Scaling theory and exactly solved models in the kinetics of irreversible aggregation
By F. Leyvraz. 2003
347 citations recorded by the source corpus.
Abstract The scaling theory of irreversible aggregation is discussed in some detail. First, we review the general theory in the simplest case of binary reactions. We then extend consideration to ternary reactions, multispecies aggregation, inhomogeneous situations with arbitrary size dependent diffusion constants as well as arbitrary production terms. A precise formulation of the scaling hypothesis is given as well as a general theory of crossover phenomena. The consequences of this definition are described at length. The specific issues arising in the case in which an infinite cluster forms at finite times (the so-called gelling case) are discussed, in order to address discrepancies between theory and recent numerical work. Finally, a large number of exactly solved models are reviewed extensively with a view to pointing out precisely in which sense the scaling hypothesis holds in these various models. It is shown that the specific definition given here will give good results for almost all cases. On the other hand, we show that it is usually possible to find counterexamples to stronger formulations of the scaling hypothesis.
Subfields: Condensed Matter Physics, Statistical and Nonlinear Physics, Water Science and Technology
View Paper: https://www.semanticscholar.org/paper/0cb2a1ee8bf3db2836d8491cbf3959584abd3d0e
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In Condensed Matter Physics
In Statistical and Nonlinear Physics
In Water Science and Technology
Citations in the corpus
- Well-posedness of Smoluchowski's coagulation equation for a class of homogeneous kernels (2006, methodology): “We refer to the review papers [4, 1, 15, 13] for more information on the physical and mathematical properties of (1.”
- An introduction to mathematical models of coagulation–fragmentation processes: A discrete deterministic mean-field approach (2006, result): “For more details on other results involving self-similarity and the asymptotic structure of solutions we refer the reader to the detailed study by Hendricks et al. [44] and the recent review by Leyvraz [45].”
- Existence of Self-Similar Solutions to Smoluchowski’s Coagulation Equation (2005, background): “Formal computations have been performed by physicists to identify s(t) and the behaviour of ψ for small and large x [5, 7, 18, 19], while several numerical simulations seem to support the validity of (1.”