Work

Fold Catastrophes in a Hopf Texture Driven by a Navier--Stokes Blow-Up Analog

Year: 2026

Type: preprint

Abstract: A two-component Bose--Einstein condensate can host a pseudospin Hopf texture coupled to the viscous normal flow of its thermal cloud. Motivated by OpenAI's reported finite-time Navier--Stokes singular solution, we evolve such a texture in a smooth flow reproducing the geometry and similarity scaling of the collapsing axisymmetric core. The evolution creates and annihilates preimage pairs while preserving the Hopf charge. The first one-to-three transition exhibits the square-root opening characteristic of a Thom $A_2$ fold. A subsequent three-to-five transition precedes a burst-like regime of recurrent fold catastrophes and near-caustic activity.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.24490

Author: Niemi, Antti J.

Institutions: Nordic Institute for Theoretical Physics, University of Science and Technology of China, Stockholm University

Language: English

Topic: Cold Atom Physics and Bose-Einstein Condensates

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Vetenskapsrådet

Award: Spontaneous dynamical self-organization

OpenAlex ID: W7213997607

Cites: 19

Cited by:

Related to: 10