Related papers: Phase instabilities in hexagonal patterns
A matrix method is formulated in a Lagrangian representation for the solution of the characteristic value problem governing modes of oscillation and instability in a collisionless stellar system. The underlying perturbation equations govern…
We develop a complete stability theory for two-dimensional periodic traveling waves of reaction-diffusion systems. More precisely, we identify a diffusive spectral stability assumption, prove that it implies nonlinear stability and provide…
This paper is concerned with the stability issue in determining absorption and diffusion coefficients in quantitative photoacoustic imaging. Assuming that the optical wave is generated by point sources in a region where the optical…
The main result of this paper states that phase retrieval in infinite-dimensional Hilbert spaces is never uniformly stable, in sharp contrast to the finite dimensional setting in which phase retrieval is always stable. This leads us to…
Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a…
The May-Leonard model for three competing species, symmetric with respect to cyclic permutation of the variables and extended by diffusive terms, is considered. Exact time-periodic solutions of the system have been found, and their…
In this note we introduce a hierarchy of phase spaces for static friction, which give a graphical way to systematically quantify the directional dependence in static friction via subregions of the phase spaces. We experimentally plot these…
Structure and dynamics of penta-hepta defects in hexagonal patterns is studied in the framework of coupled amplitude equations for underlying plane waves. Analytical solution for phase field of moving PHD is found in the far field, which…
We present a simple analytical model for the determination of the stable phases of strained heteroepitaxial systems in (1+1) dimensions. In order for this model to be consistent with a subsequent dynamic treatment, all expressions are…
The amplitude equation for an unstable electrostatic wave is analyzed using an expansion in the mode amplitude $A(t)$. In the limit of weak instability, i.e. $\gamma\to 0^+$ where $\gamma$ is the linear growth rate, the nonlinear…
For decades now, low-energy models of QCD have shown indications that a crystalline quark phase could be stable at high chemical potentials. Beyond models, however, there are numerous difficulties in investigating such a hypothesis in full…
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…
This paper establishes suficient conditions for the orbital stability of one-parameter spatially periodic traveling-wave solutions for one-dimensional dispersive equations. Our method of proof combines known techniques with some new ideas.…
A set of coupled complex Ginzburg-landau type amplitude equations which operates near a Hopf-Turing instability boundary is analytically investigated to show localized oscillatory patterns. The spatial structure of those patterns are the…
A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a…
We study the statics and the dynamics of domain patterns in proper hexagonal-orthorhombic ferroelastics; these patterns are of particular interest because they provide a rare physical realization of disclinations in crystals. Both our…
We study hexagon patterns in non-Boussinesq convection of a thin rotating layer of water. For realistic parameters and boundary conditions we identify various linear instabilities of the pattern. We focus on the dynamics arising from an…
Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…
We consider a generalised non-commutative space-time in which non-commutativity is extended to all phase space variables. If strong enough, non-commutativity can affect stability of the system. We perform stability analysis on a couple of…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…