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Four-dimensional reflection groups and electrostatics
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DOI：10.1016/j.aop.2020.168291.png)
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摘要
En 中文
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 that derives from the reflection group D-4 and requires 191 image charges. (C) 2020 Elsevier Inc. All rights reserved.
Keyword:
Conducting cavity
Method of images
Reflection group
Exactly solvable problem
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期刊
IF:
3
论文数:
5.5K
被引数:
1.8W
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