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Related papers: Disclinations in limiting Landau-de Gennes theory

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We study tensor-valued minimizers of the Landau-de Gennes energy functional on a simply-connected planar domain $\Omega$ with non-contractible boundary data. Here the tensorial field represents the second moment of a local orientational…

Analysis of PDEs · Mathematics 2015-06-16 Dmitry Golovaty , Alberto Montero

We study global minimizers of the Landau-de Gennes (LdG) energy functional for nematic liquid crystals, on arbitrary three-dimensional simply connected geometries with topologically non-trivial and physically relevant Dirichlet boundary…

Analysis of PDEs · Mathematics 2015-09-28 Apala Majumdar , Adriano Pisante , Duvan Henao

We study energy minimization of a continuum Landau-de Gennes energy functional for nematic liquid crystals, in three-dimensional axisymmetric domains and in a restricted class of $\mathbb{S}^1$-equivariant (i.e., axially symmetric)…

Analysis of PDEs · Mathematics 2021-02-01 Federico Dipasquale , Vincent Millot , Adriano Pisante

We study a modified Landau-de Gennes model for nematic liquid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional domains,…

Analysis of PDEs · Mathematics 2019-05-01 Giacomo Canevari , Apala Majumdar , Bianca Stroffolini

We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains. Assuming smooth and uniaxial (e.g. homeotropic) boundary conditions and a corresponding physically…

Analysis of PDEs · Mathematics 2020-10-28 Federico Dipasquale , Vincent Millot , Adriano Pisante

We consider energy minimizing configurations of a nematic liquid crystal around a spherical colloid particle, in the context of the Landau-de Gennes model. The nematic is assumed to occupy the exterior of a ball of radius r_0, satisfy…

Analysis of PDEs · Mathematics 2016-05-25 Stan Alama , Lia Bronsard , Xavier Lamy

We study the behaviour of global minimizers of a continuum Landau-de Gennes energy functional for nematic liquid crystals, in three-dimensional axially symmetric domains domains diffeomorphic to a ball (a nematic droplet) and in a…

Analysis of PDEs · Mathematics 2022-02-24 Federico Dipasquale , Vincent Millot , Adriano Pisante

We study a class of Landau-de Gennes energy functionals with a sextic bulk energy density in a three-dimensional domain. We examine the asymptotic behavior of uniformly bounded minimizers in two distinct scenarios: one where their energy…

Analysis of PDEs · Mathematics 2024-04-02 Wei Wang , Zhifei Zhang

We study uniaxial energy minimizers within the Landau-de Gennes theory for nematic liquid crystals, subject to dirichlet boundary conditions. Topological defects in such minimizers correspond to the zeros of the corresponding equilibrium…

Analysis of PDEs · Mathematics 2010-05-31 Apala Majumdar

In our previous work,, we studied asymptotic behavior of minimizers of the Landau-de Gennes energy functional on planar domains as the nematic correlation length converges to zero. Here we improve upon those results, in particular by…

Analysis of PDEs · Mathematics 2021-09-27 Dmitry Golovaty , Jose Alberto Montero

We consider a variational two-dimensional Landau-de Gennes model in the theory of nematic liquid crystals in a disk of radius $R$. We prove that under a symmetric boundary condition carrying a topological defect of degree $\frac{k}{2}$ for…

Analysis of PDEs · Mathematics 2020-06-24 Radu Ignat , Luc Nguyen , Valeriy Slastikov , Arghir Zarnescu

We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau-de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special temperature. There is one essential model…

Mathematical Physics · Physics 2019-10-30 Lidong Fang , Apala Majumdar , Lei Zhang

The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional defined on the space of vector fields $H^1(S,T)$, where $S$ and $T$ are surfaces of revolution. The energy functional we consider is closely related…

Analysis of PDEs · Mathematics 2023-07-25 Giovanni Di Fratta , Valeriy Slastikov , Arghir Zarnescu

In the present work, we study minimizers of the Landau-de Gennes free energy in a bounded domain $\Omega\subset \mathbb{R}^3$. We prove that at low temperature minimizers do not vanish, even for topologically non-trivial boundary…

Analysis of PDEs · Mathematics 2014-11-18 Andres Contreras , Xavier Lamy

The aim of this article is twofold. First, in the large-body limit and when the temperature is below the nematic-isotropic transition threshold, we verify that the $\mathbb{S}^2$-valued energy-minimizing harmonic map on a bounded smooth…

Analysis of PDEs · Mathematics 2026-05-19 Ho Man Tai , Yong Yu

We study minimizers of the Landau-de Gennes energy in $\mathbb{R}^3\setminus B_1(0)$ with external magnetic field in the large particle limit. We impose strong tangential anchoring and uniaxiality of the $Q-$tensor on the boundary. We…

Analysis of PDEs · Mathematics 2024-11-01 Lia Bronsard , Dean Louizos , Dominik Stantejsky

The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional in the class of $\mathbb{S}^2$-valued maps defined in cylindrical surfaces. The model naturally arises as a curved thin-film limit in the theories of…

Analysis of PDEs · Mathematics 2022-10-11 Giovanni Di Fratta , Alberto Fiorenza , Valeriy Slastikov

In this article we prove existence of minimizers of the Landau-de Gennes energy for liquid crystals with homogeneous external magnetic field and strong uniaxial planar anchoring. Next we consider the asymptotics of solutions to the joint…

Analysis of PDEs · Mathematics 2025-08-06 Lia Bronsard , Dean Louizos , Dominik Stantejsky

We study a class of Landau-de Gennes energy functionals in the asymptotic regime of small elastic constant $L>0$. We revisit and sharpen the results in [18] on the convergence to the limit Oseen-Frank functional. We examine how the…

Analysis of PDEs · Mathematics 2014-10-14 Luc Nguyen , Arghir Zarnescu

We consider an asymptotic regime for two-dimensional ferromagnetic films that is consistent with the formation of transition layers (N\'eel walls). We first establish compactness of S2-valued magnetizations in the energetic regime of N\'eel…

Analysis of PDEs · Mathematics 2014-06-12 Raphael Cote , Radu Ignat , Evelyne Miot
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