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Science China mathematics 2024年第2期67卷 237-252页

作者： Hong-Lin Liao Tao Tang Tao Zhou School of mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China SUSTech international center for mathematics Shenzhen 518055China NCMIS&LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The positive definiteness of real quadratic forms with convolution structures plays an important rolein stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysistool to handle discrete convolution kernels resulting from variable-step approximations for convolution operators.More precisely, for a class of discrete convolution kernels relevant to variable-step L1-type time discretizations, weshow that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Ourproof is based on an elementary constructing strategy by using the properties of discrete orthogonal convolutionkernels and discrete complementary convolution kernels. To our knowledge, this is the first general result onsimple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using theunified theory, we obtain the stability for some simple nonuniform time-stepping schemes straightforwardly.

关键词： discrete convolution kernels positive definiteness variable time-stepping orthogonal convolution kernels complementary convolution kernels

Revealing excited states of rotational Bose-Einstein condensates

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The Innovation 2024年第1期5卷 41-48页

作者： Jianyuan Yin Zhen Huang Yongyong Cai Qiang Du Lei Zhang School of Mathematical Sciences Laboratory of Mathematics and Applied MathematicsPeking UniversityBeijing 100871China Department of mathematics National University of SingaporeSingapore 119076Singapore Department of mathematics University of CaliforniaBerkeleyBerkeleyCA 94720USA School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China Department of Applied Physics and Applied mathematics and Data Science Institute Columbia UniversityNew YorkNY 10027USA Beijing international center for Mathematical Research Center for Quantitative BiologyCenter for Machine Learning ResearchPeking UniversityBeijing 100871China

Rotational Bose-Einstein condensates can exhibit quantized vortices as topological excitations.In this study,the ground and excited states of the rotational Bose-Einstein condensates are systematically studied by calculating the stationary points of the Gross-Pitaevskii energy functional.Various excited states and their connections at different rotational frequencies are revealed in solution landscapes constructed with the constrained high-index saddle dynamics method.Four excitation mechanisms are identified:vortex addition,rearrangement,merging,and splitting.We demonstrate changes in the ground state with increasing rotational frequencies and decipher the evolution of the stability of ground states.

关键词： method rotational excited

Symmetry transformation of nonlinear optical current of tilted Weyl nodes and application to ferromagnetic MnBi_(2)Te_(4)

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Chinese Physics B 2024年第4期33卷 160-171页

作者：卢倬成冯济 international center for Quantum Materials School of PhysicsPeking UniversityBeijing 100871China

A Weyl node is characterized by its chirality and tilt.We develop a theory of how nth-order nonlinear optical conductivity behaves under transformations of anisotropic tensor and tilt, which clarifies how chirality-dependent and-independent parts of optical conductivity transform under the reversal of tilt and chirality.Built on this theory, we propose ferromagnetic Mn Bi2Te4as a magnetoelectrically regulated, terahertz optical device, by magnetoelectrically switching the chiralitydependent and-independent DC photocurrents.These results are useful for creating nonlinear optical devices based on the topological Weyl semimetals.

关键词： nonlinear optical response topological Weyl semimetals chiral anomaly

AWells-Riley/based COVID-19 infectiousrisk assessment model combining both short rangeandroom scale effects

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Building Simulation 2024年第1期17卷 93-111页

作者： Yinshuai Feng Yifan Fan Xiaoyu Luo Jian Ge College of Civil Engineering and Architecture Zhejiang UniversityHangzhouChina center for Balance Architecture Zhejiang UniversityHangzhouChina international Research center for Green Building and Low-Carbon City International CampusZhejiang UniversityHainingChina

There is growing evidence of the high transmission potential of COVID-19 through virus-laden aerosols.Because aerosols are inhaled in various concentrations,an overall assessment of transmission risks at different indoor scales is crucial.However,a comprehensive risk assessment method that evaluates the direct link between short-range and room-scale zones is stl lacking.In this paper,a risk assessment model combining both short-range and room-scale effects is developed to obtain effective reproduction number in confined indoor environments,called Turbulent Jet Wells Riley(TJWR)model.Combined with the viral load data and aerosol generation data of different human respiratory activities,the Monte Carlo simulation method is applied to calculate the quanta emission rate,which further provides the input parameters of the TJWR model.Three known outbreaks(Hangzhou banquet hall X,Guangzhou restaurant Y,and Hong Kong restaurant Z,China)are chosen to validate the TJWR model.Results show that the TJWR model is more efficient than the original Wells-Riley model.The average relative error of the TJWR model ranges between 9%and 44%,while for the Wells-Riley model,it ranges between 57%and 78%.The TJWR model also proves that infection risk assessments using the well-mixed assumption can systematically underestimate the transmission risk for those close to the source.Additionally,there is a significant positive linear correlation between the total number of exposed individuals at the short-range and the effective reproduction number.This newly developed TJWR model has great potential for rapid and real-time overall airborne transmission risk assessment in buildings and cities.

关键词： COVID-19 airborne transmission infection risk Wells-Riley model Monte Carlo simulation

Magnetism and Superconductivity in the t–J Model of La_(3)Ni_(2)O_7 Under Multiband Gutzwiller Approximation

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Chinese Physics Letters 2024年第5期41卷 97-106页

作者：薛洁然王垡 international center for Quantum Materials School of PhysicsPeking UniversityBeijing 100871China Collaborative Innovation center of Quantum Matter Beijing 100871China

The recent discovery of possible high temperature superconductivity in single crystals of La_(3)Ni_(2)O_(7) under pressure renews the interest in research on nickelates.The density functional theory calculations reveal that both d_(z^(2)) and d_(x^(2)-y^(2)) orbitals are active,which suggests a minimal two-orbital model to capture the low-energy physics of this system.In this work,we study a bilayer two-orbital t–J model within multiband Gutzwiller approximation,and discuss the magnetism as well as the superconductivity over a wide range of the hole doping.Owing to the inter-orbital super-exchange process between d_(z^(2)) and d_(x^(2)-y^(2)) orbitals,the induced ferromagnetic coupling within layers competes with the conventional antiferromagnetic coupling,and leads to complicated hole doping dependence for the magnetic properties in the system.With increasing hole doping,the system transfers to A-type antiferromagnetic state from the starting G-type antiferromagnetic(G-AFM)state.We also find the inter-layer superconducting pairing of d_(x^(2)-y^(2)) orbitals dominates due to the large hopping parameter ofd_(z^(2)) along the vertical inter-layer bonds and significant Hund’s coupling between d_(z^(2)) and d_(x^(2)-y^(2)) orbitals.Meanwhile,the G-AFM state and superconductivity state can coexist in the low hole doping regime.To take account of the pressure,we also analyze the impacts of inter-layer hopping amplitude on the system properties.

关键词： properties doping orbital

Deformation of Rigid Conjugate Self-dual Galois Representations

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1599-1644页

作者： Yi Feng LIU Yi Chao TIAN Liang XIAO Wei ZHANG Xin Wen ZHU Institute for Advanced Study in mathematics Zhejiang UniversityHangzhou 310058P.R.China Morningside center of Mathemnatics AMSSChinese Academy of SciencesBeijing 100190P.R.China New Cornerstone Lab Beijing International Center for Mathematical ResearchPeking Ui Beijing 100871P.R.China Department of mathematics Massachusetts Institute of TechnologyCambridge MA 02139United States Department of mathematics Stanford UniversityStanfordCA 94305United States

In this article,we study deformations of conjugate self-dual Galois representations.The study is twofold.First,we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field,satisfying a certain property called rigid.Second,we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve,as well as to a regular algebraic conjugate self-dual cuspidal representation.

关键词： Galois deformation rigid conjugate self-dual Galois representations

Photo-responsive functional materials based on light-driven molecular motors

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Light(Science & Applications) 2024年第3期13卷 407-420页

作者： Yanping Deng Guiying Long Yang Zhang Wei Zhao Guofu Zhou Ben L.Feringa Jiawen Chen SCNU-UG international Joint Laboratory of Molecular Science and Displays National Center for International Research on Green OptoelectronicsSouth China Normal UniversityGuangzhou 510006China Stratingh Institute for Chemistry University of GroningenNijenborgh 49747AG GroningenThe Netherlands

In the past two decades,the research and development of light-triggered molecular machines have mainly focused on developing molecular devices at the nanoscale.A key scientific issue in the field is how to amplify the controlled motion of molecules at the nanoscale along multiple length scales,such as the mesoscopic or the macroscopic scale,or in a more practical perspective,how to convert molecular motion into changes of properties of a macroscopic material.Light-driven molecular motors are able to perform repetitive unidirectional rotation upon irradiation,which offers unique opportunities for responsive macroscopic systems.With several reviews that focus on the design,synthesis and operation of the motors at the nanoscale,photo-responsive macroscopic materials based on light-driven molecular motors have not been comprehensively summarized.In the present review,we first discuss the strategy of confining absolute molecular rotation into relative rotation by grafting motors on surfaces.Secondly,examples of self-assemble motors in supramolecular polymers with high internal order are illustrated.Moreover,we will focus on building of motors in a covalently linked system such as polymeric gels and polymeric liquid crystals to generate complex responsive functions.Finally,a perspective toward future developments and opportunities is given.This review helps us getting a more and more clear picture and understanding on how complex movement can be programmed in light-responsive systems and how man-made adaptive materials can be invented,which can serve as an important guideline for further design of complex and advanced responsive materials.

关键词： functions materials material

The risk of mpox importation and subsequent outbreak potential in Chinese mainland: a retrospective statistical modelling study

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Infectious Diseases of Poverty 2024年第1期13卷 63-73页

作者： Xiaowei Deng Yuyang Tian Junyi Zoul Juan Yang Kaiyuan Sun Hongjie Yu School of Public Health Key Laboratory of Public Health SafetyMinistry of EducationFudan UniversityShanghai 200032China Division of international Epidemiology and Population Studies Fogarty International CenterNational Institutes of HealthBethesdaMDUSA

Background The 2022-2023 mpox(monkeypox)outbreak has spread rapidly across multiple countries in the non-endemic region,mainly among men who have sex with men(MSM).In this study,we aimed to evaluate mpox's importation risk,border screening effectiveness and the risk of local outbreak in Chinese mainland.Methods We estimated the risk of mpox importation in Chinese mainland from April 14 to September 11,2022 using the number of reported mpox cases during this multi-country outbreak from Global.health and the international air-travel data from Official Aviation Guide.We constructed a probabilistic model to simulate the effectiveness of a border screening scenario during the mpox outbreak and a hypothetical scenario with less stringent quarantine requirement.And we further evaluated the mpox outbreak potential given that undetected mpox infections were introduced into men who have sex with men,considering different transmissibility,population immunity and population activity.Results We found that the reduced international air-travel volume and stringent border entry policy decreased about 94% and 69% mpox importations respectively.Under the quarantine policy,15-19% of imported infections would remain undetected.Once a case of mpox is introduced into active MSM population with almost no population immunity,the risk of triggering local transmission is estimated at 42%,and would rise to>95% with over six cases.Conclusions Our study demonstrates that the reduced international air-travel volume and stringent border entry policy during the COvID-19 pandemic reduced mpox importations prominently.However,the risk could be sub-stantially higher with the recovery of air-travel volume to pre-pandemic level.Mpox could emerge as a public health threat for Chinese mainland given its large MSM community.

关键词： Mpox(Monkeypox) Importation risk international air travel Statistical modelling Men who have sex with men

The top-order energy of quasilinear wave equations in two space dimensions is uniformly bounded

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Fundamental Research 2024年第2期4卷 270-283页

作者： Shijie Dong Philippe G.LeFloch Zhen Lei Southern University of Science and Technology SUSTech International Center for Mathematicsand Department of MathematicsShenzhen 518055China Fudan University School of Mathematical Sciences220 Handan RoadShanghai 200433China Laboratoire Jacques-Louis Lions and Centre National de la Recherche Scientifique Sorbonne Université4 Place JussieuParis 75252France Shanghai center for Mathematical Sciences Shanghai 200433China

Alinhac solved a long-standing open problem in 2001 and established that quasilinear wave equations in two space dimensions with quadratic null nonlinearities admit global-in-time solutions,provided that the initial data are compactly supported and sufficiently small in Sobolev norm.In this work,Alinhac obtained an upper bound with polynomial growth in time for the top-order energy of the solutions.A natural question then arises whether the time-growth is a true phenomenon,despite the possible conservation of basic energy.In the present paper,we establish that the top-order energy of the solutions in Alinhac theorem remains globally bounded in time.

关键词： Quasilinear wave equation Global-in-time solution Uniform energy bounds Quadratic null nonlinearity Hyperboloidal foliation method Vector field method

Optimizing high-coordination shell of Co-based single-atom catalysts for efficient ORR and zinc-air batteries

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Journal of Energy Chemistry 2024年第8期95卷 306-314页

作者： Yugang Qi Qing Liang Kexin Song Xinyan Zhou Meiqi Liu Wenwen Li Fuxi Liu Zhou Jiang Xu Zou Zhongjun Chen Wei Zhang Weitao Zheng Key Laboratory of Automobile Materials MOE School of Materials Science & Engineering Electron Microscopy Center and International Center of Future Science Jilin Provincial International Cooperation Key Laboratory of High-Efficiency Clean Energy Materials Jilin University Institute of High Energy Physics Chinese Academy of Sciences

Atom-level modulation of the coordination environment for single-atom catalysts(SACs) is considered as an effective strategy for elevating the catalytic performance. For the MNxsite, breaking the symmetrical geometry and charge distribution by introducing relatively weak electronegative atoms into the first/second shell is an efficient way, but it remains challenging for elucidating the underlying mechanism of interaction. Herein, a practical strategy was reported to rationally design single cobalt atoms coordinated with both phosphorus and nitrogen atoms in a hierarchically porous carbon derived from metal-organic frameworks. X-ray absorption spectrum reveals that atomically dispersed Co sites are coordinated with four N atoms in the first shell and varying numbers of P atoms in the second shell(denoted as Co-N/P-C).The prepared catalyst exhibits excellent oxygen reduction reaction(ORR) activity as well as zinc-air battery performance. The introduction of P atoms in the Co-SACs weakens the interaction between Co and N,significantly promoting the adsorption process of *OOH, resulting in the acceleration of reaction kinetics and reduction of thermodynamic barrier, responsible for the increased intrinsic activity. Our discovery provides insights into an ultimate design of single-atom catalysts with adjustable electrocatalytic activities for efficient electrochemical energy conversion.

关键词： Electrocatalytic Oxygen reduction reaction Shell coordination optimization Single atom catalyst