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Journal of Nonlinear science 2023年第5期33卷 1-2页

作者： Hittmeir, Sabine Klein, Rupert Li, Jinkai Titi, Edriss S. Fakultät für Mathematik Universität Wien Wien Austria FB Mathematik and Informatik Freie Universität Berlin Berlin Germany South China Research Center for Applied Mathematics and Interdisciplinary Studies School of Mathematical Sciences South China Normal University Guangzhou People’s Republic of China Department of Mathematics Texas A &M University College Station USA Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge UK Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel

On powers of Hamilton cycles in Ramsey-Turán Theory

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arXiv 2023年

作者： Chen, Ming Han, Jie Tang, Yantao Yang, Donglei School of Mathematics and Statistics Jiangsu Normal University Xuzhou China School of Mathematics and Statistics Center for Applied Mathematics Beijing Institute of Technology Beijing China Zhongtai Securities Institute for Financial Studies Shandong University Jinan China Data Science Institute Shandong University Jinan China

We prove that for r ∈ N with r ≥ 2 and µ > 0, there exist α > 0 and n0 such that for every n ≥ n0, every n-vertex graph G with δ(G) ≥ (1 − 1r + µ) n and α(G) ≤ αn contains an r-th power of a H...

We prove that for r ∈ N with r ≥ 2 and µ > 0, there exist α > 0 and n0 such that for every n ≥ n0, every n-vertex graph G with δ(G) ≥ (1 − 1r + µ) n and α(G) ≤ αn contains an r-th power of a Hamilton cycle. We also show that the minimum degree condition is asymptotically sharp for r = 2, 3 and the r = 2 case was recently conjectured by Staden and Treglown. © 2023, CC BY.

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Fe2+ partitioning in Al-free pyrolite: consequences for seismic velocities and heterogeneities

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arXiv 2024年

作者： Zhuang, Jingyi Wentzcovitch, Renata Department of Earth and Environmental Sciences Columbia University New YorkNY10027 United States Lamont–Doherty Earth Observatory Columbia University PalisadesNY10964 United States Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States Data Science Institute Columbia University New YorkNY10027 United States Center for Computational Quantum Physics Flatiron Institute New YorkNY10010 United States

Iron partitioning among the main lower mantle phases, bridgmanite (Bm) and ferropericlase (Fp), has non-monotonic behavior owing to the high-spin to low-spin crossover in ferrous iron (Fe2+) in Fp. Results of previous studies of the iron partitioning coefficient between these phases, KD, still have considerable uncertainty. Here, we investigate the Fe2+ partitioning behavior using well-documented ab initio free energy results plus new updates. Although we focus on Fe2+ only, we describe the effect of this iron spin crossover (ISC) on KD and of the latter on compositions and seismic velocities in a pyrolitic aggregate. Our results suggest that its velocities are mainly affected by the ISC and less so by the Fe2+ partitioning. In contrast, iron partitioning manifests in thermally induced velocity heterogeneity ratios. Prediction of the seismological parameter RS/P (∂ ln VS/∂ ln VP ) including iron partitioning effects resembles quantitatively RS/P ’s inferred from several tomographic studies down to 2,400 km depth. Copyright © 2024, The Authors. All rights reserved.

关键词： Iron

A Compact X-Ray Laser with Ion Source and Crystal Cavity

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arXiv 2024年

作者： Li, Shuang School of Electrical and Optoelectronic Engineering West Anhui University Luan237012 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Shanghai EBIT Lab Institute of Modern Physics Department of Nuclear Science and Technology Fudan University Shanghai200433 China

X-ray free-electron lasers (XFELs) are renowned for their high brightness, significantly impacting biology, chemistry, and nonlinear X-ray optics. However, current XFELs are large, expensive, and exhibit significant shot-to-shot instability. Here, we propose a novel compact apparatus for generating X-ray lasers. The setup integrates an ion source to produce highly charged ions as the gain medium. The X-ray optical cavity employs crystal Bragg diffraction for high reflectivity at large angles, and two parabolic compound refractive lenses (CRLs) focus the X-rays. Pumping is achieved through electron collision excitations. This X-ray laser offers compact dimensions, reduced costs, and enhanced coherence, positioning it as a promising seed for XFELs. With further optimization, this device has the potential to rival XFELs and revolutionize both scientific research and industrial applications. © 2024, CC BY-NC-ND.

关键词： X ray lasers

Continuous partitioning for graph-based semi-supervised learning 24

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Continuous partitioning for graph-based semi-supervised lear...

Proceedings of the 38th International Conference on Neural Information Processing Systems

作者： Chester Holtz Pengwen Chen Zhengchao Wan Chung-Kuan Cheng Gal Mishne Halicioğlu Data Science Institute University of California San Diego La Jolla CA Department of Applied Mathematics National Chung Hsing University South District Taichung Taiwan Department of Mathematics University of Missouri Columbia MO Department of Computer Science University of California San Diego La Jolla CA

ISBN: (纸本)9798331314385

Laplace learning algorithms for graph-based semi-supervised learning have been shown to suffer from degeneracy at low label rates and in imbalanced class regimes. Here, we propose CutSSL: a framework for graph-based semi-supervised learning based on continuous nonconvex quadratic programming, which provably obtains integer solutions. Our framework is naturally motivated by an exact quadratic relaxation of a cardinality-constrained minimum-cut graph partitioning problem. Furthermore, we show our formulation is related to an optimization problem whose approximate solution is the mean-shifted Laplace learning heuristic, thus providing new insight into the performance of this heuristic. We demonstrate that CutSSL significantly surpasses the current state-of-the-art on k-nearest neighbor graphs and large real-world graph benchmarks across a variety of label rates, class imbalance, and label imbalance regimes. Our implementation is available on github https://***/Mishne-Lab/CutSSL.

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Detection of Large Guide Field Electron-Only Reconnection in a Filamentary Current Sheet Immersed in a Large-Scale Magnetopause Reconnection Exhaust

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Physical Review Letters 2025年第11期134卷 115201-115201页

作者： P. S. Pyakurel T. D. Phan M. Øieroset J. F. Drake M. A. Shay A. Mallet J. Stawarz S. Wang M. Oka Space Sciences Laboratory University of California Berkeley California 94720 USA Department of Physics and the Institute for Physical Science and Technology University of Maryland College Park Maryland 20742 USA Department of Physics and Astronomy University of Delaware Newark Delaware 19716 USA Department of Mathematics Physics and Electrical Engineering Northumbria University Newcastle upon Tyne NE1 8ST United Kingdom Institute of Space Physics and Applied Technology Peking University Beijing China

We present the Magnetospheric Multiscale (MMS) mission’s observations of large-scale reconnection with a laminar ion exhaust containing many electron-scale filamentary current sheets, one of which exhibited a super-ion-Alfvénic electron jet flowing opposite to the ion exhaust jet, identified as electron-only reconnection. Despite the close proximity (a few electron inertial lengths) of the four MMS spacecraft, they recorded different electron-only reconnection signatures, including differences in the magnitude and profile of the electron jet, parallel electric fields, and dissipation j·E′≡j·[E+ve×B], indicating extremely short-scale spatial and temporal variability. Furthermore, the leading spacecraft did not detect reconnection signatures, suggesting that MMS may have witnessed the onset of electron-only reconnection. Hall magnetic field perturbations associated with an electron-scale current sheet were detected after the onset. The dissipation j·E′ in the electron-only current sheet was dominated by the component perpendicular to the magnetic field, contrasting with the dominance of the parallel component in previous large guide field reconnection events.

关键词： Magnetopause

An implicit unified gas-kinetic wave-particle method for radiative transport process

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arXiv 2023年

作者： Liu, Chang Li, Weiming Wang, Yanli Song, Peng Xu, Kun Institute of Applied Physics and Computational Mathematics Beijing China HEDPS Center for Applied Physics and Technology College of Engineering Peking University Beijing China Department of Mathematics Hong Kong University of Science and Technology Hong Kong Department of Mechanical and Aerospace Engineering Hong Kong University of Science and Technology Hong Kong Beijing Computational Science Research Center Beijing100193 China

The unified gas-kinetic wave-particle method (UGKWP) has been developed for the multiscale gas, plasma, and multiphase flow transport processes for the past years. In this work, we propose an implicit unified gas-kinetic wave-particle (IUGKWP) method to remove the Courant–Friedrichs–Lewy (CFL) time step constraint. Based on the local integral solution of the radiative transfer equation (RTE), the particle transport processes are categorized into the long-λ streaming process and the short-λ streaming process comparing to a local physical characteristic time tp. In the construction of the IUGKWP method, the long-λ streaming process is tracked by the implicit Monte Carlo (IMC) method;the short-λ streaming process is evolved by solving the implicit moments equations;and the photon distribution is closed by a local integral solution of RTE. In the IUGKWP method, the multiscale flux of radiation energy and the multiscale closure of photon distribution are constructed based on the local integral solution. The IUGKWP method preserves the second-order asymptotic expansion of RTE in the optically thick regime and adapts its computational complexity to the flow regime. The numerical dissipation is well controlled, and the teleportation error is significantly reduced in the optically thick regime. The computational complexity of the IUGKWP method decreases exponentially as the Knudsen number approaches zero, and the computational efficiency is remarkably improved in the optically thick regime. The IUGKWP is formulated on a generalized unstructured mesh, and multidimensional 2D and 3D algorithms are developed. Numerical tests are presented to validate the capability of IUGKWP in capturing the multiscale photon transport process. The algorithm and code will apply in the engineering applications of inertial confinement fusion (ICF). Copyright © 2023, The Authors. All rights reserved.

关键词： Radiative transfer

Evidence for topological origin of large spin-shift current in antiferromagnetic Ti4C3

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arXiv 2025年

作者： Sufyan, Ali Abdullah, Hasan M. Larsson, J. Andreas Tyner, Alexander C. Nordita KTH Royal Institute of Technology Stockholm University Stockholm106 91 Sweden Department of Physics University of Connecticut StorrsCT06269 United States Applied Physics Division of Materials Science Department of Engineering Sciences and Mathematics LuleåUniversity of Technology LuleåSE-97187 Sweden Department of Physics Faculty of Applied Science Taiz University Taiz Yemen Wallenberg Initiative Materials Science for Sustainability LuleåUniversity of Technology LuleåSE-97187 Sweden

The shift current is a non-linear photocurrent generally associated with the underlying quantum geometry. However, a topological origin for the shift photocurrent in non-centrosymmetric systems has recently been proposed. The corresponding topological classification goes beyond the ten-fold paradigm and is associated with the presence of a reverting Thouless pump (RTP). In this work we examine an antiferromagnetic monolayer within the family of MXenes, Ti4C3. This material is centrosymmetric, however, magnetic ordering violates inversion symmetry. We demonstrate evidence of an RTP in each spin-sector which has been perturbed, destroying quantization of the invariant. Nevertheless, a giant spin-resolved shift current persists. We further investigate the mid-gap edge states and classification of the system as a fragile topological insulator to which trivial bands have been coupled. Copyright © 2025, The Authors. All rights reserved.

关键词： Topology

On the Uncrossed Number of Graphs

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arXiv 2024年

作者： Balko, Martin Hliněný, Petr Masařík, Tomáš Orthaber, Joachim Vogtenhuber, Birgit Wagner, Mirko H. Department of Applied Mathematics Faculty of Mathematics and Physics Charles University Czech Republic Faculty of Informatics Masaryk University Brno Czech Republic Institute of Informatics Faculty of Mathematics Informatics and Mechanics University of Warsaw Poland Institute of Software Technology Graz University of Technology Austria Institute of Computer Science Osnabrück University Germany

Visualizing a graph G in the plane nicely, for example, without crossings, is unfortunately not always possible. To address this problem, Masařík and Hliněný [10] recently asked for each edge of G to be drawn without crossings while allowing multiple different drawings of G. More formally, a collection D of drawings of G is uncrossed if, for each edge e of G, there is a drawing in D such that e is uncrossed. The uncrossed number unc(G) of G is then the minimum number of drawings in some uncrossed collection of G. No exact values of the uncrossed numbers have been determined yet, not even for simple graph classes. In this paper, we provide the exact values for uncrossed numbers of complete and complete bipartite graphs, partly confirming and partly refuting a conjecture posed by Hliněný and Masařík [10]. We also present a strong general lower bound on unc(G) in terms of the number of vertices and edges of G. Moreover, we prove NP-hardness of the related problem of determining the edge crossing number of a graph G, which is the smallest number of edges of G taken over all drawings of G that participate in a crossing. This problem was posed as open by Schaefer in his book [18].MSC Codes 68R10 Copyright © 2024, The Authors. All rights reserved.

关键词： Graph theory

Dynamic mode decomposition of nonequilibrium electron-phonon dynamics: accelerating the first-principles real-time Boltzmann equation

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arXiv 2023年

作者： Maliyov, Ivan Yin, Jia Yao, Jia Yang, Chao Bernardi, Marco Department of Applied Physics and Materials Science California Institute of Technology PasadenaCA91125 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Physics California Institute of Technology PasadenaCA91125 United States

Nonequilibrium dynamics governed by electron-phonon (e-ph) interactions plays a key role in electronic devices and spectroscopies and is central to understanding electronic excitations in materials. The real-time Boltzmann transport equation (rt-BTE) with collision processes computed from first principles can describe the coupled dynamics of electrons and atomic vibrations (phonons). Yet, a bottleneck of these simulations is the calculation of e-ph scattering integrals on dense momentum grids at each time step. Here we show a data-driven approach based on dynamic mode decomposition (DMD) that can accelerate the time propagation of the rt-BTE and identify dominant electronic processes. We apply this approach to two case studies, high-field charge transport and ultrafast excited electron relaxation. In both cases, simulating only a short time window of ∼10% of the dynamics suffices to predict the dynamics from initial excitation to steady state using DMD extrapolation. Analysis of the momentum-space modes extracted from DMD sheds light on the microscopic mechanisms governing electron relaxation to steady state or equilibrium. The combination of accuracy and efficiency makes our DMD-based method a valuable tool for investigating ultrafast dynamics in a wide range of materials. Copyright © 2023, The Authors. All rights reserved.

关键词： Dynamic mode decomposition