Bifurcations in Volume-Preserving Systems

Broer, Hendrik; Hanßmann, Heinz

doi:10.1007/s10440-019-00254-4

Cited by 3 publications

(1 citation statement)

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“…Indeed, from a topological point of view they are necessary: singularities have to be created and annihilated in pairs, which topologically manifests as a saddlenode bifurcation, where a saddle and a node are annihilated or created together [23]. In the case of a divergencefree field, this turns into a center-saddle bifurcation [28]: creation/annihilation events cannot take place with just saddle points, and the field can either have no singularities, or must exhibit points with a different topology alongside the saddle points.…”

Section: Restriction To a 2d Light Fieldmentioning

confidence: 99%

Poynting singularities in the transverse flow-field of random vector waves

et al. 2020

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In order to utilize the full potential of tailored flows of electromagnetic energy at the nanoscale, we need to understand its general behaviour given by its generic representation of interfering random waves. For applications in on-chip photonics as well as particle trapping, it is important to discern the topological features in the flow field between the commonly investigated cases of fully vectorial light fields and their 2D equivalents. We demonstrate the distinct difference between these cases in both the allowed topology of the flow-field and the spatial distribution of its singularities, given by their pair correlation function g(r). Specifically, we show that a random field confined to a 2D plane has a divergence-free flow-field and exhibits a liquid-like correlation, whereas its freely propagating counterpart has no clear correlation and features a transverse flow-field with the full range of possible 2D topologies around its singularities.

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Section: Restriction To a 2d Light Fieldmentioning

confidence: 99%