Multilayered Sphere Research Articles

The characteristics of layers for stratified Luneberg lens

The dependence of characteristics of a stratified Luneberg lens on the layer parameters has been studied in numerical experiments using a mathematical model based on the rigorous solution of the electrodynamic problem of diffraction on a multilayer sphere.

Optical models for conjugates of gold and silver nanoparticles with biomacromolecules

We discuss optical models for gold and silver nanoparticle bioconjugates that consist of a metal core and a polymer shell formed by recognizing and target molecules. A universal dependence of the normalized spectral shift of the extinction maximum on the shell/core thickness ratio has been found in the dipole approximation. Using Mie's theory for multilayer spheres, we have calculated the extinction and static light-scattering spectra (at 90∘), as well as the differential spectra related to the adsorption of recognizing and target molecules. The differential spectra possess a characteristic resonance that is red-shifted as compared with the known resonance of gold particles. Having in mind an optimization of conjugate-nanosensors, we have studied the following problem: what particle size is optimal for the transduction of polymer adsorption events into variations of recorded optical signals? The maximal values of the differential resonance are observed for gold particles with diameters of about 40–60nm (extinction) or 70–90nm (scattering). In the case of silver particles, the corresponding optimal diameters are equal to 20–40nm for extinction and 30–50nm for scattering.

Elastodynamic solution for spherically symmetric problems of a multilayered hollow sphere

The elastodynamic solution of a multilayered hollow sphere for spherically symmetric problems is obtained by decomposition into two parts, one being the quasi-static and the other the dynamic solution. The quasi-static solution is firstly derived by means of the state-space method, and the dynamic solution is obtained by utilizing the separation of variables method and the orthotropic expansion technique. The solutions for displacement and stresses are obtained in result. The present method is suitable for a multilayered spherically isotropic hollow sphere, with arbitrary thickness of each of the layers and arbitrary initial conditions, subjected to arbitrary form of a spherically symmetric dynamic load at the internal and external surfaces. Numerical results are finally presented.

Coupled Problem of Thermoelasticity for Multilayered Spheres with Time-Dependent Boundary Conditions

Coupled Problem of Thermoelasticity for Multilayered Spheres with Time-Dependent Boundary Conditions

Generalized coupled transient thermoelastic problem of multilayered spheres by the hybrid numerical method

This paper deals with axisymmetric quasi-static coupled thermoelastic problems for multilayered spheres. Laplace transforms and finite difference methods are used to analyse the problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. Solutions are obtained for the temperature and thermal deformation distributions for the transient and steady state. It is demonstrated that the computational procedures established in this paper are capable of solving the generalized thermoelasticity problem of multilayered spheres.

Improved recursive algorithm for light scattering by a multilayered sphere.

An improved recurrence algorithm to calculate the scattering field of a multilayered sphere is developed. The internal and external electromagnetic fields are expressed as a superposition of inward and outward waves. The alternative yet equivalent expansions of fields are proposed by use of the first kind of Bessel function and the first kind of Hankel function instead of the first and the second kinds of Bessel function. The final recursive expressions are similar in form to those of Mie theory for a homogeneous sphere and are proved to be more concise and convenient than earlier forms. The new algorithm avoids the numerical difficulties, which give rise to significant errors encountered in practice by previous methods, especially for large, highly absorbing thin shells. Various calculations and tests show that this algorithm is efficient, numerically stable, and accurate for a large range of size parameters andrefractive indices.

RCS computation of large inhomogeneous objects using a fast integral equation solver

In this paper, we apply a fast Fourier transform (FFT) accelerated volume integral equation solver to compute the radar cross section of large-scale inhomogeneous objects. This method is related to Bojarski's k-space method and the subsequent conjugate-(CG) and biconjugate-gradient (BCG) FFT algorithms. The method developed here combines the weak-form discretization with the BCG and stabilized BCG (BCGS) solvers. We show that this method has marked improvements over related algorithms. The numerical method has been validated by Mie series for multilayer spheres and applied to some practical problems. With this method we are currently able to solve a three-dimensional problem with a volume of size 3648/spl lambda//sup 3/ (21.23 million unknowns) on a single workstation.

Drying of Liquid Dispersions—A Unified Approach to Kinetics and Modeling

The article presents a unified approach to interpretation of drying kinetics and modeling of the drying process for suspensions, solutions, emulsions and pastes. The approach is based on phenomenological analysis of temperature-moisture relationships T(X) with account for temperature plateaux that actually show-up, or could exist under certain drying conditions. In addition, a unified mathematical model is proposed that includes the differential equations for mass and heat diffusion along with their analytical solutions for a multi-layer plate, cylinder and sphere. Interconnections in the simultaneous heat-mass transfer, cross-effects and any other details of a real process are taken into account separately, by semi-empirical temperature-moisture function T(X). The principles of piece-wise multizone approximation of these temperature-moisture curves are presented. The hyperbolic and two-arc approximations for each separate zone are described. The set of 12 organic and inorganic materials either synthetic or of animal and plant origin such as meat processing sludge, heavy corn steep water, gelatin, starch, sugar, salt, combined latex emulsion, P-salt, gamma acid, dispersing and bleaching agents was taken as example for the development and validation of this approach.

A Multilayer Model for Gold Nanoparticle Bioconjugates: Application to Study of Gelatin and Human IgG Adsorption Using Extinction and Light Scattering Spectra and the Dynamic Light Scattering Method

A new model of colloidal gold (CG) bioconjugates is proposed. The model consists of a gold core and a primary polymer shell formed during conjugate synthesis. Additionally, the conjugate includes a secondary shell formed during its interaction with target molecules. Each of the inhomogeneous shells is modeled by the arbitrary number of discrete layers. Using Mie theory for multilayered spheres, we calculated the extinction and static light scattering (SLS, at 90°) spectra, as well as differential spectra ΔA(λ), ΔI(λ) describing the effects of primary and secondary shells. Our calculations are performed for the conjugates with gold particle diameters d = 10–160 nm and two 5-nm shells. The primary shell consists of two 2.5-nm layers with the refractive indices of 1.50 and 1.45; the secondary shell, of two 2- and 3-nm layers with the refractive indices of 1.45 and 1.40. The differential spectra are related to the adsorption of target molecules and possess a characteristic resonance that is shifted to the red region of spectra compared to the usual localized plasmon resonances of gold particles. The maximal values of differential resonances ΔAmax and ΔImax are observed for gold particles with diameters about 40–60 nm (extinction spectra) or 70–90 nm (the SLS spectra). The adsorption of human gamma-globulin (hIgG) and gelatin onto 15- and 34-nm gold particles was studied using the SLS and extinction spectra in combination with the dynamic light scattering measurements. It is shown that the thickness of adsorbed layer is equal to 5–6 nm for hIgG and to 15–18 nm for gelatin. The experimental extinction and SLS spectra for CG + hIgG conjugates are well explained by a simple model with the gold core and homogeneous polymer coating. For the CG + gelatin conjugates, we used the new model with inhomogeneous polymer coating, which is modeled by 10 discrete layers with the total thickness of 16–18 nm and exponential spatial profile of shell refractive index.

Scattering by an arbitrary multi-layered spheroid: theory and numerical results

In this paper a simple algorithm is presented for calculating light scattering by a multi-layered spheroid for both normal and oblique incidence. Results of several numerical tests are given. They present the extinction efficiency for different aspect-ratio spheroids in comparison with that of the proper multi-layered sphere and cylinder.

Three-dimensional static analysis of multi-layered piezoelectric hollow spheres via the state space method

A general non-axisymmetric exact analysis of the statics of a laminated piezoelectric hollow sphere is presented in the paper by using a state space method. To select a proper set of state variables, three displacement functions and two stress functions are introduced. It is found that the basic equations of a spherically isotropic piezoelectric medium are eventually turned to two separated state equations with constant coefficients, the solutions of which are then obtained by virtue of matrix theory. The continuity conditions at each interface are then used to derive two relationships between respective boundary variables at the inner and outer spherical surfaces. No matter how many layers the sphere contains, the orders of the final solving equations remain unaltered.

Rapidly recomputable EEG forward models for realistic headshapes

With the increasing availability of surface extraction techniques for magneticresonance and x-ray computed tomography images, realistic head models can bereadily generated as forward models in the analysis of electroencephalography (EEG) andmagnetoencephalography (MEG) data.Inverse analysis of this data, however, requires that the forward model becomputationally efficient. We propose two methods for approximating the EEGforward model using realistic head shapes. The `sensor-fitted sphere' approachfits a multilayer sphere individually to each sensor, and the`three-dimensional interpolation' scheme interpolates using a grid on which anumerical boundary element method (BEM) solution has been precomputed. We havecharacterized the performance of each method in terms of magnitude andsubspace error metrics, as well as computational and memory requirements. Wehave also made direct performance comparisons with traditional sphericalmodels. The approximation provided by the interpolative scheme had an accuracynearly identical to full BEM, even within 3 mm of the inner skull surface.Forward model computation during inverse procedures was approximately 30 timesfaster than for a traditional three-shell spherical model. Cast in thisframework, high-fidelity numerical solutions currently viewed ascomputationally prohibitive for solving the inverse problem (e.g. linearGalerkin BEM) can be rapidly recomputed in a highly efficient manner. Thesensor-fitting method has a similar one-time cost to the BEM method, and whileit produces some improvement over a standard three-shell sphere, itsperformance does not approach that of the interpolation method. In bothmethods, there is a one-time cost associated with precomputing the forwardsolution over a set of grid points.

Nonuniform Luneburg and two-shell lens antennas: radiation characteristics and design optimization

Design optimization of radially nonuniform spherical lens antennas is the focus of this paper. In particular, special attention is given to the optimal design of nonuniform Luneburg (1964) lens antennas. One of the important engineering objectives of designing an optimal Luneburg lens antenna is to use as small number of shells as possible while maintaining an acceptable gain and sidelobe performance. In a typical radially uniform design, by reducing the number of shells, the gain is decreased and the grating lobes are increased. This deficiency in the radiation performance of the uniform lens antenna can be overcome by designing the nonuniform lens antenna. This necessitates the optimum selection of each layer thickness and permittivity. A genetic algorithm (GA) optimizer with adaptive cost function is implemented to obtain the optimal design. In this manner, the GA optimizer simultaneously determines the optimal material and its thickness for each shell by controlling the gain and sidelobes envelope of the radiation pattern. Various lens geometries, including air gaps and feed offset from the lens surface, are analyzed by using the dyadic Green's functions of the multilayered dielectric sphere. Many useful engineering design guidelines have been suggested for the optimum construction of the lens. The results have been satisfactory and demonstrate the utility of the GA/adaptive cost-function algorithm. Additionally, the radiation characteristics of a novel two-shell lens antenna have been studied, and its performance is compared to the Luneburg lens.

Plane Wave Scattering By an Achiral Multilayered Sphere in an Infinitely Extended Chiral Host Medium - Abstract

An analytic solution to the problem of plane wave scattering by an achiral multilayered sphere in a host chiral medium is obtained in this paper. By applying the radiation-to-scattering transform, the scattering problem can be considered as the specific radiation problems where the radiated source equivalent to the electromagnetic plane wave is located at infinity. The volumetric currents which generate right circular polarization (RCP) and left circular polarization (LCP) plane waves, respectively, are found. An integral equation consisting the volumetric current distributions and the dyadic Green's functions is formulated to obtain both the equivalent incident wave fields and the scattered fields. Two-layered lossless and lossy dielectric spheres and a conducting sphere with a dielectric coated layer buried in an infinitely extended host chiral medium are considered and the expressions for the scattered fields in far-zone are found in explicit analytic form. The characteristics of scattered fields are illustrated and discussed in terms of the circular polarization degree and linear polarization degree against different chiral admittances and sizes.

Plane Wave Scattering by an Achiral Multilayered Sphere in an Infinitely Extended Chiral Host Medium

Plane Wave Scattering by an Achiral Multilayered Sphere in an Infinitely Extended Chiral Host Medium

Free vibration of multi-layered spherically isotropic hollow spheres

A three-dimensional analysis is carried out for the free vibrations of a multi-layered spherically isotropic hollow sphere using a state-space method. By the introduction of three displacement functions and two stress functions, two independent state equations with varying coefficients are derived. Taylor's expansion theorem is then employed to obtain solutions to the two state equations and relationships between the state variables at the upper and lower surfaces of each lamina are established. A variable substitution technique is particularly used to make the derivation more natural and simpler. By virtue of the continuity conditions between two adjacent layers, two sets of linear algebraic equations about the boundary variables at the inner and outer surfaces of a multi-layered hollow sphere are obtained. Frequency equations for the free vibrations are then presented.

Light scattering by multilayer ellipsoids in the Rayleigh approximation

A problem of light scattering by multilayer confocal ellipsoids is solved in the Rayleigh approximation. The electric field of a light wave is assumed constant and a set of Laplace equations with the corresponding boundary conditions is considered. The final expression for the polarizability of a particle is represented in the matrix form (2×2 matrices) in terms of parameters of a nucleus and subsequent layers. Numerical calculations of the scattering and absorption efficiencies of small multilayer spheres obtained using the exact (the generalization of the Mie theory) and approximate solutions well agree with each other.

Electromagnetic scattering from target buried in layer of randomly distributed trunks

An electromagnetic scattering model for two adjacent trunks and a deterministic target (sphere) above a rough surface ground plane was analyzed by using the reciprocity theorem and image theory. A finite-length multilayer dielectric cylinder was used to model the trunk. The iterative algorithm and spherical vector wave function were used to calculate the scattering amplitude matrix of the finite-length multilayer dielectric cylinder and sphere, respectively. The validity of the method was checked by numerical computations based on the moment method. Finally, the influences of the bark layer and the roughness of the surface on the scattering pattern of a target (sphere) are also discussed in the L-band, C-band, and X-band. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 24: 162–166, 2000.

Isolable and Fluorescent Mesoscopic Micelles Made of an Amphiphilic Derivative of Tris-bipyridyl Ruthenium Hexafluorophosphate

Bis(2,2'-bipyridyl)(dioctadecyl-2-[2,2‘-dipyridylmethylene] malonate) ruthenium(II) dihexafluorophosphate has been synthesized and was converted to an amphiphilic distearyl ester, 2b. Light-induced charge transfer from ruthenium to the pyridyl ligands occurred preferably to the malonate-type ligand. Its reduction potential was less negative by 400 mV than that of bipyridyl. Whereas the chloroform solution of the dioctadecyl ester 2b did not show any luminescence, the aqueous suspension produced between 30 and 150% of the emission intensity of the symmetrical ruthenium tris(bipyridine) complex in water. Transmission electron microscopy at cryogenic temperature of the sonicated aqueous solution of 2b revealed multilayer spheres without an entrapped water volume. The solid, onion-type sphere is totally filled with interdigitated bilayers of 2b and has therefore the character of a rigid, spherical micelle, not that of a vesicle. The headgroup layer consists of a back-to-back ruthenium complex bilayer; their alkyl chains point inward and outward. The spherical micelles were isolated from water in solid form and were stable on mica and gold surfaces for many hours as was shown by atomic force microscopy. Incorporation of 2b into fluid host vesicles or micelles lead to complete loss of luminescence. Various redox active water- or membrane-soluble agents quenched 30−50% of the emission, which indicates some energy transfer over several layers.

Introduction of quantum finite-size effects in the Mie's theory for a multilayered metal sphere in the dipolar approximation: Application to free and matrix-embedded noble metal clusters

A mixed classical/quantum model for calculating the optical response of free and matrix-embedded multilayered metal spheres in the dipolar approximation is presented. The conduction electrons are quantum-mechanically treated in the framework of the time-dependent local-density-approximation formalism (TDLDA), whereas the surrounding matrix, the ionic metal backgrounds and the non-metallic materials are classically described through homogeneous charge distributions or/and dielectric media. Except for the TDLDA calculations, the present formalism is completely analytical and can be applied to coated spheres with any number of metal or dielectric layers. Contrary to the previous TDLDA-based models involving an inner or/and an outer dielectric medium (one or two interfaces), all the dielectric effects (screening and absorption) are self-consistently calculated. In particular, the interband transitions and the mutual interplay between the conduction and core electrons are self-consistently treated. The deficiencies of the previous models are analyzed, and the results are compared with the classical Mie's theory, over the entire spectral range. The building-up of the classical absorption spectrum, consisting of the surface plasmon resonance and the interband transitions, is clearly observed as the cluster size increases.