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pro vyhledávání: '"A. Sandier"'
In this work we extend some of the results of Ignat and Jerrard for Ginzburg-Landau vortices of tangent vector fields on two-dimensional Riemannian manifolds to the setting of complex hermitian line bundles. In particular, we elucidate the locations
Externí odkaz:
http://arxiv.org/abs/2405.08622
We explore the applications of random matrix theory (RMT) in the training of deep neural networks (DNNs), focusing on layer pruning that is reducing the number of DNN parameters (weights). Our numerical results show that this pruning leads to a drast
Externí odkaz:
http://arxiv.org/abs/2310.03165
Autor:
Sandier, Étienne, Sternberg, Peter
We construct an entire solution $U:\mathbb{R}^2\to\mathbb{R}^2$ to the elliptic system \[ \Delta U=\nabla_uW(U), \] where $W:\mathbb{R}^2\to [0,\infty)$ is a `triple-well' potential. This solution is a local minimizer of the associated energy \[ \int
Externí odkaz:
http://arxiv.org/abs/2305.13474
Autor:
Aftalion, Amandine, Sandier, Etienne
We study the ground state of the Gross Pitaveskii energy in a strip, with a phase imprinting condition, motivated by recent experiments on matter waves solitons. We prove that when the width of the strip is small, the ground state is a one dimensiona
Externí odkaz:
http://arxiv.org/abs/2205.06031
The aim of this article is to study the magnetic Ginzburg-Landau functional with an oscillating pinning term. We consider here oscillations of the pinning term that are much faster than the coherence length \(\varepsilon>0\) which is also the inverse
Externí odkaz:
http://arxiv.org/abs/2203.16150
We consider the full three-dimensional Ginzburg-Landau model of superconductivity with applied magnetic field, in the regime where the intensity of the applied field is close to the "first critical field" $H_{c_1}$ at which vortex filaments appear, a
Externí odkaz:
http://arxiv.org/abs/2110.06858
Autor:
Aftalion, Amandine, Sandier, Etienne
We study minimizers of a Gross-Pitaevskii energy describing a two-component Bose-Einstein condensate set into rotation. We consider the case of segregation of the components in the Thomas-Fermi regime, where a small parameter $\epsilon$ conveys a sin
Externí odkaz:
http://arxiv.org/abs/1901.08307
Autor:
Sandier, Étienne, Sternberg, Peter
Publikováno v:
Communications on Pure & Applied Mathematics; Nov2024, Vol. 77 Issue 11, p4163-4211, 49p
Autor:
Sandier, Etienne, Shafrir, Itai
We prove that a local minimizer of the Ginzburg-Landau energy in ${\mathbb R}^3$ satisfying the condition $\liminf_{R\to\infty}E(u;B_R)/RlnR < 2\pi$ must be constant. The main tool is a new sharp eta-ellipticity result for minimizers in dimension thr
Externí odkaz:
http://arxiv.org/abs/1612.00821
We propose an abstract framework for the homogenization of random functionals which may contain non-convex terms, based on a two-scale $\Gamma$-convergence approach and a definition of Young measures on micropatterns which encodes the profiles of the
Externí odkaz:
http://arxiv.org/abs/1601.04344