Elasticity, stability, and ideal strength of beta-SiC in plane-wave-based ab initio calculations

On the basis of the pseudopotential plane-wave method and the local-density-functional theory, this paper studies energetics, stress-strain relation, stability, and ideal strength of beta-SiC under various loading modes, where uniform uniaxial extension and tension and biaxial proportional extension are considered along directions [001] and [111]. The lattice constant, elastic constants, and moduli of equilibrium state are calculated and the results agree well with the experimental data. As the four SI-C bonds along directions [111], [(1) over bar 11], [11(1) over bar] and [111] are not the same under the loading along [111], internal relaxation and the corresponding internal displacements must be considered. We find that, at the beginning of loading, the effect of internal displacement through the shuffle and glide plane diminishes the difference among the four Si-C bonds lengths, but will increase the difference at the subsequent loading, which will result in a crack nucleated on the {111} shuffle plane and a subsequently cleavage fracture. Thus the corresponding theoretical strength is 50.8 GPa, which agrees well with the recent experiment value, 53.4 GPa. However, with the loading along [001], internal relaxation is not important for tetragonal symmetry. Elastic constants during the uniaxial tension along [001] are calculated. Based on the stability analysis with stiffness coefficients, we find that the spinodal and Born instabilities are triggered almost at the same strain, which agrees with the previous molecular-dynamics simulation. During biaxial proportional extension, stress and strength vary proportionally with the biaxial loading ratio at the same longitudinal strain.

Interferometric Measurement of Density in Nonstationary Shock Wave Reflection Flow and Comparison with CFD

We present density measurements from the application of interferometry and Fourier transform fringe analysis to the problem of nonstationary shock wave reflection over a semicircular cylinder and compare our experimental measurements to theoretical results from a CFD simulation of the same problem. The experimental results demonstrate our ability to resolve detailed structure in this complex shock wave reflection problem, allowing visualization of multiple shocks in the vicinity of the triple point, plus visualization of the shear layer and an associated vortical structure. Comparison between CFD and experiment show significant discrepancies with experiment producing a double Mach Reflection when CFD predicts a transitional Mach reflection.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Abel Inversion of Axially-Symmetric Shock Wave Flows

Finite-fringe interferograms produced for axisymmetric shock wave flows are analyzed by Fourier transform fringe analysis and an Abel inversion method to produce density field data for the validation of numerical models. For the Abel inversion process, we use basis functions to model phase data from axially-symmetric shock wave structure. Steady and unsteady flow problems are studied, and compared with numerical simulations. Good agreement between theoretical and experimental results is obtained when one set of basis functions is used during the inversion process, but the shock front is smeared when another is used. This is because each function in the second set of basis functions is infinitely differentiable, making them poorly-suited to the modelling of a step function as is required in the representation of a shock wave.

An analysis of subgrid-resolved scale interactions with use of results from direct numerical simulations

Subgrid nonlinear interaction and energy transfer are analyzed using direct numerical simulations of isotropic turbulence. Influences of cutoff wave number at different ranges of scale on the energetics and dynamics have been investigated. It is observed that subgrid-subgrid interaction dominates the turbulent dynamics when cut-off wave number locates in the energy-containing range while resolved-subgrid interaction dominates if it is in the dissipation range; By decomposing the subgrid energy transfer and nonlinear interaction into 'forward' and 'backward' groups according to the sign of triadic interaction, we find that individually each group has very large contribution, but the net of them is much smaller, implying that tremendous cancellation happens between these two groups.

Characters of Surface Deformation and Surface Wave in Thermal Capillary Convection

In the field of fluid mechanics, free surface phenomena is one of the most important physical processes. In the present research work, the surface deformation and surface wave caused by temperature difference of sidewalls in a rectangular cavity have been investigated. The horizontal cross-section of the container is 52 mmx42 mm, and there is a silicon oil layer of height 3.5 mm in the experimental cavity. Temperature difference between the two side walls of the cavity is increased gradually, and the flow on the liquid layer will develop from stable convection to un-stable convection. An optical diagnostic system consisting of a modified Michelson interferometer and image processor has been developed for study of the surface deformation and surface wave of thermal capillary convection. The Fourier transformation method is used to interferometer fringe analysis. The quantitative results of surface deformation and surface wave have been calculated from a serial of the interference fringe patterns.The characters of surface deformation and surface wave have been obtained. They are related with temperature gradient and surface tension. Surface deformation is fluctuant with time, which shows the character of surface wave. The cycle period of the wave is 4.8 s, and the amplitudes are from 0 to 0.55 mu m. The phase of the wave near the cool side of the cavity is opposite and correlative to that near the hot side. The present experiment proves that the surface wave of thermal capillary convection exists on liquid free surface, and it is wrapped in surface deformation.

Numerical Analysis on Intermittent Flow in a Longitudinal Section of Bingham Fluid along a Slope

The transition process of intermittent flow in a longitudinal section of Bingham fluid from initial distribution to fully developed state was numerically investigated in this paper. The influences of slope dimensionless runoff Q* and viscosity μ0* on the dimensionless surge speed U* were also presented in a wide range of parameters. By one typical example, the intermittent flow possessed wave characteristics and showed a supercritical flow conformation for a fully developed flow. The distributions of gravity and bed drag along the flow path and the velocity distribution of flow field were also analyzed.

The Optical Methods on Measuring Surface Deformation and Surface Wave in The Thermal Capillary Convection

An optical diagnostic system consisting of the Michelson interferometer with the image processor has been developed for the study of the kinetics of the thermal capillary convection. The capillary convection, surface deformation, surface wave and the velocity field in a rectangular cavity with different temperature's sidewalls have been investigated by optical interference method and PIV technique. In order to calculate the surface deformation from the interference fringe, Fourier transformation is used to grating analysis. The quantitative results of the surface deformation and surface wave have been calculated from the interference fringe pattern.

Analysis of instability of a cylindrical soap film of finite dimensions

By means of experiments of instability of a uniform cylindrical soap film, Boys had showed that the bubble molded by the film is unstable when its length is greater than its circumference. Recently that is generally called the Rayleigh Criterion. In this paper, a linear theory in hydrodynamics is applied to analyze the stability of the cylindrical soap film supported by two equal size disks; all conditions of the stationary wave on the end plates of two disks are given. From here we get that the Rayleigh Criterion on the stability of the cylindrical soap film is proved.

Moment Tensor Analysis of the Acoustic Emission Source in the Rock Damage Process

To further investigate the mechanism of acoustic emission (AE) in the rock fracture experiment, moment tensor analysis was carried out. The AE sources characterized by crack sizes, orientations and fracture modes, are represented by a time-dependent momen

Shear deformation analysis on laser-induced reverse bulging and plugging

A new kind of failure mode is observed in circular brass foils in which their peripheries are fixed and their surfaces are subjected to a long pulsed laser over a central region. The failure is classified into three stages; they are referred to as thermal bulging, localized shear deformation and perforation by plugging. A distinct feature of the failure mode is that bulging and plugging occurred in the direction opposite to the incident laser beam. To study the failure mode, we investigate the non-linear response of heated, non-homogeneous circular plates. Based on the large deflection equations of Berger [J. Appl. Mech. 22 (3), 465-472 (1965)], Ohnabe and Mizuguchi [Int. J. Non-Linear Mech. 28 (4), 365-372 (1993)] and the parabolic shear deformation theory of Bhimaraddi and Stevens [J. Appl. Mech. 51 (1), 195-198 (1984)], we have derived new coupled governing equations of shear deformation and deflection. The new equations are solved, for the plate with a clamped edge, by the Galerkin and iterative methods. The numerical results for the shear deformation distribution are in good agreement with the experimental observation.

Hill Instability Analysis Of Tlp Tether Subjected To Combined Platform Surge And Heave Motions

This paper presents the Hill instability analysis of Tension Leg Platform (TLP) tether it, deep sea. The 2-D nonlinear beam model which is Undergoing Coupled axial and transverse vibrations, is applied. The governing equations are reduced to nonlinear Hill equation by use of the Galerkin's method and the modes superposition principle. The Hill instability charted Lip to large parameters is obtained. An important parameter M is defined and can he expressed as the functions of tether length, the platform surge and heave motion amplitudes. Some example studies are performed for various environmental conditions. The results demonstrate that the nonlinear coupling between the axial and transverse vibrations has a significant effect on the response of structure.. It needs to be considered for the accurate dynamic analysis of long TLP tether subjected to the combined platform surge and heave motions.

A Linear Stability Analysis Of Large-Prandtl-Number Thermocapillary Liquid Bridges

A linear stability analysis is applied to determine the onset of oscillatory thermocapillary convection in cylindrical liquid bridges of large Prandtl numbers (4 <= Pr <= 50). We focus on the relationships between the critical Reynolds number Re-c, the azimuthal wave number m, the aspect ratio F and the Prandtl number Pr. A detailed Re-c-Pr stability diagram is given for liquid bridges with various Gamma. In the region of Pr > 1, which has been less studied previously and where Re, has been usually believed to decrease with the increase of Pr, we found Re-c exhibits an early increase for liquid bridges with Gamma around one. From the computed surface temperature gradient, it is concluded that the boundary layers developed at both solid ends of liquid bridges strengthen the stability of basic axisymmetric thermocapillary convection at large Prandtl number, and that the stability property of the basic flow is determined by the "effective" part of liquid bridge. (c) 2008 Published by Elsevier Ltd on behalf of COSPAR.

Wavelike patterns in one-dimensional coupled map lattices

We investigate the existence of wavelike solution for the logistic coupled map lattices for which the spatiotemporal periodic patterns can be predicted by a simple two-dimensional mapping. The existence of such wavelike solutions is proved by the implicit function theorem with constraints. We also examine the stabilities of these wave solutions under perturbations of uniform small deformation type. We show that in some specific cases these perturbations are completely general. The technique used in this paper is also applicable to investigate other space-time regular patterns.