Related papers: Velocity Selection for Propagating Fronts in Super…
The problem of the giant vortex state around a magnetic dot which is embedded in a superconducting film is investigated. The full non-linear, self-consistent Ginzburg-Landau equations are solved numerically in order to calculate the free…
Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed…
Front propagation in two dimensional steady and unsteady cellular flows is investigated in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. In the steady case, by means of a simplified model, we…
Vortices carrying fractions of a flux quantum are predicted to exist in multiband superconductors, where vortex core can split between multiple band-specific components of the superconducting condensate. Using the two-component…
We study two superconducting systems using the Landau-Ginzburg equations. The first is a superconducting half-space with an applied magnetic field parallel to the surface. We calculate the maximum applied field that still supports…
We consider the Ginzburg-Landau functional, defined on a two-dimensional simply connected domain with smooth boundary, in the situation when the applied magnetic field is piecewise constant with a jump discontinuity along a smooth curve. In…
We introduce a new velocity selection criterion for fronts propagating into unstable and metastable states. We restrict these fronts to large finite intervals in the comoving frame of reference and require their centers be insensitive to…
In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction…
We establish exponential bounds on the Ginzburg-Landau order parameter away from the curve where the applied magnetic field vanishes. In the units used in this paper, the estimates are valid when the parameter measuring the strength of the…
We study 2D fronts propagating up a co-moving reaction rate gradient in finite number reaction-diffusion systems. We show that in a 2D rectangular channel, planar solutions to the deterministic mean-field equation are stable with respect to…
This paper gives a complete description of the solutions of the one dimensional Ginzburg-Landau equations which model superconductivity phenomena in infinite slabs. We investigate this problem over the entire range of physically important…
The problem of velocity selection for reaction fronts has been intensively investigated, leading to the successful marginal stability approach for propagation into an unstable state. Because the front velocity is controlled by the leading…
We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such resonant invasion speeds can be determined solely based on…
We investigated the propagation of turbulent fronts in pipe flow at high Reynolds numbers by direct numerical simulation. We used a technique combining a moving frame of reference and an artificial damping to isolate the fronts in short…
In this paper, we first focus on the speed selection problem for the reaction-diffusion equation of the monostable type. By investigating the decay rates of the minimal traveling wave front, we propose a sufficient and necessary condition…
The nonlinear Ginzburg-Landau equations are solved numerically in order to investigate the vortex structure in thin superconducting disks of arbitrary shape. Depending on the size of the system and the strength of the applied magnetic field…
Using an expansion of the order parameter over the eigenfunctions of the linearized first Ginzburg-Landau (GL) equation, we obtain numerically the saddle points of the free energy separating the stable states with different number of…
We introduce and study a new class of fronts in finite particle number reaction-diffusion systems, corresponding to propagating up a reaction rate gradient. We show that these systems have no traditional mean-field limit, as the nature of…
The empirical velocity of a reaction-diffusion front, propagating into an unstable state, fluctuates because of the shot noises of the reactions and diffusion. Under certain conditions these fluctuations can be described as a diffusion…
G-equations are level-set type Hamilton-Jacobi partial differential equations modeling propagation of flame front along a flow velocity and a laminar velocity. In consideration of flame stretching, strain rate may be added into the laminar…