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出版商:
Springer
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出版日期:
2024-08-01
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售價:
$5,760
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貴賓價:
9.5 折
$5,472
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語言:
英文
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頁數:
74
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裝訂:
Quality Paper - also called trade paper
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ISBN:
9819922461
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ISBN-13:
9789819922468
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.
商品描述(中文翻譯)
本書討論了一些縮放性質，並描述了由映射所描述的非線性系統中混沌動力學的兩相轉變。混沌動力學由相空間中兩個非常接近的初始條件的時間演化的不可預測性所決定。隨著時間的推移，它們之間的距離以指數方式發散。書中探討了混沌擴散，導致了縮放不變性，這是連續相變的特徵。本書考慮了兩種不同類型的轉變。其中一種考慮了在二維、非線性且保持面積的映射中觀察到的從可積分性到不可積分性的轉變，因此是一種保守動力學，涉及作用和角度變數。另一種轉變同樣考慮了由非線性映射所給出的動力學，並描述了對於耗散標準映射的無限混沌擴散的抑制，以及在時間依賴的撞球中對費米加速的抑制的等效轉變。
本書使讀者能夠理解縮放理論在相變和其他在非線性系統中常見的臨界動力學中的一些應用。這包括從可積分性到不可積分性的轉變，以及從有限擴散到無限擴散的轉變，這也可以應用於能量擴散，因此也涉及費米加速。後者是撞球動力學中一個熱門話題，近幾年來引發了許多重要的出版物。這是一本適合高年級或研究生水平的學生或動力系統與控制工程、數學、物理、機械和電氣工程研究人員的良好參考書。
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模型中的混沌海洋的尺度調查。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特性，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），另一個涉及非線性動力學（2019年），兩者均由Blucher編輯。
