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Using the density functional formalism we derive expression for the distortion free energy for systems with continuous broken symmetry and use it to derive expression for the elastic constants of smectic phases in which director is tilted…

Soft Condensed Matter · Physics 2009-11-07 Yashwant Singh , Jokhan Ram

Disclination configurations of a nematic liquid crystal are studied within a self-consistent molecular field theory. The theory is based on a tensor order parameter, and can accommodate anisotropic elastic energies without the known…

Soft Condensed Matter · Physics 2020-08-05 Cody D. Schimming , Jorge Viñals

In arXiv:1906.09232v2, Golovaty et al. present a $Q$-tensor model for liquid crystal dynamics which reduces to the well-known Oseen-Frank director field model in uniaxial states. We study a closely related model and present an energy stable…

Numerical Analysis · Mathematics 2024-09-17 Jacob Elafandi , Franziska Weber

Motivated by problems arising in tear film dynamics, we present a model for the extensional flow of thin sheets of nematic liquid crystal. The rod-like molecules of these substances impart an elastic contribution to its response. We rescale…

Fluid Dynamics · Physics 2023-06-28 M. J. Taranchuk , L. J. Cummings , T. A. Driscoll , R. J. Braun

We consider nematic liquid crystals in a bounded, convex polyhedron described by a director field n(r) subject to tangent boundary conditions. We derive lower bounds for the one-constant elastic energy in terms of topological invariants.…

Mathematical Physics · Physics 2009-11-10 A Majumdar , JM Robbins , M Zyskin

In this paper we are interested in the Landau-de Gennes functional introduced to study the transition between the smectic and nematic phases of a liquid crystal. We define a reduced functional by constraining the director field to satisfy a…

Mathematical Physics · Physics 2009-06-04 Nicolas Raymond

We study the flat phase of nematic elastomer membranes with rotational symmetry spontaneously broken by in-plane nematic order. Such state is characterized by a vanishing elastic modulus for simple shear and soft transverse phonons. At…

Soft Condensed Matter · Physics 2009-11-10 Xiangjun Xing , Ranjan Mukhopadhyay , T. C. Lubensky , Leo Radzihovsky

This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects. The method targets minimization of the system free energy…

Numerical Analysis · Mathematics 2014-02-17 J. H. Adler , T. J. Atherton , D. B. Emerson , S. P. MacLachlan

In this work we recover the Oseen-Frank theory of nematic liquid crystals as a $\Gamma$-limit of a particular mean-field free energy as the sample size becomes infinitely large. The Frank constants are not necessarily all equal. Our…

Analysis of PDEs · Mathematics 2017-03-21 Jamie M. Taylor

We study the low-frequency, long-wavelength dynamics of soft and semi-soft nematic elastomers using two different but related dynamic theories. Our first formulation describes the pure hydrodynamic behavior of nematic elastomers in which…

Soft Condensed Matter · Physics 2009-11-10 Olaf Stenull , T. C. Lubensky

A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…

Analysis of PDEs · Mathematics 2019-02-19 Leonard Kreutz , Paolo Piovano

The nonlinear elastic properties of nematic liquid crystals have acquired new interest with the recent experimental observation of bulk modulated nematic phases which are composed by achiral molecules. We extend the Oseen-Zocher-Frank's…

Soft Condensed Matter · Physics 2018-11-09 I. Lelidis , G. Barbero

In this work, we study the nematic-isotropic phase transition based on the dynamics of the Landau--De Gennes theory of liquid crystals. At the critical temperature, the Landau--De Gennes bulk potential favors the isotropic phase and nematic…

Analysis of PDEs · Mathematics 2021-07-28 Tim Laux , Yuning Liu

In this paper we study the asymptotic behaviour via Gamma-convergence of some integral functionals which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals are defined in…

Functional Analysis · Mathematics 2007-05-23 Nadia Ansini , Francois Bille Ebobisse

We carry out a variational study for integral functionals that model the stored energy of a heterogeneous material governed by finite-strain elastoplasticity with hardening. Assuming that the composite has a periodic microscopic structure,…

Analysis of PDEs · Mathematics 2024-03-08 Elisa Davoli , Chiara Gavioli , Valerio Pagliari

We consider a continuum model describing the dynamic behavior of nematic liquid crystal elastomers (LCEs) and implement a numerical scheme to solve the governing equations. In the model, the Helmholtz free energy and Rayleigh dissipation…

Materials Science · Physics 2015-05-19 Wei Zhu , Michael Shelley , Peter Palffy-Muhoray

We derive a mathematical model of a nematic electrolyte based on a variational formulation of nematodynamics. Extending our previous work, we consider a general setup which incorporates dielectric anisotropy of the liquid-crystalline matrix…

Soft Condensed Matter · Physics 2016-07-20 O. M. Tovkach , M. Carme Calderer , Dmitry Golovaty , Oleg Lavrentovich , Noel J. Walkington

A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is studied. It was derived in a previous work as a reinforced limit when the thickness of the insulating layer covering the bottom plate tends to zero. This…

Analysis of PDEs · Mathematics 2020-04-01 Philippe Laurençot , Katerina Nik , Christoph Walker

We consider a non-local free energy functional, modelling a competition between entropy and pairwise interactions reminiscent of the second order virial expansion, with applications to nematic liquid crystals as a particular case. We build…

Analysis of PDEs · Mathematics 2021-05-27 Giacomo Canevari , Jamie M. Taylor

We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic…

Analysis of PDEs · Mathematics 2015-05-13 Apala Majumdar , Arghir Zarnescu