非均匀振荡介质中的缺陷、分区与重整化负扩散系数
Defects, parcellation, and renormalized negative diffusivities in non-homogeneous oscillatory media
AI总结：
本文完整刻画了具有频率梯度的Ginzburg-Landau模型相图，揭示平台与缺陷的形成机制，并将缺陷来源归结为扩散系数的非线性重整化，同时给出缺陷数量与长度的标度关系。
摘要：
空间非均匀性可以使空间延展振子簇在不同频率平台上同步。受生理节律的启发，我们完整刻画了具有频率梯度的Ginzburg-Landau（GL）模型的相图。对于大梯度和扩散，静止态是稳定的，其周围的线性谱映射到非厄米Bloch-Torrey方程上。当复特征值对变得不稳定时，平台的前驱体开始增长，并由GL振幅消失的缺陷所分隔。非线性效应要么使平台振幅饱和，要么导致锁相态，鞍结分岔将这两种机制区分开来。在平台区域中，我们将缺陷的形成追溯到扩散系数的非线性重整化，并确定了缺陷数量和长度随动力学参数的标度关系。
英文摘要：
Spatial non-homogeneities can synchronize clusters of spatially-extended oscillators in different frequency plateaus. Motivated by physiological rhythms, we fully characterize the phase diagram of a Ginzburg-Landau (GL) model with a gradient of frequencies. For large gradients and diffusion, the rest state is stable, and the linear spectrum around it maps onto the non-Hermitian Bloch-Torrey equation. When complex pairs of eigenvalues turn unstable, precursors of plateaus grow, separated by defects where the GL amplitude vanishes. Nonlinear effects either saturate the amplitude of plateaus or lead to a phase-locked state, with saddle-node bifurcations separating the two regimes. In the region of plateaus, we trace the formation of defects to a non-linear renormalization of the diffusivity, and determine the scaling of their number and length vs dynamical parameters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
