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Novel Electronic Orders on the Kagome Lattice Near Van Hove Singularities 认领 引用
1
作者 Da Wang Wan-Sheng Wang +3 位作者 Meng Yao Yi-Qun Liu Jia-Xin Yin Qiang-Hua Wang 《Chinese Physics Letters》 SCIE EI CAS CSCD 2026年第6期82-86,共5页
The kagome lattice is unique in that Dirac bands,van Hove singularities,and flat band are all present in the band structure.In particular,the Bloch states near the upper van Hove points are sublattice polarized,while ... The kagome lattice is unique in that Dirac bands,van Hove singularities,and flat band are all present in the band structure.In particular,the Bloch states near the upper van Hove points are sublattice polarized,while they are pair-wise mixed in sublattice contents near the lower van Hove points.These features,combined with correlation effects,may lead to novel electronic orders.We briefly review our theo-retical investigations on the kagome lattice near the van Hove fillings by the singular-mode functional renormalization group,quantum Monte Carlo,and effective mean field theory.We establish rich phases of the model under extended Hubbard interactions or Su-Schrief-fer-Heeger-like electron-phonon coupling.Among these phases,three types of 2×2 orders are of particular interest.Near the upper van Hove filling,we predicted the 2×2 charge bond order in 2013,which is highly relevant in AV3Sb5(A=K,Rb,Cs)kagome materials.In the superconducting channel,we constructed a self-consistent theory for the 2×2 pair density wave,which is made possible by the sublat-tice polarization and attractive pairing interaction on the nearest neighbor bonds,predicting anisotropic energy gap in momentum space and quantized thermal Hall conductance in the chiral case of the pair density wave,which are consistent with recent photoemission and transport experiments.Near the lower van Hove filling,we further predicted a topological 2×2 non-collinear antiferromagnetic state with spins on neighboring sites orthogonal as Cartesian axes in three dimensions,which is a Chern insulator supporting quantized thermal Hall conductance. 展开更多
关键词 bloch states van hove kagome lattice correlation effectsmay Van Hove singularities band structurein electronic orderswe flat band
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Singular closed orbits and chaotic behavior of a double-winged quasi-zero-stiffness system 认领 引用
2
作者 Xinyi HUANG S.LENCI Qingjie CAO 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2026年第3期509-534,I0005-I0006,共26页
The complex chaotic behavior of a quasi-zero-stiffness(QZS)double-winged system with symmetric impact boundaries is investigated with Melnikov functions and numerical simulations.The analysis reveals the coexistence o... The complex chaotic behavior of a quasi-zero-stiffness(QZS)double-winged system with symmetric impact boundaries is investigated with Melnikov functions and numerical simulations.The analysis reveals the coexistence of multiple attractors.As a key mass parameter varies,the mechanism underlying degenerate singular closed orbits is elucidated,based upon which five distinct types of singular closed orbits are discovered,exhibiting both smooth and discontinuous(SD)characteristics.The chaotic threshold of each singular orbit is obtained by Melnikov functions and verified by numerical simulations.The numerical results further demonstrate the coexistence of SD motions.For zero damping systems,the Kolmogorov-Arnold-Moser(KAM)structures are exhibited to present the complex quasi-periodic and resonant behavior coexisting with chaotic and periodic motions.These findings advance the understanding of chaotic dynamics in nonsmooth multi-well impact systems. 展开更多
关键词 chaotic behavior Melnikov function singular closed orbit Kolmogorov-Arnold-Moser(KAM)structure resonance
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NONLINEAR SINGULAR EIGENVALUE PROBLEMS 认领 引用
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作者 Nikolaos S.PAPAGEORGIOU Zijia PENG 《Acta Mathematica Scientia》 SCIE CSCD 2026年第3期1484-1499,共16页
We study a nonlinear eigenvalue problem driven by a general nonhomogeneous differential operator,involving a reaction term that is singular at x=0 and becomes superlinear as x→+∞.Unlike the usual case in the literat... We study a nonlinear eigenvalue problem driven by a general nonhomogeneous differential operator,involving a reaction term that is singular at x=0 and becomes superlinear as x→+∞.Unlike the usual case in the literature,the singular term and the perturbation are not decoupled.By using variational methods in combination with truncation and comparison techniques,we establish a global existence and multiplicity theorem with respect to the parameter(eigenvalue)λ>0.Additionally,we demonstrate the existence of a minimal positive solution uλ*and investigate the continuity and monotonicity properties of the mapλ→uλ*. 展开更多
关键词 singular and superlinear reaction nonlinear regularity nonlinear maximum principle truncations and comparisons minimal positive solutions
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The λ-pure Singularity Category of a Grothendieck Category 认领 引用
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作者 WANG Xi YAO Hailou 《数学进展》 CSCD 北大核心 2026年第2期330-342,共13页
Let A be a Grothendieck category.Theλ-pure singularity category Dλ-sgb(A)of A is a Verdier quotient of the boundedλ-pure derived category Dλb(A)by a thick subcategory Kb(PPλ),i.e.,Dλ-sgb(A):... Let A be a Grothendieck category.Theλ-pure singularity category Dλ-sgb(A)of A is a Verdier quotient of the boundedλ-pure derived category Dλb(A)by a thick subcategory Kb(PPλ),i.e.,Dλ-sgb(A):=Dλb(A)/K b(PPλ).We mainly verify that Dλ-sgb(A)is triangle equivalent to another quotient category under a special condition.And we also prove that a triangle equivalence between special homotopy categories induces aλ-pure derived equivalence,and it induces aλ-pure singular equivalence too. 展开更多
关键词 λ-presentable object λ-pure projective object λ-pure singularity category triangle equivalence
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The probability of success in solving linear systems of equations using quantum singular value transformation 认领 引用 被引量：1
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作者 Leigh Lapworth 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2026年第6期138-151,共14页
Quantum linear equation solvers generate a solution vector that sits in a subspace of the quantum computer’s larger state space.Accessing the solution vector relies on applying measurement projectors that remove comp... Quantum linear equation solvers generate a solution vector that sits in a subspace of the quantum computer’s larger state space.Accessing the solution vector relies on applying measurement projectors that remove components in the orthogonal subspace.This study examines the probability that the projectors are successful and how the success probability is influenced by the properties of the linear system,e.g.,the matrix condition number,and approximations made in the quantum solver.The analysis is performed within a non-linear computational fluid dynamics code where,at each iteration,a linearised system is passed to an emulated quantum solver.The linear systems are solved using quantum singular value transformation,for which the accuracy of the matrix inversion polynomial can be controlled via user input.The results show that success probabilities vary between 10−6and 10−2for the cases considered.More accurate approximations have lower success probabilities and require longer circuits.Less accurate approximations are analysed and show that variations during the non-linear iterations are related to the eigen content of the right-hand side vector.The use of amplitude amplification is shown to be able to increase success probabilities from 10−6to 10−2,in accordance with theory,but at a cost of a 100 times increase in circuit depth.Whilst these results are specific to the fluid flow test cases,they are generalisable to other types of linear solvers. 展开更多
关键词 Quantum linear equation solver Quantum singular value transformation Success probability Computational fluid dynamics
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Coexistence of near-EF Van Hove Singularity and in-Gap Topological Dirac Surface States in Superconducting Electrides 认领 引用
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作者 Yin Yang Peihan Sun +9 位作者 Ye Shen Zhijun Tu Pengcheng Ma Hongrun Zhen Tianqi Wang Longli Tian Tian Cui Hechang Lei Kai Liu Zhonghao Liu 《Chinese Physics Letters》 SCIE EI CAS CSCD 2026年第1期213-217,共5页
Superconducting elect rides have attracted growing attention for their potential to achieve high superconducting transition temperatures(TC)under pressure.However,many known elect rides are chemically reactive and ... Superconducting elect rides have attracted growing attention for their potential to achieve high superconducting transition temperatures(TC)under pressure.However,many known elect rides are chemically reactive and unstable,making high-quality single-crystal growth,characterization,and measurements difficult,and most do not exhibit superconductivity at ambient pressure.In contrast,La3 In stands out for its ambient-pressure superconductivity(TC∼9.4 K)and the availability of high-quality single crystals.Here,we investigate its low-energy electronic structure using angle-resolved photoemission spectroscopy and first-principles calculations.The bands near the Fermi energy(EF)are mainly derived from La 5d and In 5p orbitals.A saddle point is directly observed at the Brillouin zone(BZ)boundary,while a three-dimensional Van Hove singularity crosses EF at the BZ corner.First-principles calculations further reveal topological Dirac surface states within the bulk energy gap above EF.The coexistence of a high density of states and in-gap topological surface states nearF suggests that La3In offers a promising platform for tuning superconductivity and exploring possible topological superconducting phases through doping or external pressure. 展开更多
关键词 ambient pressure superconductivity superconducting elect rides gap topological Dirac surface states La superconducting electrides near efVan Hove singularity angle resolved photoemission spectroscopy elect rides
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Physics-informed neural networks with Poincaré-Lighthill-Kuo method for singular perturbation problems 认领 引用
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作者 Qingyong Luo Lei Zhang Guowei He 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2026年第6期211-222,共12页
Physics-informed neural networks(PINNs)have recently emerged as a powerful tool to solve differential equations for nonlinear mechanics.However,PINNs struggle with singular perturbation problems due to their locally a... Physics-informed neural networks(PINNs)have recently emerged as a powerful tool to solve differential equations for nonlinear mechanics.However,PINNs struggle with singular perturbation problems due to their locally abrupt behavior and singularities.The Poincaré-Lighthill-Kuo(PLK)method has been efficiently used to address these problems by applying perturbation expansions to both dependent and independent variables.This paper proposes a combination of the PLK method and PINNs,termed PLK-PINNs.The PLK-PINNs employ a parametric expression through two neural networks:one representing the mapping from parametric variables to independent variables,and the other approximating the solution of dependent variables with respect to parametric variables.Moreover,an auxiliary loss term is proposed to constrain the Jacobian determinant of the mapping within a constant sign interval to ensure the bijectivity of the mapping.The effectiveness of the proposed method is demonstrated through tests on typical singularity-shift and secular-term problems,with conventional PINNs in comparison. 展开更多
关键词 Physics-informed neural networks Singular perturbation problems Poincaré-Lighthill-Kuo method Parametric expressions
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LOCAL WELLPOSEDNESS AND SINGULARITY FORMATION FOR THE MULTI-SPECIES VLASOV-RIESZ-FOKKER-PLANCK SYSTEM 认领 引用
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作者 Yiliu WANG Shu WANG 《Acta Mathematica Scientia》 SCIE CSCD 2026年第4期1809-1826,共18页
We investigate the local well-posedness and singularity formation of the multispecies Vlasov-Riesz-Fokker-Planck system with general interaction fields.Local existence and uniqueness are established via a classical a ... We investigate the local well-posedness and singularity formation of the multispecies Vlasov-Riesz-Fokker-Planck system with general interaction fields.Local existence and uniqueness are established via a classical a priori estimate approach in weighted Sobolev spaces;this requires careful treatment of the regularity of the field induced by general potentials.By applying a second-order Grönwall inequality to the moment of inertia,we derive an improved sufficient condition for blow-up compared to previous results.The singularity formation criterion varies depending on different field configurations,and is only determined by the initial energy and spatial charge density. 展开更多
关键词 Vlasov-Riesz-Fokker-Planck system multi species local wellposedness singularity formation weighted Sobolev space
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THE STRONGLY SINGULAR CALDERÓN-ZYGMUND OPERATORS AND THEIR COMMUTATORS ON MUSIELAK-ORLICZ HARDY SPACES 认领 引用
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作者 Xiao WANG Wenchang SUN 《Acta Mathematica Scientia》 SCIE CSCD 2026年第4期1643-1658,共16页
In this paper,we prove the boundedness of strongly singular Calderón-Zygmund operators and their corresponding commutators when mapping from Musielak-Orlicz Hardy spaces into Musielak-Orlicz spaces.By introducing... In this paper,we prove the boundedness of strongly singular Calderón-Zygmund operators and their corresponding commutators when mapping from Musielak-Orlicz Hardy spaces into Musielak-Orlicz spaces.By introducing a specific subspace of BMO,we further show that the commutators generated by functions within this subspace and strongly singular Calderón-Zygmund operators remain bounded under the same mapping framework. 展开更多
关键词 strongly singular Calderón-Zygmund operators commutators Musielak-Orlicz Hardy spaces
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Pure Singularity Categories over Triangular Matrix Rings 认领 引用
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作者 Meiqi YAN Hailou YAO 《Journal of Mathematical Research with Applications》 CSCD 2026年第2期197-208,共12页
In this paper,we identify conditions on the change of rings to induce functors between the two pure derived(resp.,pure singularity)categories.Then we construct recollements of pure derived categories and pure singular... In this paper,we identify conditions on the change of rings to induce functors between the two pure derived(resp.,pure singularity)categories.Then we construct recollements of pure derived categories and pure singularity categories for a formal triangular matrix ring,respectively.As an application,we study the pure global dimension of a formal triangular matrix ring. 展开更多
关键词 pure derived category pure singularity category triangular matrix ring recollement
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Stripping singularities accelerates cycle expansions 认领 引用
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作者 Huanyu Cao Yueheng Lan 《Communications in Theoretical Physics》 SCIE CAS CSCD 2026年第5期218-226,共9页
The convergence of cycle expansions in non-hyperbolic systems has long been an outstanding challenge,primarily due to the presence of singularities in natural measures and the attributed weak shadowing properties of u... The convergence of cycle expansions in non-hyperbolic systems has long been an outstanding challenge,primarily due to the presence of singularities in natural measures and the attributed weak shadowing properties of unstable periodic orbits.Here,we introduce a novel layered approximation scheme that effectively decomposes the natural measure into distinct singular and hyperbolic layers.For the singular components,we employ analytical approximations,whereas for the hyperbolic components,we utilize cycle expansions.A key innovation of our approach is the incorporation of dynamical information beyond periodic orbits,which is essential for achieving a more accurate approximation of the natural measure and for precisely calculating observable averages.By integrating additional dynamical details,the new scheme more effectively captures the subtleties of the system's behavior that are not fully represented by a limited set of periodic orbits alone.This invariance allows us to refine the approximation of the natural measure in both the singular and the hyperbolic layers,thereby yielding a more reliable estimation of observable averages. 展开更多
关键词 chaotic dynamics observable average cycle expansion singular natural measure
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Three-Dimensional van Hove Singularities and Charge Density Wave Evolution in Kagome Lattice KV3Sb5 认领 引用
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作者 Yu Huang Haiyang Ma +13 位作者 Wei Xia Zhicheng Jiang Wenchuan Jing Xiangqi Liu Jiayu Liu Yuming Shi Xun Ma Runfeng Zhang Jin-Feng Jia Jishan Liu Mao Ye Zhengtai Liu Yanfeng Guo Dawei Shen 《Chinese Physics Letters》 SCIE EI CAS CSCD 2025年第12期226-238,共13页
The kagome metals AV3Sb5(A=K,Rb,Cs)feature intertwined Dirac fermions,topological flat bands,and van Hove singularities(vHS)near the Fermi level,which give rise to a range of exotic,strongly correlated phenomena... The kagome metals AV3Sb5(A=K,Rb,Cs)feature intertwined Dirac fermions,topological flat bands,and van Hove singularities(vHS)near the Fermi level,which give rise to a range of exotic,strongly correlated phenomena such as charge density waves(CDW)and superconductivity.Although the vHS from V 3d states have been implicated in CDW formation,their three-dimensional nature and temperature evolution remain poorly understood.In this study,we used high-resolution angle-resolved photoemission spectroscopy and density functional theory to reveal pronounced out-of-plane dispersion of vHS and their temperature dependence in KV3Sb5.The identified c-axis band folding and scattering channels were directly linked to the CDW order.These results demonstrate that the CDW transition in this family involves cooperative coupling between electron correlations and structural modulation along the c axis.This offers new insights into the interplay of topology,correlations,and lattice instabilities in kagome metals. 展开更多
关键词 kagome metals dirac fermionstopological flat bandsand van hove singularities vhs near charge density waves cdw three dimensional van hove singularities kv sb c axis band folding charge density wave evolution
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Double topological phase singularities in highly absorbing ultra-thin film structures for ultrasensitive humidity sensing 认领 引用 被引量：1
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作者 Xiaowen Li Jie Sheng +8 位作者 Zhengji Wen Fangyuan Li Xiran Huang Mingqing Zhang Yi Zhang Duo Cao Xi Shi Feng Liu Jiaming Hao 《Opto-Electronic Advances》 SCIE EI CAS CSCD 2025年第3期37-47,共11页
Phase singularities(PSs)in topological darkness-based sensors have received significant attention in optical sensing due to their rapid,ultra-sensitive,and label-free detection capabilities.Here,we present both experi... Phase singularities(PSs)in topological darkness-based sensors have received significant attention in optical sensing due to their rapid,ultra-sensitive,and label-free detection capabilities.Here,we present both experimental and theoretical investigations of an ultrasensitive and multiplexed phase-sensitive sensor utilizing dual topological PSs in the visible and near-infrared regions.This sensor uses a simple structure,which consists of an ultra-thin highly absorbing film deposited on a metal substrate.We demonstrate the achievement of dual-polarization darkness points for s-and p-polarizations at different incident angles.Furthermore,we theoretically explain the double topological PSs accompanied by a perfect±π-jump near a zero-reflection point,based on the temporal coupled-mode formalism.To validate its multifunctional capabilities,humidity sensing tests were carried out.The results demonstrate that the sensor has a detection limit reaching the level of 0.12‰.These findings go beyond the scope of conventional interference optical coatings and highlight the potential applications of this technology in gas sensing and biosensing domains. 展开更多
关键词 double topological darkness phase singularity thin-film optics ultrasensitive sensing
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Ocean singularity analysis and global heat flow prediction reveal anomalous bathymetry and heat flow 认领 引用 被引量：1
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作者 Yang Zhang Qiuming Cheng +1 位作者 Tao Hong Junjie Ji 《Geoscience Frontiers》 SCIE CAS CSCD 2025年第3期193-204,共12页
The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and... The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges. 展开更多
关键词 Heat flow Bathymetry Fractal density Power-law model Singularity analysis Similarity method
Singular optimal control of ascent stage for a surface-to-air missile 认领 引用
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作者 Wengui LEI Wanchun CHEN +1 位作者 Liang YANG Xiaopeng GONG 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2025年第8期527-541,共15页
This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the ty... This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the typical Goddard problem.First,the classical Legendre-Clebsch condition is applied to derive optimal conditions for the singular angle of attack,revealing that the missile turns by gravity along the singular arc.Second,the higher-order differentiation of the switching function provides the necessary conditions to determine the optimal thrust,expressed as linear functions of the costate variables.The vanishing coefficient determinant is then employed to decouple the control and costate variables,yielding the singular thrust solely dependent on state variables and identifying the singular surface.Moreover,the analytical singular control can be regarded as path constraints subject to the typical Optimal Control Problem(OCP),enabling the GPOPS-Ⅱ,a direct method framework that does not involve the singular condition,to solve the SOCP.Finally,three cases with different structures are presented to evaluate the performance of the proposed method.The results show that it takes a few steps to obtain the numerical optimal solution,which is consistent with the analytical solution derived from the calculus of variations,highlighting its great computational accuracy and effectiveness. 展开更多
关键词 Singular optimal control Optimal control problem Goddard problem Singular surface Pseudospectral method Surface-to-air missiles
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Co-Evolution of Magmatic and Sedimentary Fluxes Coupling with Supercontinents:Insight from Singularity Analysis of Deep-Time Geological Records 认领 引用
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作者 Molei Zhao Guoxiong Chen +2 位作者 Jie Yang Yuanzhi Zhou Qiuming Cheng 《Journal of Earth Science》 SCIE CAS CSCD 2025年第5期2308-2316,共9页
Continental crust is the long-term achievements of Earth's evolution across billions of years.The continental rocks could have been modified by various types of geological processes,such as metamorphism,weathering... Continental crust is the long-term achievements of Earth's evolution across billions of years.The continental rocks could have been modified by various types of geological processes,such as metamorphism,weathering,and reworking.Therefore,physical or chemical properties of rocks through time record the composite effects of geological,biological,hydrological,and climatological processes.Temporal variations in these time series datasets could provide important clues for understanding the co-evolution of different layers on Earth.However,deciphering Earth's evolution in deep time is challenged by incompleteness,singularity,and intermittence of geological records associated with extreme geological events,hindering a rigorous assessment of the underlying coupling mechanisms.Here,we applied the recently developed local singularity analysis and wavelet analysis method to deep-time U-Pb age spectra and sedimentary abundance record across the past 3.5 Gyrs.Standard cross-correlation analysis suggests that the singularity records of marine sediment accumulations and magmatism intensity at continental margin are correlated negatively(R2=0.8),with a delay of~100 Myr.Specifically,wavelet coherence analysis suggests a~500-800 Myr cycle of correlation between two records,implying a coupling between the major downward processes(subduction and recycling sediments)and upward processes(magmatic events)related to the aggregation and segregation of supercontinents.The results clearly reveal the long-term cyclic feedback mechanism between sediment accumulation and magmatism intensity through aggregation of supercontinents. 展开更多
关键词 singularity theory deep-time data magmatic and sedimentary fluxes co-evolution big data tectonics
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Optical Singularities in Photonic Microstructures with Rosette Symmetries:A Unified Theoretical Scheme 认领 引用
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作者 Jie Yang Jiafu Wang +3 位作者 Xinmin Fu Yueting Pan Tie Jun Cui Xuezhi Zheng 《Engineering》 SCIE EI CSCD 2025年第2期59-69,共11页
Optical singularities are topological defects of electromagnetic fields;they include phase singularity in scalar fields,polarization singularity in vector fields,and three-dimensional(3D)singularities such as optical ... Optical singularities are topological defects of electromagnetic fields;they include phase singularity in scalar fields,polarization singularity in vector fields,and three-dimensional(3D)singularities such as optical skyrmions.The exploitation of photonic microstructures to generate and manipulate optical singularities has attracted wide research interest in recent years,with many photonic microstructures having been devised to this end.Accompanying these designs,scattered phenomenological theories have been proposed to expound the working mechanisms behind individual designs.In this work,instead of focusing on a specific type of microstructure,we concentrate on the most common geometric features of these microstructures—namely,symmetries—and revisit the process of generating optical singularities in microstructures from a symmetry viewpoint.By systematically employing the projection operator technique in group theory,we develop a widely applicable theoretical scheme to explore optical singularities in microstructures with rosette(i.e.,rotational and reflection)symmetries.Our scheme agrees well with previously reported works and further reveals that the eigenmodes of a symmetric microstructure can support multiplexed phase singularities in different components,such as out-of-plane,radial,azimuthal,and left-and right-handed circular components.Based on these phase singularities,more complicated optical singularities may be synthesized,including C points,V points,L lines,Néel-and bubble-type optical skyrmions,and optical lattices,to name a few.We demonstrate that the topological invariants associated with optical singularities are protected by the symmetries of the microstructure.Lastly,based on symmetry arguments,we formulate a so-called symmetry matching condition to clarify the excitation of a specific type of optical singularity.Our work establishes a unified theoretical framework to explore optical singularities in photonic microstructures with symmetries,shedding light on the symmetry origin of multidimensional and multiplexed optical singularities and providing a symmetry perspective for exploring many singularity-related effects in optics and photonics. 展开更多
关键词 Optical singularity Optical vortex Photonic microstructures Symmetries Group representation theory
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ASYMPTOTIC STABILIZATION IN A TWO-DIMENSIONAL SINGULAR CHEMOTAXIS-NAVIER-STOKES SYSTEM WITH INDIRECT SIGNAL CONSUMPTION 认领 引用
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作者 Feng DAI Bin LIU 《Acta Mathematica Scientia》 SCIE CSCD 2025年第4期1355-1383,共29页
This paper deals with the singular chemotaxis-Navier-Stokes system with indirect signal consumption nt+u·▽v=△n-Х▽·(n/v▽u);vt+u·▽v=△v-uw;wt+u·▽w=△w-w+n;ut+(u·▽)u=△u-▽P+... This paper deals with the singular chemotaxis-Navier-Stokes system with indirect signal consumption nt+u·▽v=△n-Х▽·(n/v▽u);vt+u·▽v=△v-uw;wt+u·▽w=△w-w+n;ut+(u·▽)u=△u-▽P+n▽Ф;▽·u=0,x∈Ω,t>0 in a bounded and smooth domainΩ⊂ℝ2 with no-fluxo-fluxo-fluxo-slip boundary conditions,whereΦ∈W2,∞(Ω).A recent literature[Dai F,Liu B.J Differential Equations,2023,369:115–155]has proved that for all reasonably regular initial data,the associated initial-boundary value problem possesses a global classical solution,but qualitative information on the behavior of solution has never been touched so far.In stark contrast to the positive effect of indirect signal consumption mechanism on the global solvability of system,the analysis of asymptotic behavior of solution to the system with indirect signal consumption is essentially complicated than that with direct signal consumption because the favorable coupled structure between cells and signal is broken down by the indirect signal consumption mechanism.The present study shows that the global classical solution exponentially stabilizes toward the corresponding spatially homogeneous equilibria under a smallness condition on the initial cell mass.In comparison to the previously known result concerning the uniform convergence of solution to the system with direct signal consumption,our result inter alia provides a more in-depth understanding on the asymptotic behavior of solution. 展开更多
关键词 chemotaxis-Navier-Stokes system singular sensitivity indirect signal consumption asymptotic stabilization
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An Approximation Method for Singular Trudinger-Moser Inequality 认领 引用
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作者 ZHU Maochun XU Wenyan JIANG Rou 《应用数学》 北大核心 2025年第1期64-70,共7页
In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to... In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball. 展开更多
关键词 Singular Trudinger-Moser inequality Approximation functional Concentration level
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Spatial correlation singularities and orbital angular momentum spectra of partially coherent beams with noncanonical vortex pairs 认领 引用 被引量：2
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作者 MEI Chao CHENG Ke +2 位作者 YI Xiao-wen FU Cai-ying ZENG Ti-xian 《中国光学（中英文）》 EI CAS CSCD 北大核心 2025年第5期1243-1254,共12页
By introducing noncanonical vortex pairs to partially coherent beams, spatial correlation singularity (SCS) and orbital angular momenta (OAM) of the resulting beams are studied using the Fraunhofer diffraction integra... By introducing noncanonical vortex pairs to partially coherent beams, spatial correlation singularity (SCS) and orbital angular momenta (OAM) of the resulting beams are studied using the Fraunhofer diffraction integral. The effect of noncanonical strength, off-axis distance and vortex sign on spatial correlation singularities in far field is stressed. Furthermore, far-field OAM spectra and densities are also investigated, and the OAM detection and crosstalk probabilities are discussed. The results show that the number of dislocations of SCS always equals the sum of absolute values of topological charges for canonical or noncanonical vortex pairs. Although the sum of the product of each OAM mode and its power weight equals the algebraic sum of topological charges for canonical vortex pairs, the relationship no longer holds in the noncanonical case except for opposite-charge vortex pairs. The changes of off-axis distance, noncanonical strength or coherence length can lead to a more dominant power in adjacent mode than that in center detection mode, which also indicates that crosstalk probabilities of adjacent modes exceed the center detection probability. This work may provide potential applications in OAM-based optical communication, imaging, sensing and computing. 展开更多
关键词 spatial correlation singularity orbital angular momentum noncanonical vortex partially coherent beam
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