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Related papers: Analysis of a variational model for nematic shells

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We analyse a recent generalised free-energy for liquid crystals posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i. e., uniform…

Soft Condensed Matter · Physics 2020-10-30 G. De Matteis , L. Martina , C. Naya , V. Turco

We study critical surfaces for a surface energy which contains the squared $L^2$ norm of the difference of the mean curvature $H$ and the spontaneous curvature $c_o$, coupled to the elastic energy of the boundary curve. We investigate the…

Differential Geometry · Mathematics 2021-02-24 Bennett Palmer , Alvaro Pampano

In materials that undergo martensitic phase transformation, macroscopic loading often leads to the creation and/or rearrangement of elastic domains. This paper considers an example {involving} a single-crystal slab made from two martensite…

Analysis of PDEs · Mathematics 2022-06-22 Sergio Conti , Robert Kohn , Oleksandr Misiats

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…

Analysis of PDEs · Mathematics 2014-11-21 Kamel Attar

In the Landau-de Gennes theory on nematic liquid crystals, the well-known Landau-de Gennes energy depends on four elastic constants; $L_1$, $L_2$, $L_3$, $L_4$. For the general case of $L_4\neq 0$, Ball-Majumdar \cite {BM} found an example…

Analysis of PDEs · Mathematics 2021-01-08 Zhewen Feng , Min-Chun Hong

We present a novel, self-consistent and robust theoretical model to investigate elastic interactions between topological defects in liquid crystal shells. Accounting for the non-concentric nature of the shell in a simple manner, we are able…

Soft Condensed Matter · Physics 2016-12-14 Alexandre Darmon , Olivier Dauchot , Teresa Lopez-Leon , Michael Benzaquen

In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…

Analysis of PDEs · Mathematics 2023-10-23 Abramo Agosti , Robert Lasarzik , Elisabetta Rocca

In this article, we study minimization of the Landau-de Gennes energy for liquid crystal elastomer.The total energy, is of the sum of the Lagrangian elastic stored energy function of the elastomer and the Eulerian Landau-de Gennes energy of…

Analysis of PDEs · Mathematics 2013-12-12 M. Carme Calderer , Carlos A. Garavito Garzon , Baisheng Yan

We propose a model for nonlinearly elastic membranes undergoing finite deformations while confined to a regular frictionless surface in $\mathbb{R}^3$. This is a physically correct model of the analogy sometimes given to motivate harmonic…

Analysis of PDEs · Mathematics 2024-06-03 Timothy J. Healey , Gokul G. Nair

Control of physical behaviors of nematic colloids and colloidal crystals has been demonstrated by tuning particle shape, topology, chirality and surface charging. However, the capability of altering physical behaviors of such soft matter…

Soft Condensed Matter · Physics 2021-01-12 Ye Yuan , Patrick Keller , Ivan I. Smalyukh

Surface energies and surface elasticity largely affect the mechanical response of nanostructures as well as the physical phenomenon associated with surfaces such as evaporation and adsorption. Studying surface energies at finite…

Materials Science · Physics 2022-07-18 Shashank Saxena , Miguel Spinola , Prateek Gupta , Dennis M. Kochmann

We study the anomalous elasticity of nematic elastomers by employing the powers of renormalized field theory. Using general arguments of symmetry and relevance, we introduce a minimal Landau-Ginzburg-Wilson elastic energy for nematic…

Soft Condensed Matter · Physics 2009-11-07 Olaf Stenull , T. C. Lubensky

Surface-induced profiles of both nematic and smectic order parameters in a nematic liquid crystal, ranging from an orienting substrate to "infinity", were evaluated numerically on base of an extended Landau theory. In order to obtain a…

Soft Condensed Matter · Physics 2009-10-31 Joachim Stelzer , Ralf Bernhard

Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk free energies of the liquid crystal with geometric properties of the…

Soft Condensed Matter · Physics 2021-03-17 Ingo Nitschke , Sebastian Reuther , Axel Voigt

In this paper, we study an elastic bilayer plate composed of a nematic liquid crystal elastomer in the top layer and a nonlinearly elastic material in the bottom layer. While the bottom layer is assumed to be stress-free in the flat…

Analysis of PDEs · Mathematics 2022-03-09 Sören Bartels , Max Griehl , Stefan Neukamm , David Padilla-Garza , Christian Palus

We propose an experimental method to fully characterize the energy exchange of particles during the physical vapor deposition process of thin surface layers. Our approach is based on the careful observation of perturbations of the…

Uniaxial nematic liquid crystals whose molecular orientation is subjected to a tangential anchoring on a curved surface offer a non trivial interplay between the geometry and the topology of the surface and the orientational degree of…

Soft Condensed Matter · Physics 2019-12-19 Michael Nestler , Ingo Nitschke , Hartmut Löwen , Axel Voigt

Geometric continuum models for fluid lipid membranes are considered using classical field theory, within a covariant variational approach. The approach is cast as a higher-derivative Lagrangian formulation of continuum classical field…

Mathematical Physics · Physics 2017-09-14 Riccardo Capovilla

We use the method of $\Gamma$-convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film attached to a general fixed surface in the limit of vanishing thickness. This paper generalizes the approach…

Analysis of PDEs · Mathematics 2017-05-24 Dmitry Golovaty , Alberto Montero , Peter Sternberg

Consider the flow of a thin layer of non-Newtonian fluid over a solid surface. I model the case of a viscosity that depends nonlinearly on the shear-rate; power law fluids are an important example, but the analysis here is for general…

Dynamical Systems · Mathematics 2009-11-13 A. J. Roberts