We relate the effective order X of the elementary binary reaction, A+A→ products, on a fractal, to the spectral dimension. For ds<2: X=1+2/ds. We regain the calsssical value (X=2) for the cubic lattice but get X=3 for the linear lattice. Supercomputer simulations (transient and steady state) and exciton fusion experiments are in quantitative agreement with the above. For percolating clusters X=2.5 and for the Sierpinski gasket X=2.45. Relevance to heterogeneous kinetics is discussed.
Peer Reviewed
http://deepblue.lib.umich.edu/bitstream/2027.42/69827/2/JCPSA6-81-12-6402-1.pdf