TY - JOUR
AU - Jackson, Steven G.
AB - Abstract: We present a new class of electrostatics problems that are exactly solvable by adding finitely many image charges. Given a charge at some location inside a cavity bounded by up to four conducting grounded segments of spheres: if the spheres have a symmetry derived via a stereographic projection from a 4D finite reflection group, then this is a solvable generalization of the familiar problem of a charge inside a spherical cavity. There are 19 three-parametric families of finite groups formed by inversions relative to at most four spheres, each member of each family giving a solvable problem. We solve a sample problem which derives from the reflection group $\mathbf{D}_{4}$ and requires 191 image charges.
TI - Four-dimensional reflection groups and electrostatics
JF - Condensed Matter
DA - 2019-04-04
UR - https://www.deepdyve.com/lp/arxiv-cornell-university/four-dimensional-reflection-groups-and-electrostatics-DOzv5f8DqW
VL - 2019
IS - 1904
DP - DeepDyve
ER -