相关论文: Pattern formation with a conservation law
We study the excitation of spatial patterns by resonant, multi-frequency forcing in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. Using weakly nonlinear analysis we show that for small amplitudes only stripe…
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 propose a new mechanism for stabilization of confined modes in lasers and semiconductor microcavities holding exciton-polariton condensates, with spatially uniform linear gain, cubic loss, and cubic self-focusing or defocusing…
Generalizing results of \cite{MC,S} and \cite{HSZ} for certain model reaction-diffusion and reaction-convection-diffusion equations, we derive and rigorously justify weakly nonlinear amplitude equations governing general Turing bifurcation…
In pattern-forming systems, localized patterns are states of intermediate complexity between fully extended ordered patterns and completely irregular patterns. They are formed by stationary fronts enclosing an ordered pattern inside an…
We report experimental study of the secondary modulational instability of a one-dimensional non-linear traveling wave in a long bounded channel. Two qualitatively different instability regimes involving fronts of spatio-temporal defects are…
A Langmuir wave (LW) model is constructed whose equilibria are consistent with stimulated Raman scatter optimization, with Hamiltonian dynamics and with rotational invariance. Linear instability analysis includes terms to all orders in wave…
We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on $CO_{2}$ gas can be reproduced…
The dynamics and stability of continuous-wave and multi-pulse structures are studied theoretically, for a generalized model of passively mode-locked fiber laser with an arbitrary nonlinearity. The model is characterized by a complex…
Pattern formation and evolution in unsynchronizable complex networks are investigated. Due to the asymmetric topology, the synchronous patterns formed in complex networks are irregular and nonstationary. For coupling strength immediately…
Time evolution of the decay process of unstable particles is investigated in field theory models. We first formulate how to renormalize the non-decay amplitude beyond perturbation theory and then discuss short-time behavior of very…
Spatial pattern formation in excitable fluctuating media was researched analytically from the point of view of the order parameters concept. The reaction-diffusion system in external noise is considered as a model of such medium. Stochastic…
Pattern formation in the classical and fractional Schnakenberg equations is studied to understand the nonlocal effects of anomalous diffusion. Starting with linear stability analysis, we find that if the activator and inhibitor have the…
We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the…
We investigate the dynamical formation of nonlinear patterns in one-dimensional ring condensates under bichromatic periodic modulation of the interaction strength. The stability phase diagram of the condensate's homogeneous density state is…
We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by…
We study the effect of external stochastic modulation on a system with O(2) symmetry that exhibits a Hopf or oscillatory instability in the absence of modulation. The study includes a random component in both the control parameter of the…
The behaviour of a space-modulated, so-called "argumental" oscillator is studied, which is represented by a model having an even-parity space-modulating function. Analytic expressions of a stability criterion and of discrete energy levels…
We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean field models for single and doubly degenerate optical parametric oscillators. Analytical expressions for the new…
The key to understanding the universal behaviour of systems driven away from equilibrium lies in the common description obtained when particular microscopic models are reduced to order parameter equations. Universal order parameter…