Scaling theory for gelling systems: work in progress
type: Item
instance of: scholarly article
title: Scaling theory for gelling systems: work in progress
zbMATH Open document ID: 1139.82034
author: F. Leyvraz
published in: Physica D
publication date: 2006-11-15T00:00:00Z
review text: It is known that systems evolving through a process of irreversible aggregation and obeying the so-called Smoluchowski equation may exhibit the phenomenon of gelation. This means that a finite amount of mass can be swallowed by ``giant'' clusters. This paper points out some accident in which gelation theory has incurred and how a fresh restart proposed by the same author [Scaling theory and exactly solved models in the kinetics of irreversible aggregation, Phys. Rep. 383, 95 (2003); Rigorous results in the scaling theory of irreversible aggregation kinetics, J. Non-linear Math. Phys. 12 (Suppl. 1) 449--465 (2005); \url{arXiv:math-ph/0602007}] can lead, case by case, to the correct results. The basic tool is to introduce a suitable scalings in order to describe the behaviour of the second moment of the mass distribution function. The scaling function is identified with the solution of a nonlinear integro-differential equation of a very peculiar type. Numerical examples are given.
Mathematics Subject Classification ID: 82C40
Mathematics Subject Classification ID: 82C26
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 82C22
zbMATH DE Number: 5073054
zbMATH Keywords: Integro-differential equations
zbMATH Keywords: Gelation
zbMATH Keywords: Coagulation
reviewed by: Antonio Fasano
MaRDI profile type: Publication
full work available at URL: j.physd.2006.08.011
OpenAlex ID: W2016912472
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DOI: 10.1016/J.PHYSD.2006.08.011
description: scientific article; zbMATH DE number 5073054