Analysis of randomly time varying systems by gaussian closure technique

The Gaussian probability closure technique is applied to study the random response of multidegree of freedom stochastically time varying systems under non-Gaussian excitations. Under the assumption that the response, the coefficient and the excitation processes are jointly Gaussian, deterministic equations are derived for the first two response moments. It is further shown that this technique leads to the best Gaussian estimate in a minimum mean square error sense. An example problem is solved which demonstrates the capability of this technique for handling non-linearity, stochastic system parameters and amplitude limited responses in a unified manner. Numerical results obtained through the Gaussian closure technique compare well with the exact solutions.

Study of turbid media with light: Recovery of mechanical and optical properties from boundary measurement of intensity autocorrelation of light

We discuss the inverse problem associated with the propagation of the field autocorrelation of light through a highly scattering object like tissue. In the first part of the work, we reconstructed the optical absorption coefficient mu(u) and particle diffusion coefficient D-B from simulated measurements which are integrals of a quantity computed from the measured intensity and intensity autocorrelation g(2)(tau) at the boundary. In the second part we recover the mean square displacement (MSD) distribution of particles in an inhomogeneous object from the sampled g(2)(tau) measure on the boundary. From the MSD, we compute the storage and loss moduli distributions in the object. We have devised computationally easy methods to construct the sensitivity matrices which are used in the iterative reconstruction algorithms for recovering these parameters from the measurements. The results of the reconstruction of mu(a), D-B, MSD and the viscoelastic parameters, which are presented, show reasonable good position and quantitative accuracy.

An Analysis of a Boundary Layer Diffusion Flame Over a Porous Flat Plate in a Confined Flow

A numerical analysis of the gas dynamic structure of a two-dimensional laminar boundary layer diffusion flame over a porous flat plate in a confined flow is made on the basis of the familiar boundary layer and flame sheet approximations neglecting buoyancy effects. The governing equations of aerothermochemistry with the appropriate boundary conditions are solved using the Patankar-Spalding method. The analysis predicts the flame shape, profiles of temperature, concentrations of variousspecies, and the density of the mixture across the boundary layer. In addition, it also predicts the pressure gradient in the flow direction arising from the confinement ofthe flow and the consequent velocity overshoot near the flame surface. The results of thecomputation performed for an n-pentane-air system are compared with experimental data andthe agreement is found to be satisfactory.

Unsteady, three-dimensional, boundary-layer flow due to a stretching surface

Abstract is not available.

Modeling dynamic demand response using Monte Carlo simulation and interval mathematics for boundary estimation

With the rapid development of various technologies and applications in smart grid implementation, demand response has attracted growing research interests because of its potentials in enhancing power grid reliability with reduced system operation costs. This paper presents a new demand response model with elastic economic dispatch in a locational marginal pricing market. It models system economic dispatch as a feedback control process, and introduces a flexible and adjustable load cost as a controlled signal to adjust demand response. Compared with the conventional “one time use” static load dispatch model, this dynamic feedback demand response model may adjust the load to a desired level in a finite number of time steps and a proof of convergence is provided. In addition, Monte Carlo simulation and boundary calculation using interval mathematics are applied for describing uncertainty of end-user's response to an independent system operator's expected dispatch. A numerical analysis based on the modified Pennsylvania-Jersey-Maryland power pool five-bus system is introduced for simulation and the results verify the effectiveness of the proposed model. System operators may use the proposed model to obtain insights in demand response processes for their decision-making regarding system load levels and operation conditions.

Unsteady laminar compressible stagnation-point boundary-layer flow over a three-dimensional body: Higher order effects

The unsteady laminar compressible three-dimensional stagnation-point boundary-layer flow with variable properties has been studied when the velocity of the incident stream, mass transfer and wall temperature vary arbitrarily with time. The second-order unsteady boundary-layer equations for all the effects have been derived by using the method of matched asymptotic expansions. Both nodal and saddle point flows as well as cold and hot wall cases have been considered. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. Computations have been carried out for an accelerating stream, a decelerating stream and a fluctuating stream. The results indicate that the unsteady free stream velocity distributions, the nature of the stagnation point, the mass transfer, the wall temperature and the variation of the density-viscosity product across the boundary significantly affect the skin friction and heat transfer. The variation of the wall temperature with time strongly affects the heat transfer whereas its effect is comparatively less on skin friction. Suction increases the skin friction and heat transfer but injection does the opposite. The skin friction in the x direction due to the combined effects of first- and second-order boundary layers is less than the skin-friction in the x direction due to the first-order boundary layers for all the parameters. The overall skin friction in the z direction and heat transfer are more or less than the first-order boundary layers depending upon the values of the various parameters.

Vibrations of a Beam in Variable Contact With a Flat Surface

We study small vibrations of cantilever beams contacting a rigid surface. We study two cases: the first is a beam that sags onto the ground due to gravity, and the second is a beam that sticks to the ground through reversible adhesion. In both cases, the noncontacting length varies dynamically. We first obtain the governing equations and boundary conditions, including a transversality condition involving an end moment, using Hamilton's principle. Rescaling the variable length to a constant value, we obtain partial differential equations with time varying coefficients, which, upon linearization, give the natural frequencies of vibration. The natural frequencies for the first case (gravity without adhesion) match that of a clamped-clamped beam of the same nominal length; frequencies for the second case, however, show no such match. We develop simple, if atypical, single degree of freedom approximations for the first modes of these two systems, which provide insights into the role of the static deflection profile, as well as the end moment condition, in determining the first natural frequencies of these systems. Finally, we consider small transverse sinusoidal forcing of the first case and find that the governing equation contains both parametric and external forcing terms. For forcing at resonance, w find that either the internal or the external forcing may dominate.

Wall Shear Fluctuations in a Turbulent Boundary Layer

IN the last two decades, the instantaneous structure of a turbulent boundary layer has been examined by many in an effort to understand the dynamics of the flow. Distinct and well-defined flow patterns that seem to have great relevance to the turbulence production mechanism have been observed in the wall region.1'2 The flow near the wall is intermittent with periodic eruptions of the fluid, a phenomenon generally termed "bursting process." Earlier investigations in this field were limited to liquid flows at low speeds and the entire flowpattern was observed using flow visualization techniques.Study was later extended to boundary-layer flows in windtunnels at higher speeds and Reynolds numbers using hot-wiresignals for the analysis of the bursting phenomenon.

Unsteady three-dimensional boundary layer flow over a flat plate with attached cylinder

The unsteady laminar incompressible three-dimensional boundary layer flow and heat transfer on a flat plate with an attached cylinder have been studied when the free stream velocity components and wall temperature vary inversely as linear and quadratic functions of time, respectively. The governing semisimilar partial differential equations with three independent variables have been solved numerically using a quasilinear finite-difference scheme. The results indicate that the skin friction increases with parameter λ which characterizes the unsteadiness in the free stream velocity and the streamwise distance Image , but the heat transfer decreases. However, the skin friction and heat transfer are found to change little along Image . The effect of the Prandtl number on the heat transfer is found to be more pronounced when λ is small, whereas the effect of the dissipation parameter is more pronounced when λ is comparatively large.

Wood properties and processing outcomes for plantation grown African mahogany (Khaya senegalensis) trees from Clare, Queensland (18 and 20 year-old trees) and Katherine, Northern Territory (14 year-old trees).

Khaya senegalensis, African mahogany, a high-value hardwood, was introduced in the Northern Territory (NT) in the 1950s; included in various trials there and at Weipa, Q in the 1960s-1970s; planted on ex mine sites at Weipa (160 ha) until 1985; revived in farm plantings in Queensland and in trials in the NT in the 1990s; adopted for large-scale, annual planting in the Douglas-Daly region, NT from 2006 and is to have the planted area in the NT extended to at least 20,000 ha. The recent serious interest from plantation growers, including Forest Enterprises Australia Ltd (FEA), has seen the establishment of some large scale commercial plantations. FEA initiated the current study to process relatively young plantation stands from both Northern Territory and Queensland plantations to investigate the sawn wood and veneer recovery and quality from trees ranging from 14 years (NT – 36 trees) to 18-20 years (North Queensland – 31 trees). Field measures of tree size and straightness were complemented with log end splitting assessment and cross-sectional disc sample collection for laboratory wood properties measurements including colour and shrinkage. End-splitting scores assessed on sawn logs were relatively low compared to fast grown plantation eucalypts and did not impact processing negatively. Heartwood proportion in individual trees ranged from 50% up to 92 % of butt cross-sectional disc area for the visually-assessed dark coloured central heartwood and lighter coloured transition wood combined. Dark central heartwood proportion was positively related to tree size (R2 = 0.57). Chemical tests failed to assist in determining heartwood – sapwood boundary. Mean basic density of whole disc samples was 658 kg/m3 and ranged among trees from 603 to 712 kg/m3. When freshly sawn, the heartwood of African mahogany was orange-red to red. Transition wood appeared to be pinkish and the sapwood was a pale yellow colour. Once air dried the heartwood colour generally darkens to pinkish-brown or orange-brown and the effect of prolonged time and sun exposure is to darken and change the heartwood to a red-brown colour. A portable colour measurement spectrophotometer was used to objectively assess colour variation in CIE L*, a* and b* values over time with drying and exposure to sunlight. Capacity to predict standard colour values accurately after varying periods of direct sunlight exposure using results obtained on initial air-dried surfaces decreased with increasing time to sun exposure. The predictions are more accurate for L* values which represent brightness than for variation in the a* values (red spectrum). Selection of superior breeding trees for colour is likely to be based on dried samples exposed to sunlight to reliably highlight wood colour differences. A generally low ratio between tangential and radial shrinkages was found, which was reflected in a low incidence of board distortion (particularly cupping) during drying. A preliminary experiment was carried out to investigate the quality of NIR models to predict shrinkage and density. NIR spectra correlated reasonably well with radial shrinkage and air dried density. When calibration models were applied to their validation sets, radial shrinkage was predicted to an accuracy of 76% with Standard Error of Prediction of 0.21%. There was also a strong predictive power for wood density. These are encouraging results suggesting that NIR spectroscopy has good potential to be used as a non-destructive method to predict shrinkage and wood density using 12mm diameter increment core samples. Average green off saw recovery was 49.5% (range 40 to 69%) for Burdekin Agricultural College (BAC) logs and 41.9% (range 20 to 61%) for Katherine (NT) logs. These figures are about 10% higher than compared to 30-year-old Khaya study by Armstrong et al. (2007) however they are inflated as the green boards were not docked to remove wane prior to being tallied. Of the recovered sawn, dried and dressed volume from the BAC logs, based on the cambial face of boards, 27% could potentially be used for select grade, 40% for medium feature grade and 26% for high feature grades. The heart faces had a slightly higher recovery of select (30%) and medium feature (43%) grade boards with a reduction in the volume of high feature (22%) and reject (6%) grade boards. Distribution of board grades for the NT site aged 14 years followed very similar trends to those of the BAC site boards with an average (between facial and cambial face) 27% could potentially be used for select grade, 42% for medium feature grade, 26% for high feature grade and 5% reject. Relatively to some other subtropical eucalypts, there was a low incidence of borer attack. The major grade limiting defects for both medium and high feature grade boards recovered from the BAC site were knots and wane. The presence of large knots may reflect both management practices and the nature of the genetic material at the site. This stand was not managed for timber production with a very late pruning implemented at about age 12 years. The large amount of wane affected boards is indicative of logs with a large taper and the presence of significant sweep. Wane, knots and skip were the major grade limiting defects for the NT site reflecting considerable amounts of sweep with large taper as might be expected in younger trees. The green veneer recovered from billets of seven Khaya trees rotary peeled on a spindleless lathe produced a recovery of 83% of green billet volume. Dried veneer recovery ranged from 40 to 74 % per billet with an average of 64%. All of the recovered grades were suitable for use in structural ply in accordance to AS/NZ 2269: 2008. The majority of veneer sheets recovered from all billets was C grade (27%) with 20% making D grade and 13% B grade. Total dry sliced veneer recovery from the logs of the two largest logs from each location was estimated to be 41.1%. Very positive results have been recorded in this small scale study. The amount of colour development observed and the very reasonable recoveries of both sawn and veneer products, with a good representation of higher grades in the product distribution, is encouraging. The prospects for significant improvement in these results from well managed and productive stands grown for high quality timber should be high. Additionally, the study has shown the utility of non-destructive evaluation techniques for use in tree improvement programs to improve the quality of future plantations. A few trees combined several of the traits desired of individuals for a first breeding population. Fortunately, the two most promising trees (32, 19) had already been selected for breeding on external traits, and grafts of them are established in the seed orchard.

Genetic burden associated with varying degrees of disease severity in endometriosis

Endometriosis is primarily characterized by the presence of tissue resembling endometrium outside the uterine cavity and is usually diagnosed by laparoscopy. The most commonly used classification of disease, the revised American Fertility Society (rAFS) system to grade endometriosis into different stages based on disease severity (I to IV), has been questioned as it does not correlate well with underlying symptoms, posing issues in diagnosis and choice of treatment. Using two independent European genome-wide association (GWA) datasets and top-level classification of the endometriosis cases based on rAFS [minimal or mild (Stage A) and moderate-to-severe (Stage B) disease], we previously showed that Stage B endometriosis has greater contribution of common genetic variation to its aetiology than Stage A disease. Herein, we extend our previous analysis to four endometriosis stages [minimal (Stage I), mild (Stage II), moderate (Stage III) and severe (Stage IV) disease] based on the rAFS classification system and compared the genetic burden across stages. Our results indicate that genetic burden increases from minimal to severe endometriosis. For the minimal disease, genetic factors may contribute to a lesser extent than other disease categories. Mild and moderate endometriosis appeared genetically similar, making it difficult to tease them apart. Consistent with our previous reports, moderate and severe endometriosis showed greater genetic burden than minimal or mild disease. Overall, our results provide new insights into the genetic architecture of endometriosis and further investigation in larger samples may help to understand better the aetiology of varying degrees of endometriosis, enabling improved diagnostic and treatment modalities.

Microstructural evolution and grain boundary sliding in a superplastic magnesium AZ31 alloy

Tensile experiments on a fine-grained single-phase Mg–Zn–Al alloy (AZ31) at 673 K revealed superplastic behavior with an elongation to failure of 475% at 1 × 10−4 s−1 and non-superplastic behavior with an elongation to failure of 160% at 1 × 10−2 s−1; the corresponding strain rate sensitivities under these conditions were 0.5 and 0.2, respectively. Measurements indicated that the grain boundary sliding (GBS) contribution to strain ξ was 30% under non-superplastic conditions; there was also a significant sharpening in texture during such deformation. Under superplastic conditions, ξ was 50% at both low and high elongations of 20% and 120%; the initial texture became more random under such conditions. In non-superplastic conditions, deformation occurred under steady-state conditions without grain growth before significant flow localization whereas, under superplastic conditions, there was grain growth during the early stages of deformation, leading to strain hardening. The grains retained equiaxed shapes under all experimental conditions. Superplastic deformation is attributed to GBS, while non-superplastic deformation is attributed to intragranular dislocation creep with some contribution from GBS. The retention of equiaxed grain shapes during dislocation creep is consistent with a model based on local recovery related to the disturbance of triple junctions.

Compressible 2nd-order boundary-layers for 3-dimensional stagnation point flows with mass-transfer

All the second-order boundary-layer effects have been studied for the steady laminar compressible 3-dimensional stagnation-point flows with variable properties and mass transfer for both saddle and nodal point regions. The governing equations have been solved numerically using an implicit finite-difference scheme. Results for the heat transfer and skin friction have been obtained for several values of the mass-transfer rate, wall temperature, and also for several values of parameters characterizing the nature of stagnation point and variable gas properties. The second-order effects on the heat transfer and skin friction at the wall are found to be significant and at large injection rates, they dominate over the results of the first-order boundary layer, but the effect of large suction is just the opposite. In general, the second-order effects are more pronounced in the saddle-point region than in the nodal-point region. The overall heat-transfer rate for the 3-dimensional flows is found to be more than that of the 2-dimensional flows.

Unsteady Self-similar Stagnation Point Boundary Layers for Micropolar Fluids

The self-similar solution of the unsteady laminar incompressible two-dimensional and axisymmetric stagnation point boundary layers for micropolar fluids governing the flow and heat transfer problem has been obtained when the free stream velocity and the square of the mass transfer vary inversely as a linear function of time. The nonlinear ordinary differential equations governing the flow have been solved numerically using a quasilinear finite-Difference scheme. The results indicate that the coupling parameter, mass transfer and unsteadiness in the free stream velocity strongly affect the skin friction, microrotation gradient and heat transfer whereas the effect of microrotation parameter is strong only on the microrotation gradient. The heat transfer is strongly dependent on the prandtl number whereas the skin friction gradient are unaffected by it.

Boundary layer transition observations on a body of revolution with surface heating and cooling in water

Boundary layer flow visualization in water with surface heat transfer was carried out on a body of revolution which had the predicted possibility of laminar separation under isothermal conditions. Flow visualization was by in-line holographic technique. Boundary layer stabilization, including elimination of laminar separation, was observed to take place on surface heating. Conversely, boundary layer destabilization was observed on surface cooling. These findings are consistent with the theoretical predictions of Wazzan et al. in The stability and transition of heated and cooled incompressible laminar boundary layers, in Proceedings of the Fourth International Heat Transfer Conference, Vol. 2, FCI 4. Elsevier, Amsterdam (1970).