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Nonlinear Extrapolation Estimates of π

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Acta Mathematicae Applicatae sinica 2024年第1期40卷 91-108页

作者： Wen-qing Xu Sha-sha Wang Da-chuan Xu beijing institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing100124China Department of mathematics and Statistics California State UniversityLong BeachCalifornia90840USA Department of mathematics and Physics Shijiazhuang Tiedao UniversityShijiazhuang050043China

The classical Archimedean approximation of π uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in R~2 and it is well-known that by using linear combinations of these basic estimates,modern extrapolation techniques can greatly speed up the approximation ***,when n vertices are randomly selected on the circle,the semiperimeter and area of the corresponding random inscribed and circumscribing polygons are known to converge to π almost surely as n→∞,and by further applying extrapolation processes,faster convergence rates can also be achieved through similar linear combinations of the semiperimeter and area of these random *** this paper,we further develop nonlinear extrapolation methods for approximating π through certain nonlinear functions of the semiperimeter and area of such *** focus on two types of extrapolation estimates of the forms χ_n=S_n~αA_n~β and Y_n(p)=(αS_n~p+βA_n~p)~(1/p) where α+β=1,p≠0,and Sn and An respectively represents the semiperimeter and area of a random n-gon inscribed in the unit circle in R~2,and Xn may be viewed as the limit of Y_n(p) when p→*** deriving probabilistic asymptotic expansions with carefully controlled error estimates for Xn and Y_n(p),we show that the choice α=4/3,β=-1/3 minimizes the approximation error in both cases,and their distributions are also asymptotically normal.

关键词： Archimedean polygons random polygons approximations ofπ extrapolation processes asymptotic convergence

Deformation and mutual influence of two cylindrical water columns in tandem subjected to shock wave

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Chinese Physics B 2024年第8期33卷 316-327页

作者：洪振宇宋洋王睿马宗强马东军王裴 institute of Applied Physics and Computational mathematics Beijing 100094China Graduate School of China Academy of Engineering Physics Beijing 100088China Center for Applied Physics and Technology Peking UniversityBeijing 100871China

The interaction between shock waves and multiple cylinders,referred to as shock–cylinder interaction(SCI),is an important phenomenon in science and ***,its underlying physical mechanisms remain *** study entailed the numerical simulation of the aerobreakup of two tandem water columns subjected to a high-speed gas flow by using an adaptive mesh refinement(AMR)-based diffusion-interface *** objective was to elucidate the changes in water–column deformation patterns over a wide range of Weber *** analysis was performed to examine the deformation of the water columns in vertical *** reveal distinct deformation patterns between the two columns as the Weber number ***,an extended exponential stretching law model was devised,and its improved capability to predict the deformation patterns was demonstrated.

关键词： shock-cylinder interaction(SCI) Weber number effect aerobreakup multiphase flow

Holder continuous weak solutions of the 2D Boussinesq equation with thermal diffusion

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Science China mathematics 2024年第8期67卷 1777-1806页

作者： Tianwen Luo Tao Tao Liqun Zhang Yau Mathematical Sciences Center Tsinghua UniversityBeijing 100084China School of mathematics Shandong UniversityJinan 250100China institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

We show the existence of Holder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic *** precisely,for any smooth e(t):[0,1]→R+andε∈(0,110),there exist v∈C 110−ε([0,1]×T2)andθ∈C 1,120−εt 2 C 2,1 x 10−ε([0,1]×T2),which satisfy(1.1)in the sense of distribution and e(t)=ˆT2|v(t,x)|2 dx,∀t∈[0,1].

关键词： 2D Boussinesq equation with thermal diffusion Holder continuous periodic weak solutions prescribed kinetic energy

Newtonian limit of Einstein equation with a cosmological constant

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Chinese Physics C 2024年第10期48卷 264-274页

作者： Li-Fang Li Zhoujian Cao Xiaokai He institute of Mechanics Chinese Academy of SciencesBeijing 100190China institute of Applied mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Fundamental Physics and Mathematical Sciences Hangzhou Institute for Advanced StudyUCASHangzhou 310024China School of mathematics and Statistics Hunan First Normal UniversityChangsha 410205China

Traditionally,the cosmological constant has been viewed as dark energy that mimics matter with negative *** that matter with negative energy provides a repulsive force,which fundamentally differs from typical gravitational forces,it has been believed that the cosmological constant effectively contributes a repulsive ***,it is important to note that the concept of gravitational force is valid only within the framework of Newtonian *** this study,we demonstrate that the traditional understanding of the gravitational force contributed by the cosmological constant is not entirely *** approach involves investigating the Newtonian limit of the Einstein equation with a cosmological *** subtleties involved in this analysis are discussed in ***,we find that the effect of the cosmological constant on Newtonian gravity is an attractive force rather than a repulsive one for ordinary *** expected,this corrective force is negligibly ***,our findings may offer a way to distinguish between dark energy and the cosmological constant,as one contributes a repulsive force while the other contributes an attractive force.

关键词： cosmological constant dark matter Einstein equation Newtonian limit dark energy

Probing dark matter particles from evaporating primordial black holes via electron scattering in the CDEX-10 experiment

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Science China(Physics,Mechanics & Astronomy) 2024年第10期67卷 83-91页

作者： Zhenhua Zhang Litao Yang Qian Yue Kejun Kang Yuanjing Li Haipeng An Greeshma C. Jianping Chang Yunhua Chen Jianping Cheng Wenhan Dai Zhi Deng Changhao Fang Xinping Geng Hui Gong Qiuju Guo Tao Guo Xuyuan Guo Li He Shengming He Jinwei Hu Hanxiong Huang Tuchen Huang Lin Jiang S.Karmakar Haubin Li Hanyu Li Jianmin Li Jin Li Qianyun Li Renmingjie Li Xueqian Li Yulan Li Yifan Liang Bin Liao FongKay Lin ShinTed Lin Jiaxuan Liu Shukui Liu Yandong Liu Yu Liu Yuanyuan Liu Hao Ma Yucai Mao Qiyuan Nie Jinhua Ning Hui Pan Ningchun Qi Jie Ren Xichao Ruan Monoj Kumar Singh Tianxi Sun Changjian Tang Yang Tian Guangfu Wang Junzheng Wang Li Wang Qing Wang Yufeng Wang Yunxiang Wang Henry Tsz-King Wong Shiyong Wu Yucheng Wu Haoyang Xing Rui Xu Yin Xu Tao Xue Yulu Yan Nan Yi Chunxu Yu Haijun Yu Jianfeng Yue Ming Zeng Zhi Zeng Bingtao Zhang Fengshou Zhang Lei Zhang Zhenyu Zhang Jizhong Zhao Kangkang Zhao Minggang Zhao Jifang Zhou Zuying Zhou Jingjun Zhu CDEX Collaboration Key Laboratory of Particle and Radiation Imaging(Ministry of Education)and Department of Engineering Physics Tsinghua UniversityBeijing 100084China Department of Physics Tsinghua UniversityBeijing 100084China institute of Physics Academia SinicaTaipei 11529China NUCTECH Company Beijing 100084China YaLong River Hydropower Development Company Chengdu 610051China College of Nuclear Science and Technology Beijing Normal UniversityBeijing 100875China College of Physics Sichuan UniversityChengdu 610065China School of Physics Peking UniversityBeijing 100871China Department of Nuclear Physics China Institute of Atomic EnergyBeijing 102413China Sino-French institute of Nuclear and Technology Sun Yet-sen UniversityZhuhai 519082China School of Physics Nankai UniversityTianjin 300071China Department of Physics Banaras Hindu UniversityVaranasi 221005India Department of Physics Beijing Normal UniversityBeijing 100875China 不详

Dark matter(DM)is a major constituent of the ***,no definite evidence of DM particles(denoted as“χ”)has been found in DM direct detection(DD)experiments to *** is a novel concept of detectingχfrom evaporating primordial black holes(PBHs).We search forχemitted from PBHs by investigating their interaction with target *** examined PBH masses range from 1×10^(15)to 7×10^(16)g under the current limits of PBH abundance *** 205.4 kg·day data obtained from the CDEX-10 experiment conducted in the China Jinping Underground Laboratory,we exclude theχ-electron(χ-e)elastic-scattering cross sectionσ_(χe)~5×10^(-29)cm^(2)forχwith a mass■keV from our *** the higher radiation background but lower energy threshold(160 eV),CDEX-10 fills a part of the gap in the previous ***(m_(χ),σ_(χe))can be determined in the future,DD experiments are expected to impose strong constraints on fPBHfor large MPBHs.

关键词： CDEX primordial black hole light dark matter particle dark matter-electron scattering high purity germanium detector

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Scaling laws governing the elastic properties of 3D graphenes

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Science China(Technological Sciences) 2024年第6期67卷 1748-1756页

作者： LI Ming LU Guo YU HaoDong LI MengLei ZHENG FaWei Centre for Quantum Physics Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement(MOE)School of PhysicsBeijing Institute of TechnologyBeijing100081China beijing Key Lab of Nanophotonics&Ultrafine Optoelectronic Systems School of PhysicsBeijing Institute of TechnologyBeijing100081China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing100088China Department of Physics Capital Normal UniversityBeijing100048China

In this study,we comprehensively investigated the scaling law for elastic properties of three-dimensional honeycomb-like graphenes(3D graphenes)using hybrid neural network potential-based molecular dynamics simulations and theoretical *** elastic constants were obtained as functions of honeycomb hole size,denoted by the graphene wall length *** five independent elastic constants in the large-L limit are proportional to L^(-1).The associated coefficients are combinations of elastic constants of two-dimensional ***-order terms including L^(-2)and L^(-3)emerge for finite L *** have three origins,the distorted areas close to the joint lines of 3D graphenes,the variation in solid angles between graphene plates,and the bending distortion of graphene ***,the chirality becomes essential with decreasing L because the joint line structures are different between the armchair and zigzag-type 3D *** findings provide insights into the elastic properties of graphene-based superstructures and can be used for further studies on graphene-based materials.

关键词： scaling law neural network elastic properties 3D graphene

UNCONDITIONAL CONVERGENCE AND ERROR ESTIMATES OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MICROPOLAR NAVIER-STOKES EQUATIONS

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Journal of Computational mathematics 2024年第1期42卷 71-110页

作者： Shipeng Mao Jiaao Sun Wendong Xue NCMIS LSECInstitute of Computational Mathematics and Scientific/Enginnering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element *** first establish some regularity results for the solution of MNSE,which seem to be not available in the ***,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete ***,certain regularity results for the time discrete solution are establishes *** on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of ***,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.

关键词： Micropolar fluids Regularity estimates Euler semi-implicit scheme Mixed finite element methods Unconditional convergence

Ionization Potential Depression Model for Warm/Hot and Dense Plasmas

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Chinese Physics Letters 2024年第8期41卷 45-57页

作者： Chensheng Wu Fuyang Zhou Jun Yan Xiang Gao Yong Wu Chunhua Zeng Jianguo Wang institute of Applied Physics and Computational mathematics Beijing 100088China Faculty of Science Kunming University of Science and TechnologyKunming 650500China

For warm/hot and dense plasmas(WDPs),ionization potential depression(IPD)plays a crucial role in determining its ionization balance and understanding the resultant microscopic plasma properties.A sophisticated and unified IPD model is necessary to resolve those existing discrepancies between theoretical and experimental ***,the applicability of those widely used IPD models nowadays is limited,especially for the nonlocal thermodynamic equilibrium(non-LTE)dense plasma produced by short-pulse *** this work,we propose an IPD model that considers inelastic atomic processes,in which three-body recombination and collision ionization processes are found to play a crucial role in determining the electron distribution and IPD for a *** IPD model is validated by reproducing latest experimental results of Al plasmas with a wide-range condition of 70 eV–700 eV temperature and 0.2–3 times solid density,as well as a typical non-LTE system of hollow Al *** is demonstrated that the present IPD model has a significant temperature dependence due to the consideration of the inelastic collision *** a lower computational cost and wider application range of plasma conditions,the proposed model is expected to provide a promising tool to study the ionization balance and the atomic processes,as well as the related radiation and particle transports properties of the WDP.

关键词： properties. collision determining

C^(α)regularity of weak solutions of non-homogeneous ultraparabolic equations with drift terms

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Science China mathematics 2024年第1期67卷 23-44页

作者： Wendong Wang Liqun Zhang School of Mathematical Sciences Dalian University of TechnologyDalian 116024China institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

We consider a class of non-homogeneous ultraparabolic differential equations with singular drift terms arising from some physical models,and prove that weak solutions are H?lder continuous,which are sharp in some sense and also generalize the well-known De Giorgi-Nash-Moser theory to degenerate parabolic equations satisfying the H?rmander hypoellipticity *** new ingredients are manifested in two aspects:on the one hand,for lower-order terms,we exploit a new Sobolev inequality suitable for the Moser iteration by improving the result of Pascucci and Polidoro(2004);on the other hand,we explore the G-function from an early idea of Kruzhkov(1964)and an approximate weak Poincaréinequality for non-negative weak sub-solutions to prove the H?lder regularity.

关键词： ultraparabolic equations Moser iteration Poincare inequality C^a regularity