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In this paper, we consider a 2D liquid crystal model with damping and examine some asymptotic behaviors of the strong solution. More precisely, we establish the asymptotic log-Harnack inequality for the transition semigroup associated with a simplified liquid crystal model driven by an additive degenerate noise via the asymptotic coupling method. As consequences of the asymptotic log-Harnack inequality, we derive the gradient estimate, the asymptotic irreducibility, the asymptotic strong Feller property, the asymptotic heat kernel estimate and the ergodicity.

We highlight changes to cell signaling under virus invasion (with the example of SARS-CoV-2), involving disturbance of membranes (plasma, mitochondrial, endothelial-alveolar) and of nanodomains, modulated by the cytoskeleton. Virus alters the mechanical properties of the membranes, impairing mesophase structures mediated by the fractal architecture initiated by actomyosin. It changes the topology of the membrane and its lipid composition distribution. Mechano-transduction, self-organization and topology far from equilibrium are omnipresent. We propose that the actomyosin contractility generates the cytoskeletons fractal organization. We focus on three membranar processus: The transition from lamellar configuration in cell and viral membranes to a bi-continuous organization in the presence of ethanolamine (the energy for this transition is provided by change of the folding of the viral fusion protein from metastable to stable state). The action of mitochondrial antiviral signaling protein on the external mitochondrial envelope in contact with mitochondrial-associated membranes, modified by viral endoribonuclease, distorting innate immune response. The increased permeability of the epithelial-alveolar-pulmonary barrier involves the cytoskeleton membranes. The pulmonary surfactant is also perturbed in its liquid crystal state. Viral subversion disorganizes membrane structure and functions and thus the metabolism of the cell. We advocate systematic multidisciplinary exploration of membrane mesophases and their links with fractal dynamics, to enable novel therapies for SARS-CoV-2 infection.

Rotating orthogonal polarization imaging provides images of the polarization properties of scattering media which are free from surface reflections. Previously the technique has been demonstrated using manually rotated Glan–Thompson polarizers to control and analyze the polarization state of the light entering and emerging from the tissue. This paper describes a system that performs these functions using liquid crystal retarders. The system is tested using a polarizing target embedded within a scattering medium and is compared with Monte Carlo simulations. The results compare well with those obtained with manual rotation of polarizers. The liquid crystal based approach has advantages over the previous system in terms of ease of use, speed, and repeatability and is therefore an important step towards taking the technique into routine clinical use.

Dielectric spectroscopy, at room temperature (20°C), is used to study the dielectric response of ternary mixtures of commercial nematic liquid crystal mixtures E7 and E33, an organic solvent N-Methyl-2-Pyrrolidone (NMP) and a triblock polymers in the frequency range from 0.01 Hz to 1 MHz. The results indicate a dielectric relaxation in the hectohertz region. Individually, both E7 and NMP have rather large low frequency conductivities; however, the low frequency (0.01–10 Hz) behavior of the mixtures has no such behavior. We attribute this behavior to an ion getter effect of the triblock polymer surfactant. Optimized ternary mixtures obtain a real dielectric constant near 230, and loss tangent less than 0.05 at frequencies near 10 mHz.

In this investigation, the dielectric behaviors of three ferroelectric liquid crystals (FLCs) belonging to a homologous series have been revealed in the frequency range of 10 Hz–10 MHz. FLCs used in this study are three-ring calamitic LCs, namely ($S$)-4-(((4-(octan-2-yloxy)phenyl)imino)methyl)phenyl 4-($n$-octyloxy)benzoate, ($S$)-4-(((4-(octan-2-yloxy)phenyl)imino)methyl)phenyl 4-($n$-decyloxy)benzoate and ($S$)-4-(((4-(octan-2-yloxy)phenyl)imino)methyl)phenyl 4-($n$-undecyloxy)benzoate. The polarizing optical microscopic and differential scanning calorimetric results confirm that these compounds, synthesized as per the known synthetic steps, show not only a ferroelectrically switchable chiral smectic C (SmC*) phase over a wide thermal range, but also other mesophases such as blue phase-I/II (BP-I/II), chiral nematic (N*) and unknown smectic (SmX) phases. Several essential dielectric parameters of the FLC phase have been measured at different temperatures. The relative permittivity has been measured with the variations of temperature and frequency. Besides, the dielectric loss and tan $\delta$ have been measured. Different dielectric relaxations have been calculated and explained at the molecular level. The systematic measurements revealed a strong anomaly, and crossover of relative permittivity values for the FLCs has been determined at selective frequencies between 1 kHz and 20 kHz. Strong dielectric anomaly/fall for the response function infers the involvement of collective response of dipolar assembly confined to ferroelectric Weiss domains.

As we know there are several mechanisms allowing us to convert absorbed energy by liquid crystal (LC) to the energy of reorientation of director. One of them is the third thermomechanical effect. Third thermomechanical effect induced by Gaussian beam was recently studied both theoretically and experimentally. It was shown that thermomechanical effects can decrease the threshold of Fréedericksz transition in dye-doped nematic liquid crystal (NLC). One of the big advantages of thermomechanical effect compared with other mechanisms (for instance giant optical nonlinearity (GON)), which are absent in the case of normal incidence of laser beam, is that it emerges at any angle of incidence of laser beam. Thermomechanical effects were also studied in NLC, containing azobenzene in their molecular structure. It was suggested that one of the mechanisms of optical nonlinearity observed in the experiment in such medium may be the thermomechanical effect.

Laser beam heating the medium induces instability in the liquid crystal (LC) cell. This instability in conjunction with influence of gravitational force results in convective motions in the cell. In this paper theoretical modeling for studying convection induced by Gaussian laser beam in nematic LC homeotrop and planar cells is presented for the first time. Velocity field and LC director distribution are obtained for various light powers and LC cell sizes by solving Navier-Stokes, heat transfer and director equations simultaneously. The modeling allows us to solve the problems of convections induced by Gaussian laser beam due to Rayleigh-Benard and Marangoni mechanisms as well. There is a good qualitative agreement between theoretical calculations and prior experimental results. The possibility of control and stability of convective motions are studied. Instabilities of the Benard cells are of thermal origin because the Prandtl number for the medium under study is considerably larger than unity.