Analytical Dispersion Model Research Articles

Advanced modeling for optical characterization of amorphous hydrogenated silicon films

Amorphous hydrogenated silicon (a-Si:H) films deposited on glass and crystalline silicon substrates are analyzed using a multi-sample method combining ellipsometry and spectrophotometry in a spectral range of 0.046–8.9eV, utilizing an analytical dispersion model based on parametrization of joint density of states and application of sum rule. This model includes all absorption processes from phonon absorption to core electron excitations. It is shown that if films deposited on both substrates are characterized together it is possible to study both phonon absorption and weak absorption processes below the band gap, i.e. the Urbach tail and absorption on localized states.

Application of sum rule to the dispersion model of hydrogenated amorphous silicon

Optical data obtained for a-Si:H films by ellipsometry and spectrophotometry in the wide photon energy range 0.046–8.9eV are fitted using the analytical dispersion models based on the application of the sum rule. The models include all absorption processes ranging from phonon absorption in IR region to core electron excitations in X-ray region. They take into account the existence of extended and localized states of valence electrons and distinguish transitions to conduction band and higher energy electron states. It is demonstrated that a combination of optical measurements over the wide range, combined with reasonable assumptions about the optical response in regions where no experimental data are available can lead to dispersion models enabling to determine the mass density of the film. Comparing the density of states determined by tight-binding method with that obtained from optical data, it is shown that an excitonic effect is significant in a-Si:H and causes a redistribution of transition probability from higher energies to the broad peak centered at 3.5eV. Moreover, it is suggested how to apply the sum rule in the commercial ellipsometric software implementing the Tauc–Lorentz model.

An analytical model for dispersion of biological particles emitted from area sources: Inclusion of dispersion in the crosswind direction

An analytical model for dispersion of biological particles such as spores and pollens released from finite area sources into the atmospheric boundary layer is proposed. The model is applicable to rectangular fields aligned with the mean wind and accounts for effects of turbulent dispersion in the vertical and crosswind direction, as well as depletion of airborne material due to dry deposition. Predictions for the mean particle concentration above the area source and ground deposition downwind from it are derived and validated against detailed numerical simulations of pollen dispersal using large eddy simulation. Effects of particle settling velocity and area source size and geometry on dispersal patterns are investigated. Results show that along the centerline above the source, effects of crosswind dispersion are negligible (except for very narrow area sources). Ground deposition fluxes downwind from the source are strongly affected by crosswind dispersion. Similarly to area sources infinitely long in the crosswind direction, deposition fluxes far from rectangular sources display a power-law decay with distance. The power-law exponent is larger than the one for infinitely wide fields and depends on the relative importance of gravitational settling and turbulent dispersion in the vertical and crosswind directions, but does not depend on source geometry. However, the distance from the source at which the power-law decay is first observed does depend on source geometry.

Analytical model for tracer dispersion in porous media

In this work, we present a novel analytical model for tracer dispersion in laminar flow through porous media. Based on a straightforward physical argument, it describes the generic behavior of dispersion over a wide range of Péclet numbers (exceeding eight orders of magnitude). In particular, the model accurately captures the intermediate scaling behavior of longitudinal dispersion, obviating the need to subdivide the dispersional behavior into a number of disjunct regimes or using empirical power-law expressions. The analysis also suggests the possible existence of a new material property, the critical Péclet number, reflecting the mesoscale geometric properties of the microscopic pore structure.

Parameterization of the eddy diffusivity in a dispersion model over homogeneous terrain in the atmospheric boundary layer

Parameterizations of the vertical eddy diffusivity over homogeneous terrain in neutral, stable and unstable conditions for the entire atmospheric boundary layer are proposed using the mixing length theory. The formulation utilizes the theoretically derived local mixing length scale that is composed of three component length scales. Proposed profiles of the eddy diffusivity in various stability conditions are compared to those reported in the literature. The proposed profiles of the eddy diffusivity are used in a generalized analytical model for dispersion of pollutants released from a continuous source in the atmospheric boundary layer. The dispersion model describing the crosswind integrated concentrations is briefly presented. By considering the proposed and other commonly applied parameterizations of eddy diffusivity, the dispersion model is evaluated with the tracer observations obtained from Copenhagen diffusion experiment in unstable conditions, Prairie Grass experiment in both unstable and stable conditions and Hanford experiment in stable conditions. The dispersion model with proposed parameterizations of the eddy diffusivity is performing reasonably well with the observations and demonstrates throughout a consistent and good performance in the concentration estimation for elevated and surface releases from a continuous point source in various stability conditions. Though the magnitudes of the various eddy diffusivities are different from the proposed one, the profiles of all parameterizations in terms of the shape have almost similar characteristics. The differences in the magnitudes of diffusion produced by various parameterizations cause minor but noticeable changes in the simulation of ground level concentrations from the dispersion model. In very stable conditions, the agreement of the model evaluations with measurements is less satisfactory and none of the parameterizations used here including proposed one is adequate to describe the atmospheric dispersion process in these conditions.

Extended Analytical Turbulent Diffusion Model for Particle Dispersion and Deposition in a Horizontal Pipe: Comparison with CFD Simulation

A 2D analytical turbulent diffusion model for particle dispersion and deposition at different heights along the pipe flow and circumferential deposition has been developed. This liquid–solid turbulent diffusion model presented in this paper has emanated from an existing gas–liquid turbulent diffusion model. This model can be used as a handy tool for quick estimation one and two-dimensional deposition fluxes of particles in water distribution networks. A comprehensive 3D numerical investigation has been carried out using multiphase mixture model available in “Fluent 6.2” to verify the above analytical model. Different particles sizes and densities were used for 3D numerical investigations. The deposition was studied as a function of particle diameter, density, and fluid velocity. The deposition of particles, along the periphery of the pipe wall and at different depths, was investigated. Both the models findings matched with qualitative phenomena such as deposition of heavier particles at the bottom of the pipe wall were higher at lower velocities and lower at higher velocities. The lighter particles were found mostly suspended with homogeneous distribution. Smaller particles were also suspended with marginal higher concentration near the bottom of the pipe wall. This marginal higher concentration of the smaller particles was found to be slightly pronounced for lower velocity. These analogies of particles are well discussed with the ratio between free-flight velocity and the gravitational settling velocity. Extended analytical model results were compared with the 3D computational fluid dynamics simulation results. Discrepancies in the model results were discussed.

A neural net-air dispersion model validation study using the Indianapolis urban data set

It is presented an integrated model composed by a dispersion model and a Neural Net (NN). The NN uses the concentrations predicted by the an analytical dispersion model as input variables of the net. This methodology was validated using Indianapolis urban data set where releases from an elevated emission source were considered. An improvement of performances is shown when the neural network is added downstream to the dispersion model. Tests reveal the system is able to reproduce the expected behaviour of pollutant concentration, with the downwind distance and stability of the atmosphere in urban area.

An analytical model for dispersion of pollutants from a continuous source in the atmospheric boundary layer

For the dispersion of a pollutant released from a continuous source in the atmospheric boundary layer (ABL), a generalized analytical model describing the crosswind-integrated concentrations is presented. An analytical scheme is described to solve the resulting two-dimensional steady-state advection–diffusion equation for horizontal wind speed as a generalized function of vertical height above the ground and eddy diffusivity as a function of both downwind distance from the source and vertical height. Special cases of this model are deduced and an extensive analysis is carried out to compare the model with the known analytical models by taking the particular forms of wind speed and vertical eddy diffusivity. The proposed model is evaluated with the observations obtained from Copenhagen diffusion experiments in unstable conditions and Hanford and Prairie Grass experiments in stable conditions. In evaluation of the model, a recently proposed formulation for the wind speed in the entire ABL is used. It is concluded that the present model is performing well with the observations and can be used to predict the short-range dispersion from a continuous release. Further, it is shown that the accurate parameterizations of wind speed and eddy diffusivity provide a significant improvement in the agreement between computed and observed concentrations.

Plasmon Dispersion in Coaxial Waveguides from Single-Cavity Optical Transmission Measurements

We determine the plasmon dispersion relation in coaxial waveguides composed of a circular channel separating a metallic core and cladding. Optical transmission measurements are performed on isolated coaxial nanoapertures fabricated on a Ag film using focused ion-beam lithography. The dispersion depends strongly on the dielectric material and layer thickness. Our experimental results agree well with an analytical model for plasmon dispersion in coaxial waveguides. We observe large phase shifts at reflection from the end facets of the coaxial cavity, which strongly affect the waveguide resonances and can be tuned by changing the coax geometry, composition, and surrounding dielectric index, enabling coaxial cavities with ultrasmall mode volumes.

An inversion technique for the retrieval of single-point emissions from atmospheric concentration measurements

The aim of the study is to propose a technique for the retrieval of point sources of atmospheric trace species from concentration measurements. The inverse problem of identifying the parameters of a point source is addressed within the assimilative framework of renormalization recently proposed for the identification of distributed emissions. This theory has been extended for the point sources based on the property that these are associated with the maximum of the renormalized estimate computed from the observations. This approach along with an analytic dispersion model is used for point source identification, and the sensitivity of the samplers is described by the same model in backward mode. The proposed technique is illustrated not only with synthetic measurements but also with seven sets of observations, corresponding to convective conditions, taken from the low-wind tracer diffusion experiment conducted at the Indian Institute of Technology Delhi in 1991. The position and intensity of the source are retrieved exactly with the synthetic measurements in all the sets validating the technique. The position of the source is retrieved with an average error of 17 m, mostly along wind; its intensity is estimated within a factor 2 for all the sets of real observations. From a theoretical point of view, the link established between point and distributed sources clarifies new concepts for the exploitation of monitoring networks. In particular, the influence of the noise on the identification of a source is related to the relative visibility of the various regions described with a renormalizing weight function. The geometry of the environment modified according to the weights is interpreted as an apparent geometry. It is analogous to the apparent flatness of the starry sky in eye's view, usually considered an impression rather than a scientific fact.

Inferring profiles of energy fluxes within a soybean canopy using Lagrangian analysis

Two one-dimensional Lagrangian analytical dispersion models were used to estimate scalar sources, sinks and fluxes within a soybean canopy from concentration profile measurements. The two models were also used to separate soil evaporation and crop transpiration in terms of the inverse analysis. The results indicate that these two models produced similar source/sink distributions most of the time, but the values of within-canopy source distributions are dependent on the parameterizations of the turbulence statistics. The performance of these two models was similar and comparable in terms of the cumulative fluxes at the top of the canopy. The inferred above-canopy fluxes are sensitive to the parameterization of turbulence statistics, but not to the choice of model. The inferred above-canopy fluxes were in agreement with eddy covariance measurements for two turbulence schemes, while overestimated (1.8–2.6 times) when using a third turbulence scheme. Results also showed that the predicted ratio of soil evaporation to total evapotranspiration is coincident with the expected trend for different growth stages of soybean, but the value is highly dependent on the choice of turbulence statistics. The variation of daily ratio of soil evaporation to total evapotranspiration with leaf area index (LAI) from the inverse analysis is in rough agreement with that estimated from an evaporation model.

A Lagrangian Solution to the Relationship between Source Strength and Concentration Profile Under Conditions of Local Advection

We propose a two-dimensional Lagrangian analytical solution for relating source strength and concentration profiles within and above a plant canopy. The new solution describes passive scalar dispersion under conditions of local advection through a fetch correction function in a one-dimensional Lagrangian analytical dispersion model. The model is capable of predicting absolute concentration profiles of passive scalars for different fetches for situations in which the reference concentration is known or the background concentration is available. Tests of the model showed good agreement with measurements from field and wind-tunnel experiments.

人工排熱による首都圏大気の気温上昇

The so-called heat island phenomena found over large urban areas are thought to arise due to many causes; one of the major causes of the phenomena is direct heating of the lower atmospheric boundary layer by anthropogenic heat emissions. However, no quantitative assessment of this cause has been reported. Recently developed numerical regional meteorological modeling techniques enable us to estimate the temperature rise resulting from anthropogenic heat emissions into the atmosphere. However, it remains difficult both to perform more than a single-year integration with these numerical meteorological models and to evaluate the annual mean temperature rise resulting from anthropogenic heat.Using a simplified analytical atmospheric dispersion model we estimated the annual mean air temperature rise in the surface layer due to direct heating by anthropogenic heat emissions in to the urban atmosphere over the Tokyo metropolitan area. The validity of this model was verified by applying it to the dispersion of nitrogen oxides over the same area. The temperature rise at the center of Tokyo resulting from anthropogenic heat emissions was estimated to be about 0.7 to 1.1°C. On the other hand, observations from our densely distributed, long-term monitoring network in this area showed that the annual mean temperature at the center of Tokyo was about 2.6 °C higher than the surrounding rural areas. We conclude that direct heating by anthropogenic heat sources accounts for 27% to 42% of the annual average observed heat-island intensity in the Tokyo metropolitan area.

Predicting Scalar Source-Sink and Flux Distributions Within a Forest Canopy Using a 2-D Lagrangian Stochastic Dispersion Model

This study proposes a two-dimensional Lagrangian stochastic dispersion model forestimating spatial and temporal variation of scalar sources, sinks, and fluxes withina forest canopy. Carbon dioxide and heat dispersion experiments were conducted forfield testing the model. These experiments also provided data for field testing a newlydeveloped one-dimensional Lagrangian analytical dispersion model. It was found that these two models produce similar scalar source-sinkand flux distribution patterns. Comparing with CO2 flux measurements, the one-dimensional model performed as well as the two-dimensional model even whenthe fetch is short (≈100 m). To drive these Lagrangian models, velocitystatistics through the canopy volume must be specified a priori. The sensitivity of thecomputed sources, sinks, and fluxes to the description of the flow statistics was furtherexamined. All in all, we found good agreement between model predicted andeddy-correlation measured CO2 and sensible heat fluxes.

Dispersion mechanisms in a street canyon

In this article, we investigate experimentally and analytically the dispersion mechanisms of a passive tracer in a two-dimensional model of a street canyon. The principal concern is the concentration transfer between the street and the external flow. In contrast to previous studies, the mass fluxes are not only inferred from mean concentration measurements but also directly measured thanks to a Particle Tracking Velocimetry technique. Visualizations of the evolution of the concentration field show the role of the shear layer at the top of the street canyon. Analytical transfer and dispersion models are derived, demonstrating the importance of external turbulence properties on the transfer. Those models are in excellent agreement with the measurements. The results presented in this article strongly suggest that the transfer in a street canyon does depend on the structure of the incoming turbulence, i.e. on the local stability conditions and on the upwind buildings.

Diffusion from a line source deployed in a homogeneous roughness layer: interpretation of wind-tunnel measurements by means of simple mathematical models

In wind-tunnel studies of atmospheric dispersion, the pollutant emission by traffic is usually considered as ground-level line source. The source performance under different flow conditions is therefore important for the adequate description of pollutant dispersion. The dispersion from a line source in the wind-tunnel model of the atmospheric boundary layer has been investigated in the present study. Specially conducted mean flow and turbulence measurements have proved the similarity between the wind-tunnel flow and the flow in the lower portion of the atmospheric boundary layer. Lateral and vertical distributions of mean concentration downwind of the source have been measured with varying source parameters and wind velocities. The concentration pattern has not revealed a significant dependence on the parameter variations. The wind-tunnel results have been further evaluated by means of analytical and numerical dispersion models. The evaluation has shown a good general agreement of measured and calculated concentration fields. Two alternative sets of equations with different parameterizations of eddy diffusivity and different values of the turbulent Schmidt number have been employed in the analytical model calculations. A better agreement with the wind-tunnel results has been achieved with a similarity-theory expression for eddy diffusivity rather than with the eddy diffusivity parameterization based on the conjugate-power-law formula. The numerical model has provided the best match for the wind-tunnel concentration data at large distances from the source. However, certain discrepancies between the wind-tunnel and numerical predictions have been marked out close to the source.

Modelling and simulation of heavy gas dispersion on the basis of modifications in plume path theory

An analytical model for heavy gas dispersion based on the modifications in plume path theory has been developed. The model takes into account the variations in temperature, density, and specific heat during the movement of heavy gas plume. The model has been tested for three hazardous gases — chlorine, natural gas and liquefied petroleum gas. The results have been compared with the recently generated experimental data as also with the outputs of other models. A good agreement is observed qualitatively as well as quantitatively. A study has also been carried out to simulate the effect of the wind speed, density of the gas, and venting speed on dispersion. Based on the simulation study a set of empirical equations has been developed. The equations are validated by theoretical as well as experimental studies.

Modelo euleriano semi-analítico para a dispersão de contaminantes na Camada Limite Planetária

An analytical air quality dispersion model based on a discretization of the planetary boundary layer in N sub-layers is presented. In each sub-layer the diffusion-advection equation is solved by the Laplace Transform techniques, considering an average value for the vertical exchange coefficient and the wind speed. As a consequence, the present approach allows to employ realistic semi-empirical profiles for the eddy diffusivity and wind speed, in such manner that the inhomogeneous turbulence can be handle. The model performance have been evaluated using the well-known Copenhagen and Prairie Grass datasets. Then, the application of the statistical evalution procedure (Hanna, 1989) over the out coming results has show that the proposed analytical dispersion model produces a good fitting of the observational data.

Air pollution loads on historical monuments: an air quality model application to the marble Arch of Titus in Rome

Atmospheric pollution is one of the reasons for stone weathering of monumental structures; at the same time old town centres are high concentration areas of pollutant sources (traffic and domestic heating) and of outdoor works of art. The use of air dispersion models represents a short means of answering many questions concerning pollution and it is a complementary way to the traditional ad hoc measurement of pollutant concentrations. An application of DIMULA, an analytical multisource dispersion model, and of CALINE 3, an air dispersion model specially developed for pollutant line sources (road links) will be described. The first was applied to the entire urban area of Rome and the second to the surroundings of the Arch of Titus. A simulation was performed relative to the period of in situ monitoring of air pollutant species and meteorological conditions. Moreover simulations of the effect of possible actions to reduce pollution around the monument (e.g., traffic limitation, use of different fuels) have been performed. Once the model has been validated, this approach, compared with the traditional approach involving a large amount of measurements, has the merits of being reliable and economical.

An Exposure‐Response Method for Assessing the Long Term Health Effects of the Bhopal Gas Disaster

Approximately 200,000 persons were exposed to methyl isocyanate in the Bhopal Gas leak in Bhopal, India. 4037 deaths have resulted and 30 per cent of the population are estimated to be suffering from long-term health effects. Though inflammatory damage to the eyes and lungs is the main cause of morbidity, other systems are also reported to be affected. For a disaster of this magnitude, there is a relative paucity of medical information. Very little information has been published on the late recovery period, a phase in which the detection of chronic and long-term effects is vital. Early cross-sectional studies suffer from a number of defects in study design, including validity and precision of exposure and outcome variables, selection of study and control groups, etc. By using exposure concentrations derived from Singh's analytic dispersion model, this paper outlines a strategy for doing community epidemiology in Bhopal using exposure strata for sampling. Pulmonary dose can be estimated from exposure concentration, duration and activity during exposure. For respiratory end-points, a sample size of 100/stratum will ensure study power of 90 per cent. Using multiple linear regression, data from the study can be used to build a model for prediction of lung function parameters. Exposure-stratified sampling techniques may provide valid estimates of exposure-response without including the total exposed community.