The Kuramoto Model: The Stability Conditions in the Presence of Phase Shift

2021 ◽  
Author(s):  
Reza Farhangi ◽  
Mohammad Taghi Hamidi Beheshti
Keyword(s):  
Phase Shift ◽  
Kuramoto Model ◽  
Stability Conditions ◽  
The Stability ◽  
The Kuramoto Model

From centralized to decentralized power system: A space-analysis for France

2020 ◽  
Vol 64 (1-4) ◽  
pp. 73-78
Author(s):  
Raphaël Cluet ◽  
Nadia Maïzi ◽  
Vincent Mazauric
Keyword(s):  
Kinetic Energy ◽  
Power System ◽  
Kuramoto Model ◽  
Energy Planning ◽  
System A ◽  
System Energy ◽  
The Stability ◽  
The Kuramoto Model ◽  
Grid Based

This paper reviews the conditions for ensuring the space consolidation and time reconciliation of all scales involved in power system energy planning. At the upper space scale, a simplified description of the grid based on the Kuramoto model is adopted to assess the stability of the synchronism state of the power system. The consequences of a massive dissemination of renewables for the future of the power system is addressed in the case of France in a long-term planning exercise up to 2050. Attention is paid to how the new capacities are dispatched among the administrative regions. While a favorable impact of sparse generation on the synchronism is obtained, the constraint on the inertia provided by the kinetic energy has to be endogenized to enforce an operable power mix under admissible disturbances.

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

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.

scholarly journals Emergent synchronous beating behavior in spontaneous beating cardiomyocyte clusters

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.

scholarly journals Causality and stability conditions of a conformal charged fluid

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Farid Taghinavaz
Keyword(s):  
Chemical Potential ◽  
Second Law Of Thermodynamics ◽  
Dense Medium ◽  
Wave Number ◽  
Second Law ◽  
Stability Conditions ◽  
Charged Fluid ◽  
Large Wave ◽  
The Stability ◽  
Large Wave Number

Abstract In this paper, I study the conditions imposed on a normal charged fluid so that the causality and stability criteria hold for this fluid. I adopt the newly developed General Frame (GF) notion in the relativistic hydrodynamics framework which states that hydrodynamic frames have to be fixed after applying the stability and causality conditions. To do this, I take a charged conformal matter in the flat and 3 + 1 dimension to analyze better these conditions. The causality condition is applied by looking to the asymptotic velocity of sound hydro modes at the large wave number limit and stability conditions are imposed by looking to the imaginary parts of hydro modes as well as the Routh-Hurwitz criteria. By fixing some of the transports, the suitable spaces for other ones are derived. I observe that in a dense medium having a finite U(1) charge with chemical potential μ0, negative values for transports appear and the second law of thermodynamics has not ruled out the existence of such values. Sign of scalar transports are not limited by any constraints and just a combination of vector transports is limited by the second law of thermodynamic. Also numerically it is proved that the most favorable region for transports $$ {\tilde{\upgamma}}_{1,2}, $$ γ ˜ 1 , 2 , coefficients of the dissipative terms of the current, is of negative values.

scholarly journals Iterative stability analysis for general polynomial control systems

2021 ◽  
Author(s):  
Bo Xiao ◽  
Hak-Keung Lam ◽  
Zhixiong Zhong
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Control Systems ◽  
Polynomial System ◽  
Stability Conditions ◽  
General Polynomial ◽  
Main Challenge ◽  
Detailed Simulation ◽  
Feasible Solutions ◽  
The Stability

AbstractThe main challenge of the stability analysis for general polynomial control systems is that non-convex terms exist in the stability conditions, which hinders solving the stability conditions numerically. Most approaches in the literature impose constraints on the Lyapunov function candidates or the non-convex related terms to circumvent this problem. Motivated by this difficulty, in this paper, we confront the non-convex problem directly and present an iterative stability analysis to address the long-standing problem in general polynomial control systems. Different from the existing methods, no constraints are imposed on the polynomial Lyapunov function candidates. Therefore, the limitations on the Lyapunov function candidate and non-convex terms are eliminated from the proposed analysis, which makes the proposed method more general than the state-of-the-art. In the proposed approach, the stability for the general polynomial model is analyzed and the original non-convex stability conditions are developed. To solve the non-convex stability conditions through the sum-of-squares programming, the iterative stability analysis is presented. The feasible solutions are verified by the original non-convex stability conditions to guarantee the asymptotic stability of the general polynomial system. The detailed simulation example is provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed approach is more capable to find feasible solutions for the general polynomial control systems when compared with the existing ones.

scholarly journals Investigation of Preferred Orientations in Planar Polycrystals

2008 ◽  
Vol 75 (5) ◽  
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.

scholarly journals The Kuramoto model: A simple paradigm for synchronization phenomena

2005 ◽  
Vol 77 (1) ◽  
pp. 137-185 ◽  
Author(s):  
Juan A. Acebrón ◽  
L. L. Bonilla ◽  
Conrad J. Pérez Vicente ◽  
Félix Ritort ◽  
Renato Spigler
Keyword(s):  
Kuramoto Model ◽  
The Kuramoto Model
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