Related papers: Wavenumber selection via spatial parameter jump
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…
We investigate the nonlinear Schr\"odinger equation on a three-edge star graph, where each edge contains a linear localized inhomogeneity in the form of a Dirac delta linear potential. Such systems are of significant interest in studying…
A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear…
Within the framework developed in \cite{Gr, JLL, RT1}, we rigorously establish the nonlinear instability of roll solutions to the two-dimensional generalized Swift-Hohenberg equation (gSHE). Our analysis is based on spectral information…
We model driven two-dimensional charge-density waves in random media via a modified Swift-Hohenberg equation, which includes both amplitude and phase fluctuations of the condensate. As the driving force is increased, we find that the defect…
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…
We study the stability of patterns arising in rotating convection in weakly anisotropic systems using a modified Swift-Hohenberg equation. The anisotropy, either an endogenous characteristic of the system or induced by external forcing, can…
We deal with the stability issue for the determination of outgoing time-harmonic acoustic waves from their far-field patterns. We are especially interested in keeping as explicit as possible the dependence of our stability estimates on the…
A hybrid asymptotic-numerical theory is developed to analyze the effect of different types of localized heterogeneities on the existence, linear stability, and slow dynamics of localized spot patterns for the two-component Schnakenberg…
We consider the one-dimensional Swift-Hohenberg equation coupled to a conservation law. As a parameter increases the system undergoes a Turing bifurcation. We study the dynamics near this bifurcation. First, we show that stationary,…
It is common practice to approximate a weakly nonlinear wave equation through a kinetic transport equation, thus raising the issue of controlling the validity of the kinetic limit for a suitable choice of the random initial data. While for…
Highly concentrated patterns have been observed in a spatially heterogeneous, nonlocal, model of BGK type implementing a velocity-jump process. We study both a linear and a nonlinear case and describe the concentration profile. In…
Zonal jets in a barotropic setup emerge out of homogeneous turbulence through a flow-forming instability of the homogeneous turbulent state (`zonostrophic instability') which occurs as the turbulence intensity increases. This has been…
We study the coarsening of two-dimensional oblique stripe patterns by numerically solving potential and nonpotential anisotropic Swift-Hohenberg equations. Close to onset, all models exhibit isotropic coarsening with a single characteristic…
This paper is devoted to the analysis of a focusing nonlinear biharmonic Schr\"odinger equation in the presence of an unbounded growing up inhomogeneous term. The first main contribution of this work is the derivation of an inhomogeneous…
The Vicsek-BGK equation is a kinetic model for alignment of particles moving with constant speed between stochastic reorientation events with sampling from a von Mises distribution. The spatially homogeneous model shows a steady state…
The coarsening and wavenumber selection of striped states growing from random initial conditions are studied in a non-relaxational, spatially extended, and far-from-equilibrium system by performing large-scale numerical simulations of…
We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction…
We report on the growth of domains of standing waves in electroconvection in a nematic liquid crystal. An ac voltage is applied to the system, forming an initial state that consists of travelling striped patterns with two different…