Related papers: Phase Slips and the Eckhaus Instability
The phase-turbulent (PT) regime for the one dimensional complex Ginzburg-Landau equation (CGLE) is carefully studied, in the limit of large systems and long integration times, using an efficient new integration scheme. Particular attention…
A general theory of the onset and development of the plasmoid instability is formulated by means of a principle of least time. The scaling relations for the final aspect ratio, transition time to rapid onset, growth rate, and number of…
A three-component Ginzburg-Landau theory for a triplet pairing is developed to understand the observed multiple phases in a new superconductor UTe$_2$ under pressure. Near the critical pressure $P_{\rm cr}$=0.2GPa where all components are…
We analyse the development of instability in the framework of nonlinear electrodynamics based on the Maxwell's equations without approach of slowly varying amplitudes and phases. The action is chosen from the Heisenberg-Euler Lagrangian,…
The paper assesses stationary probability distributions in out of equilibrium systems. In the phenomenology proposed, no free energy can be well defined. Fluctuations of Landau free energy couplings arise when the intrinsic chemical…
We formulate the gauge invariant Lorentz covariant Ginzburg-Landau theory which describes nonstationary regimes: relaxation of a superconducting system accompanied by eigen oscillations of internal degrees of freedom (Higgs mode and…
We study a Ginzburg-Landau model of structural phase transition in two dimensions, in which a single order parameter is coupled to the tetragonal and dilational strains. Such elastic coupling terms in the free energy much affect the phase…
A study was made of the instability that arises when acoustic and gravity waves propagate in an inhomogeneous medium which is characterized by oscillatory approach of the reaction coordinates to the steady state. It is shown that loss of…
In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based…
We consider a mechanism for area preserving Hamiltonian systems which leads to the enhanced probability, $P(\lambda, t)$, to find small values of the finite time Lyapunov exponent, $\lambda$. In our investigation of chaotic dynamical…
We study large-scale dynamics in the Ginzburg-Landau equation (GLE) using a reduced description derived from a WKB expansion. Rigorous mathematical results establishing that this reduced equation accurately approximates the full GLE are…
The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This sudy is restricted to the impact of…
We give an iterative method to estimate the disturbance of semi-wavefronts of the equation: $\dot{u}(t,x) = u''(t,x) +u(t,x)(1-u(t-h,x)),$ $x \in \mathbb{R},\ t >0;$ where $h>0.$ As a consequence, we show the exponential stability, with an…
A selfconsistent system of equations describing evolution of linear spherically symmetric perturbations in Fridmann world by an arbitrary equation of state is obtained. The perturbations singular part corresponding to massive particle-like…
We present a new Ginzburg-Landau theory for superconductivity in UPt$_3$, based upon a multicomponent order parameter transforming under an irreducible space group representation; the phase is staggered in real space. Our model can explain…
In this paper, we study a phenomenological model for pattern formation in electroconvection, and the effect of noise on the pattern. As such model we consider an anisotropic Swift-Hohenberg equation adding an additive noise. We prove the…
Averaging principle is an effective method for investigating dynamical systems with highly oscillating components. In this paper, we study three types of averaging principle for stochastic complex Ginzburg-Landau equations. Firstly, we…
The long-time behavior of the solutions for a non-isothermal model in superfluidity is investigated. The model describes the transition between the normal and the superfluid phase in liquid 4He by means of a non-linear differential system,…
The paper deals with the study of superfluidity by a Ginzburg-Landau model that investigates the material by a second order phase transition, in which any particle has simultaneouly a normal and superfluid motion. This pattern is able to…
In this paper, we study the fourth-order Schr\"{o}dinger equation \begin{equation*} i \partial_t u + {\Delta}^2 u - \gamma \Delta u = \pm |u|^{s-1}u \end{equation*} on the lattice $\mathbb{Z}^d$ with dimensions $d=1,2$ and parameter $\gamma…