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We develop a theory for a generic instability of a Fermi liquid in dimension d>1 against the formation of a Luttinger-liquid-like state. The density of states at the Fermi level is the order parameter for the ensuing quantum phase…

Strongly Correlated Electrons · Physics 2013-10-01 T. R. Kirkpatrick , D. Belitz

In this work, we present three linear numerical schemes to model nematic liquid crystals using the Landau-de Gennes $\textbf{Q}$-tensor theory. The first scheme is based on using a truncation procedure of the energy, which allows for an…

Numerical Analysis · Mathematics 2024-03-27 Justin Swain , Giordano Tierra

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

We formulate a hydrodynamic theory of $p-$atic liquid crystals, namely two-dimensional anisotropic fluids endowed with generic $p-$fold rotational symmetry. Our approach, based on an order parameter tensor that directly embodies the…

Soft Condensed Matter · Physics 2022-08-17 Luca Giomi , John Toner , Niladri Sarkar

The phase-ordering kinetics of a bulk uniaxial nematic liquid crystal is addressed using techniques that have been successfully applied to describe ordering in the O(n) model. The method involves constructing an appropriate mapping between…

Condensed Matter · Physics 2009-10-30 Robert A. Wickham

We present a convergent and constraint-preserving numerical discretization of a mathematical model for the dynamics of a liquid crystal subjected to an electric field. This model can be derived from the Oseen-Frank director field theory,…

Numerical Analysis · Mathematics 2021-04-23 Franziska Weber

In this article we discuss nonstationary models for inhomogeneous liquid crystals driven out of equilibrium by flow. Emphasis is put on those models which are used in the mathematics as well as in the physics literature, the overall goal…

Soft Condensed Matter · Physics 2018-12-20 Etienne Emmrich , Sabine H. L. Klapp , Robert Lasarzik

Motivated by recent experiments, the isotropic-nematic phase transition in chromonic liquid crystals is studied. As temperature decreases, nematic nuclei nucleate, grow, and coalesce, giving rise to tactoid microstructures in an isotropic…

Soft Condensed Matter · Physics 2017-08-25 Chiqun Zhang , Amit Acharya , Noel J. Walkington , Oleg D. Lavrentovich

The deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher-Taylor leaky dielectric model. The main assumption of the…

Fluid Dynamics · Physics 2016-12-21 Debasish Das , David Saintillan

We present a general, model-independent, quantum statistical treatment of the connection between the quantum and hydrodynamical pictures of reservoir driven macroscopic systems. This treatment is centred on the large scale properties of…

Mathematical Physics · Physics 2007-10-08 Geoffrey Sewell

A statistical theory of cholesteric liquid crystals composed of short rigid biaxial molecules is presented. It is derived in the thermodynamic limit at a small density and a small twist. The uniaxial (biaxial) cholesteric phase is regarded…

Soft Condensed Matter · Physics 2009-10-21 A. Kapanowski

We introduce a new mesoscopic model for nematic liquid crystals (LCs). We extend the particle-based stochastic rotation dynamics method, which reproduces the Navier-Stokes equation, to anisotropic fluids by including a simplified…

Soft Condensed Matter · Physics 2015-05-20 Kuang-Wu Lee , Marco G. Mazza

The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly…

Analysis of PDEs · Mathematics 2015-04-07 Matthias Hieber , Jan Pruess

This letter presents a theory on the coalescence of two spherical liquid droplets that are initially stationary. The evolution of the radius of a liquid neck formed upon coalescence was formulated as an initial value problem and then solved…

Fluid Dynamics · Physics 2019-06-13 Xi Xia , Chengming He , Peng Zhang

We provide a general macrostatistical formulation of nonequilibrium steady states of reservoir driven quantum systems. This formulation is centred on the large scale properties of the locally conserved hydrodynamical observables, and our…

Mathematical Physics · Physics 2009-11-11 Geoffrey L. Sewell

Liquid crystals are materials that experience an intermediate phase where the material can flow like a liquid, but the molecules maintain an orientation order. The Frank-Oseen model is a continuum model of a liquid crystal. The model…

Numerical Analysis · Mathematics 2024-05-07 Lucas Bouck , Ricardo H. Nochetto

A theoretical analysis is presented of a nematic liquid crystal confined between substrates pat- terned with squares that promote vertical and planar alignment. Two approaches are used to eluci- date the behavior across a wide range of…

Soft Condensed Matter · Physics 2015-06-05 Candy Anquetil-Deck , Douglas J Cleaver , Timothy James Atherton

The classical theory of liquid crystal elasticity as formulated by Oseen and Frank describes the (orientable) optic axis of these soft materials by a director $\mathbf{n}$. The ground state is attained when $\mathbf{n}$ is uniform in space;…

Soft Condensed Matter · Physics 2020-01-22 Andrea Pedrini , Epifanio G. Virga

We propose a continuum tensorial model for chiral smectic C (SmC$^*$) liquid crystals using a tensor-valued order parameter $\mathbf{Q}$ to describe orientational order and a real-valued order parameter $\delta\rho$ to capture layer…

Soft Condensed Matter · Physics 2025-09-09 Jingmin Xia , Jinbing Wu , Yucen Han

The macroscopic fluctuation theory provides a complete hydrodynamic description of non-equilibrium classical diffusive systems. As a first step towards a diffusive theory of open quantum systems, we show how to construct a microscopic open…

Statistical Mechanics · Physics 2020-06-24 Ohad Shpielberg