Layered Sphere Research Articles

Unequal-sphere packing model for the structural arrangement of the well-ordered adsorbate-substrate system

In order to understand the well-ordered adsorbate-substrate systems at atomic level, a method is developed based on the simulation of packing arrangements for layers of unequal spheres, in three-dimensional space. The model, based on geometrical principles, is developed for fcc structure consisting of two hexagonal ordered layers. During simulation, adsorbate spheres were accommodated in different positions, forming a great variety of structures, in dependence of the intersphere distance of the upper layer spheres. Using the average height of the adsorbate layer on the flat substrate as a determinant parameter, several specific structures have been selected as the most probable: $(\ensuremath{\surd}3\ifmmode\times\else\texttimes\fi{}\ensuremath{\surd}3)\mathrm{R}30\ifmmode^\circ\else\textdegree\fi{}$, $(\ensuremath{\surd}7\ifmmode\times\else\texttimes\fi{}\ensuremath{\surd}7)\mathrm{R}19.1\ifmmode^\circ\else\textdegree\fi{}$, and $(3\ifmmode\times\else\texttimes\fi{}3)$. Indeed, they correspond to typical accommodations of the iodine adatoms on the Pt(111) surface, earlier found in experimental studies, which clearly supports the validity of our model. The model developed in our study could completely and satisfactorily describe the accommodation process of the iodine adlayer on the Pt(111) surface. This methodology could be of great help for interpretation of scanning tunneling microscopy images, better understanding of adlayer structures, and design of adsorbate-substrate systems with exciting properties.

Solving the Problem of Gravitational Compression of a Layered Sphere (by the Example of the Earth)

The problem of spherically symmetric, gravitational compression of an isotropic hyperelastic layered sphere which modeling the region of the Earth below the Mohorovicic boundary is solved. The known mechanical characteristics of the Earth in the compressed state are used to find its characteristics in the unstrained state obtained by adiabatic or isothermal stress relief. The stress state differs significantly from the state of purely hydrostatic compression. The minimum bulk compression and maximum radial tension occur not on the boundary of the sphere but in depth at certain distances from the boundary.

FREE VIBRATIONS OF HOMOGENEOUS AND LAYERED PIEZOELECTRIC HOLLOW SPHERES

A finite element formulation in spherical coordinates is presented for the study of the vibrations of piezoelectric homogeneous and layered hollow spheres. The finite element model is based on nine-node Lagrangian interpolation functions. Representative cases are considered including solid elastic spheres and hollow homogeneous and laminated piezoelectric spheres. The accuracy of the proposed formulation is verified by comparison with existing solutions showing excellent agreement. Several new results are presented for different piezoelectric materials in both tabular and graphical format.

Analysis of a Passive Circular Loop Antenna Radiating in the Presence of a Layered Chiral Sphere Using Method of Moments

In this paper, electromagnetic radiation due to a passive thin circular loop antenna when placed on the surface of a two-layered chiral sphere is analyzed and its far-zone radiation patterns are obtained. The method of moments is employed in this analysis to formulate the current distribution along the circular loop in the presence of the layered chiral sphere. The dyadic Green's functions defining electromagnetic fields due to source in the outer region are applied. In the Galerkin's procedure for the method of moments, basis functions used in the work are sine and cosine functions which form a Fourier series in the expansion. Effects of various geometrical and dielectric parameters of the chiral sphere are discussed. Associated with these parameters, waves and fields in such an electromagnetic system are characterized and discussed.

The “Skin–skull–brain model”: a new instrument for the study of gunshot effects

In order to create and study wound morphology, a “skin–skull–brain model” had to be designed which would make the laboratory reproduction of a real ballistic injury possible. To simulate the human skin, an artificial skin (a silicon cap) is used. This silicon scalp contains synthetic fibers (artificial leather) to simulate the collagen and fat of the scalp. The artificial skull is a layered polyurethane sphere (19 cm o.d.; and 5, 6, or 7 mm thick) constructed in a specially designed form with a Tabula externa, Tabula interna, and a porous Diploe sandwiched in between. The periostium of the artificial skull is made of latex. This elastic latex layer prevents the bone fragments from scattering after the model has been struck by gunfire. The brain itself is simulated with ordnance gelatin, 10% at 4 °C, a material well known in wound ballistics. Gunshots were fired at a distance of 10 m from the model. During the evaluation of the “skin–skull–brain model”, it was possible to show that injuries inflicted to this model are fully comparable to the morphology of equivalent real gunshot injuries. Using the “skin–skull–brain model” has some significant advantages: the model is inexpensive, easy to construct, instantly available for use, and eliminates ethics conflicts. The main advantage of such a model is, in comparison with biological substances, the high reproducibility of inflicted traumas.

Light scattering by nonspherical particles: Application to coccoliths detached from Emiliania huxleyi

Computation of the light scattering properties of marine particles has typically been effected using Mie theory (i.e., modeling the particles as homogeneous or layered spheres). Because scattering by irregularly shaped particles is significantly different from that of spheres, particularly in backscattering directions, it is of interest to examine the efficacy of using more complex formulations of light scattering that are not limited to spherically symmetric particles. We applied the discrete dipole approximation (DDA) to the computation of the scattering properties of detached calcium carbonate coccoliths from the coccolithophorid Emiliania huxleyi. Three distinct models of E. huxleyi coccoliths were studied: thin disks with a diameter of approximately 2.75 µm, washers with a 1.38‐ µm hole in the disk, and two parallel disks joined by a hollow tube (a "fishing reel"). The model coccoliths all had the same volume (mass ~ 0.19 pg carbon) and disk diameter and a refractive index of 1.20 relative to water. DDA computations for randomly oriented model coccoliths showed that the total scattering cross section and its spectral variation are similar for each of the three particle shapes and agree well with measurements made in natural E. huxleyi blooms both on a per‐coccolith and per‐calcite concentration basis. The backscattering cross section and its spectral variation was found to be strongly dependent on particle morphology. This dependence was shown to be due to multiple reflections within the particle. Scattering and backscattering coefficients for volume‐equivalent spheres were within a factor of two of those for the disklike models.

Numerical calculation of light scattering from a layered sphere by the boundary-element method

It is demonstrated in the present investigation that the scattering from a layered (i.e., coated) sphere can be calculated numerically by application of the boundary-element method both inside and outside the sphere. A homogeneous sphere is treated first to prove that the computer algorithm is correctly applied, and then the same procedure is followed to deal with a coated sphere. A three-layered sphere will admit of similar treatment, but that is not demonstrated in this study. The scattering intensities from a homogeneous sphere, obtained numerically, are shown to agree well with the analytical Mie solution. It is expected that the calculation algorithm of the analytical Mie-type solution can be improved with the help of the present numerical method.

Radiation of a Dipole Antenna on the Surface of a Partially Screened Layered Sphere: Axially Symmetric Case

Radiation of a Dipole Antenna on the Surface of a Partially Screened Layered Sphere: Axially Symmetric Case

Light scattering by a “soft” layered sphere: Analysis by the method of spectral expansion in Kotel’nikov-Shannon choice functions

Light scattering by a two-layer “soft” sphere is studied. The analysis is made by the method of expansion in the spatial spectrum in Kotel’nikov-Shannon choice functions. In the case where changes of relative refractive indices of the first (Δn 1 and the second ((Δn 2) layers have the same sign, the scattering indicatrices are found to be close to the indicatrices for a homogeneous sphere with averaged effective parameters, and the integrated cross sections should be close as well. However, in the case where Δn 1 and Δn 2 have opposite signs, changes in the indicatrix are stronger. The major lobe becomes weaker and, in certain cases, even vanishes, whereas the side lobes and backward scattering increase in intensity. The physical interpretation of the results that can be used for the analysis of experimental data is given.

Optimization of the damping decrement of free oscillations of a viscoelastic layered sphere with a limitation on weight

The problem of synthesis of a multilayer spherical shell with maximum damping of natural oscillations from a finite set of viscoelastic materials is considered with a limitation on weight. The necessary conditions of optimality are obtained, a computational algorithm is derived, and an example of calculation is presented.

Electroelastic fields in layered piezoelectric spheres

Analytic and discrete-layer models are used to study the displacement and electrostatic potential fields in the static and free vibration response of layered piezoelectric spheres. The analytic solution is developed for the lowest harmonic for purposes of comparison. The discrete-layer model is based on approximations to the variational form of the equations of motion and the charge equation. The displacements and electrostatic potential are separated into functions in the radial direction of the sphere and those for spherical surfaces. General expressions are given for arbitrary approximation functions. For purposes of numerical examples, piecewise quadratic Lagrange interpolation polynomials are used in the radial direction, with spherical harmonics in the circumferential and azimuthal directions. The results from these numerical models are compared with earlier studies for elastic spheres, and several new results are presented for layered piezoelectric spheres.

Effects of black carbon content, particle size, and mixing on light absorption by aerosols from biomass burning in Brazil

Black carbon mass absorption efficiencies of smoke particles were measured for various types of biomass fires during the Smoke, Clouds, and Radiation‐Brazil (SCAR‐B) experiment using thermal evolution measurements for black carbon and optical absorption methods. The obtained results range between 5.2 and 19.3 m2 g−1 with an average value of 12.1±4.0 m2 g−1. Particle size distributions and optical properties were also measured to provide a full set of physical parameters for modeling calculations. Mie theory was used to model the optical properties of the particles assuming both internal and external mixtures coupling the modeling calculations with the experimental results obtained during the campaign. For internal mixing, a particle model with a layered structure consisting of an absorbing black carbon core, surrounded by a nonabsorbing shell, was assumed. Also, for internal mixing, a discrete dipole approximation code was used to simulate packed soot clusters commonly found in electron microscopy photographs of filters collected during the experiment. The modeled results for layered spheres and packed clusters explain black carbon mass absorption coefficients up to values of about 25 m2 g−1, but measurements show even higher values which were correlated with the chemical composition and characteristics of the structure of the particles. Unrealistic high values of black carbon absorption efficiencies were linked to high concentrations of K, which influence the volatilization of black carbon (BC) at lower temperatures than usual, possibly causing artifacts in the determination of BC by thermal technique. The modeling results are compared with nephelometer and light absorption measurements.

Refined coseismic displacement modeling for the 1994 Shikotan and Sanriku‐oki earthquakes

We consider refined modeling of GPS measurements of coseismic displacement for two large earthquakes occurring in the Japan and Kurile Trenches. Calculations are performed for a layered sphere and the homogeneous half‐space more commonly used to model such data, using fault geometry and slip distributions from previously published studies. We show that the difference between the layered sphere and homogeneous half‐space calculations can be significant, as expected from previous theoretical studies. However, it does not appear large enough to seriously affect results from previously published studies of these earthquakes. Nevertheless, the fact that the effects of sphericity and especially layering are measurable in coseismic observations of great earthquakes at moderate distances indicates that these effects should be taken into account in order to fully exploit the precision of modern GPS measurements.

Ultrasonic Characterization of Inertial Confinement Fusion Targets

Inertial confinement fusion (ICF) targets designed to achieve ignition must meet strict surface smoothness and sphericity requirements. One potentially valuable method for evaluating the quality of these targets is resonant ultrasound spectroscopy (RUS). When applied to simple geometries, such as layered spheres or rectangular parallelepipeds, RUS may yield significant information about alloy homogeneity, elastic constants, cavity geometry, the presence of gross defects such as cracking or hemishell bonding problems, and properties of interior fluids. The strengths of RUS techniques for ICF target characterization include applicability at all temperatures of interest with a single apparatus, high sensitivity in frequency spectral measurements, and the inherent acoustic indifference to optically opaque samples. Possible applications and the limitations of RUS methods for examining layer geometry and material properties are addressed. Preliminary room temperature experiments with a deuterium-filled aluminum shell are used to evaluate the utility of many of the described applications. The frequency spectrum compares favorably with theory and displays measurable mode splitting, acoustic-mode resonance widths indicative of cavity boundary dissipative mechanisms, and low-Q elastic modes. The acoustic cavity resonance structure confirms the internal gas density and is used to calculate the two lowest even-order cavity boundary perturbation amplitudes.

Symmetry-breaking bifurcations in spherical Couette flow

The solutions of the nonlinear and linearized Navier-Stokes equations are computed to investigate the instabilities and the secondary two- and three-dimensional regimes in the flow of an incompressible viscous fluid in a thin gap between two concentric differentially rotating spheres. The numerical technique is finite difference in the radial direction, spectral in the azimuthal direction, and pseudo-spectral in the meridional direction. The study follows the experiments by Yavorskaya, Belyaev and co-workers in which a variety of steady axisymmetric and three-dimensional travelling wave secondary regimes was observed in the case of a thin layer and both boundary spheres rotating. In agreement with the experimental results three different types of symmetry-breaking primary bifurcations of the basic equilibrium are detected in the parameter range under consideration.

Volume current method for modeling light scattering by inhomogeneously perturbed spheres

A volume current method (VCM) for calculating the optical scattering by inhomogeneous spheres is presented. The method is applicable to spheres having small refractive-index perturbations. In this method the internal and scattered fields are approximated with a separation-of-variables solution, in which each mode has its own effective-average refractive index. These fields generate an additional volume polarization current in the regions where the refractive index differs from the average refractive index of the sphere. The fields radiated by these polarization currents are then added to the approximate fields radiated by the unperturbed sphere. When they are tested with off-centered layered spheres, the fields calculated with the VCM compare well with those found with separation of variables so long as the changes in the refractive index are small. When the host sphere is near resonance and the perturbation is in a region where the resonant fields are large, the perturbations must be smaller than when the sphere is off resonance.

Effective elastic properties of suspensions of radially symmetric particles

Abstract In this work we study the exact solution to the single-inclusion problem in elastostatics for inclusions which have a spherically symmetric elastic profile. We present a systematic scheme by which the so-called intrinsic moduli, which determine the response of a particle to an external field, can be calculated. For that purpose a transfer-matrix method is developed, which enables us to express the intrinsic moduli of the particle in terms of the moduli of its constituent layers. This method works in both two and three dimensions. In the case of two layers the results of the generalised self-consistent scheme of Christensen and Lo could be easily rederived. The calculated intrinsic moduli can be substituted in previously derived mean-field expressions, thus providing us with expressions for the effective elastic moduli of suspensions of layered spheres (or circles).

Scattering by spherically stratified microwave lens antennas

A comprehensive treatment of scattering by sources in the region of a spherically stratified object composed of discrete shells is presented and compared with measured results. The work encompasses the developments necessary for a thorough understanding of the focusing mechanism of a spherical lens. The method used is a modal technique that employs separation of variables in order to determine an eigenfunction representation of the incident and scattered fields. This formulation provides the Green's function required for the calculation of the scattering from a multiple layered sphere excited by an infinitesimal current element. The algorithm allows both near- and far-field predictions. The scattering by more complicated source field distributions is modeled by applying superposition with the appropriate coordinate transformations. From a practical standpoint, the present analysis allows the limitations of spherical lenses to be determined while providing the information required to optimize the lens design. A system was built based on the new design data, and its measured radiation characteristics are compared to the theoretical predictions. Excellent agreement is observed in most cases. >

Effect of Air Bubbles on Radar Backscattering by Hailstones

Abstract Computational results have been obtained for radar backscattering cross sections of spherical model hailstones containing air bubbles inside the surface water or spongy ice layer. The effective refractive indices of water-air or water-ice-air mixtures have been obtained using the Maxwell-Garnett and Bruggeman effective medium approximations. The radar backscattering cross sections have been calculated for a layered sphere composed of an ice core and water-air or ice-water-air outside layer. The amount of air in a surface layer was varied between 0% and 20% by volume. The presence of air bubbles in the surface layer shifts positions of the backscattering peaks and modifies the backscattered intensifies at peak values. The dependence of the backscattering cross section on the air bubbles volume fraction is stronger at shorter wavelengths.

Polarizability Matrix of Layered Chiral Sphere

Polarizability Matrix of Layered Chiral Sphere