Aggregation driven by a localized source. (19th June 2015) - Krapivsky, P L
Abstract We study aggregation driven by a localized source of monomers. The densities become stationary and have algebraic tails far away from the source. We show that in a model with mass-independent reaction rates and diffusion coefficients, the density of monomers decays as <?CDATA ${{r}^{-β (d)}}$?> <?MML r − β ( d ) ?><inline-graphic xlink:href="ark:/27927/pgj14kmzx25" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> in d dimensions. The decay exponent has irrational values in physically relevant dimensions: <?CDATA $β (3)=(\sqrt{17}+1)/2$?> <?MML β ( 3 ) = <!--false buildup--> ( 17 + 1 ) / 2 ?><inline-graphic xlink:href="ark:/27927/pgj14kmzrkv" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> and <?CDATA $β (2)=\sqrt{8}$?> <?MML β ( 2 ) = 8 ?><inline-graphic xlink:href="ark:/27927/pgj14kmzxt9" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />. We also study Brownian coagulation with a localized source and establish the behavior of the total cluster density and the total number of of clusters in the system. The latter quantity exhibits a logarithmic growth with time.