{"product_id":"branching-processes-applied-to-cell-surface-aggregation-phenomena-von-catherine-a-macken-alan-s-perelson","title":"Branching Processes Applied to Cell Surface Aggregation Phenomena","description":"\u003cp\u003eAggregation 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 \u0026gt; 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.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783540156567\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783540156567","offer_id":39425809809501,"sku":"9783540156567","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/35b184b6-be52-43f1-a881-37f7edf99b99.jpg?v=1776319154","url":"https:\/\/shop.autorenwelt.de\/products\/branching-processes-applied-to-cell-surface-aggregation-phenomena-von-catherine-a-macken-alan-s-perelson","provider":"Autorenwelt Shop","version":"1.0","type":"link"}