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Two-dimensional localized modes in nonlinear systems with linear nonlocality and moiré lattices

Frontiers of physics 2024年第4期19卷 265-273页

作者： Xiuye Liu Jianhua zeng Center for Attosecond Science and Technology State Key Laboratory of Transient Optics and PhotonicsXi’an Institute of Optics and Precision Mechanics of Chinese Academy of SciencesXi’an 710119China University of Chinese Academy of Sciences Beijing 100049China Collaborative lnnovation Center of Extreme Optics Shanxi UniversityTaiyuan 030006China

Periodic structures structured as photonic crystals and optical lattices are fascinating for nonlinear waves engineering in the optics and ultracold atoms ***éphotonic and optical lattices—two-dimensional twisted patterns lie somewhere in between perfect periodic structures and aperiodic ones—are a new emerging investigative tool for studying nonlinear localized waves of diverse ***,a theory of two-dimensional spatial localization in nonlinear periodic systems with fractional-order diffraction(linear nonlocality)and moiréoptical lattices is ***,the flat-band feature is well preserved in shallow moiréoptical lattices which,interact with the defocusing nonlinearity of the media,can support fundamental gap solitons,bound states composed of several fundamental solitons,and topological states(gap vortices)with vortex charge s=1 and 2,all populated inside the finite gaps of the linear Bloch-wave *** the linear-stability analysis and direct perturbed simulations,the stability and instability properties of all the localized gap modes are surveyed,highlighting a wide stability region within the first gap and a limited one(to the central part)for the third *** findings enable insightful studies of highly localized gap modes in linear nonlocality(fractional)physical systems with shallow moirépatterns that exhibit extremely flat bands.

关键词： moiréoptical lattices gap solitons and vortices ultracold atoms Gross-Pitaevskii/nonlinear fractional Schrödinger equation nonlinear fractional systems

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Nonsolvable Groups with Three Nonlinear Irreducible Character Codegrees

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Chinese Annals of Mathematics,Series B 2024年第2期45卷 173-178页

作者： Dongfang YANG Yu zeng Department of Mathematics Changshu Institute of TechnologyChangshu 215500JiangsuChina

For an irreducible characterχof a?nite group G,the codegree ofχis de-?ned as|G:ker(χ)|/χ(1).In this paper,the authors determine?nite nonsolvable groups with exactly three nonlinear irreducible character codegrees,... 详细信息

关键词： Character codegree Nonsolvable group

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Discovery of Partial Differential Equations from Highly Noisy and Sparse Data with Physics-Informed Information Criterion

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Research 2024年第1期2023卷 247-259页

作者： Hao Xu Junsheng zeng Dongxiao Zhang BIC-ESAT EREand SKLTCSCollege of EngineeringPeking UniversityBeijing 100871P.R.China Institute of Applied Physics and Computational Mathematics Beijing 100088P.R.China Eastern Institute for Advanced Study Eastern Institute of TechnologyNingbo 315200ZhejiangP.R.China National Center for Applied Mathematics Shenzhen(NCAMS) Southern University of Science and TechnologyShenzhen 518055GuangdongP.R.China Department of Mathematics and Theories Peng Cheng LaboratoryShenzhen 518000GuangdongP.R.China

Data-driven discovery of partial differential equations(PDEs)has recently made tremendous progress,and many canonical PDEs have been discovered successfully for proof of ***,determining the most proper PDE without prior references remains challenging in terms of practical *** this work,a physics-informed information criterion(PIC)is proposed to measure the parsimony and precision of the discovered PDE *** proposed PIC achieves satisfactory robustness to highly noisy and sparse data on 7 canonical PDEs from different physical scenes,which confirms its ability to handle difficult *** PIC is also employed to discover unrevealed macroscale governing equations from microscopic simulation data in an actual physical *** results show that the discovered macroscale PDE is precise and parsimonious and satisfies underlying symmetries,which facilitates understanding and simulation of the physical *** proposition of the PIC enables practical applications of PDE discovery in discovering unrevealed governing equations in broader physical scenes.

关键词： process canonical proof

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CFD-DEM study of impacts of the porous distributor medium on fluidization characteristics of a 2D-fluidized bed

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Particuology 2024年第4期87卷 54-73页

作者： Fei Wang Yishan zeng Hao Yan School of Mechanical Engineering Hefei University of TechnologyHefei230009China

Gas-solid bubbling fluidized beds are widely used in chemical,energy,construction,and other industrial fields due to their excellent fluidization performance.2D-fluidized beds with planar rectangular columns of finite thickness are widely used in fluidized bed studies,and it is essential for understanding the hydrodynamics of gas-particle ***,the distributor(porous medium)at the bottom of the bed has a crucial influence on the fluidization performance of the 2D-fluidized *** this work,the fluidization mechanism and gas-solid dynamic characteristics of the fluidized bed under three porous media are studied by CFD-DEM coupled with the porous medium model,and the accuracy of numerical simulation is verified by a high-speed photography *** show that with the increase in the flow resistance of the porous medium,the average and standard deviation of the bubble diameter decrease,and the time and position of particles in the dead zone to participate in the core-annular flow *** a low fluidization velocity,the dead zone in the bed can be considerably reduced by increasing the flow resistance.

关键词： Fluidized bed CFD-DEM Porous medium Bubble dynamics Solid mixing

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Prescribed Performance Evolution Control for Quadrotor Autonomous Shipboard Landing

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IEEE/CAA Journal of Automatica Sinica 2024年第5期11卷 1151-1162页

作者： Yang Yuan Haibin Duan Zhigang zeng State Key Laboratory of Virtual Reality Technology and Systems the School of Automation Science and Electrical EngineeringBeihang UniversityBeijing 100083China State Key Laboratory of Virtual Reality Technology and Systems the School of Automation Science and Electrical EngineeringBeihang UniversityBeijing 100083 Virtual Reality Fundamental Research Laboratory Department of Mathematics and TheoriesPeng Cheng LaboratoryShenzhen 518000China School of Artificial Intelligence and Automation Huazhong University of Science and TechnologyWuhan 430074China

The shipboard landing problem for a quadrotor is addressed in this paper,where the ship trajectory tracking control issue is transformed into a stabilization control issue by building a relative position *** guarantee both transient performance and steady-state landing error,a prescribed performance evolution control(PPEC)method is developed for the relative position *** addition,a novel compensation system is proposed to expand the performance boundaries when the input saturation occurs and the error exceeds the predefined *** the wind and wave on the relative position model,an adaptive sliding mode observer(ASMO)is designed for the disturbance with unknown upper *** on the dynamic surface control framework,a shipboard landing controller integrating PPEC and ASMO is established for the quadrotor,and the relative position control error is guaranteed to be uniformly ultimately *** results have verified the feasibility and effectiveness of the proposed shipboard landing control scheme.

关键词： error integrating stabilization

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An accurate and efficient space-time Galerkin spectral method for the subdiffusion equation

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Science China Mathematics 2024年第10期67卷 2387-2408页

作者： Wei zeng Chuanju Xu School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper, we design and analyze a space-time spectral method for the subdiffusion ***, we are facing two difficulties. The first is that the solutions of this equation are usually singular near the initial time. Consequently, traditional high-order numerical methods in time are inefficient. The second obstacle is that the resulting system of the space-time spectral approach is usually large and time-consuming to solve. We aim at overcoming the first difficulty by proposing a novel approach in time, which is based on variable transformation techniques. Suitable ψ-fractional Sobolev spaces and a new variational framework are introduced to establish the well-posedness of the associated variational problem. This allows us to construct our space-time spectral method using a combination of temporal generalized Jacobi polynomials(GJPs) and spatial Legendre polynomials. For the second difficulty, we propose a fast algorithm to effectively solve the resulting linear system. The fast algorithm makes use of a matrix diagonalization in space and QZ decomposition in time. Our analysis and numerical experiments show that the proposed method is exponentially convergent with respect to the polynomial degrees in both space and time directions, even though the exact solution has very limited regularity.

关键词： subdiffusion equations variable transformation Ψ-Sobolev spaces well-posedness space-time Galerkin spectral method error estimate fast algorithm

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Structural integration of solar desalination system

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Science China Materials 2024年第6期67卷 2039-2041页

作者： Diling Yang Hao Zhang Hongbo zeng School of Materials and Environmental Engineering Hunan University of HumanitiesScience and TechnologyLoudi 417000China Department of Chemical and Materials Engineering University of AlbertaEdmontonAlberta T6G 1H9Canada

As population grow and climate change place significant water stress on numerous regions,the demand for efficient and environmentally friendly water resource solutions becomes increasingly *** address this challenge,desalination technology has received much attention and is widely employed,with a recent emphasis on solar-powered solutions driven by the global push for carbon neutrality.

关键词： neutral system integration

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Achieving structurally stable O3-type layered oxide cathodes through site-specific cation-anion co-substitution for sodium-ion batteries

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Journal of Energy Chemistry 2024年第6期93卷 411-418,I0011页

作者： Yihao Shen Chen Cheng Xiao Xia Lei Wang Xi Zhou Pan zeng Jianrong zeng Liang Zhang Institute of Functional Nano&Soft Materials(FUNSOM) Soochow UniversitySuzhou 215123JiangsuChina Institute for Advanced Study School of Mechanical EngineeringChengdu UniversityChengdu 610106SichuanChina Shanghai Synchrotron Radiation Facility Shanghai Advanced Research InstituteChinese Academy of SciencesShanghai 201204China Shanghai Institute of Applied Physics Chinese Academy of SciencesShanghai 201800China Jiangsu Key Laboratory of Advanced Negative Carbon Technologies Soochow UniversitySuzhou 215123JiangsuChina

O3-type layered oxides have garnered great attention as cathode materials for sodium-ion batteries because of their abundant reserves and high theoretical ***,challenges persist in the form of uncontrollable phase transitions and intricate Na^(+)diffusion pathways during cycling,resulting in compromised structural stability and reduced capacity over *** study introduces a special approach employing site-specific Ca/F co-substitution within the layered structure of O_(3)-NaNi_(0.5)Mn_(0.5)O_(2) to effectively address these ***,the strategically site-specific doping of Ca into Na sites and F into O sites not only expands the Na^(+)diffusion pathways but also orchestrates a mild phase transition by suppressing the Na^(+)/vacancy ordering and providing strong metal-oxygen bonding strength,*** as-synthesized Na_(0.95)Ca_(0.05)Ni_(0.5)Mn_(0.5)O_(1.95)F_(0.05)(NNMO-CaF)exhibits a mild O3→O3+O'3→P3 phase transition with minimized interlayer distance variation,leading to enhanced structural integrity and stability over extended *** a result,NNMO-CaF delivers a high specific capacity of 119.5 mA h g^(-1)at a current density of 120 mA g^(-1)with a capacity retention of 87.1%after 100 *** study presents a promising strategy to mitigate the challenges posed by multiple phase transitions and augment Na^(+)diffusion kinetics,thus paving the way for high-performance layered cathode materials in sodium-ion batteries.

关键词： Sodium-ion batteries O3-type layered oxides Site-specific co-doping Phase transition

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Locally Self-Injective Property of FI^(m)

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Algebra Colloquium 2024年第1期31卷 97-110页

作者： Duo zeng LCSM(Ministry of Education) School of Mathematics and Statistics Hunan Normal UniversityChangsha 410081China

We consider the locally self-injective property of the product FI^(m) of category FI of finite sets and ***,we prove that the external tensor product commutes with the coinduction functor,and hence preserves injective *** corollaries,every projective FI^(m)-module over a field of characteristic O is injective,and the Serre quotient of the category of finitely generated FI^(m)-modules by the category of finitely generated torsion FI^(m)-modules is equivalent to the category of finite-dimensional FI^(m)-modules.

关键词： self-injective property Serre quotient FI^(m)-modules

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A COUPLED METHOD COMBINING CROUZEIX-RAVIART NONCONFORMING AND NODE CONFORMING FINITE ELEMENT SPACES FOR BOIT CONSOLIDATION MODEL

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Journal of Computational Mathematics 2024年第4期42卷 911-931页

作者： Yuping zeng Mingchao Cai Liuqiang Zhong School of Mathematics Jiaying UniversityMeizhou 514015China Department of Mathematics Morgan State University1700 E Cold Spring LnBaltimoreMD 21251USA School of Mathematical Science South China Normal UniversityGuangzhou 520631China

A mixed finite element method is presented for the Biot consolidation problem in *** precisely,the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements,while the fuid pressure is approximated by using the node conforming finite *** well-posedness of the fully discrete scheme is established,and a corresponding priori error estimate with optimal order in the energy norm is also *** experiments are provided to validate the theoretical results.

关键词： Poroelasticity Nonconforming finite element Inf-sup condition A priori error estimate

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