Kraemer A, Schmiedeberg M, Sanders D (2015)
Publication Status: Published
Publication Type: Journal article
Publication year: 2015
Publisher: AMER PHYSICAL SOC
Book Volume: 92
Journal Issue: 5
DOI: 10.1103/PhysRevE.92.052131
We study the structure of quasiperiodic Lorentz gases, i.e., particles bouncing elastically off fixed obstacles arranged in quasiperiodic lattices. By employing a construction to embed such structures into a higher-dimensional periodic hyperlattice, we give a simple and efficient algorithm for numerical simulation of the dynamics of these systems. This same construction shows that quasiperiodic Lorentz gases generically exhibit a regime with infinite horizon, that is, empty channels through which the particles move without colliding, when the obstacles are small enough; in this case, the distribution of free paths is asymptotically a power law with exponent -3, as expected from infinite-horizon periodic Lorentz gases. For the critical radius at which these channels disappear, however, a new regime with locally finite horizon arises, where this distribution has an unexpected exponent of -5, previously observed only in a Lorentz gas formed by superposing three incommensurable periodic lattices in the Boltzmann-Grad limit where the radius of the obstacles tends to zero.
APA:
Kraemer, A., Schmiedeberg, M., & Sanders, D. (2015). Horizons and free-path distributions in quasiperiodic Lorentz gases. Physical Review E, 92(5). https://doi.org/10.1103/PhysRevE.92.052131
MLA:
Kraemer, Ata, Michael Schmiedeberg, and David Sanders. "Horizons and free-path distributions in quasiperiodic Lorentz gases." Physical Review E 92.5 (2015).
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