Effective electroelastic constants for three-phase confocal elliptical cylinder model in piezoelectric quasicrystal composites

A three-phase confocal elliptical cylinder model is proposed to analyze micromechanics of one-dimensional hexagonal piezoelectric quasicrystal （PQC） compos- ites. Exact solutions of the phonon, phason, and electric fields are obtained by using the conformal mapping combined with the Laurent expansion technique when the model is subject to far-field anti-plane mechanical and in-plane electric loadings. The effective elec- troelastic constants of several different composites made up of PQC, quasicrystal （QC）, and piezoelectric （PE） materials are predicted by the generalized self-consistent method. Numerical examples are conducted to show the effects of the volume fraction and the cross-sectional shape of inclusion （or fiber） on the effective electroelastic constants of these composites. Compared with other micromechanical methods, the generalized self- consistent and Mori-Tanaka methods can predict the effective electroelastic constants of the composites consistently.

A universal elliptical disc(UED)model to represent natural rock fractures

Since natural fractures are often non-equidimensional,the circular disc model still has great limitations.By contrast,the elliptical disc model is more applicable to representing natural fractures,especially for slender ones.This paper developed a universal elliptical disc(UED)model by incorporating the center point,size,and azimuth of fractures as variables.Specifically,with respect to the azimuth of elliptical fractures in three-dimensional(3D)space,we proposed a paradigm to construct its probability density function(PDF)by coupling the orientation and rotation angle of long axis based on three coordinate transformations.To illustrate the construction process of the PDF of the fracture azimuth,we took the orientation following the Fisher distribution and the rotation angle following Von Mises distribution as an example.A rock slope is used to show the use of the developed UED model,and the 3D DFNs for the slope rock mass are generated by Monte Carlo simulation.In addition,the DFNs for the rock mass are also generated based on the existing circular disc model and non-universal elliptical disc model.The comparison results from the three models clearly illustrate the superiority of the UED model over the existing circular and non-universal elliptical disc models.

Heat transfer simulation of annular elliptical fin-and-tube heat exchanger by transition SST model

In this study,thermo-fluid characteristics of elliptical annular finned tube heat exchanger were numerically studied in detail.Transition SST model was utilized to simulate turbulent flow.Effects of air velocities,horizontal to vertical fin diameter ratios,and fin densities were examined in detail.The simulations indicate superior performance of elliptical fin layout.It was shown that pressure drop of annular elliptical fin can be only one half of that of a circular annular fin while containing comparable heat transfer performance.The vertical elliptical annular fin may even contain a higher heat transfer performance over circular fin.Correlations are proposed to estimate the Nu number and pressure drop based on the annular circular fin.The maximum deviations between the proposed correlations and simulations regarding pressure drop and heat transfer coefficient are 5.6%and 3.2%,respectively.For further elaboration of the superiority of the elliptical layout from the second law perspective,normalized entropy generation was also studied.In all cases,the entropy generation rate in circular fin was higher than that of an elliptical fin.

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。

An Elliptical Wind Field Model of Typhoons

An elliptical wind field model of typhoons is put forward based on the characteristics of the typhoon wind fields occurring in the Yellow Sea and Bohai Sea. By contrasting it with the circular typhoon wind field model, it is found that the elliptical model can adequately represent the real wind field and trace the process of a typhoon storm surge. The numerically simulated results of storm surges by using the elliptical model are in good agreement with the observations and markedly better than those by using the circular model.

Application of the Static Headland-Bay Beach Concept to a Sandy Beach: A New Elliptical Model

The headland-bay beach is one of the most common coastal types in the world.Its morphology reflects the changes that occurred during long-term evolution of the sandy coast.Several headland-bay beach models have been proposed to simulate the coastline’s configuration in equilibrium.In this paper,a new elliptical model is proposed,described,and applied.On the east coast of Laizhou Bay in Shandong Province from Longkou Port to Diaolongzui,four typical headland-bay beaches have developed,and four headland-bay beach models are used in this paper to simulate the morphology of these beaches to assess the applicability of each model.The simulation results of the elliptical model verify that it is applicable to the study area.In addition,the elliptical model is easy to use.Through simulation and field investigations,we concluded that most of the coastal segments in this area will remain in an erosion state,and the human activity has a significant impact on the shoreline’s evolution.

Simulation for MSS-2 low-perigee elliptical orbit satellites:an example of lithospheric magnetic field modelling

A future constellation of at least four geomagnetic satellites(designated Macao Scientific Satellite-1(MSS-1)and Macao Scientific Satellite-2(MSS-2))was recently proposed,to continue high-quality geomagnetic observations in the post-Swarm period,focusing especially on collecting data that will provide a global,three-dimensional survey of the geomagnetic field.In this paper,we present a simulation of two years of orbits(2020.01.01-2022.01.01)of two satellites(tentatively denoted as MSS-2)that are constellated in elliptical(200×5,300 km)low-perigee orbits.By comparing error variances of Gauss coefficients,we investigate the sensitivity of lithospheric magnetic field modelling to data collected from various satellite orbits,including a near circular reference orbit of 300×350km,and elliptical orbit of 180×5,300 km,220×5,300 km,200×3,000 km and 200×1,500 km.We find that in two years the two MSS-2 satellites can collect 35,000 observations at altitude below 250 km,data that will be useful in advancing the quality of lithospheric magnetic field modelling;this number of observations reflects the fact that only 4.5%of the flight time of these satellites will be below250 km(just 6.4%of their flight time below 300 km).By combining observations from the MSS-2 satellites’elliptical orbits of 200×5,300km with observations from a circular reference orbit,the variance of the geomagnetic model can be reduced by a factor of 285 at spherical harmonic degree n=200 and by a factor of 1,300 at n=250.The planned lower perigee of their orbits allows the new satellites to collect data at unprecedentedly lower altitudes,thus dramatically improving the spatial resolution of satellite-derived lithospheric field models,(up to 80%at n=150).In addition,lowering the apogee increases the time interval during which the satellites fly at near-Earth altitudes,thus improving the model predictions at all spherical harmonic degrees(around 52%-62%at n=150).The upper limit of the expected improvement to the field model at the orbital apogee is not as good as at the perigee.However,data from the MSS-1 orbit can help fill the gap between data from the MSS-2 orbits and from the circular reference orbit for the low-degree part of the model.The feasibility of even lower-altitude flight requires further discussion with satellite engineers.

A New Elliptical Cross-Section Mathematical Model of Woven Fabric Based on Jacobian Transformation

In order to give a true reflection of the spatial structure of woven fabric, a circular mathematical model is established based on the Peirce＇s model and the principle of the coordinate transformation. The circular model uses arcs and tangent lines as the yarn flexion shape and selects the circle as the yarn cross-section. Then, a new elliptical cross-section mathematical model is rapidly built by the Jaeobian transformation of the circular model. The Matiab software is used for the 3D simulation. It is shown that 3D simulations of woven fabrics with different weft and warp yarn counts, weft and warp densities, structure phases, weaves and flattening coefficients are successfully realized by Matiab basing on the elliptical mathematical model.

基于Elliptical Copula函数的相关性模型研究

针对沪深股指构建了两种基于Elliptical Copula函数的相关性模型,并利用参数估计的结果计算其相关性指标.结果表明,Elliptical Copula函数在金融相关性分析中比传统方法合理有效,其中学生氏t-copula函数在服从厚尾分布的相关性模型中比高斯Copula更具实际意义.

Dynamics and screening characteristics of a vibrating screen with variable elliptical trace

The ideal motion characteristics for the vibrating screen was presented according to the principle of screening process with constant bed thickness.A new vibrating screen with variable elliptical trace was proposed.An accurate mechanical model was constructed according to the required structural motion features.Applying multi-degree-of-freedom vibration theory,characteristics of the vibrating screen was analyzed.Kinematics parameters of the vibrating screen which motion traces were linear,circular or elliptical were obtained.The stable solutions of the dynamic equations gave the motions of the vibrating screen by means of computer simulations.Technological parameters,including amplitude,movement velocity and throwing index,of five specific points along the screen surface were gained by theoretical calculation.The results show that the traces of the new designed vibrating screen follow the ideal screening motion.The screening efficiency and processing capacity may thus be effectively improved.

Closing law and stress intensity factor of elliptical crack under compressive loading

The solution of surface displacement of an elliptical crack under compressive-shear loading was obtained by using the complex function method. The closing mode was established by analyzing the geometrical condition of closing crack, and the corresponding critical stress was solved. The result corrects the traditional viewpoint, in which there exist only open or close states for an elliptical crack, and points out that the local closing is also one of crack states. Based on them, the effect of the closed crack on stress intensity factor was discussed in detail, and its rational formulae are put forward.

Elliptical inclusion in an anisotropic plane:non-uniform interface effects

We study the plane deformation of an elastic composite system made up of an anisotropic elliptical inclusion and an anisotropic foreign matrix surrounding the inclusion.In order to capture the influence of interface energy on the local elastic field as the size of the inclusion approaches the nanoscale,we refer to the Gurtin-Murdoch model of interface elasticity to describe the inclusion-matrix interface as an imaginary and extremely stiff but zero-thickness layer of a finite stretching modulus.As opposed to isotropic cases in which the effects of interface elasticity are usually assumed to be uniform(described by a constant interface stretching modulus for the entire interface),the anisotropic case considered here necessitates non-uniform effects of interface elasticity(described by a non-constant interface stretching modulus),because the bulk surrounding the interface is anisotropic.To this end,we treat the interface stretching modulus of the anisotropic composite system as a variable on the interface curve depending on the specific tangential direction of the interface.We then devise a unified analytic procedure to determine the full stress field in the inclusion and matrix,which is applicable to the arbitrary orientation and aspect ratio of the inclusion,an arbitrarily variable interface modulus,and an arbitrary uniform external loading applied remotely.The non-uniform interface effects on the external loading-induced stress distribution near the interface are explored via a group of numerical examples.It is demonstrated that whether the nonuniformity of the interface effects has a significant effect on the stress field around the inclusion mainly depends on the direction of the external loading and the aspect ratio of the inclusion.

Second Law Analysis and Optimization of Elliptical Pin Fin Heat Sinks Using Firefly Algorithm

One of the most significant considerations in the design of a heat sink is thermal management due to increasing thermal flux and miniature in size.These heat sinks utilize plate or pin fins depending upon the required heat dissipation rate.They are designed to optimize overall performance.Elliptical pin fin heat sinks enhance heat transfer rates and reduce the pumping power.In this study,the Firefly Algorithm is implemented to optimize heat sinks with elliptical pin-fins.The pin-fins are arranged in an inline fashion.The nature-inspired metaheuristic algorithm performs powerfully and efficiently in solving numerical global optimization problems.Based on mass,energy,and entropy balance,three models are developed for thermal resistance,hydraulic resistance,and entropy generation rate in the heat sink.The major axis is used as the characteristic length,and the maximum velocity is used as the reference velocity.The entropy generation rate comprises the combined effect of thermal resistance and pressure drop.The total EGR is minimized by utilizing the firefly algorithm.The optimization model utilizes analytical/empirical correlations for the heat transfer coefficients and friction factors.It is shown that both thermal resistance and pressure drop can be simultaneously optimized using this algorithm.It is demonstrated that the performance of FFA is much better than PPA.

Elliptic Flow Splitting between Particles and their Antiparticles in Au＋Au Collisions from a Multiphase Transport Model

The elliptic flow v2, for π±, K±, p and p in Au＋Au collisions at center-of-mass energies √sNN=7.7, 11.5, 14.5 and 19.6 GeV, is analyzed using a multiphase transport model. A significant difference in the v2 values for p and p is observed, and the values of v2 splitting are larger compared with π＋ and π-, K＋ and K-. The difference increases with decreasing the center-of-mass energy. The effect of the quark coalescence mechanism in a multi-phase transport model to the value of elliptic difference △v2 between p and p- has been discussed. The simulation of Au＋Au collisions at 14.5 GeV shows that the effect of hadron cascade to △v2 is not obvious, and a larger patton-scattering cross section can lead to a larger △v2.

基于MDL Shape Model及EFD的行人轮廓2D＋time表示

针对智能监控的行人轮廓特征提取,先利用MDL shape model得到紧致但能充分表征轮廓几何特征标志点之间的对应关系,再利用椭圆傅里叶分解把行人轮廓表示为一系列不同频率下椭圆傅里叶系数组成的向量,最后得到行人2D+time轮廓的描述向量。实验结果表明,此方法不但可以在几何上直观地表示行人轮廓,而且大大降低了轮廓向量的维数。

MICROMECHANICAL DAMAGE MODEL FOR ROCKS AND CONCRETES SUBJECTED TO COUPLED TENSILE AND SHEAR STRESSES

Based on the analysis of the deformation in an infinite isotropic elastic matrix with an embedded elliptic crack under far field coupled tensile and shear stresses, the energy release rate and a mixed fracture criterion are obtained using an energy balance approach. The additional compliance tensor induced by a single opening elliptic microcrack in a representative volume element is derived, and the effect of microcracks with random orientations is analyzed with the Taylor＇s scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes is obtained and is verified with experimental results.

Mathematical model and numerical method for spontaneous potential log in heterogeneous formations

This paper introduces a new spontaneous potential log model for the case in which formation resistivity is not piecewise constant. The spontaneous potential satisfies an elliptic boundary value problem with jump conditions on the interfaces. It has beer/ shown that the elliptic interface problem has a unique weak solution. Furthermore, a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic problems. Numerical results show validity and effectiveness of the proposed method.

A FULLY ELLIPTIC CALCULATING PROCEDURE FOR THREE-DIMENSIONAL THERMAL POLLUTION

The use of the mathematical models so far for three-dimensional flow has some limitations because of their simplifications. Many characteristics of the flow field can not be predicted by these models. In this paper the three dimensional elliptic governing equations are solved by finite-volume methods; the buoyancy extensions of the widely tested k-?. model is adapted. The method is first applied to calculate the field of side discharge into open channel flow. The results are in good agreement with those of ref. [7]. Then it is further used to the intake discharge problem which is of a typical layout in cooling-water projects, and the calculated results, which predict in detail the charactreistics of flow field, are reasonable.

The Evolution of Elliptic Flow Under First Order Phase Transition

Elliptic flow for non-central Au＋Au collisions at √SNN=200 GeV is investigated with a 2＋1 dimensional hydrodynamic model. We analyze the softening effect by the velocity along the axis. The contribution of the elliptic flow from the QGP phase, mixed phase and hadron gas phase is studied. The relation between the sound horizon and evolution of the elliptic flow is discussed.

A micromechanical damage model for rocks and concretes under triaxial compression

Based on analysis of deformation in an infinite isotropic elastic matrix containing an embedded elliptic crack, subject to far field triaxial compressive stress, the energy release rate and a mixed fracture criterion are obtained by using an energy balance approach. The additional compliance tensor induced by a single closed elliptic microcrack in a representative volume element and its in-plane growth is derived. The additional compliance tensor induced by the kinked growth of the elliptic microcrack is also obtained. The effect of the microcracks, randomly distributed both in geometric characteristics and orientations, is analyzed with the Taylor＇s scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes under triaxial compression is obtained and experimentally verified.