An effective medium model for elastic waves in microcrack damaged media

Direct numerical simulations of waves traveling through microcrack-damaged media are conducted and the results are compared to effective medium calculations to determine the applicability of the latter for studying wave propagation. Both tensile and compressive waves and various angular distributions of randomly-located cracks are considered. The relationships between the input wavelength and the output wave speed and output signal strength are studied. The numerical simulations show that the wave speed is nearly constant when 1/ka > 60 for tensile waves and 1/ka > 10 for compressive waves, where k is the wave number and a is the average half-crack length. The direct simulations also show that when the input wavelength is much longer than the crack length, 1/ka > 60, the wave can pass through the damaged medium relatively unattenuated. On the other hand, when the input wavelength is shorter than a “cut off” wave length, the output wave magnitude decreases linearly with the input wavelength. The effective medium wave speed and magnitude calculations are not dependent on the input wavelength and therefore the results correspond well with the numerical simulations for large 1/ka. This suggests a minimum wavelength for which the homogenized methods can be used for studying these problems.     

Three-dimensional characterization of the light distribution from diffusing cylindrical optical-fiber tips

A rapid and sensitive technique for quantitatively examining the three-dimensional light distribution from optical-fiber diffusers for photodynamic therapy applications was developed. We have used this system to evaluate the longitudinal and azimuthal uniformity of the light output from cylindrical diffusing tips and have determined a standard detector configuration for assessing the optical quality of these diffusers. As an example of the sensitivity and the accuracy of this method, the effect of microbending of the fiber on the output intensity distribution, as well as the effect of the choice of laser used, was investigated and was seen to have a significant impact on the uniformity of these diffusers.     

Utility based maintenance analysis using a Random Sign censoring model

Industrial systems subject to failures are usually inspected when there are evident signs of an imminent failure. Maintenance is therefore performed at a random time, somehow dependent on the failure mechanism. A competing risk model, namely a Random Sign model, is considered to relate failure and maintenance times. We propose a novel Bayesian analysis of the model and apply it to actual data from a water pump in an oil refinery. The design of an optimal maintenance policy is then discussed under a formal decision theoretic approach, analyzing the goodness of the current maintenance policy and making decisions about the optimal maintenance time.     

The identification of model effective dimensions using global sensitivity analysis

It is shown that the effective dimensions can be estimated at reasonable computational costs using variance based global sensitivity analysis. Namely, the effective dimension in the truncation sense can be found by using the Sobol' sensitivity indices for subsets of variables. The effective dimension in the superposition sense can be estimated by using the first order effects and the total Sobol' sensitivity indices. The classification of some important classes of integrable functions based on their effective dimension is proposed. It is shown that it can be used for the prediction of the QMC efficiency. Results of numerical tests verify the prediction of the developed techniques.     

An effective stress based numerical model for hydro-mechanical analysis in unsaturated porous media

 A fully coupled flow-deformation model is presented for the behaviour of unsaturated porous media. The governing equations are derived based on the equations of equilibrium, effective stress concept, Darcy's law, Henry's law, and the conservation of fluid mass. Macroscopic coupling between the flow and deformation fields is established through the effective stress parameters. The microscopic link between the volumetric deformations of the two pore system (i.e. the pore-air and the pore-water) is established using Betti's reciprocal theorem. Both links are essential for a proper modelling of flow and deformation in unsaturated porous media. The discretised form of the governing equations is obtained using the finite element technique. As application of the model, experimental results from several laboratory tests reported in the literature are modelled numerically. Good agreement is obtained between the numerical and the experimental results in all cases.     

Imaging with diffusing light: an experimental study of the effect of background optical properties

The overall image quality and diagnostic potential of time-resolved transmittance imaging depend on sensitivity to optical contrast, capacity to discriminate scattering from absorption contributions, and spatial resolution. We have investigated experimentally the effects of the optical properties of the background medium on the overall image quality of optical imaging based on fitting the experimental data to the solution of the diffusion equation and on time gating. Images were acquired from phantoms with different background optical properties, while the optical contrast between inhomogeneities and background is kept constant. Data were collected every 0.2 cm over a 6 cm x 6 cm area from realistic tissue phantoms containing cylindrical inhomogeneities (1 cm high and 1 cm in diameter) embedded in a 5-cm-thick turbid slab. The optical coefficients of the background were varied in the ranges of 5-15 cm(-1) for transport scattering and 0.02-0.08 cm(-1) for absorption. The optical contrast for the inclusions was kept at values of -50% and +50% for the scattering and -75% and +300% for the absorption. The results show that both high scattering and high absorption are beneficial.     

Investigation of an adaptive sampling method for data interpolation using radial basis functions

An adaptive sampling method is presented for optimizing the location of data points in parameter space for multidimensional data interpolation. The method requires a small number of points to begin, and achieves a compromise between space‐filling updates and local refinement in areas where the data are nonlinear, as measured by the Laplacian. A smooth separation function quantifies the sample spacing, and this is blended with the Laplacian to form a criterion on which to assess potential new sample positions. Validation results are presented using two‐dimensional analytic test cases, which demonstrate that the method can recover known optimal designs and gives improvement over data‐independent approaches. In addition, a detailed analysis of the various model parameters is presented. Initial findings are very promising, and it is hoped that further work using the method to generate an aerodynamic database using CFD simulations will lead to a reduction in the number of points required for a given modelling accuracy. Copyright © 2010 John Wiley & Sons, Ltd.     

Transmittance analysis of three-dimensional photonic crystals by the effective medium theory

A simple method for calculating the transmittance of three-dimensional photonic crystals is proposed. The crystals are divided into multilayer thin films, and each film is divided into rectangles with a minute width to calculate the effective permittivity of the film by the effective medium theory. Transmittance of the multilayer thin films is calculated with the matrix method. As the number of atomic layers increases, remarkable stop bands appear. When the refractive index of photonic atoms increases, the stop band shifts to a lower frequency, the band widens, and the number of bands increases. Polarization and incident angle dependences are also analyzed. The limit of application for this calculation method is also discussed.     

Constitutive modelling for granular media using an anisotropic distortional yield model

Summary It has been attempted here to model the mechanical response of granular media through a combination of analytical, numerical and experimental techniques. Based on the experimental evidence obtained from a series of triaxial laboratory experiments on specimens made of glass beads, the model attempts to simulate the movement of yield surfaces and the stress-strain relationships. It is found that the yield surface distorts in the direction of loading in a manner analogous to that of metals. An anisotropic distortional yield model is formulated in order to describe the experimental behavior exhibited by these granular media. From the experimental yield surfaces the parameters of the model have been evaluated and a hardening rule, based on the Phillips rule, has been determined. Associativity on the -plane has been observed experimentally. Using these concepts the constitutive formulation has been presented and the stress-strain curves have been generated. From the comparisons of these curves we observe a good correlation between the model and the experimental observations.     

Simulation and analysis of the effective permittivity for two-phase composite medium

Based on the effective medium theory, we calculated the complex effective permittivity of the twophase composite medium, consisting of circular inclusions embedded in a surrounding host. Results show that the maximum dielectric loss of the composite medium can be obtained by tuning the dielectric properties of the inclusion. This was confirmed by the results in literature. The local high temperature, as a consequence of the local electric field enhancement phenomenon, is the main reason that microwave heating can lead to a dramatic increase in the chemical reaction rate.     

Flow and conduction of inhomogeneous media. II. Variation of the basic model of an inhomogeneous medium

On the basis of a basic model of an inhomogeneous medium, different variations are proposed. Analytical dependences are obtained for the conduction of the in homogeneous medium and the results of calculation and experiment are compared.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 46, No. 2, pp. 247–252, February, 1982.     

Quantitative reconstruction of refractive index distribution and imaging of glucose concentration by using diffusing light

We show that a two-step reconstruction method can be adapted to improve the quantitative accuracy of the refractive index reconstruction in phase-contrast diffuse optical tomography (PCDOT). We also describe the possibility of imaging tissue glucose concentration with PCDOT. In this two-step method, we first use our existing finite-element reconstruction algorithm to recover the position and shape of a target. We then use the position and size of the target as a priori information to reconstruct a single value of the refractive index within the target and background regions using a region reconstruction method. Due to the extremely low contrast available in the refractive index reconstruction, we incorporate a data normalization scheme into the two-step reconstruction to combat the associated low signal-to-noise ratio. Through a series of phantom experiments we find that this two-step reconstruction method can considerably improve the quantitative accuracy of the refractive index reconstruction. The results show that the relative error of the reconstructed refractive index is reduced from 20% to within 1.5%. We also demonstrate the possibility of PCDOT for recovering glucose concentration using these phantom experiments.     

Linear elasticity of planar delaunay networks: Random field characterization of effective moduli

Summary A study is conducted of the influence of microscale geometric and physical randomness on effective moduli of a continuum approximation of disordered microstructures. A particular class of microstructures investigated is that of planar Delaunay networks made up of linear elastic rods connected by joints. Three types of networks are considered: Delaunay networks with random geometry and random spring constants, modified Delaunay networks with random geometry and random spring constants, and regular triangular networks with random spring constants. Using a structural mechanics method, a numerical study is conducted of the first and second order characteristics of random fields of effective moduli. In view of duality of the Delaunay triangulations to the Voronoi tessellations, these results provide the basis for development of analytical models of various heterogeneous solids, e.g. granular, fibrous.     

A descriptive analysis of light vehicle-heavy vehicle interactions using in situ driving data

Two recently completed on-road in situ (naturalistic) data collection efforts provided a large data set in which to conduct an examination of crashes, near-crashes, and crash-relevant conflicts (referred to as critical incidents throughout this paper) that occurred between light vehicles (LV) and heavy vehicles (HV). Video and non-video data collected during the two studies were used to characterize critical incidents that were recorded between LV and HV drivers. Across both studies, 210 LV-HV critical incidents were recorded. Of these, 78% were initiated by LV drivers, while the remaining 22% were initiated by HV drivers. Aggressive driving, on the part of the LV driver, was found to be the primary Contributing Factor for LV driver-initiated incidents. For HV driver-initiated incidents, the primary Contributing Factor was poor driving techniques. These results suggest that future efforts at addressing LV-HV interaction incidents should include focusing on aggressive LV drivers. Additionally, it is recommended that HV drivers might benefit from improved driver training that includes instruction on defensive driving skills. The in situ methodology provides an alternative to traditional crash databases, developed from police accident reports, for studying crash causation and driver behavior.     

Analysis of an apoptotic core model focused on experimental design using artificial data

The activation of caspases is a central mechanism in apoptosis. To gain further insights into complex processes like this, mathematical modelling using ordinary differential equations (ODEs) can be a very powerful research tool. Unfortunately, the lack of measurement data is a common problem in building such kinetic models, because it practically constrains the identifiability of the model parameters. An existing mathematical model of caspase activation during apoptosis was used in order to design future experimental setups that will help to maximise the obtained information. For this purpose, artificial measurement data are generated in silico to simulate potential experiments, and the model is fitted to this data. The model is also analysed using observability gramian and sensitivity analyses. The used analysis methods are compared. The artificial data approach allows one to make conclusions about system properties, identifiability of parameters and the potential information content of additional measurements for the used caspase activation model. The latter facilitates to improve the experimental design of further measurements significantly. The performed analyses reveal that several kinetic parameters are not at all, or only scarcely, identifiable, and that measurements of activated caspase 8 will maximally improve the parameter estimates. Furthermore, we can show that many assays with inhibitor of apoptosis protein (IAP) knockout cells only provide redundant information for our needs and as such do not have to be carried out.     

A model of the angular distribution of light scattered by multilayered media

Abstract

A model for calculating the spatial distribution of light flux scattered from multilayered inhomogeneous media, with index of refraction mismatches between layers, is described. By separating volume and surface properties, a compact matrix formulation is constructed for the solution of this problem, based on the application of the Discrete Ordinate Method to solve the Radiative Transfer Equation. Results are compared with those obtained with other techniques in order to evaluate the accuracy and efficiency of the proposed method. An optimization of the numerical procedure has been achieved, allowing application of the method to systems with a large number of slabs.     

Refined-scale panel data crash rate analysis using random-effects tobit model

Random effects tobit models are developed in predicting hourly crash rates with refined-scale panel data structure in both temporal and spatial domains. The proposed models address left-censoring effects of crash rates data while accounting for unobserved heterogeneity across groups and serial correlations within group in the meantime. The utilization of panel data in both refined temporal and spatial scales (hourly record and 1-mile roadway segments on average) exhibits strong potential on capturing the nature of time-varying and spatially varying contributing variables that is usually ignored in traditional aggregated traffic accident modeling. 1-year accident data and detailed traffic, environment, road geometry and surface condition data from a segment of I-25 in Colorado are adopted to demonstrate the proposed methodology. To better understand significantly different characteristics of crashes, two separate models, one for daytime and another for nighttime, have been developed. The results show major difference in contributing factors towards crash rate between daytime and nighttime models, implying considerable needs to investigate daytime and nighttime crashes separately using refined-scale data. After the models are developed, a comprehensive review of various contributing factors is made, followed by discussions on some interesting findings.     

Baseline correction method using an orthogonal basis for gas chromatography/mass spectrometry data

A baseline correction method that uses basis set projection to estimate spectral backgrounds has been developed and applied to gas chromatography/mass spectrometry (GC/MS) data. An orthogonal basis was constructed using singular value decomposition (SVD) for each GC/MS two-way data object from a set of baseline mass spectra. A novel aspect of this baseline correction method is the regularization parameter that prevents overfitting that may produce negative peaks in the corrected mass spectra or ion chromatograms. The number of components in the basis, the regularization parameter, and the mass spectral range from which the spectra were sampled to construct the basis were optimized so that the projected difference resolution (PDR) or signal-to-noise ratio (SNR) was maximized. PDR is a metric similar to chromatographic resolution that indicates the separation of classes in a multivariate data space. This new baseline correction method was evaluated with two synthetic data sets and a real GC/MS data set. The prediction accuracies obtained by using the fuzzy rule-building expert system (FuRES) and partial least-squares-discriminant analysis (PLS-DA) as classifiers were compared and validated through bootstrapped Latin partition (BLP) between data before and after baseline correction. The results indicate that baseline correction of the two-way GC/MS data using the proposed methods resulted in a significant increase in average PDR values and prediction accuracies.