The Becker-Döring equations with exponentially size-dependent rate coefficients

This paper is concerned with an analysis of the Becker-Doring equations which lie at the heart of a number of descriptions of non-equilibrium phase transitions and related complex dynamical processes. The Becker-Doring theory describes growth and fragmentation in terms of stepwise addition or removal of single particles to or from clusters of similar particles and has been applied to a wide range of problems of physicochemical and biological interest within recent years. Here we consider the case where the aggregation and fragmentation rates depend exponentially on cluster size. These choices of rate coefficients at least qualitatively correspond to physically realistic molecular clustering scenarios such as occur in, for example, simulations of simple fluids. New similarity solutions for the constant monomer Becker-Doring system are identified, and shown to be generic in the case of aggregation and fragmentation rates that depend exponentially on cluster size.

[1]  J. Wattis,et al.  Generalized coarse-grained Becker-Döring equations , 2003 .

[2]  J. Wattis,et al.  General Becker–Döring equations: effect of dimer interactions , 2002 .

[3]  J. King,et al.  Asymptotic solutions of the Becker–Döring equations with size-dependent rate constants , 2002 .

[4]  P. Coveney,et al.  Renormalization-theoretic analysis of non-equilibrium phase transitions: I. The Becker-Döring equations with power law rate coefficients , 2001, cond-mat/0109110.

[5]  R. Strey,et al.  DETERMINATION OF CONDENSATION AND EVAPORATION COEFFICIENTS OF ARGON CLUSTERS , 2001 .

[6]  D. Duncan,et al.  Approximating the Becker—Döring cluster equations , 2001 .

[7]  E. Marques.  Size and Stability of Catanionic Vesicles: Effects of Formation Path, Sonication, and Aging , 2000 .

[8]  J. Wattis.  A Becker-Döring model of competitive nucleation , 1999 .

[9]  D. Hall.  Polydispersity of Sodium Dodecyl Sulfate (SDS) Micelles , 1999 .

[10]  J. King,et al.  Asymptotic solutions of the Becker-Döring equations , 1998 .

[11]  Juan J. L. Velázquez,et al.  The Becker–Döring Equations and the Lifshitz–Slyozov Theory of Coarsening , 1998 .

[12]  Oliver Penrose,et al.  The Becker-Döring equations at large times and their connection with the LSW theory of coarsening , 1997 .

[13]  P. Coveney,et al.  General nucleation theory with inhibition for chemically reacting systems , 1997 .

[14]  P. Coveney,et al.  Analysis of a generalized Becker—Döring model of self-reproducing micelles , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[15]  P. Luisi,et al.  Autopoietic Self-Reproduction of Fatty Acid Vesicles , 1994 .

[16]  Pier Luigi Luisi,et al.  Autocatalytic self-replicating micelles as models for prebiotic structures , 1992, Nature.

[17]  P. Krapivsky,et al.  Nonscaling and source-induced scaling behaviour in aggregation model of movable monomers and immovable clusters , 1991 .

[18]  Jack Carr,et al.  The Becker-Döring cluster equations: Basic properties and asymptotic behaviour of solutions , 1986 .

[19]  M. .. Moore.  Studies in Statistical Mechanics Vol VII – Fluctuation Phenomena , 1980 .

[20]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[21]  I. Lifshitz,et al.  The kinetics of precipitation from supersaturated solid solutions , 1961 .

[22]  F. P. D. Costa,et al.  Asymptotic behaviour of low density solutions to the generalized Becker-Döring equations , 1998 .

[23]  J. Carr,et al.  Numerical approximation of a metastable system , 1995 .

[24]  R. Howie,et al.  Crystal growth , 1982, Nature.

[25]  R. Becker,et al.  Kinetische Behandlung der Keimbildung in übersättigten Dämpfen , 1935 .