Negative refraction and tiling billiards-Reference-Cited by-同舟云学术

Negative refraction and tiling billiards

Published:2018-03-26 Issue:2 Volume:18 Page:133-159
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Davis Diana¹,DiPietro Kelsey²,Rustad Jenny³,St Laurent Alexander⁴

Affiliation:

1. Mathematics Department, Swarthmore College , 500 College Avenue , Swarthmore PA 19081 , USA

2. Department of Applied and Computational Mathematics and Statistics , University of Notre Dame , 153 Hurley Hall , Notre Dame , IN 46556 , USA

3. Department of Mathematics , University of Maryland , 4176 Campus Drive, College Park, MD 20742 , Maryland , USA

4. Department of Mathematics and Department of Computer Science , Brown University , 151 Thayer Street , Providence , RI 02912 , USA

Abstract

Abstract We introduce a new dynamical system that we call tiling billiards, where trajectories refract through planar tilings. This system is motivated by a recent discovery of physical substances with negative indices of refraction. We investigate several special cases where the planar tiling is created by dividing the plane by lines, and we describe the results of computer experiments.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2017-0053/pdf

Reference22 articles.

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4. G. A. Galperin, Nonperiodic and not everywhere dense billiard trajectories in convex polygons and polyhedrons. Comm. Math. Phys. 91 (1983), 187–211. MR723547 Zbl 0529.70001

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1. Tiling billards on triangle tilings, and interval exchange transformations;Journal of the London Mathematical Society;2024-01

2. Tiling billiards and Dynnikov’s helicoid;Transactions of the Moscow Mathematical Society;2022-03-15

3. No-slip billiards with particles of variable mass distribution;Chaos: An Interdisciplinary Journal of Nonlinear Science;2022-02

4. Periodicity and ergodicity in the trihexagonal tiling;Commentarii Mathematici Helvetici;2018-11-20