Related papers: Ginzburg-Landau vortex dynamics driven by an appli…
We derive rigorously the reduced dynamical laws for quantized vortex dynamics of the complex Ginzburg-Landau equation on torus when the core size of vortex $\varepsilon\to 0$. The reduced dynamical laws of the complex Ginzburg-Landau…
This paper is devoted to an analysis of vortex-nucleation for a Ginzburg-Landau functional with discontinuous constraint. This functional has been proposed as a model for vortex-pinning, and usually accounts for the energy resulting from…
Rotating waves are a fascinating feature of a wide array of complex systems, particularly those arising in the study of many chemical and biological processes. With many rigorous mathematical investigations of rotating waves relying on the…
Time dependent Ginzburg-Landau equation is solved for type II superconductors numerically, and the dynamics of entering vortices, geometric defects and pinning effects have been investigated. A superconducting wire with ratchet defects is…
We study the dynamics of vortices in d-wave superconductors using a phenomenological time-dependent Ginzburg-Landau equation with mixing of s- and d-wave components. We present numerical simulations under an external driving current $J$…
In this note, a brief introduction to the physical and mathematical background of the two-component Ginzburg-Landau theory is given. From this theory we derive a boundary value problem whose solution can be obtained in part by solving a…
We investigate the pinning and driven dynamics of vortices interacting with twin boundaries using large scale molecular dynamics simulations on samples with near one million pinning sites. For low applied driving forces, the vortex lattice…
A classical result in the study of Ginzburg-Landau equations is that, for Dirichlet or Neumann boundary conditions, if a sequence of functions has energy uniformly bounded on a logarithmic scale then we can find a subsequence whose…
The generalized time-dependent Ginzburg-Landau (GTDGL) theory was first proposed to describe better gap superconductors and the phenomenon of thermal phase-slips (PSs) in defect-free systems. However, there is a lack of information about…
In the present paper we develop an algorithm to solve the time dependent Ginzburg-Landau (TDGL) equations, by using the link variables technique, for circular geometries. In addition, we evaluate the Helmholtz and Gibbs free energy, the…
Let $\Omega$ be a smooth bounded domain in $\mathbb{R}^2$. For $\epsilon>0$ small, we construct non-constant solutions to the Ginzburg-Landau equations $-\Delta u=\frac{1}{\epsilon^2}(1-|u|^2)u$ in $\Omega$ such that on $\partial \Omega$ u…
We investigate the dynamics of magnetic vortices in type II superconductors with normal state pinning sites using the Ginzburg-Landau equations. Simulation results demonstrate hopping of vortices between pinning sites, influenced by…
We study the three-dimensional Ginzburg-Landau model of superconductivity for strong applied magnetic fields varying between the second and third critical fields. In this regime, it is known from physics that superconductivity should be…
By using different continuation methods, we unveil a wide region in the parameter space of the discrete cubic-quintic complex Ginzburg-Landau equation, where several families of stable vortex solitons coexist. All these stationary solutions…
Starting from the time-dependent Ginzburg-Landau (TDGL) equations for a type II superconductor, we derive the equations of motion for the displacement field of a moving vortex lattice without inertia or pinning. We show that it is linearly…
Dynamics of homogeneous moving vortex matter is considered beyond the linear response. The framework is the time dependent Ginzburg - Landau equation within the lowest Landau level approximation. Both disorder and thermal fluctuations are…
We consider the dissipative heat flow and conservative Gross-Pitaevskii dynamics associated with the Ginzburg-Landau energy posed on a Riemannian 2-manifold M. We show the limiting vortices of the solutions to these two problems evolve…
Within the framework of the generalized time-dependent Ginzburg-Landau equations, we studied the influence of the magnetic self-field induced by the currents inside a superconducting sample driven by an applied transport current. The…
In this work we explore the interplay between superconductivity and nematicity in the framework of a Ginzburg Landau theory with a nematic order parameter coupled to the superconductor order parameter, often used in the description of…
The dynamics of 2D pancake vortices in Josephson-coupled superconducting/normal - metal multilayers is considered within the time-dependent Ginzburg-Landau theory. For temperatures close to $T_{c}$ a viscous drag force acting on a moving 2D…