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.

Surface waves in a vertically excited circular cylindrical container

The nonlinear free surface amplitude equation, which has been derived from the inviscid fluid by solving the potential equation of water waves with a singular perturbation theory in a vertically oscillating rigid circular cylinder, is investigated successively in the fourth-order Runge-Kutta approach with an equivalent time-step. Computational results include the evolution of the amplitude with time, the characteristics of phase plane determined by the real and imaginary parts of the amplitude, the single-mode selection rules of the surface waves in different forced frequencies, contours of free surface displacement and corresponding three-dimensional evolution of surface waves, etc. In addition, the comparison of the surface wave modes is made between theoretical calculations and experimental measurements, and the results are reasonable although there are some differences in the forced frequency.

Instability of the vertically forced surface wave in a circular cylindrical container

The nonlinear amplitude equation, which was derived by Jian Yongjun employing expansion of two-time scales in inviscid fluids in a vertically oscillating circular cylindrical vessel, is modified by introducing a damping term due to the viscous dissipation of this system. Instability of the surface wave is analysed and properties of the solutions of the modified equation are determined together with phase-plane trajectories. A necessary condition of forming a stable surface wave is obtained and unstable regions are illustrated. Research results show that the stable pattern of surface wave will not lose its stability to an infinitesimal disturbance.

Instability Analysis Of Torsional Mems/Nems Actuators Under Capillary Force

The static and dynamic instabilities of a torsional MEMS/NEMS actuator caused by capillary effects are studied, respectively. An instability number, eta, is defined, and the critical gap distance, g(cr), between the mainplate and the substrate is derived. According to the values of eta and g, the instability criteria of the actuator are presented. The dimensionless motion equation of the MEMS/NEMS torsional actuator is derived when it makes nonlinear oscillation under capillary force. The qualitative analysis of the nonlinear equation is made, and the phase portraits are presented on the phase plane. In addition, the bifurcation phenomena in the system are also analyzed. (C) 2008 Elsevier Inc. All rights reserved.

Electric characteristics of pseudo-spark during breakdown phase

An analysis of the time-dependent resistive voltage and power deposition during the breakdown phase of pseudo-spark is presented. The voltage and current were measured by specially designed low-inductance capacitive voltage divider and current measuring resistor. The measured waveforms of voltage and current are digitized and processed by a computer program to remove the inductive component, so as to obtain resistive voltage and power deposition. The influence of pressure, cathode geometry and charging voltage of storage capacitors on the electrical properties in the breakdown phase are investigated. The results suggest that the breakdown phase of pseudo-spark consists of three stages. The first stage is mainly hollow cathode discharge. In the second stage, field-enhanced thermionic emission takes place, resulting in a fast voltage drop and sharp rise of discharge current. The third stage of discharge depends simply on the parameters of the discharge circuit.

A reliable phase unwrapping algorithm based on the local fitting plane and quality map

A fast and reliable phase unwrapping (PhU) algorithm, based on the local quality-guided fitting plane, is presented. Its framework depends on the basic plane-approximated assumption for phase values of local pixels and on the phase derivative variance (PDV) quality map. Compared with other existing popular unwrapping algorithms, the proposed algorithm demonstrated improved robustness and immunity to strong noise and high phase variations, given that the plane assumption for local phase is reasonably satisfied. Its effectiveness is demonstrated by computer-simulated and experimental results.

Pure-phase plates for super-Gaussian focal-plane irradiance profile generations of extremely high order

A set of recursive formulas for diffractive optical plates design is described. The pure-phase plates simulated by this method homogeneously concentrate more than 96% of the incident laser energy in the desired focal-plane region. The intensity focal-plane profile fits a lath-order super-Gaussian function and has a nearly perfect flat top. Its fit to the required profile measured in the mean square error is 3.576 x 10(-3). (C) 1996 Optical Society of America

Microstructure and Optical Properties of Nonpolar m-Plane GaN Films Grown on m-Plane Sapphire by Hydride Vapor Phase Epitaxy

Thick nonpolar (10 (1) over bar0) GaN layers were grown on m-plane sapphire substrates by hydride vapor phase epitaxy (HVPE) using magnetron sputtered ZnO buffers, while semipolar (10 (1) over bar(3) over bar) GaN layers were obtained by the conventional two-step growth method using the same substrate. The in-plane anisotropic structural characteristics and stress distribution of the epilayers were revealed by high. resolution X-ray diffraction and polarized Raman scattering measurements. Atomic force microscopy (AFM) images revealed that the striated surface morphologies correlated with the basal plane stacking faults for both (10 (1) over bar0) and (10 (1) over bar(3) over bar) GaN films. The m-plane GaN surface showed many triangular-shaped pits aligning uniformly with the tips pointing to the c-axis after etching in boiled KOH, whereas the oblique hillocks appeared on the semipolar epilayers. In addition, the dominant emission at 3.42eV in m-plane GaN films displayed a red shift with respect to that in semipolar epilayers, maybe owing to the different strain states present in the two epitaxial layers. [DOI: 10.1143/JJAP.47.3346]

Growth of (10(1)over-bar(3)over-bar) semipolar GaN on m-plane sapphire by hydride vapor phase epitaxy

The crystalline, surface, and optical properties of the (10 (1) over bar(3) over bar) semipolar GaN directly grown on m-plane sapphire substrates by hydride vapor phase epitaxy (HVPE) were investigated. It was found that the increase of V/III ratio led to high quality (10 (1) over bar(3) over bar) oriented GaN epilayers with a morphology that may have been produced by step-flow growth and with minor evidence of anisotropic crystalline structure. After etching in the mixed acids, the inclined pyramids dominated the GaN surface with a density of 2 X 10(5) cm(-2), revealing the N-polarity characteristic. In the low-temperature PL spectra, weak BSF-related emission at 3.44eV could be observed as a shoulder of donor-bound exciton lines for the epilayer at high V/III ratio, which was indicative of obvious reduction of BSFs density. In comparison with other defect related emissions, a different quenching behavior was found for the 3.29 eV emission, characterized by the temperature-dependent PL measurement. (C) 2009 Elsevier B.V. All rights reserved.

Hydride Vapor Phase Epitaxy Growth of Semipolar, 10(1)over-bar(3)over-barGaN on Patterned m-Plane Sapphire

We have investigated the hydride vapor-phase epitaxy growth of (10 (1) over bar(3) over bar)-oriented GaN thick films on patterned sapphire substrates (PSSs) (10 (1) over bar0). From characterization by atomic force microscopy, scanning electron microscopy, double-crystal X-ray diffraction, and photoluminescence (PL), it is determined that the crystalline and optical qualities of (10 (1) over bar(3) over bar) GaN epilayers grown on the cylindrical PSS are better than those on the flat sapphire. However, two main crystalline orientations (10 (1) over bar(3) over bar) and (11 (2) over bar2) dominate the GaN epilayers grown on the pyramidal PSS, demonstrating poor quality. After etching in the mixed acids, these (10 (1) over bar(3) over bar) GaN films are dotted with oblique pyramids, concurrently lining along the < 30 (3) over bar2 > direction, indicative of a typical N-polarity characteristic. Defect-related optical transitions of the (10 (1) over bar(3) over bar) GaN epilayers are identified and detailedly discussed in virtue of the temperature-dependent PL. In particular, an anomalous blueshift-redshift transition appears with an increase in temperature for the broad blue luminescence due to the thermal activation of the shallow level.

FROM DIMER TO POLYMER .2. EXTENDED TO SYSTEMS POSSESSING 2-FOLD SCREW AXIS OR GLIDE PLANE

The approach for constructing the qualitative band structure of a polymer from corresponding dimer has been extended to the system possessing two-fold screw axis or. glide plane. The classification of energy levels of the dimer in the present case depends on pseudo-symmetry/antisymmetry instead of psendo-in-phase/out-of-phase property of the orbitals. Several typical conductive polymers are then discussed follow this approach. Among them are cis-polyacetylene, polyparaphenylene with a twist ang...

An Analytical Solution for Three-Dimensional Diffraction of Plane P-Waves by a Hemispherical Alluvial Valley with Saturated Soil Deposits

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot's dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot's dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

Characterization of Air-Water Two-Phase Vertical Flow by Using Electrical Resistance Imaging

The characterization of air-water two-phase vertical flow in a 12 m flow loop with 1.5 m of vertical section is studied by using electrical resistance tomography (ERT). By applying a fast data collection to a dual-plane ERT sensor and an iterative image reconstruction algorithm, relevant information is gathered for implementation of flow characteristics, particularly for flow regime recognition. A cross-correlation method is also used to interpret the velocity distribution of the gas phase on the cross section. The paper demonstrates that ERT can now be deployed routinely for velocity measurements and this capability will increase as faster measurement systems evolve.

Formation of shear bands in plane sheet

The formation of shear bands in plane sheet is studied, both analytically and experimentally, to enhance the fundamental understanding of this phenomenon and to develop a capability for predicting material failure. The evolution of voids is measured and its interaction with the process of shear banding is examined. The evolving dilatancy in plasticity is shown to have a vital role in analysing the shear-band type of bifurcation, and tremendously reduces the theoretical value of critical stresses. The analyses, referring to both localized and diffuse modes of bifurcation, fairly explain the corresponding observations obtained through testing a dual-phase steer sheet and provide a justification of the constitutive model used.