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The Mean Time to Absorption on Horizontal Partitioned Sierpinski Gasket Networks

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arXiv 2022年

作者： Zhang, Zhizhuo Wu, Bo Yu, Zuguo School of Mathematics Southeast University Nanjing210023 China School of Applied Mathematics Nanjing University of Finance and Economics Nanjing210023 China Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China

The random walk is one of the most basic dynamic properties of complex networks, which has gradually become a research hotspot in recent years due to its many applications in actual networks. An important characteristic of the random walk is the mean time to absorption, which plays an extremely important role in the study of topology, dynamics and practical application of complex networks. Analyzing the mean time to absorption on the regular iterative self-similar network models is an important way to explore the influence of self-similarity on the properties of random walks on the network. The existing literatures have proved that even local self-similar structures can greatly affect the properties of random walks on the global network, but they have failed to prove whether these effects are related to the scale of these self-similar structures. In this article, we construct and study a class of Horizontal Partitioned Sierpinski Gasket network model based on the classic Sierpinski gasket network, which is composed of local self-similar structures, and the scale of these structures will be controlled by the partition coefficient k. Then, the analytical expressions and approximate expressions of the mean time to absorption on the network model are obtained, which prove that the size of the self-similar structure in the network will directly restrict the influence of the self-similar structure on the properties of random walks on the network. Finally, we also analyzed the mean time to absorption of different absorption nodes on the network to find the location of the node with the highest absorption efficiency. Copyright © 2022, The Authors. All rights reserved.

关键词： Complex networks

Multifractal analysis of complex networks

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Chinese Physics B 2012年第8期21卷 080504-1-080504-1-080504-11页

作者： Wang, Dan-Ling Yu, Zu-Guo Anh, V. School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane QC 4001 Australia School of Mathematics and Physics University of Science and Technology Beijing Beijing 10083 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 China

Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal dimensions. Multifractal analysis is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we introduce a new box-covering algorithm for multifractal analysis of complex networks. This algorithm is used to calculate the generalized fractal dimensions Dq of some theoretical networks, namely scale-free networks, small world networks, and random networks, and one kind of real network, namely protein - protein interaction networks of different species. Our numerical results indicate the existence of multifractality in scale-free networks and protein - protein interaction networks, while the multifractal behavior is not clear-cut for small world networks and random networks. The possible variation of Dq due to changes in the parameters of the theoretical network models is also discussed. © 2012 Chinese Physical Society and IOP Publishing Ltd.

关键词： Small-world networks

A decoupling two-grid method for the time-dependent poisson-nernst-planck equations

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arXiv 2018年

作者： Shen, Ruigang Shu, Shi Yang, Ying Lu, Benzhuo School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan411105 China School of Mathematics and Computational Science Guangxi Colleges Universities Key Laboratory of Data Analysis and Computation Guangxi Key Laboratory of Cryptography and information Security Guilin University of Electronic Technology Guilin Guangxi541004 China Institute of Computational Mathematics and Scientific/Engineering Computing National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We study a two-grid strategy for decoupling the time-dependent Poisson-Nernst-Planck equations describing the mass concentration of ions and the electrostatic potential. The computational system is decoupled to smaller systems by using coarse space solutions at each time level, which can speed up the solution process compared with the finite element method combined with the Gummel iteration. We derive the optimal error estimates in L2 norm for both semi- and fully discrete finite element approximations. Based on the a priori error estimates, the error estimates in H1 norm are presented for the two-grid algorithm. The theoretical results indicate this decoupling method can retain the same accuracy as the finite element method. Numerical experiments including the Poisson-Nernst-Planck equations for an ion channel show the efficiency and effectiveness of the decoupling two-grid method. Copyright © 2018, The Authors. All rights reserved.

关键词： Finite element method

PRISTA-Net: Deep Iterative Shrinkage Thresholding Network for Coded Diffraction Patterns Phase Retrieval

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arXiv 2023年

作者： Liu, Aoxu Fan, Xiaohong Yang, Yin Zhang, Jianping The School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan411105 China The School of Mathematics and Computational Science Xiangtan University the Key Laboratory of Intelligent Computing & Information Processing the Ministry of Education Xiangtan411105 China The School of Mathematics and Computational Science Xiangtan University the National Center for Applied Mathematics in Hunan Xiangtan411105 China

The problem of phase retrieval (PR) involves recovering an unknown image from limited amplitude measurement data and is a challenge nonlinear inverse problem in computational imaging and image processing. However, many of the PR methods are based on black-box network models that lack interpretability and plug-and-play (PnP) frameworks that are computationally complex and require careful parameter tuning. To address this, we have developed PRISTA-Net, a deep unfolding network (DUN) based on the first-order iterative shrinkage thresholding algorithm (ISTA). This network utilizes a learnable nonlinear transformation to address the proximal-point mapping sub-problem associated with the sparse priors, and an attention mechanism to focus on phase information containing image edges, textures, and structures. Additionally, the fast Fourier transform (FFT) is used to learn global features to enhance local information, and the designed logarithmic-based loss function leads to significant improvements when the noise level is low. All parameters in the proposed PRISTA-Net framework, including the nonlinear transformation, threshold parameters, and step size, are learned end-to-end instead of being manually set. This method combines the interpretability of traditional methods with the fast inference ability of deep learning and is able to handle noise at each iteration during the unfolding stage, thus improving recovery quality. Experiments on Coded Diffraction Patterns (CDPs) measurements demonstrate that our approach outperforms the existing state-of-the-art methods in terms of qualitative and quantitative evaluations. Our source codes are available at https://***/liuaxou/PRISTA-Net. Copyright © 2023, The Authors. All rights reserved.

关键词： Mapping

A multigrid-reduction-in-time solver with a new two-level convergence for unsteady fractional Laplacian problems

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arXiv 2019年

作者： Yue, Xiaoqiang Pan, Kejia Zhou, Jie Weng, Zhifeng Shu, Shi Tang, Juan Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China School of Mathematics and Statistics HNP-LAMA Central South University Changsha410083 China School of Mathematical Sciences Fujian Province University Key Laboratory of Computation Science Huaqiao University Quanzhou362021 China

The multigrid-reduction-in-time (MGRIT) technique has proven to be successful in achieving higher run-time speedup by exploiting parallelism in time. The goal of this article is to develop and analyze a MGRIT algorithm, using FCF-relaxation with time-dependent time-grid propagators, to seek the finite element approximations of unsteady fractional Laplacian problems. The multigrid with line smoother proposed in [L. Chen, R. H. Nochetto, et al., Math. Comp. 85 (2016) 2583–2607] is chosen to be the spatial solver. Motivated by [B. S. Southworth, SIAM J. Matrix Anal. Appl. 40 (2019) 564–608], we provide a new temporal eigenvalue approximation property and then deduce a generalized two-level convergence theory which removes the previous unitary diagonalization assumption on the fine and coarse time-grid propagators required in [X. Q. Yue, S. Shu, et al., Comput. Math. Appl. 78 (2019) 3471–3484]. Numerical computations are included to confirm the theoretical predictions and demonstrate the sharpness of the derived convergence upper bound. Copyright © 2019, The Authors. All rights reserved.

关键词： Finite element method

Paired 2-Disjoint Path Covers of Burnt Pancake Graphs with Faulty Elements

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SSRN

SSRN 2024年

作者： Li, Pingshan Chen, Congzhen Liu, Xianglin Xiangtan University China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Key Laboratory of Intelligent Computing & Information Processing of Education China Key Laboratory for Computation and Simulation in Science and Engineering China National Center for Applied Mathematics in Hunan China Guangxi Vocational University of Agriculture Guangxi Nanning530007 China

It is a key issue in parallel processing to find $k$-disjoint paths in the underlying graph of an interconnected network such that these disjoint paths pass through all vertices of the network, this is known as paired $k$-disjoint path cover problems or unpaired $k$-disjoint path cover problems. In 2024, Dvo\v{r}\'{a}k and Gu (Theoretical Computer science, $986 (2024) 114327$) showed that there exist two disjoint paths whose vertices partition the vertex of the burnt pancake graph even if it contains at most $n-4$ faulty elements (vertices or edges) and they proposed an open problem: is it possible to improve the upper bound $n-4$ to $n-3$? In this paper, we provide a positive answer to this problem. © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

Enhancement of photoluminescence efficiency in GeSe ultrathin slab by thermal treatment and annealing: experiment and first-principles molecular dynamics simulations

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Scientific reports 2018年第1期8卷 17671页

作者： Yuliang Mao Xin Mao Hongquan Zhao Nandi Zhang Xuan Shi Jianmei Yuan Hunan Key Laboratory for Micro-Nano Energy Materials and Devices School of Physics and Optoelectronic Xiangtan University Hunan 411105 China. ylmao@***. Hunan Key Laboratory for Micro-Nano Energy Materials and Devices School of Physics and Optoelectronic Xiangtan University Hunan 411105 China. Chongqing institute of Green and Intelligent Technology Chinese Academy of Sciences Chongqing 401120 China. hqzhao@***. Chongqing institute of Green and Intelligent Technology Chinese Academy of Sciences Chongqing 401120 China. Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan 411105 China.

The effect of thermal treatment and annealing under different temperatures from 100 °C to 250 °C on the photoluminescence spectroscopy of the GeSe ultrathin slab is reported. After the thermal treatment and annealing under 200 °C, we found that the photoluminescence intensity of A exciton and B exciton in GeSe ultrathin slab is increased to twice as much as that in untreated case, while is increased by ~84% in the photoluminescence intensity of C exciton. Combined by our experimental work and theoretical simulations, our study confirms the significant role of thermal treatments and annealing in reducing surface roughness and removing the Se vacancy to form more compact and smoother regions in GeSe ultrathin slab. Our findings imply that the improved quality of GeSe surface after thermal treatments is an important factor for the photoluminescence enhancement.

关键词： Thermal Treatment First-principles Molecular Dynamics simulations Smoother Regions Reduced Surface Roughness GeSi Samples

Uniform convergence of multigrid finite element method for time-dependent riesz tempered fractional problem

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arXiv 2017年

作者： Chen, Minghua Bu, Weiping Qi, Wenya Wang, Yantao School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex Systems Lanzhou University Lanzhou730000 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China South University of Science and Technology of China Shenzhen518055 China

In this article a theoretical framework for the Galerkin finite element approximation to the time-dependent Riesz tempered fractional problem is provided without the fractional regularity assumption. Because the time-dependent problems should become easier to solve as the time step τ → 0, which correspond to the mass matrix dominant [R. E. Bank and T. Dupont, Math. Comp., 153 (1981), pp. 35-51]. Based on the introduced and analysis of the fractional τ-norm, the uniform convergence estimates of the V-cycle multigrid method with the time-dependent fractional problem is strictly proved, which means that the convergence rate of the V-cycle MGM is independent of the mesh size h and the time step τ. The numerical experiments are performed to verify the convergence with only O(NlogN) complexity by the fast Fourier transform method, where N is the number of the grid points. To the best of our knowledge, this is the first proof for the convergence rate of the V-cycle multigrid finite element method with τ → 0. Copyright © 2017, The Authors. All rights reserved.

关键词： Fast Fourier transforms

Design and Characterization of Low-Carbon Supersulfated Cement Prepared Using As-Received Electrolysis Manganese Dioxide Residue

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SSRN

SSRN 2023年

作者： Ma, Wenbo Bai, Tianwen Zhu, Wei Guo, Shuaicheng School of Mechanical Engineering and Mechanics Xiangtan University Xiangtan411105 China College of Civil Engineering Xiangtan University Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China Key Laboratory of Building Safety and Energy Efficiency of the Ministry of Education Hunan University Changsha410082 China International Science Innovation Collaboration Base for Green & Advanced Civil Engineering Materials of Hunan Province Hunan University Changsha410082 China Key Laboratory for Green & Advanced Civil Engineering Materials and Application Technology of Hunan Province College of Civil Engineering Hunan University Changsha410082 China

Utilizing electrolysis manganese dioxide residue (EMDR) to prepare the supersulfated cement can achieve effective waste recycling, and its application can reduce the carbon emission caused by Portland cement. This study aims to quantitatively build the correlation between the mechanical performance and cementitious matrix composition of EMDR-based supersulfated cement. The supersulfated cement containing clinker, slag and as received EMDR is designed and prepared based on the simplex centroid design method. The compressive strength, tensile strength and flexural strength of the EMDR based supersulfated cement paste were measured at 3-day, 7-day and 28-day ages. The compressive strength of the electrolysis manganese dioxide residue (EMDR) based supersulfated cement first increases and then decreases with the mass ratio between slag and EMDR. The added cement clinker can increase the compressive strength at 3-day and 7-day ages, but the 28-day age strength first decrease and then increase with the cement clinker content. Meanwhile, the flexural and tensile performances of the EMDR based supersulfated cement generally increase with the clinker content. The measured elastic modulus results indicated the added clinker could enhance the stiffness of the stiffness development. Then the strength development mechanisms of EMDR-based supersulfated cement are analyzed based on phase and microstructure characterization. It is found the clinker can accelerate the reaction rate between the slag and EMDR, and the consumption rate of the gypsum contained in EMDR. The calcium silicate hydrate (CSH) gel phase's contribution to tensile strength is more significant than that of ettringite phase. Based on the mechanism analysis, the index of [SO3]/[Al2O3] molar ratio is proposed for the matrix design of EMDR based SSC. This study can support the design and application of EMDR-based supersulfated cement. © 2023, The Authors. All rights reserved.

关键词： Aluminum oxide