# gst: singular bifurcations, an approach

<< Bifurcation analysis is traditionally based on the assumption of a regular perturbative expansion, close to the bifurcation point, in terms of a variable describing the passage of a system from one state to another. However, it is shown that a regular expansion is not the rule due to the existence of hidden singularities in many models, paving the way to a new paradigm in nonlinear science, that of singular bifurcations. The theory is first illustrated on an example borrowed from the field of active matter (phoretic microswimers), showing a singular bifurcation. >>

AA << then present a universal theory on how to handle and regularize these bifurcations, bringing to light a novel facet of nonlinear sciences that has long been overlooked. >>️

Alexander Farutin, Chaouqi Misbah. Singular bifurcations and regularization theory. Phys. Rev. E 109, 064218. Jun 27, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.064218

Alexander Farutin, Chaouqi Misbah. Singular Bifurcations : a Regularization Theory. arXiv: 2112.12094v2 [cond-mat.soft]. Jan 6, 2022. 

https://arxiv.org/abs/2112.12094 

Also: transition, singularity, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transition, singularity, bifurcation

# phys: stable vortex loops intersected by point singularities (in magnets)

<< Vortex rings are remarkably stable structures that occur in a large variety of systems (..) Although vortex rings have also been predicted to exist in ferromagnets, they have not yet been observed. >>

AA << imaged three-dimensional structures forming closed vortex loops in a bulk micromagnet. The cross-section of these loops consists of a vortex–antivortex pair and, on the basis of magnetic vorticity (they) identify these configurations as magnetic vortex rings. >>

<< In addition, (they) observe stable vortex loops intersected by point singularities at which the magnetization within the vortex and antivortex cores reverses. >>

Claire Donnelly, Konstantin L. Metlov, et al. Experimental observation of vortex rings in a bulk magnet. Nature Physics. doi: 10.1038/ s41567-020-01057-3. Nov 30,  2020.

https://www.nature.com/articles/s41567-020-01057-3

Magnetic vortices come full circle. 

Paul Scherrer Institute. Nov 30, 2020.

https://phys.org/news/2020-11-magnetic-vortices-full-circle.html

# gst: multiple singularities by optical vortices (a 30y review)

<< Vortices are common phenomena that widely exist in nature, from quantum vortices in liquid nitrogen to ocean circulation and typhoon vortices and even spiral galaxies in the Milky Way. Vortices also exist in optics, the concept of which was first proposed by theoretical physicist Pierre Coullet and colleagues [Opt. Commun. 73, 403 (1989)] thirty years ago. Hitherto, owing to their amazing structures, optical vortices have engendered tremendous advanced applications such as optical tweezers, quantum entanglement, and nonlinear optics, throughout every branch of modern optics. >>

Commemorating 30 years of optical vortices: A comprehensive review. 

Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences. Nov 4, 2019.

https://m.phys.org/news/2019-11-commemorating-years-optical-vortices-comprehensive.html

Yijie Shen, Xuejiao Wang, et al. Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities. Light: Science & Applications volume 8, Article number: 90. Oct 2, 2019.

https://www.nature.com/articles/s41377-019-0194-2