Multiple-scale structures: from Faraday waves to soft-matter quasicrystals

Self-assembly of soft-matter quasicrystals and their approximants.

The surprising recent discoveries of quasicrystals and their approximants in soft-matter systems poses the intriguing possibility that these structures can be realized in a broad range of nanoscale and microscale assemblies. It has been theorized that soft-matter quasicrystals and approximants are largely entropically stabilized, but the thermodynamic mechanism underlying their formation remain...

FAR Faraday Waves

On Faraday waves

The standing waves of frequency wand wavenumber k that are induced on the surface of a liquid of depth d that is subjected to the vertical displacement a, cos 2wt are determined on the assumptions t1mt: the effects of lateral boundaries are negligible: £ = ka, tanh kd ~ 1 and 0 < £-0 = 0(0'), where 0 is the linear damping ratio of a free wave of frequency w; the ""wes form a square pattern (whi...

Theoretical Model for Faraday Waves with Multiple-Frequency Forcing

A simple generalization of the Swift-Hohenberg equation is proposed as a model for the patternforming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a fluid driven by a linear combination of two frequencies. The model exhibits steady-state solutions with 2-, 4-, 6-, and 12-fold symmetric patterns, similar to th...

Hysteretic Faraday waves.

We report on the numerical and theoretical study of the subcritical bifurcation of parametrically amplified waves appearing at the interface between two immiscible incompressible fluids when the layer of the lower fluid is very shallow. As a critical control parameter is surpassed, small amplitude surface waves bifurcate subcritically toward highly nonlinear ones with twice their amplitude. We ...