2002/09/06 by Supriya Krishnamurthy, R. Rajesh, Oleg Zaboronski
Environmental Science · Mathematics · Physics and Astronomy · #Coagulation and Flocculation Studies #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.66.066118
published as Phys. Rev. E, Vol 66, 066118 (2002) · 11 pages, 6 figures, Revtex 4
arxiv created 2002/09/06 · openalex publication_date 2002/12/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
The large-time small-mass asymptotic behavior of the average mass distribution P(m,t) is studied in a d-dimensional system of diffusing aggregating particles for 1<~d<~2. By means of both a renormalization group computation as well as a direct resummation of leading terms in the small-reaction-rate expansion of the average mass distribution, it is shown that P(m,t)\ensuremath∼(1/td)(m1/d/√(t))^eKR for m\ensuremath≪td/2, where eKR=\ensuremathε+O(\ensuremathε2) and \ensuremathε=2\ensuremath-d. In two dimensions, it is shown that P(m,t)\ensuremath∼ln(m)ln(t)/t2 for m\ensuremath≪t/ln(t). Numerical simulations in two dimensions supporting the analytical results are also presented.