Rigorous Results in the Scaling Theory of Irreversible Aggregation Kinetics

DOI

10.2991/jnmp.2005.12.s1.37How to use a DOI?

Abstract

The kinetic equations describing irreversible aggregation and the scaling approach dveloped to describe them in the limit of large times and large sizes are tersely reviewed. Next, a system is considered in which aggregates can only react with aggregates of their own size. The existence of a scaling solution of the kinetic equations can then be shown rigorously in the case in which the total mass of the system is conserved. A large number of detailed properties of the solution, previously predicted by qualittive arguments, can be shown rigorously as well in this system. In the case in which gelation occurs, some sketchy rigorous results are shown, and numerical evidence for the existence of a scaling solution is presented. These are the first explicit examples of typical scaling behaviour for systems exhibiting gelation.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - François Leyvraz
PY  - 2005
DA  - 2005/01/01
TI  - Rigorous Results in the Scaling Theory of Irreversible Aggregation Kinetics
JO  - Journal of Nonlinear Mathematical Physics
SP  - 449
EP  - 465
VL  - 12
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s1.37
DO  - 10.2991/jnmp.2005.12.s1.37
ID  - Leyvraz2005
ER  -