Faraday instability is a famous pattern-forming experimental setup where a layer of fluid is vertically vibrated. If the oscillation is strong enough, the free surface of this layer deforms and patterns

of different shapes can be observed. The observable patterns range from a wide variety of regu-

lar structures: crystalline patterns, quasi-crystals, super-lattices to the more recently discovered

localized structures like oscillons, solitons or kinks. We simulated for the first time the Faraday

instability in three dimensions. The simulation is performed in a horizontally periodic box, using

finite differences for the solution of Navier-Stokes equations in the fluid bulk and a Front-Tracking

method to treat the interface. Validations have been performed in the linear regime where the

instability thresholds provided by the simulations are compared with a Floquet analysis, and in the

nonlinear regime where spatio-temporal spectra of the obtained patterns (squares and hexagons)

are compared with measurements of an experimental article.

The simulation of hexagons exhibits very interesting dynamics. After being sustained for a dozen of

periods of oscillation, the hexagonal state passes from the original symmetry group D6 to a structure

with less symmetries (Z2 x Z2) and a limit cycle is finally observed where all the symmetries are

broken; we indeed notice an alternation between patterns that are either close to parallelograms or

Expositor: Gonzalo Palma

DFI

Viernes 17 de agosto, 16 h

Av Blanco Encalada 2008, tercer piso

Sala de Seminarios

En esta charla daré un recuento de los avances más recientes de la cosmología, tanto teórica como observacional, para entender el universo a gran escala. En particular, contaré cómo observaciones próximas a realizarse podrían ayudarnos a comprender aspectos claves (y posiblemente revolucionarios) sobre el origen del Universo.