arXiv subjects

Kamel Attar

Publications and source records attributed to Kamel Attar.

4 recordsLinked to original sources

arXiv2021

Breakdown of superconductivity in a magnetic field with self-intersecting zero set

We prove that the lowest eigenvalue of the Laplace operator with a magnetic field having a self-intersecting zero set is a monotone function of the parameter defining the strength of the magnetic field, in a neighborhood of infinity. We apply this monotonicity result on the study of the transition from superconducting to normal states for the Ginzburg-Landau model, and prove that the transition occurs at a unique threshold value of the applied magnetic field.

math-ph↗

arXiv2015

Pinning with a variable magnetic field of the two dimensional Ginzburg-Landau model

We study the Ginzburg-Landau energy of a superconductor with a variable magnetic field and a pinning term in a bounded smooth two dimensional domain $Ω$. Supposing that the Ginzburg-Landau parameter and the intensity of the magnetic field are large and of the same order, we determine an accurate asymptotic formula for the minimizing energy. This asymptotic formula displays the influence of the pinning term. Also, we discuss the existence of non-trivial solutions and prove some asymptotics of the third critical field.

math.AP↗

arXiv2014

Energy and Vorticity of the Ginzburg-Landau Model with Variable Magnetic Field

We consider the Ginzburg-Landau functional with a variable applied magnetic field in a bounded and smooth two dimensional domain. The applied magnetic field varies smoothly and is allowed to vanish non-degenerately along a curve. Assuming that the strength of the applied magnetic field varies between two characteristic scales, and the Ginzburg-Landau parameter tends to $+\infty$, we determine an accurate asymptotic formula for the minimizing energy and show that the energy minimizers have vortices. The new aspect in the presence of a variable magnetic field is that the density of vortices in the sample is not uniform.

math.AP↗

arXiv2013

The ground state energy of the two dimensional Ginzburg-Landau functional with variable magnetic field

We consider the Ginzburg-Landau functional with a variable applied magnetic field in a bounded and smooth two dimensional domain. We determine an accurate asymptotic formula for the minimizing energy when the Ginzburg-Landau parameter and the magnetic field are large and of the same order. As a consequence, it is shown how bulk superconductivity decreases in average as the applied magnetic field increases.

math.AP↗