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1. What makes low-frequency earthquakes low frequency

   https://doi.org/10.1126/sciadv.adh3688  

   Wang, Qing-Yu; Frank, William B.; Abercrombie, Rachel E.; Obara, Kazushige; Kato, Aitaro (August 2023, Science Advances)

   Low-frequency earthquakes, atypical seismic events distinct from regular earthquakes, occur downdip of the seismogenic megathrust where an aseismic rheology dominates the subduction plate boundary. Well situated to provide clues on the slip regime of this unique faulting environment, their distinctive waveforms reflect either an unusual rupture process or unusually strong attenuation in their source zone. We take advantage of the unique geometry of seismicity in the Nankai Trough to isolate the spectral signature of low-frequency earthquakes after correcting for empirically derived attenuation. We observe that low-frequency earthquake spectra are consistent with the classical earthquake model, yet their rupture duration and stress drop are orders of magnitude different from ordinary earthquakes. We conclude their low-frequency nature primarily results from an atypical seismic rupture process rather than near-source attenuation. 

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2. Low-frequency conductivity of low wear high-entropy alloys

   https://doi.org/10.1038/s41467-024-49035-0  

   Yeh, Cheng-Hsien; Hsu, Wen-Dung; Liu, Bernard Haochih; Yang, Chan-Shan; Kuan, Chen-Yun; Chang, Yuan-Chun; Huang, Kai-Sheng; Jhang, Song-Syun; Lu, Chia-Yen; Liaw, Peter K; et al (December 2024, Nature Communications)

   Abstract High-entropy alloys (HEAs) provide new research avenues for alloy combinations in the periodic table, opening numerous possibilities in novel-alloy applications. However, their electrical characteristics have been relatively underexplored. The challenge in establishing an HEA electrical conductivity model lies in the changes in electronic characteristics caused by lattice distortion and complexity of nanostructures. Here we show a low-frequency electrical conductivity model for the Nb-Mo-Ta-W HEA system. The cocktail effect is found to explain trends in electrical-conductivity changes in HEAs, while the magnitude of the reduction is understood by the calculated plasma frequency, free electron density, and measured relaxation time by terahertz spectroscopy. As a result, the refractory HEA Nb₁₅Mo₃₅Ta₁₅W₃₅thin film exhibits both high hardness and excellent conductivity. This combination of Nb₁₅Mo₃₅Ta₁₅W₃₅makes it suitable for applications in atomic force microscopy probe coating, significantly improving their wear resistance and atomic-scale image resolution. 

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3. Submodular Clustering in Low Dimensions

   https://doi.org/10.4230/LIPIcs.SWAT.2020.8  

   Backurs, Arturs; Har-Peled, Sariel (January 2020, 17th Scandinavian Symposium and Workshops on Algorithm Theory)

   We study a clustering problem where the goal is to maximize the coverage of the input points by k chosen centers. Specifically, given a set of n points P ⊆ ℝ^d, the goal is to pick k centers C ⊆ ℝ^d that maximize the service ∑_{p∈P}φ(𝖽(p,C)) to the points P, where 𝖽(p,C) is the distance of p to its nearest center in C, and φ is a non-increasing service function φ: ℝ+ → ℝ+. This includes problems of placing k base stations as to maximize the total bandwidth to the clients - indeed, the closer the client is to its nearest base station, the more data it can send/receive, and the target is to place k base stations so that the total bandwidth is maximized. We provide an n^{ε^-O(d)} time algorithm for this problem that achieves a (1-ε)-approximation. Notably, the runtime does not depend on the parameter k and it works for an arbitrary non-increasing service function φ: ℝ+ → ℝ+. 

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4. Low Degree Points on Curves

   https://doi.org/10.1093/imrn/rnaa137  

   Smith, Geoffrey; Vogt, Isabel (June 2020, International Mathematics Research Notices)

   Abstract In this paper, we investigate an arithmetic analogue of the gonality of a smooth projective curve $$C$$ over a number field $$k$$: the minimal $$e$$ such that there are infinitely many points $$P \in C(\bar{k})$$ with $$[k(P):k] \leqslant e$$. Developing techniques that make use of an auxiliary smooth surface containing the curve, we show that this invariant can take any value subject to constraints imposed by the gonality. Building on work of Debarre–Klassen, we show that this invariant is equal to the gonality for all sufficiently ample curves on a surface $$S$$ with trivial irregularity. 

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5. Low-redshift Lyman Continuum Survey (LzLCS): Radio continuum properties of low-z Lyman continuum emitters

   https://doi.org/10.1051/0004-6361/202348416  

   Bait, Omkar; Borthakur, Sanchayeeta; Schaerer, Daniel; Momjian, Emmanuel; Sebastian, Biny; Saldana-Lopez, Alberto; Flury, Sophia R; Chisholm, John; Marques-Chaves, Rui; Jaskot, Anne E; et al (August 2024, Astronomy & Astrophysics)

   Context.Sources that leak Lyman continuum (LyC) photons and lead to the reionisation of the universe are an object of intense study using multiple observing facilities. Recently, the Low-redshift LyC Survey (LzLCS) has presented the first large sample of LyC emitting galaxies at low redshift (z ∼ 0.3) with theHubbleSpace Telescope Cosmic Origins Spectrograph. The LzLCS sample contains a robust estimate of the LyC escape fraction (f_esc^LyC) for 66 galaxies, spanning a wide range off_esc^LyCvalues. Aims.Here, we aim to study the dependence off_esc^LyCon the radio continuum (RC) properties of LzLCS sources. Overall, RC emission can provide unique insights into the role of supernova feedback, cosmic rays (CRs), and magnetic fields from its non-thermal emission component. RC emission is also a dust-free tracer of the star formation rate (SFR) in galaxies. Methods.In this study, we present Karl G. Jansky Very Large Array (VLA) RC observations of the LzLCS sources at gigahertz (GHz) frequencies. We performed VLAC(4−8 GHz) andS(2−4 GHz) band observations for a sample of 53 LzLCS sources. We also observed a sub-sample of 17 LzLCS sources in theL(1−2 GHz) band. We detected RC from bothC- andS-bands in 24 sources for which we are able to estimate their radio spectral index across 3−6 GHz, denoted asα_6 GHz^3 GHz. We also used the RC luminosity to estimate their SFRs. Results.The radio spectral index of LzLCS sources spans a wide range, from flat (≥ − 0.1) to very steep (≤ − 1.0). They have a steeper meanα_6 GHz^3 GHz(≈ − 0.92) compared to that expected for normal star-forming galaxies (α_6 GHz^3 GHz ≈ −0.64). They also show a larger scatter inα_6 GHz^3 GHz(∼0.71) compared to that of normal star-forming galaxies (∼0.15). The strongest leakers in our sample show flatα_6 GHz^3 GHz, weak leakers haveα_6 GHz^3 GHzclose to normal star-forming galaxies and non-leakers are characterized by steepα_6 GHz^3 GHz. We argue that a combination of young ages, free-free absorption, and a flat cosmic-ray energy spectrum can altogether lead to a flatα_6 GHz^3 GHzfor strong leakers. Non-leakers are characterized by steep spectra which can arise due to break or cutoff at high frequencies. Such a cutoff in the spectrum can arise in a single injection model of CRs characteristic of galaxies which have recently stopped star-formation. The dependence off_esc^LyConα_6 GHz^3 GHz(which is orientation-independent) suggests that the escape of LyC photons is not highly direction-dependent at least to the first order. The radio-based SFRs (SFR^RC) of LzLCS sources show a large offset (∼0.59 dex) from the standard SFR^RCcalibration. We find that addingα_6 GHz^3 GHzas a second parameter helps us to calibrate the SFR^RCwith SFR_UVand SFR_Hβwithin a scatter of ∼0.21 dex. Conclusions.For the first time, we have found a relation betweenα_6 GHz^3 GHzandf_esc^LyC. This hints at the interesting role of supernovae feedback, CRs, and magnetic fields in facilitating the escape (alternatively, and/or the lack) of LyC photons. 

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