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THE OPTIMAL CONVERGENCE ORDER OF THE DISCONTINUOUS FINITE ELEMENT METHODS FOR FIRST ORDER HYPERBOLIC SYSTEMS

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Journal of Computational Mathematics 2008年第5期26卷 689-701页

作者： tie zhang Datao Shi Zhen Li Department of Mathematics and School of Information Science and Engineering Northeastern University Shenyang 110004 China

In this paper, a discontinuous finite element method for the positive and symmetric, first-order hyperbolic systems （steady and nonsteady state） is constructed and analyzed by using linear triangle elements, and the O（h^2）-order optimal error estimates are derived under the assumption of strongly regular triangulation and the Ha-regularity for the exact solutions. The convergence analysis is based on some superclose estimates of the interpolation approximation. Finally, we discuss the Maxwell equations in a two-dimensional domain, and numerical experiments are given to validate the theoretical results.

关键词： First order hyperbolic systems Discontinuous finite element method Convergence order estimate.

Preparation of silver nanoparticles through the reduction of straw-extracted lignin and its antibacterial hydrogel

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International Journal of Minerals,Metallurgy and Materials 2025年第2期32卷 504-514页

作者： Lou zhang Shuo Li Fu Tang Jingkai zhang Yuetong Kang Hean zhang Lidong Li State Key Laboratory for Advanced Metals and Materials School of Materials Science and EngineeringUniversity of Science and Technology BeijingBeijing 100083China

Silver nanoparticles(Ag NPs)have attracted attention in the field of biomaterials due to their excellent antibacterial ***,the reducing and stabilizing agents used for the chemical reduction of Ag NPs are usually toxic and may cause water *** this work,Ag NPs(31.2 nm in diameter)were prepared using the extract of straw,an agricultural waste,as the reducing and stabilizing *** analysis revealed that the straw extract contained lignin,the structure of which possesses phenolic hydroxyl and methoxy groups that facilitate the reduction of silver salts into Ag *** surfaces of Ag NPs were negatively charged due to the encapsulation of a thin layer of lignin molecules that prevented their *** the prepared Ag NPs were added to the precursor solution of acrylamide,free radical polymerization was triggered without the need for extra heating or light irradiation,resulting in the rapid formation of an Ag NP-polyacrylamide composite *** inhibition zone test proved that the composite hydrogel possessed excellent antibacterial ability due to the presence of Ag *** prepared hydrogel may have potential applications in the fabrication of biomedical materials,such as antibacterial dressings.

关键词： silver nanoparticles hydrogel straw extraction antibacterial

FINITE DIFFERENCE APPROXIMATION FOR PRICING THE AMERICAN LOOKBACK OPTION

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Journal of Computational Mathematics 2009年第4期27卷 484-494页

作者： tie zhang Shuhua zhang Danmei Zhu Department of Mathematics School of Information Science and Engineering Northeastern University Shenyang 110003 China Research Center for Mathematics and Economies Tianjin University of Finance and Economics Tianjin 300222 China Department of Mathematics School of Information Science and Engineering Northeastern University Shenyang 110004 China

In this paper we are concerned with the pricing of lookback options with American type constrains. Based on the differential linear complementary formula associated with the pricing problem, an implicit difference scheme is constructed and analyzed. We show that there exists a unique difference solution which is unconditionally stable. Using the notion of viscosity solutions, we also prove that the finite difference solution converges uniformly to the viscosity solution of the continuous problem. Furthermore, by means of the variational inequality analysis method, the O（△t ＋ △x^2）-order error estimate is derived in the discrete L2-norm provided that the continuous problem is sufficiently regular. In addition, a numerical example is provided to illustrate the theoretical results.

关键词： American lookback options Finite difference approximation Stability andconvergence Error estimates.

Arbitrarily rotating polarization direction and manipulating phases in linear and nonlinear ways using programmable metasurface

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Light(Science & Applications) 2024年第9期13卷 1789-1800页

作者： Wei Liu Si Ran Wang Jun Yan Dai Lei zhang Qiao Chen Qiang cheng tie Jun Cui State Key Laboratory of Millimeter Waves Southeast UniversityNanjing 210096China Institute of Electromagnetic Space Southeast UniversityNanjing 210096China Frontiers Science Center for Mobile Information Communication and Security Southeast UniversityNanjing 210096China Electrical Engineering Department Chalmers University of TechnologyGothenburg 41258Sweden

Independent controls of various properties of electromagnetic(EM)waves are crucially required in a wide range of *** metasurface is a promising candidate to provide an advanced platform for manipulating EM ***,we propose an approach that can arbitrarily control the polarization direction and phases of reflected waves in linear and nonlinear ways using a stacked programmable ***,we extend the space-timecoding theory to incorporate the dimension of polarization,which provides an extra degree of freedom for manipulating EM *** proof-of-principle application examples,we consider polarization rotation,phase manipulation,and beam steering at linear and nonlinear *** validation,we design,fabricate,and measure a metasurface *** experimental results show good agreement with theoretical predictions and *** proposed approach has a wide range of applications in various areas,such as imaging,data storage,and wireless communication.

关键词： surface nonlinear rotating

Harmonic information transitions of spatiotemporal metasurfaces

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Light(Science & Applications) 2020年第1期9卷 58-70页

作者： Haotian Wu Xin Xin Gao Lei zhang Guo Dong Bai Qiang cheng Lianlin Li tie Jun Cui State Key Laboratory of Millimetre Waves Southeast University210096 NanjingChina Institute of Electromagnetic Space Southeast University210096 NanjingChina State Key Laboratory of Advanced Optical Communication Systems and Networks Department of ElectronicsPeking University100871 BeijingChina

Facilitated by ultrafast dynamic modulations,spatiotemporal metasurfaces have been identified as a pivotal platform for manipulating electromagnetic waves and creating exotic physical phenomena,such as dispersion cancellation,Lorentz reciprocity breakage,and Doppler *** by emerging information-oriented technologies,we hereby probe the information transition mechanisms induced by spatiotemporal variations and present a general model to characterize the information processing capabilities of the spatiotemporal *** theory and abstract number theory are adopted through this investigation,by which the group extension and independent controls of multiple harmonics are proposed and demonstrated as two major tools for information transitions from the spatiotemporal domain to the spectra-wavevector *** incorporating Shannon’s entropy theory into the proposed model,we further discover the corresponding information transition efficiencies and the upper bound of the channel capacity of the spatiotemporal *** results of harmonic information transitions show great potential in achieving high-capacity versatile information processing systems with spatiotemporal metasurfaces.

关键词： surface transitions surfaces

A plasmonic route for the integrated wireless communication of subdiffraction-limited signals

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Light(Science & Applications) 2020年第1期9卷 930-938页

作者： Hao Chi zhang Le Peng zhang Pei Hang He Jie Xu cheng Qian Francisco J.Garcia-Vidal tie Jun Cui State Key Laboratory of Millimeter Waves Southeast University210096 NanjingChina Departamento de Fisica Teorica de la Materia Condensada and Condensed Matter Physics Center(IFIMAC) Universidad Autonoma de MadridMadridSpain Donostia International Physics Center(DIPC) Donostia/San SebastianSpain

Perfect lenses,superlenses and time-reversal mirrors can support and spatially separate evanescent waves,which is the basis for detecting subwavelength information in the far ***,the inherent limitations of these methods have prevented the development of systems to dynamically distinguish subdiffraction-limited *** the physical merits of spoof surface plasmon polaritons(SPPs),we demonstrate that subdiffraction-limited signals can be transmitted on planar integrated SPP channels with low loss,low channel interference,and high gain and can be radiated with a very low environmental ***,we show how deep subdiffraction-limited signals that are spatially coupled can be distinguished after line-of-sight wireless *** a visualized demonstration,we realize the high-quality wireless communication of two movies on subwavelength channels over the line of sight in real time using our plasmonic scheme,showing significant advantages over the conventional methods.

关键词： communication spatially diffraction

Crack propagation simulation in brittle elastic materials by a phase field method

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Theoretical & Applied Mechanics Letters 2019年第6期9卷 339-352页

作者： Xingxue Lu cheng Li Ying tie Yuliang Hou Chuanzeng zhang School of Mechanical Engineering Zhengzhou UniversityZhengzhou 450001China Department of Civil Engineering University of SiegenD-57076 SiegenGermany

To overcome the difficulties of re-meshing and tracking the crack-tip in other computational methods for crack propagation simulations,the phase field method based on the minimum energy principle is introduced by defining a continuous phase field variable(x)∈[0,1]to characterize discontinuous cracks in brittle *** method can well describe the crack initiation and propagation without assuming the shape,size and orientation of the initial crack in *** this paper,a phase field method based on Miehe's approach[Miehe et al.,***.(2010)]is applied to simulate different crack propagation problems in twodimensional(2D),isotropic and linear elastic *** numerical implementation of the phase field method is realized within the framework of the finite element method(FEM).The validity,accuracy and efficiency of the present method are verified by comparing the numerical results with other reference results in *** numerical examples are presented to show the effects of the loading type(tension and shear),boundary conditions,and initial crack location and orientation on the crack propagation path and force-displacement ***,for a single edge-cracked bi-material specimen,the influences of the loading type and the crack location on the crack propagation trajectory and force-displacement curve are also investigated and *** is demonstrated that the phase field method is an efficient tool for the numerical simulation of the crack propagation problems in brittle elastic materials,and the corresponding results may have an important relevance for predicting and preventing possible crack propagations in engineering applications.

关键词： Brittle fracture Phase field method Crack propagation Finite element method

Accurate and broadband manipulations of harmonic amplitudes and phases to reach 256 QAM millimeter-wave wireless communications by time-domain digital coding metasurface

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National Science Review 2022年第1期9卷 36-46页

作者： Ming Zheng Chen Wankai Tang Jun Yan Dai Jun Chen Ke Lei zhang cheng zhang Jin Yang Lianlin Li Qiang cheng Shi Jin tie Jun Cui Institute of Electromagnetic Space Southeast University State Key Laboratory of Terahertz and Millimeter Waves City University of Hong Kong State Key Laboratory of Advanced Optical Communication Systems and Networks Department of Electronics Peking University National Mobile Communications Research Laboratory Southeast University State Key Laboratory of Millimeter Waves Southeast University Center of Intelligent Metamaterials Pazhou Laboratory

We propose a theoretical mechanism and new coding strategy to realize extremely accurate manipulations of nonlinear electromagnetic harmonics in ultrawide frequency band based on a time-domain digital coding metasurface(TDCM).Using the proposed mechanism and coding strategy,we design and fabricate a millimeter-wave(mmWave) TDCM,which is composed of reprogrammable meta-atoms embedded with positive-intrinsic-negative *** controlling the duty ratios and time delays of the digital coding sequences loaded on a TDCM,experimental results show that both amplitudes and phases of different harmonics can be engineered at will simultaneously and precisely in broad frequency band from 22 to33 GHz,even when the coding states are imperfect,which is in good agreement with theoretical *** on the fabricated high-performance TDCM,we further propose and experimentally realize a large-capacity mmWave wireless communication system,where 256 quadrature amplitude modulation,along with other schemes,is *** new wireless communication system has a much simpler architecture than the currently used mmWave wireless systems,and hence can significantly reduce the hardware *** believe that the proposed method and system architecture can find vast application in future mmWave and terahertz-wave wireless communication and radar systems.

关键词： metasurface time-domain digital coding accurate and broadband harmonic control 256 QAM millimeter-wave wireless communications

Discontinuous Galerkin Finite Element Method for a Nonlinear Boundary Value Problem

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Acta Mathematicae Applicatae Sinica 2014年第2期30卷 521-532页

作者： tie zhang Jian-Bao LI Department of Mathematics Northeastern University

In this paper, we investigate the a priori and a posteriori error estimates for the discontinuous Galerkin finite element approximation to a regularization version of the variational inequality of the second kind. We show the optimal error estimates in the DG-norm （stronger than the H1 norm） and the L2 norm, respectively. Furthermore, some residual-based a posteriori error estimators are established which provide global upper bounds and local lower bounds on the discretization error. These a posteriori analysis results can be applied to develop the adaptive DG methods.

关键词： variational inequality DG method optimal error estimate a posteriori error analysis