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arXiv 2019年

作者： Xu, Yong Zhang, Hao Li, Yongge Zhou, Kuang Liu, Qi Kurths, Jürgen Department of Applied Mathematics Northwestern Polytechnical University Xi’an710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China Department of Engineering Mechanics Northwestern Polytechnical University Xi’an710072 China Center for Mathematical Sciences School of Mathematics and Statistics HuazhongUniversity of Science and Technology Wuhan430074 China Potsdam Institute for Climate Impact Research Potsdam14412 Germany Department of Physics Humboldt University Berlin Berlin12489 Germany

The probability density function of stochastic differential equations is governed by the Fokker-Planck (FP) equation. A novel machine learning method is developed to solve the general FP equations based on deep neural networks. The proposed algorithm does not require any interpolation and coordinate transformation, which is different from the traditional numercial methods. The main novelty of this paper is that penalty factors are introduced to overcome the local optimization for the deep learning approach, and the corresponding setting rules are given. Meanwhile, we consider a normalization condition as a supervision condition to effectively avoid that the trial solution is zero. Several numerical examples are presented to illustrate performances of the proposed algorithm, including one- and two-dimensional systems. All the results suggest that the deep learning is quite feasible and effective to calculate the FP equation. Further, influences of the number of hidden layers, the penalty factors, and the optimization algorithm are discussed in detail. These results indicate that the performances of the machine learning technique can be improved through constructing the neural networks appropriately. Copyright © 2019, The Authors. All rights reserved.

关键词： Deep neural networks

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Kinetostatic Modeling of Compliant Mechanisms Via Reduced-Mode Cosserat Rod Model

SSRN

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SSRN 2023年

作者： Wu, Ke Wang, Wei Li, Xin Hu, Junzhe Chen, Pengyu Cheng, Ran Sun, Qidi Liu, Lifu Zhou, Luna Xu, Xin Zhang, Shucheng Deng, Zicheng Chen, Rui Zheng, Gang INRIA Lille-Nord Europe 40 Avenue Halley Villeneuve d’Ascq59650 France State Key Laboratory of Mechanical Transmission University of Chongqing Chongqing400030 China LS2N - équipe ReV - Robotique Et Vivant Institut Mines Telecom Atlantique Nantes France Chongqing University China Chongqing University University of Cincinnati Joint Co-op Institute Chongqing University Chongqing400044 China Center for Robotics Research University of Cincinnati CincinnatiOH45221 United States MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China Hong Kong

Compliant mechanisms (CMs), which are normally composed of rigid blocks and flexible members, utilize the elastic deflection of all these built-in flexible members, totransfer motion, force and energy. In the current literature, geometrically nonlinear Euler Bernoulli beam theory and its related methods are commonly used for modelingthese flexible members. However, its governing ordinary differential equation (ODE) only considers the main contributor to beam deflections: bending, without taking careof shear and axial stretch along the beam. To take care of more possible strains, Cosserat rod theory, serves as a better alternative for high accuracy. However, it stillsuffers from relatively complex modeling and time-consuming computation. In this paper, we propose a reduced-mode Cosserat rod model to bypass the need ofconducting complex modeling, providing a more compact formulation. The detailed derivations are presented step by step, and we also propose a mode selectionmethod to meet the requirements of different engineering scenarios. Numerical examples are provided to verify the reduced-mode model as well as the feasibility ofmodeling CMs. In particular, modeling flexible springs and related mechanisms has been proved valid via this proposed model. © 2023, The Authors. All rights reserved.

关键词： Boundary value problems

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Reverse Aperiodic Resonance in Low- to High-Dimensional Bistable systems: A Complement to Stochastic Resonance Studies in Logic Circuits

arXiv

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arXiv 2024年

作者： Shen, Mengen Yang, Jianhua Sanjuán, Miguel A.F. Chen, Huatao Wang, Zhongqiu Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment School of Mechanical and Electrical Engineering China University of Mining and Technology Jiangsu Xuzhou221116 China Nonlinear Dynamics Chaos and Complex Systems Group Departamento de Física Universidad Rey Juan Carlos Tulipán s/n Móstoles Madrid28933 Spain Division of Dynamics and Control School of Mathematics and Statistics Shandong University of Technology Zibo255000 China School of Computer Science and Technology China University of Mining and Technology Jiangsu Xuzhou221116 China

As circuits continue to miniaturize, noise has become a significant obstacle to performance optimization. Stochastic resonance in logic circuits offers an innovative approach to harness noise constructively;however, current implementations are limited to basic logical functions such as OR, AND, NOR, and NAND, restricting broader applications. This paper introduces a three-dimensional (3D) coupling model to investigate the counterintuitive phenomena that arise in nonlinear systems under noise. Compared to the one-dimensional Langevin equation and the two-dimensional Duffing equation, the 3D coupling model features more adjustable parameters and coupling interactions, enhancing the system's dynamic behavior. The study demonstrates that increasing noise intensity triggers reverse aperiodic resonance, leading to signal phase reversal and amplitude amplification. This phenomenon is attributed to the motion of Brownian particles in a bistable potential well. Additionally, reverse aperiodic resonance addresses the lack of logical negation in traditional stochastic resonance systems by introducing noise-driven phase reversal, providing a novel alternative to conventional inverters. © 2024, CC BY.

关键词： Stochastic systems

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Harmonic-Gaussian double-well potential stochastic resonance with its application to enhance weak fault characteristics of machinery

arXiv

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arXiv 2023年

作者： Qiao, Zijian Chen, Shuai Lai, Zhihui Zhou, Shengtong Sanjuán, Miguel A.F. School of Mechanical Engineering and Mechanics Ningbo University Ningbo315211 China State Key Laboratory of Performance Monitoring and Protecting of Rail Transit Infrastructure East China Jiaotong University Nanchang330013 China Yangjiang529500 China Zhejiang Provincial Key Laboratory of Part Rolling Technology Ningbo315211 China Guangdong Provincial Key Laboratory of Micro/Nano Optomechatronics Engineering College of Mechatronics and Control Engineering Shenzhen University Shenzhen518060 China Nonlinear Dynamics Chaos and Complex Systems Group Departamento de Física Universidad Rey Juan Carlos Tulipán s/n Móstoles Madrid28933 Spain

Noise is ubiquitous and unwanted in detecting weak signals, which would give rise to incorrect filtering frequency-band selection in signal filtering-based methods including fast kurtogram, teager energy operators and wavelet packet transform filters and meanwhile would result in incorrect selection of useful components and even mode mixing, end effects and etc. in signal decomposition-based methods including empirical mode decomposition, singular value decomposition and local mean decomposition. On the contrary, noise in stochastic resonance (SR) is beneficial to enhance weak signals of interest embedded in signals with strong background noise. Taking into account that nonlinear systems are crucial ingredients to activate the SR, here we investigate the SR in the cases of overdamped and underdamped harmonic-Gaussian double-well potential systems subjected to noise and a periodic signal. We derive and measure the analytic expression of the output signal-to-noise ratio (SNR) and the steady-state probability density (SPD) function under approximate adiabatic conditions. When the harmonic-Gaussian double-well potential loses its stability, we can observe the antiresonance phenomenon, whereas adding the damped factor into the overdamped system can change the stability of the harmonic-Gaussian double-well potential, resulting that the antiresonance behavior disappears in the underdamped system. Then, we use the overdamped and underdamped harmonic-Gaussian double-well potential SR to enhance weak useful characteristics for diagnosing incipient rotating machinery failures. Theoretical and experimental results show that adjusting both noise intensity and system parameters can activate overdamped and underdamped harmonic-Gaussian double-well potential SR in which there is a bell-shaped peak for the SNR. Additionally, the underdamped harmonic-Gaussian double-well potential SR is independent of frequency-shifted and rescaling transform to process large machine parameter signal

关键词： Empirical mode decomposition

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Soft-Landing dynamics of a Type of Four-Legged Space Lander

SSRN

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SSRN 2024年

作者： Shi, Tengfei Shi, Tengfei Yang, Yinping Zhang, Zhijuan Liu, Cuicui Liu, Caishan Ma, Daolin Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province School of Mechanics and Aerospace Engineering Southwest Jiaotong University Chengdu610031 China State Key Laboratory for Turbulence and Complex Systems College of Engineering Peking University Beijing100871 China Institute of Dynamics and Control College of Mechanical Engineering and Applied Electronics Technology Beijing University of Technology Beijing100871 China China Academy of Space Technology Beijing100094 China School of Naval Architecture Ocean and Civil Engineering Shanghai Jiao Tong University Shanghai200240 China Key Laboratory of Marine Intelligent Equipment and System Ministry of Education Shanghai200240 China

Analyzing the landing dynamics response is essential for enhancing the success rate of surface explorations on Mars, the moon, or asteroids. This paper develops a comprehensive dynamics model for a space lander equipped with four sets of buffer legs, each consisting of a primary strut, two secondary struts, and a footpad, during its soft landing process. The degrees of freedom of the main body and the footpads are defined as generalized coordinates to describe the motion of the space lander. The compression force of the buffer struts is obtained by interpolating real experimental data, and the contact force between the footpad and the ground is calculated using Archimedes law for granular media. Then, the dynamical model for the lander in terms of minimal degrees of freedom can be constructed by applying the Lagrange equations of the second kind. The proposed dynamics model is validated by the experiments of a single-legged lander vertical touchdown and a four-legged lander free touchdown. Moreover, histories of buffer force, acceleration of the main body, and other key physical quantities are computed to investigate the landing process. This highly efficient and accurate dynamics model provides a method to perform extensive simulations to design and optimize a soft landing process. © 2024, The Authors. All rights reserved.

关键词： Landing

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Metamorphosis of discontinuity lines and rectification of magnetic flux avalanches in the presence of noncentrosymmetric pinning forces

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Physical Review B 2021年第22期103卷 224514-224514页

作者： M. Motta L. Burger Lu Jiang J. D. González Acosta Ž. L. Jelić F. Colauto W. A. Ortiz T. H. Johansen M. V. Milošević C. Cirillo C. Attanasio Cun Xue A. V. Silhanek B. Vanderheyden Departamento de Física Universidade Federal de São Carlos 13565-905 São Carlos São Paulo Brazil Montefiore Research Unit Department of Electrical Engineering and Computer Science Université de Liège 4000 Sart Tilman Belgium School of Aeronautics Northwestern Polytechnical University Xi'an 710072 China Facultad de Ingeniería Universidad del Magdalena Santa Marta Colombia Departement Fysica Universiteit Antwerpen Groenenborgerlaan 171 B-2020 Antwerpen Belgium Nokia Bell Labs Antwerp Belgium Department of Physics University of Oslo POB 1048 Blindern 0316 Oslo Norway CNR-SPIN c/o Università degli Studi di Salerno I-84084 Fisciano (Sa) Italy Dipartimento di Fisica “E.R. Caianiello” Università degli Studi di Salerno I-84084 Fisciano (Sa) Italy School of Mechanics Civil Engineering and Architecture and MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an 710072 China Experimental Physics of Nanostructured Materials Q-MAT CESAM Université de Liège B-4000 Sart Tilman Belgium

Considering a noncentrosymmetric pinning texture composed of a square array of triangular holes, the magnetic flux penetration and expulsion are investigated experimentally and theoretically. A direct visualization of the magnetic landscape obtained using a magneto-optical technique on a Nb film is complemented by a multiscale numerical modeling. This combined approach allows the magnetic flux dynamics to be identified from the single flux quantum limit up to the macroscopic electromagnetic response. Within the theoretical framework provided by time-dependent Ginzburg-Landau simulations, an estimation of the in-plane current anisotropy is obtained and its dependence with the radius of the curvature of hole vertices is addressed. These simulations show that current crowding plays an important role in channeling the flux motion, favoring hole-to-hole flux hopping rather than promoting interstitial flux displacement in between the holes. The resulting anisotropy of the critical current density gives rise to a distinct pattern of discontinuity lines for increasing and decreasing applied magnetic fields, in sharp contrast to the invariable patterns reported for centrosymmetric pinning potentials. This observation is partially accounted for by the rectification effect, as demonstrated by finite-element modeling. At low temperatures, where magnetic field penetration is dominated by thermomagnetic instabilities, highly directional magnetic flux avalanches with a fingerlike shape are observed to propagate along the easy axis of the pinning potential. This morphology is reproduced by numerical simulations. Our findings demonstrate that anisotropic pinning landscapes and, in particular, ratchet potentials produce subtle modifications to the critical state field profile that are reflected in the distribution of discontinuity lines.

关键词： Flux pinning Magneto-optical effect Monolayer films Superconductors Finite-element method Landau-Ginzburg theory

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Digital Metamaterials: Designing 3D Digital Metamaterial for Elastic Waves: From Elastic Wave Polarizer to Vibration control (Adv. Sci. 16/2019)

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Advanced Science 2019年第16期6卷 1970097-1970097页

作者： Huan Liu Quan Zhang Kai Zhang Gengkai Hu Huiling Duan State Key Laboratory of Turbulence and Complex Systems Department of Mechanics and Engineering Science BIC-ESAT College of Engineering Peking university Beijing 100871 China School of Aerospace Engineering Beijing Institute of Technology Beijing 100081 China Key Laboratory of Dynamics and Control of Flight Vehicle School of Aerospace Engineering Beijing Institute of Technology Beijing 100081 China CAPT HEDPS and IFSA Collaborative Innovation Center of MoE Peking University Beijing 100871 China

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Correction: COVID-19 Vaccine Tweets After Vaccine Rollout: Sentiment-Based Topic Modeling

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Journal of medical Internet research 2022年第3期24卷 e37841页

作者： Luwen Huangfu Yiwen Mo Peijie Zhang Daniel Dajun Zeng Saike He Fowler College of Business San Diego State University San Diego CA United States. Center for Human Dynamics in the Mobile Age San Diego State University San Diego CA United States. The State Key Laboratory of Management and Control for Complex Systems Institute of Automation Chinese Academy of Sciences Beijing China. University of Chinese Academy of Sciences Beijing China.

[This corrects the article DOI: 10.2196/31726.].

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26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 Antwerp, Belgium. 15-20 July 2017 Abstracts

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BMC NEUROSCIENCE 2017年第Sup1期18卷 95-176页

作者： [Anonymous] Department of Neuroscience Yale University New Haven CT 06520 USA Department Physiology & Pharmacology SUNY Downstate Brooklyn NY 11203 USA NYU School of Engineering 6 MetroTech Center Brooklyn NY 11201 USA Kings County Hospital Center Brooklyn NY 11203 USA Departament de Matemàtica Aplicada Universitat Politècnica de Catalunya Barcelona 08028 Spain Institut de Neurobiologie de la Méditerrannée (INMED) INSERM UMR901 Aix-Marseille Univ Marseille France Center of Neural Science New York University New York NY USA Aix-Marseille Univ INSERM INS Inst Neurosci Syst Marseille France Laboratoire de Physique Théorique et Modélisation CNRS UMR 8089 Université de Cergy-Pontoise 95300 Cergy-Pontoise Cedex France Department of Mathematics and Computer Science ENSAT Abdelmalek Essaadi’s University Tangier Morocco Laboratory of Natural Computation Department of Information and Electrical Engineering and Applied Mathematics University of Salerno 84084 Fisciano SA Italy Department of Medicine University of Salerno 84083 Lancusi SA Italy Dipartimento di Fisica Università degli Studi Aldo Moro Bari and INFN Sezione Di Bari Italy Data Analysis Department Ghent University Ghent Belgium Coma Science Group University of Liège Liège Belgium Cruces Hospital and Ikerbasque Research Center Bilbao Spain BIOtech Department of Industrial Engineering University of Trento and IRCS-PAT FBK 38010 Trento Italy Department of Data Analysis Ghent University Ghent 9000 Belgium The Wellcome Trust Centre for Neuroimaging University College London London WC1N 3BG UK Department of Electronic Engineering NED University of Engineering and Technology Karachi Pakistan Blue Brain Project École Polytechnique Fédérale de Lausanne Lausanne Switzerland Departement of Mathematics Swansea University Swansea Wales UK Laboratory for Topology and Neuroscience at the Brain Mind Institute École polytechnique fédérale de Lausanne Lausanne Switzerland Institute of Mathematics

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