Proof of dynamical scaling in Smoluchowski's coagulation equation with constant kernel

Markus Kreer, Oliver Penrose

Research output: Contribution to journalArticle

Abstract

Smoluchowski's coagulation equation for irreversible aggregation with constant kernel is considered in its discrete version[Figure not available: see fulltext.] where ct=c1(t) is the concentration of l-particle clusters at time t. We prove that for initial data satisfying c1(0)>0 and the condition 0 =cl(0) <A (1+?)-l(A ?>0), the solutions behave asymptotically like c1(t)~t-2˜c(lt-1) as t?8 with lt-1 kept fixed. The scaling function ˜c(?) is (1/gr)?, where {Mathematical expression}, a conserved quantity, is the initial number of particles per unit volume. An analous result is obtained for the continuous version of Smoluchowski's coagulation equation {Mathematical expression} where c(v, t) is the oncentration of clusters of size v. © 1994 Plenum Publishing Corporation.

Original languageEnglish
Pages (from-to)389-407
Number of pages19
JournalJournal of Statistical Physics
Volume75
Issue number3-4
DOIs
Publication statusPublished - May 1994

Keywords

  • cluster growth
  • dynamical scaling
  • kinetics of first-order phase transitions
  • Smoluchowski's coagulation equations

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