Search

The objective of this research is to investigate the findings in the perturbed restricted three-body problem involving oblate spheroids as the primary bodies. The analysis focuses on examining the influence of small perturbations in Coriolis and centrifugal forces, as well as the implementation of a new mean motion. The dynamical system is formulated, and the equations of motion for the infinitesimal body are derived accordingly. Five equilibrium points are identified within the current configuration, and their positions are subsequently affected by variations in mass, oblateness, and perturbed centrifugal force parameters. Furthermore, we have performed a comprehensive numerical and graphical analysis to observe and understand the impact of the various parameters on the position of the equilibrium points. We have also conducted a detailed stability analysis to examine the behavior of the equilibrium points. It is observed that the collinear equilibrium points are unstable, indicating that even slight disturbances can cause the system to deviate from these points. However, the non-collinear equilibrium points exhibited stability under certain combinations of the involved parameters. By plotting the zero velocity curves for different values of the Jacobian constant, we have gained insights into the regions where the infinitesimal body can freely move. Remarkably, our observations showed that as the Jacobian constant decreased within the considered range of parameters, the permissible regions of motion for the infinitesimal body expanded, providing it with more freedom in it. [ABSTRACT FROM AUTHOR]

This study analyzes the motion of two infinitesimal bodies in the restricted problem of bodies, including an oblate spheroid and straight segment as primary bodies, along with the photogravitational effect of the more massive primary. The pertinent equations of motion of the infinitesimal bodies in the dimensionless variables are obtained by incorporating the effect caused by the oblateness, radiation pressure, and straight segment. On close examination of the parameters involved in the problem, a study of the equilibrium points of the dynamical system reveals that six of them are collinear with primary bodies' centers, while the remaining eight are not. An in-depth study is done on how the position of the equilibrium points changes with respect to the radiation parameter. The permissible and forbidden regions of motion are shown, and it is inferred that when the Jacobian constant is decreased, the permissible regions of motion expand. Furthermore, a linear stability analysis of the generated equilibrium points is done, and we observe that all the equilibrium points are unstable for a set of values of the model's parameters. [ABSTRACT FROM AUTHOR]

Triboelectric nanogenerators (TENGs) to harvest ocean wave blue energy is flourishing, yet the research horizon has been limited to centimeter‐level TENG. Here, for the first time, a TENG shell is advanced for ocean energy harvesting to 0.5 m and an excellent frictional areal density of 1.03 cm−1 and economies of scale are obtained. The unique structure of the multi‐arch shape is adopted to untie the difficulty of fully getting the extensive friction layer contact. An inside steel plate is vertically placed in the center of every TENG block, which can activate the TENG to achieve complete contact even at a tilt angle of 7 degrees. The proposed half‐meter TENG (HM‐TENG) has a broad response band from 0.1 to 2 Hz, a total transferred charge quantity up to 67.2 µC, and one single TENG can deliver an open‐circuit voltage of 368 V. Coupled with the self‐stabilizing and susceptible features the ellipsoid shell brings, the HM‐TENG can readily accommodate itself to the all‐weather, all‐sea wave energy harvesting. Muchmore, the HM‐TENG is also applied to RF signal transmitters. This work takes the first step toward near‐meter‐scale enclosures and provides a new direction for large‐scale wave energy harvesting. [ABSTRACT FROM AUTHOR]

• The superellipsoid model is statistically superior to the oblate spheroid model for 60% of platelets. • Precision of recognized platelet fractions is increased by suggestion of superellipsoid model. • The inverse light scattering problem was solved faster using the hybrid method. • The DIRECT method employs linear interpolation between the regular database node. In this work, we propose a new optical model to describe the morphology of a platelet in the form of a special axisymmetric superellipsoid. This model is more general than the widely used classical oblate spheroid model of the platelet and includes the oblate spheroid as a special case. The inverse light scattering (ILS) problem within the developed optical model was solved using the light scattering profile (LSP) of individual platelets obtained by the scanning flow cytometer. Solving the ILS problem we used a hybrid method that combines the DIRECT algorithm of global optimization with the linear interpolation between the nodes of the pre-calculated regular database of superellipsoid LSPs. The statistical F-test shows that the new optical model is better than the conventional oblate spheroid model in more than 60 percent of cases. This made it possible to obtain the refined shape index distributions for platelets consisting of three fractions, namely resting, partially and fully activated platelets. [ABSTRACT FROM AUTHOR]

Abstract Triboelectric nanogenerators (TENGs) to harvest ocean wave blue energy is flourishing, yet the research horizon has been limited to centimeter‐level TENG. Here, for the first time, a TENG shell is advanced for ocean energy harvesting to 0.5 m and an excellent frictional areal density of 1.03 cm−1 and economies of scale are obtained. The unique structure of the multi‐arch shape is adopted to untie the difficulty of fully getting the extensive friction layer contact. An inside steel plate is vertically placed in the center of every TENG block, which can activate the TENG to achieve complete contact even at a tilt angle of 7 degrees. The proposed half‐meter TENG (HM‐TENG) has a broad response band from 0.1 to 2 Hz, a total transferred charge quantity up to 67.2 µC, and one single TENG can deliver an open‐circuit voltage of 368 V. Coupled with the self‐stabilizing and susceptible features the ellipsoid shell brings, the HM‐TENG can readily accommodate itself to the all‐weather, all‐sea wave energy harvesting. Muchmore, the HM‐TENG is also applied to RF signal transmitters. This work takes the first step toward near‐meter‐scale enclosures and provides a new direction for large‐scale wave energy harvesting.

We here analyzed the effects of viscosity, oblateness of the primary m1, length parameter l, and perturbations in the Coriolis and centrifugal forces on the stability of the equilibrium points of the Robe's problem. In the setting, it is assumed that the two primaries m1, an oblate spheroid of incompressible homogeneous viscous fluid of density ρ1 and m2, a finite straight segment of length 2l revolve around their common center of mass in circular orbits while third body m3 (a small solid sphere of density ρ3) moves inside m1. Two collinear {L1, L2} and infinite non-collinear equilibrium points are evaluated and found that the location of equilibrium points remain unaffected by viscosity. However, the effects of oblateness and perturbation in the centrifugal force are quite noticeable from the expressions of the equilibrium points. The stability criterion for L1 and L2 are stated whereas the non-collinear equilibrium points are found to be unstable. It is observed that the viscosity has a substantial effect on the stability as it changes the nature of stability from marginal stability to asymptotic stability. The perturbations do not affect the stability of L1 but affect the stability of L2. Moreover, the effect of oblateness on the stability of the equilibrium points is quite evident. A very important observation of the study is that the oblateness parameter A neutralizes the effects of the length parameter l and perturbation ε2, on the stability of equilibrium point L1. The results obtained are applied on Earth-Moon, Jupiler-Amalthea, Jupiler-Ganymede systems (astrophysical problems) to predict the stability of L1. [ABSTRACT FROM AUTHOR]

Abstract Long-term deformation of Kusatsu-Shirane and Asama volcanoes in central Japan were investigated using Global Navigation Satellite System (GNSS) measurements. Large postseismic deformation caused by the 2011 Tohoku earthquake—which obscures the long-term volcanic deformation—was effectively removed by approximating the postseismic and other recent tectonic deformation in terms of quadrature of the geographical eastings/northings. Subsequently, deformation source parameters were estimated by the Markov Chain Monte Carlo (MCMC) method and linear inversion, employing an analytical model that calculates the deformation from an arbitrary oriented prolate/oblate spheroid. The deformation source of Kusatsu-Shirane volcano was found to be a sill-like oblate spheroid located a few kilometers northwest of the Yugama crater at a depth of approximately 4 $$\text {km}$$ km , while that of Asama was also estimated to be a sill-like oblate spheroid beneath the western flank of the edifice at a depth of approximately 12 $$\text {km}$$ km , along with the previously reported shallow east–west striking dike at a depth of approximately 1 $$\text {km}$$ km . It was revealed that (1) volume changes of the Kusatsu-Shirane deformation source and the shallow deformation source of Asama were correlated with the volcanic activities of the corresponding volcanoes, and (2) the Asama deep source has been steadily losing volume, which may indicate that the volcano will experience fewer eruptions in the near future.

Base shear and sloshing response control in ground-supported circular cylindrical liquid storage tank is achieved by oblate spheroid base isolation (OSBI) system used along with floating surface diaphragm on the contained liquid. The new base isolation system, OSBI proposed herein is based on rolling-friction mechanism in ellipsoidal-shaped isolators in both the horizontal axes. The surface diaphragm is proposed to float on the free liquid surface to control the sloshing amplitude. The tank is analyzed using the coupled acoustic-structural (CAS) approach in finite element method (FEM). In order to have conformity of the present FE model, the FEM results are compared with the mechanical lumped-mass model of the tank (without surface diaphragm). The seismic response is investigated for the tank subjected to harmonic and real-earthquake excitations. The parameters considered for the analysis are the aspect ratio of the tank, eccentricity of the isolator, and thickness of the diaphragm. The seismic response quantities evaluated are base shear, sloshing displacement, and impulsive hydrodynamic pressure in the tank. Further, to study the effectiveness of the OSBI, the seismic responses of the tank subjected tri-directional components are compared with the two horizontal bi-directional components of the earthquakes. Also, the sloshing displacement with and without surface diaphragm in the non-isolated and base-isolated tanks are compared. From the results, it is observed that the OSBI system is efficient in mitigating the seismic responses in the tanks and the surface diaphragm is efficient in controlling the sloshing displacement. The superior performance of the proposed isolator depends on the design parameters, namely, eccentricity, and coefficient of rolling friction selected. The effectiveness of the surface diaphragm depends on the choice of material and thickness adopted. [ABSTRACT FROM AUTHOR]

Associating the influences of viscosity and oblateness in the finite straight segment model of the Robe's problem, the linear stability of the collinear and non-collinear equilibrium points for a small solid sphere are analyzed. This small solid sphere is moving inside the first primary which is a homogeneous incompressible viscous fluid whose hydrostatic equilibrium figure is an oblate spheroid. The second primary is a finite straight segment. The existence of the equilibrium points is discussed after deriving the pertinent equations of motion of the small solid sphere. It is found that viscosity does not affect the location and number of equilibrium points but affects the stability as it converts the marginal stability to asymptotic stability. However, oblateness affects the locations of the equilibrium points. Applicability of the results of this study to an astrophysical problem is discussed, and we have calculated a lower bound on the ratio of the orbital radius and the total mass of the primaries of an astrophysical problem to which the results obtained may be applied. This ratio is called the scaling factor. [ABSTRACT FROM AUTHOR]

We consider the collinear restricted four-body problem (CR4BP), where the test particle of infinitesimal mass is moving under the gravitational influence of the three primary bodies. It is further assumed that the central primary is a non-spherical body, particularly either an oblate or prolate spheroid, whereas the peripheral primaries are spherical in shape. A numerical analysis is presented to unveil the effect of the oblateness and prolateness parameters on the position of equilibrium points (EPs) and their linear stability in the CR4BP. Moreover, the permissible regions of possible motion as determined by the zero-velocity surface and associated equipotential curves and the basins of convergence linked with the EPs on the orbital plane are presented. The existence and number of collinear EPs and non-collinear EPs in the problem depend on the combination of the mass parameter of the primaries and the oblateness/prolateness parameter. Additionally, the application of the problem in the Saturn-Moon(1)-Moon(2)-System has been presented. [ABSTRACT FROM AUTHOR]

This study examines the hydrodynamic parameters of a unique geometry that could be used effectively for wave energy extraction applications. In particular, we are concerned with the oblate spheroidal geometry that provides the advantage of a wider impact area on waves, closer to the free surface where the hydrodynamic pressure is higher. In addition, the problem is formulated and solved analytically via a method that is robust and most importantly very fast. In particular, we develop an analytical formulation for the radiation problem of a fully submerged oblate spheroid in a liquid field of finite water depth. The axisymmetric configuration of the spheroid is considered, i.e., the axis of symmetry is perpendicular to the undisturbed free surface. In order to solve the problem, the method of the image singularities system is employed. This method allows for the expansion of the velocity potential in a series of oblate spheroidal harmonics and the derivation of analytical expressions for the hydrodynamic coefficients for the translational degrees of freedom of the body. Numerical simulations and validations are presented taking into account the slenderness ratio of the spheroid, the immersion below the free surface and the water depth. The validations ensure the correctness and the accuracy of the proposed method. Utilizing the same approach, the whole process is implemented for a disc as well, given that a disc is the limiting case of an oblate spheroid since its semi-minor axis approaches zero. [ABSTRACT FROM AUTHOR]

In this article, we aim at obtaining the analytical expressions (not previously found and not recorded in the literature) for the exact curved surface area of a hemiellpsoid in terms of Appell's double hypergeometric function of first kind. The derivation is based on Mellin-Barnes type contour integral representations of generalized hypergeometric function pFq(z), Meijer's G-function and analytic continuation formula for Gauss function. Moreover, we obtain some special cases related to ellipsoid, Prolate spheroid and Oblate spheroid. The closed forms for the exact curved surface area of a hemiellpsoid are also verified numerically by using Mathematica Program. [ABSTRACT FROM AUTHOR]

Long-term deformation of Kusatsu-Shirane and Asama volcanoes in central Japan were investigated using Global Navigation Satellite System (GNSS) measurements. Large postseismic deformation caused by the 2011 Tohoku earthquake—which obscures the long-term volcanic deformation—was effectively removed by approximating the postseismic and other recent tectonic deformation in terms of quadrature of the geographical eastings/northings. Subsequently, deformation source parameters were estimated by the Markov Chain Monte Carlo (MCMC) method and linear inversion, employing an analytical model that calculates the deformation from an arbitrary oriented prolate/oblate spheroid. The deformation source of Kusatsu-Shirane volcano was found to be a sill-like oblate spheroid located a few kilometers northwest of the Yugama crater at a depth of approximately 4 km , while that of Asama was also estimated to be a sill-like oblate spheroid beneath the western flank of the edifice at a depth of approximately 12 km , along with the previously reported shallow east–west striking dike at a depth of approximately 1 km . It was revealed that (1) volume changes of the Kusatsu-Shirane deformation source and the shallow deformation source of Asama were correlated with the volcanic activities of the corresponding volcanoes, and (2) the Asama deep source has been steadily losing volume, which may indicate that the volcano will experience fewer eruptions in the near future. [ABSTRACT FROM AUTHOR]

We consider the Robe’s restricted three-body problem in which the bigger primary is assumed to be a hydrostatic equilibrium figure as an oblate spheroid filled with a homogeneous incompressible fluid, around which a circular motion is described by the second primary, that is a finite straight segment. The aim of this note is to investigate the effect of oblateness and length parameters on the motion of an infinitesimal body that lies inside the bigger primary. The locations of the equilibrium points are approximated by the series expansions and it is found that two collinear equilibrium points lying on the line segment joining the centers of the primaries, exist. The noncollinear equilibrium points lie on a circle and are infinite in number. No out-of-plane equilibrium point exists. Based on the linear stability analysis, it is observed that the collinear equilibrium points can be stable under certain conditions whereas the non-collinear ones are always unstable. [ABSTRACT FROM AUTHOR]

Optical fiber line, considered to be highly effective for signal transmission, sometimes suffer from fiber cut resulting in signal loss. It is highly desired that the exact cut location is found by use of fiber length so that entire fiber cable need not be replaced. An optoelectronic instrument OTDR (Optical Time-Domain Reflectometer) is used to find the position of the cut along the fiber length. There is the need to find the physical location on the GIS map which can provide the exact location where the replacement of fiber or maintenance activity has to be carried out. This paper proposes Vincenty’s formula to be used for fiber cut localization using GIS mapping which assumes the Earth to be oblate spheroid instead of exact sphere. This method will be highly accurate than any other method for exact localization of fiber cut. [ABSTRACT FROM AUTHOR]

In this study, we have examined the stability of triangular equilibrium points in the photogravitational restricted three- body problems (R3BP) as well as the effect of radiation, where both primaries are oblate spheroid. The results confirm the position of triangular equilibrium points of our problem and it also depicts that the equations of motion are affected by radiation pressure force, oblateness and sources of radiation. Stability conditions were discussed using the characteristic equation. All classical results involving photogravitational and oblateness in R3BP may be verified in the near future employing this result. [ABSTRACT FROM AUTHOR]

Commonly based on the liquid diffusion theory, drying theoretical studies in porous materials has been directed to plate, cylinder, and sphere, and few works are applied to non-conventional geometries. In this sense, this work aims to study, theoretically, the drying of solids with oblate spheroidal geometry based on the thermodynamics of irreversible processes. Mathematical modeling is proposed to describe, simultaneously, the heat and mass transfer (liquid and vapor) during the drying process, considering the variability of the transport coefficients and the convective boundary conditions on the solid surface, with particular reference to convective drying of lentil grains at low temperature and moderate air relative humidity. All the governing equations were written in the oblate spheroidal coordinates system and solved numerically using the finite-volume technique and the iterative Gauss–Seidel method. Numerical results of moisture content, temperature, liquid, vapor, and heat fluxes during the drying process were obtained, analyzed, and compared with experimental data, with a suitable agreement. It was observed that the areas near the focal point of the lentil grain dry and heat up faster; consequently, these areas are more susceptible to the appearance of cracks that can compromise the quality of the product. In addition, it was found that the vapor flux was predominant during the drying process when compared to the liquid flux.

• Heat conduction from oblate spheroids and from bispheres are solved analytically. • Constant heat flux is applied on the surfaces of oblate spheroids and bispheres. • Nusselt numbers vary almost linearly with the dimensionless geometric parameters. • Approximate formulas are proposed for temperature distributions and Nusselt numbers. We theoretically examine heat transfer by conduction from oblate spheroidal and bispherical surfaces into a stationary, infinite medium. The surfaces are presumed to maintain a constant heat flux. Assuming steady-state condition and uniform thermal conductivity, we analytically solve Laplace's equation for the temperature distribution and discuss the challenge of dealing with the Neumann (uniform flux) versus more convenient Dirichlet (isothermal) boundary condition. The solutions are obtained in boundary-fitting coordinate systems using the method of separation of variables and eigenfunction expansion. And, exact expressions for the average Nusselt number are presented along with their approximations. [ABSTRACT FROM AUTHOR]

The use of saliva sampling as a minimally-invasive means for drug testing and monitoring physiology is a subject of great interest to researchers and clinicians. This study describes a new optical method based on non-axially symmetric focusing of light using an oblate spheroid sample chamber. The device is simple, lightweight, low cost and is easily attached to several different brands/models of smartphones (Apple, Samsung, HTC and Nokia) for the measurement of sodium ion levels at physiologically-relevant saliva concentrations. The sample and fluorescent reagent solutions are placed in a specially-designed, lightweight device that excludes ambient light and concentrates 470-nm excitation light, from a low-power photodiode, within the sample through non-axially-symmetric refraction. The study found that smartphone cameras and post-image processing quantitated sodium ion concentration in water over the range of 0.5–10 mM, yielding best-fit regressions of the data that agree well with a data regression of microplate luminometer results. The data suggest that fluorescence can be used for the measurement of salivary sodium ion concentrations in low-resource or point-of-care settings. With further fluorescent assay testing, the device may find application in a variety of enzymatic or chemical assays.

Highlights • The influence of droplet sphericity on evaporation rate is studied. • Experiments of oblate spheroidal droplets evaporation in acoustic field were conducted. • A numerical model for evaporation of an oblate droplet is compared with experiments of single drop evaporation. Abstract The modelling of evaporation in which droplet geometry deviates from sphericity, i.e., oblate spheroid, when the droplet experiences high dynamic stresses or a high Weber number, is important in many applications. The validation of such theoretical models is often difficult to achieve experimentally. The acoustic levitation technique was used to investigate the evaporation of an oblate spheroid for different liquids. Evaporation of oblate droplet at constant aspect ratio is realized through the course of evaporation in the acoustic levitator by continuously adjusting the applied acoustic force on the droplet. A Two-dimensional axisymmetric computational model in oblate coordinate system is presented to predict droplet evaporation driven by the acoustic boundary layer, the model calculates the vapor flux at each grid point on droplet surface. The evaporation follows the d2-law and a good agreement between model prediction and experiments is demonstrated. The acoustic levitator allows for the study of the evaporation of freely suspended deformed droplets and validates the theoretical model of oblate droplet evaporation. [ABSTRACT FROM AUTHOR]

Forces external to the oblate spheroid shape, observed from planetary to galactic scales, are demonstrably non-central, which has important ramifications for planetary science. We simplify historic formulae and derive new analytical solutions for the gravitational potential and force outside a constant density oblate. Numerical calculations that sum point mass contributions in a >10 9 element mesh confirm our equations. We show that contours of constant force and potential about oblate bodies are closely approximated by two confocal families whose foci ( f ) respectively are (9/10) ½ ae and (3/5) ½ ae for a body with f  =  ae . This leads to useful approximations that address internal density variations. We demonstrate that the force on a general point is not directed towards the oblate's center, nor are forces simply proportional to the inverse square of that distance, despite forces in the equatorial and axial directions pointing towards the center. Our results explain complex dynamics of galactic systems. Because most planets and stars have an aspect ratio >0.9, the spherical approximation is reasonable except for orbits within ∼2 body radii. We show that applying the “generalized” potential, which assumes central forces, yields J 2 values half those expected for oblate bodies, and probably underestimates masses of Uranus and Neptune by ∼0.2%. We show that the inner Saturnian moons are subject to non-central forces, which may affect calculations of their orbital precession. Our new series should improve interpretation of flyby data. [ABSTRACT FROM AUTHOR]

In this paper, we study the invariant manifold and its application in transfer trajectory problem from a low Earth parking orbit to the Sun-Earth $L_{1}$ and $L_{2}$ -halo orbits with the inclusion of radiation pressure and oblateness. Invariant manifold of the halo orbit provides a natural entrance to travel the spacecraft in the solar system along some specific paths due to its strong hyperbolic character. In this regard, the halo orbits near both collinear Lagrangian points are computed first. The manifold's approximation near the nominal halo orbit is computed using the eigenvectors of the monodromy matrix. The obtained local approximation provides globalization of the manifold by applying backward time propagation to the governing equations of motion. The desired transfer trajectory well suited for the transfer is explored by looking at a possible intersection between the Earth's parking orbit of the spacecraft and the manifold. [ABSTRACT FROM AUTHOR]