The effect of voids shape on hypervelocity cylindrical cavity expansion and shock waves formation in transversely isotropic porous materials

This paper investigates the steady-state dynamic radial expansion of a pressurized circular cylindrical cavity in an infinite porous medium modeled with the constitutive framework developed by Monchiet et al. (2008), which considers the material to display a periodic porous microstructure with spheroidal voids and matrix described by the orthotropic yield criterion of Hill (1948). For that purpose, we have extended the formulation of dos Santos et al. (2019) to consider oblate and prolate voids, which allows to assess the role of the initial voids shape on the elastoplastic-anisotropic fields that develop near the cavity. The theoretical development follows the cavity expansion formalism of Cohen and Durban (2013) and employs the artificial viscosity approach of Lew et al. (2001) to avoid singularities in the field variables due to the formation of plastic shock waves. The main outcome of this work is a relationship between the critical cavity expansion velocity for which plastic shocks emerge and the initial aspect ratio of the spheroidal voids. The results show that the formation of shocks is delayed for oblate voids, in comparison with spherical and prolate voids. These findings have been substantiated for different anisotropic behaviors and initial void volume fractions.

Precipitation Downscaling with Gibbs Sampling: An Improved Method for Producing Realistic, Weather-Dependent, and Anisotropic Fields

Downscaling precipitation fields is a necessary step in a number of applications, especially in hydrological modeling where the meteorological forcings are frequently available at too coarse resolution. In this article, we review the Gibbs sampling disaggregation model (GSDM), a stochastic downscaling technique originally proposed by Gagnon et al. The method is capable of introducing realistic, weather-dependent, and possibly anisotropic fine-scale details, while preserving the mean rain rate over the coarse-scale pixels. The main developments compared to the former version are (i) an adapted Gibbs sampling algorithm that enforces the downscaled fields to have a similar texture to that of the analysis fields, (ii) an extensive test of various meteorological predictors for controlling specific aspects of the texture such as the anisotropy and the spatial variability, and (iii) a review of the regression equations used in the model for defining the conditional distributions. A perfect-model experiment is conducted over a domain in the southeastern United States. The metrics used for verification are based on the concept of gridded, stratified variogram, which is introduced as an effective way of reproducing the abilities of human eyes for detecting differences in the field texture. Results indicate that the best overall performances are obtained with the most sophisticated, predictor-based GSDM variant. The 600-hPa wind is found to be the best year-round predictor for controlling the anisotropy. For the spatial variability, kinematic predictors such as wind shear are found to be best during the convective periods, while instability indices are more informative elsewhere.

Is Localization of Wireless Sensor Networks in Irregular Fields a Challenge?

Wireless sensor networks have been considered as an emerging technology for numerous applications of cyber-physical systems. These applications often require the deployment of sensor nodes in various anisotropic fields. Localization in anisotropic fields is a challenge because of the factors such as non-line of sight communications, irregularities of terrains, and network holes. Traditional localization techniques, when applied to anisotropic or irregular fields, result in colossal location estimation errors. To improve location estimations, this paper presents a comparative analysis of available localization techniques based on taxonomy framework. A detailed discussion on the importance of localization of sensor nodes in irregular fields from the reported real-life applications is presented along with challenges faced by existing localization techniques. Further, taxonomy based on techniques adopted by localization methods to address the effects of irregular fields on location estimations is reported. Finally, using the designed taxonomy framework, a comparative analysis of different localization techniques addressing irregularities and the directions towards the development of an optimal localization technique is addressed.

Enhanced positive vertex-centered finite volume scheme for anisotropic convection-diffusion equations

This article is about the development and the analysis of an enhanced positive control volume finite element scheme for degenerate convection-diffusion type problems. The proposed scheme involves only vertex unknowns and features anisotropic fields. The novelty of the approach is to devise a reliable upwind approximation with respect to flux-like functions for the elliptic term. Then, it is shown that the discrete solution remains nonnegative. Under general assumptions on the data and the mesh, the convergence of the numerical scheme is established owing to a recent compactness argument. The efficiency and stability of the methodology are numerically illustrated for different anisotropic ratios and nonlinearities.

Polar Functions for Anisotropic Gaussian Random Fields

LetXbe an (N,d)-anisotropic Gaussian random field. Under some general conditions onX, we establish a relationship between a class of continuous functions satisfying the Lipschitz condition and a class of polar functions ofX. We prove upper and lower bounds for the intersection probability for a nonpolar function andXin terms of Hausdorff measure and capacity, respectively. We also determine the Hausdorff and packing dimensions of the times set for a nonpolar function intersectingX. The class of Gaussian random fields that satisfy our conditions includes not only fractional Brownian motion and the Brownian sheet, but also such anisotropic fields as fractional Brownian sheets, solutions to stochastic heat equation driven by space-time white noise, and the operator-scaling Gaussian random field with stationary increments.