Related papers: Disclinations in limiting Landau-de Gennes theory
We consider the Landau-de Gennes variational problem on a bound\-ed, two dimensional domain, subject to Dirichlet smooth boundary conditions. We prove that minimizers are maximally biaxial near the singularities, that is, their biaxiality…
We investigate prototypical profiles of point defects in two dimensional liquid crystals within the framework of Landau-de Gennes theory. Using boundary conditions characteristic of defects of index $k/2$, we find a critical point of the…
We consider the minimization of a p-Ginzburg-Landau energy functional over the class of radially symmetric functions of degree one. We prove the existence of a unique minimizer in this class, and show that its modulus is monotone increasing…
We study nematic liquid crystalline films within the framework of the Landau-de Gennes theory in the limit when both the thickness of the film and the nematic correlation length are vanishingly small compared to the lateral extent of the…
The Landau-Zener transition in a two level system can be suppressed or enhanced by coupling to an environment, depending on the temperature and the environment spectral function. We consider the marginal spectral function, when the…
The Cahn-Hilliard energy landscape on the torus is explored in the critical regime of large system size and mean value close to $-1$. Existence and properties of a "droplet-shaped" local energy minimizer are established. A standard mountain…
We study the two dimensional Lennard-Jones energy per particle of lattices and we prove that the minimizer among Bravais lattices with sufficiently large density is triangular and that is not the case for sufficiently small density. We give…
We consider the Landau-de Gennes variational model for nematic liquid crystals, in three-dimensional domains. More precisely, we study the asymptotic behaviour of minimizers as the elastic constant tends to zero, under the assumption that…
We study the Landau-Lifshitz model for the energy of multi-scale transition layers -- called "domain walls" -- in soft ferromagnetic films. Domain walls separate domains of constant magnetization vectors $m^\pm \in \mathbb{S}^2$ that differ…
We study Z(2) lattice gauge theory on triangulations of a compact 3-manifold. We reformulate the theory algebraically, describing it in terms of the structure constants of a bidimensional vector space H equipped with algebra and coalgebra…
We study the Landau-de Gennes theory in the one constant limit. The bulk domain is the exterior of a spherical colloid. A Rapini-Papoular surface potential is imposed on the colloid surface, supplemented by a homogeneous far-field condition…
The Lowest Landau Level on a torus is studied. The dimension of the many-body Hilbert space is obtained and is found to be different from the formula given by Haldane. Our result can be tested in numerical investigations of the low-energy…
We consider, in a smooth bounded multiply connected domain $\dom\subset\R^2$, the Ginzburg-Landau energy $\d E_\v(u)=1/2\int_\dom{|\n u|^2}+\frac{1}{4\v^2}\int_\dom{(1-|u|^2)^2}$ subject to prescribed degree conditions on each component of…
We consider $\mathbb{S}^2$-valued maps on a domain $\Omega\subset\mathbb{R}^N$ minimizing a perturbation of the Dirichlet energy with vertical penalization in $\Omega$ and horizontal penalization on $\partial\Omega$. We first show the…
In this paper, we study the defect structure of minimizer of a Landau-de Gennes energy functional in three-dimensional domains, subject to constraint $|Q|=1$. The set of defects is identified by discontinuities in both the eigenframe and…
On a two-dimensional Riemannian manifold without boundary we consider the variational limit of a family of functionals given by the sum of two terms: a Ginzburg-Landau and a perimeter term. Our scaling allows low-energy states to be…
We study a variational model which combines features of the Ginzburg-Landau model in 2D and of the Mumford-Shah functional. As in the classical Ginzburg-Landau theory, a prescribed number of point vortices appear in the small energy regime;…
For the Landau-de Gennes functional modeling nematic liquid crystals in dimension three, we prove that, if the energy is bounded by $C(\log\frac{1}{\varepsilon}+1)$, then the sequence of minimizers…
Motivated by the construction of time-periodic solutions for the three-dimensional Landau-Lifshitz-Gilbert equation in the case of soft and small ferromagnetic particles, we investigate the regularity properties of minimizers of the…
We analyze Ginzburg--Landau minimization problems in two dimensions with either a strong or weak" tangential boundary condition. These problems are motivated by experiments in liquid crystal with boundary defects. In the singular limit when…