The rate dependent response of a bistable chain at finite temperature |
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| Institution: | 1. Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel;2. Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544, USA;3. Department of Physics, University of California at San Diego, La Jolla, CA, USA;1. Department of Engineering Mechanics, Zhejiang University, Hangzhou, People’s Republic of China;2. Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Hangzhou, People’s Republic of China;1. Université Paris-Est, Laboratoire Navier (UMR 8205), CNRS, ENPC, IFSTTAR, 6 & 8 avenue Blaise Pascal, 77455 Marne-la-Vallée, France;2. Université Grenoble Alpes, 3SR, CNRS, Domaine Universitaire BP53, 38041 Grenoble Cedex 9, France;1. Division of Engineering and Applied Science, California Institute of Technology Pasadena, CA 91125, USA;2. Lehrstuhl für Festörpermechanik, Universität Siegen, D-57068 Siegen, Germany;3. VHIT S.p.A. – Società Unipersonale Bosch Group Italy (EAD2), Strada Vicinale delle Sabbione, 5, 26010 Offanengo, CR, Italy;1. Department of Computer Science, Loughborough University, UK;2. Department of Computer Science, Kiel University, Germany;1. Faculty of Aerospace Engineering, Technion, Haifa 32000, Israel;2. Faculty of Mechanical Engineering, Technion, Haifa 32000, Israel |
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| Abstract: | We study the rate dependent response of a bistable chain subjected to thermal fluctuations. The study is motivated by the fact that the behavior of this model system is prototypical to a wide range of nonlinear processes in materials physics, biology and chemistry. To account for the stochastic nature of the system response, we formulate a set of governing equations for the evolution of the probability density of meta-stable configurations. Based on this approach, we calculate the behavior for a wide range of parametric values, such as rate, temperature, overall stiffness, and number of elements in the chain. Our results suggest that fundamental characteristics of the response, such as average transition stress and hysteresis, can be captured by a simple law which folds the influence of all these factors into a single non-dimensional quantity. We also show that the applicability of analytical results previously obtained for single-well systems can be extended to systems having multiple wells by proper definition of rate and of the transition stress. |
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| Keywords: | Thermal fluctuations Energy barriers Bistable chain Hysteresis Transition stress |
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