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Liquid crystal elastomers realize a fascinating new form of soft matter that is a composite of a conventional crosslinked polymer gel (rubber) and a liquid crystal. These {\em solid} liquid crystal amalgams, quite similarly to their…
Electro-hydrodynamic phenomena in liquid crystals constitute an old but still very active research area. The reason is that these phenomena play the key role in various applications of liquid crystals and due to the general interest of…
Topological defects are a ubiquitous phenomenon in diverse physical systems. In nematic liquid crystals (LCs), they are dynamic, physicochemically distinct, sensitive to stimuli, and are thereby promising for a range of applications.…
Liquid crystal droplets are of great interest from physics and applications. Rigorous mathematical analysis is challenging as the problem involves harmonic maps (and in general the Oseen-Frank model), free interfaces and topological defects…
Wrinkles commonly develop in a thin film deposited on a soft elastomer substrate when the film is subject to compression. Motivated by recent experiments [Agrawal et al., Soft Matter 8, 7138 (2012)] that show how wrinkle morphology can be…
Liquid crystals formed of bent-core molecules are exotic materials that exhibit the twist-bend nematic phase. This arises when an energetic preference for nonzero local bend distortion is accommodated via twist in the texture, resulting in…
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…
A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form…
A nematic membrane is a sheet with embedded orientational order, which can occur in biological cells, liquid crystal films, manufactured materials, and other soft matter systems. By formulating the free energy of nematic films using tensor…
The displacement of a fluid by another less viscous one in a quasi-two dimensional geometry typically leads to complex fingering patterns. In an isotropic system, dense-branching growth arises, which is characterized by repeated…
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…
Optical birefringence measurements on a rod-like liquid crystal (8OCB), imbibed in silica channels (7 nm diameter), are presented and compared to the thermotropic bulk behavior. The orientational and positional order of the confined liquid…
The surface alignment of lyotropic chromonic liquid crystals (LCLCs) can be not only planar (tangential) but also homeotropic, with self-assembled aggregates perpendicular to the substrate, as demonstrated by mapping optical retardation and…
The geometric shape, symmetry, and topology of colloidal particles often allow for controlling colloidal phase behavior and physical properties of these soft matter systems. In liquid crystalline dispersions, colloidal particles with low…
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…
The ability to manipulate polar entities with multiple external fields opens exciting possibilities for emerging functionalities and novel applications in spin systems, photonics, metamaterials, and soft matter. Liquid crystals (LCs),…
We investigate the dynamics of active nematic liquid crystals on deformable membranes, focusing on the interplay between active stress and anisotropic curvature coupling. Using a minimal model, we simulate the coupled evolution of the…
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…
The structure of liquid foams follows simple geometric rules formulated by Plateau 150 years ago. By placing such foam on a microtextured hydrophilic surface, we show that the bubble footprint exhibits a morphological transition. This…
Liquid crystal elastomers are cross-linked polymer networks covalently bonded with liquid crystal mesogens. In the nematic phase, due to strong coupling between mechanical strain and orientational order, these materials display…