相关论文: Quasipatterns in parametrically forced systems

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…

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 present an experimental study of quasiperiodic transitions between a highly ordered square-lattice pattern and a disordered, defect-riddled state, in a circular Faraday system. We show that the transition is driven initially by a…

A nonlinear theory of pattern selection in parametric surface waves (Faraday waves) is presented that is not restricted to small viscous dissipation. By using a multiple scale asymptotic expansion near threshold, a standing wave amplitude…

We present an experimental investigation of superlattice patterns generated on the surface of a fluid via parametric forcing with 2 commensurate frequencies. The spatio-temporal behavior of 4 qualitatively different types of superlattice…

Periodic configurations have dominated the design of phononic and elastic-acoustic metamaterial structures for the past decades. Unlike periodic crystals, quasicrystals lack translational symmetry but are unrestricted in rotational…

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…

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…

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…

Quasipatterns (two-dimensional patterns that are quasiperiodic in any spatial direction) remain one of the outstanding problems of pattern formation. As with problems involving quasiperiodicity, there is a small divisor problem. In this…

We present here a study of selection of rhombic patterns close to a bicritical point at the onset of primary surface instability in viscous fluids under two-frequency vertical vibration. Rhombic patterns appear to be natural at the primary…

Fracture in quasi-statically driven systems is studied by means of a discrete spring-block model. Developed from close comparison with desiccation experiments, it describes crack formation induced by friction on a substrate. The model…

We introduce an approach to computing the free energy of quasicrystals, which we use to calculate phase diagrams for systems of two-dimensional patchy particles with five regularly arranged patches that have previously been shown to form…

Metamaterials enable the emergence of novel physical properties due to the existence of an underlying sub-wavelength structure. Here, we use the Faraday instability to shape the fluid-air interface with a regular pattern. This pattern…

We consider a class of ordinary differential equations describing one-dimensional systems with a quasi-periodic forcing term and in the presence of large damping. We discuss the conditions to be assumed on the mechanical force and the…

We consider a class of ordinary differential equations describing one-dimensional quasiperiodically forced systems in the presence of large damping. We give a fully constructive proof of the existence of response solutions, that is…

Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the…

We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case…

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…

Model patchy particles have been shown to be able to form a wide variety of structures, including symmetric clusters, complex crystals and even two-dimensional quasicrystals. Here, we investigate whether we can design patchy particles that…