The time finite element as a robust general scheme for solving nonlinear dynamic equations including chaotic systems

Schemes that can be proven to be unconditionally stable in the linear context can yield unstable solutions when used to solve nonlinear dynamical problems. Hence, the formulation of numerical strategies for nonlinear dynamical problems can be particularly challenging. In this work, we show that time finite element methods because of their inherent energy momentum conserving property (in the case of linear and nonlinear elastodynamics), provide a robust time-stepping method for nonlinear dynamic equations (including chaotic systems). We also show that most of the existing schemes that are known to be robust for parabolic or hyperbolic problems can be derived within the time finite element framework; thus, the time finite element provides a unification of time-stepping schemes used in diverse disciplines. We demonstrate the robust performance of the time finite element method on several challenging examples from the literature where the solution behavior is known to be chaotic. (C) 2015 Elsevier Inc. All rights reserved.

Effect of RF power on the structural, optical and gas sensing properties of RF-sputtered Al doped ZnO thin films

The effect of Radio Frequency (RF) power on the properties of magnetron sputtered Al doped ZnO thin films and the related sensor properties are investigated. A series of 2 wt% Al doped ZnO; Zn0.98Al0.02O (AZO) thin films prepared with magnetron sputtering at different RF powers, are examined. The structural results reveal a good adhesive nature of thin films with quartz substrates as well as increasing thickness of the films with increasing RF power. Besides, the increasing RF power is found to improve the crystallinity and grain growth as confirmed by X-ray diffraction. On the other hand, the optical transmittance is significantly influenced by the RF power, where the transparency values achieved are higher than 82% for all the AZO thin films and the estimated optical band gap energy is found to decrease with RF power due to an increase in the crystallite size as well as the film thickness. In addition, the defect induced luminescence at low temperature (77 K) and room temperature (300 K) was studied through photoluminescence spectroscopy, it is found that the defect density of electronic states of the Al3+ ion increases with an increase of RF power due to the increase in the thickness of the film and the crystallite size. The gas sensing behavior of AZO films was studied for NO2 at 350 degrees C. The AZO film shows a good response towards NO2 gas and also a good relationship between the response and the NO2 concentration, which is modeled using an empirical formula. The sensing mechanism of NO2 is discussed.

Optical and Morphological Properties of Sol Gel derived Titanium dioxide Films

Titanium oxide (Titania) thin films were synthesized on different substrates via the sol-gel dip-coating method using alkoxide solution. Some selected samples were also prepared with different percentage of Lead (Pb). The influence of Pb addition in precursor sol on the optical properties of titanium dioxide thin films was studied. The optical transmittance in the visible region has increased with increase in weight percentage of lead. The refractive index was slightly decreased with Pb addition. Crystallization of these coatings was achieved through thermal annealing at temperatures above 400 degrees C. The structural properties and surface morphology of the crystallized coatings were studied by Scanning Electron Microscopy. Increase in average grain size from 250 nm to 350 nm with increase in Pb concentration is observed. Films were appeared to more coarse with increase in Pb addition. An increase in Pb addition resulted increase in average roughness from 12 nm to 25 nm.

Structural, Optical, and Piezoelectric Response of Lead-Free Ba0.95Mg0.05Zr0.1Ti0.9O3 Nanocrystalline Powder

Nanocrystalline powders of Ba1-xMgxZr0.1Ti0.9O3 (x = 0.025-0.1) were synthesized via citrate assisted sol-gel method. Interestingly, the one with x = 0.05 in the system Ba1-xMgxZr0.1Ti0.9O3 exhibited fairly good piezoelectric response aside from the other physical properties. The phase and structural confirmation of synthesized powder was established by X-ray powder diffraction (XRD) and Raman Spectroscopic techniques. Two distinct Raman bands i.e., 303 and 723 cm(-1) characteristic of tetragonal phase were observed. Thermogravimetric analysis (TGA) was performed to evaluate the phase decomposition of the as-synthesized Ba0.95Mg0.05Zr0.1Ti0.9O3 sample as a function of temperature. The average crystallite size associated with Ba0.95Mg0.05Zr0.1Ti0.9O3 was calculated using Scherrer formula based on the XRD data and was found to be 25 nm. However, Scanning and Transmission Electron Microscopy studies revealed the average crystallite size to be in the range of 30-40 nm, respectively. Kubelka-Munk function was employed to determine the optical band gap of these nanocrystallites. A piezoelectric response of 26 pm/V was observed for Ba0.95Mg0.05Zr0.1Ti0.9O3 nanocrystal by Piezoresponse Force Microscopy (PFM) technique. Photoluminescence (PL) study carried out on these nanocrystals exhibited a blue emission (470 nm) at room temperature.

An out-of-plane linear motion measurement system based on optical beam deflection

Measurement of out-of-plane linear motion with high precision and bandwidth is indispensable for development of precision motion stages and for dynamic characterization of mechanical structures. This paper presents an optical beam deflection (OBD) based system for measurement of out-of-plane linear motion for fully reflective samples. The system also achieves nearly zero cross-sensitivity to angular motion, and a large working distance. The sensitivities to linear and angular motion are analytically obtained and employed to optimize the system design. The optimal shot-noise limited resolution is shown to be less than one angstrom over a bandwidth in excess of 1 kHz. Subsequently, the system is experimentally realized and the sensitivities to out-of-plane motions are calibrated using a novel strategy. The linear sensitivity is found to be in agreement with theory. The angular sensitivity is shown to be over 7.5-times smaller than that of conventional OBD. Finally, the measurement system is employed to measure the transient response of a piezo-positioner, and, with the aid of an open-loop controller, reduce the settling time by about 90%. It is also employed to operate the positioner in closed-loop and demonstrate significant minimization of hysteresis and positioning error.

COUPLED OPTICAL-THERMAL-FLUID MODELING OF A DIRECTLY HEATED TUBULAR SOLAR RECEIVER FOR SUPERCRITICAL CO2 BRAYTON CYCLE

Recent studies have evaluated closed-loop supercritical carbon dioxide (s-CO2) Brayton cycles to be a higher energy density system in comparison to conventional superheated steam Rankine systems. At turbine inlet conditions of 923K and 25 MPa, high thermal efficiency (similar to 50%) can be achieved. Achieving these high efficiencies will make concentrating solar power (CSP) technologies a competitive alternative to current power generation methods. To incorporate a s-CO2 Brayton power cycle in a solar power tower system, the development of a solar receiver capable of providing an outlet temperature of 923 K (at 25 MPa) is necessary. The s-CO2 will need to increase in temperature by similar to 200 K as it passes through the solar receiver to satisfy the temperature requirements of a s-CO2 Brayton cycle with recuperation and recompression. In this study, an optical-thermal-fluid model was developed to design and evaluate a tubular receiver that will receive a heat input similar to 2 MWth from a heliostat field. The ray-tracing tool SolTrace was used to obtain the heat-flux distribution on the surfaces of the receiver. Computational fluid dynamics (CFD) modeling using the Discrete Ordinates (DO) radiation model was used to predict the temperature distribution and the resulting receiver efficiency. The effect of flow parameters, receiver geometry and radiation absorption by s-CO2 were studied. The receiver surface temperatures were found to be within the safe operational limit while exhibiting a receiver efficiency of similar to 85%.

Numerical solution of the incompressible Navier-Stokes equations with an upwind compact difference scheme

A new finite difference method for the discretization of the incompressible Navier-Stokes equations is presented. The scheme is constructed on a staggered-mesh grid system. The convection terms are discretized with a fifth-order-accurate upwind compact difference approximation, the viscous terms are discretized with a sixth-order symmetrical compact difference approximation, the continuity equation and the pressure gradient in the momentum equations are discretized with a fourth-order difference approximation on a cell-centered mesh. Time advancement uses a three-stage Runge-Kutta method. The Poisson equation for computing the pressure is solved with preconditioning. Accuracy analysis shows that the new method has high resolving efficiency. Validation of the method by computation of Taylor's vortex array is presented.

Optical Diagnostic and Modeling Solution Growth Process of Sodium Chlorate Crystals

Both a real time optical interferometric experiment and a numerical simulation of two-dimension non-steady state model were employed to study the growth process of aqueous sodium chlorate crystals. The parameters such as solution concentration distribution, crystal dimensions, growth rate and velocity field were obtained by both experiment and numerical simulation. The influence of earth gravity during crystal growth process was analyzed. A reasonable theory model corresponding to the present experiment is advanced. The thickness of concentration boundary layer was investigated especially. The results from the experiment and numerical simulation match well.

Characteristics and Sub-Characteristics of Two-Dimensional Parabolized Stability Equations

特征分析表明：对原始扰动量的抛物化稳定性方程组(PSE),它在亚超音速区分别具有椭圆和抛物特性,给出PSE特征对马赫数的依赖关系,阐明PSE仅把信息对流-扩散传播特性抛物化,而保留了信息对流-扰动传播特性,因此PSE应称为扩散抛物化稳定性方程(DPSE)。

Growth and optical properties of peculiar ZnO tetrapods

Regular ZnO tetrapods with different morphologies have been obtained on Si(100) substrate via the chemical vapour deposition approach. Varying the growth temperature and gas rate, we have obtained different structured ZnO materials: tetrapods with a large hexagonal crown, a flat top and a small hexagonal crown. The results suggest that these tetrapods are all single crystals with a wurtzite structure that grow along the (0001) direction. However, photoluminescence spectra shows that their optical properties are quite different: for those with large hexagonal crown, the green emission overwhelms that of the near band-edge (NBE) ultraviolet (UV) peak, while others have only a strong NBE UV peak at ~386 nm.

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.

Steady Patterns of Microparticles Formed by Optical Tweezers

In this paper, we propose a method for forming steady patterns of microparticles in a dispersion using optical tweezers. We demonstrate how to control the congregation of particles in a dispersion and to manually fabricate a pattern, The steady pattern (nay be useful for in-depth research, and the method will have applications in biology and nanotechnology.

Modified Simplified Rate Equation Model of Flowing Chemical Oxygen-Iodine Laser and its Application

A modified simplified rate equation (RE) model of flowing chemical oxygen-iodine laser (COIL), which is adapted to both the condition of homogeneous broadening and inhomogeneous broadening being of importance and the condition of inhomogeneous broadening being predominant, is presented for performance analyses of a COIL. By using the Voigt profile function and the gain-equal-loss approximation, a gain expression has been deduced from the rate equations of upper and lower level laser species. This gain expression is adapted to the conditions of very low gas pressure up to quite high pressure and can deal with the condition of lasing frequency being not equal to the central one of spectral profile. The expressions of output power and extraction efficiency in a flowing COIL can be obtained by solving the coupling equations of the deduced gain expression and the energy equation which expresses the complete transformation of the energy stored in singlet delta state oxygen into laser energy. By using these expressions, the RotoCOIL experiment is simulated, and obtained results agree well with experiment data. Effects of various adjustable parameters on the performances of COIL are also presented.