Choi Chulho, Ha Meesoon, Kahng Byungnam
Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Sep;88(3):032126. doi: 10.1103/PhysRevE.88.032126. Epub 2013 Sep 18.
We present a systematic analysis of dynamic scaling in the time evolution of the phase order parameter for coupled oscillators with nonidentical natural frequencies in terms of the Kuramoto model. This provides a comprehensive view of phase synchronization. In particular, we extend finite-size scaling (FSS) in the steady state to dynamics, determine critical exponents, and find the critical coupling strength. The dynamic scaling approach enables us to measure not only the FSS exponent associated with the correlation volume in finite systems but also thermodynamic critical exponents. Based on the extended FSS theory, we also discuss how the sampling of natural frequencies and thermal noise affect dynamic scaling, which is numerically confirmed.
我们基于Kuramoto模型，对具有不同固有频率的耦合振子的相位序参量时间演化中的动态标度进行了系统分析。这提供了相位同步的全面视图。特别地，我们将稳态下的有限尺寸标度（FSS）扩展到动力学，确定临界指数，并找到临界耦合强度。动态标度方法不仅使我们能够测量与有限系统中相关体积相关的FSS指数，还能测量热力学临界指数。基于扩展的FSS理论，我们还讨论了固有频率的采样和热噪声如何影响动态标度，这在数值上得到了证实。
