Complex Transition of Double-Diffusive Convection in a Rectangular Enclosure with Height-to-Length Ratio Equal to 4: Part I

This is the first part of direct numerical simulation (DNS) of double-diffusive convection in a slim rectangular enclosure with horizontal temperature and concentration gradients. We consider the case with the thermal Rayleigh number of 10^5, the Pradtle number of 1, the Lewis number of 2, the buoyancy ratio of composition to temperature being in the range of [0,1], and height-to-width aspect ration of 4. A new 7th order upwind compact scheme was developed for approximation of convective terms, and a three-stage third-order Runge-Kutta method was employed for time advancement. Our DNS suggests that with the buoyancy ratio increasing form 0 to 1, the flow of transition is a complex series changing fromthe steady to periodic, chaotic, periodic, quasi-periodic, and finally back to periodic. There are two types of periodic flow, one is simple periodic flow with single fundamental frequency (FF), and another is complex periodic flow with multiple FFs. This process is illustrated by using time-velocity histories, Fourier frequency spectrum analysis and the phase-space rajectories.

Kramers Escape Rate in Nonlinear Diffusive Media

In this paper, we study nonlinear Kramers problem by investigating overdamped systems ruled by the one-dimensional nonlinear Fokker-Planck equation. We obtain an analytic expression for the Kramers escape rate under quasistationary conditions by employing

An Effective Method of Determining the Residual Stress Gradients in a Micro-Cantilever

A method of determining the micro-cantilever residual stress gradients by studying its deflection and curvature is presented. The stress gradients contribute to both axial load and bending moment, which, in prebuckling regime, cause the structural stiffness change and curving up/down, respectively. As the axial load corresponds to the even polynomial terms of stress gradients and bending moment corresponds to the odd polynomial terms, the deflection itself is not enough to determine the axial load and bending moment. Curvature together with the deflection can uniquely determine these two parameters. Both linear analysis and nonlinear analysis of micro-cantilever deflection under axial load and bending moment are presented. Because of the stiffening effect due to the nonlinearity of (large) deformation, the difference between linear and nonlinear analyses enlarges as the micro-cantilever deflection increases. The model developed in this paper determines the resultant axial load and bending moment due to the stress gradients. Under proper assumptions, the stress gradients profile is obtained through the resultant axial load and bending moment.

Diffusive Wave Solutions for Open Channel Flows with Uniform and Concentrated Lateral Inflow

The diffusive wave equation with inhomogeneous terms representing hydraulics with uniform or concentrated lateral inflow intoa river is theoretically investigated in the current paper. All the solutions have been systematically expressed in a unified form interms of response function or so called K-function. The integration of K-function obtained by using Laplace transform becomesS-function, which is examined in detail to improve the understanding of flood routing characters. The backwater effects usuallyresulting in the discharge reductions and water surface elevations upstream due to both the downstream boundary and lateral infloware analyzed. With a pulse discharge in upstream boundary inflow, downstream boundary outflow and lateral inflow respectively,hydrographs of a channel are routed by using the S-functions. Moreover, the comparisons of hydrographs in infinite, semi-infiniteand finite channels are pursued to exhibit the different backwater effects due to a concentrated lateral inflow for various channeltypes.

Diffusive waves in a channel with concentrated lateral inflow

In the current paper an analytical solution for diffusive wave equation with the concentrate-distributed lateral inflow is yielded. Finite-difference numerical method is also employed to validate this model. The backwater effects drawn from lateral inflow on the mainstream are examined finally.

Short-pulse laser absorption in very steep plasma density gradients

An analytical fluid model for resonance absorption during the oblique incidence by femtosecond laser pulses on a small-scale-length density plasma [k(0)L is an element of(0.1,10)] is proposed. The physics of resonance absorption is analyzed more clearly as we separate the electric field into an electromagnetic part and an electrostatic part. It is found that the characteristics of the physical quantities (fractional absorption, optimum angle, etc.) in a small-scale-length plasma are quite different from the predictions of classical theory. Absorption processes are generally dependent on the density scale length. For shorter scale length or higher laser intensity, vacuum heating tends to be dominant. It is shown that the electrons being pulled out and then returned to the plasma at the interface layer by the wave field can lead to a phenomenon like wave breaking. This can lead to heating of the plasma at the expanse of the wave energy. It is found that the optimum angle is independent of the laser intensity while the absorption rate increases with the laser intensity, and the absorption rate can reach as high as 25%. (c) 2006 American Institute of Physics.

Diffusive coevolution and mutualism maintenance mechanisms in a fig-fig wasp system

In reciprocal mutualism systems, the exploitation events by exploiters might disrupt the reciprocal mutualism, wherein one exploiter species might even exclude other coexisting exploiter species over an evolutionary time frame. What remains unclear is how such a community is maintained. Niche partitioning, or spatial heterogeneity among the mutualists and exploiters, is generally believed to enable stability within a mutualistic system. However, our examination of a reciprocal mutualism between a fig species (Ficus racemosa) and its pollinator wasp (Ceratosolen fusciceps) shows that spatial niche partitioning does not sufficiently prevent exploiters from overexploiting the common resource (i.e., the female flowers), because of the considerable niche overlap between the mutualists and exploiters. In response to an exploiter, our experiment shows that the fig can (1) abort syconia-containing flowers that have been galled by the exploiter, Apocryptophagus testacea, which oviposits before the pollinators do; and (2) retain syconia-containing flowers galled by Apocryptophagus mayri, which oviposit later than pollinators. However, as a result of (2), there is decreased development of adult non-pollinators or pollinator species in syconia that have not been sufficiently pollinated, but not aborted. Such discriminative abortion of figs or reduction in offspring development of exploiters while rewarding cooperative individuals with higher offspring development by the fig will increase the fitness of cooperative pollinating wasps, but decrease the fitness of exploiters. The fig fig wasp interactions are diffusively coevolved, a case in which fig wasps diversify their genotype, phenotype, or behavior as a result of competition between wasps, while figs diverge their strategies to facilitate the evolution of cooperative fig waps or lessen the detrimental behavior by associated fig wasps. In habitats or syconia that suffer overexploitation, discriminative abortion of figs or reduction in the offspring development of exploiters in syconia that are not or not sufficiently pollinated will decrease exploiter fitness and perhaps even drive the population of exploiters to local extinction, enabling the evolution and maintenance of cooperative pollinators through the movement between habitats or syconia (i.e., the metapopulations).

Two opposite gradients of hole density in as-grown and annealed (Ga,Mn)As layers

The depth distribution of the hole density p in 500 nm-thick (Ga,Mn)As layers is investigated. From Raman scattering spectra, it is found that the gradients of p are opposite in the as-grown and annealed layers. At the region around the free surface, with increasing etching depth, p significantly increases in the as-grown layer; however, p decreases distinctly in the annealed layer. Then, in the bulk, p becomes almost homogeneous for both cases. The etching-depth dependence of Curie temperature obtained from magnetic measurements is in agreement with the distribution characterization of p. These results suggest that annealing induces outdiffusion of Mn interstitials towards the free surface, and incomplete outdiffusion during the growth leads to an accumulation of Mn interstitials around the free surface of the as-grown (Ga,Mn)As. (c) 2006 Elsevier B.V. All rights reserved.

Effect of channel surface wettability and temperature gradients on the boiling flow pattern in a single microchannel

The objective of this paper is to investigate the effects of channel surface wettability and temperature gradients on the boiling flow pattern in a single microchannel. The test section consists of a bottom silicon substrate bonded with a top glass cover. Three consecutive parts of an inlet fluid plenum, a central microchannel and an outlet fluid plenum were etched in the silicon substrate. The central microchannel had a width of 800 mu m and a depth of 30 mu m. Acetone liquid was used as the working fluid. High outlet vapor qualities were dealt with here. The flow pattern consists of a fluid triangle (shrinkage of the liquid films) and a connected long liquid rivulet, which is generated in the central microchannel in the timescale of milliseconds. The peculiar flow pattern is formed due to the following reasons: (1) the liquid rivulet tends to have a large contact area with the top hydrophilic channel surface of the glass cover, but a smaller contact area with the bottom silicon hydrophobic surface. (2) The temperature gradient in the chip width direction at the top channel surface of the glass cover not only causes the shrinkage of the liquid films in the central microchannel upstream, but also attracts the liquid rivulet populated near the microchannel centerline. (3) The zigzag pattern is formed due to the competition between the evaporation momentum forces at the vapor-liquid interfaces and the force due to the Marangoni effect. The former causes the rivulet to deviate from the channel centerline and the latter draws the rivulet toward the channel centerline. (4) The temperature gradient along the flow direction in the central microchannel downstream causes the breakup of the rivulet to form isolated droplets there. (5) Liquid stripes inside the upstream fluid triangle were caused by the small capillary number of the liquid film, at which the large surface tension force relative to the viscous force tends to populate the liquid film locally on the top glass cover surface.

Investigations of phase inversion and frictional pressure gradients in upward and downward oil–water flow in vertical pipes

The present study has attempted to investigate phase inversion and frictional pressure gradients during simultaneous vertical flow of oil and water two-phase through upward and downward pipes. The liquids selected were white oil (44 mPa s viscosity and 860 kg/m3 density) and water. The measurements were made for phase velocities varying from 0 to 1.24 m/s for water and from 0 to 1.87 m/s for oil, respectively. Experiments were carried either by keeping the mixture velocity constant and increasing the dispersed phase fraction or by keeping the continuous phase superficial velocity constant and increasing the dispersed phase superficial velocity. From the experimental results, it is shown that the frictional pressure gradient reaches to its lower value at the phase inversion point in this work. The points of phase inversion are always close to an input oil fraction of 0.8 for upward flow and of 0.75 for downward flow, respectively. A few models published in the literature are used to predict the phase inversion point and to compare the results with available experimental data. Suitable methods are suggested to predict the critical oil holdup at phase inversion based on the different viscosity ratio ranges. Furthermore, the frictional pressure gradient is analyzed with several suitable theoretical models according to the existing flow patterns. The analysis reveals that both the theoretical curves and the experimental data exhibit the same trend and the overall agreement of predicted values with experimental data is good, especially for a high oil fraction.