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cond-mat.soft2025
From Knots to Crystals: Machine-Learned Potentials for Self-Assembling Topological Solitons in Liquid Crystals
Arunkumar Bupathy, Darian Hall, Ivan I. Smalyukh +3
Knotted fields in classical and quantum systems have long been recognized for their non-trivial topologies and particle-like behavior, but practical applications have been limited…
cond-mat.soft2025
Fusion and Fission of Particle-like Chiral Nematic Vortex Knots
Darian Hall, Jung-Shen Benny Tai, Louis H. Kauffman +1
Vortex knots have been seen decaying in many physical systems. Here we describe topologically protected vortex knots, which remain stable and undergo fusion and fission while conse…
cond-mat.soft2025
Analysis of Hopf solitons as generalized fold maps
Yuta Nozaki, Darian Hall, Ivan I. Smalyukh +1
The Hopf index, a topological invariant that quantifies the linking of preimage fibers, is fundamental to the structure and stability of hopfions. In this work, we propose a new ma…