Journal articles: 'Spheroidal geometry'

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Ivers, D. J. "Kinematic dynamos in spheroidal geometries." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2206 (October 2017): 20170432. http://dx.doi.org/10.1098/rspa.2017.0432.

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The kinematic dynamo problem is solved numerically for a spheroidal conducting fluid of possibly large aspect ratio with an insulating exterior. The solution method uses solenoidal representations of the magnetic field and the velocity by spheroidal toroidal and poloidal fields in a non-orthogonal coordinate system. Scaling of coordinates and fields to a spherical geometry leads to a modified form of the kinematic dynamo problem with a geometric anisotropic diffusion and an anisotropic current-free condition in the exterior, which is solved explicitly. The scaling allows the use of well-developed spherical harmonic techniques in angle. Dynamo solutions are found for three axisymmetric flows in oblate spheroids with semi-axis ratios 1≤ a / c ≤25. For larger aspect ratios strong magnetic fields may occur in any region of the spheroid, depending on the flow, but the external fields for all three flows are weak and concentrated near the axis or periphery of the spheroid.

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Kiani, Mostafa, Nabi Chegini, Abdolreza Safari, and Borzoo Nazari. "SPHEROIDAL SPLINE INTERPOLATION AND ITS APPLICATION IN GEODESY." Geodesy and cartography 46, no. 3 (October 12, 2020): 123–35. http://dx.doi.org/10.3846/gac.2020.11316.

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The aim of this paper is to study the spline interpolation problem in spheroidal geometry. We follow the minimization of the norm of the iterated Beltrami-Laplace and consecutive iterated Helmholtz operators for all functions belonging to an appropriate Hilbert space defined on the spheroid. By exploiting surface Green’s functions, reproducing kernels for discrete Dirichlet and Neumann conditions are constructed in the spheroidal geometry. According to a complete system of surface spheroidal harmonics, generalized Green’s functions are also defined. Based on the minimization problem and corresponding reproducing kernel, spline interpolant which minimizes the desired norm and satisfies the given discrete conditions is defined on the spheroidal surface. The application of the results in Geodesy is explained in the gravity data interpolation over the globe.

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Momoh, O. D., M. N. O. Sadiku, and S. M. Musa. "Solution of Axisymmetric Potential Problem in Oblate Spheroid Using the Exodus Method." Journal of Computational Engineering 2014 (March 17, 2014): 1–6. http://dx.doi.org/10.1155/2014/126905.

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This paper presents the use of Exodus method for computing potential distribution within a conducting oblate spheroidal system. An explicit finite difference method for solving Laplace’s equation in oblate spheroidal coordinate systems for an axially symmetric geometry was developed. This was used to determine the transition probabilities for the Exodus method. A strategy was developed to overcome the singularity problems encountered in the oblate spheroid pole regions. The potential computation results obtained correlate with those obtained by exact solution and explicit finite difference methods.

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Xue, Changfeng, Robert Edmiston, and Shaozhong Deng. "Image Theory for Neumann Functions in the Prolate Spheroidal Geometry." Advances in Mathematical Physics 2018 (2018): 1–13. http://dx.doi.org/10.1155/2018/7683929.

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Interior and exterior Neumann functions for the Laplace operator are derived in terms of prolate spheroidal harmonics with the homogeneous, constant, and nonconstant inhomogeneous boundary conditions. For the interior Neumann functions, an image system is developed to consist of a point image, a line image extending from the point image to infinity along the radial coordinate curve, and a symmetric surface image on the confocal prolate spheroid that passes through the point image. On the other hand, for the exterior Neumann functions, an image system is developed to consist of a point image, a focal line image of uniform density, another line image extending from the point image to the focal line along the radial coordinate curve, and also a symmetric surface image on the confocal prolate spheroid that passes through the point image.

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Pincak, R. "Spheroidal geometry approach to fullerene molecules." Physics Letters A 340, no. 1-4 (June 2005): 267–74. http://dx.doi.org/10.1016/j.physleta.2005.04.023.

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Vafeas, Panayiotis, Eleftherios Protopapas, and Maria Hadjinicolaou. "On the Analytical Solution of the Kuwabara-Type Particle-in-Cell Model for the Non-Axisymmetric Spheroidal Stokes Flow via the Papkovich–Neuber Representation." Symmetry 14, no. 1 (January 15, 2022): 170. http://dx.doi.org/10.3390/sym14010170.

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Modern engineering technology often involves the physical application of heat and mass transfer. These processes are associated with the creeping motion of a relatively homogeneous swarm of small particles, where the spheroidal geometry represents the shape of the embedded particles within such aggregates. Here, the steady Stokes flow of an incompressible, viscous fluid through an assemblage of particles, at low Reynolds numbers, is studied by employing a particle-in-cell model. The mathematical formulation adopts the Kuwabara-type assumption, according to which each spheroidal particle is stationary and it is surrounded by a confocal spheroid that creates a fluid envelope, in which the Newtonian fluid moves with a constant velocity of arbitrary orientation. The boundary value problem in the fluid envelope is solved by imposing non-slip conditions on the surface of the spheroid, which is also considered as non-penetrable, while zero vorticity is assumed on the fictitious spheroidal boundary along with a uniform approaching velocity. The three-dimensional flow fields are calculated analytically for the first time, in the spheroidal geometry, by virtue of the Papkovich–Neuber representation. Through this, the velocity and the total pressure fields are provided in terms of a vector and the scalar spheroidal harmonic potentials, which enables the thorough study of the relevant physical characteristics of the flow fields. The newly obtained analytical expressions generalize to any direction with the existing results holding for the asymmetrical case, which were obtained with the aid of a stream function. These can be employed for the calculation of quantities of physical or engineering interest. Numerical implementation reveals the flow behavior within the fluid envelope for different geometrical cell characteristics and for the arbitrarily-assumed velocity field, thus reflecting the different flow/porous media situations. Sample calculations show the excellent agreement of the obtained results with those available for special geometrical cases. All of these findings demonstrate the usefulness of the proposed method and the powerfulness of the obtained analytical expansions.

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Öztürk, Yavuz, Ali Can Aktaş, and Bekir Aktaş. "A Z-gradient coil on spheroidal geometry." Journal of Magnetism and Magnetic Materials 552 (June 2022): 169169. http://dx.doi.org/10.1016/j.jmmm.2022.169169.

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Anastasiou, Eirini I., and Ioannis K. Chatjigeorgiou. "The Radiation Problem of a Submerged Oblate Spheroid in Finite Water Depth Using the Method of the Image Singularities System." Fluids 7, no. 4 (April 8, 2022): 133. http://dx.doi.org/10.3390/fluids7040133.

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

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Sten, J. C. E., and E. A. Marengo. "Inverse Source Problem in an Oblate Spheroidal Geometry." IEEE Transactions on Antennas and Propagation 54, no. 11 (November 2006): 3418–28. http://dx.doi.org/10.1109/tap.2006.884292.

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Ghosh, Mithun. "Dark matter halo with charge in pseudo-spheroidal geometry." Modern Physics Letters A 36, no. 25 (August 20, 2021): 2150178. http://dx.doi.org/10.1142/s0217732321501789.

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The concept of dark matter (DM) hypothesis comes out as a result from the input of the observed flat rotational velocity. With the assumption that the galactic halo is pseudo-spheroidal and filled with charged perfect fluid, we have obtained a solution which has inkling to a (nearly) flat universe, compatible with the modern day cosmological observations. Various other important aspects of the solution such as attractive gravity in the halo region and the stability of the circular orbit are also explored. Also, the matter in the halo region satisfies the known equation of state which indicates its non-exotic nature.

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Sten, Johan C. E., and Edwin A. Marengo. "Inverse Source Problem in the Spheroidal Geometry: Vector Formulation." IEEE Transactions on Antennas and Propagation 56, no. 4 (April 2008): 961–69. http://dx.doi.org/10.1109/tap.2008.919176.

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12

Kanters, Ren� P. F., and J. J. Steggerda. "Recognition of toroidal and spheroidal geometry in metal clusters." Journal of Cluster Science 1, no. 3 (September 1990): 229–39. http://dx.doi.org/10.1007/bf00702742.

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Bjørge, Isabel M., Ana M. S. Costa, A. Sofia Silva, João P. O. Vidal, J. Miguel Nóbrega, and João F. Mano. "Tuneable spheroidal hydrogel particles for cell and drug encapsulation." Soft Matter 14, no. 27 (2018): 5622–27. http://dx.doi.org/10.1039/c8sm00921j.

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BURNETT, DAVID S. "RADIATION BOUNDARY CONDITIONS FOR THE HELMHOLTZ EQUATION FOR ELLIPSOIDAL, PROLATE SPHEROIDAL, OBLATE SPHEROIDAL AND SPHERICAL DOMAIN BOUNDARIES." Journal of Computational Acoustics 20, no. 04 (November 29, 2012): 1230001. http://dx.doi.org/10.1142/s0218396x12300010.

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One of the most popular radiation boundary conditions for the Helmholtz equation in exterior 3-D regions has been the sequence of operators developed by Bayliss et al.1 for computational domains with spherical exterior boundaries. The present paper extends those spherical operators to triaxial ellipsoidal boundaries by utilizing two mathematical constructs originally developed for ellipsoidal acoustic infinite elements.2 The two constructs are: (i) a radial/angular coordinate system for ellipsoidal geometry, and (ii) a convergent ellipsoidal radial expansion for exterior fields, analogous to the classical spherical multipole expansion. The ellipsoidal radial and angular coordinates are smooth generalizations of the traditional radial and angular coordinates used in spherical, prolate spheroidal and oblate spheroidal systems. As a result, all four coordinate systems and their corresponding radiation boundary conditions are included within this single ellipsoidal system, varying smoothly from one to the other. The geometric flexibility of this system enables the exterior boundary of the computational domain to closely circumscribe objects with a wide range of aspect ratios, thereby reducing the size and cost of 3-D computational models.

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DASSIOS, G. "The fundamental solutions for irrotational and rotational Stokes flow in spheroidal geometry." Mathematical Proceedings of the Cambridge Philosophical Society 143, no. 1 (July 2007): 243–53. http://dx.doi.org/10.1017/s0305004107000291.

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AbstractThe Stokes operator E2 governs the irrotational axisymmetric Stokes flow and its square governs the corresponding rotational flow. In spheroidal coordinates the elements of the solution space ker E2 enjoy a spectral decomposition into separable eignefunction, while the elements of the ker E4 accept a spectral decomposition in terms of semiseparable eigensolutions involving 3D-by-3D eigenfunctions of the Gegenbauer operator. These spectral characteristics are utilized to construct the fundamental solutions for both the E2 and the E4 operators in spheroidal geometry. The fundamental solution for E2 is expressed in terms of the elements of the irrotational space ker E2, while the fundamental solution for E4 is expressed in terms of the corresponding generalized eigenfunctions alone.

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CHATTOPADHYAY, PRADIP KUMAR, RUMI DEB, and BIKASH CHANDRA PAUL. "RELATIVISTIC SOLUTION FOR A CLASS OF STATIC COMPACT CHARGED STAR IN PSEUDO-SPHEROIDAL SPACETIME." International Journal of Modern Physics D 21, no. 08 (August 2012): 1250071. http://dx.doi.org/10.1142/s021827181250071x.

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Considering Vaidya–Tikekar metric, we obtain a class of solutions of the Einstein–Maxwell equations for a charged static fluid sphere. The physical 3-space (t = const. ) here is described by pseudo-spheroidal geometry. The relativistic solution for the theory is used to obtain models for charged compact objects; thereafter, a qualitative analysis of the physical aspects of compact objects are studied. The dependence of some of the properties of a superdense star on the parameters of the three geometry is explored. We note that the spheroidicity parameter a plays an important role for determining the properties of a compact object. A nonlinear equation of state (EOS) is required to describe a charged compact object with pseudo-spheroidal geometry, which we have shown for known masses of compact objects. We also note that the size of a static compact charged star is more than that of a static compact star without charge.

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Noir, J., and D. Cébron. "Precession-driven flows in non-axisymmetric ellipsoids." Journal of Fluid Mechanics 737 (November 26, 2013): 412–39. http://dx.doi.org/10.1017/jfm.2013.524.

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AbstractWe study the flow forced by precession in rigid non-axisymmetric ellipsoidal containers. To do so, we revisit the inviscid and viscous analytical models that have been previously developed for the spheroidal geometry by, respectively, Poincaré (Bull. Astronomique, vol. XXVIII, 1910, pp. 1–36) and Busse (J. Fluid Mech., vol. 33, 1968, pp. 739–751), and we report the first numerical simulations of flows in such a geometry. In strong contrast with axisymmetric spheroids, where the forced flow is systematically stationary in the precessing frame, we show that the forced flow is unsteady and periodic. Comparisons of the numerical simulations with the proposed theoretical model show excellent agreement for both axisymmetric and non-axisymmetric containers. Finally, since the studied configuration corresponds to a tidally locked celestial body such as the Earth’s Moon, we use our model to investigate the challenging but planetary-relevant limit of very small Ekman numbers and the particular case of our Moon.

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Kariotou, Foteini, Panayiotis Vafeas, and Polycarpos K. Papadopoulos. "Mathematical Modeling of the Evolution of the Exterior Boundary in Spheroidal Tumour Growth." International Journal of Mathematical Models and Methods in Applied Sciences 16 (March 12, 2022): 56–63. http://dx.doi.org/10.46300/9101.2022.16.11.

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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.

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Biria, Ashley D., and Ryan P. Russell. "Equinoctial elements for Vinti theory: Generalizations to an oblate spheroidal geometry." Acta Astronautica 153 (December 2018): 274–88. http://dx.doi.org/10.1016/j.actaastro.2017.11.013.

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TIKEKAR, RAMESH, and KANTI JOTANIA. "RELATIVISTIC SUPERDENSE STAR MODELS OF PSEUDO SPHEROIDAL SPACE–TIME." International Journal of Modern Physics D 14, no. 06 (June 2005): 1037–48. http://dx.doi.org/10.1142/s021827180500722x.

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The physically viable models of compact stars like SAX (J1808.4-3658) can be obtained using Vaidya–Tikekar ansatz prescribing spheroidal geometry for their interior space–time. We discuss here the suitability of an alternative ansatz in this context. The models of superdense star are proposed using a general three parameter family of solutions of relativistic field equations obtained adopting the alternative ansatz. The setup is shown to admit physically viable models of superdense stars and strange matter stars such as Her. X-1.

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Stark, C. R., and D. A. Diver. "Evolution of spheroidal dust in electrically active sub-stellar atmospheres." Astronomy & Astrophysics 644 (December 2020): A131. http://dx.doi.org/10.1051/0004-6361/202037589.

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Context. Understanding the source of sub-stellar polarimetric observations in the optical and near-infrared is key to characterizing sub-stellar objects and developing potential diagnostics for determining properties of their atmospheres. Differential scattering from a population of aligned, non-spherical dust grains is a potential source of polarization that could be used to determine geometric properties of the dust clouds. Aims. This paper addresses the problem of the spheroidal growth of dust grains in electrically activated sub-stellar atmospheres. It presents the novel application of a mechanism whereby non-spherical, elongated dust grains can be grown via plasma deposition as a consequence of the surface electric field effects of charged dust grains. Methods. We numerically solve the differential equations governing the spheroidal growth of charged dust grains via plasma deposition as a result of surface electric field effects in order to determine how the dust eccentricity and the dust particle eccentricity distribution function evolve with time. From these results, we determine the effect of spheroidal dust on the observed linear polarization. Results. Numerical solutions show that e ≈ 0.94 defines a watershed eccentricity, where the eccentricity of grains with an initial eccentricity less than (greater than) this value decreases (increases) and spherical (spheroidal) growth occurs. This produces a characteristic bimodal eccentricity distribution function yielding a fractional change in the observed linear polarization of up to ≈0.1 corresponding to dust grains of maximal eccentricity at wavelengths of ≈1 μm, consistent with the near infrared observational window. Order of magnitude calculations indicate that a population of aligned, spheroidal dust grains can produce degrees of polarization P ≈ 𝒪(10−2 − 1%) consistent with observed polarization signatures. Conclusions. The results presented here are relevant to the growth of non-spherical, irregularly shaped dust grains of general geometry where non-uniform surface electric field effects of charged dust grains are significant. The model described in this paper may also be applicable to polarization from galactic dust and dust growth in magnetically confined plasmas.

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Yue, Kan, Mingjun Huang, Ryan L. Marson, Jinlin He, Jiahao Huang, Zhe Zhou, Jing Wang, et al. "Geometry induced sequence of nanoscale Frank–Kasper and quasicrystal mesophases in giant surfactants." Proceedings of the National Academy of Sciences 113, no. 50 (November 28, 2016): 14195–200. http://dx.doi.org/10.1073/pnas.1609422113.

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Frank–Kasper (F-K) and quasicrystal phases were originally identified in metal alloys and only sporadically reported in soft materials. These unconventional sphere-packing schemes open up possibilities to design materials with different properties. The challenge in soft materials is how to correlate complex phases built from spheres with the tunable parameters of chemical composition and molecular architecture. Here, we report a complete sequence of various highly ordered mesophases by the self-assembly of specifically designed and synthesized giant surfactants, which are conjugates of hydrophilic polyhedral oligomeric silsesquioxane cages tethered with hydrophobic polystyrene tails. We show that the occurrence of these mesophases results from nanophase separation between the heads and tails and thus is critically dependent on molecular geometry. Variations in molecular geometry achieved by changing the number of tails from one to four not only shift compositional phase boundaries but also stabilize F-K and quasicrystal phases in regions where simple phases of spheroidal micelles are typically observed. These complex self-assembled nanostructures have been identified by combining X-ray scattering techniques and real-space electron microscopy images. Brownian dynamics simulations based on a simplified molecular model confirm the architecture-induced sequence of phases. Our results demonstrate the critical role of molecular architecture in dictating the formation of supramolecular crystals with “soft” spheroidal motifs and provide guidelines to the design of unconventional self-assembled nanostructures.

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Zhang, Keke, Kit H. Chan, and Xinhao Liao. "On precessing flow in an oblate spheroid of arbitrary eccentricity." Journal of Fluid Mechanics 743 (March 5, 2014): 358–84. http://dx.doi.org/10.1017/jfm.2014.58.

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AbstractWe consider a homogeneous fluid of viscosity $\nu $ confined within an oblate spheroidal cavity of arbitrary eccentricity $\mathcal{E}$ marked by the equatorial radius $d$ and the polar radius $d \sqrt{1-\mathcal{E}^2}$ with $0<\mathcal{E}<1$. The spheroidal container rotates rapidly with an angular velocity ${\boldsymbol{\Omega}}_0 $ about its symmetry axis and precesses slowly with an angular velocity ${\boldsymbol{\Omega}}_p$ about an axis that is fixed in space. It is through both topographical and viscous effects that the spheroidal container and the viscous fluid are coupled together, driving precessing flow against viscous dissipation. The precessionally driven flow is characterized by three dimensionless parameters: the shape parameter $\mathcal{E}$, the Ekman number ${\mathit{Ek}}=\nu /(d^2 \delimiter "026A30C {\boldsymbol{\Omega}}_0\delimiter "026A30C )$ and the Poincaré number ${\mathit{Po}}=\pm \delimiter "026A30C {\boldsymbol{\Omega}}_p\delimiter "026A30C / \delimiter "026A30C \boldsymbol{\Omega}_0\delimiter "026A30C $. We derive a time-dependent asymptotic solution for the weakly precessing flow in the mantle frame of reference satisfying the no-slip boundary condition and valid for a spheroidal cavity of arbitrary eccentricity at ${\mathit{Ek}}\ll 1$. No prior assumptions about the spatial–temporal structure of the precessing flow are made in the asymptotic analysis. We also carry out direct numerical simulation for both the weakly and the strongly precessing flow in the same frame of reference using a finite-element method that is particularly suitable for non-spherical geometry. A satisfactory agreement between the asymptotic solution and direct numerical simulation is achieved for sufficiently small Ekman and Poincaré numbers. When the nonlinear effect is weak with $\delimiter "026A30C {\mathit{Po}}\delimiter "026A30C \ll 1$, the precessing flow in an oblate spheroid is characterized by an azimuthally travelling wave without having a mean azimuthal flow. Stronger nonlinear effects with increasing $\delimiter "026A30C {\mathit{Po}}\delimiter "026A30C $ produce a large-amplitude, time-independent mean azimuthal flow that is always westward in the mantle frame of reference. Implications of the precessionally driven flow for the westward motion observed in the Earth’s fluid core are also discussed.

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Dassios, George, and Panayiotis Vafeas. "On the Spheroidal Semiseparation for Stokes Flow." Research Letters in Physics 2008 (February 13, 2008): 1–4. http://dx.doi.org/10.1155/2008/135289.

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Many heat and mass transport problems involve particle-fluid systems, where the assumption of Stokes flow provides a very good approximation for representing small particles embedded within a viscous, incompressible fluid characterizing the steady, creeping flow. The present work is concerned with some interesting practical aspects of the theoretical analysis of Stokes flow in spheroidal domains. The stream function ψ, for axisymmetric Stokes flow, satisfies the well-known equation E4ψ=0. Despite the fact that in spherical coordinates this equation admits separable solutions, this property is not preserved when one seeks solutions in the spheroidal geometry. Nevertheless, defining some kind of semiseparability, the complete solution for ψ in spheroidal coordinates has been obtained in the form of products combining Gegenbauer functions of different degrees. Thus, the general solution is represented in a full-series expansion in terms of eigenfunctions, which are elements of the space kerE2 (separable solutions), and in terms of generalized eigenfunctions, which are elements of the space kerE4 (semiseparable solutions). In this work we revisit this aspect by introducing a different and simpler way of representing the aforementioned generalized eigenfunctions. Consequently, additional semiseparable solutions are provided in terms of the Gegenbauer functions, whereas the completeness is preserved and the full-series expansion is rewritten in terms of these functions.

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Dabade, Vivekanand, Navaneeth K. Marath, and Ganesh Subramanian. "Effects of inertia and viscoelasticity on sedimenting anisotropic particles." Journal of Fluid Mechanics 778 (July 30, 2015): 133–88. http://dx.doi.org/10.1017/jfm.2015.360.

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An axisymmetric particle sedimenting in an otherwise quiescent Newtonian fluid, in the Stokes regime, retains its initial orientation. For the special case of a spheroidal geometry, we examine analytically the effects of weak inertia and viscoelasticity in driving the particle towards an eventual steady orientation independent of initial conditions. The generalized reciprocal theorem, together with a novel vector spheroidal harmonics formalism, is used to find closed-form analytical expressions for the $O(\mathit{Re})$ inertial torque and the $O(\mathit{De})$ viscoelastic torque acting on a sedimenting spheroid of an arbitrary aspect ratio. Here, $\mathit{Re}=UL/{\it\nu}$ is the Reynolds number, with $U$ being the sedimentation velocity, $L$ the semi-major axis and ${\it\nu}$ the fluid kinematic viscosity, and is a measure of the inertial forces acting at the particle scale. The Deborah number, $\mathit{De}=({\it\lambda}U)/L$, is a dimensionless measure of the fluid viscoelasticity, with ${\it\lambda}$ being the intrinsic relaxation time of the underlying microstructure. The analysis is valid in the limit $\mathit{Re},\mathit{De}\ll 1$, and the effects of viscoelasticity are therefore modelled using the constitutive equation of a second-order fluid. The inertial torque always acts to turn the spheroid broadside-on, while the final orientation due to the viscoelastic torque depends on the ratio of the magnitude of the first ($N_{1}$) to the second normal stress difference ($N_{2}$), and the sign (tensile or compressive) of $N_{1}$. For the usual case of near-equilibrium complex fluids – a positive and dominant $N_{1}$ ($N_{1}>0$, $N_{2}<0$ and $|N_{1}/N_{2}|>1$) – both prolate and oblate spheroids adopt a longside-on orientation. The viscoelastic torque is found to be remarkably sensitive to variations in ${\it\kappa}$ in the slender-fibre limit (${\it\kappa}\gg 1$), where ${\it\kappa}=L/b$ is the aspect ratio, $b$ being the radius of the spheroid (semi-minor axis). The angular dependence of the inertial and viscoelastic torques turn out to be identical, and one may then characterize the long-time orientation of the sedimenting spheroid based solely on a critical value ($\mathit{El}_{c}$) of the elasticity number, $\mathit{El}=\mathit{De}/\mathit{Re}$. For $\mathit{El}<\mathit{El}_{c}~({>}\mathit{El}_{c})$, inertia (viscoelasticity) prevails with the spheroid settling broadside-on (longside-on). The analysis shows that $\mathit{El}_{c}\sim O[(1/\text{ln}\,{\it\kappa})]$ for ${\it\kappa}\gg 1$, and the viscoelastic torque thus dominates for a slender rigid fibre. For a slender fibre alone, we also briefly analyse the effects of elasticity on fibre orientation outside the second-order fluid regime.

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Soares de Melo, J. C., R. Soares Gomez, J. B. Silva Júnior, A. X. Mesquita de Queiroga, R. Lima Dantas, A. G. Barbosa de Lima, and Wilton Pereira Silva. "Drying of Oblate Spheroidal Solids via Model Based on the Non-Equilibrium Thermodynamics." Diffusion Foundations 25 (January 2020): 83–98. http://dx.doi.org/10.4028/www.scientific.net/df.25.83.

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Food drying is one of the most used methods of preservation. To accurately describe moisture migration within biological products (grains, fruits, vegetables, etc.) during drying and explain the effects of this process on the quality of the material, have been proposed several mathematical models, but few incorporate the phenomena of simultaneous heat and mass transport applied to complex geometry. In this sense, this paper aims to present a mathematical model, based on the thermodynamics of irreversible processes to describe the heat and mass transfer (liquid and vapor) during the drying of bodies with oblate spheroidal geometry. This model was applied to describe drying of lentil, considering the variables transport coefficients and equilibrium conditions at the surface of the solid. Results of the average moisture content, average temperature, liquid flux, vapor flux, and moisture content and temperature distributions inside a lentil kernel during drying process, at different temperatures (40 and 60 oC) were presented and analyzed.

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Gkaraklova, Sofia, Pavlos Chotzoglou, and Eva Loukogeorgaki. "Frequency-Based Performance Analysis of an Array of Wave Energy Converters around a Hybrid Wind–Wave Monopile Support Structure." Journal of Marine Science and Engineering 9, no. 1 (December 22, 2020): 2. http://dx.doi.org/10.3390/jmse9010002.

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In this paper, we investigate, in the frequency domain, the performance (hydrodynamic behavior and power absorption) of a circular array of four semi-immersed heaving Wave Energy Converters (WECs) around a hybrid wind–wave monopile (circular cylinder). The diffraction/radiation problem is solved by deploying the conventional boundary integral equation method. Oblate-spheroidal and hemispherical-shaped WECs are considered. For each geometry, we assess the effect of the array’s net radial distance from the monopile and of the incident wave direction on the array’s performance under regular waves. The results illustrate that by placing the oblate spheroidal WECs close to the monopile, the array’s power absorption ability is enhanced in the low frequency range, while the opposite occurs for higher wave frequencies. For hemispherical-shaped WECs, the array’s power absorption ability is improved when the devices are situated close to the monopile. The action of oblique waves, with respect to the WECs’ arrangement, increases the absorbed power in the case of oblate spheroidal WECs, while these WECs show the best power absorption ability among the two examined geometries. Finally, for the most efficient array configuration, consisting of oblate spheroidal WECs situated close to the monopile, we utilize an “active” Power Take-Off (PTO) mechanism, facilitating the consideration of a variable with frequency PTO damping coefficient. By deploying this mechanism, the power absorption ability of the array is significantly enhanced under both regular and irregular waves.

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28

Grafarend, Erik W. "Geophysical models of the surface global vorticity vector." Symposium - International Astronomical Union 128 (1988): 411. http://dx.doi.org/10.1017/s0074180900119813.

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Within the framework of Newtonian kinematics the local vorticity vector is introduced and averaged with respect to global earth geometry, namely the ellipsoid of revolution. For a deformable body like the earth the global vorticity vector is defined as the earth rotation. A decomposition of the Lagrangean displacement and of the Lagrangean vorticity vector into vector spherical harmonics, namely into spheroidal and toroidal parts, proves that the global vorticity vector only contains toroidal coefficients of degree and order one (polar motion) and toroidal coefficients of degree one and order zero (length of the day) in the case of an ellipsoidal earth. Once we assume an earth model of type ellipsoid of revolution the earth rotation is also slightly dependent on the ellipsoidal flattening and the radial derivative of the spheroidal coefficients of degree two and order one.

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29

Maffei, Stefano, Andrew Jackson, and Philip W. Livermore. "Characterization of columnar inertial modes in rapidly rotating spheres and spheroids." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2204 (August 2017): 20170181. http://dx.doi.org/10.1098/rspa.2017.0181.

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We consider fluid-filled spheres and spheroidal containers of eccentricity ϵ in rapid rotation, as a proxy for the interior dynamics of stars and planets. The fluid motion is assumed to be quasi-geostrophic (QG): horizontal motions are invariant parallel to the rotation axis z , a characteristic which is handled by use of a stream function formulation which additionally enforces mass conservation and non-penetration at the boundary. By linearizing about a quiescent background state, we investigate a variety of methods to study the QG inviscid inertial wave modes which are compared with fully three-dimensional (3D) calculations. We consider the recently proposed weak formulation of the inviscid system valid in spheroids of arbitrary eccentricity, to which we present novel closed-form polynomial solutions. Our modal solutions accurately represent, in both spatial structure and frequency, the most z -invariant of the inertial wave modes in a spheroid, and constitute a simple basis set for the analysis of rotationally dominated fluids. We further show that these new solutions are more accurate than those of the classical axial-vorticity equation, which is independent of ϵ and thus fails to properly encode the container geometry. We also consider the effects of viscosity for the cases of both no-slip and stress-free boundary conditions for a spherical container. Calculations performed under the columnar approximation are compared with 3D solutions and excellent agreement has been found despite fundamental differences in the two formulations.

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30

Lawrence, C. J., and S. Weinbaum. "The unsteady force on a body at low Reynolds number; the axisymmetric motion of a spheroid." Journal of Fluid Mechanics 189 (April 1988): 463–89. http://dx.doi.org/10.1017/s0022112088001107.

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In a recent paper by Lawrence & Weinbaum (1986) an unexpected new behaviour was discovered for a nearly spherical body executing harmonic oscillations in unsteady Stokes flow. The force was not a simple quadratic function in half-integer powers of the frequency parameter λ2 = −ia2ω/ν, as in the classical solution of Stokes (1851) for a sphere, and the force for an arbitrary velocity U(t) contained a new memory integral whose kernel differed from the classical t−½ behaviour derived by Basset (1888) for a sphere. A more general analysis of the unsteady Stokes equations is presented herein for the axisymmetric flow past a spheroidal body to elucidate the behaviour of the force at arbitrary aspect ratio. Perturbation solutions in the frequency parameter λ are first obtained for a spheroid in the limit of low- and high-frequency oscillations. These solutions show that in contrast to a sphere the first order corrections for the component of the drag force that is proportional to the first power of λ exhibit a different behaviour in the extreme cases of the steady Stokes flow and inviscid limits. Exact solutions are presented for the middle frequency range in terms of spheroidal wave functions and these results are interpreted in terms of the analytic solutions for the asymptotic behaviour. It is shown that the force on a body can be represented in terms of four contributions; the classical Stokes and virtual mass forces; a newly defined generalized Basset force proportional to λ whose coefficient is a function of body geometry derived from the perturbation solution for high frequency; and a fourth term which combines frequency and geometry in a more general way. In view of the complexity of this fourth term, a relatively simple correlation is proposed which provides good accuracy for all aspect ratios in the range 0.1 < b/a < 10 where exact solutions were calculated and for all values of λ. Furthermore, the correlation has a simple inverse Laplace transform, so that the force may be found for an arbitrary velocity U(t) of the spheroid. The new fourth term transforms to a memory integral whose kernel is either bounded or has a weaker singularity than the t−½ behaviour of the Basset memory integral. These results are used to propose an approximate functional form for the force on an arbitrary body in unsteady motion at low Reynolds number.

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31

Chattopadhyay, P. K., and B. C. Paul. "Relativistic strange stars with anisotropy and B-parameter in pseudo spheroidal space time." Proceedings of the International Astronomical Union 8, S291 (August 2012): 362–64. http://dx.doi.org/10.1017/s174392131202412x.

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AbstractA class of compact cold stars in the presence of strange matter is obtained for a pseudo-spheroidal geometry. Considering the strange matter equation of state $p = \frac{1}{3}(\rho-4B)$ with pressure anisotropy described by Vaidya-Tikekar metric, we determine the parameter B both inside and on the surface of the star for different values of anisotropy parameter α. In the anisotropic case, we note that a stable model of a compact star may be realized.

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32

Iyengar, T., and T. Radhika. "Stokes flow of an incompressible micropolar fluid past a porous spheroidal shell." Bulletin of the Polish Academy of Sciences: Technical Sciences 59, no. 1 (March 1, 2011): 63–74. http://dx.doi.org/10.2478/v10175-011-0010-5.

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Stokes flow of an incompressible micropolar fluid past a porous spheroidal shellConsider a pair of confocal prolate spheroids S0and S1where S0is within S1. Let the spheroid S0be a solid and the annular region between S0and S1be porous. The present investigation deals with a flow of an incompressible micropolar fluid past S1with a uniform stream at infinity along the common axis of symmetry of the spheroids. The flow outside the spheroid S1is assumed to follow the linearized version of Eringen's micropolar fluid flow equations and the flow within the porous region is assumed to be governed by the classical Darcy's law. The fluid flow variables within the porous and free regions are determined in terms of Legendre functions, prolate spheroidal radial and angular wave functions and a formula for the drag on the spheroid is obtained. Numerical work is undertaken to study the variation of the drag with respect to the geometric parameter, material parameter and the permeability parameter of the porous region. An interesting feature of the investigation deals with the presentation of the streamline pattern.

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33

SARWE, SANJAY, and RAMESH TIKEKAR. "NON-ADIABATIC GRAVITATIONAL COLLAPSE OF A SUPERDENSE STAR." International Journal of Modern Physics D 19, no. 12 (October 2010): 1889–904. http://dx.doi.org/10.1142/s0218271810018098.

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The relativistic equations governing the non-adiabatic shear-free collapse of massive superdense stars in the presence of dissipative forces producing heat flow in the background of space–times of the Vaidya–Tikekar ansatz with associated physical three-spaces that have the three-spheroidal geometry are formulated. It is shown how the system can be used to examine the development and progress of the collapse during subsequent epochs until the radiating star becomes a black hole.

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34

Ricciardi, G. F., and W. L. Stutzman. "A Near-Field to Far-Field Transformation for Spheroidal Geometry Utilizing an Eigenfunction Expansion." IEEE Transactions on Antennas and Propagation 52, no. 12 (December 2004): 3337–49. http://dx.doi.org/10.1109/tap.2004.836445.

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35

Xue, Changfeng, and Shaozhong Deng. "Green’s function and image system for the Laplace operator in the prolate spheroidal geometry." AIP Advances 7, no. 1 (January 2017): 015024. http://dx.doi.org/10.1063/1.4974156.

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36

Huré, J.-M. "Nested spheroidal figures of equilibrium – II. Generalization to layers." Monthly Notices of the Royal Astronomical Society 512, no. 3 (February 25, 2022): 4047–61. http://dx.doi.org/10.1093/mnras/stac521.

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ABSTRACT We present a vectorial formalism to determine the approximate solutions to the problem of a composite body made of ${\cal L}$ homogeneous, rigidly rotating layers bounded by spheroidal surfaces. The method is based on the first-order expansion of the gravitational potential over confocal parameters, thereby generalizing the method described in Paper I for ${\cal L}=2$. For a given relative geometry of the ellipses and a given set of mass-density jumps at the interfaces, the sequence of rotation rates and interface pressures is obtained analytically by recursion. A wide range of equilibria result when layers rotate in an asynchronous manner, although configurations with a negative oblateness gradient are more favourable. In contrast, states of global rotation (all layers move at the same rate), found by solving a linear system of ${\cal L}-1$ equations, are much more constrained. In this case, we mathematically demonstrate that confocal and coelliptical configurations are not permitted. Approximate formula for small ellipticities are derived. These results reinforce and prolongate known results and classical theorems restricted to small elliptiticities. Comparisons with the numerical solutions computed from the Self-Consistent-Field method are successful.

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Hejnowicz, Zygmunt, Jerzy Nakielski, and Krystyna Hejnowicz. "Modeling of spatial variations of growth within apical domes by means of the growth tensor. L Growth specified on dome axis." Acta Societatis Botanicorum Poloniae 53, no. 1 (2014): 17–28. http://dx.doi.org/10.5586/asbp.1984.003.

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By using the growth tensor and a natural curvilinear coordinate system for description of the distribution of growth in plant organs, three geometric types of shoot apical domes (parabolic, elliptical and hyperbolic) were modeled. It was assumed that apical dome geometry remains unchanged during growth and that the natural coordinate systems are paraboloidal and prolate spheroidal. Two variants of the displacement velocity fields V were considered. One variant is specified by a constant relative elemental rate of growth along the axis of the dome. The second is specified by a rate increasing proportionally with distance from the geometric focus of the coordinate systems (and the apical dome). The growth tensor was used to calculate spatial variations of growth rates for each variant of each dome type. There is in both variants a clear tendency toward lower growth rates in the distal region of the dome. A basic condition for the existence of a tunica is met.

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38

Charalambopoulos, Antonios, and George Dassios. "On the Vekua Pair in Spheroidal Geometry and its Role in Solving Boundary Value Problems." Applicable Analysis 81, no. 1 (January 2002): 85–113. http://dx.doi.org/10.1080/0003681021000021088.

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39

Phan, Anh-Luan, Dai-Nam Le, Van-Hoang Le, and Pinaki Roy. "The influence of electric field and geometry on relativistic Landau levels in spheroidal fullerene molecules." Physica E: Low-dimensional Systems and Nanostructures 114 (October 2019): 113639. http://dx.doi.org/10.1016/j.physe.2019.113639.

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40

Dassios, G. "Interrelation between Papkovich-Neuber and Stokes general solutions of the stokes equations in spheroidal geometry." Quarterly Journal of Mechanics and Applied Mathematics 57, no. 2 (May 1, 2004): 181–203. http://dx.doi.org/10.1093/qjmam/57.2.181.

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41

Hernández-Díaz, W. N., I. I. Ruiz-López, M. A. Salgado-Cervantes, G. C. Rodríguez-Jimenes, and M. A. García-Alvarado. "Modeling heat and mass transfer during drying of green coffee beans using prolate spheroidal geometry." Journal of Food Engineering 86, no. 1 (May 2008): 1–9. http://dx.doi.org/10.1016/j.jfoodeng.2007.08.025.

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42

Hadjinicolaou, M., and E. Protopapas. "On the R -semiseparation of the Stokes bi-stream operator in inverted prolate spheroidal geometry." Mathematical Methods in the Applied Sciences 37, no. 2 (June 19, 2013): 207–11. http://dx.doi.org/10.1002/mma.2841.

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43

Calvet, Ramon Gonzalez. "On a New Analytic Theory of the Moon's Motion III: Further Corrections." Journal of Geometry and Symmetry in Physics 59 (2021): 67–99. http://dx.doi.org/10.7546/jgsp-59-2021-67-99.

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Further corrections to the analytic theory of the lunar motion deduced from the first-order approximation to the Lagrange equations of the Sun-Earth-Moon system expressed in relative coordinates and accelerations are evaluated. Those terms arising from the second-order approximation, the planetary perturbations and Earth's spheroidal shape are calculated and bounded, all of them being very small. Finally, Earth's gravitational parameter is calculated from gravity data finding a value slightly higher than that provided by Jet Propulsion Laboratory.

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44

Gavze, Ehud, and Alexander Khain. "Gravitational Collision of Small Nonspherical Particles: Swept Volumes of Prolate and Oblate Spheroids in Calm Air." Journal of the Atmospheric Sciences 79, no. 6 (June 2022): 1493–514. http://dx.doi.org/10.1175/jas-d-20-0336.1.

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Abstract The aggregation rate of ice crystals depends on their shape and intercrystal relative velocity. Unlike spherical particles, the nonspherical ones can have various orientations relative to the gravitational force in the vertical direction and can approach each other at many different angles. Furthermore, the fall velocity of such particles could deviate from the vertical direction velocity. These properties add to the computational complexity of nonspherical particle collisions. In this study, we derive general mathematical expressions for gravity-induced swept volumes of spheroidal particles. The swept volumes are shown to depend on the particles’ joint orientation distribution and relative velocities. Assuming that the particles are Stokesian prolate and oblate spheroids of different sizes and aspect ratios, the swept volumes were calculated and compared to those of equivalent volume spheres. Most calculated swept volumes were larger than the swept volumes of equivalent spherical particles, sometimes by several orders of magnitude. This was due to both the complex geometry and the side drift, experienced by spheroids falling with their major axes not parallel to gravity. We expect that the collision rate between nonspherical particles is substantially higher than that of equivalent volume spheres because the collision process is nonlinear. These results suggest that the simplistic approach of equivalent spheres might lead to serious errors in the computation of the collision rate.

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45

Ledbetter, Hassel, Subhendu Datta, and Martin Dunn. "Elastic Properties of Particle-Occlusion Composites: Measurements and Modeling." Journal of Engineering Materials and Technology 117, no. 4 (October 1, 1995): 402–7. http://dx.doi.org/10.1115/1.2804733.

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We review some of our recent studies on the effective elastic constants of composites where the occluded phase is spherical or spheroidal (oblate or prolate). From constituent properties and phase geometry, we estimated the composites’ effective macroscopic elastic constants using two models: the Ledbetter-Datta scattered-plane-wave ensemble-average model and the Mori-Tanaka effective-field model. We measured elastic constants by three principal methods: resonance, pulse-echo, and acoustic-resonance spectroscopy. We show microstructures, measurements, and model calculations for five representative composites: SiCp/Al, Al2O3-mullitep/Al, Al2O3p/ mullite, graphitep/ferrite (cast iron), voids/Ti.

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Legrice, I. J., P. J. Hunter, and B. H. Smaill. "Laminar structure of the heart: a mathematical model." American Journal of Physiology-Heart and Circulatory Physiology 272, no. 5 (May 1, 1997): H2466—H2476. http://dx.doi.org/10.1152/ajpheart.1997.272.5.h2466.

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A mathematical description of cardiac anatomy is presented for use with finite element models of the electrical activation and mechanical function of the heart. The geometry of the heart is given in terms of prolate spheroidal coordinates defined at the nodes of a finite element mesh and interpolated within elements by a combination of linear Lagrange and cubic Hermite basis functions. Cardiac microstructure is assumed to have three axes of symmetry: one aligned with the muscle fiber orientation (the fiber axis); a second set orthogonal to the fiber direction and lying in the newly identified myocardial sheet plane (the sheet axis); and a third set orthogonal to the first two, in the sheet-normal direction. The geometry, fiber-axis direction, and sheet-axis direction of a dog heart are fitted with parameters defined at the nodes of the finite element mesh. The fiber and sheet orientation parameters are defined with respect to the ventricular geometry such that 1) they can be applied to any heart of known dimensions, and 2) they can be used for the same heart at various states of deformation, as is needed, for example, in continuum models of ventricular contraction.

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Kusova, Aleksandra M., Aleksandr E. Sitnitsky, Vladimir N. Uversky, and Yuriy F. Zuev. "Effect of Protein–Protein Interactions on Translational Diffusion of Spheroidal Proteins." International Journal of Molecular Sciences 23, no. 16 (August 17, 2022): 9240. http://dx.doi.org/10.3390/ijms23169240.

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One of the commonly accepted approaches to estimate protein–protein interactions (PPI) in aqueous solutions is the analysis of their translational diffusion. The present review article observes a phenomenological approach to analyze PPI effects via concentration dependencies of self- and collective translational diffusion coefficient for several spheroidal proteins derived from the pulsed field gradient NMR (PFG NMR) and dynamic light scattering (DLS), respectively. These proteins are rigid globular α-chymotrypsin (ChTr) and human serum albumin (HSA), and partly disordered α-casein (α-CN) and β-lactoglobulin (β-Lg). The PPI analysis enabled us to reveal the dominance of intermolecular repulsion at low ionic strength of solution (0.003–0.01 M) for all studied proteins. The increase in the ionic strength to 0.1–1.0 M leads to the screening of protein charges, resulting in the decrease of the protein electrostatic potential. The increase of the van der Waals potential for ChTr and α-CN characterizes their propensity towards unstable weak attractive interactions. The decrease of van der Waals interactions for β-Lg is probably associated with the formation of stable oligomers by this protein. The PPI, estimated with the help of interaction potential and idealized spherical molecular geometry, are in good agreement with experimental data.

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Sakalli, I., and A. Al-Badawi. "Exact solutions to a massive charged scalar field equation in the magnetically charged stringy black-hole geometry and Hawking radiation." Canadian Journal of Physics 87, no. 4 (April 2009): 349–52. http://dx.doi.org/10.1139/p09-024.

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Exact solutions of a massive complex scalar field equation in the geometry of a Garfinkle–Horowitz–Strominger (stringy) black hole with magnetic charge is explored. The separated radial and angular parts of the wave equation are solved exactly in the nonextreme case. The angular part is shown to be an ordinary spin-weighted spheroidal harmonics with a spin-weight depending on the magnetic charge. The radial part is achieved to reduce a confluent Heun equation with a multiplier. Finally, based on the solutions, it is shown that the Hawking temperature of the magnetically charged stringy black hole has the same value as that of the Schwarzschild black hole.

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Polychronopoulos, Nickolas D., Apostolos A. Gkountas, Ioannis E. Sarris, and Leonidas A. Spyrou. "A Computational Study on Magnetic Nanoparticles Hyperthermia of Ellipsoidal Tumors." Applied Sciences 11, no. 20 (October 13, 2021): 9526. http://dx.doi.org/10.3390/app11209526.

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The modelling of magnetic hyperthermia using nanoparticles of ellipsoid tumor shapes has not been studied adequately. To fill this gap, a computational study has been carried out to determine two key treatment parameters: the therapeutic temperature distribution and the extent of thermal damage. Prolate and oblate spheroidal tumors, of various aspect ratios, surrounded by a large healthy tissue region are assumed. Tissue temperatures are determined from the solution of Pennes’ bio-heat transfer equation. The mortality of the tissues is determined by the Arrhenius kinetic model. The computational model is successfully verified against a closed-form solution for a perfectly spherical tumor. The therapeutic temperature and the thermal damage in the tumor center decrease as the aspect ratio increases and it is insensitive to whether tumors of the same aspect ratio are oblate or prolate spheroids. The necrotic tumor area is affected by the tumor prolateness and oblateness. Good comparison is obtained of the present model with three sets of experimental measurements taken from the literature, for animal tumors exhibiting ellipsoid-like geometry. The computational model enables the determination of the therapeutic temperature and tissue thermal damage for magnetic hyperthermia of ellipsoidal tumors. It can be easily reproduced for various treatment scenarios and may be useful for an effective treatment planning of ellipsoidal tumor geometries.

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Еремин, Ю. А. "Влияние пространственной дисперсии в металлах на оптические характеристики биметаллических плазмонных наночастиц." Оптика и спектроскопия 129, no. 8 (2021): 1079. http://dx.doi.org/10.21883/os.2021.08.51205.1872-21.

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The problem of diffraction of an electromagnetic plane wave field on a core-shell nanoparticle composed of two plasmon metals is considered. The effect of spatial dispersion in metals on the absorption cross section is investigated on the basis of the Discrete Sources method. Various combinations of core and shell metals: Au@Ag and Ag@Au of spheroidal particles, as well as the effect of elongation and asymmetry of particle geometry on energy absorption are being studied. It was found that taking into account the spatial dispersion, both in the core and in the shell, leads to a significant decrease in the absorption cross section and a shift of the plasmon resonance to the shorter wavelength region.

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Journal articles on the topic 'Spheroidal geometry'

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