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Aerosol Can Market: Comprehensive Analysis of Applications, Trends, and Regional ExpansionThe 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...0 Commentarii 0 Distribuiri 786 Views 0 previzualizare
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The early bird catches the worm.The early worm ...The early bird catches the worm.The early worm ...0 Commentarii 0 Distribuiri 229 Views 0 previzualizare
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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...0 Commentarii 0 Distribuiri 787 Views 0 previzualizare
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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 Commentarii 0 Distribuiri 933 Views 0 previzualizare
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