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The optical properties of liquid crystals serve as the basis for display, diagnostic, and sensing technologies. Such properties are generally controlled by relying on electric fields. In this work, we investigate the effects of microfluidic…

In this paper, we investigate an optimal boundary control problem for a two dimensional simplified Ericksen--Leslie system modelling the incompressible nematic liquid crystal flows. The hydrodynamic system consists of the Navier--Stokes…

Analysis of PDEs · Mathematics 2023-07-28 C. Cavaterra , E. Rocca , H. Wu

The theory of turbulent Newtonian fluids turns out that the choice of the boundary condition is a relevant issue, since it can modify the behavior of the fluid by creating or avoiding a strong boundary layer. In this work we study…

Analysis of PDEs · Mathematics 2017-05-03 Nikolai Chemetov , Fernanda Cipriano

We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in $\mathbb{R}^2$. We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a…

Analysis of PDEs · Mathematics 2023-08-09 Yannick Sire , Yantao Wu , Yifu Zhou

We study the equilibrium configuration of a nematic liquid crystal bounded by a rough surface. The wrinkling of the surface induces a partial melting in the degree of orientation. This softened region penetrates the bulk up to a length…

Soft Condensed Matter · Physics 2007-05-23 Paolo Biscari , Stefano Turzi

In this paper, we investigate the Cauchy problem for the incompressible nematic liquid crystal flows in three-dimensional whole space. First of all, we establish the global existence of solution by energy method under assumption of small…

Analysis of PDEs · Mathematics 2015-01-27 Jincheng Gao , Qiang Tao , Zheng-an Yao

In this paper, we consider a simplified Ericksen-Leslie model for the nematic liquid crystal flow. The evolution system consists of the Navier-Stokes equations coupled with a convective Ginzburg-Landau type equation for the averaged…

Analysis of PDEs · Mathematics 2013-05-07 Maurizio Grasselli , Hao Wu

We present a lattice Boltzmann algorithm for liquid crystal hydrodynamics. The coupling between the tensor order parameter and the flow is treated consistently allowing investigation of a wide range of non-Newtonian flow behavior. We…

Soft Condensed Matter · Physics 2007-05-23 Colin Denniston , E. Orlandini , J. M. Yeomans

We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible nematic liquid crystal flows on the whole space $\mathbb{R}^{2}$ with vacuum as far field density. It is proved that the 2D nonhomogeneous…

Analysis of PDEs · Mathematics 2017-10-20 Lin Li , Qiao Liu , Xin Zhong

In this article, we study Stochastic mass critical nonlinear Schr\"odinger equations with a multiplicative noise in 3D with a slight time decay ($\langle t \rangle^{-\epsilon}$), and prove associated space-time bound and scattering…

Analysis of PDEs · Mathematics 2020-10-22 Chenjie Fan , Zehua Zhao

In this paper, we investigate the Cauchy problem for the compressible nematic liquid crystal flows in three-dimensional whole space. First of all, we establish the time decay rates for compressible nematic liquid crystal flows by the method…

Analysis of PDEs · Mathematics 2015-03-11 Jincheng Gao , Qiang Tao , Zheng-an Yao

We analyze the existence and stability of two-component vector solitons in nematic liquid crystals for which one of the components carries angular momentum and describes a vortex beam. We demonstrate that the nonlocal, nonlinear response…

Optics · Physics 2015-05-13 Zhiyong Xu , Noel F. Smyth , Antonmaria A. Minzoni , Yuri S. Kivshar

We present explicit expressions of the helicity conservation in nematic liquid crystal flows, for both the Ericksen-Leslie and Landau-de Gennes theories. This is done by using a minimal coupling argument that leads to an Euler-like equation…

Soft Condensed Matter · Physics 2010-10-18 François Gay-Balmaz , Cesare Tronci

We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can…

We study a simplified system of the original Ericksen--Leslie equations for the flow of nematic liquid crystals. This is a coupled non-parabolic dissipative dynamic system. We show the convergence of global classical solutions to single…

Analysis of PDEs · Mathematics 2010-11-04 Hao Wu

We summarise some recent results on solution landscapes for two-dimensional (2D) problems in the Landau--de Gennes theory for nematic liquid crystals. We study energy-minimizing and non energy-minimizing solutions of the Euler--Lagrange…

Soft Condensed Matter · Physics 2021-08-02 Yucen Han , Apala Majumdar

We report hybrid lattice Boltzmann (HLB) simulations of the hydrodynamics of an active nematic liquid crystal sandwiched between confining walls with various anchoring conditions. We confirm the existence of a transition between a passive…

Soft Condensed Matter · Physics 2009-11-13 D. Marenduzzo , E. Orlandini , M. E. Cates , J. M. Yeomans

This work aims to control the dynamics of certain non-Newtonian fluids in a bounded domain of $\mathbb{R}^d$, $d=2,3$ perturbed by a multiplicative Wiener noise, the control acts as a predictable distributed random force, and the goal is to…

Optimization and Control · Mathematics 2025-02-19 Yassine Tahraoui , Fernanda Cipriano

In this paper we provide a sufficient condition, in terms of the horizontal gradient of two horizontal velocity components and the gradient of liquid crystal molecular orientation field, for the breakdown of local in time strong solutions…

Analysis of PDEs · Mathematics 2016-05-03 Jihong Zhao

We analyse the influence of a surface viscosity on the orientational dynamics of a nematic liquid crystal subjected to an oscillatory Couette flow. Approximate analytical solutions of nematohydrodynamic equations for small flow amplitudes…

Soft Condensed Matter · Physics 2007-05-23 I. Sh. Nasibullayev , A. P. Krekhov , M. V. Khazimullin