A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

Determination of dispersion and nonlinear coefficients of photonic crystal fibers by degenerated FWM method

使用四波混频测试光子晶体光纤的色散和非线性参数

On the nature of over-dispersion in motor vehicle crash prediction models

Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts—variation over and above that accounted for by the Poisson density. The extra-variation – or dispersion – is theorized to capture unaccounted for variation in crashes across sites. The majority of studies have assumed fixed dispersion parameters in over-dispersed crash models—tantamount to assuming that unaccounted for variation is proportional to the expected crash count. Miaou and Lord [Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes methods. Transport. Res. Rec. 1840, 31–40] challenged the fixed dispersion parameter assumption, and examined various dispersion parameter relationships when modeling urban signalized intersection accidents in Toronto. They suggested that further work is needed to determine the appropriateness of the findings for rural as well as other intersection types, to corroborate their findings, and to explore alternative dispersion functions. This study builds upon the work of Miaou and Lord, with exploration of additional dispersion functions, the use of an independent data set, and presents an opportunity to corroborate their findings. Data from Georgia are used in this study. A Bayesian modeling approach with non-informative priors is adopted, using sampling-based estimation via Markov Chain Monte Carlo (MCMC) and the Gibbs sampler. A total of eight model specifications were developed; four of them employed traffic flows as explanatory factors in mean structure while the remainder of them included geometric factors in addition to major and minor road traffic flows. The models were compared and contrasted using the significance of coefficients, standard deviance, chi-square goodness-of-fit, and deviance information criteria (DIC) statistics. The findings indicate that the modeling of the dispersion parameter, which essentially explains the extra-variance structure, depends greatly on how the mean structure is modeled. In the presence of a well-defined mean function, the extra-variance structure generally becomes insignificant, i.e. the variance structure is a simple function of the mean. It appears that extra-variation is a function of covariates when the mean structure (expected crash count) is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean (expected crash count), extra-Poisson variation is not significantly related to these variables. If these results are generalizable, they suggest that model specification may be improved by testing extra-variation functions for significance. They also suggest that known influences of expected crash counts are likely to be different than factors that might help to explain unaccounted for variation in crashes across sites

Stress-optical dispersion in rubidium chloride and rubidium bromide crystals

The stress-optical coefficients C = (n3/2) (q11−q12) and C′ = (n3/2)q44 of RbCl and RbBr crystals have been measured at room temperature (26°C) over the wave length range 5750-2500 A.

Dispersion of the stress-optic coefficient in glasses

The stress-optic coefficient (n3/2)(q11-q12) has been determined for a series of 18 optical glasses of different compositions in the wavelength range 5700-3200 Å. The coefficients are negative for all the glasses except for a high-lead-content glass of density 6·7 and refractive index 1·89. The numerical value of the coefficient decreases as one proceeds to the ultraviolet. This behaviour is just the opposite of what is observed in fused silica. By applying Mueller's theory, the strain polarizability constant and its dispersion have been evaluated.

Dispersion of the stress-optic coefficient in glasses

The stress-optic coefficient (n3/2)(q11-q12) has been determined for a series of 18 optical glasses of different compositions in the wavelength range 5700-3200 Å. The coefficients are negative for all the glasses except for a high-lead-content glass of density 6·7 and refractive index 1·89. The numerical value of the coefficient decreases as one proceeds to the ultraviolet. This behaviour is just the opposite of what is observed in fused silica. By applying Mueller's theory, the strain polarizability constant and its dispersion have been evaluated.

Polarization relaxation, dielectric dispersion, and solvation dynamics in dense dipolar liquid

A unified treatment of polarization relaxation, dielectric dispersion and solvation dynamics in a dense, dipolar liquid is presented. It is shown that the information of solvent polarization relaxation that is obtained by macroscopic dielectric dispersion experiments is not sufficient to understand dynamics of solvation of a newly created ion or dipole. In solvation, a significant contribution comes from intermediate wave vector processes which depend critically on the short range (nearest‐neighbor) spatial and orientational order that are present in a dense, dipolar liquid. An analytic expression is obtained for the time dependent solvation energy that depends, in addition to the translational and rotational diffusion coefficients of the liquid, on the ratio of solute–solvent molecular sizes and on the microscopic structure of the polar liquid. Mean spherical approximation (MSA) theory is used to obtain numerical results for polarization relaxation, for wave vector and frequency dependent dielectric function and for time dependent solvation energy. We find that in the absence of translational contribution, the solvation of an ion is, in general, nonexponential. In this case, the short time decay is dominated by the longitudinal relaxation time but the long time decay is dominated by much slower large wave vector processes involving nearest‐neighbor molecules. The presence of a significant translational contribution drastically alters the decay behavior. Now, the long‐time behavior is given by the longitudinal relaxation time constant and the short time dynamics is controlled by the large wave vector processes. Thus, although the continuum model itself is conceptually wrong, a continuum model like result is recovered in the presence of a sizeable translational contribution. The continuum model result is also recovered in the limit of large solute to solvent size ratio. In the opposite limit of small solute size, the decay is markedly nonexponential (if the translational contribution is not very large) and a complete breakdown of the continuum model takes place. The significance of these results is discussed.

Correlation equations for average deposition rate coefficients of nanoparticles in a cylindrical pore

Nanoparticle deposition behavior observed at the Darcy scale represents an average of the processes occurring at the pore scale. Hence, the effect of various pore-scale parameters on nanoparticle deposition can be understood by studying nanoparticle transport at pore scale and upscaling the results to the Darcy scale. In this work, correlation equations for the deposition rate coefficients of nanoparticles in a cylindrical pore are developed as a function of nine pore-scale parameters: the pore radius, nanoparticle radius, mean flow velocity, solution ionic strength, viscosity, temperature, solution dielectric constant, and nanoparticle and collector surface potentials. Based on dominant processes, the pore space is divided into three different regions, namely, bulk, diffusion, and potential regions. Advection-diffusion equations for nanoparticle transport are prescribed for the bulk and diffusion regions, while the interaction between the diffusion and potential regions is included as a boundary condition. This interaction is modeled as a first-order reversible kinetic adsorption. The expressions for the mass transfer rate coefficients between the diffusion and the potential regions are derived in terms of the interaction energy profile. Among other effects, we account for nanoparticle-collector interaction forces on nanoparticle deposition. The resulting equations are solved numerically for a range of values of pore-scale parameters. The nanoparticle concentration profile obtained for the cylindrical pore is averaged over a moving averaging volume within the pore in order to get the 1-D concentration field. The latter is fitted to the 1-D advection-dispersion equation with an equilibrium or kinetic adsorption model to determine the values of the average deposition rate coefficients. In this study, pore-scale simulations are performed for three values of Peclet number, Pe = 0.05, 5, and 50. We find that under unfavorable conditions, the nanoparticle deposition at pore scale is best described by an equilibrium model at low Peclet numbers (Pe = 0.05) and by a kinetic model at high Peclet numbers (Pe = 50). But, at an intermediate Pe (e.g., near Pe = 5), both equilibrium and kinetic models fit the 1-D concentration field. Correlation equations for the pore-averaged nanoparticle deposition rate coefficients under unfavorable conditions are derived by performing a multiple-linear regression analysis between the estimated deposition rate coefficients for a single pore and various pore-scale parameters. The correlation equations, which follow a power law relation with nine pore-scale parameters, are found to be consistent with the column-scale and pore-scale experimental results, and qualitatively agree with the colloid filtration theory. These equations can be incorporated into pore network models to study the effect of pore-scale parameters on nanoparticle deposition at larger length scales such as Darcy scale.

Dispersion, population dynamics and stock assessment of Caspian Sea prawns, genus Palaemon in Guilan Province coastal waters

Biological aspects, population dynamics and stock assessment of the Caspian Sea prawns Palaemon adspersus and Palaemon eleganse were investigated in Guilan coastal water of the Caspian Sea. Sampling was done monthly with a bottom trawl with mesh size of 3 mm in cod end in 0 - 5 m and 5 - 10 m depth in areas as Astra, Shafa Roud, Anzali, Chonchanan Chamkhaleh and Chaboksar during year 2002. Results of one year sampling showed that mean total length of Palaemon adspersus (pooled data) was 39.9±6.84 mm (X±SD) and mean wiegth was 1.133±0.67 g. The mean total length of females and males was 41.6±7.5 mm and 37.9±5.2 mm respectively and mean weight for the mentioned sexes was 1.353±0.65 g and 0.868±0.38 g respectively. There was significant differences in mean length and weight of females and males (P<0.05). The mean total annual sex ratio of males: females for this species was 1.4 and this sex ratio deviated significantly from 1:1 (X2, P<0.05) and biased towards males in the population of this species. The spawning season of Palaemon adspersus begins in April and ends in September with a peak in June . Mean fecundity of this species was 1994.5 ± 506.6 . The growth coefficients Loo and K for females were estimated as 58.5 mm and 2.3 /Year and for males as 55.9 mm and 2.6 /year respectively . The mean CPUA ( catch / Km2 ) for this species was 9.99 ± 33.2 kg / km2 and the correspondance biomass was calculated as 5067.7 kg in 0 - 10 m depth . The mean total length of Palaemon elegans (pooled data ) was 27.5 ± 5.7 mm (X±S.D) and mm and 24.01±4.18 mm respectively and mean weight for the mentioned sexes were was 0.553 ± 0.3 g and 0.237±0.15 g respectively. There was significant differences in mean length and weight of females and males (P<0.05). The mean total annual sex ratio of males:females for this species was 0.57 and in this species also sex ratio differed significantly from 1:1 (X2, P<0.05) and skewed towards females in the population of this species. The spawning season of Palaemon elegans extended from May to September with a peak in July . Mean fecundity of this species was 642.7±313.4. The growth coefficients LOO and K for females were estimated as 42.119 mm and 2.40 /Year and 33.87 mm and 2.50 /year for males respectively. The mean. CPUA ( catch/ Km2 ) for this species was 0.75±3.86 kg/km2 and the correspondance biomass was calculated as 382.1 kg in 0-10 m depth .

Lateral diffusivity coefficients from the dynamics of a SF6 patch in a coastal environment

The dispersion of a patch of the tracer sulfur hexafluoride (SF6) is used to assess the lateral diffusivity in the coastal waters of the western part of the Gulf of Lion (GoL), northwestern Mediterranean Sea, during the Latex10 experiment (September 2010). Immediately after the release, the spreading of the patch is associated with a strong decrease of the SF6 concentrations due to the gas exchange from the ocean to the atmosphere. This has been accurately quantified, evidencing the impact of the strong wind conditions during the first days of this campaign. Few days after the release, as the atmospheric loss of SF6 decreased, lateral diffusivity coefficient at spatial scales of 10 km has been computed using two approaches. First, the evolution of the patch with time was combined with a diffusion-strain model to obtain estimates of the strain rate (γ = 2.5 10- 6 s- 1) and of the lateral diffusivity coefficient (Kh = 23.2 m2s− 1). Second, a steady state model was applied, showing Kh values similar to the previous method after a period of adjustment between 2 and 4.5 days. This implies that after such period, our computation of Kh becomes insensitive to the inclusion of further straining of the patch. Analysis of sea surface temperature satellite imagery shows the presence of a strong front in the study area. The front clearly affected the dynamics within the region and thus the temporal evolution of the patch. Our results are consistent with previous studies in open ocean and demonstrate the success and feasibility of those methods also under small-scale, rapidly-evolving dynamics typical of coastal environments.

Wind-tunnel modelling of dispersion from a scalar area source in urban-like roughness

A wind-tunnel study was conducted to investigate ventilation of scalars from urban-like geometries at neighbourhood scale by exploring two different geometries a uniform height roughness and a non-uniform height roughness, both with an equal plan and frontal density of λ p = λ f = 25%. In both configurations a sub-unit of the idealized urban surface was coated with a thin layer of naphthalene to represent area sources. The naphthalene sublimation method was used to measure directly total area-averaged transport of scalars out of the complex geometries. At the same time, naphthalene vapour concentrations controlled by the turbulent fluxes were detected using a fast Flame Ionisation Detection (FID) technique. This paper describes the novel use of a naphthalene coated surface as an area source in dispersion studies. Particular emphasis was also given to testing whether the concentration measurements were independent of Reynolds number. For low wind speeds, transfer from the naphthalene surface is determined by a combination of forced and natural convection. Compared with a propane point source release, a 25% higher free stream velocity was needed for the naphthalene area source to yield Reynolds-number-independent concentration fields. Ventilation transfer coefficients w T /U derived from the naphthalene sublimation method showed that, whilst there was enhanced vertical momentum exchange due to obstacle height variability, advection was reduced and dispersion from the source area was not enhanced. Thus, the height variability of a canopy is an important parameter when generalising urban dispersion. Fine resolution concentration measurements in the canopy showed the effect of height variability on dispersion at street scale. Rapid vertical transport in the wake of individual high-rise obstacles was found to generate elevated point-like sources. A Gaussian plume model was used to analyse differences in the downstream plumes. Intensified lateral and vertical plume spread and plume dilution with height was found for the non-uniform height roughness

Bias from ignoring price dispersion in demand estimation

Consumers often pay different prices for the same product bought in the same store at the same time. However, the demand estimation literature has ignored that fact using, instead, aggregate measures such as the “list” or average price. In this paper we show that this will lead to biased price coefficients. Furthermore, we perform simple comparative statics simulation exercises for the logit and random coefficient models. In the “list” price case we find that the bias is larger when discounts are higher, proportion of consumers facing discount prices is higher and when consumers are more unwilling to buy the product so that they almost only do it when facing discount. In the average price case we find that the bias is larger when discounts are higher, proportion of consumers that have access to discount are similar to the ones that do not have access and when consumers willingness to buy is very dependent on idiosyncratic shocks. Also bias is less problematic in the average price case in markets with a lot of bargain deals, so that prices are as good as individual. We conclude by proposing ways that the econometrician can reduce this bias using different information that he may have available.

Coordination polymer adsorbent for matrix solid-phase dispersion extraction of pesticides during analysis of dehydrated Hyptis pectinata medicinal plant by GC/MS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Performance of a reciprocal shaker in mechanical dispersion of soil samples for particle-size analysis

A dispersão da amostra de solo é uma etapa fundamental da análise granulométrica, sendo realizada mediante o uso de dispersantes químicos e agitação mecânica. O objetivo deste trabalho foi avaliar a eficiência de mesa agitadora reciprocante de baixa rotação na dispersão mecânica de amostras de solos de diferentes classes texturais. Foram realizadas análises granulométricas em 61 amostras com quatro repetições, empregando o método da pipeta para determinação da fração argila e tamisagem para determinação das frações areia grossa, areia fina e areia total, sendo o silte determinado por diferença. Na avaliação de desempenho, os resultados obtidos com uso da mesa agitadora reciprocante (MAR) foram comparados com dados disponíveis para as mesmas amostras oriundos de relatórios do Ensaio de Proficiência IAC para Laboratórios de Análises de Solos - Prolab/IAC. Análises de acurácia foram realizadas com base nos valores dos intervalos de confiança definidos para cada fração granulométrica componente de cada amostra ensaiada. Indicadores gráficos também foram utilizados na comparação de dados, por meio de dispersão e ajuste linear. A estatística descritiva indicou preponderância de baixa variabilidade em mais de 90 % dos resultados obtidos para as amostras de texturas arenosa, média e argilosa e em 68 % dos obtidos para as amostras de textura muito argilosa, indicando boa repetibilidade dos resultados obtidos com a MAR. Média variabilidade foi mais frequentemente associada à fração silte, seguida da fração areia fina. Os resultados das análises de sensibilidade indicam acurácia de 100 % nas três frações granulométricas - areia total, silte e argila - para todas as amostras analisadas pertencentes às classes texturais muito argilosa, argilosa e média. Para as nove amostras de textura arenosa, a acurácia média foi de 85,2 %, e os maiores desvios ocorreram em relação à fração silte. Nas aproximações lineares, coeficientes de correlação igual (silte) ou superiores (areia total e argila) a 0,93, bem como diferenças menores do que 0,16 entre os coeficientes angulares das retas e o valor unitário, indicam alta correlação entre os resultados de referência (Prolab/IAC) e os obtidos nos ensaios com a MAR. Conclui-se pelo desempenho satisfatório da mesa agitadora reciprocante de baixa rotação para dispersão mecânica de amostras de solo de diferentes classes texturais para fins de análise granulométrica, permitindo recomendar o uso alternativo do equipamento quando se emprega agitação lenta. As vantagens do uso do equipamento nacional incluem o baixo custo, a possibilidade de análise simultânea de grande número de amostras e o uso de frascos comuns, de vidro ou de plástico, baratos e de fácil reposição.

LARVAL DISPERSION IN CHRYSOMYA-MEGACEPHALA, CHRYSOMYA-PUTORIA AND COCHLIOMYIA-MACELLARIA (DIPT, CALLIPHORIDAE)

Horizontal and vertical frequency distribution of larvae in three species of Calliphoridae were studied. Correlation between horizontal and vertical dispersion and larval size was also assessed. The experiment was monitored depositing vials with larvae at one end of a cardboard box covered with wood shavings. Chrysomya megacephala and C., putoria reached 2.9 m from the starting portion of the box. Co. macellaria reached only 2.0 m from the starting portion of the box. The majority of pupae of the three species were found at 4 and 5 cm depth from the surface of the box. Correlation coefficients between pupal size and horizontal and vertical migration were usually very low, and apparently no clear pattern emerges from this data set. This study revealed variation in the dispersion patterns although the two Chrysomya species are more similar in their postfeeding larval behaviour compared to Co. macellaria.