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   Shokrieh, Farbod; Wright, Cameron (September 2023, SIAM Journal on Discrete Mathematics)
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   https://doi.org/10.1007/JHEP09(2020)139  

   Fan, Wei; Fotopoulos, Angelos; Stieberger, Stephan; Taylor, Tomasz R. (September 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract Conformally soft gluons are conserved currents of the Celestial Conformal Field Theory (CCFT) and generate a Kac-Moody algebra. We study celestial amplitudes of Yang-Mills theory, which are Mellin transforms of gluon amplitudes and take the double soft limit of a pair of gluons. In this manner we construct the Sugawara energy-momentum tensor of the CCFT. We verify that conformally soft gauge bosons are Virasoro primaries of the CCFT under the Sugawara energy-momentum tensor. The Sugawara tensor though does not generate the correct conformal transformations for hard states. In Einstein-Yang- Mills theory, we consider an alternative construction of the energy-momentum tensor, similar to the double copy construction which relates gauge theory amplitudes with gravity ones. This energy momentum tensor has the correct properties to generate conformal transformations for both soft and hard states. We extend this construction to supertranslations. 

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3. On the general dyadic grids on

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   Anderson, Theresa C.; Hu, Bingyang (July 2022, Canadian Journal of Mathematics)

   Abstract Adjacent dyadic systems are pivotal in analysis and related fields to study continuous objects via collections of dyadic ones. In our prior work (joint with Jiang, Olson, and Wei), we describe precise necessary and sufficient conditions for two dyadic systems on the real line to be adjacent. Here, we extend this work to all dimensions, which turns out to have many surprising difficulties due to the fact that $d+1$ , not $2^d$ , grids is the optimal number in an adjacent dyadic system in $$\mathbb {R}^d$$ . As a byproduct, we show that a collection of $d+1$ dyadic systems in $$\mathbb {R}^d$$ is adjacent if and only if the projection of any two of them onto any coordinate axis are adjacent on $$\mathbb {R}$$ . The underlying geometric structures that arise in this higher-dimensional generalization are interesting objects themselves, ripe for future study; these lead us to a compact, geometric description of our main result. We describe these structures, along with what adjacent dyadic (and n -adic, for any n ) systems look like, from a variety of contexts, relating them to previous work, as well as illustrating a specific exa. 

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5. On a neck, on a spit: controls on the shape of free spits

   https://doi.org/10.5194/esurf-4-193-2016  

   Ashton, A. D.; Nienhuis, J.; Ells, K. (January 2016, Earth Surface Dynamics)

   null (Ed.)

   Abstract. We investigate the controls upon the shape of freely extending spits using a one-contour-line model of shoreline evolution. In contrast to existing frameworks that suggest that spits are oriented in the direction of alongshore sediment transport and that wave refraction around the spit end is the primary cause of recurving, our results suggest that spit shoreline shapes are perhaps best understood as graded features arising from a complex interplay between distinct morphodynamic elements: the headland updrift of the spit, the erosive "neck" (which may be overwashing), and the depositional "hook". Between the neck and the hook lies a downdrift-migrating "fulcrum point" which tends towards a steady-state trajectory set by the angle of maximum alongshore sediment transport. Model results demonstrate that wave climate characteristics affect spit growth; however, we find that the rate of headland retreat exerts a dominant control on spit shape, orientation, and progradation rate. Interestingly, as a spit forms off of a headland, the rate of sediment input to the spit itself emerges through feedbacks with the downdrift spit end, and in many cases faster spit progradation may coincide with reduced sediment input to the spit itself. Furthermore, as the depositional hook rests entirely beyond the maximum in alongshore sediment transport, this shoreline reach is susceptible to high-angle wave instability throughout and, as a result, spit depositional signals may be highly autogenic. 

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