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.

Crystallization behaviors of bayerite from sodium chromate alkali solutions

In order to clean production of chromium compounds, it is a critical process to remove aluminates and utilize aluminum compounds from artificial chromate alkali solutions. The effects of Na2 Cr O4 on the neutralization curve, Al（OH）3 precipitation efficiency and induction period of bayerite were investigated. The results indicate that the neutralization curve of the artificial chromate alkali solutions shows three distinct regions and its induction period is longer than that of pure sodium aluminate solutions at the same aluminum concentration. And the decreased temperature and volume fraction of CO2 enhance the particle size of bayerite β-Al（OH）3. Bayerite composed of agglomerates of rods and cone frustums was obtained from alkali metal chromate solutions with 28.5% CO2（volume fraction） at temperatures ranging from 50 °C to 70 °C. Coarse bayerite with particle size（d50） from 24.2 μm to 29.3 μm extremely has few impurities, which is suitable for comprehensive utilization.

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.

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.

Model of apparent crystal growth rate and kinetics of seeded precipitation from sodium aluminate solution

Based on the population balance equation in a batch crystallizer characteristic of seeded precipitation, a model to calculate the rate of apparent crystal growth of aluminum hydroxide from the size distribution was deve- loped. The simulation results indicate that the rate of apparent crystal growth during seeded precipitation exhibits a manifest dependence on the crystal size. In general, there is an obvious increase in the apparent crystal growth rate with the augment in crystal size. The apparent activation energy increases with the increase of characteristic crystal size, which indicates that the growth of small crystals is controlled by surface chemical reaction; it is gradually controlled by both the surface reaction and diffusion with the augment in crystal size.

Kinetics of crystal growth on seeded precipitation of sodium aluminate solutions with new device

A new device was designed,which can effectively avoid the undesired nucleation and agglomeration of fine particles on the experimental results during the sead ed precipitation of sodium aluminate solution,and moreover,the experimental co nditions are nearly kept constant during the experiment. With the new device,it is proven that a good result can be obtained on the kinetics study of the cryst al growth in seeded precipitation of sodium aluminate solution.Experiments were carried out with the concentration of Na2O （Nk）170 g/L,the mole ratio of Na2O to Al2O3 （αk） all between 1.52 to 2.01,at 65,70,75 ℃,respectively. And the kinetics equation of crystal growth of gibbsite was deduc ed.

ON GLOBAL BEHAVIOR OF WEAK SOLUTIONS OF COMPRESSIBLE FLOWS OF NEMATIC LIQUID CRYSTALS

In this article, we investigate the global behavior of weak solutions of a simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals in time in a bounded three-dimension domain-arbitrary forces. By adapting the arguments for the compressible Navier-Stokes equations, and carefully analyzing the direction field of liquid crystals in the equations of angular momentum, we show the existence of bounded absorbing sets, global bounded trajectories, and global attractors to weak solutions of compressible flows of nematic liquid crystals with the adiabatic constant γ〉5/3.

The stress field and energy of screw dislocation in smectic A liquid crystals and the mistakes of the classical solution

The mistakes in the classical solution of a screw dislocation in smectic A liquid crystals are pointed out. A serious problem with the well-known theory is pointed, which may be named de Gennes-Kleman-Pershan paradox and has existed for many decades in the scientific community of liquid crystal study. The correct solution is given in this paper by a simplest, elementary, and straight forward method. In connection with this, the stress field and energy of dislocation are discussed in detail. The present article provides the correct stress field and dislocation energy as well.

Facile synthesis of single-crystalline rutile TiO_2 nano-rods by solution method

A convenient and scalable technique for the synthesis of rutile titanium dioxide(TiO2) nano-rods was presented by using bulk TiO2 powder, sodium hydroxide(NaOH) and distilled water as raw materials. X-ray diffraction(XRD) and field emission scanning electron microscopy(FESEM) studies indicate that the prepared sample is crystalline and free from any impurities, however, it has no distinct shape and possesses a huge degree of agglomeration, and the average crystal size is around 40 nm. After annealing the sample at 600 °C for 2 h, it is observed through FESEM that nano-rods are formed. And XRD analysis shows that the nano-rods are single crystalline with distinct and smooth surfaces in different sizes with average length of about 1 μm and diameter of about 80 nm. Further UV-visible spectroscopy and Raman studies were conducted for the prepared sample and the band gap of the final product is found to be 3.40 eV.

Study on Solution Crystallization of Musk Ketone and Musk Xylene

The ternary phase diagrams of musk ketone, musk xylene and various solvent were obtained by calcu- lations. Moreover, the double saturated lines were found to be curve for the first time. The methods to separate eutectic mixtures of musks by solution crystallization were suggested on the basis of these phase diagrams. A new process was proposed to get musk ketone and musk xylene from the eutectics by adding acetonitrile and heptane in turn, which was verified by experiments. Musk xylene with purity of 97.50% and musk ketone with purity of 98.10% were obtained.

Stability of Crystal Growth Face and Dissolution Face in Crystallization from Solution under Microgravity

The stability of the shapes of crystal growth face and dissolution face in a two-dimensional mathematical model of crystal growth from solution under microgravity is studied. It is proved that the stable shapes of crystal growth face and dissolution face do exist, which are suitably shaped curves with their upper parts inclined backward properly.The stable shapes of crystal growth faces and dissolution faces are calculated for various values of parameters, Ra, Pr and Sc. It is shown that the stronger the convection relative to the diffusion in solution is, the more backward the upperparts of the stable crystal growth face and dissolution face are inclined. The orientation and the shape of dissolution face hardly affect the stable shape of crystal growth face and vice versa.

Science Letters:New solutions of shear waves in piezoelectric cubic crystals

Acoustic wave propagation in piezoelectric crystals of classes 43m and 23 is studied. The crystals Tl3VS4 and Tl3TaSe4 （43m） of the Chalcogenide family and the crystal Bi12TiO20 （23） possess strong piezoelectric effect. Because the surface Bleustein-Gulyaev waves cannot exist in piezoelectric cubic crystals, it was concluded that new solutions for shear-horizontal surface acoustic waves （SH-SAWs） are found in the monocrystals using different electrical boundary conditions such as electrically ＂short＂ and ＂open＂ free-surfaces for the unique [ 101 ] direction of wave propagation. For the crystal Tl3TaSe4 with coefficient of electromechanical coupling （CEMC） Ke^2=e^2/（C×g）-1/3, the phase velocity Vph for the new SH-SAWs can be calculated with the following formula： Vph=（Vα＋Vt）/2, where Vt is the speed of bulk SH-wave, Vt=Vt4（1＋Ke^2）^1/2, Vα=αKVt4, αK=2[Ke（1＋Ke^2）^1/2-Ke^2]^1/2, and Vt4=（C44/p）^1/2. It was found that the CEMC K2 evaluation for Tl3TaSe4 gave the value of K^2=2（Vf-Vm）/Vf-0.047 （-4.7%）, where Vf-848 m/s and Vm-828 m/s are the new-SAW velocities for the free and metallized surfaces, respectively. This high value of KZ（Tl3TaSe4） is significantly greater than K2（Tl3VS4）-3% and about five times that of K2（Bi12YiO20）.

Crystal Structure and Solution Structural Dynamic Feature of 1,8-Dibenzoyl-2,7-Dimethoxynaphthalene

The crystal structure and the dynamic feature of molecular structure in solution for 1,8-dibenzoyl-2,7-dimethoxynaph-thalene are revealed by X-ray crystallographic analysis and VT-NMR measurements. In crystal, the molecule of the title compound is located on a twofold rotation axis. The two benzoyl groups are situated in an opposite direction. The dihedral angle between the mean planes of the phenyl ring and the naphthalene ring system is 80.25(6). The benzene ring and carbonyl moiety in each benzoyl group are almost coplanar. The molecular packing is stabilized by weak C–H…O hydrogen bonds and aπ-πstacking interaction between the benzene rings [centroid-centroid and interplanar distances of 3.6383(10) and 3.294 , respectively]. In solution, the temperature-dependent rotation behavior of the C–C bond between the benzene ring and the ketonic carbonyl group has been observed by1H VT-NMR measurements. Furthermore, comparison of the C–C bond rotation behavior between the benzene ring and the carbonyl group with 1-ben-zoyl-2,7-dimethoxynaphthalene has clarified that the C–C bond between the ketonic carbonyl group and the naphthalene ring rotates slower than the 1,8-dibenzoylated homologue.

Fractal Interpretation of Ultrasonic Crystallization of Solutions

Experiments were performed on the crystallization of a CuSO4 solution upon the action of the temperature gradient with the forming of mono crystals three wedges crystal system （prisms）. We found that the fractal dimension of crystals equals 2.45, which is consistent with the literature data. Crystal growth is represented as the N-rd translation of each side of the crystal lattice with its own speed and with relation to the formation of similar structures--fractals. A mathematical model of ultrasonic crystallization of a CuSO4 solution was proposed. The model is based on the combined use of differential transport equations of momentum, mass, energy and sound waves and a method of similarity and dimensional analysis. The calculated formulas for the concentration of Ccr, the equivalent diameter of the formed crystals dcr and the intensity of internal energy source Ф, associated with the interaction of crystals with the hydro mechanical, heat and sound fields were obtained. Fractal interpretation of ultrasonic crystallization of the CuSO4 solution was made. It was found that on the growth of crystal size d^r directly affects translation N, i.e., an increase in the number of sets of crystals of infinitely small size e, correspond to the size of the crystal lattice. In turn, translation of crystals depends on the geometry of the crystallizer and the physical parameters of external force fields, acting on the CuSO4 solution. A connection of results of the mathematical modeling with the results of fractal analysis of the ultrasonic crystallization of solutions was established.

Experimental Study on Preparation of Natural Gas Hydrate by Crystallization

In this paper, the saturated solution crystallization method is proposed to promote the formation of hydrate by means of the known similarities between the hydrate formation process and the crystallization process. In this method,adding the second phase crystals was used to replace the spontaneous formation of hydrate crystal nuclei to form hydrate.The effects of saturated Na_2SO_4, MgSO_4, NH_4HCO_3 and CuSO_4 solutions on the formation rates of natural gas hydrate and gas storage capacity were investigated. The results showed that the saturated solution had an influence on the hydrate formation process. Under the given experimental conditions, the saturated Na_2SO_4 solution showed a highest increase in the hydrate formation rate, and the average hydrate formation rate in its presence was 11.8 times higher than that obtained in the deionized water. Moreover, the largest formation rate of gas hydrates observed in the saturated Na_2SO_4 solution was 386 times bigger than that in the deionized water, and the gas storage capacity increased by 10 times. In addition, the average hydrate formation rate in the saturated Mg SO_4 solution was faster than that in water by 20 times. The largest formation rate of gas hydrates in the saturated MgSO_4 solution was 165 times faster than that obtained in the deionized water, and the gas storage capacity increased by 6.2 times. The saturated NH_4HCO_3 and saturated CuSO_4 solutions also influenced the formation process of hydrate. Therefore, the crystallization method of saturated solution can be used to achieve a highefficiency preparation of natural gas hydrates, which provides theoretical guidance for the storage of natural gas in the form of hydrate.

Phase Diagram, Growth and Optical Property of the LaBWO_6 Crystal

The phase diagram, growth and optical property of LaBWO6 crystal are reported. LaBWO6 crystal melts congruently at 1078 ℃. Based on the pseudo-ternary phase diagram of LaBWO6-（Li2WO4/LiF） -B203, the LaBWO6 crystals have been firstly grown by the flux method. LaBWO6 crystal crystallizes in the orthorhombic system, space group P222 with a = 4.1, b = 10.31 and c = 21.71 A. LaBWO6 Crystal exhibits high transparency in a range from 327 to 1100 nm. The absorption edge of the crystal in the UV range is at 293 nm. The SHG efficient of LaBWO6 crystal is 0.3 times as large as that of the KDP crystal.

Electrochemical Performance of Zn（002） and Zn（100） Single Crystals in 6.0mol·L^-1 KOH

In this article, the electrochemical performance of the electrodes of zinc polycrystal, Zn（002） and Zn（100） single crystals were studied by the Tafel line extrapolation of the potentio-dynamic polarization curves, the cyclic voltammetry and the charge/discharge experiment. The results shows that in 6.0 mol·L^-1 KOH solution the corrosion rate of Zn polycrystal, Zn（100） and Zn（002） single crystals decreases in turn; and the reversibility and the charge/discharge performance of Zn single crystal was superior to Zn polycrystal. The dendrite growth of the surface of Zn polycrvstal was easier than Zn single crystal during the stages of charge/discharge.

Growth and Solvent Effects of a Promising Nonlinear Optical Sodium Paranitrophenolate Dihydrate (NO_2-C_H_4-ONa·2H_2O) Single Crystal

Sodium paranitrophenolate dihydrate (NPNa·2H2O) is an excellent semiorganic nonlinear optical (NLO) material, crystallizes both in water and methanol with high degree of transparency. Good optical quality single crystals of dimension upto 18 mm×6 mm×3 mm are obtained by isothermal solvent evaporation technique. The solubility of the crystal in different solvents was measured gravimetrically. The single crystals of NPNa·2H2O show variation in physical properties and growth rate in different solvents. Methanol or ethanol solution yields crystals of bipyramidal shape with clear morphology. However, methanol grown crystal is exhibiting improved hardness parameters and possesses excellent thermal stability as compared to water grown crystals. The effects of solvent on hardness parameter along with thermal and optical properties of NPNa·2H2O was revealed in this paper.

Pulsation Treatment on the Modification of Crystal with Cold Simulation

Since the separation of crystal of KCl saturated aqueous is similar to the crystallization of liquid metals, the melts nucleation can be simulated by the experiment of the crystal of salt aqueous solution. In this experiment pulsation treatment was imposed on KCl saturated aqueous in order to study the effect of pulsation treatment on crystallization in the salt solution, and the influence of different pulsation treating time, super-heating and bine of prescription were investigated. The results show that it is possible to modify the crystallization over satured solution temperature and the degree of under-cooling for salt crystal separation was reduced by applying pulse treating on KCl saturated aqueous solution. In addition, this technology may generate embryos for nucleation even at the temperature over melting point or satured solubility.

Growth and Characterization of a New Semi-Organic Nonlinear Optical Crystal: Thiosemicarbazide Cadmium Acetate

A new semi-organic nonlinear optical thiosemicarbazide cadmium acetate (TSCA) material has been synthesized. TSCA single crystals were grown from aqueous solution by slow evaporation method. The solubility of TSCA has been determined for various temperatures. The grown crystals were characterized by single crystal X-ray diffraction (XRD), FTIR, UV-Vis., thermal and second harmonic generation (SHG) analysis. Single crystal XRD study has been carried out to identify the lattice parameters. FTIR studies confirm the functional groups present in the grown crystal. Optical transmission studies have confirmed that the grown crystal is highly transparent. Thermogravimetric and differential thermal analyses reveal the good thermal stability of the material. The SHG conversion efficiency of TSCA was determined using Kurtz powder technique and found two times that of potassium dihydrogen orthophosphate (KDP).