Electrostatic image theory for layered dielectric sphere

Lindell, Ismo V.; Ermutlu, M.E.; Sihvola, Ari

doi:10.1049/ip-h-2.1992.0035

Cited by 23 publications

(16 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Over one century later, these remarkable results had been rediscovered independently by Lindell [8][9][10] and Norris [14] in the 1990s. Below, we include in Table 1 the results in Norris's paper that give the magnitudes and the positions of various images.…”

Section: Image Line Charges For a Source Point Chargementioning

confidence: 99%

“…This construction is based on a result of over 100 year history dating back to Neumann in 1883 [7] and Lindell in 1994 [8][9][10], which extended the Kelvin image [11] for a conducting sphere to the case of a dielectric sphere. In the case of a dielectric sphere, in addition to an image point charge at the Kelvin image inverse point, there is an image line charge along a ray extending from the inverse point to infinity or to the center of the sphere depending on whether the source charge is inside or outside the sphere and where an observation point is located.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Extending the fast multipole method to charges inside or outside a dielectric sphere

Cai

Deng

Jacobs

2007

Journal of Computational Physics

View full text Add to dashboard Cite

Section: Image Line Charges For a Source Point Chargementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extending the fast multipole method to charges inside or outside a dielectric sphere

Cai

Deng

Jacobs

2007

Journal of Computational Physics

View full text Add to dashboard Cite

“…However, in the present paper, apart from such a brute-force procedure, we shall follow the spirit of Refs. [18, 20] to seek the analytical solution of the expansion coefficients in some recursive way.…”

Section: Numerical Methods For General Three-layer Dielectric Modelsmentioning

confidence: 99%

“…As the result, the original continuous radial dielectric profile is approximated by a multi-step (piecewise constant) one, and consequently the original Poisson equation with the continuous radial dielectric profile reduces to one for layered dielectric spheres. By exploiting the analytical solution of the step-like model, the solution of the Poisson equation for layered dielectric spheres was well-studied in the literature [18, 20, 21]. Based upon these works, Bolcatto et al then obtained an explicit formula for the self-polarization energy [7].…”

Section: Analytical Solution For a Novel Three-layer Dielectric Modelmentioning

confidence: 99%

A robust numerical method for self-polarization energy of spherical quantum dots with finite confinement barriers

Deng

2010

Computer Physics Communications

View full text Add to dashboard Cite

By utilizing a novel three-layer dielectric model for the interface between a spherical quantum dot and the surrounding matrix, a robust numerical method for calculating the self-polarization energy of a spherical quantum dot with a finite confinement barrier is presented in this paper. The proposed numerical method can not only overcome the inherent mathematical divergence in the selfpolarization energy which arises for the simplest and most widely used step-like model of the dielectric interface, but also completely eliminate the potential numerical divergence which may occur in the Bolcatto-Proetto's formula [J. Phys.: Condens. Matter 13, 319-334 (2001)], an approximation method commonly employed for more realistic three-layer dielectric models such as the linear and the cosine-like models frequently mentioned in the literature. Numerical experiments have demonstrated the convergence of the proposed numerical method as the number of the steps used to discretize the translation layer in a three-layer model goes to infinity, an important property that the Bolcatto-Proetto's formula appears not necessarily to possess.

show abstract

“…Finally, by using a recursive method in analogy to the analysis of transmission lines [1,4,11,13,[33][34][35][36], those constant expansion coefficients C (l) np and D (l) np can be determined from the following interface conditions for l = 1, 2, . .…”

Section: Modelsmentioning

confidence: 99%

Three-layer dielectric models for generalized Coulomb potential calculation in ellipsoidal geometry

Xue

Deng

2011

Phys. Rev. E

View full text Add to dashboard Cite

This paper concerns a basic electrostatic problem: How to calculate generalized Coulomb and self-polarization potentials in heterogeneous dielectric media. In particular, with simulations of ellipsoidal semi-conductor quantum dots and elongated bio-macromolecules being its target applications, this paper extends the so-called three-layer dielectric models for generalized Coulomb and self-polarization potential calculation from the spherical and the spheroidal geometries to the tri-axial ellipsoidal geometry. Compared to the simple step-like dielectric model, these threelayer dielectric models can overcome the mathematical divergence in the self-polarization energy by employing continuous radial dielectric functions. More specifically, in this paper, the novel quasi-harmonic three-layer dielectric model for the ellipsoidal geometry is first discussed, and the explicit analytical series solutions of the corresponding electrostatic problem are obtained in terms of the ellipsoidal harmonics. Then, a robust numerical procedure working for general three-layer dielectric models is developed. The key component of the numerical method is to subdivide the transition layer of the underlying three-layer model into multiple sublayers, and then in each one of them approximate the select dielectric function of the transition layer by one of the quasi-harmonic functional form rather than simply by a constant value as one would normally do. As the result, the numerical method has no numerical divergence.

show abstract

Electrostatic image theory for layered dielectric sphere

Cited by 23 publications

References 3 publications

Extending the fast multipole method to charges inside or outside a dielectric sphere

Extending the fast multipole method to charges inside or outside a dielectric sphere

A robust numerical method for self-polarization energy of spherical quantum dots with finite confinement barriers

Three-layer dielectric models for generalized Coulomb potential calculation in ellipsoidal geometry

Contact Info

Product

Resources

About