MSc Projects 2013-2014 Arghir Zarnescu. Turbulence-the most important unsolved problem of classical physics (R. Feynman)

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Presentation transcript:

MSc Projects Arghir Zarnescu

Turbulence-the most important unsolved problem of classical physics (R. Feynman)

Turbulent versus laminar flows

Navier-Stokes Equations classical formulation

Navier-Stokes equations-turbulent solutions

Prerequisites: Essential :  Functional Analysis (Harmonic Analysis and Wavelets)  Measure Theory  PDE Theory Desirable: Some elements of probability theory

Topological Classification of Liquid Crystal Defects

Defects and topological restrictions: The hairy ball theorem

A defect that requires line fields

Prerequisites Essential: General Topology Algebraic Topology

Dynamics on graphs (joint project with Istvan Kiss)

Allen-Cahn equation on graphs and

An alphabet of graphs: graphlets

Prerequisites Essential: A good understanding of Ordinary Differential Equations Computational skills (Maple/Matlab/Mathematica) Desirable: some experience with dynamical systems