Pattern formation during the oscillatory photoelectrodissolution of n-type silicon: turbulence, clusters and chimeras

Schoenleber, Konrad; Zensen, Carla; Heinrich, A.; Krischer, Katharina

doi:10.1088/1367-2630/16/6/063024

Cited by 47 publications

(43 citation statements)

References 45 publications

(52 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Stable chimera states and desynchronized solutions, which do not arise for homogeneous phase-lag parameters, emerge as a result of competition between synchronized in-phase, anti-phase equilibria, and fully incoherent states when the phase-lags are near ± π 2 (cosine coupling). These findings elucidate previous experimental results involving a network of mechanical oscillators and provide further insight into the breakdown of synchrony in biological systems.in real-world systems such as experimental systems ranging from metronomes 24 to (electro-)chemical oscillators and lasing systems 23,25,26,31 . Moreover, by applying control, they may be relevant for functional applications in neurobiology 15,27,32 .…”

supporting

confidence: 83%

See 1 more Smart Citation

Chimera states in two populations with heterogeneous phase-lag

Martens

Bick

Panaggio

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

The simplest network of coupled phase-oscillators exhibiting chimera states is given by two populations with disparate intra-and inter-population coupling strengths. We explore the effects of heterogeneous coupling phase-lags between the two populations. Such heterogeneity arises naturally in various settings, for example as an approximation to transmission delays, excitatory-inhibitory interactions, or as amplitude and phase responses of oscillators with electrical or mechanical coupling. We find that breaking the phase-lag symmetry results in a variety of states with uniform and non-uniform synchronization, including in-phase and anti-phase synchrony, full incoherence (splay state), chimeras with phase separation of 0 or π between populations, and states where both populations remain desynchronized. These desynchronized states exhibit stable, oscillatory, and even chaotic dynamics. Moreover, we identify the bifurcations through which chimeras emerge. Stable chimera states and desynchronized solutions, which do not arise for homogeneous phase-lag parameters, emerge as a result of competition between synchronized in-phase, anti-phase equilibria, and fully incoherent states when the phase-lags are near ± π 2 (cosine coupling). These findings elucidate previous experimental results involving a network of mechanical oscillators and provide further insight into the breakdown of synchrony in biological systems. The synchronization of oscillators is a ubiquitous phenomenon that manifests itself in a wide range of biological and technological settings, including the beating of the heart 1 , flashing fireflies 2 , pedestrians on a bridge locking their gait 3 , circadian clocks in the brain 4 , superconducting Josephson junctions 5 , chemical oscillations 6,7 , metabolic oscillations in yeast cells 8,9 , and life cycles of phytoplankton 10 . Recent studies have reported the emergence of solutions where oscillators break into localized synchronized and desynchronized populations, commonly known as chimera states 11,12 . These solutions have been studied in the Kuramoto-Sakaguchi model with homogeneous coupling phase-lag 13-16 . Significant progress has been made understanding how chimera states emerge with respect to different topologies 17-20 , their robustness towards heterogeneity 21,22 , how they manifest in real-world experiments such as (electro-) chemical and mechanical oscillator systems 23-25 and laser systems 26 , and recently in explaining their basins of attraction 15 and controllability 15,27 . Here we generalize one of the simplest systems in which chimera states are known to occur, two populations of identical phase-oscillators with heterogeneous intra-and inter-population coupling, to account for effects of breaking the symmetry in the phase-lag parameters. Using syma) Electronic mail: erik.martens@ds.mpg.de; http://eam.webhop.net metry considerations, numerical methods and perturbative approaches, we explore and explain the emergence of dynamics which only occur for heterogeneous phase lags, including new...

show abstract

supporting

confidence: 83%

“…in real-world systems such as experimental systems ranging from metronomes 24 to (electro-)chemical oscillators and lasing systems 23,25,26,31 . Moreover, by applying control, they may be relevant for functional applications in neurobiology 15,27,32 .…”

mentioning

confidence: 99%

Chimera states in two populations with heterogeneous phase-lag

Martens

Bick

Panaggio

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…Chimeras have also been observed in experimental setups 9,14,15 . In this section, we apply our approach to experimental data as described by Schönleber et al 32 is shown in figure 15b, where the homogeneous oscillation of a small region in an otherwise inhomogeneously oscillating background can be observed. Figure 16a shows the pairwise correlation coefficients of the cross-section with a point inside the coherent cluster (here y = 80): a strong linear correlation within this cluster and the diminishing correlation with the remaining oscillators is evident.…”

Section: B Experimental Observation Of Chimerasmentioning

confidence: 99%

A classification scheme for chimera states

Kemeth

Haugland

Schmidt

et al. 2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

171

123

View full text Add to dashboard Cite

We present a universal characterization scheme for chimera states applicable to both numerical and experimental data sets. The scheme is based on two correlation measures that enable a meaningful definition of chimera states as well as their classification into three categories: stationary, turbulent, and breathing. In addition, these categories can be further subdivided according to the time-stationarity of these two measures. We demonstrate that this approach is both consistent with previously recognized chimera states and enables us to classify states as chimeras which have not been categorized as such before. Furthermore, the scheme allows for a qualitative and quantitative comparison of experimental chimeras with chimeras obtained through numerical simulations.

show abstract

“…Recently, a dynamic state which is qualitatively distinct and it has a counter-intuitive structure, referred to in current literature as a "chimera state", was discovered in numerical simulations of non-locally coupled oscillator arrays 167 . That discovery was followed by intense theoretical 271,272,273,274,275,276,277,278,279,280,281,282 and experimental 283,284,285,286,287,288,289,290,291,292,293,294 activity. A chimera state is characterized by the coexistence of synchronous and asynchronous clusters (subgroups) of oscillators, even though they are coupled symmetrically and they are identical 295,168 .…”

Section: Collective Counter-intuitive Dynamic Statesmentioning

confidence: 99%

Superconducting metamaterials

Lazarides

Tsironis

2018

Physics Reports

View full text Add to dashboard Cite

Metamaterials, i.e. artificial, man-made media designed to achieve properties not available in natural materials, have been the focus of intense research during the last two decades. Many properties have been discovered and multiple designs have been devised that lead to multiple conceptual and practical applications. Superconducting metamaterials made of superconducting metals have the advantage of ultra low losses, a highly desirable feature. The additional use of the celebrated Josephson effect and SQUID (superconducting quantum interference device) configurations enrich the domain of superconducting metamaterials and produce further specificity and functionality. SQUID-based metamaterials are both theoretically investigated but also fabricated and analyzed experimentally in many laboratories and exciting new phenomena have been found both in the classical and quantum realms. The enticing feature of a SQUID is that it is a unique nonlinear oscillator that can be actually manipulated through multiple external means. This domain flexibility is inherited to SQUID-based metamaterials and metasurfaces, i.e. extended units that contain a large arrangement of SQUIDs in various interaction configurations. Such a unit can be viewed theoretically as an assembly of weakly coupled nonlinear oscillators and as such presents a nonlinear dynamics laboratory where numerous, classical as well as quantum complex, spatio-temporal phenomena may be explored. In this review we focus primarily on SQUID-based superconducting metamaterials and present basic properties related to their individual and collective responses to external drives; the work summarized here is primarily theoretical and computational with nevertheless explicit presentation of recent experimental works. We start by showing how a SQUID-based system acts as a genuine metamaterial with right as well as left handed properties, demonstrate that the intrinsic Josephson nonlinearity leads to wide-band tunability, intrinsic nonlinear as well as flat band localization. We explore further exciting properties such as multistability and self-organization and the emergence of counter-intuitive chimera states of selective, partial organization. We then dwell into the truly quantum regime and explore the interaction of electromagnetic pulses with superconducting qubit units where the coupling between the two yields phenomena such as self-induced transparency and superradiance. We thus attempt to present the rich behavior of coupled superconducting units and point to their basic properties and practical utility. Abstract1 Contents 2 1. High-frequency magnetism, in particular, exhibited by magnetic metamaterials, is considered one of the "forbidden fruits" in the Tree of Knowledge that has been brought forth by metamaterial research 9 . Their unique properties allow them to form a material base for other functional devices with tuning and switching capabilities 9,10,11 . The scientific activity on metamaterials which has exploded since their first experimental demonstration 12,13...

show abstract

Pattern formation during the oscillatory photoelectrodissolution of n-type silicon: turbulence, clusters and chimeras

Cited by 47 publications

References 45 publications

Chimera states in two populations with heterogeneous phase-lag

Chimera states in two populations with heterogeneous phase-lag

A classification scheme for chimera states

Superconducting metamaterials

Contact Info

Product

Resources

About