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Planar and Spherical
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Exotic Patterns in Faraday Waves
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- 1 Date & Time: Thu, 20 February 2020, 11:30 to
- 2 Start
- 3 The Faraday instability: Floquet analysis, numerical simulation, and exotic patterns
- 4 History -- Experiments
- 5 Hydrodynamic Instabilities
- 6 History -- Theory & Numerics
- 7 Benjamin & Ursell inviscid linear stability analysis Linear problem is homogeneous in x,y,
- 8 Linear stability problem reduces to:
- 9 Result of viscous stability analysis
- 10 Exotic Patterns
- 11 Two-frequency forcing
- 12 Back to single-frequency forcing
- 13 Equations and numerical methods
- 14 Compare numerical simulation with Floquet analysis Nicolas Perinet
- 15 Hexagonal lattice
- 16 Computations carried out in minimal hexagonal domain: smallest rectangular domain that can accommodate hexagons
- 17 Velocity field at various instants
- 18 Hexagonal pattern over one subharmonic oscillation period
- 19 Long-time evolution
- 20 Stroboscopic films show long-time behavior
- 21 Fourier spectra
- 22 Fourier spectra : time evolution
- 23 Questions: Is this time-dependent behavior in the minimal domain related to the competition between squares and hexagons in a large domain?
- 24 High Performance Computing with BLUE
- 25 Faraday Super-squares
- 26 Experimental study of the Faraday instability
- 27 What about a spherical interface subjected to a radical force?
- 28 Planar and Spherical
- 29 Numerical Floquet analysis
- 30 Full nonlinear simulations using BLUE
- 31 Predictions from symmetry theory Busse, Golubitsky, Chossat, Matthews, ...
- 32 Formulas when patterns are aligned along axis asymmetric
- 33 l= 3 tetrahedron
- 34 Impossible for pure capillary waves
