Introduction to Vector Field Topology

Günther, Tobias; Rojo, Irene Baeza

doi:10.1007/978-3-030-83500-2_15

Cited by 9 publications

(6 citation statements)

References 113 publications

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“…Note that, due to the opposite values of OAM and SAM of the composing modes, LPVB are vectorial fields with no net OAM or SAM. However, they are topologically characterized by their Poincaré index, p-the number of complete rotations of the polarization tilt along a closed loop around the axis [40]-which coincides with the OAM charge of the RCP mode, i.e.…”

Section: Resultsmentioning

confidence: 99%

“…Among them, linear-polarized vector beams (LPVB) present a transversal distribution of linearly polarized states with different tilt angles [39]. This spatially-varying orientation confers the beam with a topological character, with well-defined Poincare index [40]. In this sense, it has been already demonstrated that the up-conversion of LPVBs to high-order harmonics in gases preserves the topology of the driving field [41,42].…”

Section: Introductionmentioning

confidence: 99%

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Interplay of crystal symmetries and light topology in high harmonic spectroscopy

García-Cabrera

Boyero-García

Zurrón-Cifuentes

et al. 2022

Preprint

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Structured ultrafast laser beams offer unique opportunities to explore the interplay of the angular momentum of light with matter at the femtosecond scale. Linearly polarized vector beams are paradigmatic examples of structured beams whose topology is characterized by a well-defined Poincaré index. It has been demonstrated that the Poincaré index is a topological invariant during high-order harmonic generation from isotropic targets, such as noble gases. As a result, harmonics are produced as extreme-ultraviolet vector beams with the same topology as the driver. In this work we demonstrate that high-order harmonic generation driven by vector beams from anisotropic crystalline targets, such as single-layer graphene, splits the harmonic field into a multibeam structure: a central vector beam that preserves the driver's topology, surrounded by a topological cluster of unitary vortices, where this symmetry is broken. We identify the target's non-linear anisotropic response as the vehicle of coupling the crystal symmetries with the driving field's topology. Our work opens the route towards using the topological analysis of the high-order harmonic field as a novel spectroscopic tool to reveal the role of symmetries in the non-linear response of matter.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interplay of crystal symmetries and light topology in high harmonic spectroscopy

García-Cabrera

Boyero-García

Zurrón-Cifuentes

et al. 2022

Preprint

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“…Since arrow length and orientation are different for differently moving observers, arrows are not useful to study the behavior of particles in the fluid and their immediate value as quality metric in a vector field comparison is limited. Arrow plots can only reveal instantaneous structures, as for example needed in streamline-oriented topology (Günther & Baeza Rojo, 2021). Nevertheless, an arrow plot is a frequent first choice to get an initial impression of the vector data, for example to investigate the amount of noise present at individual grid points.…”

Section: Discussionmentioning

confidence: 99%

Lagrangian Coherent Structures and Vortex Formation in High Spatiotemporal‐Resolution Satellite Winds of an Atmospheric Kármán Vortex Street

et al. 2021

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Recent advances in geostationary imaging have enabled the derivation of high spatiotemporal‐resolution cloud‐motion winds for the study of mesoscale unsteady flows. Due to the general absence of ground truth, the quality assessment of satellite winds is challenging. In the current limited practice, straightforward plausibility checks on the smoothness of the retrieved wind field or tests on aggregated trends such as the mean velocity components are applied for quality control. In this study, we demonstrate additional diagnostic tools based on feature extraction from the retrieved velocity field. Lagrangian Coherent Structures (LCS), such as vortices and transport barriers, guide and constrain the emergence of cloud patterns. Evaluating the alignment of the extracted LCS with the observed cloud patterns can potentially serve as a test of the retrieved wind field to adequately explain the time‐dependent dynamics. We discuss the suitability and expressiveness of direct, geometry‐based, texture‐based, and feature‐based flow visualization methods for the quality assessment of high spatiotemporal‐resolution winds through the real‐world example of an atmospheric Kármán vortex street and its laboratory archetype, the 2D cylinder flow.

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“…Concepts and algorithms from computational topology [26] have been investigated, adapted and extended by the visualization community for more than twenty years [51]. Specifically, a large body of literature has been dedicated to the analysis and visualization of flow data with topological methods and we refer the readers to a series of surveys on the topic [19,38,69,89,96,113], including a recent iteration [47]. A substantial line of work [83,84,88] focused on extending topological techniques to uncertain vector fields, where flow variability is encoded via a pointwise estimator (e.g.…”

Section: Related Workmentioning

confidence: 99%

Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows -- An Experimental Study

Nauleau¹,

Vivodtzev²,

Bridel-Bertomeu³

et al. 2022

Preprint

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1: Topological Data Analysis protocols applied on an ensemble dataset of a Kelvin-Helmholtz instability. (a) The 180 members of the ensemble obtained with variations of timesteps, interpolation schemes, orders, resolutions and Riemann solvers (Tab. 1). (b)The top cluster represents the time separation of t 0 and t 1 for the flows S 1 and S 2 with the Wasserstein distance and the bottom cluster with the L 2 -norm. Red lines show the timestep separation with our clustering method whereas the sphere colors are the ground truth, illustrating the limitation of the L 2 -norm. (c) Persistence curve protocol: Differences between integrals of persistence curves (gray area) of the enstrophy computed with a SLAU2 solver, an order 7 TENO scheme and a resolution of 1024 × 1024 for various configurations (S 1 at t 0 , S 2 and S 3 at t 1 ). These integral differences exhibit the appearance of vortices (critical points) as the time increases. (d) Outlier distance protocol: Wasserstein distance matrix for 5 configurations S 1 (t 0 , HLLC), S 2 (t 1 , Roe), S 3 (t 1 , HLLC), S 4 (t 2 , Roe), S 5 (t 2 , HLLC) computed with an order 7 WENO-Z interpolation scheme at 512 × 512. The sum of each row the configuration maximizing this distance between solvers and timesteps, here S 1 . (e) Unsupervised classification: Wasserstein distance matrix for the previous configurations with an order 7 WENO-Z interpolation scheme at 256 × 256. The clustering based on the Wasserstein distance and colored according to the Kmeans clustering method successfully segments the time steps.

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Introduction to Vector Field Topology

Cited by 9 publications

References 113 publications

Interplay of crystal symmetries and light topology in high harmonic spectroscopy

Interplay of crystal symmetries and light topology in high harmonic spectroscopy

Lagrangian Coherent Structures and Vortex Formation in High Spatiotemporal‐Resolution Satellite Winds of an Atmospheric Kármán Vortex Street

Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows -- An Experimental Study

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