TY - JOUR A1 - Gong, Chen Chris A1 - Libeskind, Noam I. A1 - Tempel, Elmo A1 - Guo, Quan A1 - Gottloeber, Stefan A1 - Yepes, Gustavo A1 - Wang, Peng A1 - Sorce, Jenny A1 - Pawlowski, Marcel T1 - The origin of lopsided satellite galaxy distribution in galaxy pairs JF - Monthly notices of the Royal Astronomical Society N2 - It is well known that satellite galaxies are not isotropically distributed among their host galaxies as suggested by most interpretations of the Λ cold dark matter (ΛCDM) model. One type of anisotropy recently detected in the Sloan Digital Sky Survey (and seen when examining the distribution of satellites in the Local Group and in the Centaurus group) is a tendency to be so-called lopsided. Namely, in pairs of galaxies (like Andromeda and the Milky Way) the satellites are more likely to inhabit the region in between the pair, rather than on opposing sides. Although recent studies found a similar set-up when comparing pairs of galaxies in ΛCDM simulations indicating that such a set-up is not inconsistent with ΛCDM, the origin has yet to be explained. Here we examine the origin of such lopsided set-ups by first identifying such distributions in pairs of galaxies in numerical cosmological simulations, and then tracking back the orbital trajectories of satellites (which at z = 0 display the effect). We report two main results: first, the lopsided distribution was stronger in the past and weakens towards z = 0. Secondly, the weakening of the signal is due to the interaction of satellite galaxies with the pair. Finally, we show that the z = 0 signal is driven primarily by satellites that are on first approach, who have yet to experience a ‘flyby’. This suggests that the signal seen in the observations is also dominated by dynamically young accretion events. KW - galaxies: evolution KW - galaxies: formation KW - galaxy: kinematics and dynamics KW - Local Group KW - dark matter KW - cosmology: theory Y1 - 2019 U6 - https://doi.org/10.1093/mnras/stz1917 SN - 0035-8711 SN - 1365-2966 VL - 488 IS - 3 SP - 3100 EP - 3108 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Gong, Chen Chris A1 - Klumpp, Stefan T1 - Modeling sRNA-Regulated Plasmid Maintenance JF - PLoS one N2 - We study a theoretical model for the toxin-antitoxin (hok/sok) mechanism for plasmid maintenance in bacteria. Toxin-antitoxin systems enforce the maintenance of a plasmid through post-segregational killing of cells that have lost the plasmid. Key to their function is the tight regulation of expression of a protein toxin by an sRNA antitoxin. Here, we focus on the nonlinear nature of the regulatory circuit dynamics of the toxin-antitoxin mechanism. The mechanism relies on a transient increase in protein concentration rather than on the steady state of the genetic circuit. Through a systematic analysis of the parameter dependence of this transient increase, we confirm some known design features of this system and identify new ones: for an efficient toxin-antitoxin mechanism, the synthesis rate of the toxin’s mRNA template should be lower that of the sRNA antitoxin, the mRNA template should be more stable than the sRNA antitoxin, and the mRNA-sRNA complex should be more stable than the sRNA antitoxin. Moreover, a short half-life of the protein toxin is also beneficial to the function of the toxin-antitoxin system. In addition, we study a therapeutic scenario in which a competitor mRNA is introduced to sequester the sRNA antitoxin, causing the toxic protein to be expressed. Y1 - 2017 U6 - https://doi.org/10.1371/journal.pone.0169703 SN - 1932-6203 VL - 12 PB - PLoS CY - San Fransisco ER - TY - JOUR A1 - Gong, Chen Chris A1 - Tönjes, Ralf A1 - Pikovsky, Arkady T1 - Coupled Möbius maps as a tool to model Kuramoto phase synchronization JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We propose Mobius maps as a tool to model synchronization phenomena in coupled phase oscillators. Not only does the map provide fast computation of phase synchronization, it also reflects the underlying group structure of the sinusoidally coupled continuous phase dynamics. We study map versions of various known continuous-time collective dynamics, such as the synchronization transition in the Kuramoto-Sakaguchi model of nonidentical oscillators, chimeras in two coupled populations of identical phase oscillators, and Kuramoto-Battogtokh chimeras on a ring, and demonstrate similarities and differences between the iterated map models and their known continuous-time counterparts. Y1 - 2020 U6 - https://doi.org/10.1103/PhysRevE.102.022206 SN - 2470-0045 SN - 2470-0053 SN - 1063-651X SN - 2470-0061 SN - 1550-2376 VL - 102 IS - 2 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Gong, Chen Chris A1 - Zheng, Chunming A1 - Toenjes, Ralf A1 - Pikovskij, Arkadij T1 - Repulsively coupled Kuramoto-Sakaguchi phase oscillators ensemble subject to common noise JF - Chaos : an interdisciplinary journal of nonlinear science N2 - We consider the Kuramoto-Sakaguchi model of identical coupled phase oscillators with a common noisy forcing. While common noise always tends to synchronize the oscillators, a strong repulsive coupling prevents the fully synchronous state and leads to a nontrivial distribution of oscillator phases. In previous numerical simulations, the formation of stable multicluster states has been observed in this regime. However, we argue here that because identical phase oscillators in the Kuramoto-Sakaguchi model form a partially integrable system according to the Watanabe-Strogatz theory, the formation of clusters is impossible. Integrating with various time steps reveals that clustering is a numerical artifact, explained by the existence of higher order Fourier terms in the errors of the employed numerical integration schemes. By monitoring the induced change in certain integrals of motion, we quantify these errors. We support these observations by showing, on the basis of the analysis of the corresponding Fokker-Planck equation, that two-cluster states are non-attractive. On the other hand, in ensembles of general limit cycle oscillators, such as Van der Pol oscillators, due to an anharmonic phase response function as well as additional amplitude dynamics, multiclusters can occur naturally. Published under license by AIP Publishing. Y1 - 2019 U6 - https://doi.org/10.1063/1.5084144 SN - 1054-1500 SN - 1089-7682 VL - 29 IS - 3 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Peter, Franziska A1 - Gong, Chen Chris A1 - Pikovskij, Arkadij T1 - Microscopic correlations in the finite-size Kuramoto model of coupled oscillators JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - Supercritical Kuramoto oscillators with distributed frequencies can be separated into two disjoint groups: an ordered one locked to the mean field, and a disordered one consisting of effectively decoupled oscillators-at least so in the thermodynamic limit. In finite ensembles, in contrast, such clear separation fails: The mean field fluctuates due to finite-size effects and thereby induces order in the disordered group. This publication demonstrates this effect, similar to noise-induced synchronization, in a purely deterministic system. We start by modeling the situation as a stationary mean field with additional white noise acting on a pair of unlocked Kuramoto oscillators. An analytical expression shows that the cross-correlation between the two increases with decreasing ratio of natural frequency difference and noise intensity. In a deterministic finite Kuramoto model, the strength of the mean-field fluctuations is inextricably linked to the typical natural frequency difference. Therefore, we let a fluctuating mean field, generated by a finite ensemble of active oscillators, act on pairs of passive oscillators with a microscopic natural frequency difference between which we then measure the cross-correlation, at both super- and subcritical coupling. Y1 - 2019 U6 - https://doi.org/10.1103/PhysRevE.100.032210 SN - 2470-0045 SN - 2470-0053 VL - 100 IS - 3 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Gong, Chen Chris A1 - Pikovskij, Arkadij T1 - Low-dimensional dynamics for higher-order harmonic, globally coupled phase-oscillator ensembles JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - The Kuramoto model, despite its popularity as a mean-field theory for many synchronization phenomenon of oscillatory systems, is limited to a first-order harmonic coupling of phases. For higher-order coupling, there only exists a low-dimensional theory in the thermodynamic limit. In this paper, we extend the formulation used by Watanabe and Strogatz to obtain a low-dimensional description of a system of arbitrary size of identical oscillators coupled all-to-all via their higher-order modes. To demonstrate an application of the formulation, we use a second harmonic globally coupled model, with a mean-field equal to the square of the Kuramoto mean-field. This model is known to exhibit asymmetrical clustering in previous numerical studies. We try to explain the phenomenon of asymmetrical clustering using the analytical theory developed here, as well as discuss certain phenomena not observed at the level of first-order harmonic coupling. Y1 - 2019 U6 - https://doi.org/10.1103/PhysRevE.100.062210 SN - 2470-0045 SN - 2470-0053 VL - 100 IS - 6 PB - American Physical Society CY - College Park ER - TY - THES A1 - Gong, Chen Chris T1 - Synchronization of coupled phase oscillators BT - theory and modelling BT - Theorie und Modellierung N2 - Oscillatory systems under weak coupling can be described by the Kuramoto model of phase oscillators. Kuramoto phase oscillators have diverse applications ranging from phenomena such as communication between neurons and collective influences of political opinions, to engineered systems such as Josephson Junctions and synchronized electric power grids. This thesis includes the author's contribution to the theoretical framework of coupled Kuramoto oscillators and to the understanding of non-trivial N-body dynamical systems via their reduced mean-field dynamics. The main content of this thesis is composed of four parts. First, a partially integrable theory of globally coupled identical Kuramoto oscillators is extended to include pure higher-mode coupling. The extended theory is then applied to a non-trivial higher-mode coupled model, which has been found to exhibit asymmetric clustering. Using the developed theory, we could predict a number of features of the asymmetric clustering with only information of the initial state provided. The second part consists of an iterated discrete-map approach to simulate phase dynamics. The proposed map --- a Moebius map --- not only provides fast computation of phase synchronization, it also precisely reflects the underlying group structure of the dynamics. We then compare the iterated-map dynamics and various analogous continuous-time dynamics. We are able to replicate known phenomena such as the synchronization transition of the Kuramoto-Sakaguchi model of oscillators with distributed natural frequencies, and chimera states for identical oscillators under non-local coupling. The third part entails a particular model of repulsively coupled identical Kuramoto-Sakaguchi oscillators under common random forcing, which can be shown to be partially integrable. Via both numerical simulations and theoretical analysis, we determine that such a model cannot exhibit stationary multi-cluster states, contrary to the numerical findings in previous literature. Through further investigation, we find that the multi-clustering states reported previously occur due to the accumulation of discretization errors inherent in the integration algorithms, which introduce higher-mode couplings into the model. As a result, the partial integrability condition is violated. Lastly, we derive the microscopic cross-correlation of globally coupled non-identical Kuramoto oscillators under common fluctuating forcing. The effect of correlation arises naturally in finite populations, due to the non-trivial fluctuations of the meanfield. In an idealized model, we approximate the finite-sized fluctuation by a Gaussian white noise. The analytical approximation qualitatively matches the measurements in numerical experiments, however, due to other periodic components inherent in the fluctuations of the mean-field there still exist significant inconsistencies. N2 - Oszillatorische Systeme unter schwacher Kopplung können durch das Kuramoto-Modell beschrieben werden. Kuramoto-Phasenoszillatoren besitzen eine Vielzahl von Modellanwendungsfällen von der Kommunikation zwischen Nervenzellen bis zu kollektiven Einflüssen auf die politische Meinungsbildung sowie ingenieurwissenschaftlichen Anwendungen wie Josephson-Kontakten und synchronisierten elektrischen Übertragungsnetzen. In dieser Dissertation werden die Beiträge der Autorin zur Theorie der Kuramoto-Oszillatorensysteme und zum Verständnis nichttrivialer dynamischer NKörpersysteme durch die Analyse ihrer reduzierten Mittelfelddynamik zusammengefasst. Der Hauptinhalt dieser Dissertation umfasst vier Teile: Zuerst wird eine teilweise integrable Theorie global gekoppelter, identischer Kuramoto-Oszillatoren so erweitert, dass sie auch den Fall reiner Phasenkopplung höherer Ordnung umfasst. Die erweiterte Theorie wird anschließend auf ein nichttriviales Modell mit harmonischer Kopplung höherer Ordnung angewendet, welches asymmetrisches Clustering aufweist. Die Theorie sagt rein auf Basis der Anfangssystembedingungen einige Eigenschaften des asymmetrischen Clustering erfolgreich voraus. Im zweiten Teil wird die Phasendynamik von Kuramoto-Oszillatoren mithilfe einer iterierten diskreten Abbildung simuliert. Diese Abbildung – eine Möbius-Abbildung – erlaubt nicht nur eine schnelle Berechnung der Phasensynchronisation sondern spiegelt die zugrundeliegende Gruppenstruktur der Phasendynamik auch exakt wieder. Die Dynamik der iterierten Abbildung wird mit verschiedenen analogen Dynamiken mit kontinuierlicher Zeitachse verglichen. Hierbei werden bekannte Phänomene, wie etwa der Phasenübergang im Kuramoto-Sakaguchi-Oszillatormodell mit einer Verteilung der natürlichen Frequenzen und “Chimärenzustände” (chimera states) bei identischen Oszillatoren nichtlokalen Kopplungstypen, repliziert. Im dritten Teil wird ein Modell von repulsiv gekoppelten, identischen, gemeinsam stochastisch getriebenen Kuramoto-Sakaguchi-Oszillatoren beschrieben, dass teilweise integrabel ist. Sowohl durch numerische Simulationen als auch theoretische Analyse wird gezeigt, dass dieses Modell keine stationären Multi-Cluster-Zustände einnehmen kann, was den Ergebnissen anderer numerischer Studien in der Literatur widerspricht. Durch eine weitergehende Analyse wird gezeigt, dass das scheinbare Auftreten von Multi-Cluster-Zuständen der Akkumulation von inhärenten Diskretisierungsfehlern der verwendeten Integrationsalgorithmen zuzuschreiben ist, welche dem Modell Phasenkopplungen höher Ordnung hinzufügen. Als Resultat dieser Effekte wird die Bedingung der teilweisen Integrabilität verletzt. Zuletzt wird die mikroskopische Kreuzkorrelation zwischen global gekoppelten, nicht identischen gemeinsam fluktuierend getriebenen Kuramoto-Oszillatoren hergeleitet. Der Korrelationseffekt entsteht auf natürliche Art und Weise in endlichen Populationen aufgrund der nichttrivialen Fluktuation des Mittelfelds. Die endliche Fluktuation wird in einem idealisierten Modell mittels gaußschem weißem Rauschen approximiert. Die analytische Annährung stimmt mit den Ergebnissen numerischer Simulationen gut überein, die inhärenten periodischen Komponenten der Fluktuation des Mittelfels verursachen allerdings trotzdem signifikante Inkonsistenzen. T2 - Synchronisation der gekoppelten Oszillatoren KW - Synchronization KW - Nonlinear Dynamics KW - Nichtlineare Dynamik KW - Synchronisation KW - Kuramoto Oscillators KW - Kuramoto-Oszillatore KW - Complex Network KW - Komplexes Netzwerk Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-487522 ER -