A second-order dynamic subgrid-scale stress model

A second-order dynamic model based on the general relation between the subgrid-scale stress and the velocity gradient tensors was proposed. A priori test of the second-order model was made using moderate resolution direct numerical simulation date at high Reynolds number ( Taylor microscale Reynolds number R-lambda = 102 similar to 216) for homogeneous, isotropic forced flow, decaying flow, and homogeneous rotating flow. Numerical testing shows that the second-order dynamic model significantly improves the correlation coefficient when compared to the first-order dynamic models.

High order asymptotic field for plane stress crack problem

This paper presents an exact analysis for high order asymptotic field of the plane stress crack problem. It has been shown that the second order asymptotic field is not an independent eigen field and should be matched with the elastic strain term of the first order asymptotic field. The second order stress field ahead of the crack tip is quite small compared with the first order stress field. The stress field ahead of crack tip is characterized by the HRR field. Hence the J integral can be used as a criterion for crack initiation.

An application of adjoint variational method to the capillary instability in liquid

In this paper, applying the direct variational approach of first-order approximation to the capillary instability problem for the eases of rotating liquid column, toroid and films on both sides of cylinder, we have obtained the necessary and sufficient conditions for motion stability of the "cylindrical coreliquid-liquid-cylindrical shell" systems. The results obtained before are found to be special cases of the present investigation. At the same time, we have explained physical essence of rotating instability and settled a few disputes in previous investigations.

Displacive To Order-Disorder Two-Step Phase Transition Model For Para-Ferroelectric Transition

Two-step phase transition model, displacive to order-disorder, is proposed. The driving forces for these two transitions are fundamentally different. The displacive phase transition is one type of the structural phase transitions. We clearly define the structural phase transition as the symmetry broking of the unit cell and the electric dipole starts to form in the unit cell. Then the dipole-dipole interaction takes place as soon as the dipoles in unit cells are formed. We believe that the dipole-dipole interaction may cause an order-disorder phase transition following the displacive phase transition. Both structural and order-disorder phase transition can be first-order or second-order or in between. We found that the structural transition temperatures can be lower or equal or higher than the order-disorder transition temperature. The para-ferroelectric phase transition is the combination of the displacive and order-disorder phase transitions. It generates a variety of transition configurations along with confusions. In this paper, we discuss all these configurations using our displacive to order-disorder two-step phase transition model and clarified all the confusions.

Modelling and simulation of the second-order Doppler error of a laser dual-frequency interferometer

Only the first- order Doppler frequency shift is considered in current laser dual- frequency interferometers; however; the second- order Doppler frequency shift should be considered when the measurement corner cube ( MCC) moves at high velocity or variable velocity because it can cause considerable error. The influence of the second- order Doppler frequency shift on interferometer error is studied in this paper, and a model of the second- order Doppler error is put forward. Moreover, the model has been simulated with both high velocity and variable velocity motion. The simulated results show that the second- order Doppler error is proportional to the velocity of the MCC when it moves with uniform motion and the measured displacement is certain. When the MCC moves with variable motion, the second- order Doppler error concerns not only velocity but also acceleration. When muzzle velocity is zero the second- order Doppler error caused by an acceleration of 0.6g can be up to 2.5 nm in 0.4 s, which is not negligible in nanometric measurement. Moreover, when the muzzle velocity is nonzero, the accelerated motion may result in a greater error and decelerated motion may result in a smaller error.

Design of high-efficiency diffraction gratings based on rigorous coupled-wave analysis for 800nm wavelength

We report on the design of a high diffraction efficiency multi-layer dielectric grating with wide incident angle and broad bandwidth for 800 nm. The optimized grating can achieve > 95% diffraction efficiency in the first order at an incident angle of 5 degrees from Littrow and a wavelength from 770nm to 830 nm, with peak diffraction efficiency of > 99.5% at 800 nm. The electric field distribution of the optimized multi-layer dielectric grating within the gratings ridge is 1.3 times enhancement of the incidence light, which presents potential high laser resistance ability. Because of its high-efficiency, wide incident, broad bandwidth and potential high resistance ability, the multi-layer dielectric grating should have practical application in Ti:sapphire laser systems.

功能菌剂的混合发酵研究

随着化工行业的发展，大量有毒有害难降解有机物随工业废水的排放进入环境，这些物质能够在环境中长期存在、积累和扩散，通过食物链对动植物的生存及人类的健康造成不良影响。本文以苯酚、对氯硝基苯、氯苯和十六烷为模拟污染物，以前期研制的功能菌剂为对象，经过紫外线线诱变筛选出优于出发菌株的功能菌，对诱变后功能菌的理化性能进行了研究，对菌种进行了鉴定，在此基础上，就其相互之间的微生态关系进行研究，为混合发酵提供理论基础，并就其最佳发酵条件及发酵参数进行了研究，最后对发酵产品的性能进行了检测。目前，国内外有关功能菌剂的研究还存在多方面的不足，主要包括：①由于多菌种混合发酵过程较为复杂，各菌之间存在复杂的相互作用，影响因素较多，关于菌种之间的相互关系研究得很少，环境功能菌剂的发酵方法大多采用单独发酵后混合的方式。单独发酵对原材料、设备和能源的利用率较低，对于多菌种制剂发酵，在设备、能源和原材料的方面造成的浪费更大，将会大幅增加菌剂的生产成本，影响多菌种功能菌剂的发展；②功能菌剂生产过程的质量控制方面研究得较少；③功能菌剂产品的稳定性、抗冲击性能研究得较少，对环境微生物制剂的研究主要集中在菌种选育和培养条件优化方面。 通过本论文研究，得到以下主要结论。 （1）在紫外线诱变处理中，用紫外线对发生一定程度退化的出发菌株进行诱变处理后，六株具有高效降解性能的菌株被筛选出来，诱变筛选出的菌株形态和ERIC-PCR指纹图谱与出发菌株相比发生了明显改变；而且诱变后的菌株对目标难降解底物的降解能力均得到改善，其中，FPN、FCB、F14、FEm对目标底物的降解率提高了20%以上；诱变后菌株经过7次连续传代接种后，对目标难降解底物的降解率无显著变化，具有一定的遗传稳定性。并对诱变后的功能菌进行了初步的鉴定，这6株菌都分别是芽孢杆菌。 （2）对诱变后的功能菌相互之间的微生态关系进行了研究，通过抑菌实验、生长量以及基质消耗量的比较，确定它们之间的生长关系是无害共栖关系，可以进行混合发酵。 （3）对该功能菌剂进行发酵培养条件研究，结果表明发酵培养基的最佳成分（g/L）：葡萄糖 31.0g/L、玉米粉10.0g/L、磷酸氢二钾1.0g/L、硫酸铵1.1g/L、硫酸镁0.55g/L。通过研究不同的培养条件对菌体生长和降解性能的影响，确定了最佳培养条件：培养基初始pH7.5；最适温度32℃；培养基装液量125mL（250 mL三角瓶），以及培养时间对降解性能的影响，培养20 h的产物对降解最为有利。通过研究添加不同目标污染物对菌体生长和降解性能的影响，确定了添加目标污染物的最佳量以及最佳时间：苯酚投加量：1.125 g/L，对氯硝基苯投加量：0.1 g/L；最佳投加时间为发酵培养开始后4 h。 （4）以摇瓶分批发酵最优条件为基础，对FPN、F10、FCB、FNa、F14 和 FEm进行了摇瓶分批发酵试验。以摇瓶分批发酵试验数据为依据，对功能菌剂分批发酵动力学进行了研究，建立了菌体生长和基质消耗的动力学模型，拟合模型能较好的反映功能菌剂分批发酵过程。 （5）功能菌剂和活性污泥协同作用，可以提高系统的生物降解能力，功能菌剂投加量为2%，新鲜活性污泥3500 mg/L，降解24 h条件下，功能菌剂和活性污泥的协同作用对COD的去除率和对照组相比，最多的提高了36.8%。功能菌剂和活性污泥协同作用以及活性污泥的单独作用，其生物降解过程均符合一级反应动力学过程，功能菌剂和活性污泥协同作用的生物降解动力学方程为：，相关系数97%。采用SBR运行方式，引入功能菌剂的SBR系统明显能够改善和提高生物降解的效率。与仅有活性污泥的系统相比，系统对COD的平均去除率可以提高27.1%，同时，系统的耐负荷冲击以及耐毒害冲击的性能比仅有活性污泥的SBR系统强，特别是负荷冲击对引入功能菌剂的SBR系统影响很小。仅有活性污泥的SBR系统经过负荷冲击和毒害冲击之后，不能恢复到冲击之前的水平，而且系统有效作用时间的周期比引入功能菌剂的SBR系统相比大大缩短，而引入功能菌剂的SBR系统处理效果较为稳定，恢复能力很强。 Along with the development of industries, many recalcitrant organic chemicals have been discharged into natural environments together with wastewaters and can exist in waters, soil and sediments for a long time without degradation. These haz-ardous substances, their byporducts and metabolizabilities can be highly toxic, mu-tagenic and carcinogenic, thereby threatening animals, plants and human health through food chain. Consequently the removal of these compounds is of significant interest in the area of wastewater treatment. In this dissertation, the phenol, hydro-quinone, chlorobenzene and hexadecane treated as the model pollutants, the func-tional microorganism agent was used as the starting strains, they treated with ultra-violet light, and then the mutant strains with high degradation ability were screened out and identified primarily, the relationship between these stains were studied, the medium composition and fermentation conditions were optimized, the degradation ability of the fermented production was tested. The literature survey indicates that the study of the microorganism agent is far from complete and more information is re-quired on following problems. 1, Because of the complexity of relationship in mixed fermentation and the complicated factors, the study is hardly to process.2, There is a lack of information on the quality control of the producing process .3, And there is a lack of information on the stability about the microorganism agent. In this dissertation, the main results of the present study could be summarized as follows: (1)The degenerate starting strains were treated with the ultraviolet light, and six mutant strains with high biodegradation ability were screened out by using the me-dium with selective pressure of model pollutants. The mutant strains had great changes in colonialmorphology and ERIC-PCR fingerprinting. And the mutant strains got obvious advantages over the starting strains in degradation ability and over 20% improvement of removal rates was achieved for FPN、FCB、F14 and FEm. The de-gradation ability of the mutant strains was stable after seven generations. After that, the mutant strains were primarily identified as bacillus respectively. (2) The relationship between these mutant strains was studied. By the compari-son of antibiosis effect, biomass and consumption of substrate, the relationships were neutralism and they could be mixed fermented. (3) The optimized cultivation conditions were as follows: glucose 31.0 g/L, corn power 10 g/L, K2HPO4 1.0 g/L, (NH4)2SO4 1.1 g/L, MgSO4 0.55 g/L, initial pH7.5, temperature 32℃, working volume 125 mL/250 mL, and cultivation time 20h (con-sidering the time effect on degradation ability), adding pollutants phenol (1.125 g/L) and hydroquinone (0.1 g/L) into the broth at 4 h after cultivation. (4) Based on the above optimum condition, the batch fermentation was per-formed with strains FPN, F10, FCB, FNa, F14 and FEm in shake flask. The batch fermentation kinetics was studied based on the experimental data. Two kinetic models were constructed which could reflect the regularity of growth and substrate consump-tion in the process of batch fermentation. (5) The co-operation of functional microorganism agent and activated sludge could raise biodegradation of system by adding some microorganism agent and 3500 mg/L fresh activated sludge. Bioaugumentation by the addition of high effective deg-radation culture enhanced the treatment effect of SBR system and the COD removal rate was increased by 20%-36.8%. Its biodegradation matched first-order dynamical reaction equation, and the reaction equation was ln0.2327.391ct=−+. The micro-organism agent had the effect of optimization to activated sludge micro-ecosystem. The SBR system adding 2% microorganism agent, the average COD removal rate of that was increased by 27.1% and stronger anti-shock ability to load and toxicant were achieved (compared with SBR system just adding activated sludge). Especially the load-shock has barely effect to the SBR system adding microorganism agent. After the load and toxicant shock, the SBR system just adding activated sludge couldn’t come back to original level and the activated sludge micro-ecosystem was frustrated. The applying of microorganism agent increased biological activity and system’s re-sistance ability to load shock and toxicant shock.

APPLICATION OF ULTRAMICROELECTRODES IN STUDIES OF HOMOGENEOUS CATALYTIC REACTIONS .3. THE CONDITION FOR QUASI-1ST AND 2ND-ORDER HOMOGENEOUS CATALYTIC REACTIONS AT ULTRAMICRODISK ELECTRODES IN THE STEADY-STATE

The conditions for quasi-first and second order homogeneous catalytic reactions and their variation with each other at an ultramicrodisk electrode in the steady state are discussed in this paper. The order of reaction can be controlled by changing the dimension of the ultramicroelectrode: the second order reaction can be changed to quasi-first by decreasing the dimension of the ultramicroelectrode. An example of this is given. The main factor effect on the reaction order is the dimension of the ultramicroelectrode. The K4Fe(CN)6-aminopyrine system is selected to confirm the theory, the experiments showing that the system is a second order reaction at a 432 mum microelectrode, and a quasi-first order reaction at a 19 mum ultramicroelectrode. The kinetic constant of the system can be determined by applying the previous theory of homogeneous catalytic reaction.

Second-order Stokes solutions for internal waves in three-layer density-stratified fluid

In this paper, internal waves in three-layer stratified fluid are investigated by using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. As expected, the first-order solutions are consistent with ordinary linear theoretical results, and the second-order solutions describe the second-order modification on the linear theory and the interactions between the two interfacial waves. Both the first-order and second-order solutions derived depend on the depths and densities of the three-layer fluid. It is also noted that the solutions obtained from the present work include the theoretical results derived by Umeyama as special cases.

Representation of microscale ocean wavenumber spectrum correct to the second order

In this paper, the analytical representations of four wave source functions in high-frequency spectrum range are given on the basis of ocean wave theory and dimensional analysis, and the perturbation method is used to solve the governing equations of ocean wave high-frequency spectrum on the basis of the temporally stationary and locally homogeneous scale relations of microscale wave. The microscale ocean wavenumber spectrum correct to the second order has an explicit structure, its first order part represents the equilibrium between different source functions, and its second order part represents the contribution of microscale wave propagation.

Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.

Perturbational Finite Volume Method For The Solution of 2-D Navier-Stokes Equations on Unstructured and Structured Colocated Meshes

Based on the first-order upwind and second-order central type of finite volume( UFV and CFV) scheme, upwind and central type of perturbation finite volume ( UPFV and CPFV) schemes of the Navier-Stokes equations were developed. In PFV method, the mass fluxes of across the cell faces of the control volume (CV) were expanded into power series of the grid spacing and the coefficients of the power series were determined by means of the conservation equation itself. The UPFV and CPFV scheme respectively uses the same nodes and expressions as those of the normal first-order upwind and second-order central scheme, which is apt to programming. The results of numerical experiments about the flow in a lid-driven cavity and the problem of transport of a scalar quantity in a known velocity field show that compared to the first-order UFV and second-order CFV schemes, upwind PFV scheme is higher accuracy and resolution, especially better robustness. The numerical computation to flow in a lid-driven cavity shows that the under-relaxation factor can be arbitrarily selected ranging from 0.3 to 0. 8 and convergence perform excellent with Reynolds number variation from 102 to 104.

An analysis of collective damage for short fatigue cracks based on equilibrium of crack numerical density

Collective damage of short fatigue cracks was analyzed in the light of equilibrium of crack numerical density. With the estimation of crack growth rate and crack nucleation rate, the solution of the equilibrium equation was studied to reveal the distinct feature of saturation distribution for crack numerical density. The critical time that characterized the transition of short and long-crack regimes was estimated, in which the influences of grain size and grain-boundary obstacle effect were investigated. Furthermore, the total number of cracks and the first order of damage moment were discussed.

Plastic constitutive behavior of short-fiber/particle reinforced composites

A cylindrical cell model based on continuum theory for plastic constitutive behavior of short-fiber/particle reinforced composites is proposed. The composite is idealized as uniformly distributed periodic arrays of aligned cells, and each cell consists of a cylindrical inclusion surrounded by a plastically deforming matrix. In the analysis, the non-uniform deformation field of the cell is decomposed into the sum of the first order approximate field and the trial additional deformation field. The precise deformation field are determined based on the minimum strain energy principle. Systematic calculation results are presented for the influence of reinforcement volume fraction and shape on the overall mechanical behavior of the composites. The results are in good agreement with the existing finite element analyses and the experimental results. This paper attempts to stimulate the work to get the analytical constitutive relation of short-fiber/particle reinforced composites.

A Lagrangian for von Karman Equations of Large Deflection Problem of Thin Circular Plate

By the semi-inverse method proposed by He, a Lagrangian is established for the large deflection problem of thin circular plate. Ritz method is used to obtain an approximate analytical solution of the problem. First order approximate solution is obtained, which is similar to those in open literature. By Mathematica a more accurate solution can be deduced.