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A Novel Perturbation-Theory-Based Approach for Free Vibrations of Bi-Directional Functionally Graded Porous Beams with a New Bi-Directional Pore Distribution Pattern

SSRN

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SSRN 2024年

作者： Chen, Chen Zhou, Lilin Li, Daokui College of Aerospace Science and Engineering National University of Defense Technology Hunan Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Hunan Changsha410073 China Aviation Engineering Institute Civil Aviation Flight University of China Sichuan Guanghan618307 China

Porosity defects usually exist in the functionally graded material (FGM) due to the inherent deficiencies in the fabricating process. Omission and miscalculation of the defects possibly resulting in overpredicted load-carrying capacities. The current assumption of pore distribution ignores the influence of material gradient which is not accurate enough. A new hypothesis of a bi-directional (2D) FG porosity distribution pattern that closer to the observation is proposed to characterize the feature. Moreover, instead of the numerical method, this study pioneers a fresh thought of perturbation approach (PA) customized for solving the governing equations of the bi-directional functionally graded porous (2D FGP) beam for the first time. First, A new hypothesis of 2D porosity distribution pattern is proposed. Second, a free vibration model of the 2D FGP beam is established by the rule of mixture, Timoshenko beam theory, and Hamilton’s principle. Then, by applying the PA, the 2D FGP beam is equivalent to an even porous homogenous beam and a small material perturbation to facilitate the computation of natural frequencies. The results of high-precision show that the PA is adaptive and applicable. Finally, discussions and analyses are conducted. It is found that, the pore distribution pattern has a significant impact on the natural frequency. The frequency of the new 2D FGP beam decreases with the increase of the material gradient, the porosity coefficient, and the power-law indexes. The influence of pores can be ignored in a rough calculation once the pore distribution is observed to approach the proposed uneven pattern. © 2024, The Authors. All rights reserved.

关键词： Natural frequencies

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MVMS-RCN: A Dual-Domain Unified CT Reconstruction with Multi-sparse-view and Multi-scale Refinement-correction

arXiv

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arXiv 2024年

作者： Fan, Xiaohong Chen, Ke Yi, Huaming 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 Centre for Mathematical Imaging Techniques Department of Mathematical Sciences The University of Liverpool LiverpoolL6972L United Kingdom The School of Mathematics and Computational Science Xiangtan University Hunan National Applied Mathematics Center Xiangtan411105 China The School of Mathematics and Computational Science Xiangtan University Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan411105 China

X-ray Computed Tomography (CT) is one of the most important diagnostic imaging techniques in clinical applications. Sparse-view CT imaging reduces the number of projection views to a lower radiation dose and alleviates the potential risk of radiation exposure. Most existing deep learning (DL) and deep unfolding sparse-view CT reconstruction methods: 1) do not fully use the projection data;2) do not always link their architecture designs to a mathematical theory;3) do not flexibly deal with multi-sparse-view reconstruction assignments. This paper aims to use mathematical ideas and design optimal DL imaging algorithms for sparse-view CT reconstructions. We propose a novel dual-domain unified framework that offers a great deal of flexibility for multi-sparse-view CT reconstruction through a single model. This framework combines the theoretical advantages of model-based methods with the superior reconstruction performance of DL-based methods, resulting in the expected generalizability of DL. We propose a refinement module that utilizes unfolding projection domain to refine full-sparse-view projection errors, as well as an image domain correction module that distills multi-scale geometric error corrections to reconstruct sparse-view CT. This provides us with a new way to explore the potential of projection information and a new perspective on designing network architectures. The multi-scale geometric correction module is end-to-end learnable, and our method could function as a plug-and-play reconstruction technique, adaptable to various applications. Extensive experiments demonstrate that our framework is superior to other existing state-of-the-art methods. Our source codes are available at https://***/fanxiaohong/MVMS-RCN. Copyright © 2024, The Authors. All rights reserved.

关键词： Geometry

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

arXiv

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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

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Enforced Freedom: Electric-Field-Induced Declustering of Ionic-Liquid Ions in the Electrical Double Layer

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Energy & Environmental Materials 2020年第3期3卷 414-420页

作者： Yufan Zhang Ting Ye Ming Chen Zachary A.H.Goodwin Guang Feng Jun Huang Alexei A.Kornyshev IEK-13 Institute of Energy and Climate ResearchForschungszentrum Jülich GmbHJülich 52425Germany State Key Laboratory of Coal Combustion School of Energy and Power EngineeringHuazhong University of Science and Technology(HUST)Wuhan 430074China Department of Chemistry Imperial College LondonMolecular Sciences Research HubWhite City CampusLondon W120BZUK Department of Physics Imperial College LondonSouth Kensington CampusLondon SW72AZUK Thomas Young Centre for Theory and Simulation of Materials Imperial College LondonSouth Kensington CampusLondon SW72AZUK Hunan Provincial Key Laboratory of Chemical Power Sources College of Chemistry and Chemical EngineeringCentral South UniversityChangsha 410083China

Ions in the bulk of solvent-free ionic liquids bind into ion pairs and *** competition between the propensity of ions to stay in a bound state,and the reduction of the energy when unbinding in electric field,determines the portion of free ions in the electrical double *** present the simplest possible mean-field theory to study this effect."Cracking"of ion pairs into free ions in electric field is accompanied by the change of the dielectric response of the ionic *** predictions from the theory are verified and further explored by molecular dynamics simulations.A particular finding of the theory is that the differential capacitance vs potential curve displays a bell shape,despite the low concentration of free charge carriers,because the dielectric response reduces the threshold concentration for the bell-to camelshape *** presented theory does not take into account overscreening and oscillating charge distributions in the electrical double *** in spite of the simplicity of the model,its findings demonstrate a clear physical effect:a preference to be a charged monopole rather than a dipole(or higher order multipole)in strong electric field.

关键词： differential capacitance ion pairs ionic liquids unbinding

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A directed continuous time random walk model with jump length depending on waiting time

The Scientific World Journal

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The Scientific World Journal 2014年第1期2014卷 182508页

作者： Shi, Long Yu, Zuguo Mao, Zhi Xiao, Aiguo 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 Institute of Mathematics and Physics Central South University of Forest and Technology Changsha Hunan 410004 China School of Mathematical Sciences Queensland University of Technology Brisbane QLD 4001 G.P.O. Box 2434 Australia

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P (x, t) of finding the walker at position x at time t is completely determined by the Laplace transform of the probability density function (t) of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived. © 2014 Long Shi et al.

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Phase behavior of symmetric diblock copolymers under 3D soft confinement

arXiv

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arXiv 2024年

作者： He, Zhijuan Huang, Jin Jiang, Kai Shi, An-Chang School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education 411105 China Laboratory of Mathematics and Complex Systems Ministry of Education School of Mathematical Sciences Beijing Normal University Beijing100875 China Department of Physics and Astronomy McMaster University HamiltonONL8S 4M1 Canada

The phase behavior of symmetric diblock copolymers under three-dimensional (3D) soft confinement is investigated using the self-consistent field theory. The soft confinement is realized in binary blends composed AB diblock copolymers and C homopolymers, where the copolymers self-assemble to form a droplet embedded in the homopolymer matrix. The phase behavior of the confined block copolymers is regulated by the degree of confinement and the selectivity of the homopolymers, resulting in a rich variety of novel structures. When the C homopolymers are neutral to the A- and B-blocks, stacked lamellae (SL) are formed where the number of layers increases with the droplet volume, resulting in a morphological transition sequence from Janus particle to square SL. When the C homopolymers are strongly selective to the B-blocks, a series of non-lamellar morphologies, including onion-, hamburger-, cross-, ring-, and cookie-like structures, are observed. A detailed free energy analysis reveals a first-order reversible transformation between SL and onion-like (OL) structures when the selectivity of the homopolymers is changed. Our results provide a comprehensive understanding of how various factors, such as the copolymer concentration, homopolymer chain length, degree of confinement, homopolymer selectivity, affect the self-assembled structures of diblock copolymers under soft 3D confinement. Copyright © 2024, The Authors. All rights reserved.

关键词： Free energy

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Multicontinuum Homogenization for Coupled Flow and Transport Equations

arXiv

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arXiv 2024年

作者： Ammosov, Dmitry Leung, W.T. Shan, Buzheng Huang, Jian Computational Technologies & Artificial Intelligence North-Eastern Federal University Yakutsk677980 Russia Department of Mathematics City University of Hong Kong Hong Kong Department of Mathematics Texas A&M University College StationTX77843 United States School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan Key Laboratory for Computation and Simulation in Science and Engineering Hunan Xiangtan411105 China

In this paper, we present the derivation of a multicontinuum model for the coupled flow and transport equations by applying multicontinuum homogenization. We perform the multicontinuum expansion for both flow and transport solutions and formulate novel coupled constraint cell problems to capture the multiscale property, where oversampled regions are utilized to avoid boundary effects. Assuming the smoothness of macroscopic variables, we obtain a multicontinuum system composed of macroscopic elliptic equations and convection-diffusion-reaction equations with homogenized effective properties. Finally, we present numerical results for various coefficient fields and boundary conditions to validate our proposed algorithm. Copyright © 2024, The Authors. All rights reserved.

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The subordinated processes controlled by a family of subordinators and corresponding Fokker-Planck type equations

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Journal of Statistical Mechanics: Theory and Experiment 2014年第12期2014卷

作者： Shi, Long Yu, Zu-Guo Huang, Hai-Lan Mao, Zhi Xiao, Ai-Guo Hunan Key Laboratory for Computation and Simulation in Science Ministry of Education Xiangtan University Xiangtan Hunan 411105 China School of Science Central South University of Forest and Technology Changsha Hunan 410004 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

In this work, we consider subordinated processes controlled by a family of subordinators which consist of a power function of a time variable and a negative power function of an α-stable random variable. The effect of parameters in the subordinators on the subordinated process is discussed. By suitable variable substitutions and the Laplace transform technique, the corresponding fractional Fokker-Planck-type equations are derived. We also compute their mean square displacements in a free force field. By choosing suitable ranges of parameters, the resulting subordinated processes may be subdiffusive, normal diffusive or superdiffusive. © 2014 IOP Publishing Ltd and SISSA Medialab srl.

关键词： diffusion

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

arXiv

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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

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Energy-Efficient Virtual Machine Placement in Data Centers Via Accelerated Genetic Algorithm with Improved Fitness computation

SSRN

引用

SSRN 2021年

作者： Hormozi, Elham Hu, Shuwen Ding, Zhe Tian, Yu-Chu Wang, You-Gan Yu, Zu-Guo Zhang, Weizhe School of Computer Science Queensland University of Technology GPO Box 2434 BrisbaneQLD4001 Australia School of Mathematical Sciences Queensland University of Technology GPO Box 2434 BrisbaneQLD4001 Australia Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China School of Cyberspace Science Harbin Institute of Technology Harbin China Cyberspace Security Research Center Peng Cheng Laboratory Shenzhen China Queensland University of Technology

Energy efficiency basically refers to how effectively energy can be utilised or consumed by any virtualised data centre giving cloud administrations. Since Genetic Algorithm (GA) is an acceptable method to solve the VM placement problem, this research formulates the Virtual Machine (VM) placement problem as a constrained optimisation problem. A considerable amount of residual resources is available for each new VM allocation, however they are distributed across multiple active PMs, rendering them inefficient. Our research focuses on improving a data centre’s energy and time efficiency by devising a technique to decrease PM’s residual resources and make them more valuable. As the most time consuming element of a GA is calculating the fitness function, this paper presents a new fitness function to simplify the fitness function calculation in GA. The results are compared to the standard GA and First Fit Decreasing (FFD) algorithm. The findings reveals a 8% energy savings for our GA compared to FFD and a 66% reduction in our GA execution time compared to the standard GA for virtualised data centres. The simulation experiments are conducted on small-, medium- and large-scale of the google data centre to demonstrate the effectiveness of our GA. © 2021, The Authors. All rights reserved.

关键词： Energy efficiency

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