Related papers: Growing stripes, with and without wrinkles

Dense granular flows are often unstable and form inhomogeneous structures. Although significant advances have been recently made in understanding simple flows, instabilities of such flows are often not understood. We present experimental…

We study the effect of directional quenching on patterns formed in simple bistable systems such as the Allen-Cahn and the Cahn-Hilliard equation on the plane. We model directional quenching as an externally triggered change in system…

We have studied the ordering kinetics of a two-dimensional anisotropic Swift-Hohenberg (SH) model numerically. The defect structure for this model is simpler than for the isotropic SH model. One finds only dislocations in the aligned…

A new class of pattern forming systems is identified and investigated: anisotropic systems that are spatially inhomogeneous along the direction perpendicular to the preferred one. By studying the generic amplitude equation of this new class…

The spiral core instability, observed in large aspect ratio Rayleigh-Benard convection, is studied numerically in the framework of the Swift-Hohenberg equation coupled to a large-scale flow. It is shown that the instability leads to…

It is shown numerically and analytically that the front propagation process in the framework of the Swift-Hohenberg model is determined by periodic nucleation events triggered by the explosive growth of the localized zero-eigenvalue mode of…

The Swift-Hohenberg equation with dispersion is considered. Traveling wave solutions of the Swift-Hohenberg equation with dispersion are presented. The classification of these solutions is given. It is shown that the Swift-Hohenberg…

Third order amplitude equations on hexagonal lattices can be used for predicting the existence and stability of stripes, up- and down-hexagons in pattern forming systems. These amplitude equations predict the nonexistence of bistable ranges…

At the intersection of two unidirectional traffic flows a stripe formation instability is known to occur. In this paper we consider coupled time evolution equations for the densities of the two flows in their intersection area. We show…

We investigate the possibility of a striped inhomoegenous phase occurring as an electronic system with an order parameter linearly coupled to the elastic degrees of freedom is tuned through the electronic phase transition. We find that in…

By using variational quantum Monte Carlo techniques, we investigate the instauration of stripes (i.e., charge and spin inhomogeneities) in the Hubbard model on the square lattice at hole doping $\delta=1/8$, with both nearest- ($t$) and…

We study pattern formation in a complex Swift Hohenberg equation with phase-sensitive (parametric) gain. Such an equation serves as a universal order parameter equation describing the onset of spontaneous oscillations in extended systems…

We consider a one-dimensional Swift-Hohenberg equation coupled to a conservation law, where both equations contain additional dispersive terms breaking the reflection symmetry $x \mapsto -x$. This system exhibits a Turing instability and we…

We study grain boundaries between striped phases in the prototypical Swift-Hohenberg equation. We propose an analytical and numerical far-field-core decomposition that allows us to study existence and bifurcations of grain boundaries…

An analytical study on crease formations in a swelling gel layer is conducted. By exploring the smallness of the layer thickness and using a method of coupled series-asymptotic expansions, the original nonlinear eigenvalue problem of…

A recent paper (Healey et al., J. Nonlin. Sci., 2013, 23:777-805.) predicted the disappearance of the stretch-induced wrinkled pattern of thin, clamped, elastic sheets by numerical simulation of the F\"oppl-von K\'arm\'an equations extended…

The evolution of a two-dimensional driven lattice-gas model is studied on an L_x X L_y lattice. Scaling arguments and extensive numerical simulations are used to show that starting from random initial configuration the model evolves via two…

In many antiferromagnetic, quasi-two-dimensional materials, doping with holes leads to "stripe" phases, in which the holes congregate along antiphase domain walls in the otherwise antiferromagnetic texture. Using a suitably parametrized…

We consider the discrete Swift-Hohenberg equation with cubic and quintic nonlinearity, obtained from discretizing the spatial derivatives of the Swift-Hohenberg equation using central finite differences. We investigate the discretization…

We investigate the formation of spiral crack patterns during the desiccation of thin layers of precipitates in contact with a substrate. This symmetry-breaking fracturing mode is found to arise naturally not from torsion forces, but from a…