Objectif
In recent years, integral structures have been found in a class of hydrodynamics problem leading to pattern formation in a regime far from equilibrium. Growth problems of this type, Laplacian Growth or Hele-Shaw problems, refer to dynamics of a moving front between two distinct phases driven by a harmonic scalar field. These problems have been primarily approached using asymptotic and complex variable methods to address both their stable and the notoriously unstable versions. The relation between the Hel e-Shaw problems and theory of integral systems is an exciting emerging research area. We also mention that it has recently been shown that there is a connection between the two free- boundary problems above and that of the support of Eigen values of an ensemble of large random normal matrices. We intend to explore this aspect of the problem in conjunction with the integral system approach. The aim of the project is two-fold: to address basic questions in the theory of unstable interfaces and multiphase flows, combining recent achievements in the theory of integrable systems with asymptotic and complex-analytic approaches. Connecting and generalizing three subjects of Hele- Shaw problems, theories of integral hierarchies and matrix models, we expect to advance under- standing of interface dynamics and account for its basic physical features. Vice versa, using the theory of interfaces, we illustrate and develop physically important integral models.
Champ scientifique
Appel à propositions
FP6-2002-MOBILITY-7
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