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1. A note on dispersing particles on a line

   https://doi.org/10.1002/rsa.20821  

   Frieze, Alan; Pegden, Wesley (October 2018, Random Structures & Algorithms)

   We consider a synchronous dispersion process introduced in pervious study of Cooper and coworkers and we show that on the infinite line the final set of occupied sites takes upO(n) space, wherenis the number of particles involved. 

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2. 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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3. A note on the periodic Hilbert transform on a strip

   https://doi.org/10.1016/j.jde.2025.01.022  

   Gómez-Serrano, Javier; Kim, Sieon (March 2025, Journal of Differential Equations)
4. A Note on the No-(d+2)-On-a-Sphere Problem

   https://doi.org/10.4230/LIPIcs.SoCG.2025.76  

   Suk, Andrew; White, Ethan Patrick (January 2025, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Aichholzer, Oswin; Wang, Haitao (Ed.)

   For fixed d ≥ 3, we construct subsets of the d-dimensional lattice cube [n]^d of size n^{3/(d + 1) - o(1)} with no d+2 points on a sphere or a hyperplane. This improves the previously best known bound of Ω(n^{1/(d-1)}) due to Thiele from 1995. 

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5. On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes

   https://doi.org/10.4007/annals.2024.199.3.6  

   Park, Jinyoung; Pham, Huy Tuan (May 2024, Annals of Mathematics)