MSc Projects 2013-2014

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