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1. Semiconductor aspects of the oxyfuel cutting torch preheat flame; Part II: The flame's internal electrical structure

   Martin, Christopher; Pond, Teresa; Tomas, Jacob; Schmit, Jenna; Miguel, Erikson; Untaroiu, Alex; Xu, Kemu (June 2020, Proceedings of the ASME Manufacturing Engineering and Science Conference)

   This two-part paper presents precise measurements of the ion currents passing between the torch and work piece of the preheat flame of an oxyfuel cutting torch as a means for replacing contemporary sensing suites. Part II presents the results of a novel spinning disc Langmuir probe technique to construct spatially resolved measurements of the flame's ion density distribution. A bias voltage is applied to a .254mm diameter wire protruding from a spinning disc, and as the wire is passed through the flame, the measured currents (on the order 10uA) are collected. The process is repeated with incremental wire depths in the flame to construct the entire planar cross-sectional ion density. Measurements reveal intense ion concentrations in the inner cones that rapidly decay by an order of magnitude in the surrounding flow. The outer cone forms a hollow cylinder of weak ion concentration that declines with distance from the inner cones in a manner consistent with recombination. 

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2. Klt varieties of general type with small volume

   https://doi.org/10.2422/2036-2145.202109_010  

   Totaro, Burt; Wang, Chengxi (January 2023, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE)

   By Hacon-McKernan-Xu, there is a positive lower bound in each dimension for the volumes of all klt varieties with ample canonical class. We show that these bounds must go to zero extremely fast as the dimension increases, by constructing a klt n-fold with ample canonical class whose volume is less than 1/2^{2^n}. These examples should be close to optimal. We also construct, for every n, a klt Fano variety of dimension n such that the space of sections of the mth power of the anticanonical bundle is zero for all m from 1 to about 2^{2^n}. Here again there is some bound in each dimension, by Birkar’s theorem on boundedness of complements, and we are showing that the bound must increase extremely fast with the dimension. 

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3. Inertia-gravity waves and geostrophic turbulence

   https://doi.org/10.1017/jfm.2021.334  

   Young, William R. (August 2021, Journal of Fluid Mechanics)

   Inertia-gravity waves in the atmosphere and ocean are transported and refracted by geostrophic turbulent currents. Provided that the wave group velocity is much greater than the speed of geostrophic turbulent currents, kinetic theory can be used to obtain a comprehensive statistical description of the resulting interaction (Savva et al. , J. Fluid Mech. , vol. 916, 2021, A6). The leading-order process is scattering of wave energy along a surface of constant frequency, $$\omega$$ , in wavenumber space. The constant- $$\omega$$ surface corresponding to the linear dispersion relation of inertia-gravity waves is a cone extending to arbitrarily high wavenumbers. Thus, wave scattering by geostrophic turbulence results in a cascade of wave energy to high wavenumbers on the surface of the constant- $$\omega$$ cone. Solution of the kinetic equations shows establishment of a wave kinetic energy spectrum $$\sim k_h^{-2}$$ , where $$k_h$$ is the horizontal wavenumber. 

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4. The quantum entropy cone of hypergraphs

   https://doi.org/10.21468/SciPostPhys.9.5.067  

   Bao, Ning; Cheng, Newton; Hernández-Cuenca, Sergio; Su, Vincent P. (January 2020, SciPost Physics)

   null (Ed.)

   In this work, we generalize the graph-theoretic techniques used for the holographic entropy cone to study hypergraphs and their analogously-defined entropy cone.This allows us to develop a framework to efficiently compute entropies and prove inequalities satisfied by hypergraphs.In doing so, we discover a class of quantum entropy vectors which reach beyond those of holographic states and obey constraints intimately related to the ones obeyed by stabilizer states and linear ranks.We show that, at least up to 4 parties, the hypergraph cone is identical to the stabilizer entropy cone, thus demonstrating that the hypergraph framework is broadly applicable to the study of entanglement entropy.We conjecture that this equality continues to hold for higher party numbers and report on partial progress on this direction.To physically motivate this conjectured equivalence, we also propose a plausible method inspired by tensor networks to construct a quantum state from a given hypergraph such that their entropy vectors match. 

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5. Positivity of divisors on blown-up projective spaces, I

   Dumitrescu, Olivia; Postinghel, Elisa (June 2023, Annali della Scuola normale superiore di Pisa Classe di scienze)

   We study l-very ample, ample and semi-ample divisors on the blown-up projective space P^n in a collection of points in general position. We establish Fujita’s conjectures for all ample divisors with the number of points bounded above by 2n and for an infinite family of ample divisors with an arbitrary number of points. 

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