Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field

Self-oscillating systems abound in the natural world and offer substantial potential for applications in controllers,micro-motors,medical equipments,and so on.Currently,numerical methods have been widely utilized for obtaining the characteristics of self-oscillation including amplitude and frequency.However,numerical methods are burdened by intricate computations and limited precision,hindering comprehensive investigations into self-oscillating systems.In this paper,the stability of a liquid crystal elastomer fiber self-oscillating system under a linear temperature field is studied,and analytical solutions for the amplitude and frequency are determined.Initially,we establish the governing equations of self-oscillation,elucidate two motion regimes,and reveal the underlying mechanism.Subsequently,we conduct a stability analysis and employ a multi-scale method to obtain the analytical solutions for the amplitude and frequency.The results show agreement between the multi-scale and numerical methods.This research contributes to the examination of diverse self-oscillating systems and advances the theoretical analysis of self-oscillating systems rooted in active materials.

ENERGY CONSERVATION FOR THE WEAK SOLUTIONS TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOW

In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.

THE EXISTENCE AND UNIQUENESS OF TIME-PERIODIC SOLUTIONS TO THE NON-ISOTHERMAL MODEL FOR COMPRESSIBLE NEMATIC LIQUID CRYSTALS IN A PERIODIC DOMAIN

In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.

Multi-dimensional multiplexing optical secret sharing framework with cascaded liquid crystal holograms

Secret sharing is a promising technology for information encryption by splitting the secret information into different shares.However,the traditional scheme suffers from information leakage in decryption process since the amount of available information channels is limited.Herein,we propose and demonstrate an optical secret sharing framework based on the multi-dimensional multiplexing liquid crystal(LC)holograms.The LC holograms are used as spatially separated shares to carry secret images.The polarization of the incident light and the distance between different shares are served as secret keys,which can significantly improve the information security and capacity.Besides,the decryption condition is also restricted by the applied external voltage due to the variant diffraction efficiency,which further increases the information security.In implementation,an artificial neural network(ANN)model is developed to carefully design the phase distribution of each LC hologram.With the advantage of high security,high capacity and simple configuration,our optical secret sharing framework has great potentials in optical encryption and dynamic holographic display.

WEAK-STRONG UNIQUENESS FOR THREE DIMENSIONAL INCOMPRESSIBLE ACTIVE LIQUID CRYSTALS

The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.

Flat multifunctional liquid crystal elements through multi-dimensional information multiplexing

Flat optical elements have attracted enormous attentions and act as promising candidates for the next generation of optical components.As one of the most outstanding representatives,liquid crystal(LC)has been widely applied in flat panel display industries and inspires the wavefront modulation with the development of LC alignment techniques.However,most LC elements perform only one type of optical manipulation and are difficult to realize the multifunctionality and light integration.Here,flat multifunctional liquid crystal elements(FMLCEs),merely composed of anisotropic LC molecules with space-variant orientations,are presented for multichannel information manipulation by means of polarization,space and wavelength multiplexing.Specifically,benefiting from the unique light response with the change of the incident polarization,observation plane,and working wavelength,a series of FMLCEs are demonstrated to achieve distinct near-and far-field display functions.The proposed strategy takes full advantage of basic optical parameters as the decrypted keys to improve the information capacity and security,and we expect it to find potential applications in information encryption,optical anti-counterfeiting,virtual/augmented reality,etc.

A review of liquid crystal spatial light modulators:devices and applications

Spatial light modulators,as dynamic flat-panel optical devices,have witnessed rapid development over the past two decades,concomitant with the advancements in micro-and opto-electronic integration technology.In particular,liquid-crystal spatial light modulator(LC-SLM)technologies have been regarded as versatile tools for generating arbitrary optical fields and tailoring all degrees of freedom beyond just phase and amplitude.These devices have gained significant interest in the nascent field of structured light in space and time,facilitated by their ease of use and real-time light manipulation,fueling both fundamental research and practical applications.Here we provide an overview of the key working principles of LC-SLMs and review the significant progress made to date in their deployment for various applications,covering topics as diverse as beam shaping and steering,holography,optical trapping and tweezers,measurement,wavefront coding,optical vortex,and quantum optics.Finally,we conclude with an outlook on the potential opportunities and technical challenges in this rapidly developing field.

Singularity Formation forthe General Poiseuille Flow of Nematic Liquid Crystals

We consider the Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model.The model is described by a coupled system consisting of a heat equation and a quasilinear wave equation.In this paper,we will construct an example with a finite time cusp singularity due to the quasilinearity of the wave equation,extended from an earlier resultonaspecial case.

Dptic properties of bile liquid crystals in human body

AIM To further study the properties of bileliquid crystals,and probe into the relationshipbetween bile liquid crystals and gallbladderstone formation,and provide evidence for theprevention and treatment of cholecystolithiasis.METHODS The optic properties of bile liquidcrystals in human body were determined by themethod of crystal optics under polarizingmicroscope with plane polarized light andperpendicular polarized light.RESULTS Under a polarizing microscope withplane polarized light,bile liquid crystalsscattered in bile appeared round,oval orirregularly round.The color of bile liquidcrystals was a little lighter than that of the bilearound.When the stage was turned round,thecolor of bile liquid crystals or the darkness andlightness of the color did not change obviously.On the border between bile liquid crystals andthe bile around,brighter Becke-Line could beobserved.When the microscope tube is lifted,Becke-Line moved inward,and when lowered,Becke-Line moved outward.Under aperpendicular polarized light,bile liquid crystalsshowd some special interference patterns,called Malta cross.When the stage was turninground at an angle of 360°,the Malta cross showed four times of extinction.In the vibratingdirection of 45° angle of relative to upper andlower polarizing plate,gypsum test-board withoptical path difference of 530 nm was inserted,the first and the third quadrants of Malta crossappeared to be blue,and the second and thefourth quadrants appeared orange.When micatest-board with optical path difference of 147 nmwas inserted,the first and the third quadrants ofMalta cross appeared yellow,and the secondand the fourth quadrants appeared dark grey.CONCLUSION The bile liquid crystals weredistributed in bile in the form of global grains.Their polychroism and absorption were slight,but the edge and Becke-Line were very clear.Itsrefractive index was larger than that of the bile.These liquid crystals were uniaxial positivecrystals.The interference colors were the firstorder grey-white.The double refractive index ofthe liquid crystals was △n=0.011-0.015.

Synthesis and characterization of non-symmetrical liquid crystals containing a cholesteryl ester moiety

In this paper, a series of chiral non-symmetrical liquid crystals （nBA-chol） consisting of a cholesteryl ester moiety as chiral entity and a biphenyl aromatic core with different terminal alkyl chain has been synthesized and investigated for their liquid crystalline properties. Effects of numbers of methylene units in the terminal alkyl chain on the phase transition temperatures and on the temperature-dependent pitch lengths of the chiral liquid crystals have been studied. The long terminal alkyl chain tends to exhibit smectic A mesophases. The pitch lengths of the cholesteric mesophases of the chiral liquid crystals decrease with increasing temperature and with increasing numbers of methylene units in the terminal alkyl chain, respectively.

GLOBAL EXISTENCE OF WEAK SOLUTIONS TO THE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS IN 2D

In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many ＂singular＂ times, at which the energy concentration occurs and the director field losses its second order derivatives.

Facile synthesis and characterization of novel thermo-chromism cholesteryl-containing hydrogen-bonded liquid crystals

Two series of novel cholesteryl-containing H-bonded liquid crystals were prepared through facile self-assembly between cholesteryl isonicotinate （proton acceptor） exhibiting a monotropic cholesteric phase, and the 4-alkoxy-benzoic acid or 4-alkoxy cinnamic acid （proton donor）. It was found that the increase of the conjugate length as well as the terminal length can contribute to enhance the interaction of molecules and thus significantly influenced the thermal behaviors of H-bonded LCs. The cholesteric reflection spectra of the induced mesogenic complexes were located in the visible region with the color tuneable thermo-sensitivity, which could be used for display application.

Mechanical model study of relationship of molecular configuration and multiphase in liquid crystal materials

A mechanical model of liquid crystals （LCs） is applied to study the polymorphism of homologous series of terphenyl compounds. With a senti-experimental molecular orbit method, we calculate the moment of inertia which represents the rotation state to describe the phase transition temperature obtained from experimental data. We propose a novel explanation of the phase sequence or polymorphism of LC materials using the two key parameters, the moment of inertia and critical rotational velocity. The effect of molecular polarity on the appearance of liquid crystalline is also discussed.

Microstructure - properties relationship of transient liquid phase diffusion bonded a third generation single crystal super alloy joint

Microstructure of transient liquid phase( TLP) diffusion bonded a third generation single crystal superalloy joint was investigated using scanning electron microscopy( SEM),and mechanical properties test of joint was carried out,for obtaining relationship between microstructure and mechanical properties of joint. The results showed that the joint contained bonding zone and base metal. The diffusion zone was obviously observed. When it was not finished for isothermal solidification process,the bonding zone would contain isothermal solidification zone and rapid solidification zone. Metallographic examination revealed that isothermal solidification zone was consisted of γ and γ' phase. Rapid solidification zone was consisted of two different structures,which were ternary eutectic of borides,γ and γ' phase developing at the edge of joint,binary eutectic of γ and γ' phase appearing in the portion of joint. When it was not enough for homogenization process under the condition of finishing isothermal solidification process,the bonding zone would contain isothermal solidification zone and borides at the interface. Under the conditions of relatively high welding temperature and long welding time,average tensile strength of joint was equivalent to that of parent material.

Diffractive characteristics of the liquid crystal spatial light modulator

The liquid crystal spatial light modulator （LC SLM） is very suitable for wavefront correction and optical testing and can produce a wavefront with large phase change and high accuracy. The LC SLM is composed of thousands of pixels and the pixel size and shape have effects on the diffractive characteristics of the LC SLM. This paper investigates the pixel effect on the phase of the wavefront with the scalar diffractive theory. The results show that the maximum optical path difference modulation is 41μm to produce the paraboloid wavefront with the peak to valley accuracy better than λ/10. Effects of the mismatch between the pixel and the period, and black matrix on the diffraction efficiency of the LC SLM are also analysed with the Fresnel phase lens model. The ability of the LC SLM is discussed for optical testing and wavefront correction based on the calculated results. It shows that the LC SLM can be used as a wavefront corrector and a compensator.

Retinal axial focusing and multi-layer imaging with a liquid crystal adaptive optics camera

With the help of adaptive optics （AO） technology, cellular level imaging of living human retina can be achieved. Aiming to reduce distressing feelings and to avoid potential drug induced diseases, we attempted to image retina with dilated pupil and froze accommodation without drugs. An optimized liquid crystal adaptive optics camera was adopted for retinal imaging. A novel eye stared system was used for stimulating accommodation and fixating imaging area. Illumination sources and imaging camera kept linkage for focusing and imaging different layers. Four subjects with diverse degree of myopia were imaged. Based on the optical properties of the human eye, the eye stared system reduced the defocus to less than the typical ocular depth of focus. In this way, the illumination light can be projected on certain retina layer precisely. Since that the defocus had been compensated by the eye stared system, the adopted 512 × 512 liquid crystal spatial light modulator （LC-SLM） corrector provided the crucial spatial fidelity to fully compensate high-order aberrations. The Strehl ratio of a subject with -8 diopter myopia was improved to 0.78, which was nearly close to diffraction-limited imaging. By finely adjusting the axial displacement of illumination sources and imaging camera, cone photoreceptors, blood vessels and nerve fiber layer were clearly imaged successfully.

Coupled vibrations and frequency shift of compound system consisting of quartz crystal resonator in thickness-shear motions and micro-beam array immersed in liquid

The dynamic characteristics of a quartz crystal resonator（QCR） in thicknessshear modes（TSM） with the upper surface covered by an array of micro-beams immersed in liquid are studied. The liquid is assumed to be inviscid and incompressible for simplicity. Dynamic equations of the coupled system are established. The added mass effect of liquid on micro-beams is discussed in detail. Characteristics of frequency shift are clarified for different liquid depths. Modal analysis shows that a drag effect of liquid has resulted in the change of phase of interaction（surface shear force）, thus changing the system resonant frequency. The obtained results are useful in resonator design and applications.

Synthesis of azobenzene-containing liquid crystalline gelator for use in liquid crystal gels

A liquid crystalline gelator containing the azobenzene chromophore was synthesized for the first time; it was used to form self- assembled network in nematic liquid crystals resulting in liquid crystal gels with distinct features.

Synthesis and Characterization of A Novel Cholesteric Liquid Crystalline Containing Carboxyl Group

A novel liquid crystal compound with a carboxyl group at one end, cholest-5-en-3-ol- (3β) hydrogen decanedioate (1) was successfuly prepared by the reaction of cholesterol with sebacoyl chloride. Its chemical structure and liquid crystalline properties were characterized by FTIR, CNMR, 1HNMR, POM and DSC. The compound with an active carboxyl group shows 13 themortropic liquid crystalline behaviour.

Relationship between Multi-Phase Formation and Molecular Structure for Liquid Crystal System

4 mechanical model of liquid crystals （ LCs ） was used to explain the phase formation and thermal properties . The LC plusses in the model are micro- machine systems consisting of an ensemble of molecular rotors, and some dynamie parameters in a semi-experiment molecular orbit method. A novel explanation on the multi-phase formation of LC system is obtained. It is found that the value of the critical rotational velueity is a key parameter for the characterization of each homologous series. The dipole moment of the molecules was also discussed.