MBI Videos

Videos by CTW: Free Boundary Problems in Biology

  • Cell migration as a free boundary problem
    Alex Mogilner
    Cells migrate on surfaces by protruding their front through growth of actin networks, retracting the rear by myosin-driven contraction and adhering to the substrate. Recent experimental and modeling efforts elucidated specific molecular and mechanical processes that allow motile cells to maintain constant distances from front to rear and from side to side while maintaining...
  • Fluctuations in a moving boundary description of diffusive interface growth
    Rodolfo Cuerno
    Stochastic generalizations of moving boundary problems appear quite naturally in the continuum description of e.g. solidification problems. Perhaps the simplest example is provided by a so-called one-sided solidification problem in which a condensed (solid) non-diffusing phase grows at the expense of a diluted diffusing phase (vapor or liquid). In this context, noise terms...
  • Propagation of fronts in non homogeneous media and applications in medicine and biology
    Henri Berestycki
    This talk is about fronts and propagation phenomena for reaction-diffusion equations in non-homogeneous media. I will discuss some specific models arising in population dynamics or in medicine where the medium imposes a direction of propagation....
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    Arshak Petrosyan
    (no description available)...
  • Modeling blood coagulation: recent trends and new ideas
    Antonio Fasano
    Blood coagulation is an extremely complex process which is the result of the action of platelets and of a large number of chemicals going through a chemical cascade. Its aim is the formation of a clot, sealing a wound The clot evolution leads to a free boundary problem. It goes in parallel with the process of clot dissolution (fibrinolysis), taking place with a slower time...
  • Regularity for almost minimizers with free boundary
    Tatiana Toro
    We study the regularity of almost minimizers for the types of functionals analyzed by Alt, Caffarelli and Freidman. Although almost minimizers do not satisfy an equation using appropriate comparison functions we prove several regularity results. For example in the one phase situation we show that almost minimizers are Lipschitz. Our approach reminiscent of the one used in ...
  • The Dynamics of Mucus, or, Why the Stomach does not Digest Itself
    James Keener
    There are a number of interesting and important biological processes that are best modelled as two-phase material mixtures. These include mucin exocytosis and transport, blood clot formation and biofilm formation. These all involve the interplay between flow, physical structure, mechanics and chemistry in a environment with complex dynamic geometry. The mathematical descri...

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