Reaction-diffusion with a time-dependent reaction rate: the single-species diffusion-annihilation process

L. Turban (1)

1 LPM - Laboratoire de physique des matériaux

We study the single-species diffusion-annihilation process with a time-dependent reaction rate, lambda(t)=lambda_0 t^-omega. Scaling arguments show that there is a critical value of the decay exponent omega_c(d) separating a reaction-limited regime for omega > omega_c from a diffusion-limited regime for omega < omega_c. The particle density displays a mean-field, omega-dependent, decay when the process is reaction limited whereas it behaves as for a constant reaction rate when the process is diffusion limited. These results are confirmed by Monte Carlo simulations. They allow us to discuss the scaling behaviour of coupled diffusion-annihilation processes in terms of effective time-dependent reaction rates.

Domaines: Autre [cond-mat.other]

L. Turban. Reaction-diffusion with a time-dependent reaction rate: the single-species diffusion-annihilation process. Journal of Physics A: Mathematical and Theoretical, 2004, 37, pp.8467. ⟨hal-00107507⟩