TY - JOUR

T1 - Generating Function Method for Calculating the Potentials of Inhomogeneous Polyhedra

AU - Nenashev, Alexey Vladimirovich

N1 - Funding Information: This work is funded by the Ministry of Science and Higher Education of the Russian Federation, grant 075-15-2020-797 (13.1902.21.0024). Publisher Copyright: Copyright © 2022 Nenashev.

PY - 2022/1/20

Y1 - 2022/1/20

N2 - We propose a method of constructing analytical, closed-form expressions for electrostatic/Newtonian potentials of non-uniform polyhedral bodies, in which the density distributions are polynomials of coordinates. Possible applications of the proposed method are spread from astronomy to nanotechnology. The method is based on the use of the generating function for the potential. Explicit expressions for the potential are derived in the case of quadratic or cubic coordinate dependence of the density within a polyhedral body.

AB - We propose a method of constructing analytical, closed-form expressions for electrostatic/Newtonian potentials of non-uniform polyhedral bodies, in which the density distributions are polynomials of coordinates. Possible applications of the proposed method are spread from astronomy to nanotechnology. The method is based on the use of the generating function for the potential. Explicit expressions for the potential are derived in the case of quadratic or cubic coordinate dependence of the density within a polyhedral body.

KW - eigenstrain

KW - exact solution

KW - generating function

KW - gravity anomaly

KW - Poisson equation

KW - polyhedron

KW - potential theory

UR - http://www.scopus.com/inward/record.url?scp=85124082695&partnerID=8YFLogxK

U2 - 10.3389/fphy.2021.795693

DO - 10.3389/fphy.2021.795693

M3 - Article

AN - SCOPUS:85124082695

VL - 9

JO - Frontiers in Physics

JF - Frontiers in Physics

SN - 2296-424X

M1 - 795693

ER -