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Acta Mechanica Sinica 2023年第3期39卷 142-152页

作者：赵云平侯秀慧张硕孙彤彤都琳邓子辰 Department of Applied Mathematics Northwestern Polytechnical UniversityXi'an 710072China Deparment of Engineering Mechanics Northwestern Polytechnical University Xi'an 710072China Ministry of Industry and Information Technology Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical UniversityXi'an 710072China

本文研究了非对称压电/石墨烯复合纳米板在粘弹性地基上、热环境及外部简谐激励作用下的动力学行为.根据Hamilton原理和Kirchhoff板理论,建立复合纳米板的动力学方程,并通过Galerkin方法对简支边界下的动力学方程进行求解,获得了一个包... 详细信息

本文研究了非对称压电/石墨烯复合纳米板在粘弹性地基上、热环境及外部简谐激励作用下的动力学行为.根据Hamilton原理和Kirchhoff板理论,建立复合纳米板的动力学方程,并通过Galerkin方法对简支边界下的动力学方程进行求解,获得了一个包含有二次非线性项的Duffing-Helmholtz方程.从解析和数值方面分别分析了非局部弹性参数、温度、粘弹性基体、电压以及纳米板的几何尺寸对系统非线性与线性频率比和非线性振动行为的影响.此外,本文揭示了系统的非对称性和二次非线性项之间的对应关系.本研究的动力学结果将为压电-石墨烯复合纳米谐振器力学性能的实验表征提供理论依据.

关键词： Asymmetric piezoelectric-graphene composite nanoplate Thermal environment Nonlinear forced vibration Wave number

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Patterns transition in a Subthalamopallidal Network under magnetic field effect

Patterns transition in a Subthalamopallidal Network under ma...

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第八届国际振动工程会议

作者： Zilu Cao Lin Du Honghui Zhang Zichen Deng Kangning An School of Mathematics and Statistics Northwestern Polytechnical University MIIT Key Laboratory of Dynamics and Control of Complex Systems School of Aeronautics Northwestern Polytechnical University

Subthalamic nucleus(STN) in basal ganglia is regarded as the role of origin of abnormal oscillation in Parkinson's Disease(PD). Synchronous and tremor-like activity of STN are the major features in PD. In this paper, we investigate the firing patterns of a subthalamopallidal model under magnetic field. Firstly, we study the effect of electromagnetic coefficient by timeseries, bifurcation analysis of interspike interval and synchronous coefficient. Results show that with the increasement of electromagnetic coefficient, the pattern of subthalamopallidal network could transfer from sparse irregular spiking to continue spiking with a stronger synchrony. It also finds that with a weaker input of globus pallidus, the network could transfer from asynchronous continue wave to synchronous continue spiking with stronger electromagnetic coefficient. Then, we research the effect of electromagnetic noise. Results indicate that noise could inhibit continue spiking, and the pattern of network transfers to episode wave. Conversely, it could induce episode wave from sparse spiking in the network. Finally, we characterize the cooperation of electromagnetic coefficient and electromagnetic noise by the statistical results of pattern transitions and synchrony, otherwise, we also give the area where two factors could adjust the abnormal oscillation of the network. This work helps to understand the activity of subthalamopallidal network under magnetic field and provide insights into the mechanisms behind the magnetic effect.

关键词： subthalamopallidal network magnetic field patterns transiton abnormal scillation

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Accelerated Stochastic Peaceman–Rachford Method for Empirical Risk Minimization

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Journal of the Operations Research Society of China 2023年第4期11卷 783-807页

作者： Jian-Chao Bai Feng-Miao Bian Xiao-Kai Chang Lin Du Research&Development Institute of Northwestern Polytechnical University in Shenzhen Shenzhen518057GuangdongChina School of Mathematics and Statistics Northwestern Polytechnical UniversityXi’an 710129ShaanxiChina Department of Mathematics The Hong Kong University of Science and TechnologyHong KongChina School of Science Lanzhou University of TechnologyLanzhou730050GansuChina School of Mathematics and Statistics the MIIT Key Laboratory of Dynamics and Control of Complex SystemsNorthwestern Polytechnical UniversityXi’an 710129ShaanxiChina

This work is devoted to studying an accelerated stochastic Peaceman–Rachford splitting method(AS-PRSM)for solving a family of structural empirical risk minimization *** objective function to be optimized is the sum of a possibly nonsmooth convex function and a finite sum of smooth convex component *** smooth subproblem in AS-PRSM is solved by a stochastic gradient method using variance reduction technique and accelerated techniques,while the possibly nonsmooth subproblem is solved by introducing an indefinite proximal term to transform its solution into a proximity *** a proper choice for the involved parameters,we show that AS-PRSM converges in a sublinear convergence rate measured by the function value residual and constraint violation in the sense of expectation and *** experiments on testing the popular graph-guided fused lasso problem in machine learning and the 3D CT reconstruction problem in medical image processing show that the proposed AS-PRSM is very efficient.

关键词： Empirical risk minimization Convex optimization Stochastic Peaceman-Rachford method Indefinite proximal term complexity

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Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

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Applied Mathematics and Mechanics(English Edition) 2021年第1期42卷 65-84页

作者： Jinzhong MA Yong XU Yongge LI Ruilan TIAN Shao juan MA J.KURTHS School of Mathematical Sciences Shanxi UniversityTaiyuan 030000China Department of Applied Mathematics Northwestern Polytechnical UniversityXi’an 710072China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical UniversityXi’an 710072China Department of Engineering Mechanics Shijiazhuang Tiedao UniversityShijiazhuang 050043China School of Mathematics&Information Science North Minzu UniversityYinchuan 750021China Potsdam Institute for Climate Impact Research Potsdam 14412Germany Department of Physics Humboldt University at BerlinBerlin 12489Germany

In real systems,the unpredictable jump changes of the random environment can induce the critical transitions(CTs)between two non-adjacent states,which are more *** an asymmetric Lévy-noise-induced tri-stable model with desirable,sub-desirable,and undesirable states as a prototype class of real systems,a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried *** first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability,which is named as the absorbed ***,a new concept of the parameter dependent basin of the unsafe regime(PDBUR)under the asymmetric Lévy noise is *** is an efficient tool for approximately quantifying the ranges of the parameters,where the noise-induced CTs from the desirable state directly to the undesirable one may *** importantly,it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.

关键词： tri-stable model asymmetric Lévy noise critical transition(CT) escape probability absorbed region parameter dependent basin of unsafe regime(PDBUR)

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Could Feedback-Based Self-Learning Help Solve Networked Prisoner's Dilemma?

Could Feedback-Based Self-Learning Help Solve Networked Pris...

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Joint 48th IEEE Conference on Decision and control and 28th Chinese control Conference

作者： Xiaojie Chen Feng Fu Long Wang State Key Laboratory for Turbulence and Complex Systems Center for Systems and ControlCollege of EngineeringPeking University Department of Zoology University of British Columbia Program for Evolutionary Dynamics Harvard University

We present a self-learning evolutionary Prisoner's Dilemma game model to study the evolution of cooperation in network-structured *** the evolutionary process,each agent updates its current strategy with a probability depending on the difference feedback between its actual score and score *** agent's score is a weighed mean of its payoff coming from its neighbors(social partners) and the payoff of its social partners obtaining from *** results show that the cooperation level in the structured populations increases with increasing the weight of partners' obtaining payoff in the *** interestingly,we find that very similar evolution of cooperation can respectively emerge in lattice,small-world and scale-free networks under the learningfeedback updating ***,we provide theoretical analysis and qualitative explanations for these numerical *** work may provide an effective way to solve the dilemma of cooperation for structured populations.

关键词： Could Feedback-Based Self-Learning Help Solve Networked Prisoner's Dilemma

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Stability Analysis of an Axially Moving Viscoelastic Beam Under Transverse Magnetic Fields and Thermal Loads

SSRN

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SSRN 2024年

作者： Wu, Sihan Xudong, Gu Zhao, Bingxin Deng, Zichen Department of Engineering Mechanics Northwestern Polytechnical University Xi’an China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an China

In this paper, an analytical method is proposed to study the stability of an axially moving viscoelastic beam under transverse magnetic fields and thermal loads. Firstly, the nonlinear control equation of the axially moving viscoelastic beam is derived by using Hamilton principle, in which the effects of thermal loads and magnetic field variations are considered based on the principle of magnetoelasticity and large deformation. Secondly, Galerkin’s method was applied to the derived continuous model to derive the discrete differential equations of each vibrating mode. Finally, the incremental harmonic balance (IHB) method was employed to determine the unstable regions in the parameter space. The influences of thermal load, axially moving velocity of the beam, viscosity coefficient, and magnetic field intensity on the regions of stability are investigated. It is found that the thermal loads, axially moving velocity and magnetic field intensity exert a significant influence on the unstable region. © 2024, The Authors. All rights reserved.

关键词： Viscoelasticity

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Frequency comb in a parametrically modulated micro-resonator

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Acta Mechanica Sinica 2022年第11期38卷 79-88页

作者： Xuefeng Wang Qiqi Yang Zhan Shi Ronghua Huan Weiqiu Zhu Xingjian Jing Zichen Deng Xueyong Wei Department of Engineering Mechanics MIIT Key Laboratory of Dynamics and Control of Complex SystemsNorthwestern Polytechnical UniversityXi’an710072China Department of Mechanics Key Laboratory of Soft Machines and Smart Devices of Zhejiang ProvinceZhejiang UniversityHangzhou310027China State Key Laboratory for Manufacturing Systems Engineering Xi’an Jiaotong UniversityXi’an710049China Department of Mechanical Engineering City University of Hong KongHong Kong999077China

In this paper,we report the frequency comb response experimentally and analytically in a rhombic micro-resonator with parametrical *** the electrostatically actuated rhombic micro-resonator is modulated axially by a low-frequency periodic excitation,a comb-like vibration response with few equidistant positioned fingers in the frequency domain is *** finger spacing of frequency comb response is exactly consistent with modulation frequency and the number and amplitude of the fingers can be tuned by modulation strength.A mixed frequency comb with extra comb fingers is further generated when the resonator is modulated simultaneously by two different low-frequency excitation *** adjusting the relation of the two modulation frequencies,unequal spacing frequency combs are achieved for the first time,which leads to a more flexible tunability of the comb spacing for different *** analysis based on the dynamic model well explains the corresponding observations.

关键词： Micro-resonator Nonlinear dynamics Vibration Parametrical modulation Frequency comb

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ADAPTIVE REGULATION TO INVARIANT SETS

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IFAC Proceedings Volumes 2005年第1期38卷 19-24页

作者： Ivan Tyukin Denis Efimov Cees van Leeuwen Laboratory for Perceptual Dynamics RIKEN Brain Science Institute 2-1 Hirosawa Wako-shi Japan Institute for Problems of Mechanical Engineering Laboratory for Control of Complex Systems V. O. Bolshoy 61 Saint-Petersburg Russia

A new framework for adaptive regulation of dynamical systems to invariant sets is proposed. The framework allows to adaptively steer the system trajectories to a desired non-equilibrium state without requiring knowled... 详细信息

关键词： adaptive systems non-equilibrium dynamics invariance algorithms in finite form

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Elucidating Platelet Interlocking Strengthening and Toughening Mechanism of Nacre: Coupled Effect of Platelet Size and Shape

SSRN

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SSRN 2024年

作者： Ji, Hongmei Liang, S.M. Li, Y.Y. Li, K.X. Yan, Yi Li, Xiao Wu Northeastern University Shenyang110819 China Department of Engineering Mechanics MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China

The platelet interlocking is universally recognized as a pivotal factor contributing to the remarkable toughness and strength of nacre in mollusk shells. Apart from variations in shape, platelets in nacre often exhibit changes in size as well. The current study has elucidated the coupled effect of platelet size and shape on the mechanical properties of nacre across different shells (Cristaria plicata, Pinctada margaritifera, and Pteria penguin) by mechanical tests and finite element (FEM) analyses. The P. penguin shell featuring inverse dovetail platelets and a minimal platelet thickness presents the most optimal mechanical properties among three shells. The FEM analyses reveal that the tensile strength of nacreous structures is primarily governed by the platelet size, while the shape of the platelets can optimize the distribution of stress within the structures. Although the dovetail platelets enhance stiffness by interlocking, they are prone to fracturing when the thickness of the platelets is minimal. Conversely, the inverse dovetail platelets are capable of optimizing stress distribution. Specifically, in the case of small sized platelets, these inverse dovetail platelets can not only effectively prevent fracturing but also redirect crack propagation along the interface, ultimately enhancing the mechanical properties of the structures. © 2024, The Authors. All rights reserved.

关键词： Tensile strength

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Model Predictive control Tailored to Epidemic Models

arXiv

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arXiv 2021年

作者： Sauerteig, Philipp Esterhuizen, Willem Wilson, Mitsuru Ritschel, Tobias K. S. Worthmann, Karl Streif, Stefan Technische Universität Ilmenau Institute for Mathematics Ilmenau Germany Technische Universität Chemnitz Automatic Control and System Dynamics Laboratory Germany Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany

We propose a model predictive control (MPC) approach for minimising the social distancing and quarantine measures during a pandemic while maintaining a hard infection cap. To this end, we study the admissible and the maximal robust positively invariant set (MRPI) of the standard SEIR compartmental model with control inputs. Exploiting the fact that in the MRPI all restrictions can be lifted without violating the infection cap, we choose a suitable subset of the MRPI to define terminal constraints in our MPC routine and show that the number of infected people decays exponentially within this set. Furthermore, under mild assumptions we prove existence of a uniform bound on the time required to reach this terminal region (without violating the infection cap) starting in the admissible set. The findings are substantiated based on a numerical case study. Copyright © 2021, The Authors. All rights reserved.

关键词： Model predictive control

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