Variational approach to the closure problem of turbulence theory

A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin-Fokker-Planck (LFP) model. The dynamic damping coefficient eta of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for eta to replace the divergent response equation of Kraichnan's direct-interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko = 1.2, which is compatible with the experimental data given by Gibson and Schwartz, (1963).

EQUIVALENT MODEL OF EXPANSION OF CEMENT MORTAR UNDER SULPHATE EROSION

The expansion property of cement mortar under the attack of sulfate ions is studied by experimental and theoretical methods. First, cement mortars are fabricated with the ratio of water to cement of 0.4, 0.6, and 0.8. Secondly, the expansion of specimen immerged in sulphate solution is measured at different times. Thirdly, a theoretical model of expansion of cement mortar under sulphate erosion is suggested by virtue of represent volume element method. In this model, the damage evolution due to the interaction between delayed ettringite and cement mortar is taken into account. Finally, the numerical calculation is performed. The numerical and experimental results indicate that the model perfectly describes the expansion of the cement mortar.

Size- And Temperature-Dependent Thermal Expansion Coefficient Of A Nanofilm

The thermal expansion coefficient (TEC) of an ideal crystal is derived by using a method of Boltzmann statistics. The Morse potential energy function is adopted to show the dependence of the TEC on the temperature. By taking the effects of the surface relaxation and the surface energy into consideration, the dimensionless TEC of a nanofilm is derived. It is shown that with decreasing thickness, the TEC can increase or decrease, depending on the surface relaxation of the nanofilm.

Influence of vapor transport equilibration on the crystal quality and thermal-expansion coefficients of gamma-LiAlO2

gamma-LiAlO2 (LAO) single crystal has been grown by the Czochralski method. However, its quality was deteriorated due to lithium volatilization during the crystal growth. The full width at half maximum value drops from 116.9 to 44.2 arc sec after the LAO slice was treated by vapor transport equilibration at 1000, 1100, and 1200 degrees C/48 h in sequence. The treated slice shows higher optical transmission than the as-grown one in the measured wavelength range of 190-1900 nm, meanwhile, its absorption edge exhibits a blueshift. According to Raman spectra, the treated slice has homogeneous quality at different depths from surface to 0.01 mm. The expansion coefficient of the treated slice for a axis drops from 17.2398x10(-6)/degrees C to 16.5240x10(-6)/degrees C, and that for c axis drops from 10.7664x10(-6)/degrees C to 10.0786x10(-6)/degrees C.

In situ synthesis of ZrO2/ZrW2O8 composites with near-zero thermal expansion

In this paper, ZrO2 and WO3 were used as the raw materials to prepare ZrO2/ZrW2O8 composites by in situ reaction method and the thermal expansion property of the composites was studied. This novel method included a heating step up to 1473 K for 24 h, which combines the synthesizing and sintering of ZrW2O8. The result indicates that ZrO2/ZrW2O8 composite shows near-zero thermal expansion when the weight ratio of ZrO2 and WO3 is 2.5:1. Compared with composites prepared previously by non-reactive sintering of ZrO2 and ZrW2O8, the composites show higher relative density and lower porosity.

Method for measurement of lattice parameter of cubic GaN layers on GaAs (001)

An extended technique derived from triple-axis diffraction setup was proposed to measure lattice parameters of cubic GaN(c-GaN) films. The fully relaxed lattice parameters of c-GaN are determined to be 4.5036+0.0004 Angstrom, which is closer to the values of a hypothetical perfect crystal. The speculated zero setting correction (Deltatheta) is very slight and within the range of the accuracy of measurement. Additionally, we applied this method to analyze strain of four different kinds of c-GaN samples. It is found that in-plane strain caused by large lattice mismatch and thermal expansion coefficients mismatch directly influence the epilayer growth at high temperatures, indicating that the relaxation of tensile strain after thermal annealing helps to improve the crystalline quality of c-GaN films and optical properties. (C) 2003 Elsevier Science B.V. All rights reserved.

Analysis of Si/GaAs Bonding Stresses with the Finite Element Method

In conjunction with ANSYS, we use the finite element method to analyze the bonding stresses of Si/GaAs. We also apply a numerical model to investigate a contour map and the distribution of normal stress,shearing stress,and peeling stress,taking into full consideration the thermal expansion coefficient as a function of temperature. Novel bonding structures are proposed for reducing the effect of thermal stress as compared with conventional structures. Calculations show the validity of this new structure.

Analytical method of predicating the instabilities of a micro arch-shaped beam under electrostatic loading

An arch-shaped beam with different configurations under electrostatic loading experiences either the direct pull-in instability or the snap-through first and then the pull-in instability. When the pull-in instability occurs, the system collides with the electrode and adheres to it, which usually causes the system failure. When the snap-through instability occurs, the system experiences a discontinuous displacement to flip over without colliding with the electrode. The snap-through instability is an ideal actuation mechanism because of the following reasons: (1) after snap-through the system regains the stability and capability of withstanding further loading; (2) the system flips back when the loading is reduced, i.e. the system can be used repetitively; and (3) when approaching snap-through instability the system effective stiffness reduces toward zero, which leads to a fast flipping-over response. To differentiate these two types of instability responses for an arch-shaped beam is vital for the actuator design. For an arch-shaped beam under electrostatic loading, the nonlinear terms of the mid-plane stretching and the electrostatic loading make the analytical solution extremely difficult if not impossible and the related numerical solution is rather complex. Using the one mode expansion approximation and the truncation of the higher-order terms of the Taylor series, we present an analytical solution here. However, the one mode approximation and the truncation error of the Taylor series can cause serious error in the solution. Therefore, an error-compensating mechanism is also proposed. The analytical results are compared with both the experimental data and the numerical multi-mode analysis. The analytical method presented here offers a simple yet efficient solution approach by retaining good accuracy to analyze the instability of an arch-shaped beam under electrostatic loading.

Estimation of Transverse Thermal Conductivity of Doubly-periodic Fiber Reinforced Composites

For steady-state heat conduction a new variational functional for a unit cell of composites with periodic microstructures is constructed by considering the quasi-periodicity of the temperature field and in the periodicity of the heat flux fields. Then by combining with the eigenfunction expansion of complex potential which satisfies the fiber-matrix interface conditions, an eigenfunction expansion-variational method (EEVM) based on a unit cell is developed. The effective transverse thermal conductivities of doubly-periodic fiber reinforced composites are calculated, and the first-order approximation formula for the square and hexagonal arrays is presented,which is convenient for engineering application. The numerical results show a good convergency of the presented method, even through the fiber volume fraction is relatively high. Comparisons with the existing analytical and experimental results are made to demonstrate the accuracy and validity of the first-order approximation formula for the hexagonal array.

Calculation of the bulk modulus of simple and complex crystals with the chemical bond method

The relation between the lattice energies and the bulk moduli on binary inorganic crystals was studied, and the concept of lattice energy density is introduced. We find that the lattice energy densities are in good linear relation with the bulk moduli in the same type of crystals, the slopes of fitting lines for various types of crystals are related to the valence and coordination number of cations of crystals, and the empirical expression of calculated slope is obtained. From crystal structure, the calculated results are in very good agreement with the experimental values. At the same time, by means of the dielectric theory of the chemical bond and the calculating method of the lattice energy of complex crystals, the estimative method of the bulk modulus of complex crystals was established reasonably, and the calculated results are in very good agreement with the experimental values.

Estimation thermal expansion coefficient from lattice energy for inorganic crystals

By using the study of the lattice energy and the structural parameters of binary inorganic crystals, a new parameter reflecting the thermal expansion property has been found, the relation between the linear expansion coefficient and new parameter has been established. A semiempirical method for evaluation of linear expansion coefficient from the lattice energy is presented, and developed to the complex crystals. The estimated values of the linear expansion coefficients of both simple and complex crystals are in good agreement with the experimental values.

Calculation of the thermal expansion coefficient for Bi2Sr2CaCu2O8

An estimation method of thermal expansion coefficient in term of lattice energy which was developed earlier for simple materials is extended to a complex material of Bi2Sr2CaCu2O8 (Bi-2212). The calculation of the chemical bond property and thermal expansion coefficient of Bi-2212 has been carried out and the theoretical values were in good agreement with the corresponding experimental results. The dependence of the thermal expansion coefficient on the different structures and on the flexible oxidation states of Bi and Cu are investigated. The results indicate that the thermal expansion coefficients of Bi-2212 are insensitive to the low lattice distortion of the average structure and the changes of formal valences of Bi and Cu ions.

A method to identify the collapse of monolayers at the air-water interface

The collapse behaviour of phthalocyanine monolayers at the air-water interface was studied by means of compression-expansion isotherms. Measurements of two cycles of compression-expansion isotherms of copper tetrakis (4'-benzyloxy-4-phenylsulfonylphenoxy) phthalocyanine showed that the difference in the area per molecule at target pressure between the first cycle and the second cycle was dependent on the target pressure. This difference was used to identify the collapse of monolayers at the air-water interface. The transfer behaviour of monolayers at the air-water interface onto a substrate at different target pressures was also studied.