From Nucleation to Large Aggregates: the Growth of Filamentary
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.
KeywordsLarge Aggregate Stefan Problem European Contract General Kinetic Equation Biological Pattern Formation
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- [AHV1]Andreucci, D., Herrero, M.A. and Velazquez, J.J.L. (2001) The classical one-phase Stefan problem: a catalogue of interface behaviours. To appear in Surveys on Mathematics in Industry.Google Scholar
- [AHV2]Andreucci, D., Herrero, M.A. and Velazquez, J.J.L. On the growth of filamentary planar structures. To appear.Google Scholar
- [M1]Meinhardt, H. (1982) Models of biological pattern formation. Academic Press.Google Scholar
- [S]Smoluchowski, M. (1916) Drei Vorträge über Diffusion, Brownische Bewegung und Koagulation von Kolloiden. Physik Z, 17, 557–585.Google Scholar