Spherical Objects Research Articles

Quantum Entropy and the Mechanism of Gravity

Quantum entropy measures the number of possible microstates of position and momentum due to quantum uncertainty. Black hole entropy is an example of quantum entropy. Classical entropy, like the Gibbs entropy of a gas, does not depend on quantum uncertainty. This paper is the first to define the quantum entropy of ordinary matter, termed “atomic entropy”. The atomic entropy at the surface of a spherical object depends on its mass and is inversely proportional to its surface area. The entropy scale factor (ESF) is a theory that all changes in the scale of spacetime are due to differences in entropy. Defining atomic entropy allows the ESF to make predictions for systems including ordinary matter. In the ESF, gravitational objects are attracted to one another because gravitational entropy, a form of quantum entropy, increases as the distance between these objects decreases. The increase in gravitational entropy increases the total entropy of the system, in accordance with the second law of thermodynamics. This paper is also the first to use the gradients in the scale of space and time predicted by the ESF to derive Newtonian gravity. Explaining the mechanism of gravity in this way provides a link between quantum physics and gravity.

Improving sensitivity in the deep regions of a volume conductor using electrical focused impedance methods.

Bioimpedance measurements are becoming important in probing the human body for diagnosis and monitoring. An age old 4-electrode technique called tetrapolar impedance measurement (TPIM), giving transfer impedance, cannot localize a specific zone besides having large zones of negative sensitivity. A new technique named the focused impedance method (FIM) from Dhaka University (DU), Bangladesh used the algebraic average of two concentric and orthogonal TPIMs, localizing a zone of interest and having reduced magnitudes of negative sensitivity. Earlier, this was implemented with electrodes applied from one side of the human body giving information to shallow depths only. To get information from deeper regions, specifically, of the thorax, the same DU group placed two electrodes of a 4-electrode version of FIM at the front and two at the back in a horizontal plane of the thorax, using physics-based visualization. This was followed by a few quantitative studies using point sensitivity, which supported the concept. However, more quantitative studies still need to be performed, particularly using objects of finite sizes, in order to establish the technique on a stronger footing. The present study was taken up with this objective. A simplified approach was used in which the volume conductor was a rectangular non-conducting container filled with saline of uniform conductivity with an embedded spherical object - first an insulator and then a conductor. Electrodes were placed at specific chosen positions following the above visualization. Percentage change in transfer impedance with the object placed at different internal positions, compared to that without the object was obtained first using COMSOL simulation and then through experimental measurements. These were performed for both TPIM and FIM. The new configuration of 4-electrode FIM gave good depth sensitivity supporting the effectiveness of the new placement of electrodes.

Numerical simulation of wave propagation through a spherical particle within the framework of generalised Lorenz-Mie theory

Holography has been widely used for measuring and visualising transients in multiphase flows. Earlier, one of the drawbacks of this approach was the need to register on various photosensitive elements and its subsequent transfer to digital format and restoration. With the development of digital technologies, direct registration of interference patterns (holographic images) into a CCD matrix became possible. However, even in digital holography there are a number of problems that need to be solved. These problems pertain to recovery algorithms, efficient data processing and resolution, among others. Currently, the numerical implementation of the restoration and processing of holographic images can be done within the framework of classical diffraction theory or with the help of generalised Lorenz-Mie theory. The first implies an indirect solution of Maxwell's equations, i.e., application of the Huygens-Fresnel principle. The second approach involves a direct solution of Maxwell's equations for the holographic problem. In the framework of this work, a numerical simulation of holographic imaging of fields from spherical particles based on the generalised Lorenz-Mie theory is proposed. Within the framework of this work, a numerical implementation of modelling of holographic images of a homogeneous sphere based on the generalised Lorenz-Mie theory is presented. The implementation code in the python programming language is presented. The results of the study demonstrate the possibility of effective use of digital holography for visualisation and analysis of spherical objects.

Nanoshell Formation at the Electrically Charged Gas-Water Interface of Collapsing Microbubbles: Insights from Atomic Force Microscopy Imaging.

AFM imaging has revealed intriguing features when bulk nanobubbles were deposited on a positively charged substrate. Numerous spherical objects, each less than 20 nm in diameter, were observed on the substrate. These objects were adorned with noticeable, tiny protrusions, each measuring a few nanometers. These findings suggest the presence of solid shells contributing to the stability of the gas bodies. Furthermore, electrically charged microbubbles appear to play a critical role in the formation of these solid shells. The collapse of microbubbles in an electrolyte aqueous solution containing iron ions leads to a condensing ionic cloud, creating conditions necessary for solid nucleation at the interface. At the end of the collapsing process, concurrent multinucleation may result in the deposition of solid material on the interface, forming solid shells with specific structures on the surfaces. This study illuminates the phenomenon of electrically charged gas-water interfaces during microbubble collapse and highlights the generation of stabilized nanoshells in aqueous solutions without the need for chemical stabilizers.

Моделирование поведения сферического объекта при сейсмической активности ядра

В работе на основе реологических моделей сложных сред упруговязкопластической дилатирующей и несжимаемой упруговязкопластической, а также классической несжимаемой идеально пластической среды определено напряженно-деформированное состояние сферического тела при постоянной внешней и динамической внутренней нагрузках. Исследовано осесимметричное состояние тела. Определены поля перемещений и напряжений в упругих и пластических областях. Ключевые слова: напряжение, перемещение, упругость, пластичность, вязкость, дилатансия, осесимметричное состояние. Based on the rheological models of complex media of an elastoviscoplastic dilating and incompressible elastoviscoplastic, as well as a classical incompressible ideally plastic medium, the stress-strain state of a spherical body is determined under constant external and dynamic internal loads. The axisymmetric state of the body is studied. Displacement and stress fields in elastic and plastic regions are determined. Keywords: stress, displacement, elasticity, plasticity, viscosity, dilatancy, axisymmetric state.

Investigation of the Motion of a Spherical Object Located at Soft Elastic and Viscoelastic Material Interface for Identification of Material Properties

Measuring the properties of soft viscoelastic materials is challenging. Here, the motion of a spherical object located at the soft elastic and viscoelastic material interface for the identification of material properties is thoroughly investigated. Formulations for different loading cases were derived. First, the theoretical models for a spherical object located at an elastic medium interface were derived, ignoring the medium viscosity. After summarizing the model for the force reducing to zero following the initial loading, we developed mathematical models for the force reducing to a lower non-zero value or increasing to a higher non-zero value, following the initial loading. Second, a similar derivation process was followed to evaluate the response of a spherical object located at a viscoelastic medium interface. Third, by performing systematic analyses, the theoretical models obtained via different approaches were compared and evaluated. Fourth, the measured and predicted responses of a spherical object located at a gelatin phantom interface were compared and the viscoelastic material properties were identified. It was seen that the frequency of oscillations of a spherical object located at the sample interface during loading was 10–15% different from that during unloading in the experimental studies here. The results showed that different loading cases have immense practical value and the formulations for different loading cases can provide an accurate determination of material properties in a multitude of biomedical and industrial applications.

Characterizing the Backscattered Spectrum of Mie Spheres

AbstractThis study describes both experimentally and theoretically an important hitherto undiscovered feature of the scattering of micron‐sized spherical objects when illuminated with highly focused circularly polarized light. This is a regime of high experimental relevance which has not been described in full detail. The experiments are complemented with the analytical formulas explaining the field scattered directed toward the backward hemispace. In particular, it is proven that this field shows a very regular oscillatory dependency with the optical size. This phenomenon is typically hidden in the total scattered field, as the field is scattered much less toward the backward hemisphere than toward the forward one. These regular oscillations are measured experimentally. It is proven that, by analyzing them, it is possible to determine the index of refraction of isolated micron‐sized particles, opening new paths for applications in sensing and metrology.

SphericalScattering: A Julia Package for Electromagnetic Scattering from Spherical Objects

SphericalScattering: A Julia Package for Electromagnetic Scattering from Spherical Objects

Born approximation of trapping forces by acoustical Bessel and vortex fields.

Acoustic radiation forces have been used to trap various objects for fundamental studies and practical applications. Born approximation method, originally introduced to solve quantum scattering problems, is herein extended to analyze trapping forces exerted by two- and three-dimensional acoustic Bessel and vortex fields on spherical and nonspherical objects of arbitrary size. The results are compared with the conventional models like the partial wave expansion and Gorkov force potential. It is shown that for weakly scattering objects (such as common soft biological particles surrounded by fluids), the Born approximation can make predictions for the trapping forces on objects whose characteristic lengths are even up to multiple wavelengths of the sound beams. With the aid of the approximation, the Gorkov force potential is applied to analyze and gain insights into trapping forces on large objects far beyond the original Rayleigh scattering regime. The effects caused by the beam parameters, object shape, and orientation on the trapping behaviors are revealed. This work is useful for the further study of acoustic radiation forces and will guide the experiment of simplified acoustic tweezers on arbitrary-shaped particles.

Nonlinear instability and scalar clouds of spherical exotic compact objects in scalar-Gauss-Bonnet theory

In this work, we present a new type of scalar clouds supported by spherically symmetric horizonless compact objects in the scalar-Gauss–Bonnet theory. Unlike the previous spontaneous scalarization that is triggered by the tachyonic instability, our scalarization arises from a nonlinear instability that is non-spontaneous. We explore two types of boundary conditions for the scalar field at the surface of the compact objects and find an infinite countable set of scalar clouds characterized by the number of nodes for both cases. Our study demonstrates that boundary conditions have a significant impact on the formation of scalar clouds. Specifically, for the Dirichlet boundary condition, scalarization is more likely to occur for compact objects with medium radii and becomes harder for ultra-compact and large ones. Conversely, for the Robin boundary condition, scalarization is easier for more compact objects.

A New Approach for Measuring Viscoelastic Properties of Soft Materials Using the Dynamic Response of a Spherical Object Placed at the Sample Interface

BackgroundThere are several techniques to characterize the mechanical properties of soft materials, such as the indentation method and the method based on the application of a spherical object placed inside the sample. The indentation systems usually yield the elastic properties of materials and their mathematical models do not consider the inertia of the sample involved in motion and radiation damping, while placing an object inside the sample is not practical and this procedure can alter the mechanical properties of the sample for the method based on the application of a bubble/sphere placed inside the sample.ObjectiveA new approach for the identification of the viscoelastic properties of soft materials using the dynamic response of a spherical object placed at the sample interface was proposed.MethodsThe spherical object placed at the sample interface was pressed using an electromagnet and the dynamic response of the spherical object was tracked using a high-speed camera, while the dynamic response of the spherical object placed at the sample interface was estimated using a comprehensive analytical model. The effects of the shear modulus, viscosity, Poisson’s ratio and density of the soft sample, the radius and density of the spherical object and the damping due to radiation were considered in this mathematical model. The shear modulus and viscosity of the soft sample were determined by matching the experimentally identified and theoretically estimated responses of the spherical object.ResultsThe shear moduli and viscosities of the three phantoms with the gelatin mass ratios of 0.20, 0.25 and 0.29 were measured to be 3450, 4300 and 4950 Pa and 12.5, 14.0 and 15.0 Pa⋅s, respectively. The shear modulus and viscosity of the phantom increases as the gelatin mass ratio increases. The frequency of oscillations of the hemisphere placed at the phantom interface increases as the gelatin mass ratio increases due to stiffness increase.ConclusionsAfter matching the experimental and theoretical steady-state displacements and amplitudes of oscillations of the hemisphere at the sample interface, the comparison of the experimentally identified and theoretically predicted frequency of oscillations further confirmed the identified material properties of the samples. The approach presented here is expected to provide valuable information on material properties in biomedical and industrial applications.

A partial compactification of the Bridgeland stability manifold

AbstractBridgeland stability manifolds of Calabi–Yau categories are of noticeable interest both in mathematics and physics. By looking at some of the known examples, a pattern clearly emerges and gives a fairly precise description of how they look like. In particular, they all seem to have missing loci, which tend to correspond to degenerate stability conditions vanishing on spherical objects. Describing such missing strata is also interesting from a mirror-symmetric perspective, as they conjecturally parametrize interesting types of degenerations of complex structures. All the naive attempts at constructing modular partial compactifications show how elusive and subtle the problem in fact is: ideally, the missing strata would correspond to stability manifolds of quotient triangulated categories, but establishing such a correspondence on the geometric level and viewing stability conditions on quotients of the original triangulated category as suitable degenerations of stability conditions is not straightforward. In this paper, we will present a method to construct such partial compactifications if some additional hypotheses are satisfied, by realizing our space of interest as a suitable metric completion of the stability manifold.

Can smoothed particle hydrodynamics simulate physically realistic movements of underwater vehicles?

ABSTRACT This work presents the first results using Smoothed Particle Hydrodynamics (SPH), a mesh-free technique, to simulate underwater vehicle motion with the goal of achieving sufficient physical realism and computation time performance capabilities. The objective is not to get very accurate values for the hydrodynamic parameters, but to show that SPH can simulate hydrodynamic parameters with the same order of magnitude as the reference, in order to allow a realistic control of robots in water. First, spherical objects are simulated to check buoyancy realism, speed limit existence, and hydrodynamic parameters in comparison with reference values. Then, horizontal and vertical movements of a capsule-shape object and a real torpedo-shape underwater robot are compared. The results show that buoyancy is respected, and that spherical objects reach a speed limit in accordance with the laws of physics. In addition, added-mass is simulated with 20 % variation on average with respect to the reference and varies homothetically with respect to the object's size. In contrast, drag forces cannot not be simulated with the same level of realism without reducing the particle size, which makes the simulation last longer. SPH for underwater robotics simulation appears to be promising, and ways of further improvements are being considered.

Acoustic radiation forces on spherical objects in a viscous fluid by Bessel beams

Acoustic radiation forces on spherical objects in a viscous fluid by Bessel beams

Optoplasmonic Effects in Highly Curved Surfaces for Catalysis, Photothermal Heating, and SERS.

Surface curvature can be used to focus light and alter optical processes. Here, we show that curved surfaces (spheres, cylinders, and cones) with a radius of around 5 μm lead to maximal optoplasmonic properties including surface-enhanced Raman scattering (SERS), photocatalysis, and photothermal processes. Glass microspheres, microfibers, pulled fibers, and control flat substrates were functionalized with well-dispersed and dense arrays of 45 nm Au NP using polystyrene-block-poly-4-vinylpyridine (PS-b-P4VP) and chemically modified with 4-mercaptobenzoic acid (4-MBA, SERS reporter), 4-nitrobenzenethiol (4-NBT, reactive to plasmonic catalysis), or 4-fluorophenyl isocyanide (FPIC, photothermal reporter). The various curved substrates enhanced the plasmonic properties by focusing the light in a photonic nanojet and providing a directional antenna to increase the collection efficacy of SERS photons. The optoplasmonic effects led to an increase of up to 1 order of magnitude of the SERS response, up to 5 times the photocatalytic conversion of 4-NBT to 4,4'-dimercaptoazobenzene when the diameter of the curved surfaces was about 5 μm and a small increase in photothermal effects. Taken together, the results provide evidence that curvature enhances plasmonic properties and that its effect is maximal for spherical objects around a few micrometers in diameter, in agreement with a theoretical framework based on geometrical optics. These enhanced plasmonic effects and the stationary-phase-like plasmonic substrates pave the way to the next generation of sensors, plasmonic photocatalysts, and photothermal devices.

Machine Learning Assisted Monte Carlo Simulation: Efficient Overlap Determination for Nonspherical Hard Bodies

AbstractStandard molecular dynamics (MD) and Monte Carlo (MC) simulations deal with spherical particles. Extending the standard simulation methodologies to the nonspherical objects is non‐trivial. To circumvent this problem, nonspherical bodies are often treated as a collection of constituent spherical objects. As the number of these constituent objects becomes large, the computational burden to simulate the system also increases. Here, an alternative way is proposed to simulate nonspherical rigid bodies having pairwise repulsive interactions. This approach is based on a machine learning (ML)‐based model, which predicts the overlap between two nonspherical bodies. The ML model is easy to train and the computation cost of its implementation remains independent of the number of constituent spheres used to represent a nonspherical rigid body. When used in MC simulation, this method is faster than the standard implementation, where overlap determination is based on calculating the distance between constituent spheres. This proposed ML‐based MC method produces similar structural features (in comparison to the standard implementation) in both two and three dimensions, and can qualitatively capture the isotropic to nematic transition of rigid rods in three dimensions. It is believed that this work is a step toward a time‐efficient simulation of non‐spherical rigid bodies.

A photoelastic method for stress analysis of granular terrain beneath a wheel

This paper presents a photoelastic method for the stress analyses of granular terrains beneath a traveling wheel. Recently, wheel terramechanics have been studied using various advanced techniques such as particle velocimetry and machine learning. However, the dynamic profiles of the stress distributions in soil have not been directly observed. In this paper, we propose a photoelastic method to experimentally demonstrate the two-dimensional stress analysis of a granular terrain. This method uses photoelastic disks as terrain particles; thus, the internal stress and propagation of the granular terrain can be visualized using the interference fringe of light. This study aimed to observe the dynamic behavior of grains, typically simulating circular or spherical objects of the granular terrain. To demonstrate the photoelastic method for simulated ground, we developed a single-wheel testbed using photoelastic materials. Moreover, the effects of mixing with non-photoelastic materials were investigated to simulate steady states with small and large wheel-slip conditions. This paper presents a force chain analysis of the photoelastic particles beneath a single traveling wheel. The force chain structure was geometrically compared with the propagation angle and length. In addition, the orientational orders of the force chains were quantitatively evaluated under both small and large wheel slip conditions. The experimental results confirmed that the photoelastic method can reveal dynamic changes in the internal stress structures of granular terrain beneath the wheel under various slip conditions.

Fatigue evaluation on the effect of impact pits with various impact conditions by a CDM‐based approach

AbstractThis work aims to quantitatively evaluate the influence of the impact velocity, location, and angle of a spherical foreign object on fatigue lives. A continuum damage mechanics (CDM)–based fatigue approach is proposed to evaluate the fatigue behavior. The experiments on a cast AlSi7Mg1 aluminum alloy with a low‐velocity impact pit are used to validate the proposed fatigue model. The comparison between the predicted lives with the experimental data indicates an excellent agreement. Based on the proposed model, the effects of various impact velocities, locations, and angles are investigated. It is found that the velocities have negligible influence on the fatigue life in low‐velocity impact cases once the pit depth is the same. The most dangerous impact location for 90° normal impact cases is inferred to be a distance away from the boundary surface. The 45° transverse impact close to the boundary is different from other studied oblique impacts and has a longer life than the corresponding normal impact. This study uses a feasible method to predict the effects of different impact conditions and provides useful guidance for engineering applications.

Impact of a spherical body on an air-inflated membrane structure

The present work studies the impact of a spherical object on an air-inflated airbag like structure which is generated by internally pressurizing two circumferentially-bonded circular membranes, described by Yeoh hyperelastic model. During impact, the frontal membrane is in contact with the spherical body, and the rear membrane with a flat rigid substrate. The quasi-static frictionless contact problem is first solved numerically using variational approach, and then the static contact profile is perturbed to consider the dynamics during impact. The velocity of the impacting body is observed to be dropping rapidly during dynamic impact as compared to the quasi-static case.

Exceptional cycles in triangular matrix algebras

An exceptional cycle in a triangulated category with Serre functor is a generalization of a spherical object. Suppose that A and B are Gorenstein algebras, given a perfect exceptional n-cycle E⁎ in Kb(A-proj) and a perfect exceptional m-cycle F⁎ in Kb(B-proj), we construct an A-B-bimodule N, and prove the product E⁎⊠F⁎ is an exceptional (n+m−1)-cycle in Kb(Λ-proj), where Λ=(AN0B). Using this construction, one gets many new exceptional cycles which is unknown before for certain class of algebras.