Rotational and Translational Characteristics of Topological...

Rotational and Translational Characteristics of Topological Vortices and Antivortices Based on Perspectives from Loops and Knots (4)

المدونات Literature

نشر بتاريخ 2025-10-20 05:27:07

49

4. Topological Significance of Loops and Knots

4.1 Topological Invariants in Loop Structures

As an important topological model for describing vortex-antivortex pairs in three-dimensional space, the stability of loop structures can be characterized by a series of topological invariants. Taking the optical vortex ring as an example, its knot number determines the topological undeformability of the structure. Changes in the knot number can reflect the interaction between vortex-antivortex pairs: co-rotating vortex pairs tend to form stable loop structures with higher knot numbers, while counter-rotating pairs may lead to structural annihilation due to a decrease in the knot number. Therefore, topological invariants provide an important theoretical tool for analyzing the stability of vortex-antivortex pairs.

4.2 Topological Phase Transition Behavior in Knot Theory

Knot theory provides an effective framework for understanding the topological phase transitions of vortex-antivortex pairs. For example, in optical vortices, changes in the kinking number can cause significant transitions in the phase structure. Such phase transitions are closely related to the rotational and translational behaviors of vortex-antivortex pairs: co-rotating vortex pairs help form topological structures with stable kinking numbers, while counter-rotating pairs may trigger topological phase transitions due to abrupt changes in the kinking number. This mechanism provides a theoretical basis for topological control in optical device design and quantum information transmission.

الرجاء تسجيل الدخول , للأعجاب والمشاركة والتعليق على هذا!

YEEZY 系列熱銷關鍵分析｜你不可錯過的 450 與 500 潮鞋指南

在現今街頭潮流文化中，yeezy鞋款無疑佔據了一席之地，無論是設計美學還是品牌故事都令人著迷。Kanye West 與 adidas 攜手推出的 YEEZY...

بواسطة 2025-06-07 01:44:08 0 2كيلو بايت

الرئيسية

Phone case

Mobile phone case factory

بواسطة 2025-06-22 23:03:53 0 2كيلو بايت

**Shenzhen Jishang Lighting Co., Ltd.** primarily **develops and manufactures** LED backlight modules, advertising modules, lightbox illumination modules, and automotive lighting modules.

--- **Headline: Make Every Night Your Advertising Spotlight!** **Body:** The...

بواسطة 2025-07-30 09:28:48 8 2كيلو بايت

Nike x Sacai聯名美學拆解與穿搭提案

解剖Nike x Sacai的設計革命基因當解構主義大師Sacai遇上運動巨擘Nike，每次聯名都像在時尚圈投下震撼彈。從2019年引爆話題的Nike Sacai Waffle Green...

بواسطة 2025-05-28 01:13:35 0 2كيلو بايت

Topological Vortex Space-Time Ontology (TVSTO)

2.2 Breakthroughs in Physical Interpretation: 2.2.1 Dark Energy: The theory proposes that the...

بواسطة 2025-10-10 07:18:28 0 348