September 2021
Chaos Editor’s Pick
  • We are happy to announce that the following article was promoted as an Editor's Pick  in Chaos: An Interdisciplinary Journal of Nonlinear Science.
    Birhythmicity, intrinsic entrainment, and minimal chimeras in an electrochemical experiment
    The coexistence of limit cycles in phase space, so called birhythmicity, is a phenomenon known to exist in many systems 7 in various disciplines. Yet, detailed experimental investigations are rare, as are studies on the interaction between 8 birhythmic components. In this article, we present experimental evidence for the existence of birhythmicity during 9 the anodic electrodissolution of Si in a fluoride-containing electrolyte using weakly illuminated n-type Si electrodes. 10 Moreover, we demonstrate several types of interaction between the coexisting limit cycles, in part resulting in peculiar 11 dynamics. The two limit cycles exhibit vastly different sensitivities with respect to a small perturbation of the electrode 12 potential, rendering the coupling essentially unidirectional. A manifestation of this is an asymmetric 1:2 intrinsic 13 entrainment of the coexisting limit cycles on an individual uniformly oscillating electrode. In this state, the phase 14 space structure mediates the locking of one of the oscillators to the other one across the separatrix. Furthermore, the 15 transition scenarios from one limit cycle to the other one at the borders of the birhythmicity go along with different types 16 of spatial symmetry breaking. Finally, the master-slave type coupling promotes two (within the experimental limits) 17 identical electrodes initialized on the different limit cycles to adopt states of different complexity: one of the electrodes 18 exhibits irregular, most likely chaotic, motion, while the other one exhibits period-1 oscillations. The coexistence of 19 coherence and incoherence is the characteristic property of a chimera state, the two coupled electrodes constituting an 20 experimental example of a smallest chimera state in a minimal network configuration. 
    For the publishers version of the full article, see here.
    For the postprint version of the full article, see here.
May 2021
PRL Editor's Suggestion
  • We are happy to announce that the following article was selected to be a PRL Editor's Suggestion
    Self-Organized Multifrequency Clusters in an Oscillating Electrochemical System withStrong Nonlinear Coupling
    We study the spatiotemporal dynamics of the oscillatory photoelectrodissolution of n-type Si in a fluoride-containing electrolyte under anodic potentials using in situ ellipsometric imaging. When lowering the illumination intensity step wise, we successively observe uniform oscillations, modulated amplitude clusters, and the coexistence of multifrequency clusters, i.e., regions with different frequencies, with a stationary domain. We argue that the multifrequency clusters emerge due to an adaptive, nonlinear, and nonlocal coupling, similar to those found in the context of neural dynamics.
    For the publishers version of the full article, see here. 
November 2020
Golden Chalk Award
October 2020
  • Collective oscillations of globally coupled bistable, nonresonant components
    Bistable microelectrodes with an S-shaped current-voltage characteristic have recently been shown to oscillate under current control, when connected in parallel. In other systems with equivalently coupled bistable components, such oscillatory instabilities have not been reported. In this paper, we derive a general criterion for when an ensemble of coupled bistable components may become oscillatorily unstable. Using a general model, we perform a stability analysis of the ensemble equilibria, in which the components always group in three or fewer clusters. Based thereon, we give a necessary condition for the occurrence of collective oscillations. Moreover, we demonstrate that stable oscillations may persist for an arbitrarily large number of components, even though, as we show, any equilibrium with two or more components on the middle, autocatalytic branch is unstable.
    For the publishers version of the full article, see here.
June 2020
ISE President Elect
  • We are happy to announce that Prof. Katharina Krischer has been elected President of the International Society of Electrochemistry (ISE).
    She will hold the chair for the next 5 years (2021-2026).
    ISE homepage
April 2020
Article featured on the cover of The Journal of Chemical Physics
  • Lateral silicon oxide/gold interfaces enhance the rate of electrochemical hydrogen evolution reaction in alkaline media
    The production of solar hydrogen with a silicon based water splitting device is a promising future technology, and silicon-based metal–insulator–semiconductor (MIS) electrodes have been proposed as suitable architectures for efficient photocathodes based on the electronic properties of the MIS structures and the catalytic properties of the metals. In this paper, we demonstrate that the interfaces between the metal and oxide of laterally patterned MIS electrodes may strongly enhance the catalytic activity of the electrode compared to bulk metal surfaces. The employed electrodes consist of well-defined, large-area arrays of gold structures of various mesoscopic sizes embedded in a silicon oxide support on silicon. We demonstrate that the activity of these electrodes for hydrogen evolution reaction (HER) increases with an increase in gold/silicon oxide boundary length in both acidic and alkaline media, although the enhancement of the HER rate in alkaline electrolytes is considerably larger than in acidic electrolytes. Electrodes with the largest interfacial length of gold/silicon oxide exhibited a 10-times larger HER rate in alkaline electrolytes than those with the smallest interfacial length. The data suggest that at the metal/silicon oxide boundaries, alkaline HER is enhanced through a bifunctional mechanism, which we tentatively relate to the laterally structured electrode geometry and to positive charges present in silicon oxide: Both properties change locally the interfacial electric field at the gold/silicon oxide boundary, which, in turn, facilitates a faster transport of hydroxide ions away from the electrode/electrolyte interface in alkaline solution. This mechanism boosts the alkaline HER activity of p-type silicon based photoelectrodes close to their HER activity in acidic electrolytes.
    For the publishers version of the full article, see here.
    For the coverpage of The Journal of Chemical Pysics Volume 152, Issue 15, 21 Apr. 2020, see here.
August 2019
  • Lyapunov spectra and collective modes of chimera states in globally coupled Stuart-Landau oscillators 
    Oscillatory systems with long-range or global coupling offer promising insight into the interplay between high-dimensional (or microscopic) chaotic motion and collective interaction patterns. Within this paper, we use Lyapunov analysis to investigate whether chimera states in globally coupled Stuart-Landau (SL) oscillators exhibit collective degrees of freedom. We compare two types of chimera states, which emerge in SL ensembles with linear and nonlinear global coupling, respectively, the latter introducing a constraint that conserves the oscillation of the mean. Lyapunov spectra reveal that for both chimera states the Lyapunov exponents split into several groups with different convergence properties in the limit of large system size. Furthermore, in both cases the Lyapunov dimension is found to scale extensively and the localization properties of covariant Lypunov vectors manifest the presence of collective Lyapunov modes. Here, however, we find qualitative differences between the two types of chimera states: Whereas the ones in the system under nonlinear global coupling exhibit only slow collective modes corresponding to Lyapunov exponents equal or close to zero, those which experience the linear mean-field coupling exhibit also faster collective modes associated with Lyapunov exponents with large positive or negative values. Furthermore, for the fastest collective mode we showed that it spreads across both synchonous and incoherent oscillators.
    For the full article preprint, see here.

    For the publishers version of the full article, see here.
  • 70th Annual Meeting of the International Society of Electrochemistry We are happy to announce that the price for best poster at this years annual meeting of the ISE was awarded to our own Thomas L. Maier. Maiers outstanding poster was choosen as one of the best ones out of the approximately 300 that were presented.
    Link to award winning poster
April 2019
  • Bichaoticity Induced by Inherent Birhythmicity During the Oscillatory Electrodissolution of Silicon The electrodissolution of p-type silicon in a fluoride-containing electrolyte is a prominent electrochemical oscillator with a still unknown oscillation mechanism. In this article, we present a study of its dynamical states occurring in a wide range of the applied voltage–external resistance parameter plane. We provide evidence that the system possesses inherent birhythmicity, and thus at least two distinct feedback loops promoting oscillatory behavior. The two parameter regions in which the different limit cycles exist are separated by a band in which the dynamics exhibit bistability between two branches with different multimode oscillations. Following the states along one path through this bistable region, one observes that each branch undergoes a different transition to chaos, namely, a period doubling cascade and a quasiperiodic route with a torus-breakdown, respectively, making Si electrodissolution one of the few experimental systems exhibiting bichaoticity.
    For the full article postprint, see here.
February 2019
  • A Physical Model for the Regime of Negative Di erential Resistance When Si is anodically oxidized in a fluoride containing electrolyte, an oxide layer is grown. Simultaneously, the layer is etched by the fluoride containing electrolyte. The resulting stationary state exhibits a negative slope of the current-voltage characteristics in a certain range of applied voltage. We propose a physical model that reproduces this negative slope. In particular, our model assumes that the oxide layer consists of both partially and fully oxidized Si and that the etch rate depends on the effective degree of oxidation. Finally, we show that our simulations are in good agreement with measurements of the current-voltage characteristics, the oxide layer thickness, the dissolution valence, and the impedance spectra of the electrochemical system.
    For the full article postprint, see here.
  • Cluster singularity: The unfolding of clustering behavior in globally coupled Stuart-Landau oscillators
    Certain swarms of fireflies are known to flash in unison. They also sometimes divide into two or more distinct yet internally synchronized groups, flashing with a certain phase lag between the groups. This is just one example of clustering dynamics in an ensemble of coupled oscillators, as it occurs naturally in many physical systems. A key problem in the understanding of clustering dynamics is the connection between its occurrence in small and large ensembles. In other words, is there a universal law governing the arrangement of cluster states, independent of the system size? This paper partially answers this question and links the phenomenon of clustering in minimal networks of globally coupled limit-cycle oscillators to clustering in ensembles of infinitely many oscillators. We demonstrate that a natural arrangement of such 2-cluster states exists: When tuning a parameter, a balanced cluster state transitions to synchronized motion via a sequence of intermediate unbalanced cluster states. Tuning an additional parameter, this sequence converges to a single point in parameter space where all cluster states are born directly at the synchronized solution. We call such a codimension-2 point a cluster singularity. Singularities of this kind may appear in any symmetrically coupled ensemble of oscillators and thus play a crucial role for the understanding of collective behavior in oscillatory systems.
    For the full article, see here.
September 2018
  • The True Fate of Pyridinium in the Reportedly Pyridinium‐Catalyzed Carbon Dioxide Electroreduction on Platinum
    Protonated pyridine (PyH+) has been reported to act as a peculiar and promising catalyst for the direct electroreduction of CO2 to methanol and/or formate. Because of recent strong incentives to turn CO2 into valuable products, this claim triggered great interest, prompting many experiments and DFT simulations. However, when performing the electrolysis in near‐neutral pH electrolyte, the local pH around the platinum electrode can easily increase, leading to Py and HCO3 being the predominant species next to the Pt electrode instead of PyH+ and CO2. Using a carefully designed electrolysis setup which overcomes the local pH shift issue, we demonstrate that protonated pyridine undergoes a complete hydrogenation into piperidine upon mild reductive conditions (near 0 V vs. RHE). The reduction of the PyH+ ring occurs with and without the presence of CO2 in the electrolyte, and no sign of CO2 electroreduction products was observed, strongly questioning that PyH+ acts as a catalyst for CO2 electroreduction.
    For the publishers version of the full article, see here.
April 2018
  • The different faces of chimera states

    Oscillatory networks play a crucial role in the understanding of complex systems such as the brain or electric power grids. Such networks may exhibit a vast variety of different dynamical phenomena, the underlying mechanisms of which still raise many questions. These phenomena include so-called chimera states, extraordinary chaotic states in which some of the oscillators show synchronized motion, whereas some others behave incoherently. Even these states might occur in different variations on which we shed some light in this letter. Starting from very small networks of just four oscillators, we show that one can distinguish such chimera states using symmetry arguments: Some chimeras behave in a way which leaves the dynamical structure unchanged when some of the oscillators are interchanged, whereas other chimera states do not have that particular invariance. This difference in the symmetry properties may also be used to distinguish between states in larger ensembles of coupled oscillators. Our results might help elucidating dynamics of partial synchrony occurring in nature, for example during unihemispheric sleep in certain animals.
    For the full article preprint, see here.


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