Optimizing synchronization stability of the Kuramoto model in complex networks and power grids

In this work we model the dynamics of power grids in terms of a two-layer network, and use the Italian high voltage power grid as a proof-of-principle example. The first layer in our model represents the power grid consisting of generators and consumers, while the second layer represents a dynamic communication network that serves as a controller of the first layer. The dynamics of the power grid is modelled by the Kuramoto model with inertia, while the communication layer provides a control signal Pc i for each generator to improve frequency synchronization within the power grid. We propose different realizations of the communication layer topology and of the control signal, and test the control performances in presence of generators with stochastic power output. When using a control topology that allows all generators to exchange information, we find that a control scheme aimed to minimize the frequency difference between adjacent nodes operates very efficiently even against the worst scenarios with the strongest perturbations. On the other hand, for a control topology where the generators possess the same communication links as in the power grid layer, a control scheme aimed at restoring the synchronization frequency in the neighborhood of the controlled node turns out to be more efficient.

Download Full-text

Emulating the local Kuramoto model with an injection-locked photonic crystal laser array

Scientific Reports ◽

10.1038/s41598-021-86982-w ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Naotomo Takemura ◽

Kenta Takata ◽

Masato Takiguchi ◽

Masaya Notomi

Keyword(s):

Photonic Crystal ◽

Nearest Neighbor ◽

Multiple Quantum Well ◽

Kuramoto Model ◽

Multiple Quantum ◽

Laser Array ◽

Novel Strategy ◽

A Chain ◽

The One ◽

The Kuramoto Model

AbstractThe Kuramoto model is a mathematical model for describing the collective synchronization phenomena of coupled oscillators. We theoretically demonstrate that an array of coupled photonic crystal lasers emulates the Kuramoto model with non-delayed nearest-neighbor coupling (the local Kuramoto model). Our novel strategy employs indirect coupling between lasers via additional cold cavities. By installing cold cavities between laser cavities, we avoid the strong coupling of lasers and realize ideal mutual injection-locking with effective non-delayed dissipative coupling. First, after discussing the limit cycle interpretation of laser oscillation, we demonstrate the synchronization of two indirectly coupled lasers by numerically simulating coupled-mode equations. Second, by performing a phase reduction analysis, we show that laser dynamics in the proposed device can be mapped to the local Kuramoto model. Finally, we briefly demonstrate that a chain of indirectly coupled photonic crystal lasers actually emulates the one-dimensional local Kuramoto chain. We also argue that our proposed structure, which consists of periodically aligned cold cavities and laser cavities, will best be realized by using state-of-the-art buried multiple quantum well photonic crystals.

Download Full-text

Partially Phase-Locked Solutions to the Kuramoto Model

Journal of Statistical Physics ◽

10.1007/s10955-021-02783-5 ◽

2021 ◽

Vol 183 (3) ◽

Author(s):

Jared C. Bronski ◽

Lan Wang

Keyword(s):

Kuramoto Model ◽

The Kuramoto Model

Download Full-text

Emergent synchronous beating behavior in spontaneous beating cardiomyocyte clusters

Scientific Reports ◽

10.1038/s41598-021-91466-y ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Kazufumi Sakamoto ◽

Yoshitsune Hondo ◽

Naoki Takahashi ◽

Yuhei Tanaka ◽

Rikuto Sekine ◽

...

Keyword(s):

Stem Cell ◽

Embryonic Stem Cell ◽

Human Embryonic Stem Cell ◽

Single Cells ◽

Embryonic Stem ◽

Kuramoto Model ◽

Distribution Analysis ◽

Cell Clusters ◽

Overdrive Suppression ◽

The Kuramoto Model

AbstractWe investigated the dominant rule determining synchronization of beating intervals of cardiomyocytes after the clustering of mouse primary and human embryonic-stem-cell (hES)-derived cardiomyocytes. Cardiomyocyte clusters were formed in concave agarose cultivation chambers and their beating intervals were compared with those of dispersed isolated single cells. Distribution analysis revealed that the clusters’ synchronized interbeat intervals (IBIs) were longer than the majority of those of isolated single cells, which is against the conventional faster firing regulation or “overdrive suppression.” IBI distribution of the isolated individual cardiomyocytes acquired from the beating clusters also confirmed that the clusters’ IBI was longer than those of the majority of constituent cardiomyocytes. In the complementary experiment in which cell clusters were connected together and then separated again, two cardiomyocyte clusters having different IBIs were attached and synchronized to the longer IBIs than those of the two clusters’ original IBIs, and recovered to shorter IBIs after their separation. This is not only against overdrive suppression but also mathematical synchronization models, such as the Kuramoto model, in which synchronized beating becomes intermediate between the two clusters’ IBIs. These results suggest that emergent slower synchronous beating occurred in homogeneous cardiomyocyte clusters as a community effect of spontaneously beating cells.

Download Full-text

Network isolators inhibit failure spreading in complex networks

Nature Communications ◽

10.1038/s41467-021-23292-9 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Franz Kaiser ◽

Vito Latora ◽

Dirk Witthaut

Keyword(s):

Complex Networks ◽

Large Scale ◽

Power Transmission ◽

Power Grids ◽

Cascading Failure ◽

Critical Infrastructures ◽

Daily Lives ◽

Supply Networks ◽

Water Transmission ◽

Complete Collapse

AbstractIn our daily lives, we rely on the proper functioning of supply networks, from power grids to water transmission systems. A single failure in these critical infrastructures can lead to a complete collapse through a cascading failure mechanism. Counteracting strategies are thus heavily sought after. In this article, we introduce a general framework to analyse the spreading of failures in complex networks and demostrate that not only decreasing but also increasing the connectivity of the network can be an effective method to contain damages. We rigorously prove the existence of certain subgraphs, called network isolators, that can completely inhibit any failure spreading, and we show how to create such isolators in synthetic and real-world networks. The addition of selected links can thus prevent large scale outages as demonstrated for power transmission grids.

Download Full-text

Modular synchronization in complex networks with a gauge Kuramoto model

EPL (Europhysics Letters) ◽

10.1209/0295-5075/83/68003 ◽

2008 ◽

Vol 83 (6) ◽

pp. 68003 ◽

Cited By ~ 16

Author(s):

E. Oh ◽

C. Choi ◽

B. Kahng ◽

D. Kim

Keyword(s):

Complex Networks ◽

Kuramoto Model

Download Full-text

Investigation of Preferred Orientations in Planar Polycrystals

Journal of Applied Mechanics ◽

10.1115/1.2912930 ◽

2008 ◽

Vol 75 (5) ◽

Cited By ~ 3

Author(s):

M. R. Tonks ◽

A. J. Beaudoin ◽

F. Schilder ◽

D. A. Tortorelli

Keyword(s):

Texture Evolution ◽

Mean Field ◽

Homogenization Method ◽

Process Models ◽

Kuramoto Model ◽

Taylor Model ◽

Crystal Plasticity Finite Element ◽

Polycrystal Plasticity ◽

Taylor Hypothesis ◽

The Kuramoto Model

More accurate manufacturing process models come from better understanding of texture evolution and preferred orientations. We investigate the texture evolution in the simplified physical framework of a planar polycrystal with two slip systems used by Prantil et al. (1993, “An Analysis of Texture and Plastic Spin for Planar Polycrystal,” J. Mech. Phys. Solids, 41(8), pp. 1357–1382). In the planar polycrystal, the crystal orientations behave in a manner similar to that of a system of coupled oscillators represented by the Kuramoto model. The crystal plasticity finite element method and the stochastic Taylor model (STM), a stochastic method for mean-field polycrystal plasticity, predict the development of a steady-state texture not shown when employing the Taylor hypothesis. From this analysis, the STM appears to be a useful homogenization method when using representative standard deviations.

Download Full-text