Spheroidal Shell Research Articles

Scattering and absorption properties of spheroidal soot-sulfate aerosols

We analyze the results of numerically exact modeling of scattering and absorption characteristics of randomly oriented polydisperse spheroidal soot particles covered by spheroidal nonabsorbing sulfate shell. Using numerically exact T-matrix method, at wavelengths 0.355 μm, 0.532 μm and 1.064 μm, we perform computations of the absorption cross section (Cabs), absorption Ångström exponent (AAE), backscattering linear depolarization ratio (LDR) and scattering matrix elements for spheroids with core volume-equal-sphere effective radius (further in the text, the term "effective radius" is used) Rc,eff = 0.1, 0.15 μm, soot volume fraction .f = 7% and 15%. Mostly, we consider the case of oblate spheroids with the axis ratio ε ranging from 1.1 to 1.8. Our size-averaged results demonstrate, in particular, that: (i) the absorption cross section depends on the degree of nonsphericity very weakly, but substantially increases with increasing aerosol size and decreases with increasing wavelength; (ii) the absorption Ångström exponent also shows a weak dependence on the spheroid axis ratio, but it is quite sensitive to the choice of the wavelength pair, particle size and amount of soot/sulfate; (iii) the backscattering linear depolarization ratio is very sensitive to particle nonsphericity, size, amount of sulfate coating and wavelength, and concentric soot-sulfate spheroidal particles could cause a wide range of the LDR values that significantly decrease with increasing wavelength. We also conclude that at backscattering angles, the elements of the normalized scattering matrix exhibit specific changes which depend on particle shape, size, and amount of coating material.

Constraining the Parameterized Neutron Star Equation of State with Astronomical Observations

Abstract We utilize the phenomenologically parameterized piecewise polytropic equations of state to study various neutron star properties. We investigate the compliance of these equations of state with several astronomical observations. We also demonstrate that the theoretical estimates of the fractional moment of inertia cannot explain all the pulsar glitches observed. We model the crust as a solid spheroidal shell to calculate the fractional moment of inertia of fast-spinning neutron stars. We also show that the braking index obtained in a simple magnetic dipole radiation model with a varying moment of inertia deviates significantly from the observed data. Future developments in both theory and observations may allow us to use the fractional moment of inertia and braking index as observational constraints for neutron star equation of state.

Mathematical Modeling of the Evolution of the Exterior Boundary in Spheroidal Tumour Growth

The present paper concerns the formulation and the evolution of the non symmetrical growth of an avascular cancerous cell colony in an analytical mathematical fashion. Although most of the existing research considers spherical tumours, here we work in the frame of a more general case of the prolate spheroidal geometry. The tumour lies inside a host spheroidal shell which provides vital nutrients, receives the debris of the dead cells and also transmittes to the tumour the pressure imposed by the surrounding on its exterior boundary. Under the aim of studying the evolution of the exterior tumour boundary, we focus on the exterior conditions under which such a geometrical structure can be sustained. To that purpose, the corresponding nutrient concentration, the inhibitor concentration and the pressure field are calculated analytically providing the necessary data for the evolution equation to be solvable. It turns out that an avascular tumour can exhibit a prolate spheroidal growth only if the external conditions for the nutrient supply and the transversally isotropic pressure field have a specific form, which is consistent with the tumour evolution. Additionally, our model exhibits a geometrical reduction to special cases and, mainly, to the spherical geometry in order to recover the existing results for the sphere.

A GBSM Indoor Channel Model With an Arbitrary Center Point of Gaussian Scatterer Distribution

This article proposes a generalized three-dimensional (3-D) geometry-based stochastic model (GBSM) channel model with an arbitrary center point of the scatterer distribution. In the proposed channel model, scatterers are assumed to be Gaussian distributed about an arbitrary point within a spheroidal shell having the transmitter and the receiver located at its focal points. Exact closed-form expressions are obtained for the joint probability density function (PDF) of the angles of arrival (AoAs) and time of arrival (ToA), and the marginal PDF of ToA. Moreover, approximate closed-form expressions are derived for the marginal PDFs of AoAs in the elevation and azimuth planes. The accuracy of the analytically derived AoA and ToA PDFs are verified by comparing with the PDFs obtained using computer and ray-tracing simulation. Furthermore, we study the characteristics of the analytically-derived AoA and ToA PDFs for different propagation scenarios. By choosing the center point and standard deviation of the scatterer distribution appropriately, our proposed 3-D channel model can be used to evaluate the performance of wireless communication technologies and systems in indoor environments.

Diffraction of low-frequency waves on elastic thin-walled shells of rotation

Asymptotic and functional relations connecting the characteristics of scattered near and far fields with elastic and spectral characteristics of thin-walled elongated elastic shells described by the Love theory were found. The study was carried out by the method of two-scale expansions. For the near scattered field, recurrent systems of boundary value problems for Laplace and Poisson equations were obtained, the solutions of which were found explicitly. The radiation patterns of the scattered field were obtained using the theory of wave potentials for the Helmholtz equation. Asymptotic formulas for the potential densities of simple and double layers were found. This made it possible to present the asymptotics of the scattered field directivity diagram in the form of parametric integrals that depend on the angles of incidence and observation, frequency, surface shape, and material characteristics of the shell. The asymptotic method was effective for strongly elongated shells when the ratio of the maximum longitudinal diameter to the maximum diameter of rotation is more than ten. For such highly elongated bodies, the use of various difference and iterative schemes is problematic due to the difficulties of triangulating the shell surface. Numerical implementations of calculations of directional diagrams of a spheroidal steel shell in water at different angles of incidence of plane waves in a wide frequency range are given. The numerical calculations performed in this work are not tied to a specific frequency, since the geometric dimensions are given in wavelengths. Calculations have shown that the radiation pattern for elongated bodies begins to differ from the spherically symmetrical one at values kl > 4. When the wave size of the shell increases, the lobes of the directional diagram appear. The lobes direction depends on the above parameters. The number of lobes, their direction and power can be changed by using special distributions of the shell surface impedances.

Spheroidal trap shell beyond diffraction limit induced by nonlinear effects in femtosecond laser trapping

Abstract Beyond diffraction limit, multitrapping of nanoparticles is important in numerous scientific fields, including biophysics, materials science and quantum optics. Here, we demonstrate the 3-dimensional (3D) shell-like structure of optical trapping well induced by nonlinear optical effects in the femtosecond Gaussian beam trapping for the first time. Under the joint action of gradient force, scattering force and nonlinear trapping force, the gold nanoparticles can be stably trapped in some special positions, or hop between the trap positions along a route within the 3D shell. The separation between the trap positions can be adjusted by laser power and numerical aperture (NA) of the trapping objective lens. With a high NA lens, we achieved dual traps with less than 100 nm separation without utilizing complicated optical systems or any on-chip nanostructures. These curious findings will greatly extend and deepen our understanding of optical trapping based on nonlinear interaction and generate novel applications in various fields, such as microfabrication/nanofabrication, sensing and novel micromanipulations.

Characteristics of a precessing flow under the influence of a convecting temperature field in a spheroidal shell

We present results from direct numerical simulations of flows in spherical and oblate spheroidal shells, driven both by precession and thermal convection, with Ekman number , non-diffusive Rayleigh numbers from to and unity Prandtl number. The applied precessional forcing spans seven orders of magnitude. Our experiments show a clear transition between a convective state and a precessing flow that can be approximated by a reduced dynamical model. The change in the flow is apparent in visualizations and a decomposition of the velocity into symmetric and antisymmetric components. For the flow dominated by precession, some parameter combinations show two stable solutions that can be realized by a hysteresis or a strong thermal forcing. An increase of the Rayleigh number at a constant precession rate exhibits established scaling properties for the heat transfer, with exponents and .

Intensity maxima position shift of spirally polarized hollow Gaussian beam with radial cosine phase modulation

The intensity maxima position shift and the focal pattern evolution principle of spirally polarized hollow Gaussian beams (HGBs), with radial cosine phase wavefront modulation, are researched by the vector diffraction theory with Debye approximation. Significant intensity maxima position shift and focal pattern transformation of spirally polarized HGBs were found by changing the value of the spiral parameter, phase parameter or beam order. The spiral parameter contributes considerably to focal splitting, the phase parameter contributes to the intensity maxima position shift, and the beam order induces a sharper radial focal pattern. When the phase parameter equals 1, the intensity maxima position shift curves dependent on spiral parameter are initially smooth, then they begin to oscillate, and their vertical coordinates gradually increase. When the phase parameter equals 2, the intensity maxima position shift curves are initially smooth, then they begin to oscillate across the focal plane along the propagation direction with increasing amplitude. The spiral parameter, phase parameter and beam order greatly affect the intensity distribution, with the appearance of many novel focal patterns in evolution process, including intensity bowl, spheroidal shell and intensity ring. Spirally polarized HGBs with radial cosine phase modulation may be applied widely in optical manipulation, particle limitation systems, laser surface modification and laser direct writing techniques.

Oblate Spheroidal Triboelectric Nanogenerator for All‐Weather Blue Energy Harvesting

AbstractTriboelectric nanogenerators (TENGs) provide one of the most promising techniques for large‐scale blue energy harvesting. However, lack of reasonable designs has largely hindered TENG from harvesting energy from both rough and tranquil seas. In this paper, an oblate spheroidal TENG assembled by two novel TENG parts is elaborately designed for both situations. The TENG in the upper part is based on spring steel plates without other substrate materials, which makes it possible to output considerable power in rough seas and occupy small space. The TENG in the lower part consists of two copper‐coated polymer films and a rolling ball which can capture small wave energy from tranquil seas. The working mechanism and output performance are systematically studied. A maximum open‐circuit voltage of 281 V and a short‐circuit current of 76 µA can be achieved by one upper part, enough to charge a commercial capacitor for potential applications. More important, the proposed oblate spheroidal shell not only guarantees high sensitivity of the TENG in the lower part, but also qualifies the TENG with unique self‐stabilization and low consumables for the next generation of TENGs with new structural design toward all‐weather blue energy harvesting.

Structure and Properties of Self-Organized 2D and 3D Antimony/Carbon Composites

The conditions of synthesis of antimony/carbon composites by interlayer self-assembly from colloidal solutions and melts are discussed. The morphology and the structure of these composites are examined. The potential to produce composites of 2D and 3D morphologies is demonstrated. The 2D composite has a multilayer graphene structure with submicron antimony inclusions, while the 3D composite has a spheroidal shell structure with a deformed film-shell with carbon nanoinclusions. The difference in properties of these composites is demonstrated: the 2D composite is conductive, while the 3D composite has a nonlinear current–voltage characteristic that indicates the emergence of novel functional properties of the spheroidal antimony/carbon composite. A model of exfoliation of the layered precursor with covalent interlayer coupling is proposed. This model provides an explanation for the experimentally observed nonlinear hydrodynamic processes in the colloidal antimony solution.

ELM: super-resolution analysis of wide-field images of fluorescent shell structures

It is often necessary to precisely quantify the size of specimens in biological studies. When measuring feature size in fluorescence microscopy, significant biases can arise due to blurring of its edges if the feature is smaller than the diffraction limit of resolution. This problem is avoided if an equation describing the feature’s entire image is fitted to its image data. In this paper we present open-source software, ELM, which uses this approach to measure the size of spheroidal or cylindrical fluorescent shells with a precision of around 10 nm. This has been used to measure coat protein locations in bacterial spores and cell wall diameter in vegetative bacilli, and may also be valuable in microbiological studies of algae, fungi and viruses. ELM is available for download at https://github.com/quantitativeimaging/ELM.

Numerical simulations of bistable flows in precessing spheroidal shells

Numerical simulations of bistable flows in precessing spheroidal shells

Axisymmetric Stokes flow past a composite spheroidal shell of immiscible fluids

We study the flow of an incompressible Newtonian fluid past a composite spheroidal shell whose shape deviates slightly from that of a sphere. A composite particle referred to in this paper is a spheroidal liquid core covered with a porous layer. The Brinkman equation is used for the flow inside the porous medium and the Stokes equation is used for the flow in the fluid region. We assume that the external and internal viscous fluids are immiscible and the viscosity of the porous medium is different than the viscosity of pure liquid. The Ochoa-Tapia and Whitaker’s stress jump boundary condition for tangential stress is applied on the porous-fluid interface. Velocity and pressure distributions are found and the drag force acting on the spheroidal shell is evaluated. The analytical solution is obtained by dividing the flow into three regions. Both type of spheroids, oblate and prolate are considered. Numerical results of the normalized hydrodynamic drag force acting on the spheroidal shell are tabulated and represented graphically for different values of the parameters characterizing the stress jump coefficient, separation parameter, permeability, deformation parameter, and viscosity ratios. The analysis of the flow pattern is done by plotting streamlines and several renowned cases are deduced.

Voronoi‐Tessellated Graphite Produced by Low‐Temperature Catalytic Graphitization from Renewable Resources

A highly crystalline graphite powder was prepared from the low temperature (800-1000 °C) graphitization of renewable hard carbon precursors using a magnesium catalyst. The resulting graphite particles are composed of Voronoi-tessellated regions comprising irregular sheets; each Voronoi-tessellated region having a small "seed" particle located near their centroid on the surface. This suggests nucleated outward growth of graphitic carbon, which has not been previously observed. Each seed particle consists of a spheroidal graphite shell on the inside of which hexagonal graphite platelets are perpendicularly affixed. This results in a unique high surface area graphite with a high degree of graphitization that is made with renewable feedstocks at temperatures far below that conventionally used for artificial graphites.

Phase Behavior of Salt-Free Polyelectrolyte Gel-Surfactant Systems.

Ionic surfactants tend to collapse the outer parts of polyelectrolyte gels, forming shells that can be used to encapsulate other species including protein and peptide drugs. In this paper, the aqueous phase behavior of covalently cross-linked polyacrylate networks containing sodium ions and dodecyltrimethylammonium ions as counterions is investigated by means of swelling isotherms, dye staining, small-angle X-ray scattering, and confocal Raman spectroscopy. The equilibrium state is approached by letting the networks absorb pure water. With an increasing fraction of surfactant ions, the state of the water-saturated gels is found to change from being swollen and monophasic, via multiphasic states, to collapsed and monophasic. The multiphasic gels have a swollen, micelle-lean core surrounded by a collapsed, micelle-rich shell, or a collapsed phase forming a spheroidal inner shell separating two micelle-lean parts. It is shown that the transition between monophasic and core-shell states can be induced by variation of the osmotic pressure and variation of the charge of the micelles by forming mixed micelles with the nonionic surfactant octaethyleneglycol monododecylether. The experimental data are compared with theoretical predictions of a model derived earlier. In the calculations, the collapsed shell is assumed to be homogeneous, an approximation introduced here and shown to be excellent for a wide range of compositions. The theoretical results highlight the electrostatic and hydrophobic driving forces behind phase separation.

T-matrix method implementation for acoustic Bessel beam scattering from elastic solids and shells

T-matrix method (TMM) has been demonstrated to be an effective tool for the application of acoustic Bessel beam (ABB) scattering from rigid shapes, owing to the fact that the incident ABBs could be appropriate to expand on the basis of spherical harmonics [Gong et al., J. Sound Vibr. 383, 233-247 (2016)]. In this work, we try to extend the TMM to further calculate ABB scattering from complicated elastic shapes, spheroids/ spheroidal shells for instance. Some numerical techniques are successfully implemented to overcome the instability problem during matrix inversion procedures for nonspherical shapes. Resonance scattering theory and ray theory [Kargl and Marston, J. Acoust. Soc. Am. 88, 1103-1113 (1990)] are employed to explore and interpret several novel properties of scattering from elastic shapes illuminated by ABBs, thus revealing the corresponding mechanism of scattering by ABBs. Furthermore, the present work will perform as a foundation work to extend the applicability of TMM to study acoustic radiation force and torque in ABBs in future. [Work supported by NSFC.]

The energy of a prolate spheroidal shell in a uniform magnetic field

The problem of the energy of a spheroidal magnetic shell, solved by methods of classical electrodynamics, arises, in particular, upon the study of thin-wall biocompatible microcapsules in connection with a pressing issue of targeted drug delivery. The drug inside a microcapsule should be released from the shell at a required instant of time by destroying the capsule’s shell. The placement inside a shell of magnetic nanoparticles sensitive to an external magnetic field theoretically makes it possible to solve both problems: to transport a capsule to the required place and to destroy its shell. In particular, the shell can be destroyed under the action of internal stress when the shape of a capsule is changed. In this paper, the analysis of the model of a magnetic microcapsule in the form of a prolate spheroidal shell is performed and formulas for the magnetostatic and magnetic free energy when the magnetic field is directed along the major axis of the spheroid are derived.

Composite spheroidal shells under external pressure

ABSTRACTBuckling, collapse, and first ply failure pressures have been obtained for a range of spheroidal FRP shells under static external pressures. Comparisons of the load carrying capacities are made for like geometries. It is shown that some prolate ellipsoids can be stronger, for up to 70% than the equivalent spheres. The effect of boundary conditions in the equatorial plane on the buckling strength is assessed for the diameter-to-wall- thickness ratio ranging from 100 to 500. Regions where the strength (FPF) rather than asymmetric bifurcation control the failure have been identified. Small perturbations in ply orientations, ±5°, have been introduced in order to assess their influence on the buckling strength. Both symmetric and asymmetric stacking with respect to the mid-plane have been analyzed (including random stacking).Initial shape imperfection positioned at the apex of a hemispherical head has been examined. The latter aimed at assessing the sensitivity of buckling pressure to deviations from perfect geometry. Results have been obtained for the lower bound approach based on the local flattening using the increased-radius. Imperfections in ellipsoids have also been studied. Axisymmetric modeling of all shells was used throughout in this study. Only the upper half of shells was modeled, and the issue of boundary conditions at the equatorial plane was also explored.

Scattering of Stationary and Non-Stationary Sound by Ideal and Elastic Scatterers, Placed near Interface of Media, in Underwater Sound Channel and in Plane Waveguide

In the review we obtained a strict solution of problem of the sound diffraction by an elastic spheroidal shell, located near the interface of a liquid medium with an elastic solid medium. Calculation of the scattered sound field for ideal bodies (a spheroid and an elliptical cylinder) is performed. These bodies are placed on the interface between the liquid and the ideal medium; it is shown, that the main role is played not by interaction of scatterers (real and imaginary), but by interference of their scattered fields. The spectrum of the scattered impulse signal for the body in an underwater sound channel is calculated. It is shown, that at large distances the dominante role is played by the spectral characteristic of the channel itself. Based on the method of imaginary sources and imaginary scatterers, the solution of the current study is to solve the diffraction problem of sound pulse signals at ideal (soft) prolate spheroid, which is put in the plane waveguide with the hard elastic bottom. In the work, it is proved that with such a formulation of problems eliminated, there exists possibility of using the method of normal waves because pulses are bundies of energy and can therefore only be distributed to the group velocity which is inherent in just the method of imaginary sources. Calculations made in the article showed that imaginary sources with small numbers exert the effect of total internal reflection, as the result of the reflection coefficient V by the hard elastic bottom which is complex and the real part of V is close to 1.0 which corresponds to V absolutely hard bottom. Found sequences of reflected pulses for the elastic hard bottom and the absolutely hard bottom floor confirmed this approach. In the final part of the article, on the basis of the received results, a solution (the method integral equations) is given, which is a much more complex problem of the diffraction at the elastic non-analytical scatterer, put in the plane waveguide with the hard elastic bottom.

Synthesis of hollow silica-sulfur composite nanospheres towards stable lithium-sulfur battery

Herein, porous hollow silica nanospheres were prepared via a facile sol-gel process in an inverse microemulsion, using self-assemblies of chiral amphiphile as a soft template and fine water droplets as a hard template. The shells of the hollow silica nanospheres are composed of flake-like nanoparticles with dense big holes on the surface. After covering a layer of sulfur on the silica nanospheres, followed by hydrothermal treatment in a D-glucose aqueous solution, silica-sulfur and silica-sulfur-carbon nanospheres were successfully fabricated. The silica-sulfur composites exhibit a stable capacity of 454 mAh g−1 at current density of 335 mA g−1 after 100 cycles with capacity retention of 85%, demonstrating a promising cathode material for rechargeable lithium-sulfur batteries. We believe that the approach for synthesis of porous hollow silica nanospheres and its carbon spheroidal shell can also be applicable for designing other electrode materials for energy storage.