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.

Complete solution of the columbus problem for large-disturbance cases

The Columbus problem has been rigorously solved by Lyapunov's direct approach to the continuous system in gencral cases of large disturbance and the theory has proved to be in strict consistency with Kelvin's experiments.

A three-dimensional analytical solution of the microheater temperature before bubble nucleation

A three-dimensional analytical solution of the microheater temperature based on heat diffusion equation is developed and compared with experimental results. Dimensionless parameters are introduced to analyze the temperature rise time and the distribution under steady state. To study the microheater temperatures before bubble nucleation, a set of working fluids and microheaters are considered. It is shown that the dimensionless time xi(-)(0) required for the temperature rise from room to 95% of the steady state temperature is about 75, not dependent on working fluids and microheaters. Heat transfer to the surrounding liquid is mainly caused by conduction, not by convection and radiation mechanisms. The microheater length affects the surface temperature uniformity, while its width influences the steady temperatures significantly, yielding the transition from heterogeneous to homogeneous nucleation mechanism from square microheaters to narrow line microheaters. 

Ultrathin-film growth of para-sexiphenyl (I): Submonolayer thin-film growth as a function of the substrate temperature

The para-sexiphenyl (p-6P) monolayer film induces weak epitaxy growth (WEG) of disk-like organic semiconductors, and their charge mobilities are increased dramatically to the level of the corresponding single crystals [Wang et al., Adv. Mater. 2007, 19, 2168]. The growth behavior and morphology of p-6P monolayer film play decisive roles on WEG. Here, we investigated the growth behavior of p-6P submonolayer film as a function of the substrate temperature. Its growth exhibited two different mechanisms at high and low substrate temperature.

A HYBRID METHOD OF FRACTIONAL STEPS WITH PREDICTOR-CORRECTOR DIFFERENCE-PSEUDOSPECTRUM FOR NUMERICAL-SOLUTION OF THE CONVECTION-DOMINATED FLOW PROBLEMS

A fractional-step method of predictor-corrector difference-pseudospectrum with unconditional L(2)-stability and exponential convergence is presented. The stability and convergence of this method is strictly proved mathematically for a nonlinear convection-dominated flow. The error estimation is given and the superiority of this method is verified by numerical test.

STUDY ON THE FORMATIONAL MECHANISM OF THE NORTHERN YELLOW (HUANGHAI) SEA COLD WATER MASS .2. DISCUSSION ON THE SOLUTION OF THE MODEL

The theoretical solution of the model of the Northern Yellow (Huanghai) Sea Cold Water Mass (NYSCWM) reveals that the NYSCWM is mainly formed through the continuous temperature increase of the overwintered water body above the Northern Yellow Sea Depression (NYSD) after spring when heat is continuously conducted from the sea surface to the deeper layer. In the NYSCWM's growing period, (June-July), nonlinear vertical convection and advection effects continuously increase, and are gradually balanced by the heat diffusion effect as the temperature increases from the surface to the bottom, which leads to the formation of an intensive thermocline and lateral front. Meanwhile, the three-dimensional circulation correspondingly occurs. In the NYSCWM's entire growing period, the horizontal circulation is always in the cyclonic motion, while the vertical circulation passes through a transition from a period with the cold centre as downwelling to a period with the cold centre as upwelling.

Characteristics of the interface of a laser-quenched steel substrate and chromium electroplate

The interface of a laser-discrete-quenched steel substrate and as-deposited chromium electroplate was investigated by ion beam etching, dissolving-substrate-away and using a Vickers microhardness tester, in an attempt to reveal the mechanism that the service life of the chromium-coated parts is increased by the duplex technique of laser pre-quenching plus chromium post-depositing. The laser quenching of the steel substrate can reduce the steep hardness gradient at the substrate/chromium interface and improve the load-bearing capacity of chromium electroplate. Moreover, the laser quenching prior to plating has an extremely great effect on the morphologies and microstructure of the substrate/chromium interface: there is a transient interlayer at the original substrate/chromium interface while there is not at the laser-quenchedzone/chromium interface; the near-substrate surface microstructure and morphologies of the free-standing chromium electrodeposits, whose substrate was dissolved away with nital 30% in volume, inherit the periodically gradient characteristics of the laser-discrete-quenched substrate surface. (c) 2006 Elsevier B.V. All rights reserved.

A solution to the upward migration of an intrusion

The evolution of the upward migration of the magma is a nonlinear and unstable problem in mathematics. It is difficult to solve it. And using the numerical method, the solution is relatively tedious and time-consuming. This paper introduces a method of the instantaneous point source to solve the linear and unstable heat conduction equation during the infinite period of time instead of the solution of the nonlinear and unstable heat conduction equation. The results obtained by this method coincide with those by the numerical method, meaning that this method offers a simple way to solve the nonlinear and unstable heat conduction equation.

An asymptotic solution of hydrodynamic equations at the mid-plane of a plume in the earths mantle

From the partial differential equations of hydrodynamics governing the movements in the Earth's mantle of a Newtonian fluid with a pressure- and temperature-dependent viscosity, considering the bilateral symmetry of velocity and temperature distributions at the mid-plane of the plume, an analytical solution of the governing equations near the mid-plane of the plume was found by the method of asymptotic analysis. The vertical distribution of the upward velocity, viscosity and temperature at the mid-plane, and the temperature excess at the centre of the plume above the ambient mantle temperature were then calculated for two sets of Newtonian rheological parameters. The results obtained show that the temperature at the mid-plane and the temperature excess are nearly independent of the rheological parameters. The upward velocity at the mid-plane, however, is strongly dependent on the rheological parameters.

Effects of Cd2+ and Pb2+ on the substrate biofilms in the integrated vertical-flow constructed wetland

The effects of single Cd2+ and Pb2+, and combined Cd2+ and Pb2+ on dehydrogenase activity and polysaccharide content of the substrate biofilms in the integrated vertical-flow constructed wetland (IVCW) were studied. Dehydrogenase activities decreased linearly with the increasing concentrations of Cd2+ and Pb2+ at different times (6, 24, 72, and 120 h). The activities at both 6 and 24 h were significantly higher than that at 72 and 120 h in the case of single and combined treatments. The single Cd2+ and Pb2+ treatments significantly inhibited dehydrogenase activities at concentrations in excess of 20 mu mol/L Cd2+ and 80 mu mol/L Pb2+, respectively. The inhibitory effect of Cd2+ was much greater than that of Pb2+. At the same time, the combined treatment of Cd2+ and Pb2+ Significantly inhibited dehydrogenase activities at all five concentrations studied and the lowest combined concentration was 1.25 mu mol/L Cd2+ and 5 mu mol/L Pb2+. A synergistic effect of Cd2+ and Pb2+ was observed. On the other hand, polysaccharide contents varied unpredictably with the increasing concentrations of Cd2+ and Pb2+ and extended experimental time. There were no significant statistical differences within the range of concentration and time studied, whether singly or in combination. These results implied that the effects of heavy metals on biofilms should be a concern for the operation and maintenance of constructed wetlands.

Instability of solution of phase retrieval in direct diffraction phase-contrast imaging with partially coherent X-ray source

The theoretical model of direct diffraction phase-contrast imaging with partially coherent x-ray source is expressed by an operator of multiple integral. It is presented that the integral operator is linear. The problem of its phase retrieval is described by solving an operator equation of multiple integral. It is demonstrated that the solution of the phase retrieval is unstable. The numerical simulation is performed and the result validates that the solution of the phase retrieval is unstable.

Influence of dielectric properties of a substrate upon plasmon resonance spectrum of supported Ag nanoparticles

Plasmon resonance spectra of supported Ag nanoparticles are studied by depositing the particles on different substrates. It was found that the dielectric properties of the substrates have significant effects on the spectral line shape, except the resonance frequency. Beyond the plasmon resonance band, the spectral shape is mainly governed by the dielectric function, particularly its imaginary part, of the substrate. The plasmon resonance band, on the other hand, may be severely distorted if the substrate is absorbing strongly.

The preparation and stability of the inclusion complex of astaxanthin with beta-cyclodextrin

Inclusion complex of astaxanthin with beta-cyclodextrin was prepared. The water solubility of the inclusion complex was < 0.5 mg/ml, which is better than that of astaxanthin. Large aggregates were observed in the aqueous solution of the inclusion complex. Furthermore, the stability of the inclusion complex against temperature and light was greatly enhanced compared to that of astaxanthin. (c) 2006 Elsevier Ltd. All rights reserved.