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1. Uniformly Acute Triangulations of Polygons

   https://doi.org/10.1007/s00454-023-00525-w  

   Bishop, Christopher J (December 2023, Discrete & Computational Geometry)

   We show that any polygon P has an acute triangulation where every angle lies in the interval I=[30, 75] (degrees), except for triangles T that contain a vertex v of P where P has an interior angle theta_v < 30; then T is an isosceles triangle with angles \theta_v and 90 -\theta_v/2. 

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2. IXPE observation of PKS 2155–304 reveals the most highly polarized blazar

   https://doi.org/10.1051/0004-6361/202449166  

   Kouch, Pouya M; Liodakis, Ioannis; Middei, Riccardo; Kim, Dawoon E; Tavecchio, Fabrizio; Marscher, Alan P; Marshall, Herman L; Ehlert, Steven R; Di_Gesu, Laura; Jorstad, Svetlana G; et al (September 2024, Astronomy & Astrophysics)

   We report the X-ray polarization properties of the high-synchrotron-peaked (HSP) blazar PKS 2155−304 based on observations with the Imaging X-ray Polarimetry Explorer (IXPE). We observed the source between Oct 27 and Nov 7, 2023. We also conducted an extensive contemporaneous multiwavelength (MW) campaign. We find that during the first half (T₁) of the IXPE pointing, the source exhibited the highest X-ray polarization degree detected for an HSP blazar thus far, (30.7 ± 2.0)%; this dropped to (15.3 ± 2.1)% during the second half (T₂). The X-ray polarization angle remained stable during the IXPE pointing at 129.4° ±1.8° and 125.4° ±3.9° duringT₁andT₂, respectively. Meanwhile, the optical polarization degree remained stable during the IXPE pointing, with average host-galaxy-corrected values of (4.3 ± 0.7)% and (3.8 ± 0.9)% during theT₁andT₂, respectively. During the IXPE pointing, the optical polarization angle changed achromatically from ∼140° to ∼90° and back to ∼130°. Despite several attempts, we only detected (99.7% conf.) the radio polarization once (duringT₂, at 225.5 GHz): with degree (1.7 ± 0.4)% and angle 112.5° ±5.5°. The direction of the broad pc-scale jet is rather ambiguous and has been found to point to the east and south at different epochs; however, on larger scales (> 1.5 pc) the jet points toward the southeast (∼135°), similarly to all of the MW polarization angles. Moreover, the X-ray-to-optical polarization degree ratios of ∼7 and ∼4 duringT₁andT₂, respectively, are similar to previous IXPE results for several HSP blazars. These findings, combined with the lack of correlation of temporal variability between the MW polarization properties, agree with an energy-stratified shock-acceleration scenario in HSP blazars. 

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3. Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of ‘stripe’ formation in human data

   https://doi.org/10.1371/journal.pcbi.1010210  

   Mullick, Pratik; Fontaine, Sylvain; Appert-Rolland, Cécile; Olivier, Anne-Hélène; Warren, William H.; Pettré, Julien (June 2022, PLOS Computational Biology)

   Fu, Feng (Ed.)

   When two streams of pedestrians cross at an angle, striped patterns spontaneously emerge as a result of local pedestrian interactions. This clear case of self-organized pattern formation remains to be elucidated. In counterflows, with a crossing angle of 180°, alternating lanes of traffic are commonly observed moving in opposite directions, whereas in crossing flows at an angle of 90°, diagonal stripes have been reported. Naka (1977) hypothesized that stripe orientation is perpendicular to the bisector of the crossing angle. However, studies of crossing flows at acute and obtuse angles remain underdeveloped. We tested the bisector hypothesis in experiments on small groups (18-19 participants each) crossing at seven angles (30° intervals), and analyzed the geometric properties of stripes. We present two novel computational methods for analyzing striped patterns in pedestrian data: (i) an edge-cutting algorithm, which detects the dynamic formation of stripes and allows us to measure local properties of individual stripes; and (ii) a pattern-matching technique, based on the Gabor function, which allows us to estimate global properties (orientation and wavelength) of the striped pattern at a time T . We find an invariant property: stripes in the two groups are parallel and perpendicular to the bisector at all crossing angles. In contrast, other properties depend on the crossing angle: stripe spacing (wavelength), stripe size (number of pedestrians per stripe), and crossing time all decrease as the crossing angle increases from 30° to 180°, whereas the number of stripes increases with crossing angle. We also observe that the width of individual stripes is dynamically squeezed as the two groups cross each other. The findings thus support the bisector hypothesis at a wide range of crossing angles, although the theoretical reasons for this invariant remain unclear. The present results provide empirical constraints on theoretical studies and computational models of crossing flows. 

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4. Optimal angle bounds for Steiner triangulations of polygons

   https://doi.org/10.1137/1.9781611977073.121  

   Christopher J. Bishop (January 2022, Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA))

   For any simple polygon P we compute the optimal upper and lower angle bounds for triangulating P with Steiner points, and show that these bounds can be attained (except in one special case). The sharp angle bounds for an N-gon are computable in time O(N), even though the number of triangles needed to attain these bounds has no bound in terms of N alone. In general, the sharp upper and lower bounds cannot both be attained by a single triangulation, although this does happen in some cases. For example, we show that any polygon with minimal interior angle θ has a triangulation with all angles in the interval I = [θ, 90°–min(36°, θ)/2], and for θ ≤ 36° both bounds are best possible. Surprisingly, we prove the optimal angle bounds for polygonal triangulations are the same as for triangular dissections. The proof of this verifies, in a stronger form, a 1984 conjecture of Gerver. 

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5. Bidirectional Bending of Thin Metals With Femtosecond Lasers

   https://doi.org/10.1115/MSEC2022-85222  

   Tessmann, Bryce; Li, Kewei; Zhao, Xin (June 2022, ASME 2022 17th International Manufacturing Science and Engineering Conference)

   Abstract Lasers have a wide range of manufacturing applications, one of which is the bending of metals. While there are multiple ways to induce bending in metals with lasers, this paper examines laser peen forming with femtosecond lasers on thin metals of 75-micrometer thickness perpendicular to the laser. The effects of multiple parameters, including laser energy, scan speed, scan pitch, and material preparation, on the bend angle of the metal are investigated. The bend angles are generated in both concave and convex directions, represented by positive and negative angles, respectively. While it is possible to create angles ranging from 0 to 90 degrees in the concave direction, the largest average convex angle found was only −26.2 degrees. The positive angles were created by high overlapping ratios and slow speeds. Furthermore, the concave angles were made by a smaller range of values than the convex angles, although this range could be expanded by higher laser energy. The positive angles also had a higher inconsistency than the negative angles, with an average standard deviation of 6.8 degrees versus an average of 2.6 degrees, respectively. The characterization of bending angles will allow for more accurate predictions, which will benefit traditional metal forming applications and more advanced applications such as origami structures with metal. 

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