Related papers: Hexagonal patterns in finite domains
In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension. This dimension stands out from the…
Segregation patterns of size-bidisperse particle mixtures in a fully-three-dimensional flow produced by alternately rotating a spherical tumbler about two perpendicular axes are studied over a range of particle sizes and volume ratios using…
Hexagonal diamond has been predicted computationally to display extraordinary physical properties including a hardness that exceeds cubic diamond. However, a recent electron microscopy study has shown that so-called hexagonal diamond…
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…
Spatio-temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be…
This paper investigates steady state solutions of a vasculogenesis model governed by coupled partial differential equations in a bounded two dimensional domain. Explicit steady state solutions are analytically constructed, and their…
Using a variational method, we prove the existence of heteroclinic solutions for a 6dimensional system of ordinary differential equations. We derive this system from the classical B{\'e}nard-Rayleigh problem near the convective instability…
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and…
This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
In this paper we study homoclinic tangles formed by transversal intersections of the stable and the unstable manifold of a {\it non-resonant, dissipative} homoclinic saddle point in periodically perturbed second order equations. We prove…
The phenomenon of pattern formation in nonlinear optical resonators is commonly related to an off-resonance excitation mechanism, where patterns occur due to mismatch between the excitation and resonance frequency. In this paper we show…
A geodynamo-model based on an \alpha-effect which has been computed under conditions suitable for the geodynamo is constructed. For a highly restricted class of radial \alpha-profiles the linear \alpha2-model exhibits oscillating solutions…
Patterns on curved surfaces are ubiquitous, yet the influence of surface geometry on pattern dynamics remains elusive. We recently reported a new mechanism of pattern propagation in which a static pattern on a flat plane becomes a…
The new concept of a system of hex equations is introduced as an overdetermined system of six five-point face-centered quad equations defined on six vertices of a hexagon. For a consistent system of hex equations, two variables on…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We study classical particles on the sites of an open chain which diffuse, coagulate and decoagulate preferentially in one direction. The master equation is expressed in terms of a spin one-half Hamiltonian $H$ and the model is shown to be…
Classical Heisenberg spins in the continuum limit (i.e. the nonlinear sigma-model) are studied on an elastic cylinder section with homogeneous boundary conditions. The latter may serve as a physical realization of magnetically coated…
By molecular dynamics simulation, discovered is a strange rigid-like nature for a hexagonally packed domain of short chain molecules. In spite of the non-bonded short-range interaction potential (Lennard-Jones potential) among chain…
The stability of convection rolls in a fluid heated from below is limited by secondary instabilities, including the skew-varicose and crossroll instabilities. We observe a stability boundary defined by the same instabilities in stripe…