arXiv subjects

Katharina Krischer

Publications and source records attributed to Katharina Krischer.

At least 19 recordsLinked to original sources

arXiv2026

Amplitude-Defect Mediated Transition to Partial Incoherence -- From Experiment to Theory

Phase-only models have contributed significantly to the understanding of synchronization; however, they do not account for dynamical scenarios where amplitude dynamics matter. This study identifies an amplitude-mediated transition from complete frequency coherence to partial incoherence, observed both in an electrochemical silicon-etching experiment and within a population of globally coupled heterogeneous Stuart-Landau oscillators. Strong coupling introduces a bimodal-amplitude distribution from which the transition to partial incoherence is triggered by successive secondary Hopf bifurcations in low-amplitude oscillators. When these modulations cause oscillators to experience amplitude defects, the winding number changes, converting the secondary frequency into a new, oscillator-specific mean frequency. This mechanism results in a partially incoherent state, in which one amplitude group maintains frequency locking while another develops a dispersed frequency branch. These findings demonstrate that amplitude defects offer a pathway to incoherence that phase-only models cannot capture.

nlin.PS↗

arXiv2026

Origin of Frequency Clusters and Self-Organized Triplet Locking in the Kuramoto Model with Inertia

We investigate the origin of frequency clusters - states where multiple groups of oscillators with distinct mean frequencies coexist. We use the Kuramoto model with inertia, where identical oscillators are globally coupled. First, we study the creation of two frequency clusters in the thermodynamic limit. Via numerical bifurcation analysis, we confirm that two frequency clusters are created by homoclinic bifurcations. Both clusters can lose their phase-synchrony in transcritical or period-doubling bifurcations. Furthermore, we investigate the creation of three frequency clusters in a system of seven oscillators. Here, the frequency clusters are destabilized by a longitudinal and a transversal period-doubling bifurcation, and the frequency clusters are also created by homoclinic bifurcations. We find that the emergence of three or more frequency clusters via a homoclinic bifurcation implies the creation of a triplet locked state, where the frequency differences exhibit a rational relation. Besides the creation of frequency clusters via a homoclinic bifurcation, we state that Hopf bifurcations cannot create frequency clusters in phase oscillators, and frequency clusters can only be created by global bifurcations.

nlin.AO↗

arXiv2025

Synchronized Bimodal Amplitude Patterns in Heterogeneous Oscillatory Media -- Experiment and Theory

We study an intricate mechanism of pattern formation in globally coupled heterogeneous oscillatory media. In anodic electrochemical etching of silicon, the electrode surface splits into two amplitude-phase regions, while all oscillators remain frequency-locked. Additionally, the relative ratio of the pattern can be tuned via a coupling term. We introduce a heterogeneous, complex Ginzburg-Landau equation with global coupling to reproduce these patterns and study their formation. Neglecting diffusion shows that frequency entrainment arises from amplitude adaptation. Diffusion, on the other hand, enforces the selection of a unique cluster ratio. In quantitative agreement with simulations, a center-manifold reduction yields a Lyapunov functional that predicts the selected ratio. Both of these results establish a theoretical framework that connects experiment and theory. Moreover, they show how heterogeneity and diffusion convert degenerate cluster dynamics into robust pattern selection.

nlin.PS↗

arXiv2025

Time delay as the origin of oscillations in anodic Si electrodissolution

Silicon is the most important semiconductor electrode with applications in photoelectrochemistry and sensor technology. Yet its electrochemistry exhibits many poorly understood phenomena, including oscillations during the anodic dissolution of silicon electrodes. In this article, we present a mathematical model based on physicochemical steps that captures these oscillations and enables a thorough understanding of the underlying mechanism. The model describes the formation and dissolution of an oxide layer, and determines the oxide composition and the electrostatic potential in the direction perpendicular to the electrode. Oscillations occur if the following conditions are fulfilled: 1. The etching speed increases with defects in the oxide layer 2. The number of defects decreases with increasing electric field strength at the Si-oxide interface. 3. There is a sufficient time delay between the production and the etching of the oxide. Numerical simulations reproduce experimental results well, including the dependence of the oscillation amplitude and period on the potential, as well as the hysteresis behavior observed in cyclic voltammetry. Based on these results, we derive a simplified time-delay differential equation model. Using linear stability analysis, we confirm the essential role of the time delay for the oscillatory oxide-layer dynamics. The basic steps of the model are general and in line with the point defect model for growth and dissolution of passive films on metal electrodes. Therefore, it is likely applicable to a variety of oscillating anodic metal or semiconductor dissolution reactions.

physics.chem-ph↗

arXiv2025

Hierarchical Clustering in Mean-Field Coupled Stuart-Landau Oscillators

Clustered solutions in oscillator networks provide an important insight into how a system might diversify from a synchronous solution into spatiotemporal complex solutions. They can therefore form a link between fully synchronized and incoherent states. Despite their fundamental role in coupled oscillator dynamics, our understanding of how these clusters form and differentiate is still quite limited. Here, we study an ensemble of globally coupled Stuart-Landau oscillators and focus on the question of how 3-cluster solutions emerge from 2-cluster solutions and how the different 3-cluster solutions are organized in parameter space. We show that the arrangement of the clusters is dictated by a co-dimension 2 point, which we coin Type-II cluster singularity. Furthermore, our study points to a hierarchical structure of higher cluster solutions.

nlin.PS↗

arXiv2024

Electrolyte effects on the alkaline hydrogen evolution reaction: a mean-field approach

This paper introduces the combination of an advanced double-layer model with electrochemical kinetics to explain electrolyte effects on the alkaline hydrogen evolution reaction. It is known from experimental studies that the alkaline hydrogen evolution current shows a strong dependence on the concentration and identity of cations in the electrolyte, but is independent of pH. To explain these effects, we formulate the faradaic current in terms of the electric potential in the double layer, which is calculated using a mean-field model that takes into account the cation and anion sizes as well as the electric dipole moment of water molecules. We propose that the Volmer step consists of two activated processes: a water reduction sub-step, and a sub-step in which a hydroxide ion is transferred away from the reaction plane through the double layer. Either of these sub-steps may limit the rate. The proposed models for these sub-steps qualitatively explain experimental observations, including cation effects, pH-independence, and the trend reversal between gold and platinum electrodes. We also assess the quantitative accuracy of the water-reduction-limited current model; we suggest that the predicted functional relationship is valid as long as the hydrogen bonding structure of water near the electrode is sufficiently maintained.

physics.chem-ph↗

arXiv2024

Volcano Transition in a System of Generalized Kuramoto Oscillators with Random Frustrated Interactions

In a system of heterogeneous (Abelian) Kuramoto oscillators with random or `frustrated' interactions, transitions from states of incoherence to partial synchronization were observed. These so-called volcano transitions are characterized by a change in the shape of a local field distribution and were discussed in connection with an oscillator glass. In this paper, we consider a different class of oscillators, namely a system of (non-Abelian) SU(2)-Lohe oscillators that can also be defined on the 3-sphere, i.e., an oscillator is generalized to be defined as a unit vector in 4D Euclidean space. We demonstrate that such higher-dimensional Kuramoto models with reciprocal and nonreciprocal random interactions represented by a low-rank matrix exhibit a volcano transition as well. We determine the critical coupling strength at which a volcano-like transition occurs, employing an Ott-Antonsen ansatz. Numerical simulations provide additional validations of our analytical findings and reveal the differences in observable collective dynamics prior to and following the transition. Furthermore, we show that a system of unit 3-vector oscillators on the 2-sphere does not possess a volcano transition.

nlin.AO↗

arXiv2023

How Metal/Insulator Interfaces Enable the Enhancement of the Hydrogen Evolution Reaction Kinetics in Two Ways

Laterally nanostructured surfaces give rise to a new dimension of understanding and improving electrochemical reactions. In this study, we present a peculiar mechanism appearing at a metal/insulator interface, which can significantly enhance the Hydrogen Evolution Reaction (HER) from water reduction by altering the local reaction conditions in two ways: facilitated adsorption of hydrogen on the metal catalyst surface and improved transfer of ions through the double layer. The mechanism is uncovered using electrodes consisting of well-defined nanometer-sized metal arrays (Au, Cu, Pt) embedded in an insulator layer (silicon nitride), varying various parameters of both the electrode (size of the metal patches, catalyst material) and the electrolyte (cationic species, cation concentration, pH). In addition, simulations of the electrochemical double layer are carried out, which support the elaborated mechanism. Knowledge of this mechanism will enable new design principles for novel composite electrocatalytic systems.

physics.chem-ph↗

arXiv2023

Multi-band metasurface-driven surface-enhanced infrared absorption spectroscopy for improved characterization of in-situ electrochemical reactions

Surface-enhanced spectroscopy techniques are the method-of-choice to characterize adsorbed intermediates occurring during electrochemical reactions, which are crucial in realizing a green sustainable future. Characterizing species with low coverages or short lifetimes have so far been limited by low signal enhancement. Recently, metasurface-driven surface-enhanced infrared absorption spectroscopy (SEIRAS) has been pioneered as a promising narrowband technology to study single vibrational modes of electrochemical interfaces during CO oxidation. However, many reactions involve several species or configurations of adsorption that need to be monitored simultaneously requiring reproducible and broadband sensing platforms to provide a clear understanding of the underlying electrochemical processes. Here, we experimentally realize multi-band metasurface-driven SEIRAS for the in-situ study of electrochemical CO2 reduction on a Pt surface. We develop an easily reproducible and spectrally-tunable platinum nano-slot metasurface. Two CO adsorption configurations at 2030 cm-1 and 1840 cm-1 are locally enhanced as a proof of concept that can be extended to more vibrational bands. Our platform provides a 41-fold enhancement in the detection of characteristic absorption signals compared to conventional broadband electrochemically roughened platinum films. A straightforward methodology is outlined starting by baselining our system in CO saturated environment and clearly detecting both configurations of adsorption, in particular the hitherto hardly detectable CO bridge configuration. Then, thanks to the signal enhancement provided by our platform, we find that the CO bridge configuration on platinum does not play a significant role during CO2 reduction in an alkaline environment. We anticipate that our technology will guide researchers in developing similar sensing platforms.

cond-mat.mes-hall↗

arXiv2023

Chimera Dynamics of Generalized Kuramoto-Sakaguchi Oscillators in Two-population Networks

Chimera dynamics is characterized by the coexistence of coherence and incoherence, arising from a symmetry-breaking mechanism. Extensive research has been performed in various systems, focusing on a system of Kuramoto-Sakaguchi (KS) phase oscillators. In recent developments, the system has been extended to the so-called generalized Kuramoto model, wherein an oscillator is situated on the surface of an M-dimensional unit sphere, rather than being confined to a unit circle. In this paper, we exploit the model introduced in New. J. Phys. 16, 023016 (2014) where the macroscopic dynamics of the system was studied using the extended Watanabe-Strogatz transformation both for real and complex spaces. Considering two-population networks of the generalized KS oscillators in 2D complex spaces, we demonstrate the existence of chimera states and elucidate different motions of the order parameter vectors depending on the strength of intra-population coupling. Similar to the KS model on the unit circle, stationary and breathing chimeras are observed for comparatively strong intra-population coupling. Here, the breathing chimera changes their motion upon decreasing intra-population coupling strength via a global bifurcation involving the completely incoherent state. Beyond that, the system exhibits periodic alternation of the two order parameters with weaker coupling strength. Moreover, we observe that the chimera state transitions into a componentwise aperiodic dynamics when the coupling strength weakens even further. The aperiodic chimera dynamics emerges due to the breaking of conserved quantities that are preserved in the stationary, breathing and alternating chimera states. We provide a detailed explanation of this scenario in both the thermodynamic limit and for finite-sized ensembles. Furthermore, we note that an ensemble in 4D real spaces demonstrates similar behavior.

nlin.AO↗

arXiv2023

Heteroclinic Switching between Chimeras in a Ring of Six Oscillator Populations

In a network of coupled oscillators, a symmetry-broken dynamical state characterized by the coexistence of coherent and incoherent parts can spontaneously form. It is known as a chimera state. We study chimera states in a network consisting of six populations of identical Kuramoto-Sakaguchi phase oscillators. The populations are arranged in a ring and oscillators belonging to one population are uniformly coupled to all oscillators within the same population and to those in the two neighboring populations. This topology supports the existence of different configurations of coherent and incoherent populations along the ring, but all of them are linearly unstable in most of the parameter space. Yet, chimera dynamics is observed from random initial conditions in a wide parameter range, characterized by one incoherent and five synchronized populations. These observable states are connected to the formation of a heteroclinic cycle between symmetric variants of saddle chimeras, which gives rise to a switching dynamics. We analyze the dynamical and spectral properties of the chimeras in the thermodynamic limit using the Ott-Antonsen ansatz, and in finite-sized systems employing Watanabe-Strogatz reduction. For a heterogeneous frequency distribution, a small heterogeneity renders a heteroclinic switching dynamics asymptotically attracting. However, for a large heterogeneity, the heteroclinic orbit does not survive; instead, it is replaced by a variety of attracting chimera states.

nlin.AO↗

arXiv2023

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 tri-stability of chimera states. Of these three coexisting chimera states, only the symmetric stationary chimera solution exists in the symmetry-reduced manifold.

nlin.CD↗

arXiv2023

Improved in-situ characterization of electrochemical interfaces using metasurface-driven surface-enhanced infrared absorption spectroscopy

Electrocatalysis plays a crucial role in realizing the transition towards green energy, driving research directions from hydrogen generation to carbon dioxide reduction. Understanding electrochemical reactions is crucial to improve their efficiency and to bridge the gap toward a sustainable zero-carbon future. Surface-enhanced infrared absorption spectroscopy (SEIRAS) is a suitable method for investigating these 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. Here, we develop and experimentally realize an integrated nanophotonic-electrochemical SEIRAS platform for the in situ investigation of molecular signal traces emerging during electrochemical experiments. Specifically, we implement a platinum nano-slot metasurface featuring strongly enhanced electromagnetic near fields and spectrally target it at the weak vibrational bending mode of adsorbed CO at ~2033 cm-1. Crucially, our platinum nano-slot metasurface provides high molecular sensitivity. The resonances can be tuned over a broad range in the mid-infrared spectrum. Compared to conventional unstructured platinum layers, our nanophotonic-electrochemical platform delivers a substantial improvement of the experimentally detected characteristic absorption signals by a factor of 27, enabling the detection of new species with weak signals, fast conversions, or low surface concentrations. By providing a deeper understanding of catalytic reactions, we anticipate our nanophotonic-electrochemical platform to open exciting perspectives for electrochemical SEIRAS, surface-enhanced Raman spectroscopy, and the study of reactions in other fields of chemistry such as photoelectrocatalysis.

cond-mat.mes-hall↗

arXiv2022

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/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.

nlin.AO↗

arXiv2021

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.

nlin.AO↗

arXiv2021

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 ansatz based on the network symmetry-induced cluster pattern dynamics of the finite size network.

nlin.AO↗

arXiv2021

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 so-called 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 cluster-splittings. At the far end of this hierarchy, the states further collide with their own mirror-images 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 high-dimensional dynamics.

nlin.AO↗

arXiv2021

Connecting minimal chimeras and fully asymmetric chaotic attractors through equivariant pitchfork bifurcations

Highly symmetric networks can exhibit partly symmetry-broken states, including clusters and chimera states, i.e., states of coexisting synchronized and unsynchronized elements. We address the $\mathbb{S}_4$ permutation symmetry of four globally coupled Stuart-Landau oscillators and uncover an interconnected web of differently symmetric solutions. Among these are chaotic $2\!-\!1\!-\!1$ minimal chimeras that arise from $2\!-\!1\!-\!1$ periodic solutions in a period-doubling cascade, as well as fully asymmetric chaotic states arising similarly from periodic $1\!-\!1\!-\!1\!-\!1$ solutions. A backbone of equivariant pitchfork bifurcations mediate between the two cascades, culminating in equivariant pitchforks of chaotic attractors.

nlin.AO↗