Dynamical Phase Transitions in Chaotic Systems
Leonel, Edson Denis
- 出版商: Springer
- 出版日期: 2024-08-01
- 售價: $5,710
- 貴賓價: 9.5 折 $5,425
- 語言: 英文
- 頁數: 74
- 裝訂: Quality Paper - also called trade paper
- ISBN: 9819922461
- ISBN-13: 9789819922468
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商品描述
This book discusses some scaling properties and characterizes two-phase transitions for chaotic dynamics in nonlinear systems described by mappings. The chaotic dynamics is determined by the unpredictability of the time evolution of two very close initial conditions in the phase space. It yields in an exponential divergence from each other as time passes. The chaotic diffusion is investigated, leading to a scaling invariance, a characteristic of a continuous phase transition. Two different types of transitions are considered in the book. One of them considers a transition from integrability to non-integrability observed in a two-dimensional, nonlinear, and area-preserving mapping, hence a conservative dynamics, in the variables action and angle. The other transition considers too the dynamics given by the use of nonlinear mappings and describes a suppression of the unlimited chaotic diffusion for a dissipative standard mapping and an equivalent transition in the suppression of Fermi acceleration in time-dependent billiards. This book allows the readers to understand some of the applicability of scaling theory to phase transitions and other critical dynamics commonly observed in nonlinear systems. That includes a transition from integrability to non-integrability and a transition from limited to unlimited diffusion, and that may also be applied to diffusion in energy, hence in Fermi acceleration. The latter is a hot topic investigated in billiard dynamics that led to many important publications in the last few years. It is a good reference book for senior- or graduate-level students or researchers in dynamical systems and control engineering, mathematics, physics, mechanical and electrical engineering.
作者簡介
Edson Denis Leonel is a Professor of Physics at São Paulo State University, Rio Claro, Brazil. He has been dealing with scaling investigation since his Ph.D. in 2003, where the first scaling investigation in the chaotic sea for the Fermi-Ulam model was studied. His research group developed different approaches and formalisms to investigate and characterize the several scaling properties in a diversity types of systems ranging from one-dimensional mappings, passing to ordinary differential equations, cellular automata, meme propagations, and also in the time-dependent billiards. There are different types of transition we considered and discussed in these scaling investigations: (i) transition from integrability to non-integrability; (ii) transition from limited to unlimited diffusion; and (iii) production and suppression of Fermi acceleration. The latter approach involves the analytical solution of the diffusion equation. His group and he published more than 160 scientific papers in respected international journals, including three papers in Physical Review Letters. He is the Author of "Scaling Laws in Dynamical Systems" (2021) by Springer and Higher Education Press and two Portuguese books, one dealing with statistical mechanics (2015) and the other one dealing with nonlinear dynamics (2019), both edited by Blucher.
作者簡介(中文翻譯)
Edson Denis Leonel 是巴西里約克拉羅的聖保羅州立大學物理學教授。他自2003年獲得博士學位以來，一直在進行尺度研究，當時首次研究了Fermi-Ulam模型在混沌海中的尺度調查。他的研究團隊開發了不同的方法和形式主義，以調查和特徵化各種系統中的多種尺度性質，這些系統包括一維映射、常微分方程、元胞自動機、迷因傳播，以及時間依賴的撞球問題。我們在這些尺度研究中考慮和討論了不同類型的轉變：(i) 從可積分性到不可積分性的轉變；(ii) 從有限擴散到無限擴散的轉變；以及 (iii) Fermi加速的產生和抑制。後者的方法涉及擴散方程的解析解。他和他的團隊在受尊敬的國際期刊上發表了超過160篇科學論文，包括三篇發表在《Physical Review Letters》上的論文。他是《動態系統中的尺度法則》（2021年，Springer和高等教育出版社出版）的作者，並且還出版了兩本葡萄牙語書籍，一本涉及統計力學（2015年），另一本涉及非線性動力學（2019年），均由Blucher編輯。
