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Veenstra J, Gamayun O, Guo X, Sarvi A, Meinersen CV, Coulais C. Non-reciprocal topological solitons in active metamaterials. Nature 2024; 627:528-533. [PMID: 38509280 DOI: 10.1038/s41586-024-07097-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Accepted: 01/22/2024] [Indexed: 03/22/2024]
Abstract
From protein motifs1 to black holes2, topological solitons are pervasive nonlinear excitations that are robust and can be driven by external fields3. So far, existing driving mechanisms all accelerate solitons and antisolitons in opposite directions3,4. Here we introduce a local driving mechanism for solitons that accelerates both solitons and antisolitons in the same direction instead: non-reciprocal driving. To realize this mechanism, we construct an active mechanical metamaterial consisting of non-reciprocally coupled oscillators5-8 subject to a bistable potential9-14. We find that such nonlinearity coaxes non-reciprocal excitations-so-called non-Hermitian skin waves5-8,15-22, which are typically unstable-into robust one-way (anti)solitons. We harness such non-reciprocal topological solitons by constructing an active waveguide capable of transmitting and filtering unidirectional information. Finally, we illustrate this mechanism in another class of metamaterials that shows the breaking of 'supersymmetry'23,24 causing only antisolitons to be driven. Our observations and models demonstrate a subtle interplay between non-reciprocity and topological solitons, whereby solitons create their own driving force by locally straining the material. Beyond the scope of our study, non-reciprocal solitons might provide an efficient driving mechanism for robotic locomotion25 and could emerge in other settings, for example, quantum mechanics26,27, optics28-30 and soft matter31.
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Affiliation(s)
- Jonas Veenstra
- Institute of Physics, Universiteit van Amsterdam, Amsterdam, The Netherlands
| | - Oleksandr Gamayun
- London Institute for Mathematical Sciences, Royal Institution, London, UK
| | - Xiaofei Guo
- Institute of Physics, Universiteit van Amsterdam, Amsterdam, The Netherlands
| | - Anahita Sarvi
- Institute of Physics, Universiteit van Amsterdam, Amsterdam, The Netherlands
| | | | - Corentin Coulais
- Institute of Physics, Universiteit van Amsterdam, Amsterdam, The Netherlands.
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2
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Zolotaryuk Y, Starodub IO. Embedded solitons in the double sine-Gordon lattice with next-neighbor interactions. Phys Rev E 2019; 100:032216. [PMID: 31640074 DOI: 10.1103/physreve.100.032216] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2018] [Indexed: 11/07/2022]
Abstract
Topological solitons can propagate without radiation in discrete media. These solutions are known as embedded solitons (ES). They come as isolated solutions and exist despite their resonance with the linear spectrum of the respective lattices. In this paper the properties of embedded solitons in the discrete double sine-Gordon equation with next-neighbor and second-neighbor interactions are investigated. Depending on the sign of these interactions they can be either destructive or favorable for the ES creation. The ES existence area depends on the width of the linear spectrum: narrowing of the spectrum widens the ES existence range and vice versa. The application to the Josephson junction arrays is discussed.
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Affiliation(s)
- Yaroslav Zolotaryuk
- Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, vul. Metrologichna 14B, 03143 Kyiv, Ukraine
| | - Ivan O Starodub
- Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, vul. Metrologichna 14B, 03143 Kyiv, Ukraine
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3
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Affiliation(s)
- W. Quapp
- Mathematisches Institut, Universität Leipzig, Leipzig, Germany
| | - J. M. Bofill
- Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, and Institut de Química Teòrica i Computacional, (IQTCUB), Universitat de Barcelona, Barcelona, Spain
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Shiroky IB, Gendelman OV. Kinks in chains with on-site bistable nondegenerate potential: Beyond traveling waves. Phys Rev E 2018; 98:012220. [PMID: 30110878 DOI: 10.1103/physreve.98.012220] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2017] [Indexed: 11/07/2022]
Abstract
This paper revisits the well-known transition fronts (kinks) in chains of coupled oscillators with nondegenerate on-site potentials. Usually, such transition fronts are considered in terms of traveling-wave solutions. We explore the loss of stability of such traveling waves. Generically, it corresponds to one of the common scenarios for fixed points of discrete maps. For example, one can encounter the quasiperiodic kink propagation (due to Hopf bifurcation), or the Feigenbaum cascade of period doublings, leading to a chaoticlike propagation pattern. The aforementioned scenarios show up, for instance, for triparabolic and φ^{4} on-site potentials. Numeric evidence suggests that the loss of stability occurs due to resonances between the frequency associated with the kink propagation, and the linear band gaps of the chain. Particular resonance mechanisms are model dependent. For the classical Atkinson-Cabrera model with a biparabolic on-site potential, the stability threshold is estimated by the simple means of linear algebra. The loss of stability in this model occurs through Hopf bifurcation. The results are in good agreement with numerical simulations.
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Affiliation(s)
- I B Shiroky
- Faculty of Mechanical Engineering, Technion, Haifa 32000, Israel
| | - O V Gendelman
- Faculty of Mechanical Engineering, Technion, Haifa 32000, Israel
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Gerloff S, Klapp SHL. Depinning and heterogeneous dynamics of colloidal crystal layers under shear flow. Phys Rev E 2017; 94:062605. [PMID: 28085345 DOI: 10.1103/physreve.94.062605] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2016] [Indexed: 11/07/2022]
Abstract
Using Brownian dynamics (BD) simulations and an analytical approach we investigate the shear-induced, nonequilibrium dynamics of dense colloidal suspensions confined to a narrow slit-pore. Focusing on situations where the colloids arrange in well-defined layers with solidlike in-plane structure, the confined films display complex, nonlinear behavior such as collective depinning and local transport via density excitations. These phenomena are reminiscent of colloidal monolayers driven over a periodic substrate potential. In order to deepen this connection, we present an effective model that maps the dynamics of the shear-driven colloidal layers to the motion of a single particle driven over an effective substrate potential. This model allows us to estimate the critical shear rate of the depinning transition based on the equilibrium configuration, revealing the impact of important parameters, such as the slit-pore width and the interaction strength. We then turn to heterogeneous systems where a layer of small colloids is sheared with respect to bottom layers of large particles. For these incommensurate systems we find that the particle transport is dominated by density excitations resembling the so-called "kink" solutions of the Frenkel-Kontorova (FK) model. In contrast to the FK model, however, the corresponding "antikinks" do not move.
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Affiliation(s)
- Sascha Gerloff
- Institut für Theoretische Physik, Hardenbergstrasse 36, Technische Universität Berlin, D-10623 Berlin, Germany
| | - Sabine H L Klapp
- Institut für Theoretische Physik, Hardenbergstrasse 36, Technische Universität Berlin, D-10623 Berlin, Germany
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6
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Zolotaryuk Y, Starodub IO. Fluxon mobility in an array of asymmetric superconducting quantum interference devices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:013202. [PMID: 25679728 DOI: 10.1103/physreve.91.013202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2014] [Indexed: 06/04/2023]
Abstract
Fluxon dynamics in the dc-biased array of asymmetric three-junction superconducting quantum interference devices (SQUIDs) is investigated. The array of SQUIDs is described by the discrete double sine-Gordon equation. It appears that this equation possesses a finite set of velocities at which the fluxon propagates with the constant shape and without radiation. The signatures of these velocities appear on the respective current-voltage characteristics of the array as inaccessible voltage intervals (gaps). The critical depinning current has a clear minimum as a function of the asymmetry parameter (the ratio of the critical currents of the left and right junctions of the SQUID), which coincides with the minimum of the Peierls-Nabarro potential.
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Affiliation(s)
- Yaroslav Zolotaryuk
- Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, vul. Metrologichna 14B, 03680 Kyiv, Ukraine
| | - Ivan O Starodub
- Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, vul. Metrologichna 14B, 03680 Kyiv, Ukraine
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Soloviev II, Klenov NV, Pankratov AL, Il'ichev E, Kuzmin LS. Effect of Cherenkov radiation on the jitter of solitons in the driven underdamped Frenkel-Kontorova model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:060901. [PMID: 23848617 DOI: 10.1103/physreve.87.060901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2012] [Revised: 04/09/2013] [Indexed: 05/14/2023]
Abstract
The effect of complex dynamics of solitons on the output noise of the system (thermal jitter) is studied in the frame of the driven underdamped Frenkel-Kontorova model. In contrast to the continuous case, we have observed a dramatic splash of the jitter. It is demonstrated that this jitter increase is related to the joining of an initial soliton with the one generated by large amplitude oscillations of the Cherenkov radiation tail, which results in the establishment of a unified soliton structure.
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Affiliation(s)
- I I Soloviev
- Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119991, Russia.
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Zolotaryuk Y. Asymmetric ac fluxon depinning in a Josephson junction array: a highly discrete limit. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:026604. [PMID: 23005873 DOI: 10.1103/physreve.86.026604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2011] [Revised: 01/19/2012] [Indexed: 06/01/2023]
Abstract
Directed motion and depinning of topological solitons in a strongly discrete damped and biharmonically ac-driven array of Josephson junctions is studied. The mechanism of the depinning transition is investigated in detail. We show that the depinning process takes place through chaotization of an initially standing fluxon periodic orbit. Detailed investigation of the Floquet multipliers of these orbits shows that, depending on the depinning parameters (either the driving amplitude or the phase shift between harmonics), the chaotization process can take place either along the period-doubling scenario or due to the type I intermittency.
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Affiliation(s)
- Yaroslav Zolotaryuk
- Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 03680 Kyiv, Ukraine.
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Braun OM, Peyrard M. Crack in the frictional interface as a solitary wave. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:026111. [PMID: 22463283 DOI: 10.1103/physreve.85.026111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2011] [Revised: 01/18/2012] [Indexed: 05/31/2023]
Abstract
We introduce and investigate a multiscale model for the propagation of rupture fronts in friction. Taking advantage of the correlation length for the motion of individual contacts in elastic theory, we introduce collective contacts which can be characterized by a master equation approach. The problem of the dynamics of a chain of those effective contacts under stress is studied. We show that it can be reduced to an analog of the Frenkel-Kontorova model. In some limits this allows us to derive analytical solutions for kinks describing the rupture fronts. Numerical simulations are used to study more complex cases.
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Affiliation(s)
- O M Braun
- Institute of Physics, National Academy of Sciences of Ukraine, 46 Science Avenue, UA-03028 Kiev, Ukraine.
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Braun OM, Hu B. Clustering of atoms in a model with multiple thermostats. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:032103. [PMID: 15903470 DOI: 10.1103/physreve.71.032103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2004] [Indexed: 05/02/2023]
Abstract
We propose a model for a one-dimensional chain of interacting particles in an external periodic potential. In this model the particles have a complex structure treated in a mean-field fashion: particle collisions are inelastic and also each particle is considered as having its own thermostat. We derived the Fokker-Planck equation for this model and demonstrated that the model has a truly equilibrium ground state. When an external dc force is applied to the atoms, the model exhibits a hysteresis even at high temperatures due to the clustering of atoms with the same velocity. Another effect of clustering is phase separation in the steady state when the system splits into regions of immobile atoms ("traffic jams") and regions of running atoms.
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Affiliation(s)
- O M Braun
- Institute of Physics, National Academy of Sciences of Ukraine, Kiev.
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Tekić J, Braun OM, Hu B. Dynamic phases in the two-dimensional underdamped driven Frenkel-Kontorova model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:026104. [PMID: 15783375 DOI: 10.1103/physreve.71.026104] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2004] [Indexed: 05/24/2023]
Abstract
We study the nonlinear dc response of a two-dimensional underdamped system of interacting atoms subject to an isotropic periodic external potential with triangular symmetry. When driving force increases, the system transfers from a disorder locked state to an ordered sliding state corresponding to a moving crystal. By varying the values of the effective elastic constant, damping, and temperature, we found different scenarios and intermediate phases during the ordering transition. For a soft atomic layer, the system passes through a plastic-channel regime that appears as a steady-state regime at higher values of the damping coefficient. For high values of the effective elastic constant, when the atomic layer is stiff, the intermediate plastic phase corresponds to a traffic-jam regime with immobile islands in the sea of running atoms. At a high driving of the stiff layer, a solitonlike elastic flow of atoms has been observed.
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Affiliation(s)
- Jasmina Tekić
- Department of Physics, Centre for Nonlinear Studies, The Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Hong Kong), Hong Kong Baptist University, Hong Kong, China
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Braun OM, Zhang H, Hu B, Tekic J. Driven kinks in the anharmonic Frenkel-Kontorova model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:066602. [PMID: 16241363 DOI: 10.1103/physreve.67.066602] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2002] [Indexed: 05/04/2023]
Abstract
Multiple and supersonic topological excitations (kinks) driven by an external dc force in the Frenkel-Kontorova model (a chain of atoms subjected to a periodic substrate potential) with the exponential interatomic interaction are studied with the help of numerical simulation. The simulation results are interpreted in terms of dynamics of two limiting cases, the exactly integrable sine-Gordon equation and the Toda chain. The stability of driven kinks and scenarios of their destruction are described for a wide range of model parameters.
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Affiliation(s)
- O M Braun
- Institute of Physics, National Ukrainian Academy of Sciences, 03650 Kiev, Ukraine.
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Braun OM, Paliy MV, Röder J, Bishop AR. Locked-to-running transition in the two-dimensional underdamped driven Frenkel-Kontorova model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:036129. [PMID: 11308731 DOI: 10.1103/physreve.63.036129] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2000] [Indexed: 05/23/2023]
Abstract
We study the nonlinear dc response of a two-dimensional underdamped system of interacting atoms subject to an isotropic periodic external potential with triangular symmetry. We consider various values of the effective elastic constant of the system, two different atomic interaction potentials, and different concentrations of atoms. In the case of a closely packed layer, when its structure is commensurate with the substrate, there is a locked-to-running transition as a function of the driving force, whose mechanism depends on the effective elastic constant. For a low elastic constant, where the layer is weakly coupled, the transition is achieved via the creation of an avalanche of moving particles that leaves a depleted region in its wake. On increasing the effective elastic constant the depleted region becomes less marked and there is a crossover to a scenario in which an island of moving particles nucleates the transition. In the case of a partially filled atomic layer, several dynamical phase transitions between states with different atomic mobility are observed. The mobility of atoms as a function of the external force can vary nonmonotonically with increasing force. For the case of a small external damping, the system can be trapped at a large force in an immobile metastable state, thus demonstrating a "fuse-safety device" on an atomic scale.
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Affiliation(s)
- O M Braun
- Institute of Physics, National Ukrainian Academy of Sciences, UA-252022 Kiev, Ukraine.
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Braun OM. Supersonic and multiple topological excitations in the driven frenkel-kontorova model with exponential interaction. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:7315-7319. [PMID: 11102091 DOI: 10.1103/physreve.62.7315] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2000] [Indexed: 05/23/2023]
Abstract
The criteria for the existence of supersonic and multiple topological excitations (kinks) in the driven Frenkel-Kontorova model (a chain of atoms placed into an external periodic potential) with anharmonic (exponential) interatomic interactions are studied.
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Affiliation(s)
- OM Braun
- Institute of Physics, National Ukrainian Academy of Sciences, 03650 Kiev-39, Ukraine
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