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静如叶 updated the cover photo
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2025-10-28 12:24:14 -

Aerosol Can Market: Comprehensive Analysis of Applications, Trends, and Regional Expansion
The aerosol can market is poised for sustained growth as industries worldwide adopt eco-friendly packaging and advanced dispensing technologies. Aerosol packaging continues to prove indispensable across diverse applications, including personal care, home maintenance, automotive, and healthcare. With growing environmental awareness and demand for convenient, portable products, the market is...

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MAYMAY Deng updated the profile picture
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MAYMAY Deng
2025-10-28 14:14:21 -

The early bird catches the worm.The early worm ...

The early bird catches the worm.The early worm ...

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Bao-hua ZHANG agregó una foto Literature
2025-10-29 01:03:31 -

A Study on Topological Vortex Ring Interactions Based on Möbius Loop and Hopf Link Concepts (1)
Abstract This paper aims to explore the complex interactions of topological vortex rings in fluid mechanics and establish a novel topological framework for them. Vortex rings, as coherent structures carrying circulation and possessing stable topological structures, undergo interactions (such as collision, threading, and merging) that are inherently processes of topological transformation. We...

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Bao-hua ZHANG agregó una foto Literature
2025-10-29 01:21:19 -

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...

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想长高的女孩 updated the profile picture
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想长高的女孩 updated the cover photo
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Bao-hua ZHANG agregó una foto Literature
2025-10-29 01:30:19 -

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...

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