TY - JOUR

T1 - On the T-matrix in the electrostatic problem for the spheroidal particle with a spherical core

AU - Фарафонов, В.Г.

AU - Устимов, В.И.

AU - Фарафонова, А.Е.

AU - Ильин, Владимир Борисович

PY - 2023/12/20

Y1 - 2023/12/20

N2 - A solution to the electrostatic problem for the spheroidal particle with a spherical core is constructed. To involve the problem geometry in a full manner, in a vicinity of the particle surface the potentials of the fields are represented by their expansions in terms of spheroidal harmonics of Laplace equation, while in a vicinity of the core surface by the expansions in terms of spherical harmonics. Matching of the fields inside the particle shell is made by using the relations between the spheroidal and spherical harmonics. The T-matrix relates the coefficients of expansions of the incident and “scattered” fields. In the present paper, both the particle polarizability related to the main matrix element T11, and the whole T-matrix are considered. The symmetry of the matrix as well as its dependence on the size of the layered particle are shown. A relationship between the T-matrices in the spherical and spheroidal systems was also found. Numerical calculations made for particles of small and large aspect ratios (a/b = 1.5 − 5.0) confirmed high efficiency of the suggested solution in contrast to the methods that use a single spherical basis.

AB - A solution to the electrostatic problem for the spheroidal particle with a spherical core is constructed. To involve the problem geometry in a full manner, in a vicinity of the particle surface the potentials of the fields are represented by their expansions in terms of spheroidal harmonics of Laplace equation, while in a vicinity of the core surface by the expansions in terms of spherical harmonics. Matching of the fields inside the particle shell is made by using the relations between the spheroidal and spherical harmonics. The T-matrix relates the coefficients of expansions of the incident and “scattered” fields. In the present paper, both the particle polarizability related to the main matrix element T11, and the whole T-matrix are considered. The symmetry of the matrix as well as its dependence on the size of the layered particle are shown. A relationship between the T-matrices in the spherical and spheroidal systems was also found. Numerical calculations made for particles of small and large aspect ratios (a/b = 1.5 − 5.0) confirmed high efficiency of the suggested solution in contrast to the methods that use a single spherical basis.

UR - https://www.mendeley.com/catalogue/4a7b6412-563f-3b26-bccd-1727238e1cbc/

U2 - 10.1007/s10958-023-06875-3

DO - 10.1007/s10958-023-06875-3

M3 - Article

VL - 277

SP - 698

EP - 709

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -