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38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Zhu, Richard L. Oster, Mathias Khoo, Yuehaw Department of Computational and Applied Mathematics University of Chicago ChicagoIL60637 United States Institute of Geometry and Practical Mathematics RWTH Aachen Aachen Germany Department of Statistics University of Chicago ChicagoIL60637 United States

Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and the physical sciences. In various settings, the polynomials depend on external parameters that may be random. We discuss a stochastic sum-of-squares (S-SOS) algorithm based on the sum-of-squares hierarchy that constructs a series of semidefinite programs to jointly find strict lower bounds on the global minimum and extract candidates for parameterized global minimizers. We prove quantitative convergence of the hierarchy as the degree increases and use it to solve unconstrained and constrained polynomial optimization problems parameterized by random variables. By employing n-body priors from condensed matter physics to induce sparsity, we can use S-SOS to produce solutions and uncertainty intervals for sensor network localization problems containing up to 40 variables and semidefinite matrix sizes surpassing 800 × 800. © 2024 Neural information processing systems foundation. All rights reserved.

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Connectivity, Traceability and Hamiltonicity

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Matematica 2022年第2期1卷 431-441页

作者： Mafuta, P. Mazorodze, J.P. Munyira, S. Mushanyu, J. Department of Mathematics and Applied Mathematics IB74 University of the Free State Bloemfontein South Africa Department of Mathematics and Computational Sciences University of Zimbabwe Harare Zimbabwe

Let G be a simple, connected, triangle-free graph with minimum degree δ, order n and leaf number L(G). If G has a cut-vertex, we prove that L(G)≥4δ-4 and n≥4δ-1. Both lower bounds are sharp. The lower bound on the leaf number strengthens a result by Mukwembi for triangle-free graphs. As corollaries, we deduce sufficient conditions for connectivity, traceability and Hamiltonicity in triangle-free graphs. As an easy extension of a result by Goodman and Hedetiniemi, we show that a simple, connected, claw-free, paw-free graph G is Hamiltonian if and only if G is not a path. We consider only simple graphs, that is, graphs with neither loops nor multiple edges. © The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2022.

关键词： 05C38 05C40 05C45 Connectivity Cycles Leaf number Minimum degree Order Paths

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Theoretical Prediction of Superconductivity in Boron Kagome Monolayer:MB3(M=Be,Ca,Sr)and the Hydrogenated CaB3

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Chinese Physics Letters 2023年第1期40卷 53-59页

作者：杨柳李牙平刘浩东焦娜倪美燕路洪艳张平 C.S.Ting School of Physics and Physical Engineering Qufu Normal UniversityQufu 273165China Institute of Applied Physics and Computational Mathematics Beijing 100088China Texas Center for Superconductivity and Department of Physics University of HoustonHoustonTexas 77204USA

Using first-principles calculations, we predict a new type of two-dimensional(2D) boride MB3(M = Be,Ca, Sr), constituted by boron kagome monolayer and the metal atoms adsorbed above the center of the boron hexagons. The band structures show that the three MB3compounds are metallic, thus the possible phononmediated superconductivity is explored. Based on the Eliashberg equation, for BeB3, CaB3, and SrB3, the calculated electron–phonon coupling constants λ are 0.46, 1.09, and 1.33, and the corresponding superconducting transition temperatures Tc are 3.2, 22.4, and 20.9 K, respectively. To explore superconductivity with higher transition temperature, hydrogenation and charge doping are further considered. The hydrogenated CaB3, i.e.,HCaB3, is stable, with the enhanced λ of 1.39 and a higher Tc of 39.3 K. Moreover, with further hole doping at the concentration of 5.8 × 1011hole/cm2, the Tc of HCaB3can be further increased to 44.2 K, exceeding the Mc Millan limit. The predicted MB3and HCaB3provide new platforms for investigating 2D superconductivity in boron kagome lattice since superconductivity based on monolayer boron kagome lattice has not been studied before.

关键词： boron doping superconductivity

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computational-Analysis of the Non-Isothermal Dynamics of the Gravity-Driven Flow of Viscoelastic-Fluid-Based Nanofluids Down an Inclined Plane

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Fluid Dynamics & Materials Processing 2023年第3期19卷 767-781页

作者： Idrees Khan Tiri Chinyoka Andrew Gill Centre for Research in Computational&Applied Mechanics University of Cape TownRondebosch7701South Africa Department of Mathematics and Applied Mathematics University of Cape TownRondebosch7701South Africa Centre for High Performance and Computing Council for Scientific and Industrial ResearchRosebankCape Town7700South Africa

The paper explores the gravity-driven flow of the thin film of a viscoelastic-fluid-based nanofluids(VFBN)along an inclined plane under non-isothermal conditions and subjected to convective cooling at the *** Newton’s law of cooling is used to model the convective heat-exchange with the ambient at the *** Giesekus viscoelastic constitutive model,with appropriate modifications to account for non-isothermal effects,is employed to describe the polymeric *** unsteady and coupled non-linear partial differential equations(PDEs)describing the model problem are obtained and solved via efficient semi-implicit numerical schemes based on finite difference methods(FDM)implemented in *** response of the VFBN velocity,temperature,thermal-conductivity and polymeric-stresses to variations in the volume-fraction of embedded nanoparticles is *** is shown that these quantities all increase as the nanoparticle volume-fraction becomes higher.

关键词： Semi-implicit numerical scheme finite difference methods viscoelastic-fluid-based nanofluid(VFBN) nonisothermal viscoelastic flow giesekus constitutive model nanofluid thermal-conductivity gravity-driven flow

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Ion-focused propagation of a relativistic electron beam in the self-generated plasma in atmosphere

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Chinese Physics B 2022年第6期31卷 334-341页

作者： Jian-Hong Hao Bi-Xi Xue Qiang Zhao Fang Zhang Jie-Qing Fan Zhi-Wei Dong School of Electrical and Electronic Engineering Department North China Electric Power UniversityBeijing 102206China Institute of Applied Physics and Computational Mathematics Beijing 100094 China

It is known that ion-focused regime(IFR)can effectively suppress expansion of a relativistic electron beam(REB).Using the particle-in-cell Monte Carlo collision(PIC-MCC)method,we numerically investigate the propagation of an REB in neutral *** results demonstrate that the beam body is charge neutralization and a stable IFR can be *** a result,the beam transverse dimensions and longitudinal velocities keep close to the initial *** also calculate the charge and current neutralization factors of the *** with envelope equations,we obtain the variations of beam envelopes,which agree well with the PIC ***,both the energy loss and instabilities of the REB may lead to a low transport efficiency during long-range *** is proved that decreasing the initial pulse length of the REB can avoid the influence of electron *** parts of REB pulses to build a long-distance IFR in advance can improve the beam quality of subsequent ***,a long-distance IFR may contribute to the implementation of long-range propagation of the REB in space environment.

关键词： ion-focused regime(IFR) charge neutralization electron avalanche relativistic electron beam(REB) particle-in-cell Monte Carlo collision(PIC-MCC)

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Two-electron interference in two-photon attosecond double ionization of neon

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Physical Review A 2024年第1期110卷 013106-013106页

作者： Siddhartha Chattopadhyay Carlos Marante Barry I. Schneider C. William McCurdy Luca Argenti Department of Physics Applied and Computational Mathematics Division Department of Chemistry Chemical Sciences Division CREOL

The pump-probe experiments enabled by x-ray free-electron lasers (XFEL) will allow us to directly observe correlated electronic motion with attosecond time resolution by detecting photoelectron pairs in coincidence. In helium, the transition between the nonsequential and sequential regime in two-photon double ionization (TPDI) is well explained by a virtual-sequential model. Much less is known, however, about the TPDI process in more complex atoms. Recently, we extended the virtual-sequential model to arbitrary light pulses [Chattopadhyay et al. Phys. Rev. A 108, 013114 (2023)]. This extension employs multichannel scattering states for the single ionization of both the neutral and the ionized target, which we initially applied to helium. In the present study, we show that our extended virtual-sequential model reproduces the qualitative features of the angularly integrated observables with available experimental results for neon, a considerably more complex target. We observe an intriguing feature of inverted two-particle interference in the joint-energy distribution of Ne compared to He. This phenomenon, attributable to the presence of a final doubly ionized state with triplet symmetry coupled to the two photoelectrons, should be observable with current experimental technologies.

关键词： Electronic excitation & ionization Single- and few-photon ionization & excitation Ultrafast phenomena Atoms First-principles calculations Perturbative methods Photoionization X-ray photoelectron spectroscopy

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Spectroscopy and molecule opacity investigation on excited states of SiS

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Chinese Physics B 2024年第5期33卷 381-387页

作者：李瑞吕浩男桑纪群刘晓华梁桂颖吴勇 College of Teacher Education Qiqihar UniversityQiqihar 161006China National Key Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China Department of Physics College of ScienceQiqihar UniversityQiqihar 161006China School of Data Science and Artificial Intelligence Jilin Engineering Normal UniversityChangchun 130052China HEDPS Center for Applied Physics and TechnologyPeking UniversityBeijing 100084China

The SiS molecule,which plays a significant role in space,has attracted a great deal of attention for many *** to complex interactions among its low-lying electronic states,precise information regarding the molecular structure of SiS is *** obtain accurate information about the structure of its excited states,the high-precision multireference configuration interaction(MRCI)method has been *** method is used to calculate the potential energy curves(PECs)of the 18Λ–S states corresponding to the lowest dissociation limit of *** core–valence correlation effect,Davidson’s correction and the scalar relativistic effect are also included to guarantee the precision of the MRCI *** on the calculated PECs,the spectroscopic constants of quasi-bound and bound electronic states are calculated and they are in accordance with previous experimental *** transition dipole moments(TDMs)and dipole moments(DMs)are determined by the MRCI *** addition,the abrupt variations of the DMs for the 1^(5)Σ^(+)and 2^(5)Σ^(+)states at the avoided crossing point are attributed to the variation of the electronic *** opacity of SiS at a pressure of 100 atms is presented across a series of *** increasing temperature,the expanding population of excited states blurs the band boundaries.

关键词： SiS opacity excited state spectroscopic constant configuration interaction

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A Certain Subclass of Analytic Functions Related to Calculus and Their Second Hankel Determinant 8th

A Certain Subclass of Analytic Functions Related to Calcul...

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8th International Arab Conference on mathematics and Computations, IACMC 2023

作者： Alsoboh, Abdullah Amourah, Ala Awad, Feras Alahmade, Ayman Gharib, Gharib Department of Mathematics Faculty of Science Philadelphia University Amman19392 Jordan Mathematics Education Program Faculty of Education and Arts Sohar University Sohar3111 Oman Applied Science Research Center Applied Science Private University Amman Jordan Department of Mathematics Faculty of Science Taibah University Medina Saudi Arabia Mathematics Department Al-Zarqa University Zarqa Jordan

ISBN: (纸本)9789819748754

In this paper, we introduce a new subclass of analytic functions defined on the symmetry domain . The subclass is characterized by a derivative operator associated with quantum calculus. We obtain estimations for the Fekete-Szegö functional problems and for the absolute values of the second and third Taylor-Maclaurin coefficients of functions belonging to this new subclass. Additionally, we derive exact upper bounds for the second Hankel functional. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.

关键词： Differentiation (calculus)

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Ordered and disordered stealthy hyperuniform point patterns across spatial dimensions

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Physical Review Research 2024年第3期6卷 033260页

作者： Peter K. Morse Paul J. Steinhardt Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute of Materials Princeton Center for Theoretical Science Program in Applied and Computational Mathematics

In previous work [Phys. Rev. X 5, 021020 (2015)] it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier space in the sense that the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. While this earlier work focused on spatial dimensions d=1–4, here we extend the analysis to higher dimensions in order to make connections to high-dimensional sphere packings and the mean-field theory of glasses. We exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice in contrast to real-space hard spheres, whose densest configuration is conjectured to be disordered. In passing, we give a concise form for the position of the first Bragg peak. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as a function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions d=2–8, which have only recently been made possible due to a highly parallelized algorithm.

关键词： Classical statistical mechanics Disordered systems

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ZERO KINEMATIC VISCOSITY-MAGNETIC DIFFUSION LIMIT OF THE INCOMPRESSIBLE VISCOUS MAGNETOHYDRODYNAMIC EQUATIONS WITH NAVIER BOUNDARY CONDITIONS

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Acta Mathematica Scientia 2021年第5期41卷 1503-1536页

作者： Fucai LI Zhipeng ZHANG Department of Mathematics Nanjing UniversityNanjing 210093China Institute of Applied Physics and Computational Mathematics Beijing 100088China

We investigate the uniform regularity and zero kinematic viscosity-magnetic diffusion limit for the incompressible viscous magnetohydrodynamic equations with the Navier boundary conditions on the velocity and perfectly conducting conditions on the magnetic field in a smooth bounded domain Ω⊂R^(3).It is shown that there exists a unique strong solution to the incompressible viscous magnetohydrodynamic equations in a finite time interval which is independent of the viscosity coefficient and the magnetic diffusivity *** solution is uniformly bounded in a conormal Sobolev space and W^(1,∞)(Ω)which allows us to take the zero kinematic viscosity-magnetic diffusion ***,we also get the rates of convergence in L^(∞)(0,T;L^(2)),L^(∞)(0,T;W^(1,p))(2≤p<∞),and L^(∞)((0,T)×Ω)for some T>0.

关键词： incompressible viscous MHD equations ideal incompressible MHD equations Navier boundary conditions zero kinematic viscosity-magnetic diffusion limit

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