Branching Processes Applied to Cell Surface Aggregation Phenomena:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1985
|
| Schriftenreihe: | Lecture Notes in Biomathematics
58 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Aggregation processes are studied within a number of different fields-- colloid chemistry, atmospheric physics, astrophysics, polymer science, and biology, to name only a few. Aggregation processes 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 aggretion was first formulated in 1916 by Smoluchowski who proposed that the time evolution 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 irreversible 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 initial condition is chosen to correspond to a monodisperse solution (i. e. , c (0) = 1 0, k > 1 co' a constant; and ck(O) ), then the Smoluchowski equation can be solved exactly (Trubnikov, 1971; Drake, 1972; Ernst, Hendriks, and Ziff, 1982; Dongen and Ernst, 1983; Spouge, 1983; Ziff, 1984). For arbitrary Kij , the solution is not known and in some cases may not even exist |
| Beschreibung: | 1 Online-Ressource (VIII, 124 p) |
| ISBN: | 9783642521157 9783540156567 |
| ISSN: | 0341-633X |
| DOI: | 10.1007/978-3-642-52115-7 |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Macken, Catherine A. |
| author_facet | Macken, Catherine A. |
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| author_sort | Macken, Catherine A. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519 |
| dewey-search | 519 |
| dewey-sort | 3519 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-52115-7 |
| format | Electronic eBook |
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| id | DE-604.BV042422589 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783642521157 9783540156567 |
| issn | 0341-633X |
| language | English |
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| physical | 1 Online-Ressource (VIII, 124 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1985 |
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| series | Lecture Notes in Biomathematics |
| series2 | Lecture Notes in Biomathematics |
| spelling | Macken, Catherine A. Verfasser aut Branching Processes Applied to Cell Surface Aggregation Phenomena by Catherine A. Macken, Alan S. Perelson Berlin, Heidelberg Springer Berlin Heidelberg 1985 1 Online-Ressource (VIII, 124 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Biomathematics 58 0341-633X Aggregation processes are studied within a number of different fields-- colloid chemistry, atmospheric physics, astrophysics, polymer science, and biology, to name only a few. Aggregation processes 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 aggretion was first formulated in 1916 by Smoluchowski who proposed that the time evolution 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 irreversible 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 initial condition is chosen to correspond to a monodisperse solution (i. e. , c (0) = 1 0, k > 1 co' a constant; and ck(O) ), then the Smoluchowski equation can be solved exactly (Trubnikov, 1971; Drake, 1972; Ernst, Hendriks, and Ziff, 1982; Dongen and Ernst, 1983; Spouge, 1983; Ziff, 1984). For arbitrary Kij , the solution is not known and in some cases may not even exist Mathematics Algebra Applications of Mathematics Mathematical and Computational Biology Mathematik Aggregation (DE-588)4000728-5 gnd rswk-swf Zellaggregat (DE-588)4127299-7 gnd rswk-swf Verzweigungsprozess (DE-588)4188184-9 gnd rswk-swf Biomathematik (DE-588)4139408-2 gnd rswk-swf Aggregation (DE-588)4000728-5 s Verzweigungsprozess (DE-588)4188184-9 s 1\p DE-604 Zellaggregat (DE-588)4127299-7 s Biomathematik (DE-588)4139408-2 s 2\p DE-604 3\p DE-604 Perelson, Alan S. Sonstige oth Lecture Notes in Biomathematics 58 (DE-604)BV005875746 58 https://doi.org/10.1007/978-3-642-52115-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Macken, Catherine A. Branching Processes Applied to Cell Surface Aggregation Phenomena Lecture Notes in Biomathematics Mathematics Algebra Applications of Mathematics Mathematical and Computational Biology Mathematik Aggregation (DE-588)4000728-5 gnd Zellaggregat (DE-588)4127299-7 gnd Verzweigungsprozess (DE-588)4188184-9 gnd Biomathematik (DE-588)4139408-2 gnd |
| subject_GND | (DE-588)4000728-5 (DE-588)4127299-7 (DE-588)4188184-9 (DE-588)4139408-2 |
| title | Branching Processes Applied to Cell Surface Aggregation Phenomena |
| title_auth | Branching Processes Applied to Cell Surface Aggregation Phenomena |
| title_exact_search | Branching Processes Applied to Cell Surface Aggregation Phenomena |
| title_full | Branching Processes Applied to Cell Surface Aggregation Phenomena by Catherine A. Macken, Alan S. Perelson |
| title_fullStr | Branching Processes Applied to Cell Surface Aggregation Phenomena by Catherine A. Macken, Alan S. Perelson |
| title_full_unstemmed | Branching Processes Applied to Cell Surface Aggregation Phenomena by Catherine A. Macken, Alan S. Perelson |
| title_short | Branching Processes Applied to Cell Surface Aggregation Phenomena |
| title_sort | branching processes applied to cell surface aggregation phenomena |
| topic | Mathematics Algebra Applications of Mathematics Mathematical and Computational Biology Mathematik Aggregation (DE-588)4000728-5 gnd Zellaggregat (DE-588)4127299-7 gnd Verzweigungsprozess (DE-588)4188184-9 gnd Biomathematik (DE-588)4139408-2 gnd |
| topic_facet | Mathematics Algebra Applications of Mathematics Mathematical and Computational Biology Mathematik Aggregation Zellaggregat Verzweigungsprozess Biomathematik |
| url | https://doi.org/10.1007/978-3-642-52115-7 |
| volume_link | (DE-604)BV005875746 |
| work_keys_str_mv | AT mackencatherinea branchingprocessesappliedtocellsurfaceaggregationphenomena AT perelsonalans branchingprocessesappliedtocellsurfaceaggregationphenomena |