Liquid crystal model of vesicle deformation in alternating electric fields

Considering the effects of osmotic pressure, elastic bending, Maxwell pressure, surface tension, as well as flexo-electric and dielectric properties of phospholipid membrane, the shape equation for sphere vesicle in alternation （AC） electric field is derived based on the liquid crystal model by minimizing the free energy due to coupled mechanical and AC electrical fields. Besides the effect of elastic bending, the influence of osmotic pressure and surface tension on the frequency dependent behavior of vesicle membrane in AC electric field is also discussed. Our theoretical results for membrane deformation are consistent with corresponding experiments. The present model provides the possibility to further disclose the frequency-depended behavior of biological cells in the coupled AC electric and different mechanical fields.

Unifying the crystallization behavior of hexagonal and square crystals with the phase-field-crystal model

By employing the phase-field-crystal models, the atomic crystallization process of hexagonal and square crystals is investigated with the emphasis on the growth mechanism and morphological change. A unified regime describing the crystallization behavior of both crystals is obtained with the thermodynamic driving force varying. By increasing the driving force,, both crystals （in the steady-state） transform from a faceted polygon to an apex-bulged polygon, and then into a symmetric dendrite. For the faceted polygon, the interface advances by a layer-by-layer （LL） mode while for the apex-bulged polygonal and the deridritic crystals, it first adopts the LL mode and then transits into the multi-layer （ML） mode in the later stage. In particular, a shift of the nucleation sites from the face center to the area around the crystal tips is detected in the early growth stage of both crystals and is rationalized in terms of the relation between the crystal size and the driving force distribution. Finally, a parameter characterizing the complex shape change of square crystal is introduced.

Elastic strain response in the modified phase-field-crystal model

To understand and develop new nanostructure materials with specific mechanical properties, a good knowledge of the elastic strain response is mandatory. Here we investigate the linear elasticity response in the modified phase-field-crystal（MPFC） model. The results show that two different propagation modes control the elastic interaction length and time, which determine whether the density waves can propagate or not. By quantitatively calculating the strain field, we find that the strain distribution is indeed extremely uniform in case of elasticity. Further, we present a detailed theoretical analysis for the orientation dependence and temperature dependence of shear modulus. The simulation results show that the shear modulus reveals strong anisotropy and the one-mode analysis provides a good guideline for determining elastic shear constants until the system temperature falls below a certain value.

Modeling and Estimation of the Kinetics of Seeded Solvent-mediated Phase Transformation in a Batch Crystallizer

Modeling the kinetics of the preparing process is necessary to produce a product with the appropriate particle properties and minimum production cost.Owing to the lackness of crystal size distributor （CSD） information,however,solvent-mediated phase transformation encounters difficulty in modeling the kinetics as compared to solution crystallization.Consequently,a model was established by making the product CSD to move along by horizontal translation to obtain the CSDs of the stable phase in the process of transformation.Then the moment method was used to solve the popular balance equation,and the least square nonlinear regression method was applied to estimate the kinetics parameters.The model has been successfully used to simulate the transformation of CaSO4？2H2O to α-CaSO4？1/2H2O in an isothermal seeded batch crystallizer with different stirring speeds,and it is beneficial to producing high performance α-CaSO4？1/2H2O crystals which have the right particle characteristics.

Applicability of Johnson-Mehl-Avrami model to crystallization kinetics of Zr_(60)Al_(15)Ni_(25) bulk amorphous alloy

The applicability of Johnson-Mehl-Avrami(JMA)model to the crystallization kinetics of Zr60Al15Ni25 bulk amorphous alloy is investigated by differential scanning calorimetry(DSC)under isochronal and isothermal conditions.A criterion xm,at which a defined function z(x)exhibits the maximum value,is introduced to check the validity of JMA model to the kinetics analysis.The value of xm has a constant of 0.632 for JMA model.It is found that the values of xm at different isothermal annealing temperatures(743,748,753 and 758 K)are almost near 0.632,which indicates that the isothermal crystallization kinetics can be modeled by JMA equation.However,the values of xm at different heating rates(10,20,30 and 40 K/min)are about 0.52,implying that JMA model is not valid to the isochronal crystallization kinetics.The reason why the JMA model is not valid to the isochronal crystallization kinetics is discussed.

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.

Plastic deformation modelling of tempered martensite steel block structure by a nonlocal crystal plasticity model

The plastic deformations of tempered martensite steel representative volume elements with different martensite block structures have been investi- gated by using a nonlocal crystal plasticity model which considers isotropic and kinematic hardening produced by plastic strain gradients. It was found that pro- nounced strain gradients occur in the grain boundary region even under homo- geneous loading. The isotropic hardening of strain gradients strongly influences the global stress-strain diagram while the kinematic hardening of strain gradi- ents influences the local deformation behaviour. It is found that the additional strain gradient hardening is not only dependent on the block width but also on the misorientations or the deformation incompatibilities in adjacent blocks.

Modelling of composite crystallization

Metal matrix composites(MMCs)have received much attention due to their promising advanced mechanical properties.The aim of this work is to create a micro-macro model of composite crystallization.The developed model is coupled with the process of heat flow in the macroscopic scale,resulting from the heat emission during the nucleation and the growth of grains.Taking into account both of these phenomena,the proposed model is distinguished by a good reflection of reality.Moreover,the presented model assumes that the function of grain density depends on the maximal supercooling and the mass volume of the reinforcement phase particles.The knowledge of the equations,describing the function of grain density depending on the degree of supercooling,is necessary in the,more and more often used,numerical modelling of the casting structure.

A MICROMECHANICAL MODEL FOR γ-TiAl BASE PST CRYSTALS

An analytical micromechanical method is proposed to examine the dependence of plastic deformation on the microstructure for a PST crystal. The sub-domain microstructure of the γ phase and the effect of the α2 phase are taken into account by a proper micromechanical formulation, the dislocation slip and twinning deformation mechanisms are considered in the context of crystal plasticity. The model can well predict the dependence of stress-strain relations on loading angle with respect to the microstructure. The influence of the twinning and lamellar spacing on the deformation behavior and biaxial yield surfaces for PST crystals are also examined.

CYCLIC DEFORMATION OF FACE CENTERED CUBIC CRYSTALS AND ITS DISLOCATION INTERACTION MODEL——Ⅱ.DISLOCATION INTERACTION MODEL OF CYCLIC DEFORMATION

A dislocation interaction model has been proposed for cyclic deformation of fcc crystals.Ac- cording to this model,cyclic stress-strain responses and saturation dislocation structures of a crystal are associated with the modes and intensities of dislocation interactions between slip systems active in the crystal; and,hence,may be predicted by the location of its tensile axis in the crystallographic triangle.This model has successfully explained the different behaviours of double-slip crystals and multi-slip behaviours of some crystals with orientations usually con- sidered as single-slip ones.

Structure defect prediction of single crystal turbine blade by dendrite envelope tracking model

The structure defects such as stray grains during unidirectional solidification can severely reduce the performance of single crystal turbine blades. A dendrite envelope tracking model is developed for predicting the structure defects of unidirectional solidification turbine blade. The normal vector of dendrite envelope is estimated by the gradient of dendrite volume fraction, and the growth velocity of the dendrite envelope (dendrite tips) is calculated with considering the anisotropy of grain growth. The solute redistribution at dendrite envelope is calculated by introducing an effective solute partition coefficient. Simulation tests show that the solute-build-up due to the rejection at envelope greatly affects grain competition and consequently solidification structure. The model is applied to predict the structure defects (e.g. stray grain) of single crystal turbine blade during unidirectional solidification. The results show that the developed model is reliable and has the following abilities: reproduce the growth competition among the different-preferential-direction grains; predict the stray grain formation; simulate the structure evolution (single crystal or dendrite grains).

Multiscale modelling and simulation of single crystal superalloy turbine blade casting during directional solidification process

As the key parts of an aero-engine,single crystal(SX)superalloy turbine blades have been the focus of much attention.However,casting defects often occur during the manufacturing process of the SX turbine blades.Modeling and simulation technology can help to optimize the manufacturing process of SX blades.Multiscale coupled models were proposed and used to simulate the physical phenomena occurring during the directional solidification(DS)process.Coupled with heat transfer(macroscale)and grain growth(meso-scale),3D dendritic grain growth was calculated to show the competitive grain growth at micro-scale.SX grain selection behavior was studied by the simulation and experiments.The results show that the geometrical structure and technical parameters had strong influences on the grain selection effectiveness.Based on the coupled models,heat transfer,grain growth and microstructure evolution of a complex hollow SX blade were simulated.Both the simulated and experimental results show that the stray grain occurred at the platform of the SX blade when a constant withdrawal rate was used in manufacturing process.In order to avoid the formation of the stray crystal,the multi-scale coupled models and the withdrawal rate optimized technique were applied to the same SX turbine blade.The modeling results indicated that the optimized variable withdrawal rate can achieve SX blade castings with no stray grains,which was also proved by the experiments.

Spin-1 Blume-Capel model with longitudinal random crystal and transverse magnetic fields:A mean-field approach

The spin-1 Blume–Capel model with transverse and longitudinal external magnetic fields h, in addition to a longitudinal random crystal field D, is studied in the mean-field approximation. It is assumed that the crystal field is either turned on with probability p or turned off with probability 1 p on the sites of a square lattice. Phase diagrams are then calculated on the reduced temperature crystal field planes for given values of γ=Ω/J and p at zero h. Thus, the effect of changing γ and p are illustrated on the phase diagrams in great detail and interesting results are observed.

Life Prediction Model for a Nickel-base Single Crystal Superalloy DD3

The possibility of a life prediction model for nickel base single crystal blades has been studied. The fatigue creep (FC) and thermal fatigue creep(TMFC) as well as creep experiments have been carried out with different hold time of DD3. The hold time and the frequency as well as the temperature range are the main factors influencing the life. An emphasis has been put on the micro mechanism of the rupture of creep, FC and TMFC. Two main factors are the voiding and degeneration of the material for the cre...

STUDY OF THE EQUILIBRIUM HCP CRYSTAL SHAPE BY THE ISING MODEL

The Isin g model is used to investigate (0001), (10^-10), (10^-11) interfaces, etc. , for the hcp lattice. The system studied here have the nearest-neighbor (NN) and next-nearest-neighbor (NNN) pair interactions. The interface energy, interface phase transition at zero temperature and roughening temperature are used to analyse the properties of these interfaces. As a special case of the hcp crystals, we give the equilibrium shape of the He crystal at T=OK.

Phase diagrams of the spin-2 Ising model in the presence of a quenched diluted crystal field distribution

We have investigated the random crystal field effects on the phase diagrams of the spin-2 Blume-Capel model for a honeycomb lattice using the effective-field theory with correlations. To do so, the thermal variations of magnetization are studied via calculating the phase diagrams of the model. We have found that the model displays both second-order and first-order phase transitions in addition to the tricritical and isolated points. Reentrant behavior is also observed for some appropriate values of certain system parameters. Besides the usual ground-state phases of the spin-2 model including ±2, ~1, and 0, we have also observed the phases ±3/2 and ±1/2, which are unusual for the spin-2 case.

Kinetic Modeling of Methylene Blue and Crystal Violet Dyes Adsorption on Alginate-Fixed Water Hyacinth in Single and Binary Systems

Removal of Methylene Blue (MB) and Crystal Violet (CV) dyes from monocomponent and binary aqueous solutions by water hyacinth-E. Crassipes roots fixed on alginate (a low-cost adsorbent) has been investigated. The extent of adsorption was evaluated as a function of solution pH, initial dye concentration, and bead biomass loading. Kinetic sorption data were analysed by widely used models: pseudo-first-order, pseudo-second-order, Elovich, and intraparticle diffusion models. The results showed that pseudo-second-order model better described the biosorption experimental data than the pseudo-first-order kinetic model for both dyes, whilst the Elovich model fitted the biosorption experimental data at lower dye concentrations. The intraparticle diffusion model indicated that sorption of CV and MB was characterized by rapid surface adsorption coupled with slow film diffusion process at higher initial dye concentration and at all initial bead biomass loading. The range of mean free energy values confirmed physical adsorption as the mechanism for dye removal from solution.

A novel method of rapidly modeling optical properties of actual photonic crystal fibres

The flexible structure of photonic crystal fibre not only offers novel optical properties but also brings some difficulties in keeping the fibre structure in the fabrication process which inevitably cause the optical properties of the resulting fibre to deviate from the designed properties. Therefore, a method of evaluating the optical properties of the actual fibre is necessary for the purpose of application. Up to now, the methods employed to measure the properties of the actual photonic crystal fibre often require long fibre samples or complex expensive equipments. To our knowledge, there are few studies of modeling an actual photonic crystal fibre and evaluating its properties rapidly. In this paper, a novel method, based on the combination model of digital image processing and the finite element method, is proposed to rapidly model the optical properties of the actual photonic crystal fibre. Two kinds of photonic crystal fibres made by Crystal Fiber A/S are modeled. It is confirmed from numerical results that the proposed method is simple, rapid and accurate for evaluating the optical properties of the actual photonic crystal fibre without requiring complex equipment.

Al-doping influence on crystal growth of Ni–Al alloy: Experimental testing of a theoretical model

Recently, a condensing potential model was developed to evaluate the crystallization ability of bulk materials [Ye X X, Ming C, Hu Y C and Ning X J 2009 J. Chem. Phys. 130 164711 and Peng K, Ming C, Ye X X, Zhang W X, Zhuang J and Ning X J 2011 Chem. Phys. Lett. 501 330], showing that the best temperature for single crystal growth is about0.6Tm, where Tm is the melting temperature, and for Ni–Al alloy, more than 6 wt% of Al-doping will badly reduce the crystallization ability. In order to verify these predictions, we fabricated Ni–Al films with different concentrations of Al on Si substrates at room temperature by pulsed laser deposition, and post-annealed the films at 833, 933, 1033（- 0.6Tm）,1133, and 1233 K in vacuum furnace, respectively. The x-ray diffraction spectra show that annealing at 0.6Tm is indeed best for larger crystal grain formation, and the film crystallization ability remarkably declines with more than 6-wt% Al doping.