Elliptical Cross Section Research Articles

Taphonomy and paleohistology of a dinosaur rib from Marília Formation, Bauru Group, in the state of Minas Gerais, Brazil

The Bauru Group (Campanian–Maastrichtian) has one of the richest fossil records of Cretaceous in South America. All dinosaur fossils from this unit were assigned to Saurischia, most of them poorly preserved. We present the histological and taphonomic analysis of a dinosaur dorsal rib fragment from the Marília Formation in the western state of Minas Gerais. Thin sections were prepared to describe the microstructures of the bone tissue and the fossilization processes involved in preserving the specimen. An elemental analysis was also performed to verify the chemical composition of the fossil and rock matrix. Haversian bone was identified in the rib cortex, and no growth marks or an external fundamental system were found. The rib probably belonged to a saurischian dinosaur because of its plank shape and elliptical cross-section. Hypotheses regarding taphonomic processes were inferred. An extended period of subaerial exposure, followed by high-energy transport, was interpreted due to extensive fractures and signs of abrasion on the outer surface of the bone. Pyrite pseudomorphs (framboids) indicate that the bone was deposited in a reductive environment. After burial, the rapid precipitation of calcite and alkaline stability allowed the preservation of apatite during the recrystallization phase. The manganese hydroxides were deposited on apatite crystals during early diagenesis. We concluded that the fossil rib presented a common taphonomic bias identified among vertebrate fossils of the Bauru Group, which is associated with the exposure of the bones to arid and semiarid climates, their transport into the depositional environments and pedogenetic influence during fossil diagenesis.

Rheology of Eyring–Powell hybrid nanofluid flow under the peristaltic effects through an elliptical conduit: Analytical investigation

In this study, we have considered the peristaltic flow of Eyring–Powell hybrid nanofluid flow across a conduit having an elliptical cross-section. The polystyrene and graphene oxide nanoparticles are considered. The mathematical model of the problem is solved analytically in the dimensionless form with the application of long wavelength approximation. The perturbation technique is adopted with polynomial solutions to solve it. The analytically acquired results are assessed and discussed comprehensively by graphical examination for various physical parameters. The disorder of the system is also studied by entropy production analysis. The pressure gradient is noted to reduce when the elliptical nature of the conduit’s cross-section reduces towards a circular shape. The percentage (volume fraction) of nanoparticles is found to have a strong impact on temperature distribution among all physical constraints.

Performance evaluation of cyclone separators with elliptical cross-section using large-eddy simulation

In the present study, cyclone separators with elliptical cross-sections have been studied numerically. Five cyclone models are considered here with the normalized (semi-) major axis (a) and minor axis (b) as: (a/D, b/D) = (0.51, 0.49), (0.52, 0.48), (0.53, 0.47), (0.54, 0.46), and (0.55, 0.45), referred to as the models A, B, C, D, and E, respectively. The standard model is of circular cross-section with a body diameter, D = 0.205 m, and is the reference model for performance comparison. It has been ensured that all the cyclones bear a similar hydraulic diameter, and hence, a nearly similar volume. Apart from the pressure drop and collection efficiency, we also evaluate the periodicity associated with the precessing vortex core around the cyclone axis by performing a fast Fourier transformation to the temporal velocity signal. Conclusive results indicate that both the pressure losses as well as collection efficiencies reduce with increasing the major axis (and reducing the minor axis) values. The mean velocity components undergo significant changes than the velocity fluctuations with stretching of the elliptical cross-section. The models with the largest major axis (or smaller minor axis) may be used as pre-separators to remove larger particles at the lowest pressure drop values.

An electric kickscooter multibody model: equations of motion and linear stability analysis

AbstractIn this work, a detailed multibody model of an electric kickscooter is presented. The model includes toroidal wheels as well as rear and front suspensions. The equations of motion are derived and linearized along the steady forward motion of the vehicle. Using an efficient linearization approach, suitable for complex multibody systems with holonomic and nonholonomic constraints, allows for obtaining the reduced linearized equations of motion as a function of the geometric, dynamic, wheels’, and suspensions’ parameters. The proposed electric kickscooter multibody model is validated with the stability results of a previously presented electric kickscooter benchmark. Since the resulting eigenvalues are parameterized regarding the design parameters, a detailed linear stability analysis of the system is performed. In particular, the influence on the stability of the toroidal geometry of the wheels, the elliptic cross-section of the toroidal wheels, the rider model, the steering axis inclination angle, the inertia tensor of the front frame, and the rear and front suspensions is analyzed. The model presented, together with the linearized equations of motion obtained in this work, enables a systematic analysis of the stability of these vehicles, which helps design new electric kickscooters with improved vehicle safety conditions and oriented to a wider range of potential users.

Entropy-based analysis of hemodynamics in elliptical arterial flows with non-Newtonian Rabinowitsch fluid

This research concerns examining the non-Newtonian blood flow behavior through an artery of elliptic cross-section, affected by several stenoses. The Rabinowitsch fluid model is used to investigate the non-Newtonian behavior of the blood for uniform and nonuniform shapes of stenosis. The mathematical equations have been converted into a dimensionless form, and their nonlinearity is reduced by applying the assumptions of mild stenosis. The resulting differential equations are solved by using analytical techniques. A new polynomial of degree eight is introduced to complete the solutions of mathematical equations. The entropy generation is studied mathematically to analyze the irreversibility effects. The detailed graphical examination delineates the physical aspects of mathematical results. The flow velocity is higher for uniform shape than for nonuniform stenosis. The rising percentage of stenosis significantly enhances the flow velocity of the stenotic region. The entropy is enormous near the stenotic wall and has small values near the centerline, which assures the smooth flow in this region. Further, the streamlines are plotted to find the position of stenosis and assess the flow nature for the growing height of stenosis and rising flow rate.

Non-Newtonian rheology of blood in elliptical cross-section artery affected by several stenosis: Prandtl fluid model

Non-Newtonian rheology of blood in elliptical cross-section artery affected by several stenosis: Prandtl fluid model

Synthetic β-sheets mimicking fibrillar and oligomeric structures for evaluation of spectral X-ray scattering technique for biomarker quantification.

Archetypical cross-β spines sharpen the boundary between functional and pathological proteins including β-amyloid, tau, α-synuclein and transthyretin are linked to many debilitating human neurodegenerative and non-neurodegenerative amyloidoses. An increased focus on development of pathogenic β-sheet specific fluid and imaging structural biomarkers and conformation-specific monoclonal antibodies in targeted therapies has been recently observed. Identification and quantification of pathogenic oligomers remain challenging for existing neuroimaging modalities. We propose two artificial β-sheets which can mimic the nanoscopic structural characteristics of pathogenic oligomers and fibrils for evaluating the performance of a label free, X-ray based biomarker detection and quantification technique. Highly similar structure with elliptical cross-section and parallel cross-β motif is observed among recombinant α-synuclein fibril, Aβ-42 fibril and artificial β-sheet fibrils. We then use these β-sheet models to assess the performance of spectral small angle X-ray scattering (sSAXS) technique for detecting β-sheet structures. sSAXS showed quantitatively accurate detection of antiparallel, cross-β artificial oligomers from a tissue mimicking environment and significant distinction between different oligomer packing densities such as diffuse and dense packings. The proposed synthetic β-sheet models mimicked the nanoscopic structural characteristics of β-sheets of fibrillar and oligomeric states of Aβ and α-synuclein based on the ATR-FTIR and SAXS data. The tunability of β-sheet proportions and shapes of structural motifs, and the low-cost of these β-sheet models can become useful test materials for evaluating β-sheet or amyloid specific biomarkers in a wide range of neurological diseases. By using the proposed synthetic β-sheet models, our study indicates that the sSAXS has potential to evaluate different stages of β-sheet-enriched structures including oligomers of pathogenic proteins.

The Width of Magnetic Ejecta Measured near 1 au: Lessons from STEREO-A Measurements in 2021–2022

Coronal mass ejections (CMEs) are large-scale eruptions with a typical radial size at 1 au of 0.21 au but their angular width in interplanetary space is still mostly unknown, especially for the magnetic ejecta (ME) part of the CME. We take advantage of STEREO-A angular separation of 20°–60° from the Sun–Earth line from 2020 October to 2022 August, and perform a two-part study to constrain the angular width of MEs in the ecliptic plane: (a) we study all CMEs that are observed remotely to propagate between the Sun–STEREO-A and the Sun–Earth lines and determine how many impact one or both spacecraft in situ, and (b) we investigate all in situ measurements at STEREO-A or at L1 of CMEs during the same time period to quantify how many are measured by the two spacecraft. A key finding is that out of 21 CMEs propagating within 30° of either spacecraft only four impacted both spacecraft and none provided clean magnetic cloud-like signatures at both spacecraft. Combining the two approaches, we conclude that the typical angular width of an ME at 1 au is ∼20°–30°, or 2–3 times less than often assumed and consistent with a 2:1 elliptical cross section of an ellipsoidal ME. We discuss the consequences of this finding for future multi-spacecraft mission designs and for the coherence of CMEs.

Analytical investigation of Carreau fluid flow through a non-circular conduit with wavy wall

Peristaltic flow through an elliptic channel has vital significance in different scientific and engineering applications. The peristaltic flow of Carreau fluid through a duct with an elliptical cross-section is investigated in this work . The proposed problem is defined mathematically in Cartesian coordinates by incorporating no-slip boundary conditions. The mathematical equations are solved in their dimensionless form under the approximation of long wavelength. The solution of the momentum equation is obtained by applying perturbation technique (We2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_e^2$$\\end{document} as perturbation parameter) along with a polynomial solution. We introduce a new polynomial of twenty degrees to solve the energy equation. The solutions of mathematical equations are investigated deeply through graphical analysis. It is noted that non-Newtonian effects are dominant along the minor axis. It is found that flow velocity is higher in the channels having a high elliptical cross-section. It is observed from the streamlines that the flow is smooth in the mid-region, but they transform into contours towards the peristaltic moving wall of the elliptic duct.

Experimental study on fragments dispersion characteristics of elliptical cross-section casing under explosive loading

To better understand the fragments dispersion characteristics of elliptical cross-section warhead (ECSW), static explosion experiments were conducted with four ECSWs and one circular cross-section warhead (CCSW). The warheads were designed with the same mass ratio of charge to the metal casing, and the difference in cross-section shape was indicated by the shape ratio. The experimental results indicated that ECSW fragments dispersion in their radial direction deviated from the normal direction of casing under explosive loading. The radial deviation angle decreased with the higher shape ratios. In the axial direction, the axial projection angle of fragment increased gradually from the major to the minor axis. Additionally, the fragment velocity and density in the minor axis direction increased noticeably compared to the major axis, and the difference reduced as the shape ratio increased. A formula for predicting the radial velocity distribution of the fragments was proposed, and the maximum relative error between the calculation and experiment results is less than 5 %. Finally, the driving mechanism of ECSW was preliminarily revealed. The findings serve as a fundamental basis for future research on ECSW and offer valuable insights for the development of innovative warhead designs.

Hierarchical buckling of elastic fiber under transverse confinement

Hierarchical buckling is a novel phenomenon observed in elastic fibers subjected to transverse confinement; however, the deformation mechanisms and modal transitions of this unique phenomenon remain to be elucidated. This paper investigates the hierarchical buckling of elastic fibers with elliptical (circular) cross-sections under transverse confinement through analytical derivations and numerical simulations. Various magnitudes of hierarchical buckling of fibers are observed with the variation of the controlled elastic matrix stiffness. An analytical solution is first derived for the fiber’s buckling phenomenon, and the hierarchical buckling is accomplished through the superposition of buckling at various modes. The theoretical results are validated against the finite element simulations with good agreement. It is demonstrated from the parametric results that the hierarchical buckling phenomenon is primarily influenced by the stiffness of the external transverse confinement (matrix), which is defined as a dimensionless parameter. It is thus illustrated from the computational results that the buckling of elastic fibers within a solid or fluid matrix can be controlled and customized. The present work provides theoretical guidance for the application of elastic fibers in stretchable conductor fibers and flexible electronic devices.

Effects of different cross-sections of Body Centered Cubic cells on pressure drop and heat transfer of additively manufactured heat sinks

In many industrial applications, heat loads management requires the design and production of compact heat exchangers which are expected to handle high thermal loads with acceptable pressure losses, while assuring good mechanical performances. These challenging targets can be achieved by filling the cavities where the cool/hot fluid circulates with lattice structures promoting the heat exchange between the fluid and the cavity boundaries. Such lattice structures can be only produced through Additive Manufacturing due to their high geometric complexity. Recent experimental investigations proved the effectiveness of some kinds of lattice structures having a circular cross section. Here the aerothermal behaviour of Body-Centred Cubic (BCC) lattice stagger arrays in a rectangular channel was experimentally investigated by considerably extending the previous studies to higher Reynolds numbers (up to 30′000) and to new types of lattice structures. Specifically, three new BCC structures having a cam-like, drop-like and elliptical cross section were explored in this work and compared against those having circular cross section. All the samples were manufactured by means of Laser Powder Bed Fusion and made from AlSi10Mg. At first, the heat exchangers were comprehensively characterized by means of optical non-destructive methods. Successively they were tested in a dedicated rig by imposing constant heat flux boundary conditions. The characteristics of the transitional or fully turbulent approaching flow to the test section are also reported thanks to dedicated flow field measurements performed by Particle Image Velocimetry. According to the obtained results, the BCC structure with the circular cross section of larger diameter is the most effective in terms of heat transfer, although it is largely penalized by the pressure losses. Similar heat transfer performances were achieved by the tapered cross section of elliptical shape with the advantage of a considerably lower friction factor. Pressure losses resulted almost identical for all the tapered cross sections but lower than those of the circular one having an equal frontal dimension. When considering the thermal performance factor the circular shape becomes unfavourable for Re>20′000, while the elliptical cross section is the best choice to efficiently promote heat transfer up to Re=30′000.

Numerical simulation of convective heat transfer behavior of nanofluids in elliptical microchannels

This study employs a numerical simulation approach to investigate the heat transfer performance of elliptical microchannel heat sinks (MCHS) with varying aspect ratios (AR) of the elliptical cross-section. The convective heat transfer behavior of water and water-based nanofluids containing CuO nanoparticles at different volume fractions within the MCHSs is examined. The research results indicate that at Re = 600, as the AR of the elliptical cross-section increases from 1:1 to 1.75:1, the thermal performance of the MCHS improves by 5.33%. Furthermore, with an increase in the volume fraction of nanofluid from 0 to 0.75%, the convective heat transfer coefficient of the nanofluid increases by 11.87%. Compared to the circle MCHS using water as the coolant, the MCHS with an elliptical cross-section with an AR of 1.75:1 and a nanofluid volume fraction of 0.75% can reduce the maximum temperature of the chip by 9.78%.

Analytical and experimental study on elliptical cross-section double-ogive-nose projectile penetration into plain concrete target

Analytical and experimental study on elliptical cross-section double-ogive-nose projectile penetration into plain concrete target

Analytical subthreshold swing model of junctionless elliptic gate-all-around (GAA) FET

<abstract> <p>An analytical subthreshold swing (SS) model has been presented to determine the SS of an elliptic junctionless gate-all-around field-effect transistor (GAA FET). The analysis of a GAA FET with an elliptic cross-section is essential because it is difficult to manufacture a GAA FET with an accurate circular cross-section during the process. The SS values obtained using the proposed SS model were compared with 2D simulation values and other papers to confirm good agreement. Using this analytical SS model, SS was analyzed according to the eccentricity of the elliptic cross-section structure. As a result, it was found that the carrier control ability within the channel improved as the eccentricity increased due to a decrease in the effective channel radius by a decrease in the minor axis length and a decrease in the minimum potential distribution within the channel, and thus the SS decreased. There was no significant change in SS until the eccentricity increased to 0.75 corresponding to the aspect ratio (AR), the ratio of the minor and major axis lengths, of 1.5. However, SS significantly decreased when the eccentricity increased to 0.87 corresponding to AR = 2. As a result of the SS analysis for changes in the device parameters of the GAA FET, changes in the channel length, radius, and oxide film thickness significantly affected the changing rate of SS with eccentricity.</p> </abstract>

Opticheskiy analog vrashchayushchegosya binarnogo boze-kondensata

Coupled nonlinear Schrödinger equations for paraxial optics with two circular polarizations of light in a defocusing Kerr medium with anomalous dispersion coincide in form with the Gross–Pitaevskii equations for a binary Bose—Einstein condensate (BEC) of cold atoms in the phase separation regime. In this case, the helical symmetry of an optical waveguide corresponds to rotation of the transverse potential confining the BEC. The “centrifugal force” considerably affects the propagation of a light wave in such a system. Numerical experiments for a waveguide with an elliptical cross section have revealed characteristic structures consisting of quantized vortices and domain walls between two polarizations, which have not been observed earlier in optics.

Analysis of the stress state at the contours of underground horizontal workings of elliptical cross-section shape subjected to all-round uniform pressure

The results of the research to determine the stress state on the contours of underground horizontal excavations, the cross-section of which has the form of an ellipse of any size and shape are presented. When changing the intensity of tensile uniform pressure applied to the points of elliptical shape cross-section excavation contours, the given values of excavation depths, ellipse parameters and rock side spreading coefficient values, the areas of the contours with tensile and compressive stresses are identified. If the depths of workings of the considered form of cross-section change, the areas where tensile and compressive stresses act at given values of the intensity of tensile uniform pressure applied to the points of working's contours, ellipse parameters and values of the coefficient of rock lateral spreading are highlighted. The graphical images of the normal tangential stresses, acting on the contours of the considered workings are given. The ranges of intensity of the tensile uniform pressure, at which, depending on the depth of excavation, values of ellipse parameters and the coefficient of rock lateral spread, tensile and (or) compressive stresses act in the points of excavation contours have been determined. The given relations and results can be applied to calculate the values of the permissible values of all-round uniform pressure in the points of the workings contours and to determine the permissible depths of their embedding. As a criterion for determining the values of these values, the condition of absente on the contours of excavations of points in which the normal tangential stresses exceed the limits of tensile and compression strength of the rock can be accepted.

Functional biomimetic design of 3D printed polyether-ether-ketone flexible chest wall reconstruction implants for restoration of the respiration

The lack of deformability of rigid chest wall reconstruction (CWR) implants presents a challenge in reducing postoperative respiratory function in patients with large chest wall defects. Flexible poly-ether-ether-ketone (PEEK) CWR implants, consisting of rib components with elliptical cross-section and costal cartilage components featuring wavy structures, were developed with adjustable design parameters that allow quantitative restoration of respiratory function. During the design process, the equivalent elastic moduli of the rib and costal cartilage components were parametrically adjusted in a validated finite element (FE) model of the chest wall to maximise chest wall deformation during respiration, while considering mechanical safety as the boundary condition. The optimal equivalent elastic moduli were then translated into design parameters for the rib and costal cartilage components, based on a database relating the equivalent elastic modulus to the design parameters of the components with elliptical cross-section and wavy structures. The flexible PEEK CWR implant increased the difference in chest circumference during respiration by 12.2% compared to rigid PEEK implant in a clinical case-based study. This study presents a strategy to address the reduced respiratory function in 3D printed CWR implants, providing a pathway for quantitative restoration of respiratory function through parameterised optimisation.

First report of Sphenothallus Hall, 1847 from the lower Cambrian of North China

Sphenothallus is a tubular organism that is one of the most widely distributed and longest-ranging genera through the Palaeozoic. Despite its apparent cosmopolitan distribution, the genus has never been reported from North China. New specimens of Sphenothallus sp. have been discovered in the upper part of the Houjiashan and base of the Mantou formations (early to middle Age 4, Epoch 2, Cambrian) in Jiangsu Province, North China. The specimens are small tubes (up to 5 mm long) and have typical Sphenothallus characteristics, such as a multilayered lamellar structure, and subcircular to elliptical transverse cross-section with a pair of longitudinal thickenings situated at the widest diameter. Our material shows that both the rate of apertural expansion and the curvature of the tubes are significantly larger in early growth stages than in the later growth stages. As the diameter of the aperture increases, the transverse cross-section of the Sphenothallus sp. tube changes from subcircular at the proximal end to elliptical or lenticular at the distal end, and its wall thickness changes from uniform to thickening longitudinally. The discovery of Sphenothallus sp. from the North China Platform represents an extension of its palaeogeographic range during the Cambrian. Rao Fu [furao@stumail.nwu.edu.cn], State Key Laboratory of Continental Dynamics, Shaanxi Key Laboratory of Early Life and Environments and Department of Geology, Northwest University, Xi’an 710069, China; Yazhou Hu [eliyazhou@nwu.edu.cn], State Key Laboratory of Continental Dynamics, Shaanxi Key Laboratory of Early Life and Environments and Department of Geology, Northwest University, Xi’an 710069, China; Timothy P. Topper* [timothy.topper@nwu.edu.cn], State Key Laboratory of Continental Dynamics, Shaanxi Key Laboratory of Early Life and Environments and Department of Geology, Northwest University, Xi’an 710069, China; Fan Liu [liufan0122@hotmail.com], State Key Laboratory of Continental Dynamics, Shaanxi Key Laboratory of Early Life and Environments and Department of Geology, Northwest University, Xi’an 710069, China; Yue liang [yueliang_nwu@outlook.com], State Key Laboratory of Continental Dynamics, Shaanxi Key Laboratory of Early Life and Environments and Department of Geology, Northwest University, Xi’an 710069, China; Zhifei Zhang corresponding author [elizf@nwu.edu.cn], State Key Laboratory of Continental Dynamics, Shaanxi Key Laboratory of Early Life and Environments and Department of Geology, Northwest University, Xi’an 710069, China. *Also affiliated with Department of Palaeobiology, Swedish Museum of Natural History, Box 50007, Stockholm 10405, Sweden.

On nonmodal stability of elliptic pipe flow

The temporal nonmodal stability of the Poiseuille flow in a pipe of axially uniform elliptic cross section is numerically studied. In particular, it is shown that the maximum amplification of kinetic energy of disturbances depends significantly on the pipe aspect ratio, and this dependence is non-monotonic. It agrees with the corresponding dependence of the energy critical Reynolds number, which is the lower limit of the Reynolds numbers enabling the growth of disturbance kinetic energy. In other words, changing the aspect ratio similarly affects both nonmodal and monotonic stability of the flow. The optimal disturbances displaying the maximum amplification are streamwise counter-rotating vortices. These disturbances are streamwise uniform at sufficiently large Reynolds numbers and may become streamwise harmonic as the Reynolds number decreases. In addition, their symmetry with respect to the cross section axes varies with the aspect ratio. Thus, the obtained results suggest that changing the aspect ratio may be a perspective tool for the passive control of the subcritical laminar-turbulent transition in pipe flows. In other words, this factor is worth considering when designing various devices (e.g., heat exchangers or ventilation systems) containing pipes to enhance their efficiency.