Review of Inverse Laplace Transform Algorithms for Laplace-Space Numerical Approaches

A boundary element method (BEM) simulation is used to compare the efficiency of numerical inverse Laplace transform strategies, considering general requirements of Laplace-space numerical approaches. The two-dimensional BEM solution is used to solve the Laplace-transformed diffusion equation, producing a time-domain solution after a numerical Laplace transform inversion. Motivated by the needs of numerical methods posed in Laplace-transformed space, we compare five inverse Laplace transform algorithms and discuss implementation techniques to minimize the number of Laplace-space function evaluations. We investigate the ability to calculate a sequence of time domain values using the fewest Laplace-space model evaluations. We find Fourier-series based inversion algorithms work for common time behaviors, are the most robust with respect to free parameters, and allow for straightforward image function evaluation re-use across at least a log cycle of time

Sexual Relationships in Hispanic Countries: a Literature Review

This is a pre-print of an article published in Current Sexual Health Reports. The final authenticated version is available online at: https://doi.org/10.1007/s11930-020-00272-6Purpose of Review: Sexuality is a complex dimension for which culture seems to play an important role, particularly in countries that are more traditional. This review summarizes the knowledge about sexual relationships in Hispanic countries, considering sexual debut, attitudes, behaviors, and satisfaction. Recent Findings: In line with the literature reviewed, the sexual double standard seems to be continuing to influence sexual relationships. Some countries show more open expressions of sexuality based on the level of gender inequality or sexualized context, and within countries, variables such as religious commitment, family characteristics, and access to resources may play important roles in sexuality. Summary: Future research, policies, and interventions should consider these specific characteristics, including these forms of expression of sexuality, in the adjustment of cross-cultural and cross-national strategies

Mixing of groundwaters with uncertain end-members: Case study in the Tepalcingo-Axochiapan aquifer, Mexico

Groundwater geochemical data from the northern portion of the Tepalcingo-Axochiapan Valley, in the state of Morelos, Mexico, are analyzed to improve the conceptual hydrogeologic model of the region. The geochemical data suggest that the chemical composition of groundwater is the result of a mixing process between two end-members represented by groundwater from an upper aquifer composed of volcanic-sedimentary rocks and groundwater from a lower aquifer composed of carbonate rocks. Analysis of published data demonstrates that the chemical composition of at least one of the end-members varies significantly in time. Mixing ratios are computed, taking into account the uncertainty in identifying end-members and the time variability in their chemical composition, using published methods. Computed mixing ratios suggest there is a significant contribution from the lower aquifer to the water pumped by the wells in the area, which should be taken into account in the conceptual hydrogeologic model of the region

Mixing of groundwaters with uncertain end-members: Case study in the Tepalcingo-Axochiapan aquifer, Mexico

Groundwater geochemical data from the northern portion of the Tepalcingo-Axochiapan Valley, in the state of Morelos, Mexico, are analyzed to improve the conceptual hydrogeologic model of the region. The geochemical data suggest that the chemical composition of groundwater is the result of a mixing process between two end-members represented by groundwater from an upper aquifer composed of volcanic-sedimentary rocks and groundwater from a lower aquifer composed of carbonate rocks. Analysis of published data demonstrates that the chemical composition of at least one of the end-members varies significantly in time. Mixing ratios are computed, taking into account the uncertainty in identifying end-members and the time variability in their chemical composition, using published methods. Computed mixing ratios suggest there is a significant contribution from the lower aquifer to the water pumped by the wells in the area, which should be taken into account in the conceptual hydrogeologic model of the region

Nonlocal and localized analyses of nonreactive solute transport in bounded randomly heterogeneous porous media: Theoretical framework

Solute transport in randomly heterogeneous media is described by stochastic transport equations that are typically solved via Monte Carlo simulation. A promising alternative is to solve a corresponding system of statistical moment equations directly. We present exact (though not closed) implicit conditional first and second moment equations for advective–dispersive transport in finite domains. The velocity and concentration are generally non-stationary due to possible trends in heterogeneity, conditioning on data, temporal variations in velocity, fluid and/or solute sources, initial and boundary conditions. Our equations are integro-differential and include non-local parameters depending on more than one point in space-time. To allow solving these equations, we close them by perturbation and develop recursive moment equations in Laplace space for the special case of steady state flow, to second order in the standard deviation of (natural) log hydraulic conductivity. We also propose a higher-order iterative closure. Our recursive equations and iterative closure are formally valid for mildly heterogeneous media, or well-conditioned strongly heterogeneous media in which the random component of heterogeneity is relatively small. The non-local moment equations suggest (and a companion paper [Morales Casique E, Neuman SP, Guadagnini A. Nonlocal and localized analyses of nonreactive solute transport in bounded randomly heterogeneous porous media: computational analysis. Adv Water Resour, submitted for publication] demonstrates numerically) that, in general, transport cannot be validly described by means of Fick_s law with a (constant or variable) macrodispersion coefficient. We show nevertheless that, under a limited set of conditions, the mean transport equation can be localized to yield a familiar-looking advection–dispersion equation with a conditional macrodispersion tensor that varies generally in spacetime. In a companion paper [Morales Casique E, Neuman SP, Guadagnini A. Nonlocal and localized analyses of nonreactive solute transport in bounded randomly heterogeneous porous media: computational analysis. Adv Water Resour, submitted for publication] we present a high-accuracy computational algorithm for our iterative non-local and recursive localized moment equations, assessing their accuracy and computational efficiency in comparison to unconditional and conditional Monte Carlo simulations

Nonlocal and localized analyses of nonreactive solute transport in bounded randomly heterogeneous porous media: Computational Analysis

In a companion paper we presented exact (though implicit and not closed) nonlocal conditional first and second moment equations for nonreactive advective–dispersive transport under both steady state and transient flow regimes in bounded, randomly heterogeneous porous domains. To allow solving our nonlocal equations we developed recursive moment equations in Laplace space for the special case of steady state flow to second order in the standard deviation of natural log hydraulic conductivity, Y, which is generally nonhomogeneous, and proposed a higher-order iterative closure scheme. We also showed that, under a limited set of conditions, the mean transport equation can be localized to yield a familiar-looking advection–dispersion equation with a conditional macrodispersion tensor that generally varies in space–time. The purpose of this paper is to explore the behavior and assess the accuracy and computational efficiency of our moment solutions in comparison to conditional and unconditional Monte Carlo simulations. To do so, we present a high-accuracy computational algorithm for our iterative nonlocal and recursive localized moment equations and corresponding computational results in two spatial dimensions conditional on measurements of Y. Our algorithm solves the moment equations by finite elements in Laplace-transformed space and inverts the solution numerically back into the time domain. Conditional results obtained with our iterative algorithm compare well with Monte Carlo simulations for log-conductivity variance of 0.3 and Peclet number Pe = 100 defined in terms of the integral scale of Y, and for Pe = 10 in the unconditional case. As log-conductivity variance, Pe and time increase the quality of our iterative moment solution deteriorates. We show that this is due to our disregarding velocity moments of order higher than two and propose that including such moments should render our iterative solution workable over a wider range of these parameters. Second-order recursive nonlocal and space-localized results are considerably less accurate than those obtained with our iterative nonlocal algorithm. Even though our moment solution does not require computing (space–time localized) macrodispersion coefficients, we nevertheless do so to examine the influence of boundaries and conditioning on their behavior. Our results support an earlier observation by the second author [Morales Casique E, Neuman SP, Guadagnini A. Nonlocal and localized analyses of nonreactive solute transport in bounded randomly heterogeneous porous media: theoretical framework. Adv Water Resour, in press., Neuman SP. Universal scaling of hydraulic conductivities and dispersivities in geologic media. Water Resour Res 1990;26(8):1749–58], based on world-wide tracer test results, that the rate at which apparent longitudinal dispersivity increases with scale diminishes with conditioning. In preliminary runs conducted on a relatively small grid without optimizing our algorithms and without parallelization, the moment solutions required considerably less computer time than did the Monte Carlo simulations

Maximum likelihood Bayesian averaging of airflow models in unsaturated fractured tuff using Occam and variance windows

We use log permeability and porosity data obtained from single-hole pneumatic packer tests in six boreholes drilled into unsaturated fractured tuff near Superior, Arizona, to postulate, calibrate and compare five alternative variogram models (exponential, exponential with linear drift, power, truncated power based on exponential modes, and truncated power based on Gaussian modes) of these parameters based on four model selection criteria (AIC, AICc, BIC and KIC). Relying primarily on KIC and cross-validation we select the first three of these variogram models and use them to parameterize log air permeability and porosity across the site via kriging in terms of their values at selected pilot points and at some single-hole measurement locations. For each of the three variogram models we estimate log air permeabilities and porosities at the pilot points by calibrating a finite volume pressure simulator against two cross-hole pressure data sets from sixteen boreholes at the site. The traditional Occam's window approach in conjunction with AIC, AICc, BIC and KIC assigns a posterior probability of nearly 1 to the power model. A recently proposed variance window approach does the same when applied in conjunction with AIC, AICc, BIC but spreads the posterior probability more evenly among the three models when used in conjunction with KIC. We compare the abilities of individual models and MLBMA, based on both Occam and variance windows, to predict space-time pressure variations observed during two cross-hole tests other than those employed for calibration. Individual models with the largest posterior probabilities turned out to be the worst or second worst predictors of pressure in both validation cases. Some individual models predicted pressures more accurately than did MLBMA. MLBMA was far superior to any of the individual models in one validation test and second to last in the other validation test in terms of predictive coverage and log scores