Landau-De Gennes theory of nematic liquid crystals: the Oseen-Frank limit and beyond

From MaRDI portal
Publication:982287

DOI10.1007/s00205-009-0249-2zbMath1304.76007arXiv0812.3131OpenAlexW3105859499MaRDI QIDQ982287

Arghir Zarnescu, Apala Majumdar

Publication date: 6 July 2010

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.3131



Mathematics Subject Classification ID

Variational methods applied to problems in fluid mechanics (76M30) Liquid crystals (76A15)


Related Items

Accelerated Gradient Descent Methods for the Uniaxially Constrained Landau-de Gennes Model ⋮ Hierarchies of critical points of a Landau-de Gennes free energy on three-dimensional cuboids ⋮ Modelling and computation of liquid crystals ⋮ Nematic Liquid Crystals in a Rectangular Confinement: Solution Landscape, and Bifurcation ⋮ A novel Landau-de Gennes model with quartic elastic terms ⋮ One-Dimensional Ferronematics in a Channel: Order Reconstruction, Bifurcations, and Multistability ⋮ Tetrahedral frame fields via constrained third-order symmetric tensors ⋮ <scp>Isotropic‐Nematic</scp> Phase Transition and Liquid Crystal Droplets ⋮ Global Solutions of Nematic Liquid Crystal Flow in Dimension Two ⋮ Stationary solutions of discrete Landau-de Gennes theory: \(3 \times 3\) Q-tensor case ⋮ On partial regularity for weak solutions to the 3D co-rotational Beris-Edwards system ⋮ Optimal Control of the Landau–de Gennes Model of Nematic Liquid Crystals ⋮ Effective surface energies in nematic liquid crystals as homogenized rugosity effects ⋮ On the convergence of an IEQ-based first-order semi-discrete scheme for the Beris-Edwards system ⋮ A two-component nonlinear variational wave system ⋮ The radial hedgehog solution in the Landau-de Gennes theory: effects of the bulk potentials ⋮ Surface, size and topological effects for some nematic equilibria on rectangular domains ⋮ Continuum mechanics of line defects in liquid crystals and liquid crystal elastomers ⋮ Front Propagation at the Nematic-Isotropic Transition Temperature ⋮ Rotational elasticity and couplings to linear elasticity ⋮ Biaxiality in the asymptotic analysis of a 2D Landau−de Gennes model for liquid crystals ⋮ Function spaces for liquid crystals ⋮ Half-integer point defects in the \(Q\)-tensor theory of nematic liquid crystals ⋮ Boundary regularity of weakly anchored harmonic maps ⋮ Order Reconstruction for Nematics on Squares with Isotropic Inclusions: A Landau--De Gennes Study ⋮ Thin-film models for an active gel ⋮ Dynamic cubic instability in a 2D Q-tensor model for liquid crystals ⋮ Γ-convergence of a mean-field model of a chiral doped nematic liquid crystal to the Oseen–Frank description of cholesterics ⋮ Parameter dependent finite element analysis for ferronematics solutions ⋮ Unique continuation for stationary and dynamical \(Q\)-tensor system of nematic liquid crystals in dimension three ⋮ Global well posedness for a Q-tensor model of nematic liquid crystals ⋮ Higher dimensional Ginzburg-Landau equations under weak anchoring boundary conditions ⋮ Minimizers of the Landau-de Gennes energy around a spherical colloid particle ⋮ Instability of point defects in a two-dimensional nematic liquid crystal model ⋮ Orientability and asymptotic convergence of \(Q\)-tensor flow of biaxial nematic liquid crystals ⋮ A review of mathematical analysis of nematic and smectic-A liquid crystal models ⋮ Stability of point defects of degree \(\pm \frac{1}{2}\) in a two-dimensional nematic liquid crystal model ⋮ Dimension Reduction for the Landau--de Gennes Model: The Vanishing Nematic Correlation Length Limit ⋮ Biaxial escape in nematics at low temperature ⋮ Oseen–Frank-type theories of ordered media as the Γ-limit of a non-local mean-field free energy ⋮ Stability of half-degree point defect profiles for 2-D nematic liquid crystal ⋮ Spherical particle in nematic liquid crystal under an external field: the Saturn ring regime ⋮ Stability of the vortex defect in the Landau-de Gennes theory for nematic liquid crystals ⋮ Global Weak Solutions for the Compressible Active Liquid Crystal System ⋮ Diffusion generated methods for denoising target-valued images ⋮ Order reconstruction patterns in nematic liquid crystal wells ⋮ Disclinations in limiting Landau-de Gennes theory ⋮ Liouville theorem for the steady-state solutions of \(Q\)-tensor system of liquid crystal ⋮ Refined asymptotics for Landau-de Gennes minimizers on planar domains ⋮ Global well-posedness for the dynamical \(Q\)-tensor model of liquid crystals ⋮ Dimension reduction for the Landau-de Gennes model on curved nematic thin films ⋮ Simulation of Q-Tensor Fields with Constant Orientational Order Parameter in the Theory of Uniaxial Nematic Liquid Crystals ⋮ A fundamental improvement to Ericksen-Leslie kinematics ⋮ Thin film liquid crystals with oblique anchoring and boojums ⋮ Mean-field limit and phase transitions for nematic liquid crystals in the continuum ⋮ Revisiting the Two-Dimensional Defect-Free Azimuthal Nematic Equilibrium on an Annulus ⋮ On the convergence of an unconditionally stable numerical scheme for the Q-tensor flow based on the invariant quadratization method ⋮ Uniaxial symmetry in nematic liquid crystals ⋮ Symmetry and multiplicity of solutions in a two-dimensional Landau-de Gennes model for liquid crystals ⋮ Recent developments of analysis for hydrodynamic flow of nematic liquid crystals ⋮ Minimizers of a Landau-de Gennes energy with a subquadratic elastic energy ⋮ An elementary proof of eigenvalue preservation for the co-rotational Beris-Edwards system ⋮ Dimension reduction for the Landau-de Gennes model in planar nematic thin films ⋮ The Oseen-Frank limit of Onsager's molecular theory for liquid crystals ⋮ Order Reconstruction for Nematics on Squares and Hexagons: A Landau--de Gennes Study ⋮ Refined approximation for minimizers of a Landau-de Gennes energy functional ⋮ Recent analytic development of the dynamic \(Q\)-tensor theory for nematic liquid crystals ⋮ Pattern formation in Landau-de Gennes theory ⋮ Dynamics and flow effects in the Beris-Edwards system modeling nematic liquid crystals ⋮ On the regularity of weak small solution of a gradient flow of the Landau–de Gennes energy ⋮ Torus-like solutions for the Landau-de Gennes model. I: The Lyuksyutov regime ⋮ Weak solutions for an initial-boundary \(\mathcal{Q}\)-tensor problem related to liquid crystals ⋮ A Landau-de Gennes theory of liquid crystal elastomers ⋮ A Reduced Study for Nematic Equilibria on Two-Dimensional Polygons ⋮ Bifurcation analysis in a frustrated nematic cell ⋮ Topological singular set of vector-valued maps. I: Applications to manifold-constrained Sobolev and BV spaces ⋮ The Q-tensor model with uniaxial constraint ⋮ Saturn ring defect around a spherical particle immersed in a nematic liquid crystal ⋮ Improved partial regularity for manifold-constrained minimisers of subquadratic energies ⋮ Line defects in the small elastic constant limit of a three-dimensional Landau-de Gennes model ⋮ Remarks on uniaxial solutions in the Landau-de Gennes theory ⋮ Error analysis of Nitsche's and discontinuous Galerkin methods of a reduced Landau-de Gennes problem ⋮ On equilibrium configurations of nematic liquid crystals droplet with anisotropic elastic energy ⋮ Global existence and regularity of solutions for active liquid crystals ⋮ Uniaxial versus biaxial character of nematic equilibria in three dimensions ⋮ Stability of the melting hedgehog in the Landau-de Gennes theory of nematic liquid crystals ⋮ On the elastic energy density of constrained \(Q\)-tensor models for biaxial nematics ⋮ From microscopic theory to macroscopic theory: a systematic study on modeling for liquid crystals ⋮ Symmetry in nonlinear PDEs: some open problems ⋮ From the Q-tensor flow for the liquid crystal to the harmonic map flow ⋮ A one-dimensional variational problem for cholesteric liquid crystals with disparate elastic constants ⋮ Orientability and energy minimization in liquid crystal models ⋮ Energy dissipation and regularity for a coupled Navier-Stokes and Q-tensor system ⋮ Global well-posedness of the two dimensional Beris-Edwards system with general Laudau-de Gennes free energy ⋮ A new approach to non-isothermal models for nematic liquid crystals ⋮ Existence and uniqueness of global classical solutions of a gradient flow of the Landau-de Gennes energy ⋮ Partial regularity for minimizers of singular energy functionals, with application to liquid crystal models ⋮ Global strong solution to the three-dimensional liquid crystal flows of Q-tensor model ⋮ Global well-posedness and decay of smooth solutions to the non-isothermal model for compressible nematic liquid crystals ⋮ Topological singular set of vector-valued maps. II: \( \varGamma \)-convergence for Ginzburg-Landau type functionals ⋮ Global Strong Solutions of the Full Navier--Stokes and $Q$-Tensor System for Nematic Liquid Crystal Flows in Two Dimensions ⋮ SCALINGS AND LIMITS OF LANDAU-DE GENNES MODELS FOR LIQUID CRYSTALS: A COMMENT ON SOME RECENT ANALYTICAL PAPERS ⋮ The Saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis ⋮ Nematic-isotropic phase transition in liquid crystals: a variational derivation of effective geometric motions ⋮ Global weak solutions to the active hydrodynamics of liquid crystals ⋮ On the covergence of minimizers of singular perturbation functionals ⋮ On minimizers of a Landau-de Gennes energy functional on planar domains ⋮ Torus-like solutions for the Landau-De Gennes model ⋮ Topological singularities for vector-valued Sobolev maps and applications ⋮ On the Landau--de Gennes Elastic Energy of Constrained Biaxial Nematics ⋮ Landau-de Gennes corrections to the Oseen-Frank theory of nematic liquid crystals ⋮ Hölder regularity and convergence for a non-local model of nematic liquid crystals in the large-domain limit ⋮ A stable scheme and its convergence analysis for a 2D dynamic Q-tensor model of nematic liquid crystals ⋮ Blowup rate estimates of a singular potential and its gradient in the Landau-de Gennes theory ⋮ Solution landscape of a reduced Landau–de Gennes model on a hexagon ⋮ Pattern formation for nematic liquid crystals -- modelling, analysis, and applications ⋮ Regularity of a Gradient Flow Generated by the Anisotropic Landau--de Gennes Energy with a Singular Potential ⋮ Existence of minimizers and convergence of critical points for a new Landau-de Gennes energy functional in nematic liquid crystals ⋮ The radial-hedgehog solution in Landau–de Gennes' theory for nematic liquid crystals ⋮ Numerical study of liquid crystal elastomers by a mixed finite element method ⋮ Phase transitions in nematics: textures with tactoids and disclinations ⋮ Uniform profile near the point defect of Landau-de Gennes model ⋮ Singular perturbation of manifold-valued maps with anisotropic energy ⋮ Regularity criteria for weak solutions to the 3d co-rotational Beris-Edwards system via the pressure ⋮ On the Ginzburg-Landau free energy density of superfluid A and B phases of Helium 3 ⋮ On the long time dynamics of the Landau-De Gennes gradient flow ⋮ Local well-posedness and small Deborah limit of a molecule-based \(Q\)-tensor system ⋮ Radial symmetry on three-dimensional shells in the Landau-de Gennes theory



Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:982287&oldid=12966358"
Powered by MediaWiki