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Tilt grain boundaries of hexagonal structures: a spectral viewpoint

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arXiv 2021年

作者： Jiang, Kai Si, Wei Xu, Jie School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan411105 China Chinese Academy of Sciences Beijing China

We propose a spectral viewpoint for grain boundaries that are generally quasiperiodic. To accurately capture the spectra computationally, it is crucial to adopt the projection method for quasiperiodic functions. Armed with the Lifshitz–Petrich free energy, we take the spectral viewpoint to examine tilt grain boundaries of the hexagonal phase. Several ingredients of grain boundaries are extracted, which are not easy to obtain from real-space profiles. We find that only a few spectra substantially contribute to the formation of grain boundaries. Their linear relation to the intrinsic spectra of the bulk hexagonal phase is independent of the tilt angle. By examining the feature of the spectral intensities, we propose a definition of the interface width. The widths calculated from this definition are consistent with visual *** Codes 65N35, 70H12, 82B24 © 2021, CC BY.

关键词： Grain boundaries

A convergence analysis of a structure-preserving gradient flow method for the all-electron Kohn-Sham model

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arXiv 2023年

作者： Shen, Yedan Wang, Ting Zhou, Jie Hu, Guanghui School of Mathematics and Information Science Guangzhou University Guangzhou China Faculty of Science and Technology University of Macau China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan China School of Mathematical Computational Sciences Xiangtan University Xiangtan China Zhuhai UM Science & Technology Research Institute Zhuhai China Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications University of Macau China

In [Dai et al, Multi. Model. Simul., 2020], a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn–Sham density functional theory, based on which a linearized method was developed in [Hu, et al, EAJAM, accepted] for further improving the numerical efficiency. In this paper, a complete convergence analysis is delivered for such a linearized method for the all-electron Kohn–Sham model. Temporally, the convergence, the asymptotic stability, as well as the structure-preserving property of the linearized numerical scheme in the method is discussed following previous works, while spatially, the convergence of the h-adaptive mesh method is demonstrated following [Chen et al, Multi. Model. Simul., 2014], with a key study on the boundedness of the Kohn–Sham potential for the all-electron Kohn–Sham model. Numerical examples confirm the theoretical results very well. Copyright © 2023, The Authors. All rights reserved.

关键词： Asymptotic stability

GLOBAL OPTIMIZATION FOR THE PORTFOLIO SELECTION MODEL WITH HIGH-ORDER MOMENTS

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arXiv 2022年

作者： Yang, Liu Yang, Yi Zhong, Suhan Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University School of Mathematics and Computational Sciences Xiangtan University Hunan Xiangtan411105 China School of Mathematics Hunan City University Hunan Yiyang413000 China Department of Mathematics Texas A&M University College StationTX77843-3368 United States

In this paper, we study the global optimality of polynomial portfolio optimization (PPO). The PPO is a kind of portfolio selection model with high-order moments and flexible risk preference parameters. We introduce a perturbation sample average approximation method, which can give a robust approximation of the PPO in form of linear conic optimization. The approximated problem can be solved globally with Moment-SOS relaxations. We summarize a semidefinite algorithm, which can be used to find reliable approximations of the optimal value and optimizer set of the PPO. Numerical examples are given to show the efficiency of the algorithm. Copyright © 2022, The Authors. All rights reserved.

关键词： Global optimization

Design and Adaptive Finite Element simulation of Conformal Transformation Optics Devices with Isotropic Materials

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SSRN

SSRN 2022年

作者： Yang, Wei He, Bin Wang, Hao Department of Mathematics Lanzhou Jiaotong University Gansu Lanzhou730070 China School of Mathematics and Statistics Anhui Normal University Anhui Wuhu241000 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Traditional transform optical devices are designed from anisotropic magnetic materials which are difficult to fabricate. In this paper, we design and simulate a conformal carpet invisible cloak and bending waveguide device with isotropic material. According to the existing conformal coordinate transformation, we deduce the perfect parameters required by the conformal device. And the finite element method and error analysis of the model equation and the basic process of adaptive algorithm are given. We first simulated a carpet cloak and bending waveguide device with perfect parameters;then we used the idea of parameter segmentation to design a carpet cloak that requires 35 isotropic materials and use the idea of layering to design the conformal bending waveguide device, and relevant numerical results are presented;finally, we designed the adaptive finite element algorithm to realize the numerical simulation of Maxwell's equations in isotropic material isotropic material. © 2022, The Authors. All rights reserved.

关键词： Error analysis

A Jacobi Collocation Method for the Fractional Ginzburg-Landau Differential Equation

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Advances in Applied Mathematics and Mechanics 2020年第1期12卷 57-86页

作者： Yin Yang Jianyong Tao Shangyou Zhang Petr V.Sivtsev Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtanHunan 411105China Department of Mathematical Sciences University of DelawareNewarkDE 19716USA International Scientific and Research Laboratory of Multiscale Model Reduction and High Performance Computing Ammosov North Eastern UniversityKulakovskogo677013YakutskRussia

In this paper,we design a collocation method to solve the fractional Ginzburg-Landau equation.A Jacobi collocation method is developed and implemented in two ***,we space-discretize the equation by the Jacobi-Gauss-Lobatto collocation(JGLC)method in one-and two-dimensional *** equation is then converted to a system of ordinary differential equations(ODEs)with the time variable based on *** second step applies the Jacobi-Gauss-Radau collocation(JGRC)method for the time ***,we give a theoretical proof of convergence of this Jacobi collocation method and some numerical results showing the proposed scheme is an effective and high-precision algorithm.

关键词： The fractional Ginzburg-Landau equation Jacobi collocation method convergence

Computationally efficient sandbox algorithm for multifractal analysis of large-scale complex networks with tens of millions of nodes

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Physical Review E 2021年第4期103卷 043303-043303页

作者： Yuemin Ding Jin-Long Liu Xiaohui Li Yu-Chu Tian Zu-Guo Yu Department of Energy and Process Engineering Norwegian University of Science and Technology 7049 Trondheim Norway School of Computer Science Queensland University of Technology Brisbane QLD 4000 Australia Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China School of Information Science and Engineering Wuhan University of Science and Technology Wuhan Hubei 430081 China

Among various algorithms of multifractal analysis (MFA) for complex networks, the sandbox MFA algorithm behaves with the best computational efficiency. However, the existing sandbox algorithm is still computationally expensive for MFA of large-scale networks with tens of millions of nodes. It is also not clear whether MFA results can be improved by a largely increased size of a theoretical network. To tackle these challenges, a computationally efficient sandbox algorithm (CESA) is presented in this paper for MFA of large-scale networks. Distinct from the existing sandbox algorithm that uses the shortest-path distance matrix to obtain the required information for MFA of networks, our CESA employs the compressed sparse row format of the adjacency matrix and the breadth-first search technique to directly search the neighbor nodes of each layer of center nodes, and then to retrieve the required information. A theoretical analysis reveals that the CESA reduces the time complexity of the existing sandbox algorithm from cubic to quadratic, and also improves the space complexity from quadratic to linear. Then the CESA is demonstrated to be effective, efficient, and feasible through the MFA results of (u,v)-flower model networks from the fifth to the 12th generations. It enables us to study the multifractality of networks of the size of about 11 million nodes with a normal desktop computer. Furthermore, we have also found that increasing the size of (u,v)-flower model network does improve the accuracy of MFA results. Finally, our CESA is applied to a few typical real-world networks of large scale.

关键词： Network formation & growth Fractals Fractal dimension characterization

Are Electric Vehicles Greener than Hybrid Electric Vehicles in Carsharing? Insights from Large-Scale Multi-Objective simulation-Optimization

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SSRN

SSRN 2024年

作者： Li, Yan Hu, Lu Li, Haobin Chew, Ek Peng Li, Hao Zhu, Juanxiu Department of Industrial Systems Engineering and Management National University of Singapore Singapore Centre of Excellence in Modelling and Simulation for Next Generation Ports National University of Singapore Singapore School of Transportation and Logistics Southwest Jiaotong University Chengdu China School of Traffic and Transportation Engineering Changsha University of Science and Technology Changsha China Hunan Key Laboratory of Smart Roadway and Cooperative Vehicle Infrastructure Systems Changsha University of Science and Technology Changsha China School of Management Xihua University Chengdu China

Hybrid electric vehicles (HEVs) are perceived as transitional products bridging the gap between fueled vehicles and electric vehicles (EVs) because people intuitively believe that EVs are more environmentally friendly than HEVs. But is this perception true in the context of carsharing services (CSSs)? This paper pioneers a general large-scale multi-objective simulation-optimization (MOSO) method to explore the values of deploying HEVs in CSSs. We firstly develop a physically logical simulation model, emulating operations of CSSs and capturing mesoscopic dynamics of shared vehicles in a link-based traffic network. This model adopts an event-driven discrete-event mechanism, enhancing efficiency while maintaining high fidelity. Subsequently, we design a simulation-optimization framework aimed at achieving Pareto optimality by jointly optimizing station capacity, fleet size, and trip pricing. The goal is twofold: to maximize operational profits and to minimize carbon emissions, thereby quantitatively analysing the potential of shared HEVs (SHEVs). To tackle the high-dimensional MOSO problem, we propose a general algorithm that incorporates the multiple gradient descent algorithm with the simultaneous perturbation stochastic approximation algorithm. Furthermore, we derive its analytical expression for bi-objective optimization problems. We theoretically prove and practically demonstrate its strong global convergence. The efficiency of this method was validated through large-scale computational experiments conducted in Chengdu, Sichuan Province, involving 66,710 decision variables. These experiments showcased the method's superiority over existing MOSO algorithms. Several groups of sensitivity experiments focusing on vehicle types and traffic scenarios reveal some interesting findings. (1) Regardless of the increase in travel distances, SHEVs, which can be viewed as shared EVs (SEVs) without range anxiety (RA), continue to primarily rely on electricity rather than fuel fo

关键词： Stochastic systems

The Control Design of Space Flying Net Robot System Based on RBF Network

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The Control Design of Space Flying Net Robot System Based on...

Chinese Automation Congress (CAC)

作者： Xu Zhang Yuanhe Liu Yan’gang Liang Kebo Li Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions College of Aerospace Science and Engineering National University of Defense Technology Changsha China

ISBN: (纸本)9781665426480

Space Flying Net Robot System (SFNRS) is a new capture method of space debris. In this paper, the SFNRS dynamic equations are established by using the lumped mass method. The previous studies about controller design assumed that the mass of the maneuvering unit in SFNRS is known and a constant while it is unknown in fact. In addition, the upper boundary of tension in the space net is often assumed as a known constant, but it is difficult to get the value. In this paper, the radial basis function (RBF) network is used to design a controller in order to overcome the shortcomings above. Finally, the simulation is carried out to verify the effectiveness and the robustness of the proposed method.

关键词： Upper bound Control design Space debris simulation Radial basis function networks Aerospace electronics Robustness

Diffeomorphic image registration with an optimal control relaxation and its implementation

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arXiv 2021年

作者： Zhang, Jianping Li, Yanyan School of Mathematics and Computational Science Hunan National Center for Applied Mathematics Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Image registration has played an important role in image processing problems, especially in medical imaging applications. It is well known that when the deformation is large, many variational models cannot ensure diffeomorphism. In this paper, we propose a new registration model based on an optimal control relaxation constraint for large deformation images, which can theoretically guarantee that the registration mapping is diffeomorphic. We present an analysis of optimal control relaxation for indirectly seeking the diffeomorphic transformation of Jacobian determinant equation and its registration applications, including the construction of diffeomorphic transformation as a special space. We also provide an existence result for the control increment optimization problem in the proposed diffeomorphic image registration model with an optimal control relaxation. Furthermore, a fast iterative scheme based on the augmented Lagrangian multipliers method (ALMM) is analyzed to solve the control increment optimization problem, and a convergence analysis is followed. Finally, a grid unfolding indicator is given, and a robust solving algorithm for using the deformation correction and backtrack strategy is proposed to guarantee that the solution is diffeomorphic. Numerical experiments show that the registration model we proposed can not only get a diffeomorphic mapping when the deformation is large, but also achieves the state-of-the-art performance in quantitative evaluations in comparing with other classical models. Copyright © 2021, The Authors. All rights reserved.

关键词： Dynamical systems