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Charan H, Chattoraj J, Ciamarra MP, Procaccia I. Transition from Static to Dynamic Friction in an Array of Frictional Disks. PHYSICAL REVIEW LETTERS 2020; 124:030602. [PMID: 32031841 DOI: 10.1103/physrevlett.124.030602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2019] [Indexed: 06/10/2023]
Abstract
The nature of an instability that controls the transition from static to dynamical friction is studied in the context of an array of frictional disks that are pressed from above on a substrate. In this case the forces are all explicit and Newtonian dynamics can be employed without any phenomenological assumptions. We show that an oscillatory instability that had been discovered recently is responsible for the transition, allowing individual disks to spontaneously reach the Coulomb limit and slide with dynamic friction. The transparency of the model allows a full understanding of the phenomenon, including the speeds of the waves that travel from the trailing to the leading edge and vice versa.
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Affiliation(s)
- Harish Charan
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Joyjit Chattoraj
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Massimo Pica Ciamarra
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Itamar Procaccia
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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Protopopescu V, Barhen J. Non-Lipschitzian control algorithms for extended mechanical systems. CHAOS (WOODBURY, N.Y.) 2004; 14:400-407. [PMID: 15189068 DOI: 10.1063/1.1721111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We derive the properties of a general control algorithm [Braiman et al., Phys. Rev. Lett. 90, 094301 (2003)] for quantities describing global features of nonlinear extended mechanical systems. The control algorithm is based on the concepts of non-Lipschitzian dynamics and global targeting. We show that (i) certain average quantities of the controlled system can be driven-exactly or approximately-towards desired targets which become linearly stable attractors for the system's dynamics; (ii) the basins of attraction of these targets are reached in very short times; and (iii) while within reasonably broad ranges the time-scales of the control and of the intrinsic dynamics may be quite different, this disparity does not affect significantly the overall efficiency of the proposed scheme, up to natural fluctuations.
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Affiliation(s)
- V Protopopescu
- Center for Engineering Science Advanced Research, Computing and Computational Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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Jung E, Lenhart S, Protopopescu V, Braiman Y. Optimal control of the transient behavior of coupled solid-state lasers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:046222. [PMID: 12786475 DOI: 10.1103/physreve.67.046222] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2002] [Revised: 12/09/2002] [Indexed: 05/24/2023]
Abstract
We apply optimal control theory to substantially reduce transient times for transitions between in-phase and out-of-phase states in coupled solid-state lasers. The control is a time-varying optical field that is injected into the cavities of each laser. We have analytically derived the optimal control and numerically solved the optimality system. Numerical simulations indicate that transient times can be significantly reduced upon increasing the injection strength very briefly.
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Affiliation(s)
- E Jung
- Department of Mathematics, Konkuk University, Hwayang-dong, Gwangjin-gu, Seoul 143-701, Korea
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Braiman Y, Barhen J, Protopopescu V. Control of friction at the nanoscale. PHYSICAL REVIEW LETTERS 2003; 90:094301. [PMID: 12689223 DOI: 10.1103/physrevlett.90.094301] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2002] [Indexed: 05/24/2023]
Abstract
We propose a new algorithm to control frictional dynamics of a small array of particles towards preassigned values of the average sliding velocity. The control is based on the concepts of non-Lipschitzian dynamics and terminal attractor. Extensive numerical simulations illustrate the robustness, efficiency, and convenience of the algorithm.
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Affiliation(s)
- Y Braiman
- Center for Engineering Science Advanced Research, Computing and Computational Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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Zheng Z, Hu B. Collective topological dynamics in the frenkel-kontorova chains. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:4294-4299. [PMID: 11088958 DOI: 10.1103/physreve.62.4294] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/1999] [Revised: 03/31/2000] [Indexed: 05/23/2023]
Abstract
Topological dynamics of an array of harmonically coupled damped dc-driven nonlinear oscillators are studied by introducing a dynamical contraction factor and a deviation factor. Different dynamical transitions are identified, and topological changes for these transitions are studied. A bifurcation from the kink state to the kink-antikink-pair state is found, which relates the topological change to the spatiotemporal dynamics of the system. The presence of antikinks leads to the extension of the localized kink, and collisions of kinks and antikinks induce strong oscillations of the topology of the array.
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Affiliation(s)
- Z Zheng
- Department of Physics, Beijing Normal University, Beijing 100875, China and Department of Physics and Center for Nonlinear Studies, Hong Kong Baptist University, Hong Kong, China
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Affiliation(s)
- Markus Porto
- School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel
| | - Michael Urbakh
- School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel
| | - Joseph Klafter
- School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel
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Tovstopyat-Nelip I, Hentschel HG. Friction and noise-induced coherent structures in boundary lubrication. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:3318-24. [PMID: 11088104 DOI: 10.1103/physreve.61.3318] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/1999] [Indexed: 11/07/2022]
Abstract
We examine the effect of stick-slip boundary conditions on the friction generated by a molecularly thin layer of a liquid lubricant separating two plates. For one-dimensional compressible flows, noise-induced coherent dissipative structures on a micron scale are generated due to cooperation between the external drive and the thermal noise. As a function of the thermal noise these structures show a peak in their amplitudes similar to stochastic resonance. At low velocities a reduction in friction with increasing thermal noise is observed.
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Kornev KG, Neimark AV, Rozhkov AN. Foam in porous media: thermodynamic and hydrodynamic peculiarities. Adv Colloid Interface Sci 1999. [DOI: 10.1016/s0001-8686(99)00013-5] [Citation(s) in RCA: 66] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Braiman Y, Hentschel HG, Family F, Mak C, Krim J. Tuning friction with noise and disorder. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 59:R4737-40. [PMID: 11969507 DOI: 10.1103/physreve.59.r4737] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/1999] [Indexed: 04/18/2023]
Abstract
We present numerical and experimental evidence which demonstrates that under certain conditions friction can be reduced by spatial disorder and/or thermal noise. We discuss possible mechanisms for this behavior.
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Affiliation(s)
- Y Braiman
- Center for Engineering Science Advanced Research, Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
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Rozman MG, Urbakh M, Klafter J. Origin of stick-slip motion in a driven two-wave potential. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:6485-6494. [PMID: 9965870 DOI: 10.1103/physreve.54.6485] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Rozman MG, Urbakh M, Klafter J. Stick-Slip Motion and Force Fluctuations in a Driven Two-Wave Potential. PHYSICAL REVIEW LETTERS 1996; 77:683-686. [PMID: 10062876 DOI: 10.1103/physrevlett.77.683] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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