Chaotic chimera attractors in a triangular network of identical oscillators

A prominent type of collective dynamics in networks of coupled oscillators is the coexistence of coherently and incoherently oscillating domains known as chimera states. Chimera states exhibit various macroscopic dynamics with different motions of the Kuramoto order parameter. Stationary, periodic and quasiperiodic chimeras are known to occur in two-population networks of identical phase oscillators. In a three-population network of identical Kuramoto-Sakaguchi phase oscillators, stationary and periodic symmetric chimeras were previously studied on a reduced manifold in which two populations behaved identically [Phys. Rev. E 82, 016216 (2010)]. In this paper, we study the full phase space dynamics of such three-population networks. We demonstrate the existence of macroscopic chaotic chimera attractors that exhibit aperiodic antiphase dynamics of the order parameters. We observe these chaotic chimera states in both finite-sized systems and the thermodynamic limit outside the Ott-Antonsen manifold. The chaotic chimera states coexist with a stable chimera solution on the Ott-Antonsen manifold that displays periodic antiphase oscillation of the two incoherent populations and with a symmetric stationary chimera solution, resulting in tristability of chimera states. Of these three coexisting chimera states, only the symmetric stationary chimera solution exists in the symmetry-reduced manifold.
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Improved In Situ Characterization of Electrochemical Interfaces Using Metasurface-Driven Surface-Enhanced IR Absorption Spectroscopy

Electrocatalysis plays a crucial role in realizing the transition toward a zero-carbon future, driving research directions from green hydrogen generation to carbon dioxide reduction. Surface-enhanced infrared absorption spectroscopy (SEIRAS) is a suitable method for investigating electrocatalytic processes because it can monitor with chemical specificity the mechanisms of the reactions. However, it remains difficult to detect many relevant aspects of electrochemical reactions such as short-lived intermediates. Herein, an integrated nanophotonic-electrochemical SEIRAS platform is developed and experimentally realized for the in situ investigation of molecular signal traces emerging during electrochemical experiments. A platinum nano-slot metasurface featuring strongly enhanced electromagnetic near fields is implemented and spectrally targets the weak vibrational mode of the adsorbed carbon monoxide at ≈2033 cm⁻¹. The metasurface-driven resonances can be tuned over a broad range in the mid-infrared spectrum and provide high molecular sensitivity. Compared to conventional unstructured platinum films, this nanophotonic-electrochemical platform delivers a 27-fold improvement of the experimentally detected characteristic absorption signals, enabling the detection of new species with weak signals, fast conversions, or low surface concentrations. By providing a deeper understanding of catalytic reactions, the nanophotonic-electrochemical platform is anticipated to open exciting perspectives for electrochemical SEIRAS, surface-enhanced Raman spectroscopy, and other fields of chemistry such as photoelectrocatalysis.
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LeLa-Preis 2023 für das Experiment des Jahres

We are happy and proud to report that Moritz Feil, who is a member of School laboratory e-conversion (Garching) has been awarded this years LeLa Prize by LernortLabor - Bundesverband der Schülerlabor

On Coexistence Patterns - Hierarchies of Intricate Partially Symmetric Solutions to Stuart-Landau 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 self-organized manner. 

As our main model, we use ensembles of various numbers of Stuart-Landau 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 so-called chimeras, which are subsequently treated within a new and broader context of related states.

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Gold–Rhodium Nanoflowers for the Plasmon-Enhanced CO₂ 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 CO₂ 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
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Chimera states under genuine local coupling

Chimera states, important forms of spatiotemporal self-organization 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 locally-coupled system, namely the interaction of an oscillatory medium, in the present case the CGLE, with a bistable internal degree of freedom.
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Nontrivial twisted states in nonlocally coupled Stuart-Landau 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 Stuart-Landau 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 finite-size 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 saddle-node 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 2-NTS.
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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 gold-rhodium nanoflowers (Au@Rh NFs) towards the plasmon-enhanced 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.
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Tuning the feature size of nanoimprinting stamps: A method to enhance the flexibility of nanoimprint lithography

In the field of nanoimprinting lithography, fabricating large-area imprinting stamps is often the most time- and resource-consuming 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 to-be 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 size-dependent properties of our nanoisland arrays according to individual experiments and applications.
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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 one-dimensional unit with a bistable current-potential 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 coupling-induced collective oscillations of bistable one-dimensional 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.
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Attracting Poisson chimeras in two-population 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. Two-population networks with distinct intra- and inter-population 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 finite-sized chimeras on two-population networks. First, we elucidate how the Kuramoto order parameter of the finite-sized globally coupled two-population 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 non-Poisson 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 intra-population coupling that keeps the network symmetries and the allowance of amplitude variations in the globally coupled two-population 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 symmetry-induced cluster pattern dynamics of the finite-size network.
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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.
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