Spherical Objects Research Articles

A three-dimensional curve interface reconstruction algorithm for two-phase fluid flow

The curve interface reconstruction algorithm has received significant attention in the context of two-dimensional two-phase flow. However, it remains absent in the three-dimensional scenario. This paper proposes a novel three-dimensional curve interface reconstruction (CIR) algorithm to address this challenge within structured meshes for the first time. Specifically, a portion of the spherical surface is employed to reconstruct the three-dimensional curve interface segment, with the radius and center coordinates determined by curvature and mass conservation constraints, respectively. To enhance curvature accuracy, a sphere-based iterative reconstruction (SIR) algorithm is proposed to calculate the reconstructed distance function (RDF) for the three-dimensional curve interface. Various tests involving the interface reconstruction of spherical, ellipsoidal, and cubic objects demonstrate that the coupled SIR and CIR (SIR-CIR, simplified by SCIR) method achieves higher accuracy than many popular methods, particularly with coarse mesh resolutions. Additionally, the SCIR method offers the advantages of straightforward implementation and coding for interface reconstruction in two-phase flow research. This advantage results in reduced computational costs compared to the coupled volume-of-fluid and level set (VOSET) method, which also utilizes an iterative method to solve RDF.

Enhanced bubble growth near an advancing solidification front

Frozen water might appear opaque since gas bubbles can get trapped in the ice during the freezing process. They nucleate and then grow near the advancing solidification front, due to the formation of a gas supersaturation region in its vicinity. A delicate interplay between the rate of mass transfer and the rate of freezing dictates the final shapes and sizes of the entrapped gas bubbles. In this work, we experimentally and numerically investigate the initial growth of such gas bubbles that nucleate and grow near the advancing ice front. We show that the initial growth of these bubbles is governed by diffusion and is enhanced due to a combination of the presence of the background gas concentration gradient and the motion of the approaching front. Additionally, we recast the problem into that of mass transfer to a moving spherical object in a homogeneous concentration field, finding good agreement between our experimental data and the existing scaling relations for that latter problem. Lastly, we address how fluid flow around the bubble might further affect this growth and qualitatively explore this through numerical simulations.

Remarks on the nodal quiver

We study an admissible subcategory of the nodal quiver which conjecturally does not admit any Bridgeland stability conditions. Specifically, we prove that its Serre functor coincides with the spherical twist associated with a 3-spherical object. As a consequence, we obtain a classification of the spherical objects, deduce the non-existence of Serre-invariant stability conditions, and construct a natural spherical functor from its structure as a categorical resolution of the nodal cubic curve.

Bionic Robot with Multifunctional Leg-Arm Mechanism for In-Orbit Assembly of Space Trusses.

This article aims to address the in-orbit assembly needs of truss structures in space missions by designing a robot capable of moving on trusses and manipulating parts. To enhance the stability of the robot during movement and part manipulation, inspiration was drawn from the Dynastes Hercules beetle. Building upon detailed research on the Dynastes Hercules beetle, a biomimetic structure was designed for the robot system. Based on specific task requirements, the overall plan of the robot was developed, and its kinematic and dynamic models were derived. A prototype of the robot was created, which is capable of both movement and assembly functions, including handling spherical and rod-like objects. Through a series of experiments conducted with the robot, the research results demonstrated that the proposed design can effectively achieve the intended functions.

Calculation of the Point of Application (Centre of Pressure) of Force and Torque Imparted on a Spherical Object from Gyroscope Sensor Data, Using Sports Balls as Practical Examples.

This study investigates the determination of the centre of pressure (COP) on spherical sports objects such as cricket balls and footballs using gyroscope data from Inertial Measurement Units (IMUs). Conventional pressure sensors are not suitable for capturing the tangential forces responsible for torque generation. This research presents a novel method to calculate the COP solely from gyroscope data and avoids the complexity of isolating user-induced accelerations from IMU data. The COP is determined from the cross-product of consecutive torque vectors intersecting the surface of the sphere. Effective noise management techniques, including filtering and data interpolation, were employed to improve COP visualisation. Experiments were conducted using a smart cricket ball and a smart football. Validation tests using spin rates between 7.5 and 12 rps and torques ranging from 0.08 to 0.12 Nm confirmed consistent COP clustering around the expected positions. Further analysis extended to various spin bowling deliveries recorded using a smart cricket ball, and a curved football kick recorded using a smart football demonstrated the wide applicability of the method. The COPs of various spin bowling deliveries showed adjacent positions on the surface of the ball, traversing through backspin, sidespin and topspin, excluding the flipper and doosra deliveries. The calculation of the COP on the surface of the soccer ball could only be achieved by increasing the data sampling frequency sevenfold using curve fitting. Knowledge and use of the COP position offers significant advances in understanding and analysing ball dynamics in sports.

Position dependence of the standing-wave radiation pressure quadrupole projection on a sphere applied to drop shape.

There have been decades of interest in using the ultrasonic radiation pressure of standing waves to deform nearly spherical objects. An analytical approach sometimes associated with the present author involves approximating projections of the radiation pressure on spheres small in comparison with the wavelength and calculating the response to that projection. In 1981, for small fluid spheres, some terms in the quadrupole projection were published along with the dependence on the size and location of the sphere. An associated application was the flattening of levitated drops in air which are attracted toward velocity antinodes of a standing wave having horizontal equiphase surfaces. In subsequent applications of those results, the predicted analytical dependence on the location of the drop is frequently neglected. For the case of small weakly deformed drops in air in normal gravity, that omission is shown to result in an overestimation of the deformation and of the magnitude of the quadrupole radiation pressure projection. The present discussion simplifies the early results when applied to oblate drops and illustrates the consequence of including the position dependence on the modified small deformation. For large trapped oblate bubbles in water (also reviewed), the shape and location depend on the size.

Characterization of human lightness discrimination thresholds for independent spectral variations.

The lightness of an object is an intrinsic property that depends on its surface reflectance spectrum. The visual system estimates an object's lightness from the light reflected off its surface. However, the reflected light also depends on object extrinsic properties of the scene, such as the light source. For stable perception, the visual system needs to discount the variations due to the object extrinsic properties. We characterize this perceptual stability for variation in two spectral properties of the scene: the reflectance spectra of background objects and the intensity of light sources. We measure human observers' thresholds of discriminating computer-generated images of 3D scenes based on the lightness of a spherical target object in the scene. We measured change in discrimination thresholds as we varied the reflectance spectra of the objects and the intensity of the light sources in the scene, both individually and simultaneously. For small amounts of extrinsic variations, the discrimination thresholds remained nearly constant indicating that the thresholds were dominated by observers' intrinsic representation of lightness. As extrinsic variation increased, it started affecting observers' lightness judgment and the thresholds increased. We estimated that the effects of extrinsic variations were comparable to observers' intrinsic variation in the representation of object lightness. Moreover, for simultaneous variation of these spectral properties, the increase in threshold squared compared to the no-variation condition was a linear sum of the corresponding increase in threshold squared for the individual properties, indicating that the variations from these independent sources combine linearly.

Framework for charged compact objects admitting conformal motion in higher dimension.

We propose a new framework for spherical charged compact objects admitting conformal motion in five-dimensional spacetime. The outer spacetime is considered as Reissner-Nordström to obtain matching conditions. The behavior of model characteristics like stress, pressure, and surface tension for the specific density profile is investigated by using Einstein's Maxwell field equations in a five-dimensional framework. For the proposed solution, all physical parameters behave very well even for variations in electric charge parameters. The existence of charged compact stars is also predicted by this study.

Spherical objects in dimensions two and three

This paper classifies spherical objects in various geometric settings in dimensions two and three, including both minimal and partial crepant resolutions of Kleinian singularities, as well as arbitrary flopping 3 -fold contractions with only Gorenstein terminal singularities. The main result is much more general: in each such setting, we prove that all objects in the associated null category \mathcal{C} with no negative Ext groups are the image, under the action of an appropriate braid or pure braid group, of some object in the heart of a bounded t-structure. The corollary is that all objects x which admit no negative Exts, and for which \mathrm{Hom}_{\mathcal{C}}(x,x)=\mathbb{C} , are the images of the simples. A variation on this argument goes further and classifies all bounded t-structures on \mathcal{C} . There are multiple geometric, topological and algebraic consequences, primarily to autoequivalences and stability conditions. Our main new technique also extends into representation theory, and we establish that in the derived category of a finite-dimensional algebra which is silting discrete, every object with no negative Ext groups lies in the heart of a bounded t-structure. As a consequence, every semibrick complex can be completed to a simple-minded collection.

Numerical Modeling of Anisotropic Particle Diffusion through a Cylindrical Channel.

The transport of molecules and particles through single pores is the basis of biological processes, including DNA and protein sequencing. As individual objects pass through a pore, they cause a transient change in the current that can be correlated with the object size, surface charge, and even chemical properties. The majority of experiments and modeling have been performed with spherical objects, while much less is known about the transport characteristics of aspherical particles, which would act as a model system, for example, for proteins and bacteria. The transport kinetics of aspherical objects is an especially important, yet understudied, problem in nanopore analytics. Here, using the Wiener process, we present a simplified model of the diffusion of rod-shaped particles through a cylindrical pore, and apply it to understand the translation and rotation of the particles as they pass through the pore. Specifically, we analyze the influence of the particles' geometrical characteristics on the effective diffusion type, the first passage time distribution, and the particles' orientation in the pore. Our model shows that thicker particles pass through the channel slower than thinner ones, while their lengths do not affect the passage time. We also demonstrate that both spherical and rod-shaped particles undergo normal diffusion, and the first passage time distribution follows an exponential asymptotics. The model provides guidance on how the shape of the particle can be modified to achieve an optimal passage time.

Autoequivalences of blow‐ups of minimal surfaces

AbstractLet be the blow‐up of in a finite set of very general points. We deduce from the work of Uehara [Trans. Amer. Math. Soc. 371 (2019), no. 5, 3529–3547] that has only standard autoequivalences, no non‐trivial Fourier–Mukai partners, and admits no spherical objects. If is the blow‐up of in 9 very general points, we provide an alternate and direct proof of the corresponding statement. Further, we show that the same result holds if is a blow‐up of finitely many points in a minimal surface of non‐negative Kodaira dimension which contains no ‐curves. Independently, we characterize spherical objects on blow‐ups of minimal surfaces of positive Kodaira dimension.

Portable Flexible Spherical Origami Joule‐Heaters with Aerogel

AbstractTrending portable smart devices are providing great convenience to the daily life. Thermal conductivity is efficient for contact heat transfer. Unfortunately, existing rigid surfaces can hardly heat objects in arbitrary shapes. Herein, a flexible origami‐structure heater fabricated by scalable laser manufacturing with temperature feedback control is proposed. The thin film origami heater is designed as a pair of semispherical origami patterns, which can conform to the curved surface of food samples more effectively. Therefore, the heat conducting area is increased to generate a fast and even heating profile to the surface of the food samples. The outer aerogel provides high thermal insulation to prevent heat dissipation in the environment. As proof of concept, the heating device can cook quail eggs within 3 minutes at a constant temperature of 100 °C. The power consumption of this heater is as low as 18 W, which standard portable chargers can power. This work significantly promotes the usability of portable heaters for cooking spherical objects, providing more conveniences during outdoor hiking and even in outer space where water‐boiling is impossible without atmosphere and gravity.

Mathematical Modeling of the Heat Transfer Process in Spherical Objects with Flat, Cylindrical and Spherical Defects

This paper proposes a method for determining the optimal parameters for the thermal testing of plant tissues of fruits and vegetables containing surface and subsurface defects in the form of areas of plant tissues with different thermophysical characteristics. Based on well-known mathematical models for objects of predominantly flat, cylindrical and spherical shapes containing flat, spherical and cylindrical regions of defects, numerical solutions of three-dimensional, non-stationary temperature fields were found, making it possible to measure the power and time of the thermal exposure of the sample surface to the radiation from infrared lamps using the finite element method. This made it possible to ensure the reliable detection of a temperature contrast of up to 4 °C between the defect and defect-free regions of the test object using modern thermal imaging cameras. In this case, subsurface defects can be detected at a depth of up to 3 mm from the surface. To determine the parameters of mathematical models of temperature fields, such as thermal conductivity and a coefficient of the thermal diffusivity of plant tissues, a new method of a pulsed heat flux from a flat heater is proposed; this differs in the method of processing experimental data and makes it possible to determine the required characteristics with high accuracy during the active stage of the experiment in a period not exceeding 1–3 min.

Artificial High- and Low-density Materials in Bone Mineral Densitometry Using Dual-energy X-ray Absorptiometry: A GATE Monte Carlo Simulation of "Black-hole" Artifact.

The objective of the study was to evaluate the effect of artificial high- and low-density materials on Bone mineral density (BMD)scans in dual-energy X-ray absorptiometry (DXA) method and emergence of black-hole artifact through GATE Monte Carlo simulation. GATE Monte Carlo code was utilized to simulate the artifact encountered in clinical scans acquired by HOLOGIC® bone densitometer. Two simplified phantoms were designed. The first one was a rectangular box with six smaller cubes inside and the second one was a body torso. Materials of cubes were spine bone, polymethyl methacrylate (PMMA), barium sulfate suspension in water, stainless steel, titanium alloy, and gold. The torso phantom contained objects of 5 vertebrae, bowel and 3 small spherical objects near the surface of the torso as piercing objects on the abdominal wall, each overlying the vertebrae. Using 100 and 140 kVp, spectral X-rays were generated to simulate DXA. For both phantoms, two simulations were carried out. The pair of projections acquired for each phantom were then subtracted and analyzed by curve fitting techniques. Except for spine bone, in which radio-opacity decreases with increasing spectral X-ray energy (from 100 to 140 kVp), other squares exhibit little changes over different energies. PMMA shows consistently very low radio-opacity. Four other materials (barium sulfate in water, stainless steel alloy, titanium alloy, and gold), all attenuate the X-ray photons substantially. Except for spine bone, other materials are barely noticeable in pairwise subtracted images. In torso phantom, piercing objects are visualized as "holes" in vertebrae. Both artificial high- and low-density materials, compared to bone, are eliminated during the subtraction of dual-energy X-ray profiles and therefore, can create black-hole artifact.

A toolkit for the dynamic study of air sacs in siamang and other elastic circular structures.

Biological structures are defined by rigid elements, such as bones, and elastic elements, like muscles and membranes. Computer vision advances have enabled automatic tracking of moving animal skeletal poses. Such developments provide insights into complex time-varying dynamics of biological motion. Conversely, the elastic soft-tissues of organisms, like the nose of elephant seals, or the buccal sac of frogs, are poorly studied and no computer vision methods have been proposed. This leaves major gaps in different areas of biology. In primatology, most critically, the function of air sacs is widely debated; many open questions on the role of air sacs in the evolution of animal communication, including human speech, remain unanswered. To support the dynamic study of soft-tissue structures, we present a toolkit for the automated tracking of semi-circular elastic structures in biological video data. The toolkit contains unsupervised computer vision tools (using Hough transform) and supervised deep learning (by adapting DeepLabCut) methodology to track inflation of laryngeal air sacs or other biological spherical objects (e.g., gular cavities). Confirming the value of elastic kinematic analysis, we show that air sac inflation correlates with acoustic markers that likely inform about body size. Finally, we present a pre-processed audiovisual-kinematic dataset of 7+ hours of closeup audiovisual recordings of siamang (Symphalangus syndactylus) singing. This toolkit (https://github.com/WimPouw/AirSacTracker) aims to revitalize the study of non-skeletal morphological structures across multiple species.

3D microscopic reconstruction of pearls using combined optical microscopy and photogrammetry

In this study, we introduce an affordable and accessible method that combines optical microscopy and photogrammetry to reconstruct 3D models of Tahitian pearls. We present a novel device designed for acquiring microscopic images around a sphere using translational displacement stages and outline our method for reconstructing these images. We successfully created 3D models of two individual pearl rings, each representing 6.3% of the pearl’s surface. Additionally, we generated a combined model representing 10.3% of the pearl’s surface. This showcases the potential for reconstructing entire pearls with appropriate instrumentation. We emphasize that our approach extends beyond pearls and spherical objects and can be adapted for various object types using appropriate acquisition devices. We provide a proof of concept demonstrating the feasibility of 3D photogrammetry using optical microscopy. Consequently, our method offers a practical and cost-effective alternative for generating 3D models at a microscopic scale, particularly when detailed internal structure information is unnecessary.

Spherical objects, transitivity and auto-equivalences of Kodaira cycles via gentle algebras

This paper studies the class of spherical objects over any Kodaira n -cycle of projective lines and provides a parametrization of their isomorphism classes in terms of closed curves on the n -punctured torus without self-intersections. Employing recent results on gentle algebras, we derive a topological model for the bounded derived category of any Kodaira cycle. The groups of triangle auto-equivalences of these categories are computed and are shown to act transitively on isomorphism classes of spherical objects. This answers a question by Polishchuk (2002) and extends earlier results by Burban–Kreußler (2012) and Lekili–Polishchuk (2019). The description of auto-equivalences is further used to establish faithfulness of a mapping class group action defined by Sibilla (2014). The final part describes the closed curves which correspond to vector bundles and simple vector bundles. This leads to an alternative proof of a result by Bodnarchuk–Drozd–Greuel (2012) which states that simple vector bundles on cycles of projective lines are uniquely determined by their multi-degree, rank and determinant. As a by-product, we obtain a closed formula for the cyclic sequence of any simple vector bundle on C_{n} as introduced by Burban–Drozd–Greuel (2001).

A Revisit of Electromagnetic Wave Scattering by a Metal Isotropic Body in a Lossless Environment with Magnetic Sensor Excitation.

This paper investigates the electromagnetic fields being scattered by a metal spherical object in a vacuum environment, providing a numerical implementation of the obtained analytical results. A time-harmonic magnetic dipole source, far enough, emits the incident field at low frequencies, oriented arbitrarily in the three-dimensional space. The aim is to find a detailed solution to the scattering problem at spherical coordinates, which is useful for data inversion. Based on the theory of low frequencies, the Maxwell-type problem is transformed into Laplace's or Poisson's interconnected equations, accompanied by the proper boundary conditions on the perfectly conducting sphere and the radiation conditions at infinity, which are solved gradually. Broadly, the static and the first three dynamic terms are sufficient, while the terms of a higher order are negligible, which is confirmed by the field graphical representation.

Extended decoupled static spherical objects in $$f({\mathbb {R}},T)$$ theory

Extended decoupled static spherical objects in $$f({\mathbb {R}},T)$$ theory

Flexural-gravity wave forces acting on a submerged spherical object over a flexible sea bed

ABSTRACT A study has been conducted to analyse the impact of an ice sheet on the flexural-gravity wave force acting on a neutrally buoyant, spherical object immersed in a sea in accordance with the linear wave hypothesis. The bottom of the sea is presumed to be protected by a surface composed of some sort of flexibility, and the top is enclosed by an ice sheet. The solution to a diffraction problem is established using the multipole method. The estimated vertical and horizontal flexural-gravity wave forces are visualized in relation to different immersion depths of the spherical body, depths of the fluid and various flexural rigidities of the ice plate and the flexible seabed. The approach adopted here is likely to be of immense significance in the construction of various spherical gadgets like a seabed pressure detector device for tsunami recognition or communication in crisis for a submarine in earthquake zones.