Neicu et al. observed experimentally spontaneous formation of the long-range orientational order and large-scale vortices in a system of vibrated macroscopic rods. We propose a phenomenological theory of this phenomenon based on a coupled system of equations for local rods density and tilt. The density evolution is described by the modified Cahn-Hilliard equation, while the tilt is described by...

The dynamics of the normal/superconducting interface in type-I superconductors has recently been derived from the time-dependent Ginzburg-Landau theory of superconductivity. In a suitable limit these equations are mapped onto a “free-boundary” problem, in which the interfacial dynamics are determined by the diffusion of magnetic flux in the normal phase. The magnetic field at the interface sati...

We report on experimental and theoretical findings of front destabilization that causes spontaneous spiral–vortex nucleation and produces a state of spatio-temporal disorder. The experiments were carried out on an oscillatory photosensitive Belousov–Zhabotinsky reaction that is periodically forced in time. Numerical studies were carried out on a modified Complex Ginzburg–Landau equation and on ...

A method of finding relative periodic orbits for differential equations with continuous symmetries is described and its utility demonstrated by computing relative periodic solutions for the one-dimensional complex Ginzburg-Landau equation (CGLE) with periodic boundary conditions. A relative periodic solution is a solution that is periodic in time, up to a transformation by an element of the equ...

This paper develops efficient techniques for calculating gradient information which may be used to optimize the placement of sensors & actuators of a given precision for the effective estimation and control of high-dimensional discretizations of infinite-dimensional linear time-invariant (LTI) systems. The necessary gradients are determined in this setting via adjoint analyses which quantify th...

We show that, for two nontrivial lambda phi(4) problems (the anharmonic oscillator and the Landau-Ginzburg hierarchical model), improved perturbative series can be obtained by cutting off the large field contributions. The modified series converge to values exponentially close to the exact ones. For lambda larger than some critical value, the method outperforms Padé's approximants and Borel sum...

We prove the Doran–Harder–Thompson conjecture in the case of elliptic curves by using ideas from SYZ mirror symmetry. The conjecture claims that when a Calabi– Yau manifold X degenerates to a union of two quasi-Fano manifolds (Tyurin degeneration), a mirror Calabi–Yau manifold of X can be constructed by gluing the two mirror Landau– Ginzburg models of the quasi-Fano manifolds. The two crucial i...

We consider the discretization of a special class of nonlinear parabolic equations, including the complex Ginzburg–Landau equation, by implicit–explicit multistep methods and establish stability under a best possible linear stability condition.

Abstract Oscillons are spatially localized, time-periodic structures that have been observed in many natural processes, often under temporally periodic forcing. Near Hopf bifurcations, such systems can be formally reduced to forced complex Ginzburg–Landau equations, with oscillons then corresponding to stationary localized patterns. In this manuscript, stationary localized structures of the pla...