concern with this problem by a number of authors [Vitukhnovsky et al, 1988;Abramson et al, 1994;Abramson, 1995;Lindenberg et al, 1994Lindenberg et al, , 1996Sancho et al, 1996].…”

“…Simulations at this level of detail require large computer capabilities and long times to reach asymptotic behaviors [Argyrakis et al, 1993;Lindenberg et al, 1994. Reaction-diffusion equations represent mesoscopic approximations to this more microscopic picture; such approximations can therefore only provide a theoretical backdrop over spatial and temporal ranges that are not too detailed and for densities that are not too low.…”

“…This initial condition, in the form of a fractal pattern, leads to more pronounced deviations from classical behavior. We also present an example of an initial distribution whose long wavelength components are more constrained than the random, namely, the case of correlated pairs [Lindenberg et al, 1994, Sancho et al, 1996.…”

“…G(t) then becomes irrelevant and the kinetics is classical. This generic sequence describes every initial condition that we have dealt with here and elsewhere [Argyrakis et al, 1993; Lindenberg et al, 1994Lindenberg et al, , 1996Sancho et al, 1996]. The differences arise in the specific …”

“…Subsequent to this initial constrained placement, each particle moves freely. Lindenberg et al [Lindenberg et al, 1994Sancho et al, 1996] have studied in detail the kinetic progression for the A + B → 0 reaction with this initial distribution. In our discretized reaction-diffusion picture we translate this into the initial random placement of pairs of cells with centers separated by a distance λ (c = λ∆x), one cell of each pair containing only species A and the other only species B (whether or not we allow initial occupancy of a cell by different species arising from different pairs is immaterial -it only changes the very early transient, as we have noted above).…”