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Relationship between the orientation of texture and heteroepitaxy of diamond and related materials films on silicon single crystal and the valence electron structure of the interface

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Science China(Technological Sciences) 2007年第5期50卷 664-673页

作者： li zhilin li ZhiFeng HUANG Qin College of Materials Science and Engineering Beijing University of Chemical Technology Beijing 100029 China College of Materials Science and Engineering Beijing University of Chemical Technology Beijing 100029 China College of Materials Science and Engineering Beijing University of Chemical Technology Beijing 100029 China

Diamond and cubic boron nitride films have already been applied practically be- cause of their excellent properties. The specific orientations of the films have spe- cial meaning on their application in optics and microelectronics fields. In this paper, the relative electron density differences of the interface between the different crystal planes of silicon substrate and those of diamond and cubic boron films are calculated with the empirical electron theory in solids and molecules. Analyses on the calculation results show that in the range of the researched films, the smaller the relative electron density difference between the film and the substrate is, the stabler the film is in thermodynamics. Therefore, the electron density difference is the essential factor of determining the orientation of the texture and heteroepitaxy of the films. The deductions accord well with the experimental facts. The calcula- tion methods and the theory not only provide a new angle of view for the research of the growth mechanism of diamond film and cubic boron nitride film on the sili- con substrate, but also provide a possible direction for the prediction of the orien- tation of other films.

关键词： films, interface electron density, texture, heteroepitaxy, diamond, cubic boron nitride

Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions

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Numerical Mathematics(Theory,Methods and Applications) 2010年第1期3卷 23-39页

作者： Yan Gong zhilin li Department of Mathematics Limestone College Gaffney SC 29340 USA. Center For Research in Scientific Computation and Department of Mathematics North Carolina State University Raleigh NC 27695-8205 USA.

In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two *** non-body-fitted meshes are *** homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the *** such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is *** examples are presented to demonstrate that such methods have second order convergence.

关键词： Immersed interface finite element methods elasticity interface problems singularity removal homogeneous and non-homogeneous jump conditions level-set function.

Numerical Solutions of the System of Singular Integro-Differential Equations in Classical Hölder Spaces

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Advances in Applied Mathematics and Mechanics 2012年第6期4卷 737-750页

作者： Iurie Caraus zhilin li Department of Mathematics and Informatics Moldova State UniversityChisinauMoldova Department of Mathematics North Carolina State UniversityRaleighNC 27695USA School of Mathematics Sciences Nanjing Normal UniversityNanjing 210046JiangsuChina

New numerical methods based on collocation methods with the mechanical quadrature rules are proposed to solve some systems of singular integrodifferential equations that are defined on arbitrary smooth closed contours of the complex *** carry out the convergence analysis in classical Hölder spaces.A numerical example is also presented.

关键词： Collocation method classical Hölder space system of singular integro-differential equation Fejér points

An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods

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Communications in Computational Physics 2012年第7期12卷 515-527页

作者： zhilin li Peng Song Center for Research in Scientific Computation&Department of Mathematics North Carolina State UniversityRaleighNC 27695USA Nanjing Normal University China Operations Research Program North Carolina StateUniversityRaleighNC 27695USA

An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular *** interface is represented by the zero level set of a lipschitz functionϕ(x,y).Our adaptive mesh refinement is done within a small tube of|ϕ(x,y)|δwith finer Cartesian *** discrete linear system of equations is solved by a multigrid *** AMR methods could obtain solutions with accuracy that is similar to those on a uniform fine grid by distributing the mesh more economically,therefore,reduce the size of the linear system of the *** examples presented show the efficiency of the grid refinement strategy.

关键词： Adaptive mesh refinement immersed boundary method immersed interface method elliptic interface problem Cartesian grid method level set representation singular sources

FOURTH-ORDER COMPACT SCHEMES FOR HELMHOLTZ EQUATIONS WITH PIECEWISE WAVE NUMBERS IN THE POLAR COORDINATES

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Journal of Computational Mathematics 2016年第5期34卷 499-510页

作者： Xiaolu Su Xiufang Feng zhilin li School of Mathematics and Computer Science NingXia University YinChuan 750021 China Department of Mathematics North Carolina State University Raleigh NC 27695 USA Nanjing Normal University Nanjing China

In this paper, fourth-order compact finite difference schemes are proposed for solving Helmholtz equation with piecewise wave numbers in polar coordinates with axis-symmetric and in some cases that the solution depends both of independent variables. The idea of the immersed interface method is applied to deal with the discontinuities in the wave number and certain derivatives of the solution. Numerical experiments are included to confirm the accuracy and efficiency of the proposed method.

关键词： Helmholtz equation Compact finite difference schemes Polar coordinate Theimmersed interface method High order method.

AN L^(∞) SECOND ORDER CARTESIAN METHOD FOR 3D ANISOTROPIC INTERFACE PROBLEMS

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Journal of Computational Mathematics 2022年第6期40卷 882-912页

作者： Baiying Dong Xiufeng Feng zhilin li School of Mathematics and Statistics NingXia UniversityYinchuan 750021China School of Mathematics and Computer Science NingXia Normal UniversityGuyuan 756000China Department of Mathematics North Carolina State UniversityRaleighNC 27695-8205USA

A second order accurate method in the infinity norm is proposed for general three dimensional anisotropic elliptic interface problems in which the solution and its derivatives,the coefficients,and source terms all can have finite jumps across one or several arbitrary smooth *** method is based on the 2D finite element-finite difference(FEFD)method but with substantial differences in method derivation,implementation,and convergence *** of challenges is to derive 3D interface relations since there is no invariance anymore under coordinate system transforms for the partial differential equations and the jump conditions.A finite element discretization whose coefficient matrix is a symmetric semi-positive definite is used away from the interface;and the maximum preserving finite difference discretization whose coefficient matrix part is an M-matrix is constructed at irregular elements where the interface cuts *** aim to get a sharp interface method that can have second order accuracy in the point-wise *** show the convergence analysis by splitting errors into several *** numerical examples are presented to confirm the convergence analysis.

关键词： 3D anisotropic PDE Cartesian meshes Finite element method Finite difference method Maximum preserving IIM Convergence analysis

A survey on one-bit compressed sensing： theory and applications

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Frontiers of Computer Science 2018年第2期12卷 217-230页

作者： zhilin li Wenbo XU Xiaobo ZHANG Jiaru liN Key Lab of Universal Wireless Communications Ministry of Education Beijing University of Posts and Telecommunications Beijing 100876 China

In the past few decades, with the growing popularity of compressed sensing （CS） in the signal processing field, the quantization step in CS has received significant attention. Current research generally considers multi-bit quantization. For systems employing quantization with a sufficient number of bits, a sparse signal can be reliably recovered using various CS reconstruction algorithms. Recently, many researchers have begun studying the one- bit quantization case for CS. As an extreme case of CS, one- bit CS preserves only the sign information of measurements, which reduces storage costs and hardware complexity. By treating one-bit measurements as sign constraints, it has been shown that sparse signals can be recovered using certain reconstruction algorithms with a high probability. Based on the merits of one-bit CS, it has been widely applied to many fields, such as radar, source location, spectrum sensing, and wireless sensing network. In this paper, the characteristics of one-bit CS and related works are reviewed. First, the framework of one-bit CS is introduced. Next, we summarize existing reconstruction algorithms. Additionally, some extensions and practical applications of one-bit CS are categorized and discussed. Finally, our conclusions and the further research topics are summarized.

关键词： compressed sensing one-bit quantization sign information support consistency

Application of the C-Me segregating theory in solid alloys to ceramics

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Science China(Technological Sciences) 2007年第4期50卷 462-471页

作者： li zhilin HUANG Qin WU YuanQi li ZhiFeng College of Materials Science and Engineering Beijing University of Chemical TechnologyBeijing 100029China

Because of its excellent properties, zirconia ceramics has already been widely applied. Its phase transformation affects its properties. The research on the mechanism of its phase transformation is very important to control the phase transformation as well as its properties. The valence electron structure of cubic zirconia, tetragonal zirconia and monoclinic zirconia are calculated with the em-pirical electron theory in solids and molecules in this paper. The results show that the total numbers of the covalent electron pairs which form their strong bond framework are 3.19184, 3.45528 and 3.79625, respectively. According to the view-point of the C-Me segregating theory in solid alloys, it can be deduced that the phase transformation order of zirconia should be liquid phase→cubic phase→tetragonal phase→monoclinic phase. The deduction from valence electron struc-ture is completely in accordance with the experimental results, so the electron theory of phase transformation in alloys can be expanded to ceramics materials.

关键词： solid alloys ceramics valence electron structure phase transformation

Numerical Validations of the Tangent linear Model for the Lorenz Equations

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Computer Modeling in Engineering & Sciences 2019年第7期120卷 83-104页

作者： Tengjin Zhao Jing Zhang zhilin li Zhiyue Zhang School of Mathematical Sciences Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex SystemsNanjing Normal UniversityNanjing210023China Department of Mathematics North Carolina State UniversityRaleighNC 27695-8205USA

The validity of the tangent linear model(TLM)is studied numerically using the example of the Lorenz equations in this *** relationship between the limit of the validity time of the TLM and initial perturbations for the Lorenz equations is investigated using the Monte Carlo sampling method.A new error function between the nonlinear and the linear evolution of the perturbations is ***,numerical sensitivity analysis is carried to establish the relationship between parameters and the validity of the TLM,such as the initial perturbation,the prediction time,the time step size and so on,by the method of mathematical statistics.

关键词： Lorenz model tangent linear model nonlinear model Monte Carlo