Spherical Bodies Research Articles

THEORETICAL STUDY OF HEAT CONDUCTION IN MULTI-LAYER SPHERICAL BODY WITH PHASE TRANSFORMATION IN LAYERS

The objective of the study is to build a simple yet informative mathematical model that describes the heat conduction in a spherical multi-layer body with phase transformation in the layers. The numerical scheme based on the theory of Markov chains is proposed to solve this problem numerically. The radial sector of the body is divided into finite number of spherical perfectly mixed cells of different volume, which form a chain of cells. The heat exchange between the cells is described with the heat conduction matrix, the entries of which depend on the local thermo-physical properties of material in the cells (heat conduction coefficient, density, specific heat capacity). These properties can vary from one cell to another and with time. The outer cell of the chain can exchange with heat with outside environment, the temperature of which can vary with time. The state of the process is observed in discrete moments of time separated by small but finite transition duration. If the temperature of a cell reaches the value, the phase transformation begins at which, the evolution of the cell thermal and phase state is described with the corresponding kinetic equation of the phase transformation. The process of melting and solidification is used as the example to verify the qualitative predictability of the model. The graphs of temperature distribution evolution and diagrams of phase content distribution in a multi-layer spherical body are presented. The obtained results on the evolution of the thermal and phase state of the ball have no contradiction to the physical sense of the process. The proposed algorithm has very low computational time (1-3 min for one regime). The other processes of the phase transformation can be easily implemented in the model, for instance, drying, exothermic and endothermic chemical reactions, etc.

Visualizations of density fluctuations before and after the passage of bluff body objects in a laboratory stratified tank

abstract One of the main causes of the formation of internal waves is the ocean currents, from the seabed's mounds. For this reason, numerous empirical studies have been carried out in laboratories on the flow of streams on artificial mounds or the passage of objects in a stratified medium. The purpose of this study is to identify the changes in the density of the layers by internal waves due to the movement of the physical model in a stratified water with different Froude numbers. This study is done in, a large stratified tank that density changes due to movement of spherical and airfoil bodies are recorded by an array of fast response sensors. Lee waves and the blocking area are well illustrated before and after waves, created by passing objects, are transmitted through the tank, and are visualized using optical shadowgraph technique. The results showed that the mean amplitude of waves increases with increasing Froude numbers. The average wave's periods before the object reaches the lowering point of 0.4D/U (D being the thickness of the moving object and U is its speed) and then increases, and the mean period after the arrival of the object decreases with the Froude number.

Characteristics of Reinforced Ultra-High Molecular Weight Polyethylene During Its Ballistic Penetration

Bulk samples of pure ultra-high molecular weight polyethylene and bulk samples reinforced with metal interlayers (steel meshes and penetrated titanium plates) are obtained by cyclic impact compaction. Experiments are carried out in which the properties of compacts made of ultrahigh molecular weight polyethylene with and without metal interlayers are studied during penetration by a lead shot whose pellets (8 mm in diameter) move at a velocity of approximately 370 m/s. The penetration depth of a pellet into a compact is experimentally determined. To estimate the penetration depth of a spherical body into a polymer, a model is proposed that describes the motion of a sphere in this medium.

Retinal and choroidal vascular structures are affected in axial spondyloarthritis: an optical coherence tomography study.

The aim of this study is to evaluate the retinal and choroidal structures in r- and nr-axSpA patients using spectral domain optical coherence tomography (SD-OCT) and to compare changes with healthy controls. In this cross-sectional study, 70 axSpA patients (50 radiographic- and 20 nr-axSpA) and 50 healthy control subjects were included. Choroidal thickness (ChT), macular thickness, retinal nerve fiber layer (RNFL), and the ganglion cell complex (GCC) were measured by SD-OCT. For ChT values, seven lines at nasal and temporal were drawn at 500-μm intervals, centering the subfoveal sclerochoroidal junction. Analysis of the data was performed with the SPSS program. Mann-Whitney U test was performed for comparison of non-normally distributed continuous data; Student's t test was used for normal distributed data. No significant difference was observed between 70 (66% male; mean age 39.7 ± 10.4years) axSpA patients (50 radiographic and 20 nr-axSpA) and 50 (mean age 41.2 ± 6.2years) healthy control subjects (p 0.417). R-axSpA and nr-axSpA groups and control group were similar in terms of spherical equivalent, intraocular pressure, axial length, and body mass index (p 0.574, p 0.874, p 0.918, p 0.344, respectively). While mean macular and GCC thicknesses were significantly lower in the patient group than in the healthy group, there was no significant difference between the two groups in terms of RNFL thickness. The present study showed that there was no significant relationship between markers and scores indicating disease activity and ChT, MT, RNFL, and GCC thicknesses. However, an increase in choroidal thickness and involvement of the retinal layers has also been demonstrated in patients with spondyloarthritis. In addition, the relationship between disease activity and retinal layer involvement is remarkable in the r-axSpA group.

DIFFERENTIAL EQUATIONS OF PLANETARY SYSTEMS

In this article will be considered many spherical bodies problem with variable masses, varying non-isotropic at different rates as celestial-mechanical model of non-stationary planetary systems. In this article were obtained differential equations of motions of spherical bodies with variable masses to reach purpose exploration of evolution planetary systems. The scientific importance of the work is exploration to the effects of masses’ variability of the dynamic evolution of the planetary system for a long period of time. According to equation of Mescherskiy, we obtained differential equations of motions of planetary systems in the absolute coordinates system and the relative coordinates system. On the basis of obtained differential equations in the relative coordinates system, we derived equations of motions in osculating elements in form of Lagrange's equations and canonically equations in osculating analogs second systems of Poincare's elements on the base aperiodic motion over the quasi-canonical cross- section.

Increased intra-mitochondrial lipofuscin aggregates with spherical dense body formation in mitochondrial myopathy

Lipofuscin aggregation may result from incomplete degradation of damaged mitochondria by autophagy-lysosome pathway, and intra-mitochondrial lipofuscin aggregation may exacerbate mitochondrial abnormalities in mitochondrial myopathy (MM) and mitochondrial disease. We examined vastus lateralis muscle biopsies from 24 patients with pathologically diagnosed MM and clinically diagnosed chronic progressive external ophthalmoplegia, in comparison to the biopsies from 3 other groups:10 patients with inclusion body myositis (IBM), 11 younger adults, and 10 older subjects with no to minimal myopathic changes. Lipofuscin aggregation in muscle fibres was assessed on autofluorescence microscopy, some histochemical stains, and electron microscopy (EM). EM analyses demonstrated intra-mitochondrial lipofuscin aggregates, spherical dense bodies (SDBs), and paracrystalline inclusions (PCIs) which were semi-quantitatively assessed. Intra-mitochondrial lipofuscin aggregates showed no significant differences between groups of MM patients and older subjects or IBM patients, but significant differences between groups of younger adults and others with associated age-related changes. Intra-mitochondrial SDBs were significantly more in MM patients than in older subjects, IBM patients, and younger adults. There was a significant positive correlation between intra-mitochondrial lipofuscin aggregates and SDBs. These findings suggest that intra-mitochondrial formation of lipofuscin SDBs is more in MM and contributing to the pathophysiology of mitochondrial disease.

Effects of the intrinsic curvature of elastic filaments on the propulsion of a flagellated microrobot

Understanding the propulsion mechanism of swimming microorganisms will facilitate the development of synthetic microswimmers for active cargo deliveries. Herein, we studied, theoretically and numerically, inertialess locomotion of a microswimmer—a spherical body propelled by two symmetrically actuated elastic filaments in the shape of a circular arc at rest, focusing on the effects of their uniform intrinsic curvature κ¯c. Combining the resistive force theory for viscous flow and Euler–Bernoulli beam theory for elastic filaments, the elasto-hydrodynamics was solved asymptotically. Our theory was verified by simulations using regularized Stokeslets posed on the filament centerlines, with and without considering hydrodynamic interactions (HIs) between the body and filaments. The asymptotic and numerical results showed qualitative agreement. Reasonable quantitative agreement between the asymptotic results and the numerical predictions neglecting body–filament HIs was observed, especially for small |κ¯c|. However, they deviated quantitatively from the numerical results with body–filament HIs, especially at a large κ¯c when the HIs became important owing to the short body–filament distance. The propulsive force generated by two arc-shaped filaments significantly depend on their uniform intrinsic curvature κ¯c. An appreciable increase in the thrust can be achieved by adjusting κ¯c, which qualitatively confirms and explains the experimentally reported propulsive enhancement facilitated by intrinsically curved appendages [Z. Ye, S. Régnier, and M. Sitti, “Rotating magnetic miniature swimming robots with multiple flexible flagella,” IEEE Trans. Rob. 30, 3–13 (2014)]. The increase in κ¯c can even change the sign of the thrust, leading to counter-intuitive, backward propulsion. The flow field reveals the hydrodynamic signature of the swimmer that shifts with time between a neutral swimmer, a pusher, and a puller.

Wave propagation in semiconvective regions of giant planets

ABSTRACT Recent observations of Jupiter and Saturn suggest that heavy elements may be diluted in the gaseous envelope, providing a compositional gradient that could stabilize ordinary convection and produce a stably stratified layer near the core of these planets. This region could consist of semiconvective layers with a staircase-like density profile, which have multiple convective zones separated by thin stably stratified interfaces, as a result of double-diffusive convection. These layers could have important effects on wave propagation and tidal dissipation that have not been fully explored. We analyse the effects of these layers on the propagation and transmission of internal waves within giant planets, extending prior work in a local Cartesian model. We adopt a simplified global Boussinesq planetary model in which we explore the internal waves in a non-rotating spherical body. We begin by studying the free modes of a region containing semiconvective layers. We then analyse the transmission of internal waves through such a region. The free modes depend strongly on the staircase properties, and consist of modes with both internal and interfacial gravity wave-like behaviour. We determine the frequency shifts of these waves as a function of the number of steps to explore their potential to probe planetary internal structures. We also find that wave transmission is strongly affected by the presence of a staircase. Very large wavelength waves are transmitted efficiently, but small-scale waves are only transmitted if they are resonant with one of the free modes. The effective size of the core is therefore larger for non-resonant modes.

TRANSLATIONAL-ROTATIONAL MOTION OF THE TRIAXIAL BODY WITH VARIABLE COMPRESSIONS IN THE PRESENCE OF REACTIVE FORCES AND MOMENTS

In this paper we investigated the translational-rotational motion of a triaxial body of constant dynamic shape and variable mass and size in a non-stationary Newtonian central gravitational field. Differential equations of the translationalrotational motion of the triaxial non-stationary body in the relative coordinate system with the origin at the center of a non-stationary spherical body are derived. The axes of the own coordinate system of the non-stationary triaxial body are directed along the principle axes of inertia of the body and we assumed that in the course of evolution their relative orientation remains unchanged. An analytical expression for the force function of the Newtonian interaction of the triaxial body of variable mass and size with a spherical body of variable size and mass is given. In the presence of reactive forces and moments the equations of translational-rotational motion of a triaxial non-stationary body in osculating elements are obtained in the presence of reactive forces and moments.

Abnormal Frequencies in a Semi-Infinite Cylindrical Vessel Filled with a Fluid and Dynamically Excited by a Spherical Oscillator

A semi-infinite circular cylindrical cavity filled with a compressible ideal fluid and containing a spherical body near its end is considered. The body surface radiates periodic pressure at given frequency and amplitude. The hydrodynamic characteristics of the system depending on the frequency of excitation and geometrical parameters are determined. The method of separation of variables, the translational addition theorems for spherical wave functions, and the expressions of spherical wave functions in terms of cylindrical ones are applied. This approach allows satisfying all the boundary conditions and finding the exact solution of the boundary-value problem. An infinite system of algebraic equations is solved. Its solution found by the truncation method is stated to converge. The determination of the pressure and velocity fields shows that the system has a number of excitation frequencies at which the acoustic characteristics exceed the amplitude of excitation by several orders of magnitude. These abnormal frequencies differ from the frequencies typical for an infinite cylindrical cavity with a spherical body. Even if the radius of the spherical oscillator is small and the abnormal phenomena in the infinite vessel are weak, they can appear strong in a semi-infinite vessel.

Study of temperature fields in a ball bearings bodies under boundary conditions of the third kind

The reliability of the rolling bearing body directly affects the continuity and duration of operation of industrial equipment. Ball bearings are often used in centrifugal pumps of thermal power plants and water supply systems. Overheating and subsequent failure of such bearings lead to failure of pumping equipment. To avoid such breakdowns, it is necessary to study the thermal processes inside the rolling elements, which can lead to their deformation and destruction. In this paper, the problems of non-stationary heat transfer inside rolling bodies (spherical bodies) are considered. An analytical solution of the problem in dimensionless values of temperatures and coordinates is obtained on the basis of Fourier and Bubnov-Galerkin methods under boundary conditions of the third kind. The solution of such a problem requires the use of an extensive mathematical apparatus, so special software tools such as Mathcad and MatLab were used in the work. So solving the problem analytically in dimensionless quantities is convenient because it allows you to scale the results to all such objects without reference to a specific rolling body. As a result, the solution is obtained in the form of a power polynomial that does not contain special functions.

The initial value problem for gravitational waves in conformal gravity

In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a Kirchhoff-like explicit solution in terms of the field and its first three time derivatives evaluated on an initial hypersurface, as well as second order spatial derivatives of the initial data. In the conformal gravity case, we establish that if the initial data is featureless on scales smaller than the length scale of conformal symmetry breaking, then we recover the ordinary behaviour of gravitational waves in general relativity. We also confirm that the effective weak field gravitational force exerted by a static spherical body in such models becomes constant on small scales; i.e. conformal gravity is effectively 2-dimensional at high energies.

Dynamics of the System Intended for Destruction of Buildings and Constructions by a Shock Method

The article deals with the dynamics of the system intended for destruction of objects by the shock method. The working organ is a spherical body suspended by a rope on a crane boom. The ball is considered to be absolutely solid. All the potential energy of the ball is converted into kinetic energy before impact. Geometric and energy conditions of interaction are obtained. The boundaries of the parameter region in which the ball touches the wall are presented. The dependences of the normal and tangential velocity before impact on the relative cable length are obtained. In the first stage, the flat rough wall does not deform on impact. The dependence of the dimensionless ball speed of the center of mass and angular velocity after impact on the relative length of the cable are presented. An increase in the dimensionless distance to the wall leads to a decrease in the kinetic energy losses of the ball and an increase in the normal dimensionless shock pulse. The algorithm and graphics allow in the process of developing projects for the demolition of buildings and structures to make a choice of technological parameters that ensure the effective operation of construction equipment.

On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation

In the framework of the special theory of relativity, elementary formulas are used to derive the formula for determining the relativistic angular momentum of a rotating ideal uniform ball. The moment of inertia of such a ball turns out to be a nonlinear function of the angular velocity of rotation. Application of this formula to the neutron star PSR J1614-2230 shows that due to relativistic corrections the angular momentum of the star increases tenfold as compared to the nonrelativistic formula. For the proton and neutron star PSR J1748-2446ad the velocities of their surface’s motion are calculated, which reach the values of the order of 30% and 19% of the speed of light, respectively. Using the formula for the relativistic angular momentum of a uniform ball, it is easy to obtain the formula for the angular momentum of a thin spherical shell depending on its thickness, radius, mass density, and angular velocity of rotation. As a result, considering a spherical body consisting of a set of such shells it becomes possible to accurately determine its angular momentum as the sum of the angular momenta of all the body’s shells. Two expressions are provided for the maximum possible angular momentum of the ball based on the rotation of the ball’s surface at the speed of light and based on the condition of integrity of the gravitationally bound body at the balance of the gravitational and centripetal forces. Comparison with the results of the general theory of relativity shows the difference in angular momentum of the order of 25% for an extremal Kerr black hole.

Production of nitric oxide by a fragmenting bolide: An exploratory numerical study

A meteoroid's hypersonic passage through the Earth's atmosphere results in ablational and fragmentational mass loss. Potential shock waves associated with a parent object as well as its fragments can modify the surrounding atmosphere and produce a range of physico‐chemical effects. Some of the thermally driven chemical and physical processes induced by meteoroid‐fragment‐generated shock waves, such as nitric oxide (NO) production, are less understood. Any estimates of meteoric NO production depend not only on a quantifiable meteoroid population and a rate of fragmentation, with a size capable of producing high temperature flows, but also on understanding the physical properties of the meteor flows along with their thermal history. We performed an exploratory pilot numerical study using ANSYS Fluent, the computational fluid dynamics (CFD) code, to investigate the production of NO in the upper atmosphere by small meteoroids (or fragments of meteoroids after they undergo a disruption episode) in the size range from 10−2 to 1 m. Our model uses the simulation of a spherical body in the continuum flow at 70‐ and 80‐km altitude to approximate the behaviour of a small meteoroid capable of producing NO. The results presented in this exploratory study are in good agreement with previous studies.

When is a spherical body of constant diameter of constant width?

We prove that a smooth convex body of diameter delta < frac{pi }{2} on the d-dimensional unit sphere S^d is of constant diameter delta if and only if it is of constant width delta . We also show this equivalence for all convex bodies on S^2. Since, as shown earlier, the equivalence on S^d is true for every delta ge frac{pi }{2}, the question whether spherical bodies of constant diameter and constant width on S^d coincide remains open for non-smooth bodies on S^d, where dge 3.

Forward flight tests of a quadcopter unmanned aerial vehicle with various spherical body diameters

This paper presents experimental results on the relation between forward airspeed, pitch angle, and power consumption of a quadcopter unmanned aerial vehicle. The quadcopter consists of an interchangeable spherical body, four cylindrical arms, and small propellers mounted at 1 m diagonal distance to minimize interference between body and propellers. This simple geometry facilitates results reproduction and comparison with simulation. Two different takeoff masses and four diameters of spherical bodies are tested for their steady-state speed and power for pitch angles up to [Formula: see text]. The steady-state horizontal flight is recorded with on-board sensors at the end of flying long straight lines at a constant pitch angle in wind-still conditions. The best effective lift-to-drag ratio increases for smaller bodies and occurs at higher speeds for increasing mass. Results show that the equivalent frontal surface stays constant for pitch angles further than [Formula: see text] up to the maximum recorded [Formula: see text] and increases linearly with the frontal surface of the body.

Thermoelastic problems of functionally graded multilayered incompressible spherical bodies

The main objective of this paper is to determine the stresses and displacements in radially graded multilayered spherical bodies made from incompressible functionally graded materials. The material properties are arbitrary functions of the radial coordinate. The body is subjected to constant pressure and a temperature field, which is an arbitrary function of the radial coordinate. An analytical method is presented to tackle these problems then compared to solutions coming from finite element simulations.

Assessment of an Optical Disdrometer by Laboratory Tests Using Spherical Bodies and All-particle Logging

Assessment of an Optical Disdrometer by Laboratory Tests Using Spherical Bodies and All-particle Logging

Structural analysis of assemblies using non-conformal spectral element method

An approach to the numerical simulation of a contact interaction between the deformable solids inside the assembly is considered in the article. A standard approach for solving such kind of problems is to imprint the boundaries and merge the solids along the common boundary zones. However this approach requires conformal discretization of the whole assembly including conformal meshes on the common boundary regions during the numerical simulation, which often causes significant problems for the industrial assemblies consisting of a large number of parts of different sizes. Test examples are considered for the verification of the developed in CAE Fidesys (www.cae-fidesys.com) algorithm of tying elastic solids by comparing simulation results with the solutions of similar problems for the case of merged solids with a conformal mesh discretization: static and modal analysis of the assemblies consisting of cubic, cylindrical and spherical bodies. A robustness of the algorithm and a continuity of the obtained solution are analyzed in case of gaps/overlaps between contacting solids. It is shown that small gaps and overlaps in CAD-model of an assembly do not influence much a correctness of numerical results and these cases are correctly and automatically processed in CAE Fidesys software module based on the described algorithm.