Branching processes applied to cell surface aggregation phenomena
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Bibliographic Information
Branching processes applied to cell surface aggregation phenomena
（Lecture notes in biomathematics, 58）
Springer-Verlag, c1985
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Bibliography: p. [110]-122
Description and Table of Contents
Description
Aggregation processes are studied within a number of different fields--c- loid chemistry, atmospheric physics, astrophysics, polymer science, and biology, to name only a few. Aggregation pro ces ses involve monomer units (e. g. , biological cells, liquid or colloidal droplets, latex beads, molecules, or even stars) that join together to form polymers or aggregates. A quantitative theory of aggre- tion was first formulated in 1916 by Smoluchowski who proposed that the time e- lution of the aggregate size distribution is governed by the infinite system of differential equations: (1) K . . c. c. - c k = 1, 2, ...k 1. J 1. J L ~ i+j=k j=l where c is the concentration of k-mers, and aggregates are assumed to form by ir- k reversible condensation reactions [i-mer + j-mer -+ (i+j)-mer]. When the kernel K . . can be represented by A + B(i+j) + Cij, with A, B, and C constant; and the in- 1. J itial condition is chosen to correspond to a monodisperse solution (i. e. , c (0) = 1 0, k > 1), then the Smoluchowski equation can be co' a constant; and ck(O) solved exactly (Trubnikov, 1971; Drake, 1972; Ernst, Hendriks, and Ziff, 1982; Dongen and Ernst, 1983; Spouge, 1983; Ziff, 1984).
For arbitrary K , the solution ij is not known and in some ca ses may not even exist.
Table of Contents
1. Introduction.- 2. Branching Processes Applied to the Aggregation of f-Valent Particles.- 3. Multitype Branching Processes.- 4. Aggregate Size Distribution on a Cell Surface.- 5. Gelation and Infinite-Sized Trees.- 6. Post-Gel Relations.- 7. Conclusions and Extensions.- List of Symbols.
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