Degree Of Ellipticity Research Articles

Stability of highly inclined non-circular wellbores in isotropic formations

The shear and tensile stabilities of highly inclined non-circular wellbores are investigated in this study. Using the equivalent-ellipse hypothesis, the non-circular geometry was approximated as an ellipse, and the corresponding stress concentration equations are presented. With the new set of stress concentration equations, a comprehensive study of the tensile and shear stabilities of an elliptical borehole was conducted, including the impact of well inclination and azimuthal angles, horizontal stress difference, degree of ellipticity, and orientation of the maximum horizontal stress to the major axis of the ellipse. Using five commonly used shear failure criteria, we observed that both Mohr–Coulomb and Drucker Prager (inscribed) failure criteria predicted higher collapse pressures, relative to the others including Drucker Prager (inscribed), Mogi-Coulomb, and Modified Lade. While Drucker Prager's (circumscribed) failure criterion underestimates the collapse pressure. Both the linear elastic and poroelastic models were used in investigating the fracture initiation orientation and pressure of highly inclined elliptical boreholes. The prediction from the poroelastic model is always less than the linear elastic model. In some instances, they predict different fracture initiation orientations. From this study, we observed that generally, a near-circular wellbore is more stable than elliptical borehole in both shear and tension. Nevertheless, there are some well inclination and azimuthal angles than can make an elliptical borehole have more shear and tensile stabilities than a near-circular wellbore.

Characterization of Surfactant Spheroidal Micelle Structure for Pharmaceutical Applications: A Novel Analytical Framework.

We introduce an innovative theoretical framework tailored for the analysis of Pair Distribution Function (PDF) data derived from Small-Angle X-ray Scattering (SAXS) measurements of core-shell micelles. The new approach involves the exploitation of the first derivative of the PDF and the derivation of analytical equations to solve the core-shell micelle structure under the hypothesis of a spheroidal shape. These analytical equations enable us to determine the micelle's aggregation number, degree of ellipticity, and contrast in electron density between the core-shell and shell-buffer regions after having determined the whole micelle size and its shell size from the analysis of the first derivative of the PDF. We have formulated an overdetermined system of analytical equations based on the unknowns that characterize the micelle structure. This allows us to establish a Figure of Merit, which is utilized to identify the most reliable solution within the system of equations.

Математическая модель для проектирования линейных асинхронных электродвигателей и ее программная реализация

Mathematical models are the main tool for the layout design of linear asynchronous electric motors. Existing design models of linear asynchronous electric motors assume that the device is powered from a source of multiphase symmetrical positive sequence current, which excludes from consideration the asymmetry of the inductor phase currents and the associated reduction in traction force. This approach is not flexible enough, since the operation of linear asynchronous electric motors in a wide range of movement speeds assumes a functional relationship between the current asymmetry coefficient and the movement speed. The study developed a mathematical model for design purposes that implements the functional relationship between the current asymmetry coefficient and the speed of movement. The mathematical model represents 13 linear equations linking geometric dimensions, current loads, electromagnetic field characteristics and mechanical forces with the speed of the secondary element of the electric motor. The current load of an electric motor has a variable degree of ellipticity depending on the speed of movement. An algorithmic study of the mathematical model was carried out and corresponding software modeling tools were developed. The proposed program algorithm, containing two subroutines, is implemented using the Maple symbolic computing software package. In order to expand the range of users, the software model is additionally implemented in C++. In this case, the functional dependence of the asymmetry coefficient of the exciting current wave on the speed of movement is implemented in the form of an iterative procedure for the case of connecting the winding of the linear asynchronous electric motors inductor to a source of symmetrical three-phase voltage according to the “triangle” circuit. Using the example of a three-phase linear asynchronous electric motors, the electromagnetic and mechanical characteristics of the electric motor were simulated. It was stated that the influence of current asymmetry on the mechanical characteristics of the linear asynchronous electric motors is small and is expressed in the region of high speeds. This makes it possible, in design tasks for the layout of an electric motor, to use models that involve powering the linear asynchronous electric motors from a symmetrical current source or to introduce a fixed asymmetry coefficient into them.

Modular Optical Diodes for Circular Polarization Based on Glass‐Supported Cellulose Nanocrystal/Polyethylene Glycol Composite Films

Depending on processing methods and conditions, cellulose nanocrystal (CNC) films exhibit linear birefringence or selective Bragg reflection. The latter means reflection of light with left‐handed circular polarization (LCP) due to CNC in a helicoidal microstructure of the same handedness. Herein, glass‐supported CNC/polyethylene glycol (CNC/PEG) composite films with PEG concentrations in the range of 0–30% w/w with selective Bragg reflection at wavelengths from 440 to 550 nm are prepared. A modular device comprised of a dip‐coated birefringent CNC‐glass sample sandwiched between two CNC/PEG‐glass samples shows different responses to light with LCP and to light with right‐handed circular polarization (RCP). The device suppresses selective Bragg reflection from the rear (front) CNC/PEG sample for incident light with LCP (RCP), even when the birefringent film does not meet the condition for a halfwave plate. This behavior resembles the performance of optical diodes for circular polarization. Polarization properties of composite films and optical diodes in terms of degree of polarization and ellipticity are discussed within the Stokes–Mueller formalism. Electromagnetic simulations of Mueller matrices reveal the equivalence of modular and in‐tandem film approaches of optical diodes.

Scattering of radially polarized partially coherent vortex beams from a random medium with semi-hard boundary

In this paper, scattering medium with a semi-hard boundary is extended to the case of a quasi-homogeneous random medium for the first time. Applying the first-order Born approximation, far-field distribution of radially polarized partially coherent vortex beams scattered upon the random medium with semi-hard boundary is studied. Spectral density distribution, degree of spectral polarization, polarization angle, and degree of ellipticity of the scattering field in the far zone are investigated. Influence of characteristics of the incident beam and scattering medium on the far-zone scattering field are discussed. In addition, phase singularity of the scattering field’s center is also described. It is interesting to find that the far-field scattering field is circularly polarized with a Gaussian distribution, though the incident field is radially polarized with a dark-hollow distribution. The center of the scattering field is completely polarized, while on the edge of the scattering field, degree of polarization shows obvious fluctuations with the change of parameters of the incident beam and medium. Results obtained here could find application in the acquisition of medium structure information.

Redshift evolution of the dark matter haloes shapes

ABSTRACT In this work, we aim at investigating the morphology evolution of Milky Way mass-like dark matter haloes selected from the cielo and IllustrisTNG projects. The connection between halo shapes and their environment has been studied in previous works at z = 0 but their connection remains yet to be fully understood. We focus on the evolution across cosmic time of the halo shapes and the relation with the infalling material, using hydrodynamical simulations. Our findings show that haloes tend to be more triaxial at earlier times as a consequence of stronger accretion in the direction of the filaments. As the haloes evolve towards a dominant isotropic accretion mode and relaxation, their shape at 20 per cent of the virial radius becomes more spherical. In agreement with previous results, baryons have an important effect within the inner regions of the haloes, driving them from triaxial to rounder shapes. We also find a correlation between the strength of the quadrupole infalling mode and the degree of ellipticity of the haloes: as the filament strength decreases steadily with redshift, the haloes became more spherical and less elliptical.

In-silico study of asymmetric remodeling of tumors in response to external biochemical stimuli

Among different hallmarks of cancer, understanding biomechanics of tumor growth and remodeling benefits the most from the theoretical framework of continuum mechanics. Tumor remodeling initiates when cancer cells seek new homeostasis in response to the microenvironmental stimuli. Cells within a growing tumor are capable to remodel their inter- and intra-connections and become more mobile to achieve a new homeostasis. This mobility enables the tumor to undergo large deformation. In this work, we studied the remodeling of homogeneous tumors, at their early stage of growth, in the context of continuum mechanics. We developed an evolution law for the remodeling-associated deformation which correlates the remodeling to a characteristic tensor of external stimuli. The asymmetric remodeling and the induced mechanical stresses were analyzed for different types of biochemical distributions. To experimentally investigate the model, we studied the remodeling of human glioblastoma (hGB) tumoroids in response to the gradient of nutrients. Using a tumoroid-on-a-chip platform, the degree of remodeling was estimated for the ellipsoidal tumoroids over time. It was observed that higher gradient of nutrients induces higher degree of ellipticity suggesting that the gradient of nutrient is a characteristic property of nutrient distribution that derives the remodeling. We also showed that remodeling gives rise to heterogeneity in cell distribution forming circumferentially aligned cells within the tumors. Compared to the existing studies on tumor growth, our work provides a biomechanical module that relates the remodeling to biochemical stimuli, and allows for large deformation. It also includes experimental component, a necessary but challenging step, that connects the theory and reality to evaluate the practicability of the model.

Возбуждение электромагнитных волн круговой поляризации полосковыми линиями передачи

The article investigates the scheme of excitation of an electromagnetic field with circular polarization due to crossed strip transmission lines. Two variants are compared: coplanar and microstrip transmission lines that excite circular polarization of the magnetic field in the space above the intersection of strip structures. The degree of ellipticity of the field at the intersection of strip structures can be changed by changing the phase mismatch between exciting oscillation sources. Modeling of these devices in the computer-aided design system made it possible to quantify the amplitudes of the components of the electromagnetic field, from which the ellipticity coefficient was calculated at different values of frequency and phase. The obtained results allow us to determine the conditions necessary for the realization of circular polarization of the magnetic field. The studied structures are planned to be used in an integral design to excite circular polarization oscillations in magnetic micro- and nanostructures.

Impurity photo-ionization cross section and stark shift of ground and two low-lying excited electron-states in a core/shell ellipsoidal quantum dot

A new investigation on photo-ionization cross section (PICS) of a donor impurity confined in a GaAs/AlGaAs core/shell elliptic quantum dots (CSEQDs) has been performed under electric field (EF) effect. By means of the finite element method (FEM), we have computed the binding energy (BE), oscillator strength Pif and PICS within the framework of the effective mass theory (EMT). Our numerical results reveal that the stark shift is greatly dependent on the strength of the EF, the degree of ellipticity β, and the states of electronic transitions. It can take positive or negative values depending on the situation. In addition, the photo-ionization describing the transition from the donor impurity ground-state (1simp) to one of the conduction sub-band states (1s0, 2s0, and 2p0) is affected by the shape of the quantum dots (QDs) and the EF. We demonstrated that varying internal and external parameters may control the photo-ionization cross-section. These characteristics can be exploited to fabricate optoelectronic devices like QD infrared photodetectors.

Sharp boundary and global regularity for degenerate fully nonlinear elliptic equations

We obtain optimal boundary and global regularity estimates for viscosity solutions of fully nonlinear elliptic equations whose ellipticity degenerates at the critical points of a given solution. We show that any solution is C1,α on the boundary of the domain, for an optimal and explicit α given only in terms of the regularity of the boundary datum and the elliptic degeneracy degree, and independent of the elliptic operator. We also obtain sharp global estimates. We use a different method from all previous results of global nature, which give C1,α regularity only for some small α>0. Our findings are new even for the model equations, involving a degenerate Laplacian.

Polarization and frequency-controlled amplification in a nonequilibrium plasma in the presence of an external magnetic field

The method of controlling the spectral and polarization characteristics of a terahertz (THz) pulse during its amplification in nonequilibrium magnetized plasma is investigated. The physical mechanism involves the well-known cyclotron resonance, which has been demonstrated to strongly influence the features of nonequilibrium plasma — in particular, its amplifying and focusing ability. According to the suggested model, a static magnetic field is applied along the propagation direction of a femtosecond UV laser, which creates a nonequilibrium plasma channel. The seed linearly polarized THz pulse propagates in the channel after the ionizing UV pulse. The conducted numerical simulations are based on the self-consistent solution of the kinetic Boltzmann equation and second-order wave equation for THz pulse propagation. It is shown that by varying the magnetic field strength one can control the pulse carrier frequency as well as change the polarization to a circular one. For long THz pulses, the presence of a magnetic field provides the possibility to detune the ellipticity degree at the output of the plasma channel.

Synthesis of large and stable colloidal gold nanoparticles (AuNPs) by seeding-growth method

Colloidal gold nanoparticles (AuNPs) have been used in various applications, mainly in biomedical sciences for therapeutic and diagnostic purposes. These AuNPs can be conjugated with biomolecules and chemical substances due to their unique physical and chemical properties. The AuNPs are usually synthesized by a chemical method; namely Turkevich method or reduction method. However, this synthesis method is not suitable for synthesis of large AuNPs due to aggregation and instability of AuNPs suspension. Thus, the aim for this study is to evaluate the seeding-growth method for synthesis of large AuNPs. The seed of 15 nm AuNPs was initially produced using the citrate reduction method, then further grown to 40, 60, and 80 nm AuNPs using the mild reduction agent, hydroxylamine. Transmission electron microscopy (TEM), dynamic light scattering (DLS), and UV–vis- NIR spectroscopy were used to characterize the as-synthesized AuNPs. The narrow particle size distribution and low polydispersity index value (PDI) for all AuNPs revealed the presence of monodisperse AuNPs. The as-synthesized AuNPs are nearly spherical as shown by the degree of ellipticity (G) close to 1.00. This result showed no agglomeration of AuNPs in the colloidal suspension. The UV–vis-NIR spectra showed peaks shifted to a longer wavelength that confirmed increasing size of AuNPs. The synthesis of different sizes of AuNPs using the seeding-growth method was successful and stable with no aggregation and agglomeration.

Concise and efficient direct-view generation of arbitrary cylindrical vector beams by a vortex half-wave plate

A concise, efficient, and practical direct-view scheme is presented to generate arbitrary cylindrical vector (CV) beams, including CV beams, vortex beams, and cylindrical vector vortex (CVV) beams, by a vortex half-wave plate (VHP). Six kinds of first-order and other high-order CV beams, such as azimuthally polarized (AP) beams, antivortex radial polarization mode beams, and three-order AP beams, are formed by simply rotating a half-wave plate. The Stokes parameters and double-slit interference of multitype CV beams are investigated in detail. The polarization parameters, including degree of polarization, polarization azimuth, and ellipticity, are obtained, which demonstrates the efficient generation of CV beams. In addition, the double-slit interference experiment is introduced in the setup, and fringe misplacement and tilt appear for CVV beams, in which the misplacement number M is 2 P + 1 for P ≤ 2 and 2 P − 1 for P ≥ 3 , where P is the polarization order number, and the fringe tilt offset is positively related to the topological charge number l of CVV beams. In addition, new types of VHPs can be formed by cascading two or more VHPs when the types of available VHPs are limited, assisting in more flexible generation of multitype CV beams. It is experimentally demonstrated that arbitrary CV beams with high quality are effectively achieved by the proposed setup, and the double-slit interference method can be utilized to determine and analyze CV beams rapidly and concisely by practical performance, which shows the potential to be implemented as a commercial device.

Mechanical behavior of sealed waterproof for shield tunnel segment joint under different assembling ellipticity.

During the construction and assembling stages of shield tunnels, the ellipticity of segment assembly, and the angle between segments are the main reasons for joint leakage of shield tunnel. In this paper, taking Chengdu Metro shield tunnel as the research background, the relationship between assembling ellipticity and segment opening angle is obtained by geometric calculation, and the waterproof effect of gasket under different segment joint angle is studied by finite element analysis method. Results of the nonlinear numerical analyses, there is a linear positive relationship between the opening angle of segments and the ellipticity degree. Meanwhile, the different side joint opening angles of the segments have different effects on the waterproof effect of the gasket, which is manifested as the external angle is greater than the internal. Based on the above research results, this article can provide some references for the design, production, processing, and quality inspection of shield tunnel gasket in the future.

Influence of Transverse Cross‐Phases on Propagations of Optical Beams in Linear and Nonlinear Regimes

AbstractIt is predicted that an orbital angular momentum (OAM) carried by an elliptic Gaussian beam (EGB) with a cross‐phase can induce an effective anisotropic diffraction (AD). At the so‐called critical OAM, such an OAM‐induced AD makes the spiraling elliptic Gaussian mode, which expands owing to the diffraction while keeping its elliptic degree changeless, exist in linearly isotropic media, where only the circular Gaussian mode is supposed to exist for a beam without an OAM. In this study, such a phenomenon is experimentally demonstrated via the propagations of the EGBs with the OAM in linearly and both‐linearly‐and‐nonlinearly isotropic media. In the former case, the spiraling elliptic Gaussian mode is observed at the critical OAM in the free space. In the latter case, the spiraling elliptic soliton predicted by Desyatnikov et al. is observed for the first time in cylindrical lead glass. The physics behind the spiraling elliptic soliton is the OAM‐induced AD, which preserves the elliptic degree of the EGB, whereas the nonlinearity only balances the diffraction of the EGB. The OAM‐induced AD is just a linear effect and has nothing to do with nonlinearity.

Nanosize CaCu3Ti4O12 Green Synthesis and Characterization of a Precursor Oxalate Obtained from Averrhoa carambola Fruit Juice and Its Thermal Decomposition to the Perovskite

Improving on the very high temperatures used in solid-state synthesis routes to prepare CCTO ignited the idea of using oxalate routes which make use of organic solvents in the synthesis of CCTOX as oxalate intermediates to the decomposition product, CCTO. The use of commercial oxalic acids and oxalate has not only recorded a solubility problem which reflects on the size, shape, homogeneity, and morphology of the final product but also has an environmental impact originating from the solvents used. Both the composition and morphology of these inhomogeneities play a role in the behaviour of the final product, pointing out the need to assess the dependence of size, shape, homogeneity, and morphology and the material performance on the sample synthesis history. In this study, nanosized particles of calcium copper titanium oxide, CaCu3Ti4O12 (CCTO), were successfully synthesized by pyrolysis of the corresponding heterometal oxalate precursors obtained via coprecipitation using the edible carambola fruit juice as a precipitating agent and investigated in detail. The precursors were characterized, and the results revealed the formation of a single molecular precursor represented by the formula CaCu3(TiO)4(C2O4)8·9H2O (CCTOX). The decomposition products, obtained via calcination in air, were subsequently subjected to thermal treatments at different temperatures for 4 hours. The morphology and microstructure were characterized, and analysis showed the formation of a single phase, CaCu3Ti4O12 (CCTO) with CuO and CaTiO3 as impurity. It was observed from microscopy that the samples obtained from sintering at 600°C for four hours had discrete particles with regular morphology, limited size distribution, high degree of homogeneity, and multiple dimensions ranging between 10 and 35 nm and showed some degree of ellipticity in shape. Increasing the sintering temperature from 600°C to 700°C and 800°C increased the grain growth in the ceramic as well as the densification. The method makes advantage of the fact that oxalate precursors decomposed at relatively lower temperatures and the fact that the oxalate in the juice is in the solution which downplays both the solubility and environmental pollution problems since no additional solvents are used.

Three-dimensional structure of polarization singularities of a light field near a dielectric spherical nanoparticle.

We numerically study the structure of polarization singularity lines in a near-field of the sub-wavelength dielectric particle when it is irradiated by a monochromatic elliptically polarized plane wave. For the various values of the ellipticity degree of the incident radiation, we trace the CT and LT-lines on which the polarization ellipse turns into a circle or a line, respectively. The continuous variation of the isotropy parameters of the singularities is visualized along the lines. The main rules of CT and LT-lines deformation, emergence, and vanishing are revealed.

Crop characterization using an improved scattering power decomposition technique for compact polarimetric SAR data

Crop characterization using Compact-Pol Synthetic Aperture Radar (CP-SAR) data is of prime interest with the rapid advancements of SAR systems towards operational applications. It is noteworthy that as a good compromise between the dual and quad-polarized SAR systems, the CP-SAR offer advantages in terms of the larger swath and lower data rate. The m − χ CP decomposition considers two out of the three Stokes child parameters: degree of polarization (m), ellipticity (χ), and orientation angle (ψ) to describe the polarized part of the quasi-monochromatic partially polarized wave. An improvement in the scattering powers was proposed in the S − Ω decomposition, which takes into accounts both the transmitted and received wave ellipticities (χt, χr) and the orientation angles (ψt, ψr). In this decomposition, S denotes the Stokes vector and Ω is the polarized power fraction. However, it may be noted that the S − Ω decomposition intrinsically ignores dominance in the target scattering mechanism while calculating the powers. In this work, improvement is proposed for the S − Ω decomposition by utilizing the degree of dominance in the scattering mechanism. The improved S − Ω (named as iS − Ω) decomposition powers are first compared with the existing m − χ and S − Ω powers for elementary (viz., trihedral and dihedral corner reflectors) and distributed targets using simulated CP-SAR data from quad-pol RADARSAT-2 data. An increase of ∼2% for odd and even-bounce powers obtained from the iS − Ω decomposition is observed for the trihedral and dihedral corner reflectors respectively. The analysis of the scattering powers for distributed targets shows that an increase of 15% and 12% in the even and odd-bounce powers is observed from iS − Ω for urban and bare soil areas respectively as compared to the m − χ and S − Ω decompositions. Besides, temporal variations in the scattering powers obtained from the iS − Ω decomposition are also analyzed for rice, cotton, and sugarcane crops at different growth stages.

Polarization characteristics of radially polarized partially coherent vortex beam in anisotropic plasma turbulence

ABSTRACT This paper introduces the propagation properties and polarization characteristics of radially polarized partially coherent vortex beams in anisotropic plasma turbulence and discusses in detail the distribution of light intensity in such beams as a function of propagation distance. In addition, we analyze how the parameters of the anisotropic plasma turbulence affect the degree of polarization, polarization orientation angle, and degree of ellipticity of the beam. The results show that the degree of polarization of the radially polarized partially coherent vortex beam satisfies the modification of the central origin zero and the gradual increase with the radius during plasma turbulent propagation. At the same time, smaller turbulence eddies in the anisotropic plasma turbulence render, more obvious the irregular structure perpendicular to the vortex-stretching direction, the smaller the influence on the polarization characteristics of the radially polarized partially coherent vortex beam. It is advantageous to the research on optical communication and the study of anisotropic plasma turbulence.

Turbulence-induced changes in the state of polarization of partially polarized, partially coherent pulsed electromagnetic beams propagating through anisotropic turbulence

The changes in the state of polarization of partially polarized, partially coherent pulsed electromagnetic beams propagating along a horizontal path through anisotropic turbulence are investigated. Unpolarized and partially polarized, partially coherent pulsed electromagnetic Gaussian Schell-model beams are compared in terms of the turbulence-induced changes in the spectral degree of polarization. Our analysis is focused on models pertaining to electromagnetic Gaussian Schell-model pulsed beams but can either be readily reduced to scalar or be readily generalized to other beam classes. Within the framework of the anisotropic generalized exponential spectrum, considering simultaneously the finite inner and outer scales of turbulence and the asymmetric property of turbulence eddies in the orthogonal x y -plane throughout the propagation path, we derive analytical expressions for the cross-spectral density matrix, spectral degree of polarization, orientation angle, and degree of ellipticity. Finally, we study the effects of the anisotropic turbulence parameter on the spectral degree of polarization, orientation angle, and degree of ellipticity of the beams. Our results can be useful for applications involving partially polarized, partially coherent pulsed beams propagating through atmospheric turbulence.