Please use this identifier to cite or link to this item:
https://hdl.handle.net/20.500.14365/5042
Title: | Statistical mechanical characterization of billiard systems | Authors: | Cetin, K. Tırnaklı, Uğur Oliveira, D.F.M. Leonel, E.D. |
Keywords: | Billiard systems Nonextensive statistical mechanics Nonlinear dynamics Phase space methods Statistical mechanics System stability Area-preserving maps Billiard systems Diverse fields Mechanical characterizations Model complexes Nonextensive statistical mechanics Phase spaces Probability: distributions Stability islands Stable orbit Probability distributions |
Publisher: | Elsevier Ltd | Abstract: | Area-preserving maps play an important role in diverse fields as they are widely used for modeling complex systems. In addition, these maps provide rich observations by presenting stable orbits and chaotic behavior separately or together in the phase space depending on the control parameter. In recent years, several studies on these maps, drawing inspiration from the phase space dynamics, have shown that nonextensive statistical mechanics provides appropriate instruments to characterize these systems. In this study, we perform a rigorous numerical analysis to delve into the statistical mechanical properties of a billiard system. Our primary goal is to confirm the presence of a q-Gaussian distribution, with an estimated q value of approximately 1.935. We accomplish this by examining the probability distribution of the cumulative sum of system iterates, focusing specifically on initial conditions within the stability islands. Our findings align seamlessly with the latest research in this field. Furthermore, we show that a multi-component probability distribution containing both Gaussian and q-Gaussians describes the entire system for some parameter regions where the phase space consists of stability islands together with the chaotic sea. © 2023 Elsevier Ltd | URI: | https://doi.org/10.1016/j.chaos.2023.114331 https://hdl.handle.net/20.500.14365/5042 |
ISSN: | 0960-0779 |
Appears in Collections: | Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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