Particle Density Estimation with Grid-Projected Adaptive Kernels

The reconstruction of smooth density fields from scattered data points is a procedure that has multiple applications in a variety of disciplines, including Lagrangian (particle-based) models of solute transport in fluids. In random walk particle tracking (RWPT) simulations, particle density is directly linked to solute concentrations, which is normally the main variable of interest, not just for visualization and post-processing of the results, but also for the computation of non-linear processes, such as chemical reactions. Previous works have shown the superiority of kernel density estimation (KDE) over other methods such as binning, in terms of its ability to accurately estimate the "true" particle density relying on a limited amount of information. Here, we develop a grid-projected KDE methodology to determine particle densities by applying kernel smoothing on a pilot binning; this may be seen as a "hybrid" approach between binning and KDE. The kernel bandwidth is optimized locally. Through simple implementation examples, we elucidate several appealing aspects of the proposed approach, including its computational efficiency and the possibility to account for typical boundary conditions, which would otherwise be cumbersome in conventional KDE

Lagrangian modeling of reactive transport in heterogeneous porous media with an automatic locally adaptive particle support volume

The particle support volume is crucial for simulating reactive transport with Lagrangian methods as it dictates the interaction among particles. Assuming that it is constant in space, the particle support volume can be selected by means of kernel density estimation theory, an approach that has been shown to provide accurate estimates in simple setups. However, the particle support volume should intuitively vary with the particle position and evolve with time so as to mimic the local behavior of the solute plume. In this paper, we present a new approach to select a locally optimal particle support volume in reactive transport simulations. We consider that each particle has a different support volume that can locally adapt its shape and size with time based on the nearby particle distribution. By introducing a new optimality criterion, closed-form expressions of the particle support volume are presented under certain assumptions. In advection-dominated transport, we propose to orient the support volume along the local velocities. Numerical simulations of solute transport in a randomly heterogeneous porous medium demonstrate that the new approach can substantially increase accuracy with a more rapid convergence to the true solution with the number of particles. The error reduction seen in local approaches is particularly important in regions with extreme (high and low) density of particles. The method is shown to be computationally efficient, displaying better results than traditional histogram or global kernel methods for the same computational effort.Peer ReviewedPostprint (published version

Thin healthy women have a similar low bone mass to women with anorexia nervosa.

An association between anorexia nerviosa (AN) and low bone mass has been demonstrated. Bone loss associated with AN involves hormonal and nutritional impairments, though their exact contribution is not clearly established. We compared bone mass in AN patients with women of similar weight with no criteria for AN, and a third group of healthy, normal-weight, age-matched women. The study included forty-eight patients with AN, twenty-two healthy eumenorrhoeic women with low weight (LW group; BMI 18.5 kg/m2 (control group), all of similar age. We measured lean body mass, percentage fat mass, total bone mineral content (BMC) and bone mineral density in lumbar spine (BMD LS) and in total (tBMD). We measured anthropometric parameters, leptin and growth hormone. The control group had greater tBMD and BMD LS than the other groups, with no differences between the AN and LW groups. No differences were found in tBMD, BMD LS and total BMC between the restrictive (n 25) and binge-purge type (n 23) in AN patients. In AN, minimum weight (P = 0.002) and percentage fat mass (P = 0.02) explained BMD LS variation (r2 0.48) and minimum weight (r2 0.42; P = 0.002) for tBMD in stepwise regression analyses. In the LW group, BMI explained BMD LS (r2 0.72; P = 0.01) and tBMD (r2 0.57; P = 0.04). We concluded that patients with AN had similar BMD to healthy thin women. Anthropometric parameters could contribute more significantly than oestrogen deficiency in the achievement of peak bone mass in AN patients

Generalizing Agarwal's method for the interpretation of recovery tests under non-ideal conditions

Pumping tests are performed during aquifer characterization to gain conceptual understanding about the system through diagnostic plots and to estimate hydraulic properties. Recovery tests consist of measuring head response in observation and/or pumping wells after pumping termination. They are especially useful when the pumping rate cannot be accurately controlled. They have been traditionally interpreted using Theis' recovery method, which yields robust estimates of effective transmissivity but does not provide information about the conceptual model. Agarwal proposed a method that has become standard in the oil industry, to obtain both early and late time reservoir responses to pumping from recovery data. However, the validity of the method has only been tested to a limited extent. In this work, we analyze Agarwal's method in terms of both drawdowns and log derivatives for non-ideal conditions: leaky aquifer, presence of boundaries, and one-dimensional flow. Our results show that Agarwal's method provides excellent recovery plots (i.e., the drawdown curve that would be obtained during pumping) and parameter estimates for nearly all aquifer conditions, provided that a constant pumping rate is used and the log derivative at the end of pumping is constant, which is too limiting for groundwater hydrology practice, where observation wells are usually monitored. We generalize Agarwal's method by (1) deriving an improved equivalent time for time-dependent pumping rate and (2) proposing to recover drawdown curves by extrapolating the pumping phase drawdowns. These yield excellent diagnostic plots, thus facilitating the conceptual model analysis for a broad range of conditions.Peer ReviewedPostprint (published version

On the formation of multiple local peaks in breakthrough curves

The analysis of breakthrough curves (BTCs) is of interest in hydrogeology as a way to parameterize and explain processes related to anomalous transport. Classical BTCs assume the presence of a single peak in the curve, where the location and size of the peak and the slope of the receding limb has been of particular interest. As more information is incorporated into BTCs (for example, with high-frequency data collection, supercomputing efforts), it is likely that classical definitions of BTC shapes will no longer be adequate descriptors for contaminant transport problems. We contend that individual BTCs may display multiple local peaks depending on the hydrogeologic conditions and the solute travel distance. In such cases, classical definitions should be reconsidered. In this work, the presence of local peaks in BTCs is quantified from high-resolution numerical simulations in synthetic fields with a particle tracking technique and a kernel density estimator to avoid either overly jagged or smoothed curves that could mask the results. Individual BTCs from three-dimensional heterogeneous hydraulic conductivity fields with varying combinations of statistical anisotropy, heterogeneity models, and local dispersivity are assessed as a function of travel distance. The number of local peaks, their corresponding slopes, and a transport connectivity index are shown to strongly depend on statistical anisotropy and travel distance. Results show that the choice of heterogeneity model also affects the frequency of local peaks, but the slope is less sensitive to model selection. We also discuss how solute shearing and rerouting can be determined from local peak quantification.Peer ReviewedPostprint (published version

A comparison of Eulerian and Lagrangian transport and non-linear reaction algorithms

When laboratory-measured chemical reaction rates are used in simulations at the field-scale, the models typically overpredict the apparent reaction rates. The discrepancy is primarily due to poorer mixing of chemically distinct waters at the larger scale. As a result, realistic field-scale predictions require accurate simulation of the degree of mixing between fluids. The Lagrangian particle-tracking (PT) method is a now-standard way to simulate the transport of conservative or sorbing solutes. The method’s main advantage is the absence of numerical dispersion (and its artificial mixing) when simulating advection. New algorithms allow particles of different species to interact in nonlinear (e.g., bimolecular) reactions. Therefore, the PT methods hold a promise of more accurate field-scale simulation of reactive transport because they eliminate the masking effects of spurious mixing due to advection errors inherent in grid-based methods. A hypothetical field-scale reaction scenario is constructed and run in PT and Eulerian (finite-volume/finite-difference) simulators. Grid-based advection schemes considered here include 1st- to 3rd-order spatially accurate total-variation-diminishing flux-limiting schemes, both of which are widely used in current transport/reaction codes. A homogeneous velocity field in which the Courant number is everywhere unity, so that the chosen Eulerian methods incur no error when simulating advection, shows that both the Eulerian and PT methods can achieve convergence in the L1 (integrated concentration) norm, but neither shows stricter pointwise convergence. In this specific case with a constant dispersion coefficient and bimolecular reaction A+B¿P, the correct total amount of product is 0.221MA0, where MA0 is the original mass of reactant A. When the Courant number drops, the grid-based simulations can show remarkable errors due to spurious over- and under-mixing. In a heterogeneous velocity field (keeping the same constant and isotropic dispersion), the PT simulations show an increased reaction total from 0.221MA0 to 0.372MA0 due to fluid deformation, while the 1st-order Eulerian simulations using ˜ 106 cells (with a classical grid Peclet number ¿x/aL of 10) have total product of 0.53MA0, or approximately twice as much additional reaction due to advection error. The 3rd-order TVD algorithm fares better, with total product of 0.394MA0, or about 1.14 times the increased reaction total. A very strict requirement on grid Peclet numbers for Eulerian simulations will be required for realistic reactions because of their nonlinear nature. We analytically estimate the magnitude of the effect for the end-member cases of very fast and very slow reactions and show that in either case, the mass produced is proportional to View the MathML source where Pe is the Peclet number. Therefore, extra mass is produced according to View the MathML source where the dispersion includes any numerical dispersion error. We test two PT methods, one that kills particles upon reaction and another that decrements a particle’s mass. For the bimolecular reaction studied here, the computational demands of the particle-killing methods are much smaller than, and the particle-number-preserving algorithm are on par with, the fastest Eulerian methods.Peer ReviewedPostprint (author's final draft

Adelante / Endavant

Séptimo desafío por la erradicación de la violencia contra las mujeres del Institut Universitari d’Estudis Feministes i de Gènere "Purificación Escribano" de la Universitat Jaume