Renormalization group approach to reaction-diffusion systems with input in disordered media

Park, Jeong-Man
February 2000
AIP Conference Proceedings;2000, Vol. 501 Issue 1, p324
Academic Journal
We consider reaction-diffusion systems of a single species (A+A→0\) with a particle input in the presence of weak potential disorders in media. Random potential disorders with sufficiently long-ranged interactions are known to lead to anomalous diffusion in the absence of reaction. Applying renormalization group (RG) theory to a field theoretic description of the reaction-diffusion process and the matching theory to the RG trajectory integrals of the systems, we find that for d<2 the density of particles decays as c(t)∼t[sup -ν] with the dynamic exponent ν=d/(2+γ¯) in the absence of input and the density grows as c(I)∼I[sup μ] with the static exponent μ=d/(d+2+γ¯) in the presence of input with γ¯=β[sup 2]γ/4π. For d>2 the behavior is mean-filed like. The results confirm the Racz’s conjecture about the relation between the static and the dynamic exponents μ=ν/(1+ν) for a single species reaction-diffusion system even in disordered media. © 2000 American Institute of Physics.


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    © 2001 American Institute of Physics.


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