29 citations · 52 across the 12 of their papers we have counts for
16 papers · 1 filter
Domain walls in the coupled Gross-Pitaevskii equations with the harmonic potential
Andres Contreras, Dmitry E. Pelinovsky, Valeriy Slastikov
We study the existence and variational characterization of steady states in a coupled system of Gross--Pitaevskii equations modeling two-component Bose-Einstein condensates with th…
Local minimizers with unbounded vorticity for the d Ginzburg-Landau functional
Andres Contreras, Robert L. Jerrard
A central focus of Ginzburg-Landau theory is the understanding and characterization of vortex configurations. On a bounded domain global minimizers, and…
First critical field of highly anisotropic three-dimensional superconductors via a vortex density model
Andres Contreras, Guanying Peng
We analyze a mean field model for d anisotropic superconductors with a layered structure, in the presence of a strong magnetic field. The mean field model arises as the -…
Singular perturbation of manifold-valued maps with anisotropic energy
Andres Contreras, Xavier Lamy
We establish small energy Hölder bounds for minimizers of \[E_\varepsilon (u):=\int_ΩW(\nabla u)+ \frac{1}{\varepsilon^2} \int_Ωf(u),\] where is a positive defi…
On the convergence of minimizers of singular perturbation functionals
Andres Contreras, Xavier Lamy, Rémy Rodiac
The study of singular perturbations of the Dirichlet energy is at the core of the phenomenological-description paradigm in soft condensed matter. Being able to pass to the limit pl…
Nearly Parallel Vortex Filaments in the 3D Ginzburg-Landau Equations
Andres Contreras, Robert L. Jerrard
We introduce a framework to study the occurrence of vortex filament concentration in Ginzburg-Landau theory. We derive a functional that describes the free-energy of a collect…
The onset of layer undulations in smectic A liquid crystals due to a strong magnetic field
A. Contreras, C. García-Azpeitia, C. J. García-Cervera +1
We investigate the effect of a strong magnetic field on a three dimensional smectic A liquid crystal. We identify a critical field above which the uniform layered state loses stabi…
Global bifurcation of vortex and dipole solutions in Bose-Einstein condensates
Andres Contreras, Carlos García-Azpeitia
The Gross-Pitaevskii equation for a Bose-Einstein condensate (BEC) with symmetric harmonic trap is given in (1). Periodic solutions of (1) play an important role in the understandi…
Boundary regularity of weakly anchored harmonic maps
Andres Contreras, Xavier Lamy, Rémy Rodiac
In this note we study the boundary regularity of minimizers of a family of weak anchoring energies that model the states of liquid crystals. We establish optimal boundary regularit…
A Degenerate Isoperimetric Problem and Traveling Waves to a Bi-stable Hamiltonian System
Stan Alama, Lia Bronsard, Andres Contreras +2
We analyze a non-standard isoperimetric problem in the plane associated with a metric having degenerate conformal factor at two points. Under certain assumptions on the conformal f…
Persistence of superconductivity in thin shells beyond
Andres Contreras, Xavier Lamy
In Ginzburg-Landau theory, a strong magnetic field is responsible for the breakdown of superconductivity. This work is concerned with the identification of the region where superco…
Biaxial escape in nematics at low temperature
Andres Contreras, Xavier Lamy
In the present work, we study minimizers of the Landau-de Gennes free energy in a bounded domain . We prove that at low temperature minimizers do not vanish,…
orbital stability of Dirac solitons in the massive Thirring model
Andres Contreras, Dmitry E. Pelinovsky, Yusuke Shimabukuro
We prove orbital stability of Dirac solitons in the massive Thirring model. Our analysis uses local well posedness of the massive Thirring model in , conservation of the…
Domain walls in the coupled Gross-Pitaevskii equations
Stan Alama, Lia Bronsard, Andres Contreras +1
A thorough study of domain wall solutions in coupled Gross-Pitaevskii equations on the real line is carried out including existence of these solutions; their spectral and nonlinear…
Stability of multi-solitons in the cubic NLS equation
Andres Contreras, Dmitry E. Pelinovsky
We address stability of multi-solitons in the cubic NLS (nonlinear Schrödinger) equation on the line. By using the dressing transformation and the inverse scattering transform meth…
Large vorticity stable solutions to the Ginzburg-Landau equations
Andres Contreras, Sylvia Serfaty
We construct local minimizers to the Ginzburg-Landau functional of superconductivity whose number of vortices N is prescribed and blows up as the parameter epsilon, inverse of the…