Abstract
We investigate with the help of analytical and numerical methods the reactionA+A→A on a one-dimensional lattice opened at one end and with an input of particles at the other end. We show that if the diffusion rates to the left and to the right are equal, for largex, the particle concentrationc(x) behaves likeA s x −1 (x measures the distance to the input end). If the diffusion rate in the direction pointing away from the source is larger than the one corresponding to the opposite direction, the particle concentration behaves likeA a x −1/2. The constantsA s andA a are independent of the input and the two coagulation rates. The universality ofA a comes as a surprise, since in the asymmetric case the system has a massive spectrum.
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Hinrichsen, H., Rittenberg, V. & Simon, H. Universality properties of the stationary states in the one-dimensional coagulation-diffusion model with external particle input. J Stat Phys 86, 1203–1235 (1997). https://doi.org/10.1007/BF02183621
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DOI: https://doi.org/10.1007/BF02183621