An explicit solution for the electric potential of the asymmetric dielectric double sphere

Pitkonen, Mikko

doi:10.1088/0022-3727/40/5/026

Cited by 9 publications

(4 citation statements)

References 8 publications

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“…Several articles considering analytical approaches to this double-sphere case can be found. [6][7][8][9] However, polarizability of a hemisphere has not been considered before, although a hemisphere is a very simple and elementary geometry. Like a sphere, it is defined by one single parameter, its radius r. The results presented in this article are also a valuable reference in testing numerical programs which are being developed for treating more complex geometries.…”

Section: Introductionmentioning

confidence: 99%

Polarizability of a dielectric hemisphere

Kettunen

Wallén

Sihvola

2007

Journal of Applied Physics

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Articles you may be interested in Alteration of gas phase ion polarizabilities upon hydration in high dielectric liquids J. Chem. Phys. 139, 044907 (2013) This article presents a method for solving the polarizability of a dielectric hemispherical object as a function of its relative electric permittivity. The polarizability of a hemisphere depends on the direction of the exciting electric field. Therefore, the polarizability can be written as a dyadic consisting of two components, the axial and the transversal polarizabilities, which can be solved separately. The solution is based on an analytical approach where the electrostatic potential function is written as a series expansion. However, no closed-form solution for the coefficients of the series is found, so they must be solved from a matrix equation. This method provides very high accuracy. However, it requires construction of large matrices which consumes both time and memory. Therefore, approximative expressions for the polarizabilities with absolute error less than 10 −5 are also presented.

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Section: Introductionmentioning

confidence: 99%

Polarizability of a dielectric hemisphere

Kettunen

Wallén

Sihvola

2007

Journal of Applied Physics

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“…and expression (A.5) derived in the Appendix, one gets the following Fredholm integral equation of the second kind for the unknown function u() (Pitkonen, 2007) and integral in (3.6) converges since (cosh )…”

Section: Heat Flux Along the Symmetry Axismentioning

confidence: 98%

“…The solution can be used to evaluate the m n  steady-state heat flux from the hot body placed in a thermally conducting environment of lower temperature. Pitkonen (2006Pitkonen ( , 2007 considered dielectric overlapping spheres and obtained solutions in the form of an integral of a parameter given by a Neumann series. He also considered the problem about touching spheres (Pitkonen, 2008) and analyzed it as an eigenfunction expansion in the tangent sphere coordinate system.…”

Section: Introductionmentioning

confidence: 99%

Effect of spherical pores coalescence on the overall conductivity of a material.

Lanzoni

Radi

Sevostianov

2020

Mechanics of Materials

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The problem about steady-state temperature distribution in a homogeneous isotropic medium containing a pore or an insulating inhomogeneity formed by two coalesced spheres of the same radius, under arbitrarily oriented uniform heat flux, is solved analytically. The limiting case of two touching spheres is analyzed separately. The solution is obtained in the form of converged integrals that can be calculated using Gauss-Laguerre quadrature rule. The temperature on the inhomogeneity's surface is used to determine components of the resistivity contribution tensor for the insulating inhomogeneity of the mentioned shape. An interesting observation is that the extreme values of these components are achieved when the spheres are already slightly coalesced.

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“…It requires either a numerical approach or a very complicated analysis using toroidal coordinate system. Several partial results have been presented for the problem [23][24][25], but only recently a full solution for this problem [26] and its generalization [27] have appeared.…”

Section: Double Spherementioning

confidence: 99%

Dielectric Polarization and Particle Shape Effects

Sihvola¹

2007

Journal of Nanomaterials

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This article reviews polarizability properties of particles and clusters. Especially the effect of surface geometry is given attention. The important parameter of normalized dipolarizability is studied as function of the permittivity and the shape of the surface of the particle. For nonsymmetric particles, the quantity under interest is the average of the three polarizability dyadic eigenvalues. The normalized polarizability, although different for different shapes, has certain universal characteristics independent of the inclusion form. The canonical shapes (sphere, spheroids, ellipsoids, regular polyhedra, circular cylinder, semisphere, double sphere) are studied as well as the correlation of surface parameters with salient polarizability properties. These geometrical and surface parameters are essential in the material modeling problems in the nanoscale.

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An explicit solution for the electric potential of the asymmetric dielectric double sphere

Cited by 9 publications

References 8 publications

Polarizability of a dielectric hemisphere

Polarizability of a dielectric hemisphere

Effect of spherical pores coalescence on the overall conductivity of a material.

Dielectric Polarization and Particle Shape Effects

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