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      Chimera States in Mechanical Oscillator Networks

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          Abstract

          The synchronization of coupled oscillators is a fascinating manifestation of self-organization that nature employs to orchestrate essential processes of life, such as the beating of the heart. Although it was long thought that synchrony or disorder were mutually exclusive steady states for a network of identical oscillators, numerous theoretical studies in recent years have revealed the intriguing possibility of `chimera states', in which the symmetry of the oscillator population is broken into a synchronous and an asynchronous part. However, a striking lack of empirical evidence raises the question of whether chimeras are indeed characteristic to natural systems. This calls for a palpable realization of chimera states without any fine-tuning, from which physical mechanisms underlying their emergence can be uncovered. Here, we devise a simple experiment with mechanical oscillators coupled in a hierarchical network to show that chimeras emerge naturally from a competition between two antagonistic synchronization patterns. We identify a wide spectrum of complex states, encompassing and extending the set of previously described chimeras. Our mathematical model shows that the self-organization observed in our experiments is controlled by elementary dynamical equations from mechanics that are ubiquitous in many natural and technological systems. The symmetry breaking mechanism revealed by our experiments may thus be prevalent in systems exhibiting collective behaviour, such as power grids, opto-mechanical crystals or cells communicating via quorum sensing in microbial populations.

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          Most cited references 34

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          Optomechanical Crystals

          Structured, periodic optical materials can be used to form photonic crystals capable of dispersing, routing, and trapping light. A similar phenomena in periodic elastic structures can be used to manipulate mechanical vibrations. Here we present the design and experimental realization of strongly coupled optical and mechanical modes in a planar, periodic nanostructure on a silicon chip. 200-Terahertz photons are co-localized with mechanical modes of Gigahertz frequency and 100-femtogram mass. The effective coupling length, which describes the strength of the photon-phonon interaction, is as small as 2.9 microns, which, together with minute oscillator mass, allows all-optical actuation and transduction of nanomechanical motion with near quantum-limited sensitivity. Optomechanical crystals have many potential applications, from RF-over-optical communication to the study of quantum effects in mesoscopic mechanical systems.
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            Chimera States for Coupled Oscillators

            Arrays of identical oscillators can display a remarkable spatiotemporal pattern in which phase-locked oscillators coexist with drifting ones. Discovered two years ago, such "chimera states" are believed to be impossible for locally or globally coupled systems; they are peculiar to the intermediate case of nonlocal coupling. Here we present an exact solution for this state, for a ring of phase oscillators coupled by a cosine kernel. We show that the stable chimera state bifurcates from a spatially modulated drift state, and dies in a saddle-node bifurcation with an unstable chimera.
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              Synchronization in Complex Oscillator Networks and Smart Grids

              The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing the interaction among them. It is known that a strongly coupled and sufficiently homogeneous network synchronizes, but the exact threshold from incoherence to synchrony is unknown. Here we present a novel, concise, and closed-form condition for synchronization of the fully nonlinear, non-equilibrium, and dynamic network. Our synchronization condition can be stated elegantly in terms of the network topology and parameters, or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters, they are statistically correct for almost all networks, and they can be applied equally to synchronization phenomena arising in physics and biology as well as in engineered oscillator networks such as electric power networks. We illustrate the validity, the accuracy, and the practical applicability of our results in complex networks scenarios and in smart grid applications.
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                Author and article information

                Journal
                31 January 2013
                2013-05-27
                Article
                10.1073/pnas.1302880110
                1301.7608

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                Proc. Natl. Acad. Sci., Vol. 110 (26), p. 10563-10567 (2013)
                Main text, supplementary info and 3 ancillary movies
                nlin.AO cond-mat.stat-mech nlin.PS physics.class-ph

                Condensed matter, Classical mechanics, Nonlinear & Complex systems

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