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Particle transport in open polygonal billiards: A scattering map
Jordan Orchard1, Federico Frascoli1, Lamberto Rondoni2,3
1Department of Mathematics, School of Science, Computing and Engineering Technologies, Swinburne University of Technology, H38, PO Box 218, Hawthorn, Victoria 3122, Australia.
Chaos (Woodbury, N.Y.)
|December 17, 2024
Summary
Polygonal billiards reveal complex particle transport in channels. Researchers derived a scattering map and average speed for ballistic modes, enhancing understanding of anomalous transport.
Area of Science:
- Dynamical systems
- Mathematical physics
- Transport phenomena
Background:
- Polygonal billiards display complex dynamics with applications in anomalous transport and mathematics.
- Understanding particle transport in channels formed by repeating polygonal cells is crucial.
Purpose of the Study:
- To analyze particle transport in infinitely long channels composed of repeating polygonal cells.
- To derive a scattering map and analytical expressions for transport properties.
Main Methods:
- Construction of an interval exchange transformation based on billiard flow discontinuities.
- Derivation of a scattering map connecting incoming and outgoing trajectories.
- Analytical calculation of the average speed of ballistic modes.
Main Results:
- An exact scattering map for the polygonal cell was derived.
- An analytical expression for the average speed of ballistic modes was obtained.
- High-accuracy description of ballistic front propagation and trajectory hierarchy.
Conclusions:
- The study provides a detailed analytical framework for particle transport in polygonal billiards.
- The findings offer insights into anomalous transport and the mathematical underpinnings of complex dynamical systems.
