Synchronization transition of the second-order Kuramoto model on lattices
| Autor: | Géza Ódor, Shengfeng Deng |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Statistical Mechanics (cond-mat.stat-mech)
General Physics and Astronomy FOS: Physical sciences Chaotic Dynamics (nlin.CD) Computational Physics (physics.comp-ph) Nonlinear Sciences - Chaotic Dynamics Physics - Computational Physics Condensed Matter - Statistical Mechanics synchronization hybrid phase transition criticality chaoticity |
| Zdroj: | Entropy; Volume 25; Issue 1; Pages: 164 |
| Popis: | The second-order Kuramoto equation describes synchronization of coupled oscillators with inertia, which occur in power grids for example. Contrary to the first-order Kuramoto equation it's synchronization transition behavior is much less known. In case of Gaussian self-frequencies it is discontinuous, in contrast to the continuous transition for the first-order Kuramoto equation. Here we investigate this transition on large 2d and 3d lattices and provide numerical evidence of hybrid phase transitions, that the oscillator phases $\theta_i$, exhibit a crossover, while the frequency spread a real phase transition in 3d. Thus a lower critical dimension $d_l^O=2$ is expected for the frequencies and $d_l^R=4$ for the phases like in the massless case. We provide numerical estimates for the critical exponents, finding that the frequency spread decays as $\sim t^{-d/2}$ in case of aligned initial state of the phases in agreement with the linear approximation. However in 3d, in the case of initially random distribution of $\theta_i$, we find a faster decay, characterized by $\sim t^{-1.8(1)}$ as the consequence of enhanced nonlinearities which appear by the random phase fluctuations. Comment: 8 pages, 10 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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