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A high order composite scheme for the second order elliptic problem with nonlocal boundary and its fast algorithm

Applied Mathematics and Computation 2014年 227卷 212-221页

作者： Cunyun Nie Shi Shu Haiyuan Yu Qianjiang An Department of Mathematics and Physics The Hunan Institution of Engineering Xiangtan City Hunan 411104 China Hunan Key Laboratory for Computation & Simulation in Science and Engineering Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan University Hunan 411105 China Department of Mathematics The Institute of Tongren Guizhou 554300 China

The elliptic problem with nonlocal boundary condition is widely applied in the field of science and engineering. Firstly, we construct a linear finite element scheme for the nonlocal boundary problem, and derive the optimal L 2 error estimate. Then, based on the quadratic finite element and the extrapolation linear finite element methods, we present a composite scheme, and prove that it is convergent order three. Furthermore, we design an upper triangular preconditioning algorithm for the linear finite element discrete system. Finally, numerical results not only validate that the new algorithm is efficient, but also show that the new scheme is convergent order three, furthermore order four on uniform grids.

关键词： The elliptic problem with nonlocal boundary condition The finite element method An upper triangular preconditioner Algebraic multigrid method

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Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions

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Physical Review E 2014年第3期89卷 032814-032814页

作者： Jin-Long Liu Zu-Guo Yu Vo Anh Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the average degree exponent 〈λ〉 increases first and then decreases with the increase of Hurst index H of the associated FBMs; the relationship between H and 〈λ〉 can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e., the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension 〈dB〉 of recurrence networks decreases with the Hurst index H of the associated FBMs, and their dependence approximately satisfies the linear formula 〈dB〉≈2−H, which means that the fractal dimension of the associated recurrence network is close to that of the graph of the FBM. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5 possesses the strongest multifractality. In addition, the dependence relationships of the average information dimension 〈D(1)〉 and the average correlation dimension 〈D(2)〉 on the Hurst index H can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic

关键词： TOPOLOGICAL property FRACTAL analysis BROWNIAN motion CORRELATION (Statistics) RECURSIVE sequences (Mathematics) COMPUTER networks

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Control of Hopf bifurcation in Internet congestion control model via time-delayed feedback control

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Information Technology Journal 2013年第18期12卷 4493-4497页

作者： Xu, Xian-Fan Fan, Guo Ding, Da-Wei Yi, Liu Han, Liu-Jun School of Electronics and Information Engineering Anhui University 230601 Hefei China Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education Anhui University 230039 Hefei China

In this study, we are concerned with controlling Hopf bifurcation in a dual model of Internet congestion control algorithms. The stability of this system depends on a communication delay parameter, and Hopf bifurcation occurs when the communication delay passes through a critical value. Comparing with previous work, a time-delayed feedback method is proposed to postpone the onset of undesired Hopf bifurcation and improve stability of the dual model. Theoretical analysis and numerical simulation are provided to verify the effectiveness of our method. © 2013 Asian Network for Scientific Information.

关键词： Hopf bifurcation

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A consistent pixel-wise blur measure for partially blurred images

A consistent pixel-wise blur measure for partially blurred i...

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IEEE International Conference on Image processing

作者： Xianyong Fang Feng Shen Yanwen Guo Christian Jacquemin Jian Zhou Shanchun Huang Anhui University Hefei Anhui CN Key Lab. of Intelligent Computing and Signal Processing Anhui University Hefei China State Key Lab. for Novel Software Technology Nanjing University Nanjing China AMI LIMSI-CNRS Orsay France

Despite numerous efforts on blur measurement of partially blurred images, there still lacks an effective blur measure that is both pixel-wise and locally sharp consistent. The paper proposes a novel method with two contributions to overcome this limitation: 1) A new pixel-based blur metric, Multi-resolution Singular Value (MSV), which leverages the average singular value of high frequency bands to measure the blur of each pixel, and 2) a locally continuous strategy, maximum-likelihood estimation (MLE) based refinement, that ensures local continuity by imposing the local sharp consistency on pixel blur in a local correcting process. Experimental results show that our method is effective to smoothly measure the partially blurred images without local discontinuity.

关键词： Maximum likelihood estimation Equations Frequency measurement Image edge detection Mathematical model Wavelet transforms

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Thin-film solar cell's characteristic with periodic structure based on FDFD method

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Guangzi Xuebao/Acta Photonica Sinica 2014年第1期43卷

作者： Wei, Yuan Xiao, Feng Wu, Bo Huang, Zhi-Xiang Wu, Xian-Liang Key Laboratory of Intelligent Computing and Signal Processing Anhui University Hefei 230039 China Department of Physics and Electronic Engineering Hefei Normal University Hefei 230061 China

Using the new inhomogeneous medium interface equivalent parameter scheme combined with the finite-difference frequency-domain method, numerical analysis on mechanism of the optical properties of the thin-film solar cell with periodic structure was presented. The plasmon resonance condition was used to study the reflection, the transmission, the absorption characteristics, and the distribution of total field. In the low frequence point, the enhancement of the total field is obviousat the interface of the medium layer and the Ag layer, and the absorption increases significantly. Furthermore, the relationship between the enhancement factor, the structure, the incident wavelength and the angle of incidence was discussed, and its intrinsic physical mechanism was also analyzed. The enhancement factor is very large at low frequency and increases with the enhancement of the incident angle. The results show that the enhancement factor can increaseto 5.7. The proposed research work can provide a relevant theory and technical reference for the design and optimization of the actual organic thin-film solar cells.

关键词： Thin film solar cells

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Plasmonic nano-rod antennas based on fast electromagnetic method

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Guangzi Xuebao/Acta Photonica Sinica 2014年第3期43卷

作者： Fang, Ming Song, Kai-Hong Wang, Juan-Juan Huang, Zhi-Xiang Wu, Xian-Liang Key Laboratory of Intelligent Computing and Signal Processing Anhui University Hefei 230039 China Department of Physics and Electronic Engineering Hefei Normal University Hefei 230061 China

On the basis of the method of moments and segments sinusoidal basis functions, the impedance matrix of plasmonic nano-rod antennas can be obtained by solving the Green's function of the discretized current nodes in closed form formulations. Compared to the method of moments with different basis functions, this method can be utilized for reducing the size of matrix equations. The simulated results show that the polarization current and scattered fields can be computed accurately by employing a small-size matrix, which leads to a fast analysis for the scattering characteristic and resonant modes of nano-rod. The accuracy of the method was successfully demonstrated by comparing the simulated results with finite difference time domain technique, which is more time-consuming than the present method. Especially when dealing with the oblique incidence problem, the advantages become more apparently. The method is effective for the calculated models in this paper, and provides a fast and efficient electromagnetic analysis way for other nano-rod antennas and nanotube devices in different shapes when doing their scattering characteristics simulation.

关键词： Finite difference time domain method

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Systematic study of finite-difference frequency-domain method for spontaneous emission in a two-dimensional environment

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Guangzi Xuebao/Acta Photonica Sinica 2014年第1期43卷

作者： Qi, Jian-Nan Huang, Zhi-Xiang Wang, Han-Lin Wu, Xian-Liang Chu, Jing-Yang Zhou, Li Key Laboratory of Intelligent Computing and Signal Processing Anhui University Hefei 230039 China Department of Physics and Electronic Engineering Hefei Normal University Hefei 230061 China

The improvement of the efficiency of spontaneous emission will give great help to the research and manufacture of optoelectronic devices such as single photon resource. The local density of elestromagnetic states was calculated which is represented by the electric dyadic Green's function through the finite-difference frequency-domain method, the local density of states and the spontaneous emission rate in different metal materials, structures and wavelengths were analyzed, and the intrinsic physical mechanism was explored. The results show that the spontaneous emission rate of atoms can be greatly enhanced when surface plasmon polariton couple to the emiter, and different structure and the refractive indices of materials have different improvement of spontaneous emission rate. This research can provide important reference for the manufacture and optimization of optoelectronic devices.

关键词： Spontaneous emission

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Crank-Nicolson difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative

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Journal of Computational Physics 2013年 242卷 670-681页

作者： Wang, Dongling Xiao, Aiguo Yang, Wei Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China

In this paper, the Crank-Nicolson (CN) difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative is studied. The existence of this difference solution is proved by the Brouwer fixed point theorem. The stability and convergence of the CN scheme are discussed in the L2 norm. When the fractional order is two, all those results are in accord with the difference scheme developed for the classical non-fractional coupled nonlinear Schrödinger equations. Some numerical examples are also presented. © 2013 Elsevier Inc.

关键词： Nonlinear equations

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Support vector machine with mixture of kernels for automatic image annotation

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High Technology Letters 2013年第3期19卷 295-300页

作者：田东平 Zhao Xiaofei Shi Zhongzhi Key Laboratory of Intelligent Information Processing Institute of Computing Technology Chinese Academy of Sciences Graduate University of Chinese Academy of Sciences

Automatic image annotation(AIA)has become an important and challenging problem in computer vision due to the existence of semantic *** this paper,a novel support vector machine with mixture of kernels(SVM-MK)for automatic image annotation is *** one hand,the combined global and local block-based image features are extracted in order to reflect the intrinsic content of images as complete as *** the other hand,SVM-MK is constructed to shoot for better annotating *** results on Corel dataset show that the proposed image feature representation method as well as automatic image annotation classifier,SVM-MK,can achieve higher annotating accuracy than SVM with any single kernel and mi-SVM for semantic image annotation.

关键词： automatic image annotation （ AIA） support vector machine （ SVM） kernel func-tion principal component analysis （PCA）

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Multifractal analysis of weighted networks by a modified sandbox algorithm

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Scientific reports 2015年第1期5卷 17628页

作者： Yu-Qin Song Jin-Long Liu Zu-Guo Yu Bao-Gen Li Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China. College of Science Hunan University of technology Zhuzhou Hunan 412007 China. School of Mathematical Sciences Queensland University of Technology Brisbane Q4001 Australia.

Complex networks have attracted growing attention in many fields. As a generalization of fractal analysis, multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. Some algorithms for MFA of unweighted complex networks have been proposed in the past a few years, including the sandbox (SB) algorithm recently employed by our group. In this paper, a modified SB algorithm (we call it SBw algorithm) is proposed for MFA of weighted networks. First, we use the SBw algorithm to study the multifractal property of two families of weighted fractal networks (WFNs): "Sierpinski" WFNs and "Cantor dust" WFNs. We also discuss how the fractal dimension and generalized fractal dimensions change with the edge-weights of the WFN. From the comparison between the theoretical and numerical fractal dimensions of these networks, we can find that the proposed SBw algorithm is efficient and feasible for MFA of weighted networks. Then, we apply the SBw algorithm to study multifractal properties of some real weighted networks - collaboration networks. It is found that the multifractality exists in these weighted networks, and is affected by their edge-weights.

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