Prolate Shape Research Articles

Tetrahedral shape and Lambda impurity effect in $^{80}$Zr with a multidimensionally constrained relativistic Hartree-Bogoliubov model

Abstract This study investigates the tetrahedral structure in $^{80}$Zr and Lambda ($\Lambda$) impurity effect in $^{81}_{~\Lambda}$Zr using the multidimensionally constrained relativistic Hartree-Bogoliubov model.
 The ground states of both $^{80}$Zr and $^{81}_{~\Lambda}$Zr exhibit a tetrahedral configuration, accompanied by prolate and axial-octupole shape isomers. 
 Our calculations reveal there are changes in the deformation parameters $\beta_{20}$, $\beta_{30}$ and $\beta_{32}$ upon $\Lambda$ binding to $^{80}$Zr, except for $\beta_{32}$ when $\Lambda$ occupies $p$-orbits. 
 Compared to the two shape isomers, the $\Lambda$ particle exhibits weaker binding energy in the tetrahedral state when occupying the $1/2^+[000](\Lambda_s)$ or $1/2^-[110]$ single-particle states. In contrast, the strongest binding occurs for the $\Lambda$ particle in the $1/2^-[101]$ state with tetrahedral shape. A large $\Lambda$ separation energy may not necessarily correlate with a significant overlap between the density distributions of the $\Lambda$ particle and the nuclear core, particularly for tetrahedral hypernuclei.

Analytical model of small- and large-amplitude drop oscillation dynamics

The mechanical energy balance over a bulk of fluid that oscillates between prolate and oblate shapes in another immiscible fluid is solved using a general spheroidal coordinate system. The drop shape is described by a unique parameter that may continuously vary over the time, making the implementation of the model rather simple. Potential flow is assumed, and inertial and viscous effects are accounted for in both the inner and outer flow fields. The characteristics of drop oscillation for small and large amplitudes are studied, and the results are compared with theoretical, experimental, and numerical data from the open literature. The rather satisfactory validation of the model over a large variety of operating conditions allows its extension to include other physical phenomenon, like evaporation and its effect on drop oscillation.

The rotational disruption of porous dust aggregates from ab initio kinematic calculations

The size of dust grains in the interstellar medium follows a distribution where most of the dust mass is made up of smaller grains. However, the redistribution from larger grains towards smaller sizes, especially by means of rotational disruption, is still poorly understood. We aim to study the dynamics of porous grain aggregates undergoing an accelerated rotation, namely, a spin-up process that rapidly increases the angular velocity of the aggregate. In particular, we aim to determine the deformation of the grains and the maximal angular velocity up to the rotational disruption event by caused by centrifugal forces. We precalculated the porous grain aggregate by means of ballistic aggregation analogous to the interstellar dust as input for subsequent numerical simulations. We performed three-dimensional (3D) N-body simulations, mimicking the radiative torque spin-up process up to the point where the grain aggregates become rotationally disrupted. Our simulations results are in agreement with theoretical models predicting a characteristic angular velocity, $ disr $, on the order of $ rad\ $, where grains become rotationally disrupted. In contrast to theoretical predictions, we show that for large porous grain aggregates ($ nm $), the $ disr $ values do not strictly decline. Instead, they reach a lower asymptotic value. Hence, such grains can withstand an accelerated rotation more efficiently up to a factor of 10 because the displacement of mass by centrifugal forces and the subsequent mechanical deformation supports the buildup of new connections within the aggregate. Furthermore, we report that the rapid rotation of grains deforms an ensemble with initially 50:50 prolate and oblate shapes, respectively, preferentially into oblate shapes. Finally, we present a best-fit formula to predict the average rotational disruption of an ensemble of porous dust aggregates dependent on the internal grain structure, total number of monomers, and applied material properties.

Existence of slowly rotating bipolytropes with prolate cores

We report the existence of hydrostatic equilibrium states for a composite body made of two rigidly rotating, homogeneous layers bounded by spheroidal surfaces, where the core has a prolate shape. These new configurations require an oblate envelope that spins faster than the core. No solution with a prolate envelope is found. For some parameters, the prolate core can even be at rest. Numerical experiments based on the self-consistent field method support this result in the case of heterogeneous layers with polytropic equations of state. The possible cancellation of the first gravitational moment, $J_2$, is discussed.

Galaxy shapes in Magneticum

Context. Despite being one of the most fundamental properties of galaxies that dictate the form of the potential, the 3D shapes are intrinsically difficult to determine from observations. The improving quality of triaxial modeling methods in recent years has made it possible to measure these shapes more accurately. Aims. This study provides a comprehensive understanding of the stellar and dark matter (DM) shapes of galaxies and the connection between them. As these shapes are the result of the formation history of a galaxy, we investigate which galaxy properties they are correlated with, which will be especially useful for interpreting the results from dynamical modeling. Methods. Using the hydrodynamical cosmological simulation Magneticum Pathfinder Box4 (uhr), we computed the stellar and DM intrinsic shapes of 690 simulated galaxies with stellar masses above 2 × 1010 M⊙ at three different radii with an iterative unweighted method. We also determined their morphologies, their projected morphological and kinematic parameters, and their fractions of in situ formed stars. Results. The DM follows the stellar component in shape and orientation at three half-mass radii, indicating that DM is heavily influenced by the baryonic potential in the inner parts of the halo. The outer DM halo is independent of the inner properties such as the DM shape or galaxy morphology, however, and is more closely related to the large-scale anisotropy of the gas inflow. Overall, DM halo shapes are prolate, consistent with previous literature. The stellar shapes of galaxies are correlated with their morphology, with early-type galaxies featuring more spherical and prolate shapes than late-type galaxies out to 3 R1/2. Galaxies with more rotational support are flatter, and the stellar shapes are connected to the mass distribution, though not to the mass itself. In particular, more extended early-type galaxies have larger triaxialities at a given mass. Finally, the shapes can be used to better constrain the in situ fraction of stars when combined with the stellar mass. Conclusions. The relations between shape, mass distribution, and in situ formed star fraction of galaxies show that the shapes depend on the details of the accretion history through which the galaxies are formed. The similarities between DM and stellar shapes in the inner regions of galaxy halos signal the importance of baryonic matter for the behavior of DM in galaxies and will be of use for improving the underlying assumptions of dynamical models for galaxies in the future. However, at large radii the shapes of the DM are completely decoupled from the central galaxy, and their shapes and spin are coupled more to the large scale inflow than to the galaxy in the center.

Role of surface charge convection on oblate droplets in different conductivity regimes

This paper presents a robust numerical model to simulate the electro-hydrodynamic flows of a neutrally buoyant liquid droplet suspending in another liquid for varying electrical conductivities ranging from near-dielectric to highly conductive fluids. The effect of such conductivity on the interfacial charge transport in the droplets has been investigated. The model is first validated with the theory of electro-rotation corresponding to the strong electric field. The results are compared with the theoretical predictions from the Quincke theory. The angular velocities at different electric field ratios agree well with theoretical predictions. Furthermore, droplet investigations are performed in distinct conductivity regimes with the electric Reynolds number ranging from 10−2 to 104. The findings reveal that conductivity influences the evolution of diverse droplet shapes in the corresponding regimes through surface charge convection. We observe prolate shapes at very low electric conductivities, while larger conductivities of droplets and suspending media lead to oblate drop shapes. With increasing electrical conductivity of the droplet and the medium, we observe the onset of distinct droplet shapes similar to the existing literature. The mechanism for the onset of different regimes is adequately explained by quantifying surface properties like tangential stress and velocity.

Correction of Presbyopia by Monocular Bi-Aspheric Ablation Profile.

The study aims to evaluate visual acuity and objective visual quality before and after the monocular bi-aspheric ablation profile for correction of presbyopia surgery. This prospective self-control study included 20 cases and 38 eyes of patients who underwent monocular bi-aspheric ablation profile correction of myopia with presbyopia at the Eye Hospital of Shandong University of Traditional Chinese Medicine from January 2023 to January 2024. These patients were selected for observation, and each patient's preoperative and postoperative uncorrected distance visual acuity (UDVA), uncorrected near visual acuity (UNVA), corrected distance visual acuity (CDVA), spherical aberration (SA) (within 6 mm), horizontal and vertical coma (within 6 mm), and corneal aspheric index (Q-value) (within 6 mm) were evaluated. Statistical data analysis was performed at different time points before and after the operation. There were statistically significant differences in UDVA between dominant and non-dominant eyes before and after surgery (Z = -3.784, p < 0.001; Z = -3.817, p < 0.001). Post-operatively, 90% of the non-dominant eyes achieved UNVA of J1 and above, and 95% of the bilateral eyes achieved UNVA of J1 and above. Significant differences were found in the SA of the dominant eyes, which showed a positive increase (Z= -3.784, p < 0.001); however, compared with the dominant eye, the SA of the non-dominant eye was negatively increased, but the difference was not statistically significant (p = 0.08). There was a significant difference in the vertical coma of the dominant eye before and after the operation, but there was no significant difference in non-dominant eyes. There was no significant difference in the change of binocular horizontal coma before and after the operation. There were significant changes in the Q value of both eyes before and after the operation (Z = -3.923, p < 0.001; Z = -3.51, p < 0.001). After the monocular bi-aspheric ablation profile, the cornea of the non-dominant eye showed a prolate shape, negative SA increased, and the UDVA and UNVA improved after the operation.

Notes on the Morphology, Anatomy, Palynology, and Karyology of Onobrychis argaea (Fabaceae), Endemic to Turkey

Onobrychis argaea belonging to the Fabaceae family, is an endangered plant species endemic to Turkey, distributed only in Kayseri Erciyes Mountain. This study represents the first comprehensive investigation into the morphology, anatomy, pollen and seed micromorphology, and chromosome characteristics of O. argaea. The previous description of the species has been expanded and modified. The pith of the root is covered with xylem tissue. In the stem cross-section, the protective tissue is periderm in the woody part and epiderm in the herbaceous part. The leaflets are amphistomatic and equifacial. The pollen grains are radially symmetric, isopolar, tricolpate, with prolate shape and reticulate-microreticulate ornamentation. The seeds are reniform, yellowish-brown, suboblate, and exhibit rugulate surface ornamentation. The number of somatic chromosomes in O. argaea is 2n = 14. The karyotype formula of this species consists of seven median chromosomes.

Maximizing the notional area in single tip field emitters

One of the critical aspects in advancing high-brightness field emitter devices is determining the conditions under which single-tip emitters should be constructed to optimize their emission area. Recent experiments have explored varying the axis ratio ξ of the cap of a single-tip emitter, ranging from an oblate semi-spheroid to a prolate shape, mounted on a nearly cylindrical conducting body. In this work, we present a strategy, based on high-accuracy computer simulations using the finite element technique, to maximize the emission area of those single-tip emitters. Importantly, our findings indicate that the notional emission area achieves its maximum when the emitter’s cap is adjusted to an oblate semi-spheroid with a characteristic axis ratio ξC≈0.85. We do a comparison of notional emission area as a function of ξ for an ellipsoidal emitter on a post and compare these results from other emitter configurations, which are feasible to fabricate.

Ontogenic transformation of the ankle from the initial mediolateral arrangement of the calcaneus and talus: Ahistological study of human embryos and early fetuses.

The human calcaneus is robust and provides a prominent heel for effective bipedal locomotion, although the adjacent talus has no muscle attachments. However, there is incomplete information about the morphological changes in these prominent bones during embryo development. We examined serial histological sections of 23 human embryos and early-term fetuses (approximately 5-10 weeks' gestational age [GA]). At a GA of 5 weeks, the precartilage talus was parallel to and on the medial side of the calcaneus, which had a prolate spheroid shape and consisted of three masses. At a GA of 6 weeks, the cartilaginous talus extended along the proximodistal axis, and the tuber calcanei became long and bulky, with a small sustentaculum talus at the "distal" side. At a GA of 6 to 8 weeks, the sustentaculum had a medial extension below the talus so that the talus "rode over" the calcaneus. In contrast, the talus had a more complex shape, depending on the growth of adjacent bones. At a GA of 9 to 10 weeks, the talus was above the calcaneus, but the medial part still faced the plantar subcutaneous tissue because of the relatively small sustentaculum. Therefore, the final morphology appeared after an additional several weeks. Muscle activity seemed to facilitate growth of the tuber calcanei, but growth of the other parts of calcaneus, including the sustentaculum, seemed to depend on active proliferation at the different sites of cartilage. Multiple tendons and ligaments seemed to fix the talus so that it remained close to the calcaneus.

On the Kinematic Nature of Apparent Disks at High Redshifts: Local Counterparts are Not Dominated by Ordered Rotation but by Tangentially Anisotropic Random Motion

It is not straightforward to physically interpret the apparent morphology of galaxies. Recent observations by the James Webb Space Telescope (JWST) revealed a dominant galaxy population at high redshifts (z > 2) that were visually classified as disks for their flattened shapes and/or exponential light profiles. The extensively accepted interpretation is that they are dynamically cold disks supported by bulk rotation. However, it is long known that flattened shapes and exponential profiles are not exclusive for rotating disk structure. To break degeneracy and assess the rotational support of typical high-z galaxies in the JWST samples, those with active star formation and stellar masses lg(M⋆/M⊙)∼9 , we study the kinematics of their equal-mass counterparts at z = 0. While these local star-forming low-mass galaxies are photometrically similar to real dynamically cold disks, they are not supported by ordered rotation but primarily by random motion, and their flattened shapes result largely from tangential orbital anisotropy. Given the empirical and theoretical evidence that young galaxies are dynamically hotter at higher redshifts, our results suggest that the high-z JWST galaxies may not be cold disks but are dynamically warm/hot galaxies with flattened shapes driven by anisotropy. While both have low rotational support, local low-mass galaxies possess oblate shapes, contrasting the prolate shapes (i.e., cigar like) of low-mass systems at high redshifts. Such shape transition (prolate ⇒ oblate) indicates an associated change in orbital anisotropy (radial ⇒ tangential), with roots likely in the assembly of their host dark matter halos.

Weakly nonlinear shape oscillations of viscoelastic drops

Axisymmetric shape oscillations of a viscoelastic drop in a vacuum are studied by a weakly nonlinear analysis. The two-lobed initial drop deformation mode is studied. The Oldroyd-B model is used for characterizing the drop liquid rheological behaviour. The equations of motion and the solutions up to second order are developed, where elastic effects appear. Solutions of the characteristic equation are validated against the decay rate and frequency of damped shape oscillations of polymer solution drops in an acoustic levitator. The theory shows enhancing or dampening of the nonlinear behaviour and enhanced mode coupling, as compared with the Newtonian case. The study reveals an excess time in the prolate shape and a frequency change, together with a quasi-periodicity of the oscillations. The Fourier power spectra of traces of the drop north pole position in time show mode coupling as a nonlinear effect. At moderate stress-relaxation Deborah number, the resultant drop motion for large Ohnesorge number, suggesting aperiodic drop behaviour, may nonetheless be oscillatory, where the drop elasticity is owing to the liquid bulk elasticity instead of surface tension. A method is developed to predict the oscillatory or aperiodic behaviour of a drop of a given size from a rheologically characterized viscoelastic Oldroyd-B liquid.

BYORP and Dissipation in Binary Asteroids: Lessons from DART

The near-Earth binary asteroid Didymos was the target of the planetary defense demonstration mission DART in 2022 September. The smaller binary component, Dimorphos, was impacted by the spacecraft in order to measure momentum transfer in kinetic impacts into rubble piles. DART and associated Earth-based observation campaigns have provided a wealth of scientific data on the Didymos–Dimorphos binary. DART revealed the largely oblate and ellipsoidal shape of Dimorphos before the impact, while the postimpact observations suggest that Dimorphos now has a prolate shape. Here we add those data points to the known properties of small binary asteroids and propose new paradigms of the radiative binary Yarkovsky–O’Keefe–Radzievskii–Paddack (BYORP) effect as well as tidal dissipation in small binaries. We find that relatively spheroidal bodies like Dimorphos made of small debris may experience a weaker and more size-dependent BYORP effect than previously thought. This could explain the observed values of period drift in several well-characterized binaries. We also propose that energy dissipation in small binaries is dominated by relatively brief episodes of large-scale movement of (likely surface) materials, rather than long-term steady-state tidal dissipation. We propose that one such episode was triggered on Dimorphos by the DART impact. Depending on the longevity of this high-dissipation regime, it is possible that Dimorphos will be more dynamically relaxed in time for the Hera mission than it was in the weeks following the impact.

Testing MOND using the dynamics of nearby stellar streams

The stellar halo of the Milky Way is built up at least in part from debris from past mergers. The stars from these merger events define substructures in phase space, for example in the form of streams, which are groups of stars that move on similar trajectories. The nearby Helmi streams discovered more than two decades ago are a well-known example. Using 6D phase-space information from the Gaia space mission, recent work showed that the Helmi streams are split into two clumps in angular momentum space. This substructure can be explained and sustained in time if the dark matter halo of the Milky Way takes a prolate shape in the region probed by the orbits of the stars in the streams. Here, we explore the behaviour of the two clumps identified in the Helmi streams in a modified Newtonian dynamics (MOND) framework to test this alternative model of gravity. We performed orbit integrations of Helmi streams member stars in a simplified MOND model of the Milky Way and using the more sophisticated phantom of RAMSES simulation framework. We find with both approaches that the two Helmi streams clumps do not retain their identity and dissolve after merely Myr. This extremely short timescale would render the detection of two separate clumps very unlikely in MONDian gravity. The observational constraints provided by the streams, which MOND fails to reproduce in its current formulation, could potentially also be used to test other alternative gravity models.

Analysis of Treatment Discontinuation in Orthokeratology: Studying Efficacy, Safety, and Patient Adherence Over Six Months.

This study aimed to evaluate the efficacy, safety, and participant compliance of orthokeratology treatment for the correction of myopic refractive errors over a six-month prospective study and to define the potential reasons for early treatment discontinuation. A total of 32 participants with low-to-moderate myopia were fitted with the spherical model of corneal refractive therapy (CRT) orthokeratology lenses (Paragon Vision Sciences) and followed over six months, with specific attention to alterations in refractive error, corneal topography, and epithelial thickness. Concurrently, participant feedback and reasons for any treatment discontinuation were documented. Significant changes in refractive error and in corneal topography were observed, with approximately 50% of the refractive error being corrected on the first night of use and 100% by the first two weeks ( P <0.001). Central epithelial thickness experienced substantial thinning, reducing to 15.65±4.49 μm (67.38%) ( P <0.001) after 6 months of lens use. Six participants withdrew from this study for varied reasons, including unmet visual expectations and difficulty adhering to the lens-wearing regimen. Notably, the dropout group exhibited higher baseline low-order aberrations and less prolate corneas than those who persisted with the treatment ( P <0.05). Orthokeratology with CRT is efficacious and safe for the correction of low-to-moderate myopia in adults, but a portion of patients discontinue the treatment in the first 6 months of contact lens wear. Special care should be taken when recommending orthokeratology in patients with higher levels of myopia and corneas with less prolate shape, providing more realistic expectations and even changing to dual axis or more sophisticated designs.

On the equilibrium points of the collinear restricted 4-body problem with non-spherical bodies

This study investigates a variation of the collinear restricted four-body problem, introducing complexity by incorporating the oblate or prolate shapes of the three primary bodies. Employing various numerical techniques, we analyze the dynamical properties of the equilibrium points within the system. In addition to identifying the coordinates of the libration points, we examine their linear stability and dynamic classifications. Our primary focus is on understanding the interplay between the system’s mass and shape parameters, revealing how they collectively influence equilibrium dynamics. Specifically, our results demonstrate that oblate-shaped peripheral bodies consistently produce six (6) equilibrium points, while prolate spheroids yield an even number – 6, 10, 14, or 18 – depending on the specific mass and shape parameters.

Anisotropic Particle Deposition Kinetics from Quartz Crystal Microbalance Measurements: Beyond the Sphere Paradigm.

Deposition kinetics of polymer particles characterized by a prolate spheroid shape on gold sensors modified by the adsorption of poly(allylamine) was investigated using a quartz crystal microbalance and atomic force microscopy. Reference measurements were also performed for polymer particles of a spherical shape and the same diameter as the spheroid shorter axis. Primarily, the frequency and dissipation shifts for various overtones were measured as a function of time. These kinetic data were transformed into the dependence of the complex impedance, scaled up by the inertia impedance, upon the particle size to the hydrodynamic boundary layer ratio. The results obtained for low particle coverage were interpolated, which enabled the derivation of Sauerbrey-like equations, yielding the real particle coverage using the experimental frequency or dissipation (bandwidth) shifts. Experiments carried out for a long deposition time confirmed that, for spheroids, the imaginary and real impedance components were equal to each other for all overtones and for a large range of particle coverage. This result was explained in terms of a hydrodynamic, lubrication-like contact of particles with the sensor, enabling their sliding motion. In contrast, the experimental data obtained for spheres, where the impedance ratio was a complicated function of overtones and particle coverage, showed that the contact was rather stiff, preventing their motion over the sensor. It was concluded that results obtained in this work can be exploited as useful reference systems for a quantitative interpretation of bioparticle, especially bacteria, deposition kinetics on macroion-modified surfaces.

Structural and dynamical equilibrium properties of hard board-like particles in parallel confinement.

We performed Monte Carlo and dynamic Monte Carlo simulations to model the diffusion of monodispersed suspensions composed of impenetrable cuboidal particles, specifically hard board-like particles (HBPs), in the presence of parallel hard walls. The impact of the walls was investigated by adjusting the size of the simulation box while maintaining constant packing fractions, fixed at η = 0.150, for systems consisting of HBPs with prolate, dual-shaped, and oblate geometries. We observed that increasing the distance between the walls led to the recovery of an isotropic bulk phase, while local particle organization near the walls remained stable. Due to their shape, oblate HBPs exhibit more efficient anchoring at wall surfaces compared to prolate shapes. The formation of nematic-like particle assemblies near the walls, confirmed by theoretical calculations based on density functional theory, significantly influenced local particle dynamics. This effect was particularly pronounced to the extent that a modest portion of cuboids near the walls tended to diffuse exclusively in planes parallel to the confinement, even more efficiently than observed in the bulk regions.

Three-dimensional choroidal contour mapping in healthy population

Purpose was to study 3-dimensional choroidal contour at choroidal inner boundary (CIB) and choroidal outer boundary (COB) in healthy eyes. Healthy eyes imaged on wide field swept-source optical coherence tomography were included. Delineation of CIB and COB was done based on our previously reported methods. Quantitative analysis of the surfaces of CIB and COB was based on analyzing best fit spherical radius (R) (overall and sectoral). One hundred and seven eyes of 74 subjects with a mean age of 46.4 ± 19.3 years were evaluated. Overall, R COB (mean ± SD: 22.5 ± 4.8 mm) < R CIB (32.4 ± 9.4 mm). Central sector had the least R at COB (7.2 ± 5.9 mm) as well as CIB (25.1 ± 14.3 mm) across all age groups. Regression analysis between R (CIB) and age (r = −0.31, r2 = 0.09) showed negative correlation (P < 0.001) and that between R (COB) and age was positive (r = 0.26, r2 = 0.07) (P = 0.01). To conclude, central sector is the steepest sector in comparison to all the other sectors. This is indicative of a prolate shape of choroidal contour at CIB and COB. Outer boundary of choroid is steeper than inner boundary across all age groups. However, with ageing, outer boundary becomes flatter and inner boundary becomes steeper.

The Strength and Shapes of Contact Binary Objects

While contact binary objects are common in the solar system, their formation mechanism is unclear. In this work we examine several contact binaries and calculate the necessary strength parameters that allow the two lobes to merge without the smaller of the two being gravitationally destroyed by the larger. We find a small but nonzero amount of cohesion or a large friction angle is required for the smaller lobe to survive the merging process, consistent with observations. This means it is possible for two previously separated rubble piles to experience a collapse of their mutual orbit and form a contact binary. The necessary strength required to survive this merger depends on the relative size, shape, and density of the body, with prolate shapes requiring more cohesion than oblate shapes.