Oblate Spheroid Research Articles

Various nanoparticle shapes and quadratic velocity impacts on entropy generation and MHD flow over a stretching sheet with joule heating

The purpose of this research was to examine the impact of NP shape on the entropy production of a water-alumina nanofluid over a permeable MHD stretching sheet at quadratic velocities with viscous dissipation and joule heating. The hot fluid is water-alumina nanofluid, which consists of four different NP shapes (brick, platelet, blade, and oblate spheroid), and the cool fluid is water itself. As a result of its exceptional ability to enhance heat transmission, Al2O3-H2O nanofluid is used extensively in industrial production. The governing PDEs are changed into a nonlinear differential system of coupled ODEs by a series of similarity transformations. The code, in MATLAB, is an effective version of the Runge-Kutta technique for obtaining numerical solutions. In the region behind a stretching sheet, the wall shear stress increases by almost 6.3% for increases in the volume fraction of nanoparticles from 0% to 2% and by 12.6% for increases from 0% to 4%. When the magnetic effect accounts for roughly 5 percent of the boundary layer flow, there is an approximately 16.4 percent increase in the rate of convective heat transfer. The frictional force and thermal entropy produced by nanofluids with blade-, brick-, and Os-shaped NPs was lower than that produced by nanofluids with platelet-shaped NPs. On the cold fluid side, the nanofluid with Os-shaped NPs develops thermal entropy at a faster rate than those with brick-, blade-, cylinder-, and platelet-shaped NPs.

Evolution of Periodic Orbits in the Sun-Jupiter and Sun-Earth Systems

Objective: The periodic orbits around smaller and larger primaries are studied in the Sun-Jupiter and Sun-Earth systems, considering smaller primary as an oblate spheroid. Methods: We used the Poincare surface section method to find the periodic orbits and discussed the differences between these orbits with and without oblateness. Findings: Different trajectories are drawn with the change of Jacobi constant and radiation pressure. Size variations, location, and eccentricity of an orbit around smaller primary are observed due to oblateness effect of the Jupiter and Earth. Oblateness of the smaller primary and radian pressure of the bigger primary have a significant effect on eccentricity, orbit shape, size, and position in phase space. Novelty : Small solar system bodies, such as asteroids and comets in the Sun-Jupiter and Sun-Earth systems, can be explored using periodic orbits. Perturbation caused by oblateness of the smaller primary must be understood and addressed during human exploration missions. Keywords: Circular Restricted Three Body Problem; Poincare Surface Sections; Jacobi Constant; Radiation Factor; Oblateness; Trajectories; Resonance

Topological data analysis of noise: Uniform unimodal distributions

Random point clouds determine random simplicial complexes which can be characterized via homology. In this work we consider Vietoris–Rips complexes built on top of random point clouds in the D-dimensional Euclidian space in two setups: (i) a homogeneous Poisson point process (HPPP) and (ii) N i.i.d. points sampled from a uniform elliptical distribution. We derive expected topological summaries for such complexes in terms of the average Betti numbers (ABN) and of the newly introduced average integral persistence landscape (AIPL). The latter summary is derived from the average persistence landscape (APL) and preserves its 1-norm. In the HPPP model, we derive general analytical expressions for the density of ABN and AIPL and their 1-norms. For finite samples, we establish the functional form of decline of the 1-norm of the APL with the decrease of the sample size and/or increase of the cloud dimensionality. Furthermore, we derive analytical estimates of boundary effects in a disk, an ellipse, a D-dimensional ball, and 3-dimensional spheroids. We develop asymptotic models accounting for degeneration of a highly eccentric ellipse or a prolate spheroid to a line-segment and of an oblate spheroid to a disk, which describe the decline or growth of the 1-norm of the APL upon degeneration of an elliptic or spheroidal point cloud to a one- or two-dimensional cloud, respectively. Our results can serve as a “null model” for selection of the hyperparameters of the method D and N, as well as for the interpretation of observations in a broad range of real-world problems.

Heat and mass transport from neutrally suspended oblate spheroid in simple shear flow

Through high-fidelity numerical simulation based on the lattice Boltzmann method, we have conducted an in-depth study on the heat and mass transport from an oblate spheroid neutrally suspended in a simple shear flow. In the simulation, the temperature and mass concentration are modeled as a passive scalar released at the surface of the spheroid. The fluid dynamics induced by the interaction between the carrier fluid and the suspended spheroid, as well as the resultant scalar transport process, have been extensively investigated. A coupled transport mechanism comprising several components of the flow around the oblate spheroid has been identified. The effects of the Reynolds number and the aspect ratio of the spheroid on the flow characteristics and scalar transport rate are examined. The variation of the nondimensional scalar transport rate suggests that the effect of spheroid shape on scalar transfer rate can be decoupled from the effects of Peclet and Reynolds numbers, which facilitates the development of a correlation of scalar transfer rate for oblate spheroids based on the well-developed correlations for a sphere.

Dynamics of inertial spheroids in a decaying Taylor–Green vortex flow

Inertial spheroids, prolates and oblates, are studied in a decaying Taylor–Green vortex (TGV) flow, wherein the flow gradually evolves from laminar anisotropic large-scale structures to turbulence-like isotropic Kolmogorov-type vortices. Along with particle clustering and its mechanisms, preferential rotation and alignment of the spheroids with the local fluid vorticity are examined. Particle inertia is classified by a nominal Stokes number St, which to first-order aims to eliminate the shape effect. The clustering varies with time and peaks when the physically relevant flow and particle time scales are of the same order. Low inertial (St<1) spheroids are subjected to the centrifuging mechanism, thereby residing in stronger strain-rate regions, while high inertial (St≫1) spheroids lag the flow evolution and modestly sample strain-rate regions. Contrary to the expectations, however, spheroids reside in high strain-rate regions when the particle and flow time scales are comparable due to the dynamic interactions between the particles and the evolving flow scales. Moderately inertial (St≤1) prolates preferentially spin and oblates tumble throughout the qualitatively different stages of the TGV flow. These preferential modes of rotation correlate with parallel and perpendicular alignments of prolate and oblate spheroids, respectively, with the local fluid vorticity. However, for high inertial spheroids preferential rotation and alignment are decorrelated due to a memory effect, i.e., inertial particles require longer time to adjust to the local fluid flow. This memory effect is not only due to high particle inertia, as in statistically steady turbulence, but also caused by the continuously evolving TGV flow scales.

An immersed boundary-lattice Boltzmann flux solver for simulation of flows around structures with large deformation

In this paper, we present an immersed boundary-lattice Boltzmann flux solver (IB-LBFS) to simulate the interactions of viscous flow with deformable elastic structures, namely, two-dimensional (2D) and three-dimensional (3D) capsules formed by elastic membranes. The IB-LBFS is based on a finite-volume formulation and makes use of hydrodynamic conservation equations with fluxes computed by a kinetic approach; thus, it is more flexible and efficient than the standard immersed boundary-lattice Boltzmann methods. The membrane of the 2D capsule is represented by a set of discrete Lagrangian points, with in-plane and bending forces acting on the membrane obtained by a finite difference method. In contrast, the membrane of a 3D capsule is discretized into flat triangular elements with membrane forces calculated by an energy-based finite-element method. The IB-LBFS is first validated by studying the deformation of a circular capsule in a linear Newtonian and a power-law shear flow. Next, the deformation dynamics of a spherical, an oblate spheroidal, and a biconcave capsule in a simple shear flow are simulated. For an initially spherical capsule, the tank-treading motion of its membrane is reproduced at the steady state; while for oblate spheroidal and biconcave capsules, the swinging and tumbling motions are observed. Furthermore, under certain parameter settings, the transient mode from tumbling to swinging motions is also found, showing a rich and complex dynamic behavior of non-spherical capsules. These results indicate that the IB-LBFS can be employed in future studies concerning the dynamics of a capsule suspension in more realistic flows.

The Photogravitational Restricted Problem of 2 + 2 Bodies with Straight Segment and Oblate Spheroid

The Photogravitational Restricted Problem of 2 + 2 Bodies with Straight Segment and Oblate Spheroid

Effects of shape on the optical properties of CdSe@Au core-shell nanocomposites

We studied the local field enhancement factor (LFEF), absorption, and extinction cross sections of spherical, cylindrical, oblate, and prolate core–shell nanocomposites (NCs) theoretically and numerically using the quasi-static approach. By solving Laplace’s equations, we obtained expressions for the LFEF, polarizability, absorption, and scattering cross sections for each of the core–shell NCs. We found that the LFEF, absorption, and extinction cross section of spherical and cylindrical core–shell NCs possess two peaks whereas oblate and prolate spheroids show three observable peaks. Moreover, the prolate core–shell spheroid shows greater tunability and larger intensity of the LFEF than its corresponding oblate structure. Furthermore, spherical nanoshells are characterized by the higher LFEF than cylindrical and spheroidal core–shells of the same size and composition. When compared, even the smallest value of the LFEF of the spherical core–shell is 11.42 and 10.09 times larger than the biggest values of oblate and prolate core-shells, respectively. The study also indicated that for spherical and cylindrical NCs, the first two peaks of the LFEF and extinction cross sections are achieved at the same corresponding frequencies. Furthermore, all peaks of the extinction cross sections of the prolate spheroid are found to be the lowest while those of the cylindrical peaks are the highest. Where there are an equal number of peaks of different shapes, the peak values are different, showing that shapes of core–shell NCs determine the intensity, the number, and the positions of peaks of the LFEF and optical cross sections. Such NCs are promising for applications in optical sensing, bio-sensing, and electronic devices. Especially, gold coated core–shell spheroids have good potential applications in multi-channel sensing.

Mass Modelling of Eggs Based on Shape Index Using Regression Analysis

This study was conducted to determine the correlation between the mass of eggs based on its geometrical dimensions characteristics such as length (L), width (W), geometric mean diameter (GMD), the first and second projection areas (PA1, PA2), criteria area (CAE), oblate spheroid volume (Vosp), measured volume (Vm) and shape index (SI). Based upon the SI, eggs were characterized as sharp (<72), normal (72 -76) and round (>76), respectively. For mass prediction, different classifications viz. dimension as 1st classification, projection area as 2nd classification, and volume as 3rd classification were considered. 1st classification (dimension), 2nd classification (projection area), and 3rd classification (volume) were considered. The analysis was executed using 33 linear regression models and the models were recommended by considering maximum coefficient of determination (R2) and minimum regression standard error (RSE). Based on the modelling analysis, 10 model equations based on the selected classifications were recommended for mass estimation. The findings of this investigation will be helpful for the researchers involved in the design and development of process equipments in the production and processing of eggs.

Rigid spheroid migration in square channel flow of power-law fluids

The characteristics of rigid spheroid migration in square channel flow of power-law fluids are numerically investigated by the three-dimensional lattice Boltzmann method. The effects of aspect ratio (α), blockage ratio of the particle (k), power-law index (n) and Reynolds number (Re) of the fluid on the inertial migration of rigid prolate and oblate spheroids are explored, respectively. The results show that the shear-thinning fluid with large fluid inertia is beneficial for fast focusing rigid particles to the equilibrium positions in square channel. There are two stages of particle migration and four stable channel face equilibrium positions for migration of spheroid; the channel corner equilibrium positions only exist for the oblate spheroid under a low inertia effect. The prolate spheroid exhibits tumbling and log-rolling (LR) rotational modes, and the LR mode is conditionally stable. For the oblate spheroid, only the LR mode exists when Re is large while two new rotational modes are captured when Re decreases. The equilibrium position of the prolate and oblate spheroids increase when α < 1.0 then decrease at larger α values, escaping the channel centreline with decreasing n and k and increasing Re. The changes of inertial focusing length, angular velocity, and rotational period of the spheroid are systematically analysed to study mechanism of spheroid migration. The current results enrich our understanding of rigid particle accumulation behaviour in channel flow of non-Newtonian fluids and may also shed light on how to efficiently focus and control particles in microfluidic devices.

Pattern Reconstruction from Near-Field Data Affected by 3D Probe Positioning Errors Collected via Planar-Wide Mesh Scanning

An effective procedure to correct known 3D probe positioning errors affecting the near-field–far-field transformation (NF–FF) with non-conventional plane rectangular scanning, named planar wide-mesh scanning (PWMS), is developed in this paper. It relies on the non-redundant sampling representations of electromagnetic fields and related optimal sampling interpolation (OSI) expansions and has been devised when a quasi-planar antenna under test is considered as suitably modelled by either a double bowl or an oblate spheroid. Such an algorithm first makes use of the so-called k-correction to compensate for the errors occurring when the actual sampling points deviate from the acquisition plane and then adopts an iterative procedure to restore the NF samples at the points specified by the used non-redundant sampling representation from those obtained at the previous step and affected by 2D positioning errors. Finally, once the regularly arranged PWMS samples have been calculated, the NF data required to compute the classic plane-rectangular NF–FF transformation are accurately evaluated by using an effective 2D OSI algorithm. Several numerical results are presented in order to assess the effectiveness of the devised approach.

Effective thermal conductivity simulations of suspensions containing non-spherical particles in shear flow

Suspensions of oblate spheroid particles can have different thermal characteristics from suspensions of spherical particles based on its orthotropic geometry. However, the effective thermal conductivity of non-spherical particle suspensions under shear flow conditions has not been reported yet. In a first step dilute suspensions are considered ignoring particle-particle interactions, and a representative volume is observed containing one single oblate spheroid rotating at the center coupled to the shear flow. The fluid-side convective heat and mass transfer is computed by the Lattice Boltzmann Method (LBM). And the Discrete Element Method (DEM) accounts for particle dynamics, while the Finite Element Method (FEM) for heat conduction inside particles. Three codes are coupled together. As predicted by Maxwell’s model and the model of Nan et al., the effective thermal conductivity of a water suspension would saturate if the conductivity of the particle exceeds 20∼30W/(mK) at stagnant state, because the thermal resistance of the particles becomes negligible in comparison to the fluid thermal resistance. The simulation results in this study confirm such saturation also to a shear flow. Besides, another saturation mechanism exists for spherical particles if the shear rate is increased to a point where particle rotation induces convective transport that supersedes conductive transport within the particle. However, this is not the case for the oblate ellipsoidal particles due to different rotating states. And comparing different rotating states, if the particle’s thermal conductivity is higher than the base fluid, the shear-induced rotation around the oblate minor axis (log-rolling) results in a higher effective thermal conductivity than around the oblate major axis (tumbling) or the rotation of a spherical particle of equivalent volume fraction. The results provide a design guideline for particle in suspensions with better heat transfer behaviors.

Spheroid-based optical cavities for tunable photon recycling and emitter temperature control in robust solar thermophotovoltaic systems

The theoretical efficiency of solar thermophotovoltaic (STPV) systems is much greater than their efficiencies achieved in practice. Optical cavities can improve the performance of STPV systems by increasing the emitter-to-PV cell view factor and by facilitating photon recycling, whereby photons are reflected back to the emitter. Photon recycling reduces losses and increases the temperature of the emitter, thereby increasing efficiency. Our study presents STPV systems comprising optical cavities in the form of oblate and prolate spheroids. The geometry of the optical cavity can be tuned to control the degree of photon recycling, emitter temperature, emission losses, and the emitter-to-PV cell effective view factor and separation distance without using complex nano- or microstructured materials or optical filters. Numerical analysis shows an optical cavity in the form of a prolate spheroid, prolate spheroid with a middle annular aperture specular reflector, and integrated oblate- and prolate-spheroid can be used to achieve efficiencies of 17.7%, 18.9%, and 22%, respectively, under solar irradiation at a concentration factor of 1500X. These robust spheroid-based optical cavities can be used to design improved STPV systems with increased durability and higher performance.

Shape control of deformable charge-patterned nanoparticles.

Deformable nanoparticles (NPs) offer unprecedented opportunities as dynamic building blocks that can spontaneously reconfigure during assembly in response to environmental cues. Designing reconfigurable materials based on deformable NPs hinges on an understanding of the shapes that can be engineered in these NPs. We solve for the low-energy shapes of charge-patterned deformable NPs by using molecular dynamics-based simulated annealing to minimize a coarse-grained model Hamiltonian characterized with NP elastic and electrostatic energies subject to a volume constraint. We show that deformable spherical NPs of radius 50nm whose surface is tailored with octahedrally distributed charged patches and double-cap charged patches adapt their shape differently in response to changes in surface charge coverage and ionic strength. We find shape transitions to rounded octahedra, faceted octahedra, faceted bowls, oblate spheroids, spherocylinders, dented beans, and dimpled rounded bowls. We demonstrate that similar shape transitions can be achieved in deformable NPs of different sizes. The effects of counterion condensation on the free-energetic drive associated with the observed deformations are examined via Manning model calculations that utilize simulation-derived estimates for the NP Coulomb energy under salt-free conditions. The charge-pattern-based shape control of deformable NPs has implications for the design of responsive nanocontainers and for assembling reconfigurable materials whose functionality hinges on the shape-shifting properties of their nanoscale building blocks.

Effects of stress-dependent growth on evolution of sulcal direction and curvature in models of cortical folding

The majority of human brain folding occurs during the third trimester of gestation. Although many studies have investigated the physical mechanisms of brain folding, a comprehensive understanding of this complex process has not yet been achieved. In mechanical terms, the “differential growth hypothesis” suggests that the formation of folds results from a difference in expansion rates between cortical and subcortical layers, which eventually leads to mechanical instability akin to buckling. It has also been observed that axons, a substantial component of subcortical tissue, can elongate or shrink under tensile or compressive stress, respectively. Previous work has proposed that this cell-scale behavior in aggregate can produce stress-dependent growth in the subcortical layers. The current study investigates the potential role of stress-dependent growth on cortical surface morphology, in particular the variations in folding direction and curvature over the course of development. Evolution of sulcal direction and mid-cortical surface curvature were calculated from finite element simulations of three-dimensional folding in four different initial geometries: (i) sphere; (ii) axisymmetric oblate spheroid; (iii) axisymmetric prolate spheroid; and (iv) triaxial spheroid. The results were compared to mid-cortical surface reconstructions from four preterm human infants, imaged and analyzed at four time points during the period of brain folding. Results indicate that models incorporating subcortical stress-dependent growth predict folding patterns that more closely resemble those in the developing human brain. Statement of SignificanceCortical folding is a critical process in human brain development. Aberrant folding is associated with disorders such as autism and schizophrenia, yet our understanding of the physical mechanism of folding remains limited. Ultimately mechanical forces must shape the brain. An important question is whether mechanical forces simply deform tissue elastically, or whether stresses in the tissue modulate growth. Evidence from this paper, consisting of quantitative comparisons between patterns of folding in the developing human brain and corresponding patterns in simulations, supports a key role for stress-dependent growth in cortical folding.

LIBRATION POINTS AND STABILITY OF AN OBLATE TEST PARTICLE IN THE SUN-EARTH SYSTEM OF THE RESTRICTED THREE-BODY PROBLEM

This paper examines libration points and stability of a test particle having the shape of an oblate spheroid under the gravitational effect of a radiating first primary and an oblate shaped second primary using the model of the restricted three-body problem. The equations of motion have been stated and the libration points examined. It is seen that there exist a pair of triangular points which are defined by the radiation pressure force of the first primary, and oblateness of the second primary and the test particle. Further, there can be up to five collinear libration points in the presence of oblateness of either the second primary or the test particle. We examine the stability of the libration points and it is seen that the triangular points are linearly stable in the sense that the roots of the characteristic equation are all distinct imaginary roots, which produce bounded motion around the triangular points, while the collinear points are unstable due to the presence of a positive root. Further, we explore the periodic orbits around linearly stable triangular points and it was seen that the orbits are elliptic. The elements of the orbits, among which are the frequency, orientation, eccentricities, lengths of the semi-major and semi-minor axis have all been obtained and are defined by the radiation pressure of the first primary and oblateness of the second primary and the test particle. These outcomes have been verified numerically when the radiating first primary is the Sun and the oblate second primary is the Earth.

Centers and dimensional evolution

From astronomy, the author cites (from astronomy questions and answers by Michael Lam 2015): if a black hole is rotating, then it will be shaped as an oblate spheroid, slightly larger around the equator than in the direction of the poles. However, the equations of general relativity tell us that rather than having one radius, the location of the event horizon, there are two important radii, the spherical event horizon on the inside, and the oblate spheroidal exterior surface. The region in between the two is called the ergosphere, where particles cannot remain at rest and objects can still escape the black hole. Such a black hole looks like this: … The artists figure is not repeated. There are different subsystems of a black hole mentioned and general relativity is quoted. It is assumed that from a decaying black holes collision or explosion the astronomers universe evolved. In this article a biological Feigenbaum evolution is presented with geometries and symmetries added. Octonians are needed for this presentation.

Electro-optic response of bipolar nematic liquid crystal confined in oblate spheroid

Electro-optic response of liquid crystals (LCs) relies on the molecular reorientation of LCs under external electric field and is important for a wide spectrum of applications. Here, we uncover an interesting electro-optic response of 5CB nematic LC confined in an oblate spheroid and subjected to external electric field. Under the planar anchoring, the nematic LC spheroid adopts a bipolar structure with the bipolar axis laid in the horizontal film plane. When a threshold electric field EF, is applied, the bipolar structure reorients from the horizontal configuration (LC molecules align along long axis direction) to the vertical configuration (LC molecules align along short axis direction), involving the competition of elastic energy, surface anchoring energy and electric field energy. In contrast to bipolar nematic LC droplets, the vertical configuration does not relax to the low-energy horizontal configuration after removing E; we argue that is due to the oblate shape of the nematic LC spheroid, which traps the bipolar structure in a local energy minimum. We use continuum simulation to demonstrate the detailed response and the reorientation dynamics of bipolar nematic spheroids under E field, showing consistent results with the experiments and confirming the proposed switching mechanism. Nevertheless, the vertical configuration of the bipolar structure could relax to the low-energy horizontal configuration by thermal cycling. Our studies provide clear experimental results that show the characteristics of the electro-optic response of oblate LC spheroids, which have both fundamental and practical implications.

Quasi-spherical superclusters

Context.Superclusters are systems with varied properties and varied fractional overdensities. Their dynamical state evolves under the influence of two components: dark energy and gravitational force. The dominant component at any spatial location and cosmic epoch is determined by the total mass and the local overdensity of the system. However, generally the dynamical state of superclusters is poorly known.Aims.We study properties of superclusters and select a sample of quasi-spherical superclusters, the dynamics of which can be studied using the Λ significance diagram.Methods.We extracted our supercluster sample with an adaptive local threshold density method from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) data and estimated their masses using the dynamical masses for member galaxies and groups. We used topological analysis based on Minkowski functionals and the positions of galaxies and galaxy groups in superclusters. Finally, we highlight the dynamical state of a few exceptional types of superclusters found in this study using the Λ significance diagram.Results.Our final sample contains 65 superclusters in the distance range of 130−450 Mpc. Supercluster masses range between 1.1 × 1015 M⊙and 1.4 × 1016 M⊙and sizes between 25 Mpc and 87 Mpc. We find that pancake-type superclusters form the low-luminosity, small, poor and low-mass end of superclusters. We find four superclusters of unusual types, exhibiting exceptionally spherical shapes. These so-called quasi-spherical systems contain a high-density core surrounded by a relatively spherical density and galaxy distribution. The mass-to-light ratio of these quasi-sphericals is higher than those of the other superclusters, suggesting a relatively high dark matter content. Using the Λ significance diagram for oblate and prolate spheroids, we find that three quasi-spherical superclusters are gravitationally bound at the present epoch.Conclusions.Quasi-spherical superclusters are among the largest gravitationally bound systems found to date, and form a special class of giant systems that, dynamically, are in between large gravitationally unbound superclusters and clusters of galaxies in an equilibrium configuration.

Shape matters: Competing mechanisms of particle shape segregation.

It is well known that granular mixtures that differ in size or shape segregate when sheared. In the past, two mechanisms have been proposed to describe this effect, and it is unclear if both exist. To settle this question, we consider a bidisperse mixture of spheroids of equal volume in a rotating drum, where the two mechanisms are predicted to act in opposite directions. We present evidence that there are two distinct segregation mechanisms driven by relative overstress. Additionally, we showed that, for nonspherical particles, these two mechanisms (kinetic and gravity) can act in different directions leading to a competition between the effects of the two. As a result, the segregation intensity varies nonmonotonically as a function of aspect ratio (AR), and, at specific points, the segregation direction changes for both prolate and oblate spheroids, explaining the surprising segregation reversal previously reported. Consistent with previous results, we found that the kinetic mechanism is dominant for (almost) spherical particles. Furthermore, for moderate aspect ratios, the kinetic mechanism is responsible for the spherical particles' segregation to the periphery of the drum, and the gravity mechanism plays only a minor role. Whereas, at the extreme values of AR, the gravity mechanism notably increases and overtakes its kinetic counterpart.