Nonclassical Kinetics in Constrained Geometries: Initial Distribution Effects

Abstract

We present a detailed study of the effects of the initial distribution on the kinetic evolution of the irreversible reaction A+B -> 0 in one dimension. Our analytic as well as numerical work is based on a reaction-diffusion model of this reaction. We focus on the role of initial density fluctuations in the creation of the macroscopic patterns that lead to the well-known kinetic anomalies in this system. In particular, we discuss the role of the long wavelength components of the initial fluctuations in determining the long-time behavior of the system. We note that the frequently studied random initial distribution is but one of a variety of possible distributions leading to interesting anomalous behavior. Our discussion includes an initial distribution with correlated A-B pairs and one in which the initial distribution forms a fractal pattern. The former is an example of a distribution whose long wavelength components are suppressed, while the latter exemplifies one whose long wavelength components are enhanced, relative to those of the random distribution.