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

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Presentation on theme: "MSc Projects 2013-2014 Arghir Zarnescu. Turbulence-the most important unsolved problem of classical physics (R. Feynman)"— Presentation transcript:

1 MSc Projects 2013-2014 Arghir Zarnescu

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

3 Turbulent versus laminar flows

4 Navier-Stokes Equations classical formulation

5 Navier-Stokes equations-turbulent solutions

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

7

8 Topological Classification of Liquid Crystal Defects

9 Defects and topological restrictions: The hairy ball theorem

10 A defect that requires line fields

11 Prerequisites Essential: General Topology Algebraic Topology

12

13 Dynamics on graphs (joint project with Istvan Kiss)

14 Allen-Cahn equation on graphs and

15 An alphabet of graphs: graphlets

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


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