In contrast to classical chemical reaction kinetics, for diffusion limited
chemical reactions the anisotropy of the geometry has far reaching effects.
We use tubular two and three-dimensional spaces to illustrate and discuss
the dimensional crossover in A + B --> 0 reactions due to dimensional compa
ctification. We find that the crossover time t(c) = W-alpha scales as alpha
= beta/(a - b), where a, b, and beta are given by the earlier and the late
time inverse density scaling of rho(-1) similar to t(a) and rho(-1) simila
r to t(b)W(beta), respectively. We also obtain a critical width W-c below (
above) which the chemical reaction progresses without (with) traversing a t
wo or three-dimensional Ovchinnikov-Zeldovich (OZ) reaction regime. As a re
sult we find that there exist different hierarchies of dimensionally forced
crossovers, depending on the initial conditions and geometric restrictions
. Kinetic phase diagrams are employed, and exponents are given for various
Euclidean and fractal compactified geometries, for the A + B and A + A elem
entary reactions. Monte Carlo simulations illustrate some of the kinetic hi
erarchies. (C) 1999 American Institute of Physics. [S0021-9606(99)00504-8].