Dynamics of vortex lines in the three-dimensional complex Ginzburg-Landau equation: Instability, stretching, entanglement, and helices

Abstract

The dynamics of curved vortex filaments is studied analytically and numerically in the framework of a three-dimensional complex Ginzburg-Landau equation ͑CGLE͒. It is shown that a straight vortex line is unstable with respect to spontaneous stretching and bending in a substantial range of parameters of the CGLE, resulting in formation of persistent entangled vortex configurations. The boundary of the three-dimensional instability in parameter space is determined. Near the stability boundary, the supercritical saturation of the instability is found, resulting in the formation of stable helicoidal vortices.

Ordered and Self-Disordered Dynamics of Holes and Defects in the One-Dimensional Complex Ginzburg-Landau Equation

“…3c). For smaller values of q m , the curves are quite intricate; this corresponds to the rapid early time evolution along the stable manifold not included in model (4). From Eq.…”

Motion of vortex lines in quantum mechanics

“…There are no exact analytic solutions of this equation with nontrivial vortex structure. One must resort either to approximations which can reveal only some features of the vortex motion (as, for example, in the early work of Fetter [10,11]) or to extensive numerical calculations (cf., for example, [12]). In the present paper we use the standard time-dependent Schrödinger equation to investigate the motion of vortex lines embedded in the probability fluid of a quantum particle.…”

Scroll Wave Instabilities in an Excitable Chemical Medium

“…For straight scrolls in homogeneous media, linear stability analyses have been performed for all three types of instabilities [18] and for the experimentally relevant case of the sproing instability in a heterogeneous medium with a gradient parallel to the scroll filament [19]. Similar scroll wave instabilities have also been reported for the oscillatory complex Ginzburg-Landau equation, for instance, for the 3D analogue of a core instability reminiscent of meandering in excitable media [20] and for primary and secondary twist-induced instabilities [21].…”