Static deformation of a multilayered magneto-electro-elastic half-space structures due to vertical inner loading

The static deformation in a multilayered magneto-electro-elastic half-space under vertical inner loading is calculated using a vector function system approach and a stiffness matrix method. Firstly, the displacement, stress, and inner loading are expanded using the vector function system, and the N-type and L&M-type problems related to the expansion coefficient are constructed. Secondly, the stable stiffness matrix method is used to solve the expansion coefficients of the L&M-type problem. After introducing the boundary condition and the discontinuity of the stress caused by inner loading, the displacement and stress are calculated through adaptive Gaussian quadrature. Finally, the numerical examples considering the circular load and point load are designed and analyzed, respectively.

Gaussian Quadrature GQ Used to Accurately Approximate the Relative Weights of Reserves, Contingent Resources, and Prospective Resources Through A Cumulative Distribution Function

The objective of this work is to numerically estimate the fraction of Reserves assigned to each Reserves category of the PRMS matrix through a cumulative distribution function. We selected 38 wells from a Permian Basin dataset available to Texas A&M University. Previous work has shown that Swanson's Mean, which relates the Reserves categories through a cdf of a normal distribution, is an inaccurate method to determine the relationship of the Reserves categories with asymmetric distributions. Production data are lognormally distributed, regardless of basin type, thus cannot follow the SM concept. The Gaussian Quadrature (GQ) provides a methodology to accurately estimate the fraction of Reserves that lie in 1P, 2P, and 3P categories – known as the weights. Gaussian Quadrature is a numerical integration method that uses discrete random variables and a distribution that matches the original data. For this work, we associate the lognormal cumulative distribution function (CDF) with a set of discrete random variables that replace the production data, and determine the associated probabilities. The production data for both conventional and unconventional fields are lognormally distributed, thus we expect that this methodology can be implemented in any field. To do this, we performed probabilistic decline curve analysis (DCA) using Arps’ Hyperbolic model and Monte Carlo simulation to obtain the 1P, 2P, and 3P volumes, and calculated the relative weights of each Reserves category. We performed probabilistic rate transient analysis (RTA) using a commercial software to obtain the 1P, 2P, and 3P volumes, and calculated the relative weights of each Reserves category. We implemented the 3-, 5-, and 10-point GQ to obtain the weight and percentiles for each well. Once this was completed, we validated the GQ results by calculating the percent-difference between the probabilistic DCA, RTA, and GQ results. We increase the standard deviation to account for the uncertainty of Contingent and Prospective resources and implemented 3-, 5-, and 10-point GQ to obtain the weight and percentiles for each well. This allows us to also approximate the weights of these volumes to track them through the life of a given project. The probabilistic DCA, RTA and Reserves results indicate that the SM is an inaccurate method for estimating the relative weights of each Reserves category. The 1C, 2C, 3C, and 1U, 2U, and 3U Contingent and Prospective Resources, respectively, are distributed in a similar way but with greater variance, incorporated in the standard deviation. The results show that the GQ is able to capture an accurate representation of the Reserves weights through a lognormal CDF. Based on the proposed results, we believe that the GQ is accurate and can be used to approximate the relationship between the PRMS categories. This relationship will aid in booking Reserves to the SEC because it can be recreated for any field. These distributions of Reserves and resources other than Reserves (ROTR) are important for planning and for resource inventorying. The GQ provides a measure of confidence on the prediction of the Reserves weights because of the low percent difference between the probabilistic DCA, RTA, and GQ weights. This methodology can be implemented in both conventional and unconventional fields.

Study of different order of Gaussian Quadrature using Linear Element Interpolation in First Order Polarization Tensor

Polarization tensor (PT) has been widely used in engineering application, particularly in electric and magnetic field areas. In this case, suitable method must be employed in the evaluation of PT in order to make sure that the tensor obtained is higher in its accuracy. Our aim in this paper is to provide simple and easy implemented method to compute first order PT which is based on Gaussian quadrature numerical integration involving linear interpolation. This study provides the comparison between two different orders of Gaussian quadrature, which is order one and order three. The numerical technique of higher order Gaussian quadrature as PT being calculated offer more accurate and higher in its convergence. Relative error for PT is calculated by using provided analytical solution and higher order Gaussian quadrature gives high accuracy and convergence compared to lower order Gaussian quadrature. In this study, the validation of the results obtained by using our proposed method is provided by comparing it with the analytical solution derived from previous researcher. We illustrate the behavior of a tensor of a sphere and ellipsoid with graphical representation.

A Small Area Estimation Method for Investigating the Relationship between Public Perception of Drug Problems with Neighborhood Prognostics: Trends in London between 2012 and 2019

The correlation of the public’s perception of drug problems with neighborhood characteristics has rarely been studied. The aim of this study was to investigate factors that correlate with public perceptions in London boroughs using the Mayor’s Office for Policing and Crime (MOPAC) Public Attitude Survey between 2012 and 2019. A subject-specific random effect deploying a Generalized Linear Mixed Model (GLMM) using an Adaptive Gaussian Quadrature method with 10 integration points was applied. To obtain time trends across inner and outer London areas, the GLMM was fitted using a Restricted Marginal Pseudo Likelihood method. The perception of drug problems increased with statistical significance in 17 out of 32 London boroughs between 2012 and 2019. These boroughs were geographically clustered across the north of London. Levels of deprivation, as measured by the English Index of Multiple Deprivation, as well as the percentage of local population who were non-UK-born and recorded vehicle crime rates were shown to be positively associated with the public’s perception of drug problems. Conversely, recorded burglary rate was negatively associated with the public’s perception of drug problems in their area. The public are influenced in their perception of drug problems by neighborhood factors including deprivation and visible manifestations of antisocial behavior.

A Novel Numerical Method for Solving Fractional Diffusion-Wave and Nonlinear Fredholm and Volterra Integral Equations with Zero Absolute Error

In this work, a new numerical method for the fractional diffusion-wave equation and nonlinear Fredholm and Volterra integro-differential equations is proposed. The method is based on Euler wavelet approximation and matrix inversion of an M×M collocation points. The proposed equations are presented based on Caputo fractional derivative where we reduce the resulting system to a system of algebraic equations by implementing the Gaussian quadrature discretization. The reduced system is generated via the truncated Euler wavelet expansion. Several examples with known exact solutions have been solved with zero absolute error. This method is also applied to the Fredholm and Volterra nonlinear integral equations and achieves the desired absolute error of 0×10−31 for all tested examples. The new numerical scheme is exceptional in terms of its novelty, efficiency and accuracy in the field of numerical approximation.

Gauss-Simpson Quadrature Algorithm for Calcaulting Additional Stress in Foundation Soils

The additional pressure at the bottom of a building’s foundation produces an additional stress in the foundation soils under the building’s foundation. In order to overcome the limitations of traditional elastic theory methods and the finite element method when calculating the additional stress in foundation soils, we use the Gauss-Simpson formula to derive the Gauss-Simpson Quadrature Algorithm based on the elasticity theory. The Gauss-Simpson Quadrature Algorithm is a method designed to calculate the additional stress in foundation soils under an irregularly shaped foundation and an irregular load distribution. This new method is based on the fact that the Gaussian quadrature formula and the Simpson formula are independent of the specific type of integrand. The finite element method with n interpolation points can only achieve an algebraic accuracy of n. The interpolation points of the Gaussian quadrature formula are n zeros of orthogonal polynomials, which can achieve an algebraic accuracy of 2n + 1. Moreover, the weights of the nodes in the quadrature formula are all positive, and thus, it has a high numerical stability. In the proposed method, the Simpson formula is necessary. The Simpson formula is used to transform the implicit additional stress formula with the integral sign into an explicit cumulative integral, which can be considered similar to the rectangular domain case to obtain an explicit analytical algebraic formula for solving the additional stress approximation. In engineering applications, we only need to provide the field engineers with the locations of the interpolation points of the Gauss-Legendre formula, the interpolated weight coefficients, and the specific type of Simpson's formula, and then, the results of the additional stress can be calculated manually, which is nearly impossible using the traditional methods and finite element methods. From the point of view of academic rigor and theoretical completeness, it is possible to use the compound Gauss-Simpson Quadrature Algorithm in conjunction with the looping function in computer programs. Under standard conditions, the proposed Gauss-Simpson Quadrature Algorithm is in good agreement with the results of the traditional elasticity theory.

On the Optimal Field Sensing in Near-Field Characterization

We deal with the problem of characterizing a source or scatterer from electromagnetic radiated or scattered field measurements. The problem refers to the amplitude and phase measurements which has applications also to interferometric approaches at optical frequencies. From low frequencies (microwaves) to high frequencies or optics, application examples are near-field/far-field transformations, object restoration from measurements within a pupil, near-field THz imaging, optical coherence tomography and ptychography. When analyzing the transmitting-sensing system, we can define “optimal virtual" sensors by using the Singular Value Decomposition (SVD) approach which has been, since long time, recognized as the “optimal” tool to manage linear algebraic problems. The problem however emerges of discretizing the relevant singular functions, thus defining the field sampling. To this end, we have recently developed an approach based on the Singular Value Optimization (SVO) technique. To make the “virtual” sensors physically realizable, in this paper, two approaches are considered: casting the “virtual” field sensors into arrays reaching the same performance of the “virtual” ones; operating a segmentation of the receiver. Concerning the array case, two ways are followed: synthesize the array by a generalized Gaussian quadrature discretizing the linear reception functionals and use elementary sensors according to SVO. We show that SVO is “optimal” in the sense that it leads to the use of elementary, non-uniformly located field sensors having the same performance of the “virtual” sensors and that generalized Gaussian quadrature has essentially the same performance.