涡旋系统的微观经典相变

IF 1 Q4 MECHANICS Mathematics and Mechanics of Complex Systems Pub Date : 2023-07-01 DOI:10.2140/memocs.2024.12.85

D. Benedetto, E. Caglioti, M. Nolasco

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引用次数: 0

摘要

我们考虑的是有界域中涡旋系统的微观可变原理。我们尤其关注该系统在第二类域中的热力学性质，即集合等价性不成立的域。对于接近于断开的磁盘（哑铃状磁畴）的连通磁畴，我们证明了该系统可能表现出任意数量的拳阶相变，而对于大能量，熵是凸的。

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Microcanonical phase transitions for the vortex system

We consider the Microcanonical Variational Principle for the vortex system in a bounded domain. In particular we are interested in the thermodynamic properties of the system in domains of second kind, i.e. for which the equivalence of ensembles does not hold. For connected domains close to the union of disconnected disks (dumbbell domains), we show that the system may exhibit an arbitrary number of fist-order phase transitions, while the entropy is convex for large energy.

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来源期刊

Mathematics and Mechanics of Complex Systems MECHANICS-

CiteScore

3.00

自引率

5.30%

发文量

期刊介绍： MEMOCS is a publication of the International Research Center for the Mathematics and Mechanics of Complex Systems. It publishes articles from diverse scientific fields with a specific emphasis on mechanics. Articles must rely on the application or development of rigorous mathematical methods. The journal intends to foster a multidisciplinary approach to knowledge firmly based on mathematical foundations. It will serve as a forum where scientists from different disciplines meet to share a common, rational vision of science and technology. It intends to support and divulge research whose primary goal is to develop mathematical methods and tools for the study of complexity. The journal will also foster and publish original research in related areas of mathematics of proven applicability, such as variational methods, numerical methods, and optimization techniques. Besides their intrinsic interest, such treatments can become heuristic and epistemological tools for further investigations, and provide methods for deriving predictions from postulated theories. Papers focusing on and clarifying aspects of the history of mathematics and science are also welcome. All methodologies and points of view, if rigorously applied, will be considered.