On the uniform tiling with electrical resistors
M. Owaidat
TL;DR
This paper computes the effective electrical resistance between arbitrary points on various infinite lattice structures in one, two, and three dimensions using lattice Green's function methods.
Contribution
It introduces a systematic approach to calculate resistances on complex infinite lattices, extending previous methods to new lattice geometries and dimensions.
Findings
Calculated resistances for triangular, square, Union Jack, simple cubic, and base-centered cubic lattices.
Demonstrated the effectiveness of lattice Green's function method for complex lattice resistance problems.
Provided explicit resistance formulas for various lattice configurations.
Abstract
We calculate the effective resistance between two arbitrary lattice points on infinite strip of the triangular lattice (ladder network) in one dimension, and on infinite modified square and Union Jack lattices in two dimensions, and on infinite decorated simple cubic and base-centered cubic lattices in three dimensions by using the general lattice Green's function method
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuasicrystal Structures and Properties · Photonic Crystals and Applications · Advanced Materials and Mechanics