Rabu, 26 Februari 2014

PDF⋙ Branching Processes Applied to Cell Surface Aggregation Phenomena (Lecture Notes in Biomathematics) by Catherine Macken, Alan S. Perelson

Branching Processes Applied to Cell Surface Aggregation Phenomena (Lecture Notes in Biomathematics) by Catherine Macken, Alan S. Perelson

Branching Processes Applied to Cell Surface Aggregation Phenomena (Lecture Notes in Biomathematics)

Branching Processes Applied to Cell Surface Aggregation Phenomena (Lecture Notes in Biomathematics) by Catherine Macken, Alan S. Perelson PDF, ePub eBook D0wnl0ad

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.

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