This article describes the results of several numerical simulations of vortex dynamics in type-
II superconductors. The underlying mathematical model is the time-dependent Ginzburg …

This book covers comprehensive bifurcation theory and its applications to dynamical
systems and partial differential equations (PDEs) from science and engineering, including in …

We review experiments and theoretical models about the possible mutual interplay between
the gravitational field and materials in the superconducting state or other macroscopic …

Transitions are to be found throughout the natural world. The laws of nature are usually
represented by differential equations, which can be regarded as dynamical systems—both …

We review and discuss some recent developments on the unconventional interaction
between superconducting systems and the local gravitational field. While it is known that …

In this paper, we consider three problems related to the mathematical study of vortex
phenomena in superconductivity based on the G--L models. First, we study the long-time …

In this paper, we study linearized Crank--Nicolson Galerkin finite element methods for time-
dependent Ginzburg--Landau equations under the Lorentz gauge. We present an optimal …

Hybrid multi-superconducting structures exist in a variety of superconducting devices, such
as superconductor–insulator–superconductor multilayer structure in superconducting radio …

This paper is concerned with numerical analysis of a finite element method for the time-
dependent Ginzburg–Landau equations under the Coulomb gauge. The main challenge is …

A typical property of a gradient-like dynamical system is that every relatively compact
trajectory approaches a set of equilibria asymptotically for large times, see eg [11, Lemma 3 …