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Collective transient ratchet transport induced by many elastically interacting particles. Sci Rep 2021; 11:16178. [PMID: 34376759 PMCID: PMC8355274 DOI: 10.1038/s41598-021-95654-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Accepted: 07/22/2021] [Indexed: 11/21/2022] Open
Abstract
Several dynamical systems in nature can be maintained out-of-equilibrium, either through mutual interaction of particles or by external fields. The particle’s transport and the transient dynamics are landmarking of such systems. While single ratchet systems are genuine candidates to describe unbiased transport, we demonstrate here that coupled ratchets exhibit collective transient ratchet transport. Extensive numerical simulations for up to \documentclass[12pt]{minimal}
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\begin{document}$$N=1024$$\end{document}N=1024 elastically interacting ratchets establish the generation of large transient ratchet currents (RCs). The lifetimes of the transient RCs increase with N and decrease with the coupling strength between the ratchets. We demonstrate one peculiar case having a coupling-induced transient RC through the asymmetric destruction of attractors. Results suggest that physical devices built with coupled ratchet systems should present large collective transient transport of particles, whose technological applications are undoubtedly appealing and feasible.
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Carusela MF, Malgaretti P, Rubi JM. Antiresonant driven systems for particle manipulation. Phys Rev E 2021; 103:062102. [PMID: 34271751 DOI: 10.1103/physreve.103.062102] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Accepted: 05/17/2021] [Indexed: 11/07/2022]
Abstract
We report on the onset of antiresonant behavior of mass transport systems driven by time-dependent forces. Antiresonances arise from the coupling of a sufficiently high number of space-time modes of the force. The presence of forces having a wide space-time spectrum, a necessary condition for the formation of an antiresonance, is typical of confined systems with uneven and deformable walls that induce entropic forces dependent on space and time. We have analyzed, in particular, the case of polymer chains confined in a flexible channel and shown how they can be sorted and trapped. The presence of resonance-antiresonance pairs found can be exploited to design protocols able to engineer optimal transport processes and to manipulate the dynamics of nano-objects.
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Affiliation(s)
- M Florencia Carusela
- Instituto de Ciencias, Universidad Nacional de General Sarmiento, Juan María Gutiérrez 1150, B1613 Los Polvorines, Buenos Aires, Argentina.,National Scientific and Technical Research Council, Argentina
| | - Paolo Malgaretti
- Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany.,IV Institute for Theoretical Physics, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.,Helmholtz Institut Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Fürther Str. 248, 90429 Nürnberg, Germany
| | - J Miguel Rubi
- Departament de Física de la Materia Condensada, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona, Spain
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Abstract
We theoretically analyse the equation of topological solitons in a chain of particles interacting via a repulsive power-law potential and confined by a periodic lattice. Starting from the discrete model, we perform a gradient expansion and obtain the kink equation in the continuum limit for a power-law exponent n ≥ 1 . The power-law interaction modifies the sine-Gordon equation, giving rise to a rescaling of the coefficient multiplying the second derivative (the kink width) and to an additional integral term. We argue that the integral term does not affect the local properties of the kink, but it governs the behaviour at the asymptotics. The kink behaviour at the center is dominated by a sine-Gordon equation and its width tends to increase with the power law exponent. When the interaction is the Coulomb repulsion, in particular, the kink width depends logarithmically on the chain size. We define an appropriate thermodynamic limit and compare our results with existing studies performed for infinite chains. Our formalism allows one to systematically take into account the finite-size effects and also slowly varying external potentials, such as for instance the curvature in an ion trap.
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Zhang Y, Li B, Zheng QS, Genin GM, Chen CQ. Programmable and robust static topological solitons in mechanical metamaterials. Nat Commun 2019; 10:5605. [PMID: 31811130 PMCID: PMC6898320 DOI: 10.1038/s41467-019-13546-y] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2019] [Accepted: 11/14/2019] [Indexed: 12/31/2022] Open
Abstract
Solitary, persistent wave packets called solitons hold potential to transfer information and energy across a wide range of spatial and temporal scales in physical, chemical, and biological systems. Mechanical solitons characteristically emerge either as a single wave packet or uncorrelated propagating topological entities through space and/or time, but these are notoriously difficult to control. Here, we report a theoretical framework for programming static periodic topological solitons into a metamaterial, and demonstrate its implementation in real metamaterials computationally and experimentally. The solitons are excited by deformation localizations under quasi-static compression, and arise from buckling-induced kink-antikink bands that provide domain separation barriers. The soliton number and wavelength demonstrate a previously unreported size-dependence, due to intrinsic length scales. We identify that these unanticipated solitons stem from displacive phase transitions with periodic topological excitations captured by the well-known [Formula: see text] theory. Results reveal pathways for robust regularizations of stochastic responses of metamaterials.
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Affiliation(s)
- Yafei Zhang
- Department of Engineering Mechanics, CNMM and AML, Tsinghua University, 100084, Beijing, P.R. China
| | - Bo Li
- Department of Engineering Mechanics, CNMM and AML, Tsinghua University, 100084, Beijing, P.R. China
| | - Q S Zheng
- Department of Engineering Mechanics, CNMM and AML, Tsinghua University, 100084, Beijing, P.R. China
| | - Guy M Genin
- Mechanical Engineering and Materials Science, Washington University, St. Louis, MO, 63130, USA
- NSF Science and Technology Center for Engineering Mechanobiology, St. Louis, MO, 63130, USA
| | - C Q Chen
- Department of Engineering Mechanics, CNMM and AML, Tsinghua University, 100084, Beijing, P.R. China.
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da Silva RM, Manchein C, Beims MW. Optimal ratchet current for elastically interacting particles. CHAOS (WOODBURY, N.Y.) 2019; 29:111101. [PMID: 31779347 DOI: 10.1063/1.5127925] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2019] [Accepted: 10/21/2019] [Indexed: 06/10/2023]
Abstract
In this work, we show that optimal ratchet currents of two interacting particles are obtained when stable periodic motion is present. By increasing the coupling strength between identical ratchet maps, it is possible to find, for some parametric combinations, current reversals, hyperchaos, multistability, and duplication of the periodic motion in the parameter space. Besides that, by setting a fixed value for the current of one ratchet, it is possible to induce a positive/negative/null current for the whole system in certain domains of the parameter space.
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Affiliation(s)
- Rafael M da Silva
- Departamento de Física, Universidade Federal da Paraíba, 58051-900 João Pessoa, PB, Brazil
| | - Cesar Manchein
- Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, SC, Brazil
| | - Marcus W Beims
- Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, PR, Brazil
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Bondarenko N, Eriksson O, Skorodumova NV, Pereiro M. Multi-polaron solutions, nonlocal effects and internal modes in a nonlinear chain. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:415401. [PMID: 31317871 DOI: 10.1088/1361-648x/ab306e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Multipolaron solutions were studied in the framework of the Holstein one-dimensional molecular crystal model. The study was performed in the continuous limit where the crystal model maps into the nonlinear Schrödinger equation for which a new periodic dnoidal solution was found for the multipolaron system. In addition, the stability of the multi-polaron solutions was examined, and it was found that cnoidal and dnoidal solutions stabilize in different ranges of the parameter space. Moreover, the model was studied under the influence of nonlocal effects and the polaronic dynamics was described in terms of internal solitonic modes.
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Affiliation(s)
- N Bondarenko
- Division of Materials theory, Department of Physics and Astronomy, Uppsala University, Box 516, 75121 Uppsala, Sweden
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Casado-Pascual J, Sánchez-Rey B, Quintero NR. Soliton ratchet induced by random transitions among symmetric sine-Gordon potentials. CHAOS (WOODBURY, N.Y.) 2019; 29:053119. [PMID: 31154783 DOI: 10.1063/1.5092797] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2019] [Accepted: 04/29/2019] [Indexed: 06/09/2023]
Abstract
The generation of net soliton motion induced by random transitions among N symmetric phase-shifted sine-Gordon potentials is investigated, in the absence of any external force and without any thermal noise. The phase shifts of the potentials and the damping coefficients depend on a stationary Markov process. Necessary conditions for the existence of transport are obtained by an exhaustive study of the symmetries of the stochastic system and of the soliton velocity. It is shown that transport is generated by unequal transfer rates among the phase-shifted potentials or by unequal friction coefficients or by a properly devised combination of potentials (N>2). Net motion and inversions of the currents, predicted by the symmetry analysis, are observed in simulations as well as in the solutions of a collective coordinate theory. A model with high efficient soliton motion is designed by using multistate phase-shifted potentials and by breaking the symmetries with unequal transfer rates.
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Affiliation(s)
- Jesús Casado-Pascual
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, 41080 Sevilla, Spain
| | - Bernardo Sánchez-Rey
- Departamento de Física Aplicada I, E.P.S., Universidad de Sevilla, Virgen de África 7, 41011 Sevilla, Spain
| | - Niurka R Quintero
- Departamento de Física Aplicada I, E.P.S., Universidad de Sevilla, Virgen de África 7, 41011 Sevilla, Spain
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Mukhopadhyay AK, Xie T, Liebchen B, Schmelcher P. Dimensional coupling-induced current reversal in two-dimensional driven lattices. Phys Rev E 2018; 97:050202. [PMID: 29906956 DOI: 10.1103/physreve.97.050202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2018] [Indexed: 06/08/2023]
Abstract
We show that the direction of directed particle transport in a two-dimensional ac-driven lattice can be dynamically reversed by changing the structure of the lattice in the direction perpendicular to the applied driving force. These structural changes introduce dimensional coupling effects, the strength of which governs the timescale of the current reversals. The underlying mechanism is based on the fact that dimensional coupling allows the particles to explore regions of phase space which are inaccessible otherwise. The experimental realization for cold atoms in ac-driven optical lattices is discussed.
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Affiliation(s)
- Aritra K Mukhopadhyay
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Tianting Xie
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- College of Mathematics, Sichuan University, Chengdu 610065, China
| | - Benno Liebchen
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine Universität Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany
| | - Peter Schmelcher
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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