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

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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A fully connected polarization-entangled network via integrated spontaneous four-wave mixing engineering

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Science China(Physics,Mechanics & Astronomy) 2025年第6期Mechanics & Astronomy) .卷 76-83页

作者： Pingyu Zhu Yan Wang Yuxing Du Miaomiao Yu Kaikai Zhang Kun Wang Ping Xu Institute for Quantum Information & State Key Laboratory of High Performance Computing College of Computer Science and TechnologyNational University of Defense Technology Hefei National Laboratory

Quantum communication is rapidly developing and is gradually being commercialized due to its technological maturity. Establishing dense communication links among multiple users in a scalable and efficient way is of great significance for realizing a large-scale quantum communication network. Here, we propose a novel scheme to construct a fully connected polarizationentangled network, utilizing the engineering of spontaneous four-wave mixings(SFWMs) and a path-polarization converter. It does not require active optical switches which limit the communication speed, or trusted nodes which lead to potential security risks. The required frequency channels in the network grow linearly with the number of users. We experimentally demonstrate a six-user fully connected network with on-chip SFWM processes motivated by four pumps. Each user in the network receives a frequency channel, and all fifteen connections between the users are implemented simultaneously. Our work opens up a promising scheme to efficiently construct fully connected large-scale networks.

关键词： quantum network quantum entanglement nonlinear optics integrated optics

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The quantum Ising model for perfect matching and solving it with variational quantum eigensolver

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Science China(Information Sciences) 2024年第9期67卷 306-320页

作者： Qilin ZHENG Pingyu ZHU Chao WU Miaomiao YU Weihong LUO Ping XU Institute for Quantum Information and State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Hefei National Laboratory

Obtaining all perfect matchings of a graph is a tough problem in graph theory, and its complexity belongs to the #P-Complete class. The problem is closely related to combinatorics, marriage matching problems, dense subgraphs, the Gaussian boson sampling, chemical molecular structures, and dimer *** this paper, we propose a quadratic unconstrained binary optimization formula of the perfect matching problem and translate it into the quantum Ising model. We can obtain all perfect matchings by mapping them to the ground state of the quantum Ising Hamiltonian and solving it with the variational quantum eigensolver. Adjusting the model's parameters can also achieve the maximum or minimum weighted perfect matching. The experimental results on a superconducting quantum computer of the Origin Quantum computing Technology Company show that our model can encode 2~n dimensional optimization space with only O（n） qubits consumption and achieve a high success probability of the ground state corresponding to all perfect matchings. In addition, the further simulation results show that the model can support a scale of more than 14 qubits, effectively resist the adverse effects of noise, and obtain a high success probability at a shallow variational depth. This method can be extended to other combinatorial optimization problems.

关键词： perfect matching Ising model quantum Hamiltonian variational quantum eigensolver quadratic unconstrained binary optimization

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high-order finite volume methods for solving compressible multicomponent flows

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Science China Mathematics 2025年第3期68卷 729-760页

作者： Feng Zheng Jianxian Qiu School of Mathematics and Statistics Fujian Key Laboratory of Mathematical Analysis and ApplicationFujian Normal UniversityFuzhou 350117China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling&High-Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper, we propose a high-order finite volume method for solving multicomponent fluid problems. Our method couples the quasi-conservative form with the reconstruction of conservative variables in a characteristic manner. The source term and numerical fluxes are carefully designed to maintain the pressure and velocity equilibrium for the interface-only problem and preserve the equilibrium of physical parameters in a single-component fluid. These ingredients enable our scheme to achieve both high-order accuracy in the smooth region and the high resolution in the discontinuity region of the solution. Extensive numerical tests are performed to verify the high resolution and accuracy of the scheme.

关键词： finite volume high-order multicomponent flows

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A Stable Arbitrarily high Order Time-Stepping Method for Thermal Phase Change Problems

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Communications in Computational Physics 2023年第2期33卷 477-510页

作者： Weiwen Wang Chuanju Xu School of Mathematical Sciences and Fujian Provincial Key Laboratory of MathematicalModeling and High Performance Scientific Computing Xiamen UniversityXiamen 361005P.R.China.

Thermal phase change problems are widespread in mathematics,nature,and *** are particularly useful in simulating the phenomena of melting and solidification in materials *** this paper we propose a novel class of arbitrarily high-order and unconditionally energy stable schemes for a thermal phase changemodel,which is the coupling of a heat transfer equation and a phase field *** unconditional energy stability and consistency error estimates are rigorously proved for the proposed schemes.A detailed implementation demonstrates that the proposed method requires only the solution of a system of linear elliptic equations at each time step,with an efficient scheme of sufficient accuracy to calculate the solution at the first *** is observed from the comparison with the classical explicit Runge-Kutta method that the new schemes allow to use larger time *** time step size strategies can be applied to further benefit from this unconditional *** experiments are presented to verify the theoretical claims and to illustrate the accuracy and effectiveness of our method.

关键词： Thermal phase change problem gradient flows unconditional energy stability auxiliary variable Runge-Kutta methods phase field

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On-chip quantum NOON state sensing for temperature and humidity

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Chinese Physics B 2024年第10期33卷 15-20页

作者： Weihong Luo Chao Wu Yuxing Du Chang Zhao Miaomiao Yu Pingyu Zhu Kaikai Zhang Ping Xu Institute for Quantum Information&State Key Laboratory of High Performance Computing College of Computer Science and TechnologyNational University of Defense TechnologyChangsha 410073China

A maximal photon number entangled state,namely NOON state,can be adopted for sensing with a quantum *** this work,we designed silicon quantum photonic chips containing two types of Mach-Zehnder interferometerswherein the two-photon NOON state,sensing element for temperature or humidity,is *** with classicallight or single photon case,two-photon NOON state sensing shows a solid enhancement in the sensing resolution *** the first demonstration of on-chip quantum photonic sensing,it reveals the advantages of photonic chips forhigh integration density,small-size,stability for multiple-parameter sensing serviceability.A higher sensing precision isexpected to beat the standard quantum limit with a higher photon number NOON state.

关键词： quantum sensing NOON state photonic chip

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Four-wave mixing Bragg scattering for small frequency shift from silicon coupled microrings

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Chinese Physics B 2025年第1期34卷 351-355页

作者： Chang Zhao Chao Wu Pingyu Zhu Yuxing Du Yan Wang Miaomiao Yu Kaikai Zhang Ping Xu Institute for Quantum Information&State Key Laboratory of High Performance Computing College of Computer Science and TechnologyNational University of Defense TechnologyChangsha 410073China

Frequency conversion is pivotal in nonlinear optics and quantum optics for manipulating and translating light signals across different wavelength *** frequency conversion between two light beams with a small frequency interval is a central *** this work,we design a pair of coupled silicon microrings wherein coupled-induced modesplitting exists to achieve a small frequency shift by the process of four-wave mixing Bragg *** an example,the signal can be up or down converted to the idler which is 15.5 GHz spaced when two pumps align with another pair of split *** results unveil the potential of coupled microring resonators for small interval frequency conversion in a high-fidelity,all-optical,and signal processing quantum frequency interface.

关键词： four-wave mixing Bragg scattering silicon coupled microrings

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Material Removal Characteristics of Single-Crystal 4H-SiC Based on Varied-Load Nanoscratch Tests

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Chinese Journal of Mechanical Engineering 2023年第4期36卷 125-138页

作者： Kun Tang Wangping Ou Cong Mao Jie Liang Moke Zhang Mingjun Zhang Yongle Hu Hunan Provincial Key Laboratory of Intelligent Manufacturing Technology for High-performance Mechanical Equipment Changsha University of Science and TechnologyChangsha 410114China

Single-crystal silicon carbide(SiC)has been widely applied in the military and civil fields because of its excellent physical and chemical ***,as is typical in hard-to-machine materials,the good mechanical properties result in surface defects and subsurface damage during precision or ultraprecision *** this study,single-and double-varied-load nanoscratch tests were systematically performed on single-crystal 4H-SiC using a nanoindenter system with a Berkovich *** material removal characteristics and cracks under different planes,indenter directions,normal loading rates,and scratch intervals were analyzed using SEM,FIB,and a 3D profilometer,and the mechanisms of material removal and crack propagation were *** results showed that the Si-plane of the single-crystal 4H-SiC and edge forward indenter direction are most suitable for material removal and *** normal loading rate had little effect on the scratch depth,but a lower loading rate increased the ductile region and critical depth of ***,the crack interaction and fluctuation of the depth-distance curves of the second scratch weakened with an increase in the scratch interval,the status of scratches and chips changed,and the comprehensive effects of the propagation and interaction of the three cracks resulted in material fractures and chip *** calculated and experimental values of the median crack depth also showed good consistency and ***,this study provides an important reference for the high-efficiency and precision machining of single-crystal SiC to ensure high accuracy and a long service life.

关键词： Single crystal silicon carbides Varied-load nanoscratch Material removal Crack propagation

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Advancing microwave absorption:Innovative strategies spanning nano-micro engineering to metamaterial design

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Nano Research 2025年第3期18卷 275-308页

作者： Beibei Zhan Xiaosi Qi Jing-Liang Yang Xiu Gong Junfei Ding Yanli Chen Fuzhong Wu Wei Zhong College of Physics Guizhou Province Key Laboratory for Photoelectrics Technology and ApplicationGuizhou UniversityGuiyang 550025China Guizhou High-level Institution Key Laboratory of High-Performance Battery Materials Guizhou UniversityGuiyang 550025China National Laboratory of Solid State Microstructures and Jiangsu Provincial Laboratory for NanoTechnology Nanjing UniversityNanjing 210093China

With the widespread adoption of communication technology,the potential hazards of electromagnetic(EM)radiation to human health and electronic devices operation have also ***,microwave absorption(MA)materials are becoming increasingly vital in the current electronic information ***,extensive researches have been conducted on the MA mechanisms and optimized strategies,leading to significant advancements in improving MA ***,there is a lack of systematic summary of various innovative engineering strategies from nano-micro scale to ***,nano-micro engineering techniques readily introduce heterointerfaces,components,or defects,*** boost dielectric loss and/or magnetic *** macroscopic strategy focuses on crafting more porous three-dimensional structures(foams,aerogels,films,etc.),which are beneficial for fine-tuning intrinsic impedance and triggering multiple reflections/scattering of EM wave(EMW).While metamaterial design featuring periodic layouts and sub-wavelength scales can also lead to energy loss via EMW ***,in this review,we aim to provide a detailed overview of various engineering strategies for enhancing MA performance from nano-micro engineering to macroscopic strategies to metamaterial ***,we elaborate the present challenges faced by MA technology and discuss potential future development opportunities and *** is our hope that this paper will offer insights and direction for the ongoing improvement of MA performance and achieving practical applications.

关键词： electromagnetic radiation microwave absorption nano-micro engineering macroscopic strategy metamaterial design

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RKDG Methods with Multi-resolution WENO Limiters for Solving Steady-State Problems on Triangular Meshes

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Communications on Applied Mathematics and Computation 2024年第3期6卷 1575-1599页

作者： Jun Zhu Chi-Wang Shu Jianxian Qiu State Key Laboratory of Mechanics and Control of Mechanical Structures and Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing University of Aeronautics and AstronauticsNanjing 210016JiangsuChina Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen UniversityXiamen 361005FujianChina

In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.

关键词： RKDG method Steady-state problem Multi-resolution WENO limiter Triangular mesh Machine zero

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