Mixing-scale dependent dispersion for transport in heterogeneous flows

Dispersion quantifies the impact of subscale velocity fluctuations on the effective movement of particles and the evolution of scalar distributions in heterogeneous flows. Which fluctuation scales are represented by dispersion, and the very meaning of dispersion, depends on the definition of the subscale, or the corresponding coarse-graining scale. We study here the dispersion effect due to velocity fluctuations that are sampled on the homogenization scale of the scalar distribution. This homogenization scale is identified with the mixing scale, the characteristic length below which the scalar is well mixed. It evolves in time as a result of local-scale dispersion and the deformation of material fluid elements in the heterogeneous flow. The fluctuation scales below the mixing scale are equally accessible to all scalar particles, and thus contribute to enhanced scalar dispersion and mixing. We focus here on transport in steady spatially heterogeneous flow fields such as porous media flows. The dispersion effect is measured by mixing-scale dependent dispersion coefficients, which are defined through a filtering operation based on the evolving mixing scale. This renders the coarse-grained velocity as a function of time, which evolves as velocity fluctuation scales are assimilated by the expanding scalar. We study the behaviour of the mixing-scale dependent dispersion coefficients for transport in a random shear flow and in heterogeneous porous media. Using a stochastic modelling framework, we derive explicit expressions for their time behaviour. The dispersion coefficients evolve as the mixing scale scans through the pertinent velocity fluctuation scales, which reflects the fundamental role of the interaction of scalar and velocity fluctuation scales in solute mixing and dispersion. © © 2015 Cambridge University Press.The authors thank three anonymous reviewers for their insightful comments. M.D. acknowledges the support of the European Research Council (ERC) through the project MHetScale (617511).Peer reviewe

Influence of pumping operational schedule on solute concentrations at a well in randomly heterogeneous aquifers

We investigate the way diverse groundwater extraction strategies affect the history of solute concentration recovered at a pumping well while taking into account random spatial variability of the system hydraulic conductivity. Considering the joint effects of spatially heterogeneous hydraulic conductivity and temporally varying well pumping rates leads to a realistic evaluation of groundwater contamination risk at the pumping well location. We juxtapose the results obtained when the pumping well extracts a given amount of water operating (a) at a uniform pumping rate and (b) under a transient regime. The analysis is performed within a numerical Monte Carlo framework. Our results show that contaminant concentration breakthrough curves (BTCs) at the well are markedly affected by the transient pumping strategy according to which the well is operated. Our results document the occurrence in time of multiple peaks in the mean and variance of flux-averaged concentrations at the extraction well operating at a transient rate. Our findings suggest that lowest and largest values of mean and variance of flux-averaged concentration at the well tend to occur at the same time. We show that uncertainty associated with detected BTCs at the well increases for pumping regimes displaying a high degree of temporal variability. As such, the choice of the type of engineering control to the temporal sequence of pumping rates could represent a key factor to drive quantification of uncertainty of the contaminant concentration detected at the well. It is documented that pumping rate fluctuations induce a temporally oscillating risk pattern at the well, thus suggesting that the selection of a dynamic pumping regime has a clear influence on the temporal evolution of risk at the well

Aesthetic Value of the Relationship between the Shapes of the Face and Permanent Upper Central Incisor

The relationship between the shapes of face and teeth has been analyzed for esthetic purposes and exploited commercially. The methodology to assess this correlation, described in the literature, does not enable reliable application of the concepts. Digital photos of face and incisors of 100 youths were measured with the software Image Tool 3.0 and classified as to shape. The same photographs were also analyzed and classified by a visual criterion. Statistical analysis of the metrical classification was performed by Pearson's correlation coefficient. The Kappa test was used to determine the coefficient of agreement between the observers and the obtained data, and to assess the agreement between both classifications (metrical and visual). The classificatory analysis made by the observers indicated a marked level of disagreement, also identified between their classification and that obtained by metrical analysis. The results indicated no relationship between the shapes of the face and the central incisor

Solute concentration at a well in non-Gaussian aquifers under constant and time-varying pumping schedule

Our study is keyed to the analysis of the interplay between engineering factors (i.e., transient pumping rates versus less realistic but commonly analyzed uniform extraction rates) and the heterogeneous structure of the aquifer (as expressed by the probability distribution characterizing transmissivity) on contaminant transport. We explore the joint influence of diverse (a) groundwater pumping schedules (constant and variable in time) and (b) representations of the stochastic heterogeneous transmissivity (T) field on temporal histories of solute concentrations observed at an extraction well. The stochastic nature of T is rendered by modeling its natural logarithm, Y = ln T, through a typical Gaussian representation and the recently introduced Generalized sub-Gaussian (GSG) model. The latter has the unique property to embed scale-dependent non-Gaussian features of the main statistics of Y and its (spatial) increments, which have been documented in a variety of studies. We rely on numerical Monte Carlo simulations and compute the temporal evolution at the well of low order moments of the solute concentration (C), as well as statistics of the peak concentration (Cp), identified as the environmental performance metric of interest in this study. We show that the pumping schedule strongly affects the pattern of the temporal evolution of the first two statistical moments of C, regardless the nature (Gaussian or non-Gaussian) of the underlying Y field, whereas the latter quantitatively influences their magnitude. Our results show that uncertainty associated with C and Cpestimates is larger when operating under a transient extraction scheme than under the action of a uniform withdrawal schedule. The probability density function (PDF) of Cpdisplays a long positive tail in the presence of time-varying pumping schedule. All these aspects are magnified in the presence of non-Gaussian Y fields. Additionally, the PDF of Cpdisplays a bimodal shape for all types of pumping schemes analyzed, independent of the type of heterogeneity considered

Santa Teresa de Jesús y la orden de predicadores : estudios históricos

Copia digital. Valladolid : Junta de Castilla y León. Consejería de Cultura y Turismo, 2009-201

Predictors of happiness among retired from urban and rural areas in Brazil

This study compared differences in degree of happiness, social support, activities performed, and health and economic situation among retirees from urban and rural areas in Minas Gerais State in Brazil. The influences of these predictors over individuals’ level of happiness were also analyzed. We included 279 retired individuals living in Abre Campo (a municipality with a population fewer than 20,000 inhabitants, which is considered a rural area) and in Belo Horizonte (a municipality with a population of almost 2.5 million inhabitants, which is considered an urban area). Participants responded to a questionnaire that included scales of happiness, social support, diversity of activities, and issues about satisfaction with health and economic situation. Retirees from the urban area had a higher happiness level than retirees from the rural area (β = 0.16). The most important predictors of happiness were health (β = 0.42), social support (β = 0.26), and economic situation (β = 0.15), but no moderation effects of urban and rural areas were found. Our findings support the implementation of actions to offer financial planning before retirement and to stimulate social support and health promotion for retirees, particularly given the importance of these factors in perception of happiness

Adaptive POD model reduction for solute transport in heterogeneous porous media

We study the applicability of a model order reduction technique to the solution of transport of passive scalars in homogeneous and heterogeneous porous media. Transport dynamics are modeled through the advection-dispersion equation (ADE) and we employ Proper Orthogonal Decomposition (POD) as a strategy to reduce the computational burden associated with the numerical solution of the ADE. Our application of POD relies on solving the governing ADE for selected times, termed snapshots. The latter are then employed to achieve the desired model order reduction. We introduce a new technique, termed Snapshot Splitting Technique (SST), which allows enriching the dimension of the POD subspace and damping the temporal increase of the modeling error. Coupling SST with a modeling strategy based on alternating over diverse time scales the solution of the full numerical transport model to its reduced counterpart allows extending the benefit of POD over a prolonged temporal window so that the salient features of the process can be captured at a reduced computational cost. The selection of the time scales across which the solution of the full and reduced model are alternated is linked to the Péclet number (Pe), representing the interplay between advective and dispersive processes taking place in the system. Thus, the method is adaptive in space and time across the heterogenous structure of the domain through the combined use of POD and SST and by way of alternating the solution of the full and reduced models. We find that the width of the time scale within which the POD-based reduced model solution provides accurate results tends to increase with decreasing Pe. This suggests that the effects of local-scale dispersive processes facilitate the POD method to capture the salient features of the system dynamics embedded in the selected snapshots. Since the dimension of the reduced model is much lower than that of the full numerical model, the methodology we propose enables one to accurately simulate transport at a markedly reduced computational cost