Oblate Spheroid Research Articles

Oscillation migration of a neutrally buoyant oblate spheroid in the elasto-inertial duct flow

Oscillation migration of a neutrally buoyant oblate spheroid in the elasto-inertial duct flow

Elasto-inertial focusing and rotating characteristics of ellipsoidal particles in a square channel flow of Oldroyd-B viscoelastic fluids

The elasto-inertial focusing and rotating characteristics of spheroids in a square channel flow of Oldroyd-B viscoelastic fluids are studied by the direct forcing/fictitious domain method. The rotational behaviours, changes in the equilibrium positions and travel distances are explored to analyse the mechanisms of spheroid migration in viscoelastic fluids. Within the present simulated parameters (1 ≤ Re ≤ 100, 0 ≤ Wi ≤ 2, 0.4 ≤ α ≤3), the results show that there are four kinds of equilibrium positions and six (five) kinds of rotational behaviours for the elasto-inertial migration of prolate (oblate) spheroids. We are the first to identify a new rotational mode for the migration of prolate spheroids. Only when the particles are initially located at a corner and wall bisector, some special initial orientations of the spheroids have an impact on the final equilibrium position and rotational mode. In other general initial positions, the initial orientation of the spheroid has a negligible effect. A higher Weissenberg number means the faster the particles migrate to the equilibrium position. The spheroid gradually changes from the corner (CO), channel centreline (CC), diagonal line (DL) and cross-section midline (CSM) equilibrium positions as the elastic number decreases, depending on the aspect ratio, initial orientation and rotational behaviour of the particles and the elastic number of the fluid. When the elastic number is less than the critical value, the types of rotational modes of the spheroids are reduced. By controlling the elastic number near the critical value, spheroids with different aspect ratios can be efficiently separated.

Perturbing and Oblateness's Impact on the Generalized Photogravitational Restricted Three-Body Problem

In this research work, the effects of perturbing and oblateness on the generalised photogravitational restricted three body problem (RTBP) are examined when the primary are regarded as radiation sources and oblate spheroid. The perturbing forces were included in the equations of motion that we developed for the system. The triangular libration points were derived in terms of the perturbing parameters using linear approximations, and their influence was seen. Applying Murray's criteria, we determined that the triangular libration points remained unstable due to the nature of the characteristics equation matching to the variational equations of motion of the system generated.

Analytic solutions for effective elastic moduli of isotropic solids containing oblate spheroid pores with critical porosity

AbstractAccurate characterization for effective elastic moduli of porous solids is crucial for better understanding their mechanical behaviour and wave propagation, which has found many applications in the fields of engineering, rock physics and exploration geophysics. We choose the spheroids with different aspect ratios to describe the various pore geometries in porous solids. The approximate equations for compressibility and shear compliance of spheroid pores and differential effective medium theory constrained by critical porosity are used to derive the asymptotic solutions for effective elastic moduli of the solids containing randomly oriented spheroids. The critical porosity in the new asymptotic solutions can be flexibly adjusted according to the elastic moduli – porosity relation of a real solid, thus extending the application of classic David‐Zimmerman model because it simply assumes the critical porosity is one. The asymptotic solutions are valid for the solids containing crack‐like oblate spheroids with aspect ratio < 0.3, nearly spherical pores (0.7 < < 1.3) and needle‐like prolate pores with > 3, instead of just valid in the limiting cases, for example perfectly spherical pores (= 1) and infinite thin cracks (0). The modelling results also show that the accuracies of asymptotic solutions are weakly affected by the critical porosity and grain Poisson's ratio , although the elastic moduli have appreciable dependency of and . We then use the approximate equations for pore compressibility and shear compliance as inputs into the Mori–Tanaka and Kuster–Toksoz theories and compare their calculations to our results from differential effective medium theory. By comparing the published laboratory measurements with modelled results, we validate our asymptotic solutions for effective elastic moduli.

Explaining the oblate morphology of dwarf spheroidals with wave dark matter perturbations

ABSTRACT We investigate whether the oblate, spheroidal morphology of common dwarf spheroidal galaxies (dSph) may result from the slow relaxation of stellar orbits within a halo of wave dark matter ($\psi$DM) when starting from an initial disc of stars. Stellar orbits randomly walk over a Hubble time, perturbed by the pervasive ‘granular’ interference pattern of $\psi$DM, that fully modulates the dark matter density on the de Broglie scale. Our simulations quantify the level of stellar disc thickening over the Hubble time, showing that distribution of stars is predicted to become an oblate spheroid of increasing radius, that plausibly accounts for the morphology of dSph galaxies. We predict a low level of residual rotation remains after a Hubble time at the 1–3 km/s level, depending on orientation, that compares with recent claims of rotation for some well-studied local dSph galaxies. This steady internal dynamical evolution may be witnessed directly with JWST for well-resolved dwarf galaxies, appearing more oblate with look back time and tending to small discs of young stars at high redshift.

Droplets can enhance microcapsule deformation in channel flow

The dynamics of soft microparticles enclosed in a droplet flowing in a channel is an unexplored fundamental problem that lies at the heart of numerous applications, including droplet-based microfluidics, tissue engineering and smart material synthesis. Here we show that enclosing a flexible capsule into a droplet can amplify the capsule’s deformation parameters in channel flow by up to two orders of magnitude. Previously unreported capsule equilibrium shapes in channel flow, including an oblate spheroid and a reversed bullet, have also been discovered. We propose two theoretical models to predict the equilibrium position of the capsule inside the droplet, and estimate the capsule deformation, respectively. The present study provides an effective but simple approach to enhance and control the deformation of soft particles in a flowing suspension, which may inspire widespread applications, from high-throughput single-cell mechanical phenotyping, enhanced cross-membrane drug delivery, to manufacturing shape-controlled non-spherical particles and artificial cells.

Profiles and some dynamic parameters of a layered inhomogeneous elliptical galaxy

Several new models of a layered inhomogeneous elliptical galaxy (EG) having the shape either a triaxial ellipsoid or an oblate or prolate spheroid and consisting of baryonic mass and dark matter with different laws of density distribution — profiles. Based on these models, some key dynamic parameters of the EG were determined: gravitational (potential) energy and rotational kinetic energy, total surface brightness, total luminosity, and velocity dispersion depending on the distance to the EG center. The relationships between the important dynamic parameters of the galaxy have been established: “mass-dimensions”, “mass-velocity dispersion”, “size-dispersion speeds–luminosity” (surface brightness). Evolutionary scenarios for the formation of EG were studied according to these models. The results obtained were applied to sixty model EGs with parameters exactly matching those that actually exist and are presented in the form of tables.

Visualizing the quantum phase transition by using quantum steering ellipsoids in the anisotropic spin XY model

Abstract Quantum steering ellipsoids (QSEs) can serve as a useful geometric tool for describing both the strength and type of quantum correlations between two subsystems of a compound system. By employing the quantum renormalization-group method, we focus on investigating the relation between QSEs and the quantum phase transition (QPT) in the anisotropic spin XY model. The results indicate that the QPT is well visualized in terms of the shape of the QSE, i.e. it is an oblate spheroid in the spin-fluid phase and a needle in the Néel phase. Meanwhile, after several iterations of renormalization, the QSE volume V undergoes a contraction mutation, and can develop two saturated values at the critical points associated with the QPT, which correspond to two different phases: the spin-fluid phase and the Néel phase. We also find that the QSE is closely associated with quantum entanglement in the model, i.e. the volume of the QSE between blocks is more than 4π/81 when the system is in the spin-fluid phase, which indicates that the system must be entangled. Furthermore, the nonanalytic and scaling behaviors of the volume of the QSE have been analyzed in detail, and the results convince us that the quantum critical properties are connected with the behavior of the QSE.

Shape effects on the local dynamics of suspensions of spheroidal particles

The effect of shape on the dynamics of suspensions of non-spherical heavy particles is examined by fully resolved numerical simulations of oblate and prolate spheroids, as well as spheres, for a density ratio of ten, volume fractions ranging from 0.5% to 5%, and Reynolds numbers between 20 and 30. The dynamics is determined both by the interactions of the particles with the fluid as well as by collisions, with the number and importance of collisions increasing with volume fractions. A single isolated oblate or prolate spheroid falling under gravity generally falls broadside on, for the governing parameters examined here, and at low-volume fractions, the majority of particles in a suspension fall that way. At higher-volume fractions, the orientation is more random. The slip velocity decreases as the volume fraction increases for all shapes, as expected, but the effect of the shape is much less than seen for a single particle. This seems to be due to two effects. For all volume fractions, the most deformed particles cluster more than spheres and less deformed particles, which increases their slip velocity. As the concentration increases, the increased particle interactions also causes more particles to fall short side-on, which reduces the frontal area and the resulting drag, increasing the slip velocity. This second effect is, of course, absent for spherical particles.

Dynamics of a driven spheroid in a slow oscillating creeping shear flow

We report the orientation dynamics of a sinusoidally driven spheroid suspended in a slow and weak/strong oscillatory shear flow without Brownian and inertial forces, derive the governing equations, find the classical Jeffery orbits, and then solve them numerically. These equations describe Jeffery's orbits for no external force and no flow oscillations. When the external forces are small, and there are no oscillations, they can be seen as perturbations of the equations that result in Jeffery's orbits. The small perturbations disturb the Jeffery orbits. We also analyze the chaotic and regular dynamics regimes in nearly quiescent, simple shear, and weak/strong and slow oscillating shear flows. We observe quantitative and qualitative differences in the particle dynamics for an oscillating shear flow compared to simple shear flow, as seen from the Poincaré sections, attractors, phase diagrams, time series, and Lyapunov exponents. The analysis indicates that the slow oscillations reduce the complexity of the dynamics of the particle compared to simple shear flow. The steady-state solutions for both prolate and oblate spheroids remain in the flow gradient plane in the case of strong oscillatory shear. At the same time, there is some disturbance from the flow gradient plane for weak oscillations due to the external force instead of inertial forces reported earlier in the literature. In addition, we propose a mechanism to improve particle separation based on shape using a combination of simple and oscillating shear flows, offering significant advantages in separating particles from a colloidal mixture that would otherwise be impossible.

Mechanism of nucleation in ferroelastic domain switching

The mechanism of domain nucleation during ferroelastic domain switching is revealed by utilizing phase-field simulations. A complete compression-tension hysteresis loop is simulated, and the results show the nucleation of new domains at domain walls (DW). Due to relaxation of strain energy, the coherent DWs of the surviving domains often form features like steps, crevices and corners, and nucleation of new domains primarily takes place at these sites in a repeated fashion. The change in elastic strain energy around these sites is sufficient to provide the energy necessary for ferroelastic domain nucleation (FDN). The present simulations reveal that the apparent ellipsoidal shape of a nucleus might be an oblate spheroid when the nucleation takes place at a crevice. The present work also reveals that nucleation of triangular shaped domains is equally probable, and they take place at the steps or corners of DWs.

Rapid formation of binary asteroid systems post rotational failure: A recipe for making atypically shaped satellites

Binary asteroid formation is a highly complex process, which has been highlighted with recent observations of satellites with unexpected shapes, such as the oblate Dimorphos by the NASA DART mission and the contact binary Selam by NASA’s Lucy mission. There is no clear consensus on which dynamical mechanisms determine the final shape of these objects. In turn, we explore a formation pathway where spin-up and rotational failure of a rubble pile asteroid lead to mass-shedding and a wide circumasteroidal debris disk in which the satellite forms. Using a combination of smooth-particle hydrodynamical and N-body simulations, we study the dynamical evolution in detail. We find that a debris disk containing matter corresponding to a few percent of the primary asteroid mass extending beyond the fluid Roche limit can consistently form both oblate and bilobate satellites via a series of tidal encounters with the primary body and mergers with other gravitational aggregates. Principally, satellites end up prolate (elongated) and on synchronous orbits, accreting mainly in a radial direction while tides from the primary asteroid keep the shape intact. However, close encounters and mergers can break the orbital state, leading to orbital migration and deformation. Satellite–satellite impacts occurring in this regime have lower impact velocities than merger-driven moon formation in e.g. planetary rings, leading to soft impacts between differently sized, non-spherical bodies. The resulting post-merger shape of the satellite is highly dependent on the impact geometry. Only moons having experienced a prior mild or catastrophic tidal disruption during a close encounter with the primary asteroid can become oblate spheroids, which is consistent with the predominantly prolate observed population of binary asteroid satellites.

Comment to the article “Mean flow induced by longitudinal libration of a fluid-filled rotating container bounded by two conical surfaces”

Developing the ideas from the author’s previous publication in the European Journal of Mechanics / B Fluids (https://doi.org/10.1016/j.euromechflu.2024.02.008), an interpolation formula is proposed for the angular velocity of mean retrograde flow in a fluid-filled oblate spheroid with arbitrary eccentricity, in the limit of very low longitudinal libration frequencies.

Effect of aspect ratio on flow-induced vibration of oblate spheroids and implications for energy generation

This study experimentally investigates the influence of aspect ratio on cross-flow flow-induced vibration (FIV) of elastically mounted oblate spheroids. The aspect ratio (ϵ=b/a) of an oblate spheroid, defined as the ratio of the major diameter (b) in the cross-flow direction to the minor diameter (a) in the streamwise direction, was varied between 1.00 and 3.20. The FIV response was characterized over a range of reduced velocity, 3.0⩽U∗=U/(fnwb)⩽12.0, where U is the free-stream velocity and fnw is the natural frequency of the system in quiescent water. The corresponding Reynolds number varied over the range 4730⩽Re⩽20120. It was found that in addition to the vortex-induced vibration (VIV) Mode I and Mode II responses observed for a sphere, on increasing the aspect ratio to ϵ=1.53 and 2.0, a galloping-dominated response, denoted by G-I, was encountered at high reduced velocities. With a further increase in aspect ratio to ϵ=2.50, the body vibration exhibited an additional VIV-like response (V-I) following the sequential appearance of Mode I, Mode II and G-I, with smooth transitions between these modes. In the case of the largest aspect ratio considered in the present study, ϵ=3.20, the spheroid intriguingly exhibited only a pure VIV Mode I before transitioning to a VIV-dominated mode, namely V-II. The largest vibration amplitude observed was 2.17b, occurring at the highest tested reduced velocity of U∗=12.0 for ϵ=2.5. Furthermore, the maximum time-averaged power coefficient was observed to be 0.165 for the thinnest oblate spheroid tested, ϵ=3.20, approximately 660% higher than that observed for VIV of a sphere. This shows the relevance of geometry for FIV energy harvesting from oblate spheroids. The findings highlight the distinctive nature of FIV responses of 3D oblate spheroids compared to 2D bluff bodies such as elliptical, D-section, and square cylinders.

Study of periodic orbits around the triangular points in the circular restricted three-body problem when both the primaries are oblate spheroids and sources of radiation

Study of periodic orbits around the triangular points in the circular restricted three-body problem when both the primaries are oblate spheroids and sources of radiation

A mean field description of steady state isotropic structural superplastic deformation

A model developed previously to treat steady state isotropic superplastic deformation turned out to be of generic value and relevant to many classes of materials from metallic materials, ceramics, intermetallic compounds, composites, bulk metallic glasses, and geological materials. The present paper demonstrates the applicability of the concept of “oblate spheroidal ensembles of atoms containing quantified excess free volume present in a general grain boundary” to predict quantitatively the response of general, high-angle grain boundaries when subjected to external stimuli, e.g., an external stress, irrespective of the nature of the atomic bonds (metallic, ionic, or covalent) in preference to purely geometric descriptions of the grain boundary. The emergence of “oblate spheroids” as a response to an external stimulus is regarded in this analysis as self-organizing and a basic phenomenon that cuts across material classes and the nature of the chemical bonds.

Systematic Implications of Palynomorph Diversity Using Microscopic Trends Among Asteraceous Flora From the Drylands of Baluchistan, Pakistan.

Pollen micromorphological traits with taxonomic implications are first reported from the study area for 50 Asteraceous taxa belonging to nine tribes. Cichorieae (21 taxa), Cardueae (11 taxa), Inuleae (six taxa), and Anthemideae (four taxa) are the leading tribes. The research included Cousinia haeckeliae, Himalaiella afghana, Pterachaenia stewartii (endemic to Afghanistan and Pakistan), and Xylanthemum macropodum (endemic to Baluchistan). Light and scanning electron microscopy were employed for the visualization of pollen photomicrographs. The data was analyzed statistically via SPSS, PAST, and Origin. Significant diagnostic qualitative and quantitative palynological traits were explored for discrimination down to the species level within the tribes. All the investigated taxa possessed radial symmetry, isopolarity, and monad form (characters for distinction at the subdivision level). The aperture types were trizonocolporate, tetrazonocolporate, and tricolporate with number position and character (NPC) formulas N3P4C5, N4P4C5, and N3P4C3. Goniotreme, peritreme, and ptychotreme types of amb were recognized. Echinate, echinate lophate, scabrate, and gemmate sculpturing were present with and without perforated surface patterns. Variations in the shapes in polar and equatorial views and lacuna shapes further assisted the separation of taxa. The observed shape classes were perprolate, prolate spheroidal, prolate, subprolate, oblate spheroidal, suboblate, and oblate. Principal component analysis, correlation, standard probability plots, and ridge line paired features plot for quantitative variables determined the positive correlation between the length and width of colpi in equatorial and polar view with polar axis and equatorial diameter and number of spines between colpi with the number of spines per pollen. The number of spines per pollen was negatively correlated with the width and length of colpi in the polar view. Multiple sample analysis of variance (ANOVA) concluded that a high statistically significant difference exists among the means of analyzed traits. The examined qualitative and quantitative palynological traits revealed noticeable variations, thus providing the source for species discrimination in Asteraceous tribes.

Dynamics around small irregularly shaped objects modeled as a mass dipole

In this work, we investigate the dynamics of a spacecraft near two primary bodies. The massive body is considered to have a spherical shape, while the less massive one is elongated and modeled as a dipole. The dipole consists of two connected masses, one is spherical and the other is an oblate spheroid. The gravitational potential of the elongated body is determined by four independent parameters. To study the dynamics, we construct the equations of motion of a spacecraft with negligible mass under the effect of the current force model. The existence and locations of the equilibrium points are analyzed for various values of the system parameters. We found that the existence and locations of the points are affected by the system parameters. Also, we studied the linear stability of the equilibrium points. We found some stable collinear points when the oblateness parameter is negative, otherwise the points are not stable. We used the curves of zero velocity to identify the regions of allowed motion. Furthermore, we discussed the 2001 SN263 asteroid system and found some stable collinear points when the oblateness parameter is negative. In addition, the triangular points of the system are stable in a linear sense.

Rotational lightcurves of Dimorphos and constraints on its post-DART impact spin state

Dimorphos, the secondary member of the binary asteroid (65803) Didymos, was impacted by NASA’s Double Asteroid Redirection Test (DART) spacecraft on September 26, 2022. Images taken with the DART’s DRACO camera before the impact showed that Dimorphos’s original shape was nearly rotationally symmetric, close to an oblate spheroid, and it was probably in a synchronous spin state. As such, it did not show a detectable secondary brightness variation before the DART impact in the integral light from the binary system. However, numerical impact models predicted that the DART impact could change both its shape and spin state, signatures of which could be detected with high-quality lightcurve observations. We have analyzed the best photometric observations of the Didymos–Dimorphos system that were taken during its favorable observing and geometric conditions in December 2022 and January 2023 and detected a significant secondary rotational lightcurve with amplitudes (in the total light from the primary and secondary) ranging from 0.008 to 0.031 mag at 7 distinct epochs. We estimate that the apparent cross section of Dimorphos varied with a relative amplitude (normalized to the mean cross section) between ±0.07 and ±0.24 over its rotation on the individual epochs. The observed changes of Dimorphos’s apparent cross-section amplitude over its rotation suggest an attitude instability, showing variations of Dimorphos’s obliquity. The lightcurve minima are approximately aligned, to within 30∘in mean anomaly, with the mutual events between the components of the binary system. The observations suggest that Dimorphos is in an excited, non-principal axis (NPA) spin state where, on average, it is tidally locked. By comparing the observations to high-fidelity simulations, we find that a moderate amount of NPA rotation in Dimorphos after the DART impact is required to reproduce the observed lightcurves. This NPA rotation is limited to around on-average synchronous or anti-synchronous configurations of Dimorphos. We also find Dimorphos elongations with the equatorial axis ratios a/b between 1.1 and 1.4 are generally consistent with the observed mean apsidal precession rate. We predict that when the ESA’s Hera spacecraft arrives to the Didymos–Dimorphos system in late 2026, it will still find Dimorphos in the NPA spin state, which places additional constraints on the operations of the spacecraft to achieve its objectives.

Interior solution of azimuthally symmetric case of Laplace equation in orthogonal similar oblate spheroidal coordinates

Curvilinear coordinate systems distinct from the rectangular Cartesian coordinate system are particularly valuable in the field calculations as they facilitate the expression of boundary conditions of differential equations in a reasonably simple way when the coordinate surfaces fit the physical boundaries of the problem. The recently finalized orthogonal similar oblate spheroidal (SOS) coordinate system can be particularly useful for a physical processes description inside or in the vicinity of the bodies or particles with the geometry of an oblate spheroid. The solution of the azimuthally symmetric case of the Laplace equation was found for the interior space in the orthogonal SOS coordinates. In the frame of the derivation of the harmonic functions, the Laplace equation was separated by a special separation procedure. A generalized Legendre equation was introduced as the equation for the angular part of the separated Laplace equation. The harmonic functions were determined as relations involving generalized Legendre functions of the first and of the second kind. Several lower-degree functions are reported. Recursion formula facilitating determination of the higher-degree harmonic functions was found. The general solution of the azimuthally symmetric Laplace equation for the interior space in the SOS coordinates is reported.