Hyperbolic damped-wave models for transient light-pulse propagation in scattering media

Transient optical transport in highly scattering media such as tissues is usually modeled as a diffusion process in which the energy flux is assumed proportional to the fluence (intensity averaged over all solid angles) gradients. Such models exhibit an infinite speed of propagation of the optical signal, and finite transmission values are predicted even at times smaller than those associated with the propagation of light. If the hyperbolic, or wave, nature of the complete transient radiative transfer equation is retained, the resulting models do not exhibit such drawbacks. Additionally, the hyperbolic equations converge to the solution at a faster rate, which makes them very attractive for numerical applications in time-resolved optical tomography.     

A perturbation analysis of rapid crack propagation in pressurised pipe

A steady state analysis is given which models rapid crack propagation in a pressurised pipe as a beam. The interaction of the gas escaping through the crack flares the pipe giving a greatly enhanced energy release rate G. The solution shows a clear maximum in G which is confirmed with numerical results. Experimental decompression times are also predicted by the model. Perturbations in the crack speed can be deduced from the steady state solution and these are shown to be harmonic and in good agreement with observations. It is also suggested that these speed oscillations could give rise to crack snaking. This revised version was published online in July 2006 with corrections to the Cover Date.     

Hyperbolic contraction measuring systems for extensional flow

In this paper an experimental method for extensional measurements on medium viscosity fluids in contraction flow is evaluated through numerical simulations and experimental measurements. This measuring technique measures the pressure drop over a hyperbolic contraction, caused by fluid extension and fluid shear, where the extensional component is assumed to dominate. The present evaluative work advances our previous studies on this experimental method by introducing several contraction ratios and addressing different constitutive models of varying shear and extensional response. The constitutive models included are those of the constant viscosity Oldroyd-B and FENE-CR models, and the shear-thinning LPTT model. Examining the results, the impact of shear and first normal stress difference on the measured pressure drop are studied through numerical pressure drop predictions. In addition, stream function patterns are investigated to detect vortex development and influence of contraction ratio. The numerical predictions are further related to experimental measurements for the flow through a 15:1 contraction ratio with three different test fluids. The measured pressure drops are observed to exhibit the same trends as predicted in the numerical simulations, offering close correlation and tight predictive windows for experimental data capture. This result has demonstrated that the hyperbolic contraction flow is well able to detect such elastic fluid properties and that this is matched by numerical predictions in evaluation of their flow response. The hyperbolical contraction flow technique is commended for its distinct benefits: it is straightforward and simple to perform, the Hencky strain can be set by changing contraction ratio, non-homogeneous fluids can be tested, and one can directly determine the degree of elastic fluid behaviour. Based on matching of viscometric extensional viscosity response for FENE-CR and LPTT models, a decline is predicted in pressure drop for the shear-thinning LPTT model. This would indicate a modest impact of shear in the flow since such a pressure drop decline is relatively small. It is particularly noteworthy that the increase in pressure drop gathered from the experimental measurements is relatively high despite the low Deborah number range explored.     

T - Vmin addressing mode and an improved equivalent circuit model for ferroelectric liquid crystal displays

The authors describe an improved model for modelling the electro-optical response of a ferroelectric liquid crystal display and discuss its applicability. The model includes the direct coupling of applied electric fields to dielectric permittivity, an effect not accounted for in previous equivalent circuits. Compared with previous models, the new model has more capability in optical response prediction and device setup optimisation when the dielectric biaxiality of ferroelectric liquid crystals is of a relatively high value. In the improved model, different trends of switching time are observed as drive voltage rises in cases of positive anisotropy and negative anisotropy. The bend in tau-V_min mode, that is, the minimum pulse area for switching directors, is measured and the mechanism of optical contrast enhancement and switching process complemented by high-frequency ac pulses is clearly explained. Results obtained from the improved model compare favourably with that obtained from numerical models and from testing of a real cell     

Numerical modelling of particle distribution effects on fatigue in Al–SiCp composites

Various reports in the literature have highlighted the effects of particle distribution on the fatigue behaviour of particulate reinforced metal matrix composites (PMMCs), although few attempts have been made at modelling such effects. A micromechanical understanding of the effects of clustering on short crack growth behaviour in Al–SiC_p composites has been achieved via finite element modelling. Comparison of preliminary models with the literature has shown that shielding/anti-shielding effects were significantly affected by the relative sizes of the particle and the overall model such that, when edge effects were removed, a crack was predicted to be accelerated rather than decelerated as it propagated through closely spaced pairs of particles. Consistent differences were identified between models with homogeneous versus clustered particle arrangements in terms of crack path morphologies and local crack–tip stress intensity fluctuations. Furthermore, predicted influences of clustering on growth rates in the numerical models were found to be consistent with previous experimental results (i.e. growth rates rose with increased clustering), demonstrating that load transfer effects associated with changes in particle distribution may play a direct role in controlling the growth of short cracks in these materials.     

Modelling of adhesive bonding for aircraft structures applying the insertion squeeze flow method

A numerical model for simulating the flow of an adhesive during an insertion squeeze flow (ISF) bonding process for joining composite structures is presented. The model is developed using the commercial CFD code FLUENT®. The numerical model is validated for a Newtonian fluid by comparing the predicted insertion forces that act during the insertion process with those obtained both from experiments and calculated using a simplified analytical model. Very good agreement is obtained. The model is then used to investigate the effect of insertion speed and adhesive viscosity on the ISF bonding process. The findings, and the further application of the numerical and analytical models, are valuable to ensure the quality of Pi-slot joints.     

Investigation of models for relating roundabout safety to predicted speed

Despite widespread recognition of operating speed as a key safety-related variable for roundabouts, there is no consensus on the best models for capturing the relationship between crashes and speed, or, for that matter, on how speed can be estimated in situations where it cannot be observed (such as when a roundabout is being designed or redesigned). This paper uses US and Italian roundabout approach-level data to investigate models relating safety to various measures of predicted speed. This is an indirect approach for developing safety models for estimating the effects of design features, the premise being that these features can better predict speed, which, in turn, can be used as a predictor of crash frequency. After exploring various possibilities, the approach average speed (AAS) – defined as the average of entry, upstream circulating and exiting speeds in this study – was found to be the speed measure that best predicts safety. US data were used to develop a Bayesian Poisson-gamma safety model based on predicted AAS with random coefficients and varying dispersion parameter. This model structure was not appropriate for the Italian data used to examine whether the approach could be generalized to data for another country. For that data, a zero-inflated Poisson (ZIP) model was found to be suitable. Notwithstanding the heterogeneity of the model structure, the investigation suggests that the indirect approach for evaluating the safety of a roundabout is a sound one in that it can preserve model parsimony while capturing the effects of design changes that affect safety.     

Experimental Testing and Full and Homogenized Numerical Models of the Low Velocity and Dynamic Deformation of the Trapezoidal Aluminium Corrugated Core Sandwich

The simulations of the low velocity and dynamic deformation of a multi‐layer 1050‐H14 Al trapezoidal zig‐zag corrugated core sandwich were investigated using the homogenized models (solid models) of a single core layer (without face sheets). In the first part of the study, the LS‐DYNA MAT‐26 material model parameters of a single core layer were developed through experimental and numerical compression tests on the single core layer. In the second part, the fidelities of the developed numerical models were checked by the split‐Hopkinson pressure bar direct impact, low velocity compression and indentation and projectile impact tests. The results indicated that the element size had a significant effect on the initial peak and post‐peak stresses of the homogenized models of the direct impact testing of the single‐layer corrugated sandwich. This was attributed to the lack of the inertial effects in the homogenized models, which resulted in reduced initial peak stresses as compared with the full model and experiment. However, the homogenized models based on the experimental stress–strain curve of the single core layer predicted the low velocity compression and indentation and projectile impact tests of the multi‐layer corrugated sandwich with an acceptable accuracy and reduced the computational time of the models significantly.     

Thermal-structural modeling of polymer Bragg grating waveguides illuminated by a light emitting diode

This study reports both analytical and numerical thermal-structural models of polymer Bragg grating (PBG) waveguides illuminated by a light emitting diode (LED). A polymethyl methacrylate (PMMA) Bragg grating (BG) waveguide is chosen as an analysis vehicle to explore parametric effects of incident optical powers and substrate materials on the thermal-structural behavior of the BG. Analytical models are verified by comparing analytically predicted average excess temperatures, and thermally induced axial strains and stresses with numerical predictions. A parametric study demonstrates that the PMMA substrate induces more adverse effects, such as higher excess temperatures, complex axial temperature profiles, and greater and more complicated thermally induced strains in the BG compared with the Si substrate.     

Iterative and transient numerical models for flow simulation of injection pultrusion

During injection pultrusion, the flow front is initially transient and approaches a quasi-steady-state in a short time. It is the steady-state flow front that determines the filling quality of the pultruded composite part. Both transient and iterative finite element/nodal volume models have been developed to predict the steady-state flow fronts during injection pultrusion processes. In the present paper, the numerical performance of the transient and iterative models is systematically investigated for various pultrusion process and material parameters, such as pull speed, injection pressure and the ratio of permeabilities in the pulling and the transverse directions. It is shown that the iterative model is numerically stable and robust. It predicts steady-state flow fronts which are in excellent agreement with those predicted by the transient model in all the cases investigated. More importantly, the iterative model is much more efficient than the transient model and the high efficiency is not affected by the modelling parameters used. It generally uses less than one tenth of the computer time required by the transient model to reach the converged solutions. Therefore, the iterative model should always be used to predict the steady-state resin flow fronts.     

Frequency translation of light waves by propagation around an optical ring circuit containing a frequency shifter: II. Theoretical analysis

Theoretical aspects of the frequency-translation ring circuit are considered through numerical simulations. We analyze the signal and noise propagation around an optical ring circuit that contains a frequency shifter, an erbium-doped fiber amplifier and a bandpass filter (BPF). The relations between the frequency-translation limit and some important parameters such as the BPF bandwidth and the polarization state are clarified. Numerical results for the frequency-translation limit are compared with reported experiments and a frequency translation of more than 100 GHz is predicted.     

Analysis of Optical Pulse Distortion Through Clouds for Satellite to Earth Adaptive Optical Communication

Abstract

Clouds, if part of an optical communication channel, cause temporal widening and attenuation of optical pulse power. Space optical communication from satellite to earth (ground or airplane) occasionally involves clouds as part of the optical channel. Here, based upon Monte Carlo simulations, mathematical models are developed for the temporal characteristics of optical pulse propagation through clouds. These include temporal impulse response, transfer function, bandwidth, received energy and bode analysis. The method presented here can be used as an inclusive framework for developing other mathematical models of other characteristics of radiation propagating through clouds, as required. Several conclusions of this work are obtained. One is that simple prediction models can be applied to adaptive methods of optical communication. Another is that using shorter wavelengths such as 0·532 μm yields least temporal widening and maximum received power, and is thus preferable for optical communication. In addition, the simulation results strongly support the use of the double gamma function model to best describe optical pulse spread through clouds. This work is the first, to the best of the authors' knowledge, to present a comprehensive analysis of space optical communication through clouds.     

A numerical model for a dew-point counter-flow indirect evaporative cooler using a modified boundary condition and considering effects of entrance regions

A numerical model for dew-point counter-flow indirect evaporative coolers was presented. Unlike the conventional models, a more realistic boundary condition on separating wall was obtained by simultaneous solving of momentum, energy, and mass transfer equations of flows coupled. In addition, the model's accuracy was increased through considering 3D hydrodynamical and thermal developing flows. The model predicted the supply air temperature and the results were compared to experimental data as well as previous numerical models. It was shown that the maximum deviation of the supply air temperature was under ±3.53 %. It was found that these modifications on the numerical model reduced the computation error about 41.1 %. Moreover, it was found that the difference between maximum errors of 3D and 2D models was about 4.5 %; however, the 3D model consumes 14 times more CPU time. Finally, the sensitivity of the system's operation was studied using the developed model.     

Improved Grey predictor rolling models for wind power prediction

A new technique for one step ahead average hourly wind speed forecasting and wind turbines' output power prediction based on using the Grey predictor models is presented. The required mathematical formulation for developing the Grey predictor models is also presented. The obtained results from the proposed models are compared with the corresponding results obtained when using the persistent model. Utilising the traditional Grey model, GM(1,1) was first investigated and showed good improvement over the persistent model. However, the generated results demonstrate the presence of intervals with overshoots in the predicted values. To reduce such overshoots, a modified version for the Grey predictor model referred to as the adaptive alpha GM(1,1) model is investigated and two new models are proposed, hereafter, referred to as the improved Grey model and the averaged Grey model. The presented results demonstrate the effectiveness, the accuracy and the superiority of the proposed averaged Grey model for wind speed and wind power prediction.     

Three-dimensional beam propagation model for the optical path of light through a nematic liquid crystal

A three-dimensional beam propagation model is presented which, given a director profile, calculates the electric and magnetic fields for a light wave as it travels through a liquid crystal structure using a predictive-corrector Crank–Nicholson numerical method and adjusts for impedance effects in the direction of propagation. The results from the model are compared to both analytical solutions for simpler director profiles and other optical models for more complicated director profiles.     

基坑开挖数值模拟中土体本构模型的选取

基坑开挖数值分析中的一个关键问题是选取一个合适的土体本构模型。该文通过对基坑开挖过程中土体的主要应力变化路径进行分析, 指出开挖条件下的土体本构模型应能合理考虑土体变形特性的应力路径相关性和压硬性。在介绍与分析几种常用土体本构模型特点的基础之上, 通过模拟应力路径三轴试验、基坑工程算例与工程实例的对比分析, 探讨了常见土体本构模型的适用性。分析表明, Hardening Soil Model采用了不同的加荷与卸荷模量, 能够反映土体应力路径的影响, 且考虑了土体模量的应力水平相关性, 能预测得到较合理的坑壁侧移、地表沉降以及支护结构的内力, 因而建议采用Hardening Soil Model进行基坑开挖数值模拟分析。     

Design of corrugated optical waveguide filters through a direct numerical solution of the coupled Gel'fand-Levitan-Marchenko integral equations

Regarding the design problem of corrugated planar optical waveguide filters, a new numerical method is presented consisting of a direct numerical solution of the coupled Gel'fand-Levitan-Marchenko integral equations. This method, which uses leapfrogging in space and time, is exact in principle and avoids some difficulties encountered in previously derived analytical methods of solution. Straightforward numerical calculations permit the design of several classes of filters such as Butterworth, Chebyshev, Cauer (elliptic) and others, as presented in the paper. The accuracy of our proposed method of design is checked in several ways, mainly through the numerical solution of the corresponding direct-scattering problem (Riccati differential equation).     

Modeling of Environmental Effects on Thermal Detection of Subsurface Damage in Concrete

A significant form of deterioration in concrete is corrosion of embedded reinforcing steel that can cause subsurface delaminations and spalling. Infrared thermography can be used to detect delaminations based on variations in surface temperature that are caused by the disruption of the heat flow through the delaminated area. The surrounding environmental conditions such as sunlight, ambient temperature variation, and wind speed are critical for heat transfer, and as such the technology depends on these environmental conditions. This paper describes a numerical model developed to predict thermal contrasts for subsurface delaminations based on a given set of environmental conditions surrounding the concrete. The finite element method (FEM) was used to perform 3-D nonlinear transient heat-transfer analysis of a large concrete block with embedded Styrofoam targets intended to provide an idealized model of subsurface delaminations. The effectiveness of the modeling was evaluated by comparing the thermal contrasts predicted by the model and those obtained from experimental testing of an actual concrete block of the same dimensions. The correlation and error between the experimental testing and the model results indicated that the model could be an effective tool for the prediction of anticipated thermal contrasts based on given weather conditions.     

Steady Non-ideal Detonations in Cylindrical Sticks of Explosives

Numerical simulations of detonations in cylindrical rate-sticks of highly non-ideal explosives are performed, using a simple model with a weakly pressure-dependent rate law and a pseudo-polytropic equation of state. Some numerical issues with such simulations are investigated, and it is shown that very high resolution (hundreds of points in the reaction zone) are required for highly accurate (converged) solutions. High-resolution simulations are then used to investigate thequalitative dependences of the detonation driving zone structure on the diameter and degree of confinement of the explosive charge. The simulation results are used to show that, given the radius of curvature of the shock at the charge axis, the steady detonation speed and the axial solution are accurately predicted by a quasi-one-dimensional theory, even for cases where the detonation propagates at speeds significantly below the Chapman-Jouguet speed. Given reaction rate and equation of state models, this quasi-one-dimensional theory offers a significant improvement to Wood-Kirkwood theories currently used in industry     

Simple Mathematical Models for Temporal,Spatial, Angular,and Attenuation Characteristics of Light Propagating Through the Atmosphere for Space Optical Communication:

Abstract

Mathematical models are developed to characterize propagation through a turbid medium at three different wavelengths in the visible and near infrared spectral range. These models are based upon relations between the temporal, angular, and spatial spread of electromagnetic unpolarized radiation, geometrical path length, particle size distribution, and the medium's propagation parameters such as Mie scattering, and absorption coefficients, Mie phase-function, and optical thickness. Calculations of the radiation characteristics were carried out using Monte Carlo simulations. Here, atmospheric particulates are used to model turbid media for optical thickness between 1 and 6, emphasizing optical communication applications, The advantage of this work is the ability to predict simply and in real time important radiation parameters relevant to any optical communication system. Results indicate very high correlation between optical thickness and propagation characteristics. For transmission, comparison is made to Bucher's model. Results are similar except for absorption effects which are not included in Bucher's model. Some important conclusions are derived such as the prediction that it is advantageous to use longer wavelength radiation through the atmosphere. In addition, there is a very dominant back scattering effect, involving up to 50% of transmitted power for optical densities as low as 6. On the other hand, power density of received scattered light is very low for conventional distances relevant to satellite optical communication, and can be neglected. On the basis of simulation results, the received radiation is of unscattered light only for any optical communication application. The dominant mechanism relating to radiation attenuation is scattering rather than absorption.