Rotational and Translational Characteristics of Topological Vortices and Antivortices Based on Perspectives from Loops and Knots (5)

0
756

5. Conclusion

Based on Topological Vortex Theory, this paper systematically studied the characteristic features of vortices and antivortices in rotational and translational motion, and thoroughly explored their intrinsic relationships with topological structures such as loops and knots. The research shows that differences in the rotational direction of vortices and antivortices can induce rich topological phase transition behaviors, while their translational characteristics can reveal propagation patterns through knot theory. Loops and knots, as important topological invariants, provide key theoretical tools for analyzing the dynamical behaviors of vortex-antivortex pairs. These results not only deepen the theoretical understanding of topological defect dynamics but also lay a theoretical foundation for applied research in related fields such as optical vortices and quantum condensed matter physics.

References

  1. Congy, T., Azam, P., Kaiser, R., & Pavloff, N. (2024). Topological Constraints on the Dynamics of Vortex Formation in a Two-Dimensional Quantum Fluid. Physical Review Letters, *132*, 033804. https://doi.org/10.1103/physrevlett.132.033804.
  2. Zhong, J., & Zhan, Q. (2023). Optical toroidal vortices under topological perspective. Physics, *52*(10), 673-681. (Note: This is a citation for the Chinese journal (Wuli)). An English version of the article is available at: https://www.thepaper.cn/newsDetail_forward_25544446.
  3. Bai, W. (2021). Research on Knot Dynamics in Bose-Einstein Condensates (Doctoral dissertation, Northwest University). https://wf.pub/thesis/article:D02560789.
  4. Zhu, R., Zheng, S., Li, X., Wang, T., Tan, C., Yu, T., Liu, Z., Wang, X., Li, J., Wang, J., & Gao, P. (2024). Atomic-Scale Tracking Topological Phase Transition Dynamics of Polar Vortex-Antivortex Pairs. Advanced Materials, 2312072. https://doi.org/10.1002/adma.202312072.
  5. Jing Wang, Rongzhen Gao, Shiyu Tang, Shouzhe Dong, etc. (2025). General principle of ferroelectric topological domain formation. Science Advances, *11*(7). https://www.science.org/doi/10.1126/sciadv.adu6223.

Academic Statement

Certain analyses and discussions in this paper have referenced and drawn upon recent cutting-edge research published in journals such as Physical Review Letters, Science Advances, and Advanced Materials, including but not limited to topological constraints on vortex-antivortex pairs in quantum fluids, the generation and characterization of optical vortex rings, and knot dynamics in Bose-Einstein condensates. The authors hereby express gratitude to the researchers and teams behind these works. This paper is intended for international academic exchange. Reproduction without permission is prohibited.

검색
카테고리
더 보기
기타
Competitive Landscape in the Generic Drug Market: Innovations, Key Players, and Strategic Moves
The global Generic Drug market size was USD 360.84 Billion in 2022 and is expected to register a...
작성자 Isha Deshpande 2025-08-26 11:18:02 0 2K
Party
電子菸推薦全攻略|SHAXIAO殺小主機與梟客XIAOKE一次性全面分析【台灣現貨】
電子 菸 推薦 近年來,電子菸市場持續升溫,無論是高端主機還是方便攜帶的一次性小煙,都吸引了眾多用戶的關注。本文將為你深入解析 SHAXIAO殺小主機、SHAXIAO一次性電子煙...
작성자 ADA ADAD 2025-08-15 03:24:56 0 2K
Networking
招聘泰国业务员ประกาศรับสมัครงานขาย
         คุณสมบัติผู้สมัคร            ...
작성자 裕婷 陈 2025-07-11 06:25:50 2 2K
Party
長夾、三折短夾、男夾與 GOSSIP 鱷魚紋鏈條皮夾解析
在高端時尚領域中,balenciaga(巴黎世家) 一直都是潮流愛好者心中的標誌性品牌。不僅以服裝、鞋履聞名,巴黎世家的 錢包...
작성자 ADA ADAD 2025-09-05 02:49:48 0 2K
Shopping
犀利士5mg哪裡買?如何購買犀利士每日錠(藥師詳解)
犀利士5mg(Cialis-5毫克)是目前市面上廣受歡迎的長期治療勃起功能障礙(ED)和前列腺肥大(BPH)藥物。它的特點在於每日服用的低劑量,使男性能夠隨時進行性生活,無需計劃或提前服藥。那麼...
작성자 Awdaw Awdawd 2025-07-14 03:58:33 0 2K