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Branching Processes Applied to Cell Surface Aggregation Phenomena

Catherine A. Macken, Alan S. Perelson (Autoren)

Buch | Softcover

VIII, 124 Seiten

1985
Springer Berlin (Verlag)
978-3-540-15656-7 (ISBN)

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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.

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.

Erscheint lt. Verlag	1.7.1985
Reihe/Serie	Lecture Notes in Biomathematics
Zusatzinfo	VIII, 124 p.
Verlagsort	Berlin
Sprache	englisch
Maße	210 x 297 mm
Gewicht	374 g
Themenwelt	Informatik ► Weitere Themen ► Bioinformatik
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Aggregation • astrophysics • Biology • Cell • Cells • Chemistry • differential equation • Distribution • Molecule • Phenomena • Physics • Polymer • Reactions • System • Units
ISBN-10	3-540-15656-9 / 3540156569
ISBN-13	978-3-540-15656-7 / 9783540156567
Zustand	Neuware