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Laplacian growth and inverse potential problems

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In the last twenty years much efforts have been done in the understanding of interface dynamics in various fields, such as hydrodynamics, combustion, non-equilibrium statistical and condensed matter physics. The problem of pattern formation is one of the most rapidly developing branches of non-linear science today. The field has grown fast and there is no need to stress its importance. The study of the front dynamics between two phases (Laplacian growth problem) that arises in a variety of non-equilibrium systems is of special interest. Closely related to this is another very important problem of interface dynamics, 2D inverse potential problem, which is to restore the form of the curve (representing an interface between two different media, like oil and water) from a half of the infinite set of its harmonic moments, either interior or exterior.

The central research objective is to deepen the understanding of the dynamics of unstable interfaces, unifying different contexts of the problem and getting through design of perturbative and pure analytic methods, from accounting for important physical features to recovering universal properties of the growth domain. The main goals, advances on which will be made in parallel during the study, are accounting for the surface tension effects of the Laplacian growth, study of the Inverse Potential Problem by means of different tools (such as theory of Schwarz functions, orthogonal polynomials in complex domain, algebraic-geometrical methods in theory of integrable equations, etc.) and establishing links with different branches of mathematical physics (such as theories of matrix ensembles, Whitham hierarchies and related geometric objects).

Wissenschaftliches Gebiet (EuroSciVoc)

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Aufforderung zur Vorschlagseinreichung

FP6-2002-MOBILITY-7
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Finanzierungsplan

IIF - Marie Curie actions-Incoming International Fellowships

Koordinator

SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI
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