相关论文: Pattern formation at the bi-critical point of the …

Through experimentation, we have discovered that with the changing of driving conditions, the Faraday waves undergo two abrupt transitions in spatiotemporal order: onset and instability. The driving amplitudes and frequencies corresponding…

We present a theoretical study of nonlinear pattern formation in parametric surface waves for fluids of low viscosity, and in the limit of large aspect ratio. The analysis is based on a quasi-potential approximation to the equations…

Many of the interesting patterns seen in recent multi-frequency Faraday experiments can be understood on the basis of three-wave interactions (resonant triads). In this paper we consider two-frequency forcing and focus on a resonant triad…

Three coupled Ginzburg-Landau equations for hexagonal patterns with broken chiral symmetry are investigated. They are relevant for the dynamics close to onset of rotating non-Boussinesq or surface-tension-driven convection. Steady and…

Parametric oscillations of an interface separating two fluid phases create nonlinear surface waves, called Faraday waves, which organise into simple patterns, like squares and hexagons, as well as complex structures, such as double…

We report novel superlattice wave patterns at the interface of a fluid layer driven vertically. These patterns are described most naturally in terms of two interacting hexagonal sublattices. Two frequency forcing at very large aspect ratio…

Motivated by the rich variety of complex periodic and quasi-periodic patterns found in systems such as two-frequency forced Faraday waves, we study the interaction of two spatially periodic modes that are nearly resonant. Within the…

We consider a spherical variant of the Faraday problem, in which a spherical drop is subjected to a time-periodic body force, as well as surface tension. We use a full three-dimensional parallel front-tracking code to calculate the…

Strong effects of the Faraday instability on suspensions of rodlike colloidal particles are reported through measurements of the critical acceleration and of the surface wave amplitude. We show that the transition to parametrically excited…

Standing wave patterns that arise on the surface of ferrofluids by (single frequency) parametric forcing with an ac magnetic field are investigated experimentally. Depending on the frequency and amplitude of the forcing, the system exhibits…

The Faraday problem is an important pattern-forming system that provides some middle ground between systems where the initial instability involves just a single mode and in which complexity then results from mode interactions or secondary…

Vertical oscillation of a fluid interface above a critical amplitude excites the Faraday instability, typically manifesting itself as a standing wave pattern. Fundamentally, the phenomenon is an example of parametric resonance. At high…

We use a free-energy minimization approach to describe the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Our approach is fully nonlinear and stems…

The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view. We consider the transitions from a steady state of an abstract nonlinear dissipative system. To shed light…

Hydrodynamic instabilities are usually investigated in confined geometries where the resulting spatiotemporal pattern is constrained by the boundary conditions. Here we study the Faraday instability in domains with flexible boundaries. This…

A direct numerical simulation of Faraday waves is carried out in a minimal hexagonal domain. Over long times, we observe the alternation of patterns we call quasi-hexagons and beaded stripes. The symmetries and spatial Fourier spectra of…

Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in…

A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…

We study of the formation of pattern-forming fronts in the presence of a rigidly-propagating parameter ramp which is slowly-varying in space. In the context of the prototypical supercritical complex Ginzburg-Landau equation, we show that…

A quasi-potential approximation to the Navier-Stokes equation for low viscosity fluids is developed to study pattern formation in parametric surface waves driven by a force that has two frequency components. A bicritical line separating…