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Quasiperiodic Symmetric Tilt FCC Grain Boundaries

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arXiv 2024年

作者： Zou, Wenwen Zhang, Juan Xu, Jie 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 LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In this work, we investigate [110] symmetric tilt FCC grain boundaries (GBs) by a recently developed approach for quasiperiodic interfaces using the Landau-Brazovskii model. On special tilt angles associated with quadratic algebraic numbers, quasiperiodic GBs exhibit generalized Fibonacci substitution rules. The transition mechanism from quasiperiodic GBs to periodic GBs is explored through sphere offsets and spectral coalescence. We also propose an accurate method to calculate the GB energy for arbitrary tilt angle and analyze the factors affecting the GB energy. The revealing GB energy change is continue along with tilt angle except periodic GBs. © 2024, CC BY-NC-SA.

关键词： Grain boundaries

Nonlinear Constitutive Model of Hydroxyl Terminated Polybutadiene Propellant Based on Parallel Rheological Frameworks

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SSRN

SSRN 2024年

作者： Zhou, Shiming Xu, Yihang Li, Daokui College of Aerospace Science and Engineering National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Changsha410073 China

In this paper, the mechanical response of HTPB propellant is established based on the parallel rheological framework, and a widely applicable nonlinear constitutive model is constructed. Firstly, the mechanical response of HTPB propellant is decoupled into equilibrium response and viscous response by cyclic tensile-relaxation experiment;then, the molecular chain elongation response in the equilibrium response is constructed based on the non-affine eight-chain model, the cross-linking response in the molecular chain network is described based on the tube model, and the viscous response is predicted based on the relaxation rheology of molecular chain;in the end, the propellant equilibrium response and viscous response are integrated to form the total propellant response based on the parallel rheological framework. Finally, the propellant equilibrium response and viscous response are integrated through a parallel rheological framework, constituting the total mechanical response of the propellant. Comparison with the propellant cyclic tensile-relaxation test, and tensile and relaxation test data shows that the established constitutive model can accurately capture the nonlinear mechanical behaviour of HTPB propellant materials. The results of this paper lay a good foundation for accurately describing propellant mechanical properties and provide a method for rapid prediction and evaluation of propellant mechanical response. © 2024, The Authors. All rights reserved.

关键词： Polybutadienes

Analytical Delta-V Approximation for Nonlinear Programming of Multi-target Rendezvous and Flyby Trajectories

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arXiv 2024年

作者： Huang, An-Yi Li, Heng-Nian Luo, Ya-Zhong State Key Laboratory of Astronautic Dynamics Xi’an710043 China National University of Defense Technology Changsha410073 China College of Aerospace Science and Engineering Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions China

This study proposes an analytical Delta-V approximation of short-timetransfers based on the linear relative motion and a gradient-based nonlinear programming model of multi-target rendezvous and fly by trajectories. In previous studies, the Lambert's solution is commonly used to evaluate Delta-Vof short-duration transfers. In this study, to avoid the iteration process forobtaining the Lambert's solution and its gradient, the linear relative motion equations are applied to form an analytical two-point boundary value model for the near-circular orbit rendezvous problems. Although the relative motion equations are usually applicable when the two orbits are close enough, and the position and velocity errors would become more significant as the orbital differences increase, the errors of the velocity increments were proved acceptable in our simulations. Moreover, the analytical formula facilitates the calculation of the gradients to the start epoch and flight time, which are used to establish a nonlinear programming model for sequence optimization that gradient-based algorithms can easily solve. simulation results demonstrated that the analytical Delta-V approximation requires much less calculation than the Lambert's solution, and the proposed gradient-based nonlinear programming algorithms can obtain similar results in less time than previous methods. Copyright © 2024, The Authors. All rights reserved.

关键词： Nonlinear programming

IMPLICIT-EXPLICIT RUNGE-KUTTA-ROSENBROCK METHODS WITH ERROR ANALYSIS FOR NONLINEAR STIFF DIFFERENTIAL EQUATIONS

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Journal of Computational Mathematics 2021年第4期39卷 599-620页

作者： Bin Huang Aiguo Xiao Gengen Zhang School of Mathematics and Computational Science&Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105China South China Research Center for Applied Mathematics and Interdisciplinary Studies South China Normal UniversityGuangzhou 510631China

Implicit-explicit Runge-Kutta-Rosenbrock methods are proposed to solve nonlinear sti ordinary di erential equations by combining linearly implicit Rosenbrock methods with explicit Runge-Kutta ***,the general order conditions up to order 3 are ***,for the nonlinear sti initial-value problems satisfying the one-sided Lipschitz condition and a class of singularly perturbed initial-value problems,the corresponding errors of the implicit-explicit methods are *** last,some numerical examples are given to verify the validity of the obtained theoretical results and the e ectiveness of the methods.

关键词： Sti di erential equations Implicit-explicit Runge-Kutta-Rosenbrock method Order conditions Convergence

ADAPTIVE FINITE ELEMENT METHOD FOR PHASE FIELD FRACTURE MODELS BASED ON RECOVERY ERROR ESTIMATES

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arXiv 2024年

作者： Tian, Tian Chunyu, Chen Liang, He Huayi, Wei School of Mathematics and Computational Science Xiangtan University Xiangtan China411105 China School of Mathematics and Computational Science Xiangtan University National Center of Applied Mathematics Hunan Hunan Key Laboratory for Computation and Simulation in Science and Engineering China Xiangtan411105 China

The phase field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to address the mesh size dependency of the model. However, existing AFEM approaches for this application frequently rely on heuristic adjustments and empirical parameters for mesh refinement. In this paper, we introduce an adaptive finite element method based on a recovery type posteriori error estimates approach grounded in theoretical analysis. This method transforms the gradient of the numerical solution into a smoother function space, using the difference between the recovered gradient and the original numerical gradient as an error indicator for adaptive mesh refinement. This enables the automatic capture of crack propagation directions without the need for empirical parameters. We have implemented this adaptive method for the Hybrid formulation of the phase field model using the open-source software package FEALPy. The accuracy and efficiency of the proposed approach are demonstrated through simulations of classical 2D and 3D brittle fracture examples, validating the robustness and effectiveness of our *** Codes 65N50, 74R10 Copyright © 2024, The Authors. All rights reserved.

关键词： Mesh generation

NEURAL NETWORK-ENHANCED hr-ADAPTIVE FINITE ELEMENT ALGORITHM FOR PARABOLIC EQUATIONS

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arXiv 2025年

作者： Hao, Jiaxiong Huang, Yunqing Yi, Nianyu Yin, Peimeng Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan University Hunan Xiangtan411105 China Department of Mathematical Sciences University of Texas at El Paso El PasoTX79968 United States

In this paper, we present a novel enhancement to the conventional hr-adaptive finite element methods for parabolic equations, integrating traditional h-adaptive and r-adaptive methods via neural networks. A major challenge in hr-adaptive finite element methods lies in projecting the previous step’s finite element solution onto the updated mesh. This projection depends on the new mesh and must be recomputed for each adaptive iteration. To address this, we introduce a neural network to construct a mesh-free surrogate of the previous step finite element solution. Since the neural network is mesh-free, it only requires training once per time step, with its parameters initialized using the optimizer from the previous time step. This approach effectively overcomes the interpolation challenges associated with non-nested meshes in computation, making node insertion and movement more convenient and efficient. The new algorithm also emphasizes SIZING and GENERATE, allowing each refinement to roughly double the number of mesh nodes of the previous iteration and then redistribute them to form a new mesh that effectively captures the singularities. It significantly reduces the time required for repeated refinement and achieves the desired accuracy in no more than seven space-adaptive iterations per time step. Numerical experiments confirm the efficiency of the proposed algorithm in capturing dynamic changes of *** Codes 92B20, 65M60, 35K57 © 2025, CC BY.

关键词： Interpolation

A POSTERIORI ERROR ESTIMATORS FOR FOURTH ORDER ELLIPTIC PROBLEMS WITH CONCENTRATED LOADS

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arXiv 2024年

作者： Cao, Huihui Huang, Yunqing Yi, Nianyu Yin, Peimeng Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Department of Mathematical Sciences University of Texas at El Paso El PasoTX79968 United States

In this paper, we study two residual-based a posteriori error estimators for the C0 interior penalty method in solving the biharmonic equation in a polygonal domain under a concentrated load. The first estimator is derived directly from the model equation without any post-processing technique. We rigorously prove the efficiency and reliability of the estimator by constructing bubble functions. Additionally, we extend this type of estimator to general fourth-order elliptic equations with various boundary conditions. The second estimator is based on projecting the Dirac delta function onto the discrete finite element space, allowing the application of a standard estimator. Notably, we additionally incorporate the projection error into the standard estimator. The efficiency and reliability of the estimator are also verified through rigorous analysis. We validate the performance of these a posteriori estimates within an adaptive algorithm and demonstrate their robustness and expected accuracy through extensive numerical examples. © 2024, CC BY-NC-ND.

关键词： Delta functions

A C0-continuous nonconforming virtual element method for linear strain gradient elasticity

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arXiv 2024年

作者： Huang, Jianguo Yu, Yue School of Mathematical Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

A robust C0-continuous nonconforming virtual element method (VEM) is developed for a boundary value problem arising from strain gradient elasticity in two dimensions, with the family of polygonal meshes satisfying a very general geometric assumption given in Brezzi et al. (2009) and Chen and Huang (2018). The stability condition of the VEMs is derived by establishing Korn-type inequalities and inverse inequalities. Some crucial commutative relations for locking-free analysis as in elastic problems are derived. The sharp and uniform error estimates with respect to both the microscopic parameter and the Lamé coefficient are achieved in the lowest-order case, which is also verified by numerical *** Codes 65N12, 65N15, 65N22, 65N30 © 2024, CC BY-NC-ND.

关键词： Boundary value problems

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

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

2021 China Automation Congress, CAC 2021

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

ISBN: (纸本)9781665426473

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. © 2021 IEEE

关键词： Controllers