Elliptical Model Research Articles

Probabilistic Seismic Hazard Analysis for China Based on Bayesian Network

Abstract Bayesian network (BN) has important applications in disaster risk analysis due to its unique causal structure and probabilistic characteristics. This research begins with a detailed introduction to probabilistic seismic hazard analysis (PSHA) for China, and the utilization of BN-based modeling for seismic hazard and risk assessment. Subsequently, a comprehensive theoretical exposition of PSHA for China based on BN is presented. This includes a clear explanation of the three-level subdivision of seismic sources and the employment of the elliptical ground-motion model (GMM) in China. Regarding BN modeling, the values, conditional probabilities, and the impact of subdivisions of the nodes are carefully discussed with the assistance of a specific example from China. The advantages of BN in terms of both holistic and probabilistic computation are then demonstrated through the disaggregation of seismic hazard and various sensitivity analyses. Finally, the article concludes by summarizing its content, highlighting the advantages of BN, and outlining future work.

Modelling the sound absorption of panels with tapered elliptic micro-perforations

A theoretical model is developed in the present study to predict the spectral characteristics of the sound absorption of solid panels with tapered elliptic micro-perforations backed by a rigid wall cavity. In the model, plane wave propagation is assumed along the length of the perforation in the presence of a viscous boundary layer at the internal wall of the perforation. End impedances are approximated using results in existing literature. Validation is done using impedance tube measurements. It is confirmed that the present tapered elliptic perforation model can give much better agreement with experimental results than the conventional cylindrical perforation model for all micro-perforation configurations tested. Results also suggest the importance of perforation density in controlling the variation of sound absorption of the panel absorbers upon changes in perforation configurations.

The general method of the tanker car mouth pose measurement

PurposeThe coupling process between the loading mechanism and the tank car mouth is a crucial step in the tank car loading process. The purpose of this paper is to design a method to accurately measure the pose of the tanker car.Design/methodology/approachThe collected image is first subjected to a gray enhancement operation, and the black parts of the image are extracted using Otsu’s threshold segmentation and morphological processing. The edge pixels are then filtered to remove outliers and noise, and the remaining effective points are used to fit the contour information of the tank car mouth. Using the successfully extracted contour information, the pose information of the tank car mouth in the camera coordinate system is obtained by establishing a binocular projection elliptical cone model, and the pixel position of the real circle center is obtained through the projection section. Finally, the binocular triangulation method is used to determine the position information of the tank car mouth in space.FindingsExperimental results have shown that this method for measuring the position and orientation of the tank car mouth is highly accurate and can meet the requirements for industrial loading accuracy.Originality/valueA method for extracting the contours of various types of complex tanker mouth is proposed. This method can accurately extract the contour of the tanker mouth when the contour is occluded or disturbed. Based on the binocular elliptic conical model and perspective projection theory, an innovative method for measuring the pose of the tanker mouth is proposed, and according to the space characteristics of the tanker mouth itself, the ambiguity of understanding is removed. This provides a new idea for the automatic loading of ash tank cars.

A comprehensive comparison of copula models and multivariate normal distribution for geo-material parametric data

Multivariate distribution models for geo-material parametric data play a crucial role in reliability-based design. Currently, two major models are commonly used: the conventional multivariate normal distribution model and the copula model (including subtypes like the elliptical copula model and Vine copula model). This study aims to assess the performance of different models including three specific copula models (Gaussian copula, t copula, and D-Vine copula models) and the conventional normal distribution model. To this end, this study employs an incomplete database comprising 693 data samples related to lacustrine soils near Dianchi Lake in Kunming city, China. Results indicate that copula models generally exhibit lower model uncertainty compared to the conventional multivariate normal distribution model. Using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), the elliptical copula ranks first, followed by Gaussian copula, with D-Vine copula ranking third. For a balanced evaluation of performance and complexity, the conventional multivariate normal distribution model is favored. This study provides valuable insights for selecting appropriate models for geo-material parametric data, aiding reliability-based design in geotechnical engineering. Additionally, it is demonstrated that sampling with replacement in the Bootstrapping technique has only a slight effect on the estimation of correlation matrices for the incomplete database.

Diversification quotients based on VaR and ES

The diversification quotient (DQ) is recently introduced for quantifying the degree of diversification of a stochastic portfolio model. It has an axiomatic foundation and can be defined through a parametric class of risk measures. Since the Value-at-Risk (VaR) and the Expected Shortfall (ES) are the most prominent risk measures widely used in both banking and insurance, we investigate DQ constructed from VaR and ES in this paper. In particular, for the popular models of elliptical and multivariate regular varying (MRV) distributions, explicit formulas are available. The portfolio optimization problems for the elliptical and MRV models are also studied. Our results further reveal favorable features of DQ, both theoretically and practically, compared to traditional diversification indices based on a single risk measure.

Determination of volume averaging correction factors using an elliptical absorbed dose model for Gamma Knife Perfexion.

The purpose of this study is to calculate volume averaging correction factors for detectors used in the dosimetry of Gamma Knife's narrow photon beams, and to determine the impact of volume averaging on the field output correction factor. Simulations of different Gamma Knife fields were done using elliptical dose model formalism with newly introduced fit functions. To determine volume averaging correction factors a calculation of the absorbed dose over the volume of the detector was performed. The elliptical dose model was tested with respect to absorbed dose distribution for different volumes and compared with the calculations of Leksell GammaPlan v.11.3.1. The largest differences in absorbed dose calculated by the elliptical model and Leksell GammaPlan are 2.25%, 1.5%, and 0.6% for 16, 8, and 4mm field sizes, respectively. Volume averaging correction factors were determined for six ionization chambers, five semiconductor detectors, a diamond, and two plastic scintillator detectors. In general, for all examined detectors the impact of volume averaging is more pronounced for smaller field sizes. All studied ionization chambers had a larger volume than other detectors, therefore the volume averaging correction factors for ionization chambers are larger for all investigated field sizes. Besides the fact that plastic scintillator detectors can be considered tissue-equivalent, volume averaging correction factor should be applied. Volume averaging correction factors for different detectors are determined and suitable detectors for dosimetry of Gamma Knife's narrow photon beams are recommended. It is shown that volume averaging has a dominant contribution to a field output correction factor.

A new multi-scale pore transport capacity model considering elliptical shape and retention effect of unequal-thickness water films

Most of current permeability evaluation models for shale gas reservoirs ignore the influence of imbibition during fracturing, moreover, several of the considerations are different from real conditions, for example, shale pore shape is circular and water film is with equal thickness, which is convenient for calculation but adverse to evaluation accuracy. In the study, shale pore shapes are closer to ellipse by statistically analyzing the scanning electron microscopy results, the thickness of water film is not equal on elliptical pore surface but related to the curvature. Based on these new insights, a quantitative model for determining the unequal thickness of water film was established, and then a new multi-scale elliptical pore permeability model, considering non-equal-thickness water film, wall roughness, stress sensibility, and retention effect, was established based on the multi-scale flow weighting theory. The prediction results of this permeability model are similar to the test results, and are more accurate than that of the previous models. Finally, factors analysis showed that the effect of roughness on permeability was small, but the negative impact of water film and stress sensitivity on permeability was significant.

Numerical analysis of porosity effects on mechanical properties for tissue engineering scaffold

Tissue engineering has emerged as a promising solution for healing fractured human bones through the utilization of porous scaffolds that offer synthetic support to the damaged bone. This current study aims to identify an optimal porous scaffold design that exhibits superior mechanical properties. Utilizing Fusion 360 software, a unit cell was modelled with circular, elliptical, and flower shapes, each oriented differently. A circular porous scaffold, comprised of eight-unit cells, was fabricated using a 3D printer. Compression tests were conducted on this printed scaffold using a Universal Testing Machine (UTM). A comparative analysis was performed between the experimental and numerical deflection, revealing an approximate 8.8% variation in comparison to the experimental deflection. Static structural analysis of the modelled scaffolds was carried out employing ANSYS software. Scaffolds constructed with PLA (Polylactic Acid) and PGA (Polyglycolic Acid) materials exhibited similar von-Mises stress results during their structural assessments. The circular geometry scaffold displayed a Von-Mises stress of 330 MPa, while the elliptical geometry scaffold exhibited 76 MPa. The findings led to the conclusion that the elliptical model possessed a lower von-Mises stress compared to the circular model, although the porosity of the elliptical model remained around 50%. Furthermore, it was observed that the Maximum Equivalent stress of the elliptical scaffold with a vertical orientation was 63% higher than that of the same scaffold with a horizontal orientation. For square geometry scaffolds, maintaining a constant porosity percentage of 83.6%, the model with 512-unit cells predicted the minimum von-Mises stress when compared to scaffolds with 1, 8, and 64 - unit cells.

Large‐strain consolidation of PVD‐improved soils considering depth‐dependent initial void ratio and initial effective stress due to soil self‐weight

AbstractA governing equation for large‐strain consolidation of PVD‐improved soil is developed based on the equivalent elliptical cylindrical model, which accounts for depth‐dependent initial void ratio and initial effective stress induced by soil self‐weight, well resistance with variable discharge capacity, time‐dependent load, and nonlinear variations of compressibility and permeability. Then, a numerical solution is obtained by means of COMSOL Multiphysics and is validated through comparisons with existing solutions and measured data. The parametric studies show that the difference between large‐strain consolidation and small‐strain consolidation reduces with the decreases of the compression index and applied load. Although the soil self‐weight has little effect on the degree of consolidation in some cases, the soil settlement will be significantly overestimated if the self‐weight is ignored. The development of consolidation slowed as the ratio of compressibility over horizontal permeability increased.

Solution structure of bilayer membrane-embedded proton-translocating pyrophosphatase revealed via small-angle X-ray scattering

The conformations and compositions of a proton-translocating pyrophosphatase Vigna radiata H+-PPase (VrPPase), stabilized by either detergent molecules or embedded in a lipid nanodisc in aqueous solution, are revealed using size exclusion chromatography coupled small-angle X-ray scattering (SEC-SAXS) with online UV–Vis absorption and refractive index (RI) detections. The integrated analysis of the scattering and optical data indicates that the large VrPPase dimer can be embedded successfully into the POPC nanodisc, with the transmembrane region immersed into the lipid aliphatic chains. The corresponding structural parameters of the protein-nanodisc complex are determined using an analytical core-multishell elliptical cylinder model. After binding with imidodiphosphate (IDP) to mimic the substrate (PPi) binding, the VrPPase embedded in the nanodisc shows no obvious structural changes. Correspondingly, the detergent-solubilized tetramers display a relatively prominent structural response to the IDP binding. About 450 n-decyl-β-d-maltopyranoside molecules are present in the detergent corona surrounding the hydrophobic area of the protein tetramer, making it difficult to attribute the structural changes observed solely to the VrPPase. Nevertheless, the combined measurements and analysis of the SEC-SAXS advance the understanding of the two types of membrane-protein complexes in terms of their compositions and structural features.

Microcapsule geometry and nanomaterial enhancement of PCMs (sp07&sp11) for free heating applications

Thermal analysis for the charging/discharging process of PCMs in different encapsulation geometries for free heating applications is performed. PCMs; sp07 and sp11 for cold climate conditions are simulated with Al2O3 and CuO nanoparticles (NPs) in circular, elliptical, rectangular, and square physical models. Complete mathematical equations of the physical model are constructed and solved using Ansys-fluent and validated using an experimental setup. Findings show that rectangular microcapsules have the shortest melting and solidification times, over 41% shorter than those of circular capsules. Minimum melting times of 79 and 135 min are realized using Al2O3 NPs with sp07 and sp11, respectively for a rectangular model. NPs inclusion increases the melting and solidification rates by 4.17–16.90%. Al2O3 NPs resulted in better thermal performances compared with CuO NPs. The largest free cooling and heating potential is 2.32K and 1.50K, respectively using sp07 with Al2O3 NPs and sp11 Al2O3 NPs, respectively for rectangular microcapsule. The study recommends sp11. Sp11 with 4 wt% Al2O3 NPs in a rectangular capsule achieved free heating and cooling degrees of 1.50K and 1.30K respectively. Complete solidification and melting times of 120 and 135 min with the largest heat transfer rates of 13.4 W and −11.6 W, respectively are achieved.

Time-varying dependence and currency tail risk during the Covid-19 pandemic

Purpose The purpose of this paper is to introduce a generalization of the time-varying correlation elliptical copula models and to analyse its impact on the tail risk of a portfolio of foreign currencies during the Covid-19 pandemic. Design/methodology/approach The authors consider a multivariate time series model where marginal dynamics are driven by an autoregressive moving average (ARMA)–Glosten-Jagannathan-Runkle–generalized autoregressive conditional heteroscedastic (GARCH) model, and the dependence structure among the residuals is given by an elliptical copula function. The correlation coefficient follows an autoregressive equation where the autoregressive coefficient is a function of the past values of the correlation. The model is applied to a portfolio of a couple of exchange rates, specifically US dollar–Japanese Yen and US dollar–Euro and compared with two alternative specifications of the correlation coefficient: constant and with autoregressive dynamics. Findings The use of the new model results in a more conservative evaluation of the tail risk of the portfolio measured by the value-at-risk and the expected shortfall suggesting a more prudential capital allocation policy. Originality/value The main contribution of the paper consists in the introduction of a time-varying correlation model where the past values of the correlation coefficient impact on the autoregressive structure.

Anticipation dynamics of pedestrians based on the elliptical social force model.

Humans have excellent predictive capabilities, and this anticipation would reflect in the interactions between people. In this work, we utilize the elliptical specification of the social force model (SFM) for pedestrian movements to study how anticipation affects motion dynamics. An elliptical potential determines the interaction between pedestrians not in contact. Anticipation is introduced by shaping the ellipse according to the relative velocity. By adjusting the time to extrapolate, we can control the strength of anticipation. Simulations are conducted in four typical scenarios, i.e., circular motion, crowd gathering, escape through a bottleneck, and free wander. In each case, the qualitative observations from visual animations are followed by quantitative analyses involving different indicators. Simulation results demonstrate that anticipation plays an important role in pedestrian dynamics in several aspects. Briefly, it helps stabilize the movement by reducing perturbations, facilitates a more ordered crowd configuration, and promotes spontaneous collective motion. The findings may set avenues for further research in anticipation dynamics.

Generalized Heisenberg–Virasoro algebra and matrix models from quantum algebra

In this paper, we construct the Heisenberg–Virasoro algebra in the framework of the R(p,q)-deformed quantum algebras. Moreover, the R(p,q)-Heisenberg–Witt n-algebras is also investigated. Furthermore, we generalize the notion of the elliptic Hermitian matrix models. We use the constraints to evaluate the R(p,q)-differential operators of the Virasoro algebra and generalize it to higher order differential operators. Particular cases corresponding to quantum algebras existing in the literature are deduced.

Elliptical and Skew-Elliptical Regression Models and Their Applications to Financial Data Analytics

Various statistical distributions have played significant roles in financial data analytics in recent decades. Among these, elliptical modeling has gained popularity, while the study and application of skew-elliptical modeling have garnered increased attention in various domains. This paper begins by acknowledging the notable accomplishments and contributions of Professor Chris Heyde in the field of financial data modeling. We provide a comprehensive review of elliptical and skew-elliptical modeling, summarizing the latest advancements. In particular, we focus on the characteristics, estimation methods, and diagnostics of elliptical and skew-elliptical distributions in regression and time series models, as well as copula modeling. Furthermore, we discuss several related applications in regression and time series models, including estimation and diagnostic methods. The main objective of this paper is to address the critical need for accurately identifying the underlying elliptical distribution, whether it is elliptical or skew-elliptical. This identification is essential for conducting local influence diagnostics and employing appropriate regression methods using suitable elliptical modeling techniques. To illustrate this process, we present examples that demonstrate the identification of the elliptical distribution, starting with the Box–Jenkins methodology and progressing to copula modeling. The inclusion of copula modeling is motivated by its effectiveness in conjunction with elliptical and skew-elliptical distributions, as it aids in distinguishing between the two. Ultimately, the findings of this paper offer valuable insights, as correctly determining the elliptical and skew-elliptical distribution enables the application of suitable local influence and regression methods, thereby contributing to financial portfolio management, business analytics, and insurance analytics, ensuring the accurate specification of models.

Marine mammal morphometrics: 3D modeling and estimation validation

Techniques of 3D modeling have earned increasing popularity in scientific studies as they offered unprecedented traits in representing objects. As with all mathematical models, the 3D model will be useful once its accuracy has been validated with direct measurements and the robustness of its predictive capability tested. Although measures of body mass and volume are essential to comprehend the life history of animals, such morphometrics, especially total volume, are challenging to obtain from marine mammals due to their elusive nature, aquatic lifestyle, and large size. In this study, accurate measurements of body volume were directly detected from fresh carcasses of eleven finless porpoises (Neophocaena asiaeorientalis sunameri) and used to validate 3D models recreated from the same animals using Blender 3D graphics. Published models using truncated cones or elliptical shapes, based on 3, 5, 8, or 19 measurements of girths or heights & widths along the body, were also applied to porpoises to verify their accuracy. The Blender-generated 3D model produced the most accurate estimates of body volume compared to conventional truncated models, with a mean error of only 2.5% to the direct volume measurements. When photogrammetric images are available, the model can predict the body volumes based on total length alone. Similar accuracy was possible with the elliptical model using 19 height & width measurements (5% increments in total length). However, significant (p < 0.001) inaccuracy resulted from truncated models with 3, 5, or 8 girth measurements and elliptical models with 3 or 5 height & width measurements, and the accuracy of these models also decreased significantly as the number of measurement sites was reduced. Moreover, Blender 3D models can be extrapolated to animals with images absent, and such predicted volumes were tested to be trustworthy (overall skill = 0.998, r = 0.998, p < 0.01). Therefore, we recommend that researchers use either digital 3D models or elliptical models with 5% increments sectioning the torso to obtain accurate estimates of the body volumes of free-ranging marine mammals.

Trilinear Immersed-Finite-Element Method for Three-Dimensional Anisotropic Interface Problems in Plasma Thrusters

Accurately solving the anisotropic interface problem is one of the difficulties in aerospace plasma applications. Based on cubic Cartesian meshes, this paper develops a trilinear nonhomogeneous immersed finite element (IFE) method for solving the complex anisotropic 3D elliptic interface model with nonhomogeneous flux jump. Compared with the existing 3D linear IFE spaces based on tetrahedron meshes, the newly designed trilinear IFE space for the target model simplifies the mesh generation, significantly reduces the number of mesh elements and interface elements, provides much more convenient and efficient ways for finding the intersections between interfaces and mesh edges, and decreases the errors. These advantages lead to much higher efficiency when solving complex anisotropic interface problems in practice. In addition, the proposed method can be easily incorporated into other typical methods based on Cartesian meshes, such as the particle-in-cell method for plasma simulation. Numerical experiments are provided to verify the optimal accuracy, high efficiency, and reliability of the proposed method for solving complex interface problems, as well as its applicability to practical plasma thruster problems.

Near-Field Single-Scattering Calculations of Aerosols: Sensitivity Studies

We model the effects of the photosensitive parameters of aerosols on their optical properties to provide a solid framework for further experimental and theoretical studies. A spherical dust particle is used to study the effects of the ambient medium, size, surface roughness, wavelength, and imaginary part of the complex refractive index. Five Gaussian random spheres with different aspect ratios are simulated to study the dependence of aerosol light scattering properties on particle shape distribution. To investigate the influence of composition, we model two typical kaolinite-like particles (pure and composite) collected from Southwest Sahara, with 0 and 2% hematite at different mixing states. Using the method of discrete-dipole approximation in DDSCAT, a comparative study is performed with the Mueller matrix elements, scattering, absorption, extinction efficiencies, single scattering albedo, and linear depolarization ratio as indicators. For single, microscopic dust particles, near-field calculations are carried out. The results show that the intensity of backscattering and the scattering efficiency decreases in water compared to dry air. Light in the visible range is more efficient for aerosol scattering experiments. A small number of impurities in the sample will increase its absorbing properties, but, in general, the scattering efficiencies strongly depend on the single-particle mixing state. Smaller particles with a diameter comparable to the wavelength of incident light show higher scattering efficiencies but lower backscattering intensities than larger particles, while surface roughness is shown to strongly alter the polarizability of the particle but has a negligible effect on its single-scattering albedo. Moreover, different shapes have a strong effect on the degree of linear polarization, but, in general, using the spherical over elliptic shape model can underestimate the scattering efficiencies by up to 4%. Finally, variation in the imaginary part of the complex RI can underestimate the single scattering albedo by up to 35.8%.

Extracting the 3D spatial structure of soil cracks in the North China Plain from paraffin casting and exploring the developmental patterns of vertical cross-sectional morphology of the cracks

Cracking from soil desiccation is a common phenomenon. Understanding the structure of cracks is highly important in the research of soil moisture and heat transportation, as well as the strength of soil structure within soil. There is limited research on the three-dimensional (3D) spatial characteristics of soil desiccation cracks. Furthermore, the absence of a dependable and precise in-situ technique for extracting and digitizing the three-dimensional crack structure means that the commonly employed simplified crack models (such as V-shaped and cuboid-shaped) have received limited testing. This study examines the feasibility of extracting the 3D structure of cracks by combining in-situ paraffin casting in sandy loam soil of North China Plain with a 3D laser scanner. Parameters (length (L), width (W), depth (D), depth to width ratio (C)), as well as the vertical cross-section profile (W ∼ D) of each crack, were used to quantitatively describe the structure of cracks. Our study demonstrated that digitalized 3D cracks with 5 μm spatial resolution can be obtained quickly by paraffin infusion combined with a 3D laser scanner. Our result based on 18 crack cross-section profiles also demonstrates that W ∼ D do not follow either the V-shaped crack model or the cuboid-shaped crack model. All of the 18 normalized vertical profiles of cracks obey the power function relationship (R2 = 0.850) rather than the linear relationship of the V-shaped model (R2 = 0.794). The shape of the soil moisture profile is convex, which contradicts the concave profile of the observed vertical cracks. Even after combining the Soil Shrinkage Characteristic Curve (SSCC) with the soil moisture profile, we still failed to replicate the observed concave crack profile. The observed crack morphology in experiments can be replicated by both the elliptical model and the parabolic model of fracture mechanics, albeit with less predictive accuracy when compared to the power function model. This suggests that the current understanding of soil desiccation cracking in soil science is deficient, as it lacks appropriate methods and theoretical mechanisms for investigating soil cracking.

Estimation of fracture size and azimuth in the universal elliptical disc model based on trace information

The geometric characteristics of fractures within a rock mass can be inferred by the data sampling from boreholes or exposed surfaces. Recently, the universal elliptical disc (UED) model was developed to represent natural fractures, where the fracture is assumed to be an elliptical disc and the fracture orientation, rotation angle, length of the long axis and ratio of short-long axis lengths are considered as variables. This paper aims to estimate the fracture size- and azimuth-related parameters in the UED model based on the trace information from sampling windows. The stereological relationship between the trace length, size- and azimuth-related parameters of the UED model was established, and the formulae of the mean value and standard deviation of trace length were proposed. The proposed formulae were validated via the Monte Carlo simulations with less than 5% of error rate between the calculated and true values. With respect to the estimation of the size- and azimuth-related parameters using the trace length, an optimization method was developed based on the pre-assumed size and azimuth distribution forms. A hypothetical case study was designed to illustrate and verify the parameter estimation method, where three combinations of the sampling windows were used to estimate the parameters, and the results showed that the estimated values could agree well with the true values. Furthermore, a hypothetical three-dimensional (3D) elliptical fracture network was constructed, and the circular disc, non-UED and UED models were used to represent it. The simulated trace information from different models was compared, and the results clearly illustrated the superiority of the proposed UED model over the existing circular disc and non-UED models.