From Nucleation to Large Aggregates: the Growth of Filamentary

  • M. A. Herrero
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 1)


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.


Large Aggregate Stefan Problem European Contract General Kinetic Equation Biological Pattern Formation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • M. A. Herrero
    • 1
  1. 1.Departamento de Matemática Aplicada, Facultad de MatemáticasUniversidad ComplutenseMadridSpain

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