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A Concept for Perpetual Electric Body Based on Topological Vortex Theory Integrating Permanent Magnets and Radioactive Elements (2)2. Theoretical Framework and Core Principles 2.1 Topological Vortices as the Microscopic Basis for "Perpetual Motion" In traditional ferroelectric materials, domain switching requires overcoming an energy barrier. In contrast, the topological vortex state (e.g., the polar vortices observed in PbTiO₃/SrTiO₃ superlattices) is a complex structure of rotating polarization vectors [1]. Its core...0 التعليقات 0 المشاركات 734 مشاهدة 0 معاينة
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A Concept for Perpetual Electric Body Based on Topological Vortex Theory Integrating Permanent Magnets and Radioactive Elements (3)2.2.3 Topological Vortex Material (Order Parameter and Response Unit): Function: To serve as the core functional phase, where the collective dynamical behavior of its topological vortex states produces detectable macroscopic electrical signals. Mechanism: Under the combined influence of the magnetic environment from the permanent magnet and the perturbations from the radioactive elements,...0 التعليقات 0 المشاركات 767 مشاهدة 0 معاينة
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A Concept for Perpetual Electric Body Based on Topological Vortex Theory Integrating Permanent Magnets and Radioactive Elements (4)5. Discussion and Prospect Despite the significant challenges, the value of this concept lies in its heuristic and forward-looking nature. Observing any sustained electrical signal generated by this triadic coupling that surpasses the noise level in experiments would be a milestone. Potential application prospects include: 1)Novel Micro-Energy Devices: Providing long-life, maintenance-free...0 التعليقات 0 المشاركات 783 مشاهدة 0 معاينة
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A Concept for Perpetual Electric Body Based on Topological Vortex Theory Integrating Permanent Magnets and Radioactive Elements (5)Academic Statement The inspiration for this paper comes from ongoing contemplation of interdisciplinary fundamental scientific questions. The concept of synthesizing a "perpetual electric body" using permanent magnets, radioactive elements, and topological vortices, is purely a heuristic and speculative theoretical discussion. Its purpose is to stimulate interdisciplinary academic thought,...0 التعليقات 0 المشاركات 784 مشاهدة 0 معاينة1
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A Study on Topological Vortex Ring Interactions Based on Möbius Loop and Hopf Link Concepts (2)2. Theoretical Foundation: Topological Invariants 2.1 Linking Number (Lk) For two simple, unknotted but mutually entwined closed curves (like an ideal Hopf link), the linking number Lk is a topological invariant representing the total number of times (with sign) one loop winds around the other. For two vortex rings, Lk quantitatively describes the topological strength of their mutual...0 التعليقات 0 المشاركات 773 مشاهدة 0 معاينة
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A Study on Topological Vortex Ring Interactions Based on Möbius Loop and Hopf Link Concepts (3)4. Superposition of Counter-rotating Vortex Rings and Knot Formation The situation is radically different when two vortex rings with opposite circulation directions (counter-rotating) interact: (1) Topological Description: Can be seen as the superposition of a positive Hopf link and a negative Hopf link. The total topological charge (net circulation) of the system is zero. (2) Dynamical...0 التعليقات 0 المشاركات 739 مشاهدة 0 معاينة1
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A Study on Topological Vortex Ring Interactions Based on Möbius Loop and Hopf Link Concepts (4)5. Discussion and Outlook The framework constructed in this study abstracts specific physical phenomena into topological operations: a. Co-rotating superposition ≈ Addition of topological charges, structure tends towards stability or higher-order linking. b. Counter-rotating superposition ≈ Subtraction of topological charges, structure tends towards generating singular knots or...0 التعليقات 0 المشاركات 687 مشاهدة 0 معاينة
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A Study on Topological Vortex Ring Interactions Based on Möbius Loop and Hopf Link Concepts (5)References Călugăreanu, G. (1959). L'intégrale de Gauss et l'analyse des nœuds tridimensionnels [The Gauss Integral and the Analysis of Three-Dimensional Knots]. Revue de mathématiques pures et appliquées, 4, 5-20. Faddeev, L. D., & Niemi, A. J. (1997). Stable knot-like structures in classical field theory. Nature, 387(6628), 58-61. Hopf, H. (1931). Über...0 التعليقات 0 المشاركات 732 مشاهدة 0 معاينة1
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An Overview of the Development of Topological Vortex Theory (TVT)1. Introduction: On the Topological Vortex Theory (TVT) and Topological vortices Topological vortices and the Topological Vortex Theory (TVT) are closely related yet distinct concepts. Their differences can be analyzed from the following dimensions: 1.1 Definition and Scope 1.1.1 Topological Vortices: Refer to vortex structures with topological defects, commonly found in physical phenomena...0 التعليقات 0 المشاركات 905 مشاهدة 0 معاينة
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An Overview of the Development of Topological Vortex Theory (TVT)1.2 Relationship and Differences 1.2.1 Subordination: Topological vortices are one of the subjects studied in TVT, but TVT has a broader scope, encompassing mathematical modeling, physical mechanisms, and philosophical implications of vortices. 1.2.2 Theoretical Extensions: TVT not only describes the static topological properties of vortices (e.g., phase singularities) but also introduces...0 التعليقات 0 المشاركات 904 مشاهدة 0 معاينة
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An Overview of the Development of Topological Vortex Theory (TVT)2. The Key Developmental Stages of Topological Vortex Theory (TVT) The development of Topological Vortex Theory (TVT) can be traced back to the study of topological phase transitions in condensed matter physics during the 1970s, and it gradually evolved into an interdisciplinary theoretical framework in the 21st century. The following are its key developmental stages: 2.1 Theoretical...0 التعليقات 0 المشاركات 936 مشاهدة 0 معاينة
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