相关论文: Hexagonal patterns in finite domains

Hexagonal circle patterns with constant intersection angles are introduced and studied. It is shown that they are described by discrete integrable systems of Toda type. Conformally symmetric patterns are classified. Circle pattern analogs…

Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…

Robust heteroclinic cycles are known to change stability in resonance bifurcations, which occur when an algebraic condition on the eigenvalues of the system is satisfied and which typically result in the creation or destruction of a…

Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…

The stability of the multiple equilibrium states of a hexagram ring with six curved sides is investigated. Each of the six segments is a rod having the same length and uniform natural curvature. These rods are bent uniformly in the plane of…

A high degree of control over the structure and dynamics of domain patterns in nonequilibrium systems can be achieved by applying nonuniform external fields near parity breaking front bifurcations. An external field with a linear spatial…

Spatio-temporal pattern formation over the square and rectangular domain has received significant attention from researchers. A wide range of stationary and non-stationary patterns produced by two interacting populations is abundant in the…

Nonlinear stripe patterns occur in many different systems, from the small scales of biological cells to geological scales as cloud patterns. They all share the universal property of being stable at different wavenumbers $q$, i.e., they are…

Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…

Turing patterns in reaction-diffusion (RD) systems have classically been studied only in RD systems which do not explicitly depend on independent variables such as space. In practise, many systems for which Turing patterning is important…

We consider surface-tension driven convection in a rotating fluid layer. For nearly insulating boundary conditions we derive a long-wave equation for the convection planform. Using a Galerkin method and direct numerical simulations we study…

Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of…

Recent experiments by Kudrolli, Pier and Gollub on surface waves, parametrically excited by two-frequency forcing, show a transition from a small hexagonal standing wave pattern to a triangular ``superlattice'' pattern. We show that…

Heterogeneity is classified in five categories---topologic, geometric, kinematic, static, and constitutive---and the first four categories are investigated in a numerical DEM simulation of biaxial compression. The simulation experiments…

The formation of normal-state domains in type-I superconducting indium films is investigated using the high resolution magneto-optical imaging technique. The observed patterns consist of coexisting circular and lamellar normal-phase domains…

Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…

We develop a theory of the domain patterns in systems with competing short-range attractive interactions and long range repulsive Coulomb interactions. We take an energetic approach, in which patterns are considered as critical points of a…

We propose a spatially continuous and temporally discrete model for pattern formation in vertically vibrated granular layers. The grain transfer and the grain mobility transitions are introduced qualitatively, but explicitly. This model…

While non-Boussinesq hexagonal convection patterns are well known to be stable close to threshold (i.e. for Rayleigh numbers $R \approx R_c$), it has often been assumed that they are always unstable to rolls already for slightly higher…

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…