Dispersion Model Parameters Research Articles

Overcoming the Contact Problem in Quantitative Attenuated Total Reflection Spectroscopy Analysis of Flat Samples.

A method for measuring the optical functions of a flat sample made of homogeneous and isotropic material, using attenuated total reflection spectroscopy when there is poor contact between the sample and the internal reflection element is presented. The approach consists in treating the spacing between the internal reflection element and the sample as an adjustable parameter, along with the dispersion model parameters, in the simultaneous fitting of s- and p-polarized spectra obtained when the gap distance is unknown. The method is tested with both synthetic and experimental (polystyrene) spectra. The results demonstrate the method's ability to accurately determine the optical functions even in the presence of a contact problem.

Quantifying the impact of meteorological uncertainty on emission estimates and the risk to aviation using source inversion for the Raikoke 2019 eruption

Abstract. Due to the remote location of many volcanoes, there is substantial uncertainty about the timing, amount and vertical distribution of volcanic ash released when they erupt. One approach to determine these properties is to combine prior estimates with satellite retrievals and simulations from atmospheric dispersion models to create posterior emission estimates, constrained by both the observations and the prior estimates, using a technique known as source inversion. However, the results are dependent not only on the accuracy of the prior assumptions, the atmospheric dispersion model and the observations used, but also on the accuracy of the meteorological data used in the dispersion simulations. In this study, we advance the source inversion approach by using an ensemble of meteorological data from the Met Office Global and Regional Ensemble Prediction System to represent the uncertainty in the meteorological data and apply it to the 2019 eruption of Raikoke. Retrievals from the Himawari-8 satellite are combined with NAME dispersion model simulations to create posterior emission estimates. The use of ensemble meteorology provides confidence in the posterior emission estimates and associated dispersion simulations that are used to produce ash forecasts. Prior mean estimates of fine volcanic ash emissions for the Raikoke eruption based on plume height observations are more than 15 times higher than any of the mean posterior ensemble estimates. In addition, the posterior estimates have a different vertical distribution, with 27 %–44 % of ash being emitted into the stratosphere compared to 8 % in the mean prior estimate. This has consequences for the long-range transport of ash, as deposition to the surface from this region of the atmosphere happens over long timescales. The posterior ensemble spread represents uncertainty in the inversion estimate of the ash emissions. For the first 48 h following the eruption, the prior ash column loadings lie outside an estimate of the error associated with a set of independent satellite retrievals, whereas the posterior ensemble column loadings do not. Applying a risk-based methodology to an ensemble of dispersion simulations using the posterior emissions shows that the area deemed to be of the highest risk to aviation, based on the fraction of ensemble members exceeding predefined ash concentration thresholds, is reduced by 49 %. This is compared to estimates using an ensemble of dispersion simulations using the prior emissions with ensemble meteorology. If source inversion had been used following the eruption of Raikoke, it would have had the potential to significantly reduce disruptions to aviation operations. The posterior inversion emission estimates are also sensitive to uncertainty in other eruption source parameters and internal dispersion model parameters. Extending the ensemble inversion methodology to account for uncertainty in these parameters would give a more complete picture of the emission uncertainty, further increasing confidence in these estimates.

Numerical Stability of Modified Lorentz FDTD Unified From Various Dispersion Models.

The finite-difference time-domain (FDTD) method has been widely used to analyze electromagnetic wave propagation in complex dispersive media. Until now, there are many reported dispersion models including Debye, Drude, Lorentz, complex-conjugate pole-residue (CCPR), quadratic complex rational function (QCRF), and modified Lorentz (mLor). The mLor FDTD is promising since the mLor dispersion model can simply unify other dispersion models. To fully utilize the unified mLor FDTD method, it is of great importance to investigate its numerical stability in the aspects of the original dispersion model parameters. In this work, the numerical stability of the mLor FDTD formulation unified from the aforementioned dispersion models is comprehensively studied. It is found out that the numerical stability conditions of the original model-based FDTD method are equivalent to its unified mLor FDTD counterparts. However, when unifying the mLor FDTD formulation for the QCRF model, a proper Courant number should be used. Otherwise, its unified mLor FDTD simulation may suffer from numerical instability, different from other dispersion models. Numerical examples are performed to validate our investigations.

Grey-Box Approach for the Prediction of Variable Residence Time Distribution in Continuous Pharmaceutical Manufacturing

Abstract Axial dispersion models are used for the prediction of residence time distribution (RTD) of the flow occurring in various processes. Such models are essential for the understanding of the flow dynamics allowing monitoring, control and material tracing specially in the scope of continuous pharmaceutical manufacturing. However, RTDs are most usually dependent on the process variables (PVs), indicating that a single constant parameter dispersion model would not be capable of capturing this variability. In this contribution a variable parameter axial dispersion model is proposed, where the dependency on the process variables are captured from experimental data using Gaussian Process Regression (GPR) models. The method is illustrated with an example of a Vibrated Fluidized Bed Dryer (VFBD), in which a number of tracer experiments are performed at diferent values of the drying process air flow rate and vibration acceleration. The axial dispersion model parameter values are identifed for each experiment. Manifolds for the axial dispersion model parameters are then constructed by the regression of the GP models on the identifed values. Comparisons between the experiments and model predictions for an example validation case are drawn showing that the proposed model is capable of producing accurate RTD predictions and certainty bounds even for points not explicitly included in regression dataset. Insight about the advantages of the method in model based controller design is given.

Modeling of Liquid Distribution in a Packed Column with Open-structure Random Packings

The scientific interest in the efficiency of packed bed columns is a part of the world-wide pursuit of sustainability of the processes. The maldistribution of the phases in the apparatus reduces the efficiency and makes difficult the prediction of process performance and scaling up. The present work aims at modeling of liquid distribution in a packed column with high performance open-structure random packings - metal Raschig Super-Rings 0.7”, 1.5” and 3” and metal Pall rings 1”. Some new approaches for estimation and calculation of model parameters are proposed and tested, using own experimental data for Raschig Super-Rings and published data for Pall rings. A new procedure for identifying one of the model parameters, called by us “overlapping confidential intervals” solution, is developed and illustrated for Raschig Super-Ring packing in the case of partial radial insensitivity (“plateau”) of the residual variance between the model and experimental data. The obtained results show that using appropriate statistical methods of estimation, the dispersion model parameters can be successfully identified achieving a very good prediction of the experimental data. Several numerical examples and case studies are considered and discussed. For the case of Pall rings, the dispersion model predictions are in very good agreement with both published experimental data and predictions made by Computational Fluid Dynamics(CFD) modeling.

Development and analysis of anatomically real breast phantoms using different dispersion models

An effective method to develop anatomically real numerical breast phantoms for T1-weighted MR images of different tissue densities is presented. The dielectric properties for breast tissues are calculated and analyzed using different dispersion models (i.e., one- and two-pole cole–cole and Debye models). The method presented in this paper propounds significant improvements in comparison with existing MRI-based numerical phantoms in terms of denoising of images, tissue segmentation, nonlinear mapping of dielectric properties with realistic shapes using all the dispersion models and densitywise classification of phantoms. This method is a multistep approach in which each MRI voxel is mapped with the appropriate dielectric properties according to different dispersion models. The MRI data was collected and interpolated according to the size of the uniform grid for finite difference time domain computations followed by the preprocessing of MR images to enhance them. Thereafter, the voxel intensities were segregated into two groups as adipose and fibro glandular tissues. These tissue intensities were assigned the corresponding dielectric properties. Three-dimensional (3-D) numerical phantoms were created according to all the dispersion models. After the comparison among the models, it has been found that, along with frequency, the dielectric properties vary according to the variation of the dispersion model parameters. It was also observed that the dielectric properties calculated from one-pole cole–cole and two-pole Debye models are more close to the real properties of breast tissues than other models. A generalized method has been defined for developing the 3-D phantoms for all classes of breast according to the inhomogeneity of fibroglandular tissues using the dispersion models. The frequency-dependent and dispersion model parameters-dependent dielectric properties have been assigned to the phantoms. These real-like phantoms after 3-D printing would help researchers working in the field of breast cancer detection studies.

Joint Multi-Fiber NODDI Parameter Estimation and Tractography Using the Unscented Information Filter.

Tracing white matter fiber bundles is an integral part of analyzing brain connectivity. An accurate estimate of the underlying tissue parameters is also paramount in several neuroscience applications. In this work, we propose to use a joint fiber model estimation and tractography algorithm that uses the NODDI (neurite orientation dispersion diffusion imaging) model to estimate fiber orientation dispersion consistently and smoothly along the fiber tracts along with estimating the intracellular and extracellular volume fractions from the diffusion signal. While the NODDI model has been used in earlier works to estimate the microstructural parameters at each voxel independently, for the first time, we propose to integrate it into a tractography framework. We extend this framework to estimate the NODDI parameters for two crossing fibers, which is imperative to trace fiber bundles through crossings as well as to estimate the microstructural parameters for each fiber bundle separately. We propose to use the unscented information filter (UIF) to accurately estimate the model parameters and perform tractography. The proposed approach has significant computational performance improvements as well as numerical robustness over the unscented Kalman filter (UKF). Our method not only estimates the confidence in the estimated parameters via the covariance matrix, but also provides the Fisher-information matrix of the state variables (model parameters), which can be quite useful to measure model complexity. Results from in-vivo human brain data sets demonstrate the ability of our algorithm to trace through crossing fiber regions, while estimating orientation dispersion and other biophysical model parameters in a consistent manner along the tracts.

A simple inversion method for determining optimal dispersion model parameters from satellite detections of volcanic sulfur dioxide

AbstractA simple inversion scheme for optimizing volcanic emission dispersion model parameters with respect to satellite detections is presented in this paper. In this scheme, multiple dispersion model simulations, obtained by varying relevant model parameters, are created and compared against satellite detections using pattern correlation as a measure of model agreement with observations. It is shown that the scheme is successful in inferring emission source parameters such as those describing the vertical extent of the nascent sulfur dioxide emissions in the November 2010 Mount Merapi eruption in Java, Indonesia. These optimal parameter values then become a basis for improved forecasts of the transport of volcanic emissions.

Simultaneous determination of dispersion model parameters and local thickness of thin films by imaging spectrophotometry

A least-squares data fitting procedure is developed for the analysis of measurements of thin films non-uniform in thickness by imaging spectroscopic reflectometry. It solves the problem of simultaneous least-squares fitting of film thicknesses in all image pixels together with shared dispersion model parameters. Since the huge number of mutually correlated fitting parameters prevents a straightforward application of the standard Levenberg–Marquardt algorithm, the presented procedure exploits the special structure of the specific least-squares problem. The free parameters are split into thicknesses and dispersion model parameters. Both groups of parameters are fitted alternately, utilising an unmodified Levenberg–Marquardt algorithm, correcting however the thicknesses during the dispersion model fitting step to preserve effective optical thicknesses. The behaviour of the algorithm is studied using experimental data of two highly non-uniform thin films of different materials, SiOxCyHz and CNx:H, and by numerical simulations using artificial data. It is found that the optical thickness correction enables the procedure to converge rapidly, permitting the analysis of large imaging spectroscopic reflectometry data sets with reasonable computational resources.

A practical method for optical dispersion model selection and parameters variations in scatterometry analysis with variable n&k's

Optical critical dimension (OCD) scatterometry in recent years became a well-accepted and powerful technique to determine the properties and grating profiles of 2D and 3D microelectronic structures (critical dimensions, side-wall angles, grating and underlying thin film thicknesses) in modern semiconductor manufacturing. However, the optical scatterometry, as any model-based metrology technique, relies on the accuracy of the OCD model which highly depends on the optical properties (the n&k's) of the materials in the structure. In practice, even small deviations in material's optical properties (from nominal model inputs) due to process condition variations might significantly affect the scatterometry measurements. A logical way to deal with this problem is to allow some degree of the n&k's variability of the most affected layer(s) in the OCD model describable by relevant dispersion model(s) (floating n&k's). Essentially, one of the largest complications for the end users (process engineers) is to decide which optical dispersion model (Cauchy, Lorentz, Tauc–Lorentz, etc.) needs to be selected to describe a material under production conditions and which parameters are more sensitive and need to be floated in the OCD model. We developed an approach which, we believe, will result in more straightforward and fast development of the OCD models. This approach provides a possibility to automatically select a most proper dispersion model which has been always an ambiguous decision for most of the end users. This methodology will allow determination of most influential model parameters to vary, eliminating potential sources of modeling error at the initial steps of the OCD modeling. A few examples to illustrate the key ideas and practical use of our procedure have been provided.

Model-Based Material Parameter Estimation for Terahertz Reflection Spectroscopy

One important yet commonly overlooked phenomenon in terahertz (THz) reflection spectroscopy is the etalon effect-interference caused by multiple reflections from dielectric layers. Material layers are present in many THz applications from the monitoring of pharmaceutical tablet coating thickness to the detection of drugs, explosives, or other contraband concealed beneath layers of packaging and/or clothing. This paper focuses on the development and implementation of a model-based material parameter estimation technique, primarily for use in reflection mode THz spectroscopy that takes the etalon effect into account. The technique is adapted from techniques developed for transmission spectroscopy of thin samples and includes a priori information; namely, the assumption that a material's complex refractive index behaves consistently with the Lorentz dispersion model. The inclusion of the multiple returns provides additional information about the material and its structure, alleviating the need for short time windows in the fast Fourier transform (FFT) processing, which can limit spectral resolution. In addition, the parametrization of the material's dielectric function offers the potential for material classification based on these estimated dispersion model parameters. The parametric model-based method is validated by comparison with results from a conventional, non-parametric method applied to transmission mode data before being applied to reflection mode data for further validation with transmission mode results. Tests are also conducted to evaluate the parametric technique's robustness against measurement noise and ambiguity in sample thickness.

Dispersion Model Parameters that Affect the Impacts from Area Sources using AERMOD

Dispersion Model Parameters that Affect the Impacts from Area Sources using AERMOD

Uncertainties in Air Toxics Calculated by the Dispersion Models AERMOD and ISCST3 in the Houston Ship Channel Area

Abstract The uncertainties in simulations of annually averaged concentrations of two air toxics (benzene and 1,3-butadiene) are estimated for two widely used U.S. air quality models, the Industrial Source Complex Short-Term, version 3, (ISCST3) model and the American Meteorological Society–Environmental Protection Agency Model (AERMOD). The effects of uncertainties in emissions input, meteorological input, and dispersion model parameters are investigated using Monte Carlo probabilistic uncertainty methods, which involve simultaneous random and independent perturbations of all inputs. The focus is on a 15 km × 15 km domain in the Houston, Texas, ship channel area. Concentrations are calculated at hypothetical receptors located at the centroids of population census tracts. The model outputs that are analyzed are the maximum annually averaged maximum concentration at any single census tract or monitor as well as the annually averaged concentration averaged over the census tracts. The input emissions uncertainties are estimated to be about a factor of 3 (i.e., covering the 95% range) for each of several major categories. The uncertainties in meteorological inputs (such as wind speed) and dispersion model parameters (such as the vertical dispersion coefficient σz) also are estimated. The results show that the 95% range in predicted annually averaged concentrations is about a factor of 2–3 for the air toxics, with little variation by model. The input variables whose variations have the strongest effect on the predicted concentrations are on-road mobile sources and some industrial sources (dependent on chemical), as well as wind speed, surface roughness, and σz. In most scenarios, the uncertainties of the emissions input group contribute more to the total uncertainty than do the uncertainties of the meteorological/dispersion input group.

Thermal stability of the optical properties of plasma deposited diamond-like carbon thin films

In present paper we studied the optical constants of the diamond-like carbon (DLC) films and their changes with annealing. The multisample modification of combined variable angle spectroscopic ellipsometry and near normal spectroscopic reflectometry was used. The optical constants of the DLC films were simulated by our recently published six-parameter dispersion model employing a parameterization of the density of electronic states (DOS). Based on the dispersion model parameters the density of π and σ electrons were evaluated. We showed that from our model and the independently determined hydrogen atomic fraction of the films before and after annealing the ratio between momentum matrix elements of π → π* and σ → σ* transitions and the correct sp 3-to-sp 2 carbon bonding configuration ratio can be calculated. It is worth to notice that the first quantity is usually assumed to be equal to unity but we showed that this assumption may cause a significant error in the determination of the sp 3-to-sp 2 ratio. Therefore, our suggested method represents a novelty in this field.

Errors associated with dual-Doppler-lidar turbulence measurements

In July 2004 a field trial was undertaken to simultaneously deploy two similar Doppler lidar systems with the aim of measuring the turbulence characteristics of the atmospheric boundary layer over an urban area. This paper outlines the characteristics of the lidar systems, details the deployment configuration of the lidars, and discusses the dispersion model parameters that can be obtained using this procedure. An error analysis is undertaken to highlight the possible problems associated with the derived data. A case study from the trial is shown to compare the dual-lidar derived data to dispersion model results from the NAME dispersion model.

Analysis and simulation of the sludge profile dynamics in a full‐scale clarifier

AbstractA one‐dimensional clarifier model was assessed for its capability to describe dynamic full‐scale sludge concentration profiles by using the settling properties calibrated with batch settling curve data collected by a SettloMeter®. These sludge concentration profiles and batch settling tests formed part of a detailed one‐month measuring campaign on a full‐scale wastewater treatment plant; the measurements showed a daily variation in settling properties. Using the settling properties obtained from batch settling tests and a one‐dimensional model without dispersion, the dynamics of the full‐scale clarifier were analysed and the need for dispersion clearly shown. The parameters of the dispersion model were estimated from the full‐scale sludge concentration profiles. The settling properties of activated sludge can be automatically determined by fitting the model to the on‐line batch settling curve measurements and are needed as input to the one‐dimensional model. This model can therefore be used for operation and control. The dispersion model parameters have to be determined from dynamic sludge concentration profiles but are assumed to be constant for a specific clarifier. Copyright © 2005 Society of Chemical Industry

Evaluation of dispersion model parameters by dual Doppler lidars over West London, England

Urban dispersion models have parameters for the turbulence and mixing height. We identify the parameters in meteorological pre-processors, which are, in principle, measurable by pulsed Doppler lidar. This technique measures radial velocity from the Doppler shifted wavelengths of backscattered laser pulses. First results obtained from single and dual lidar operations are described. Using two scanning lidars increases the range of parameters that can be sensed remotely. Scanned Dual Doppler lidar provides a novel remote sensing method for studying the rural-urban interface. Results are presented from a recent field experiment at an airfield site in West London. Results are compared with data from the Met Office operational dispersion model, NAME, a model using numerical weather forecast data. We show three methods for the urban mixing height. The paper concludes by considering the potential merits of dual-lidar remote sensing of urban dispersion model parameters.

Use of artificial neural networks to predict thickness and optical constants of thin films from reflectance data

Artificial neural networks and the Levenberg–Marquardt algorithm are combined to calculate the thickness and refractive index of thin films from spectroscopic reflectometry data. Two examples will be discussed, the first is a measurement of thickness and index of transparent films on silicon, and the second is a measurement of three thicknesses and index of poly-silicon in a rough poly-silicon on oxide stack. A neural network is a set of simple, highly interconnected processing elements imitating the activity of the brain, which are capable of learning information presented to them. Reflectometry has been used by the semiconductor industry to measure thin film thickness for decades. Modeling the optical constants of a film in the visible region with a Cauchy dispersion model allows the determination of both thickness and refractive index of most transparent thin films from reflectance data. The use of an alloy interpolation model for the optical constants of poly-silicon allows the determination of thicknesses and poly optical constants. In this work artificial neural networks are used to obtain good initial estimates for thickness and dispersion model parameters, these estimates are then used as the starting point for the Levenberg–Marquardt algorithm which converges to the final solution in a few iterations. These measurement programs were implemented on a Nanometrics NanoSpec 8000XSE.

Characterization of small intestinal transit time distribution in humans

This report is aimed at characterizing small intestinal transit time distribution and presenting a slope-based method to determine compartmental transit and dispersion model parameters. The intradose, intrasubject, and intersubject means and variances were defined to examine small intestinal transit time distribution in individuals and populations. Equations were derived to determine the optimum number of compartments and the dispersion coefficient. It was found that the intra- or intersubject variance was significantly smaller than the intradose variance. The optimum number of compartments and the dispersion coefficient were estimated to be seven and 0.78 cm 2/s, respectively, in agreement with the literature data.

Application of sodar to air pollution meteorology†

Abstract A complete description of urban diffusion and dispersion generally requires knowledge of emission sources, an appropriate dispersion model, atmospheric stability, mixing height and dispersion parameters, etc. To determine the air pollution related to meteorological parameters, a remote sensing acoustic sounding system has been found to be a useful tool. This paper describes the techniques developed at the National Physical Laboratory, New Delhi to determine Pasquill stability classification, mixing height and diffusion coefficients from monostatic sodar echograms. On the assumption that the Gaussian plume model holds good, concentrations of particulate matter with distances have been compared with actually observed values of particulate matter concentration to show the validity of approach