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Anisotropic fluids, such as nematic liquid crystals, can form non-spherical equilibrium shapes known as tactoids. Predicting the shape of these structures as a function of material parameters is challenging and paradigmatic of a broader…

Numerical Analysis · Mathematics 2025-02-04 James H. Adler , Anca S. Andrei , Timothy J. Atherton

In this paper, we propose a systematic way of liquid crystal modeling to build connection between microscopic theory and macroscopic theory. A new Q-tensor theory based on Onsager's molecular theory which leads to liquid crystals with…

Analysis of PDEs · Mathematics 2015-06-16 Jiequn Han , Yi Luo , Wei Wang , Pingwen Zhang

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

In this paper, we consider the Q-tensor model of nematic liquid crystals, which couples the Navier-Stokes equations with a parabolic-type equation describing the evolution of the directions of the anisotropic molecules, in the half-space.…

Analysis of PDEs · Mathematics 2025-11-07 Daniele Barbera , Miho Murata , Yoshihiro Shibata

A generalized notion of a nonlocal tensor order parameter is introduced within the framework of the phenomenological approach. This parameter has the form of a traceless tensor correlation function or a tensor integral operator. Based on…

Soft Condensed Matter · Physics 2017-07-14 Alexey N. Kudryavtsev , Petr A. Purtov , Sergey I. Trashkeev

A complex non-Newtonian fluid models the nematic liquid crystal flows confined in a bounded domain in $\mathbb{R}^3$ is considered. The system is a forced incompressible Navier-Stokes equation coupled with a parabolic type Q-tensor flows.…

Analysis of PDEs · Mathematics 2017-01-17 Yao Xiao

Liquid crystal networks exploit the coupling between the responsivity of liquid-crystalline mesogens, e.g., to electric fields, and the (visco)elastic properties of a polymer network. Because of this, these materials have been put forward…

Soft Condensed Matter · Physics 2021-12-01 Guido L. A. Kusters , Nicholas B. Tito , Cornelis Storm , Paul van der Schoot

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

We study nematic liquid crystal configurations in confined geometries within the continuum Landau--De Gennes theory. These nematic configurations are mathematically described by symmetric, traceless two-tensor fields, known as…

Analysis of PDEs · Mathematics 2009-07-01 Apala Majumdar

Machine learning algorithms have been available since the 1990s, but it is much more recently that they have come into use also in the physical sciences. While these algorithms have already proven to be useful in uncovering new properties…

Computational Physics · Physics 2020-05-13 Higor Y. D. Sigaki , Ervin K. Lenzi , Rafael S. Zola , Matjaz Perc , Haroldo V. Ribeiro

We present a numerical method, based on a tensor order parameter description of a nematic phase, that allows fully anisotropic elasticity. Our method thus extends the Landau-de Gennes $\mathbf{Q}$-tensor theory to anisotropic phases. A…

Soft Condensed Matter · Physics 2021-05-28 Cody D. Schimming , Jorge Viñals , Shawn W. Walker

Small-scale liquid flows on solid surfaces provide convincing details in liquid animation, but they are difficult to be simulated with efficiency and fidelity, mostly due to the complex nature of the surface tension at the contact front…

Graphics · Computer Science 2018-11-07 Rajaditya Mukherjee , Qingyang Li , Zhili Chen , Shicheng Chu , Huamin Wang

This manuscript establishes a pathway to reconstruct material parameters from measurements within the Landau-de Gennes model for nematic liquid crystals. We present a Bayesian approach to this inverse problem and analyse its properties…

Numerical Analysis · Mathematics 2025-10-15 Heiko Gimperlein , Ruma R. Maity , Apala Majumdar , Michael Oberguggenberger

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

We discuss a 3D model describing the time evolution of nematic liquid crystals in the framework of Landau-de Gennes theory, where the natural physical constraints are enforced by a singular free energy bulk potential proposed by J.M. Ball…

Analysis of PDEs · Mathematics 2012-07-09 Eduard Feireisl , Elisabetta Rocca , Giulio Schimperna , Arghir Zarnescu

We consider the one-constant Landau - de Gennes model for nematic liquid crystals. The order parameter is a traceless tensor field $\mathbf{Q}$, which is constrained to be uniaxial: $\mathbf{Q} = s (\mathbf{n}\otimes\mathbf{n} - d^{-1}…

Numerical Analysis · Mathematics 2019-11-12 Juan Pablo Borthagaray , Ricardo H. Nochetto , Shawn W. Walker

We propose an efficient numerical scheme, based on the method of lines, for solving the Landau-de Gennes equations describing the relaxational dynamics of nematic liquid crystals. Our method is computationally easy to implement, balancing…

Soft Condensed Matter · Physics 2009-11-13 A. K. Bhattacharjee , Gautam I. Menon , R. Adhikari

A systematic analysis of defect textures in facetted nanoparticles with polygonal configurations embedded in a nematic matrix is performed using the Landau-de Gennes model, homeotropic strong anchoring in a square domain with uniform…

Materials Science · Physics 2013-11-22 Paul M. Phillips , N. Mei , Ezequiel R. Soule , Linda Reven , Alejandro D. Rey

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

Modeling and simulation studies using a high-order Landau-de Gennes type model for the direct isotropic/smectic-A liquid crystal transition are presented showing the existence of meta-stable nematic pre-ordering under certain conditions, in…

Soft Condensed Matter · Physics 2009-06-29 Nasser Mohieddin Abukhdeir , Alejandro D. Rey