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From nucleation to large aggregates: the growth of filamentary

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Herrero, Miguel A. (2002) From nucleation to large aggregates: the growth of filamentary. In Progress in industrial mathematics at ECMI 2000. Mathematics in Industry : The European Consortium for Mathematics in Industry (1). Springer, Berlin, pp. 16-27. ISBN 978-3-642-07647-3

Official URL: http://link.springer.com/chapter/10.1007%2F978-3-662-04784-2_2#


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Abstract

We shall briefly review some early nucleation models, and then examine some aspects of the subsequent evolution of their solutions. Such situation is characterised by the onset of comparatively large clusters that can diffuse into the medium and interact among themselves. We next discuss some situations where the aggregates being formed, whose actual shape is one of the major questions under consideration, do posses a filamentary nature, and can sometimes generate a percolating network. Finally, a particularly interesting case of such tree-like structures, that of vascular systems, will be addressed, and some facts (and open questions) concerning their simulation via reaction-diffusion equations will be discussed.


Item Type:Book Section
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Papers from the 11th European Conference on Mathematics in Industry held in Palermo, September 26–30, 2000

Subjects:Sciences > Mathematics > Differential equations
Sciences > Mathematics > Operations research
ID Code:22583
Deposited On:27 Aug 2013 06:47
Last Modified:12 Dec 2018 15:07

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