Aktuelles
March 2023

LeLaPreis 2023 für das Experiment des Jahres
We are happy and proud to report that Moritz Feil, who is a member of School laboratory econversion (Garching) has been awarded this years LeLa Prize by LernortLabor  Bundesverband der Schülerlabor

On Coexistence Patterns  Hierarchies of Intricate Partially Symmetric Solutions to StuartLandau Oscillators with Nonlinear Global Coupling
We are happy to announce that Dr. Sindre W. Haugland's Ph.D. thesis was published in the Springer Theses Recognizing Outstanding Ph.D. Research.
This book is about coexistence patterns in ensembles of globally coupled nonlinear oscillators. Coexistence patterns in this respect are states of a dynamical system in which the dynamics in some parts of the system differ significantly from those in other parts, even though there is no underlying structural difference between the different parts. In other words, these asymmetric patterns emerge in a selforganized manner.
As our main model, we use ensembles of various numbers of StuartLandau oscillators, all with the same natural frequency and all coupled equally strongly to each other. Employing computer simulations, bifurcation analysis and symmetry considerations, we uncover the mechanism behind a wide range of complex patterns found in these ensembles. Our starting point is the creation of socalled chimeras, which are subsequently treated within a new and broader context of related states.
January 2023

Gold–Rhodium Nanoflowers for the PlasmonEnhanced CO_{2} Electroreduction Reaction upon Visible Light
Bimetallic nanostructures combining catalytic and plasmonic properties are a class of materials that might possess improved efficiency and/or selectivity in electrocatalytic reactions. In this paper, we described the application of gold–rhodium core–shell nanoflowers (Au@Rh NFs) as a model system for the electrochemical CO_{2} reduction reaction. The nanoparticles consist of a gold nucleus surrounded by rhodium branches, combining Au localized surface plasmon resonance (LSPR) in the visible range of the spectrum and Rh catalytic properties. The influence of LSPR excitation on the catalytic properties was evaluated for different excitation wavelengths and various Au@Rh NF metallic ratios. Our catalysts showed enhanced activity upon LSPR excitation, demonstrating that LSPR excitation may lead to improved performance even with a low content of metallic NFs (2% Au + Rh in Carbon Vulcan). Electrochemical impedance spectroscopy (EIS) experiments performed under LSPR excitation suggest that the superior activity under illumination is related to lower energetic barriers that facilitate the desorption of adsorbed species compared to dark conditions.L
For the publishers version of the full article, see here.
October 2022

Chimera states under genuine local coupling
Chimera states, important forms of spatiotemporal selforganization in ensembles of identical oscillators, have been found in a wide variety of systems, provided that the coupling between the oscillators was nonlocal or global. Therefore, it is generally assumed that a locally coupled oscillatory medium, as described by the complex Ginzburg–Landau equation (CGLE), does not support chimera states. Here we show an alternative mechanism that does indeed lead to chimera states in a purely locallycoupled system, namely the interaction of an oscillatory medium, in the present case the CGLE, with a bistable internal degree of freedom.
For the publishers version of the full article, see here.

Nontrivial twisted states in nonlocally coupled StuartLandau oscillators
A twisted state is an important yet simple form of collective dynamics in an oscillatory medium. Here we describe a nontrivial type of twisted state in a system of nonlocally coupled StuartLandau oscillators. The nontrivial twisted state (NTS) is a coherent traveling wave characterized by inhomogeneous profiles of amplitudes and phase gradients, which can be assigned a winding number. To further investigate its properties, several methods are employed. We perform a linear stability analysis in the continuum limit and compare the results with Lyapunov exponents obtained in a finitesize system. The determination of covariant Lyapunov vectors allows us to identify collective modes. Furthermore, we show that the NTS is robust to small heterogeneities in the natural frequencies and present a bifurcation analysis revealing that NTSs are born or annihilated in a saddlenode bifurcation and change their stability in Hopf bifurcations. We observe stable NTSs with winding number 1 and 2. The latter can lose stability in a supercritical Hopf bifurcation, leading to a modulated 2NTS.
For the publishers version of the full article, see here.
May 2022

Gold–rhodium nanoflowers for the plasmon enhanced ethanol electrooxidation under visible light for tuning the activity and selectivity
Direct ethanol fuel cells (DEFCs) are a promising power source, but the low selectivity to ethanol complete oxidation is still challenging. The localized surface plasmon resonance (LSPR) excitation has been reported to accelerate and drive several chemical reactions, including the ethanol oxidation reaction (EOR), coming as a strategy to improve catalysts performance. Nonetheless, metallic nanoparticles (NPs) that present the LSPR excitation in the visible range are known for leading to the incomplete oxidation of ethanol. Thus, we report here the application of goldrhodium nanoflowers (Au@Rh NFs) towards the plasmonenhanced EOR. These hybrid materials consist of a Au spherical nucleus covered by Rh branches shell, combining plasmonic and catalytic properties. Firstly, the Au@Rh NFs metallic ratio was investigated in dark conditions to obtain an optimal catalyst. Experiments were also performed under light irradiation. Our data demonstrated an improvement of 352% in current density and 36% in selectivity to complete ethanol oxidation under 533 nm laser incidence. Moreover, the current density showed a linear increase with the laser power density, indicating a photochemical effect and thus enhancement due to the LSPR properties.
For the publishers version of the full article, see here.
April 2022

Tuning the feature size of nanoimprinting stamps: A method to enhance the flexibility of nanoimprint lithography
In the field of nanoimprinting lithography, fabricating largearea imprinting stamps is often the most time and resourceconsuming step. Specifically in research, it is often not reasonable to produce a new imprinting stamp for each new experimental configuration. Therefore, the lack of flexibility in feature sizes makes prototyping and tailoring the feature sizes according to their application challenging. To overcome these restrictions, we developed an imprinting stamp reproduction and tuning method which enables the size of the features of existing imprinting stamps to be tuned within nanometer precision. For replication, we first fabricate a chromium nanoisland array on silicon dioxide using the tobe tuned imprinting stamp. Then, the silicon dioxide is anisotropically etched in a reactive ion etching process with chromium as a hard mask. The formed replica of the imprinting stamp is subsequently tuned in an isotropic etching step with hydrofluoric acid. The method enables us to tune the size of the features of our nanoimprinting stamps within nanometer precision without influencing their shape with a yield above 96%. The tuned stamps are then used to fabricate metal nanoisland arrays with the respective tuned sizes. To evaluate the influence of the feature sizes, we exemplarily study the plasmonic resonance of gold nanoisland arrays fabricated using stamps with different feature diameters. Here, we see a good agreement between measured and simulated plasmonic resonance wavelengths of the samples. Hence, with the tuning method, we can tailor specific sizedependent properties of our nanoisland arrays according to individual experiments and applications.
For the publishers version of the full article, see here.
November 2021

Bifurcations of Clusters and Collective Oscillations in Networks of Bistable Units
We investigate dynamics and bifurcations in a mathematical model that captures electrochemical experiments on arrays of microelectrodes. In isolation, each individual microelectrode is described by a onedimensional unit with a bistable currentpotential response. When an array of such electrodes is coupled by controlling the total electric current, the common electric potential of all electrodes oscillates in some interval of the current. These couplinginduced collective oscillations of bistable onedimensional units are captured by the model. Moreover, any equilibrium is contained in a cluster subspace, where the electrodes take at most three distinct states. We systematically analyze the dynamics and bifurcations of the model equations: We consider the dynamics on cluster subspaces of successively increasing dimension and analyze the bifurcations occurring therein. Most importantly, the system exhibits an equivariant transcritical bifurcation of limit cycles. From this bifurcation, several limit cycles branch, one of which is stable for arbitrarily many bistable units.
For the publishers version of the full article, see here.

Attracting Poisson chimeras in twopopulation networks
Chimera states, i.e., dynamical states composed of coexisting synchronous and asynchronous oscillations, have been reported to exist in diverse topologies of oscillators in simulations and experiments. Twopopulation networks with distinct intra and interpopulation coupling have served as simple model systems for chimera states since they possess an invariant synchronized manifold in contrast to networks on a spatial structure. Here, we study dynamical and spectral properties of finitesized chimeras on twopopulation networks. First, we elucidate how the Kuramoto order parameter of the finitesized globally coupled twopopulation network of phase oscillators is connected to that of the continuum limit. These findings suggest that it is suitable to classify the chimera states according to their order parameter dynamics, and therefore, we define Poisson and nonPoisson chimera states. We then perform a Lyapunov analysis of these two types of chimera states, which yields insight into the full stability properties of the chimera trajectories as well as of collective modes. In particular, our analysis also confirms that Poisson chimeras are neutrally stable. We then introduce two types of “perturbation” that act as small heterogeneities and render Poisson chimeras attracting: A topological variation via the simplest nonlocal intrapopulation coupling that keeps the network symmetries and the allowance of amplitude variations in the globally coupled twopopulation network; i.e., we replace the phase oscillators by Stuart–Landau oscillators. The Lyapunov spectral properties of chimera states in the two modified networks are investigated, exploiting an approach based on network symmetryinduced cluster pattern dynamics of the finitesize network.
For the publishers version of the full article, see here.
October 2021
 We are happy to announce that the following Nature Communications' article was featured as an Editors’ Highlights webpage of recent research called “Applied physics and mathematics.”
Between synchrony and turbulence: Intricate hierarchies of coexistence patterns
Coupled oscillators, even identical ones, display a wide range of behaviours, among them synchrony and incoherence. The 2002 discovery of socalled chimera states, states of coexisting synchronized and unsynchronized oscillators, provided a possible link between the two and definitely showed that different parts of the same ensemble can sustain qualitatively different forms of motion. Here, we demonstrate that globally coupled identical oscillators can express a range of coexistence patterns more comprehensive than chimeras. A hierarchy of such states evolves from the fully synchronized solution in a series of clustersplittings. At the far end of this hierarchy, the states further collide with their own mirrorimages in phase space – rendering the motion chaotic, destroying some of the clusters and thereby producing even more intricate coexistence patterns. A sequence of such attractor collisions can ultimately lead to full incoherence of only single asynchronous oscillators. Chimera states, with one large synchronized cluster and else only single oscillators, are found to be just one step in this transition from low to highdimensional dynamics.
For the publishers version of the full article, see here.
September 2021
Editor’s Pick and Cover Page of Chaos
 We are happy to announce that the following article was promoted as an Editor's Pick in Chaos: An Interdisciplinary Journal of Nonlinear Science. and chosen as its coverpage.
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 fluoridecontaining electrolyte using weakly illuminated ntype 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 masterslave 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 period1 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
SelfOrganized Multifrequency Clusters in an Oscillating Electrochemical System withStrong Nonlinear Coupling
We study the spatiotemporal dynamics of the oscillatory photoelectrodissolution of ntype Si in a fluoridecontaining 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
 We are happy and proud to report that Prof. Katharina Krischer has been awarded this years Golden Chalk for sustainably good teaching by the Fachschaft Mathematik, Physik und Informatik.
October 2020
 Collective oscillations of globally coupled bistable, nonresonant components
Bistable microelectrodes with an Sshaped currentvoltage 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 (20212026).
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 siliconbased 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 welldefined, largearea 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 10times 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 ptype 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 StuartLandau oscillators
Oscillatory systems with longrange or global coupling offer promising insight into the interplay between highdimensional (or microscopic) chaotic motion and collective interaction patterns. Within this paper, we use Lyapunov analysis to investigate whether chimera states in globally coupled StuartLandau (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 meanfield 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 ptype silicon in a fluoridecontaining 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 torusbreakdown, 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 Dierential 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 currentvoltage 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 currentvoltage 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 StuartLandau 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 limitcycle oscillators to clustering in ensembles of infinitely many oscillators. We demonstrate that a natural arrangement of such 2cluster 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 codimension2 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 CO_{2} to methanol and/or formate. Because of recent strong incentives to turn CO_{2} 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 HCO_{3}^{−} being the predominant species next to the Pt electrode instead of PyH^{+} and CO_{2}. 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 CO_{2} in the electrolyte, and no sign of CO_{2} electroreduction products was observed, strongly questioning that PyH^{+} acts as a catalyst for CO_{2} 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 socalled 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.
Older
 Python code for the classification of chimera states is now available, and can be installed using (sudo) pip install classify_chimeras or from source via the GitHub repository.
For further reading, see A classification scheme for chimera states.  New group picture now online here