Tootfinder

The ribbon category of representations of a crossed module
Ony Aubril
https://arxiv.org/abs/2510.01809 https://arxiv.org/pdf/2510.01809

The ribbon category of representations of a crossed module
The theory of representations of a crossed module is a direct generalization of the theory of representations of groups. For a finite group G, the Drinfeld quantum double of the group G is a Hopf algebra that represents a special case of crossed module of finite groups. Here we study how to extend the construction of the Drinfeld quantum double for any other kind of crossed module of finite groups. This leads to a Hopf algebra D(G, H) that presents similarities with a Drinfeld double. We then s…

Holey sheets: Double-Threshold Rupture of Draining Liquid Films
Ayush K. Dixit, Chunheng Zhao, St\'ephane Zaleski, Detlef Lohse, Vatsal Sanjay
https://arxiv.org/abs/2509.12789

Holey sheets: Double-Threshold Rupture of Draining Liquid Films
Classical rupture is attributed to molecular (van der Waals) forces acting at nanometric thicknesses. Nonetheless, micron-thick liquid sheets routinely perforate far above the scale where these molecular forces act, yet the mechanism that selects opening versus healing has remained unclear. Using direct numerical simulations of a draining sheet with an entrained air bubble (cavity), we show that irreversible rupture occurs only when a deterministic double-threshold is crossed: (i) the outward d…