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Nucleation and phase transition of decagonal quasicrystals

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arXiv 2024年

作者： Zhou, Tiejun Zhang, Lei Zhang, Pingwen Shi, An-Chang Jiang, Kai Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Beijing International Center for Mathematical Research Peking University Beijing100871 China School of Mathematics and Statistics Wuhan University Wuhan430072 China School of Mathematical Sciences Peking University Beijing100871 China Department of Physics and Astronomy McMaster University HamiltonL8S 4M1 Canada

In this work, we study the nucleation of quasicrystals from liquid or periodic crystals by developing an efficient order-order phase transition algorithm, namely the nullspace-preserving saddle search method. Specifically, we focus on nucleation and phase transitions of the decagonal quasicrystal (DQC) based on the Lifshitz-Petrich model. We present the nucleation path of DQC from the liquid and demonstrate one- and two-stage transition paths between DQC and periodic crystals. We provide a perspective of the group-subgroup phase transition and nucleation rates to understand the nucleation and phase transition mechanisms involving DQC. These results reveal the one-step and stepwise modes of symmetry breaking or recovery in the phase transition from DQC, where the stepwise modes are more probable. Copyright © 2024, The Authors. All rights reserved.

关键词： Quasicrystals

Nest-DGIL: Nesterov-optimized Deep Geometric Incremental Learning for CS Image Reconstruction

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arXiv 2023年

作者： Fan, Xiaohong Yang, Yin Chen, Ke Feng, Yujie 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 Hunan National Applied Mathematics Center Xiangtan411105 China The Centre for Mathematical ImagingTechniques Department of Mathematical Sciences The University of Liverpool Department of Mathematics and Statistics University of Strathclyde Glasgow United Kingdom The School of Mathematics and Computational Science Xiangtan University The Key Laboratory of Intelligent Computing & Information Processing The Ministry of Education Xiangtan411105 China

Proximal gradient-based optimization is one of the most common strategies to solve inverse problem of images, and it is easy to implement. However, these techniques often generate heavy artifacts in image reconstruction. One of the most popular refinement methods is to fine-tune the regularization parameter to alleviate such artifacts, but it may not always be sufficient or applicable due to increased computational costs. In this work, we propose a deep geometric incremental learning framework based on the second Nesterov proximal gradient optimization. The proposed end-to-end network not only has the powerful learning ability for high-/low-frequency image features, but also can theoretically guarantee that geometric texture details will be reconstructed from preliminary linear reconstruction. Furthermore, it can avoid the risk of intermediate reconstruction results falling outside the geometric decomposition domains and achieve fast convergence. Our reconstruction framework is decomposed into four modules including general linear reconstruction, cascade geometric incremental restoration, Nesterov acceleration, and post-processing. In the image restoration step, a cascade geometric incremental learning module is designed to compensate for missing texture information from different geometric spectral decomposition domains. Inspired by the overlap-tile strategy, we also develop a post-processing module to remove the block effect in patch-wise-based natural image reconstruction. All parameters in the proposed model are learnable, an adaptive initialization technique of physical parameters is also employed to make model flexibility and ensure converging smoothly. We compare the reconstruction performance of the proposed method with existing state-of-the-art methods to demonstrate its superiority. Our source codes are available at https://***/fanxiaohong/Nest-DGIL. Copyright © 2023, The Authors. All rights reserved.

关键词： Image reconstruction

Theory of polygonal phases self-assembled from T-shaped liquid crystalline molecules

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arXiv 2023年

作者： He, Zhijuan Wang, Xin Zhang, Pingwen Shi, An-Chang Jiang, Kai Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China School of Mathematics and Statistics Wuhan University Wuhan430072 China School of Mathematical Sciences Peking University Beijing100871 China Department of Physics and Astronomy McMaster University HamiltonONL8S 4M1 Canada

Extensive experimental studies have shown that numerous ordered phases can be formed via the self-assembly of T-shaped liquid crystalline molecules (TLCMs) composed of a rigid backbone, two flexible end chains and a flexible side chain. However, a comprehensive understanding of the stability and formation mechanisms of these intricately nanostructured phases remains incomplete. Here we fill this gap by carrying out a theoretical study of the phase behaviour of TLCMs. Specifically, we construct phase diagrams of TLCMs by computing the free energy of different ordered phases of the system. Our results reveal that the number of polygonal edges increases as the length of side chain or interaction strength increases, consistent with experimental observations. The theoretical study not only reproduces the experimentally observed phases and phase transition sequences, but also systematically analyzes the stability mechanism of the polygonal phases. Copyright © 2023, The Authors. All rights reserved.

关键词： Free energy

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

Summary of Lagrangrian Transport Models of Radionuclides in the Marine Environment 30

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Summary of Lagrangrian Transport Models of Radionuclides in ...

30th International Conference on Nuclear engineering, ICONE 2023

作者： Qu, Zhengzhe Nie, Baojie Wang, Liang Fan, Zhixiang Fu, Jia Fan, Qunchao Xie, Feng Institute of Nuclear and New Energy Technology Collaborative Innovation Center of Advanced Nuclear Energy Technology Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University Beijing100084 China School of Nuclear Science and Engineering Shanghai Jiao Tong University Shanghai200240 China Nuclear and Radiation Safety Center Ministry of Ecology and Environment Beijing100082 China State Environmental Protection Key Laboratory of Nuclear and Radiation Safety Regulatory Simulation and Validation Beijing100082 China School of Physics and Chemistry Research Center for Advanced Computation Xihua University Chengdu610039 China

ISBN: (纸本)9784888982566

The transport of radionuclides in the marine has been a hot issue of social concern since the Fukushima accident, especially the Japanese government announced to discharge the wastewater from Fukushima Daiichi Nuclear Power Plant (FDNPP) into Pacific Ocean in 2021, which can directly affect the environment and human health. Regarding inland nuclear power plants, freshwater habitats such as reservoirs and rivers could also be polluted by the radioactive effluents. An adequate model is expected to be instrumental in assessing radioactive pollution in various water environments. Scientists have proposed various models to simulate the advection and diffusion of radionuclides released by the Fukushima nuclear accident in the marine in different marine environmental conditions. In this study, the behaviors of radionuclides in water bodies are introduced, including advection, turbulent mixing, decay, and interaction with sedimentss and biota. The processes of Lagrangian models, which are commonly used to simulate the transport of radionuclides in the marine, are explained in detail. The research progress and application examples of radionuclide transport models in rivers and marines in recent years are systematically summarized. Current research can provide suggestions for the development of numerical models for describing the transport behavior of radionuclides in the marine environment. © 2023 by JSME.

关键词： Radioisotopes

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

Financing strategy of SMEs based on the shortage of environmental protection funds

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Procedia Computer science 2022年 199卷 1521-1528页

作者： Wang Haiyang Zhuang Xiaohui College of Automation and Electronic Engineering Qingdao University of Science & Technology Qingdao 260061 China School of Management Shandong Key Laboratory of Social Supernetwork Computation and Decision Simulation Shandong University Jinan Shandong 250100 China

With the development of society, environmental protection issues have received increasing attention. The increase in environmental protection requirements has greatly affected small and medium-sized enterprises（SMEs）. Due to the poor credit status and imperfect systems of SMEs, financing is difficult and expensive, which makes environmental protection funds insufficient, leading to outstanding environmental protection problems. In the supply chain, in order to maintain the stability of the supply chain, the core enterprises will help SMEs to alleviate the funding difficulties. This article starts from the supply chain financing of SMEs, explores the specific ways that core enterprises can help SMEs in supply chain financing, and analyses the feasibility of financing methods. Through analysis and demonstration, it is found that core enterprises can help SMEs with supply chain financing through prepayments, help small and medium-sized suppliers solve the problem of insufficient environmental protection funds, and core enterprises can obtain benefits from it.

关键词： Supply Chain Finance Small medium-sized enterprises (SMEs) Prepayments

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

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