论文标题
流体动力晶格的离散复合物Ginzburg-Landau方程
A discrete complex Ginzburg-Landau equation for a hydrodynamic active lattice
论文作者
论文摘要
与离散平均方程相连的离散和周期性复杂的Ginzburg-Landau方程是系统地衍生自驱动和耗散振荡器模型的，接近超临界Hopf分叉的开始。振荡器模型的灵感来自最近的实验，该实验探索了在垂直振动的流体浴场上弹跳的自前线毫米液滴的准二维晶格的主动振动。我们的系统推导提供了晶格系统的本构特性与所得振幅方程的系数之间的直接联系，为比较出现的非线性非线性动力学铺平了道路 - 即分散的明亮和深色的孤子，呼吸器，呼吸器和行进波 - 与实验相对。此外，振幅方程使我们能够合理化导致这些不同动态状态的连续分叉。预计本文介绍的框架适用于更广泛的振荡器，其特征在于粒子之间存在动态耦合电位。更广泛地说，我们的结果表明，非线性振荡器与主动物质物理学之间的更深层次的联系。
A discrete and periodic complex Ginzburg-Landau equation, coupled to a discrete mean equation, is systematically derived from a driven and dissipative oscillator model, close to the onset of a supercritical Hopf bifurcation. The oscillator model is inspired by recent experiments exploring active vibrations of quasi-one-dimensional lattices of self-propelled millimetric droplets bouncing on a vertically vibrating fluid bath. Our systematic derivation provides a direct link between the constitutive properties of the lattice system and the coefficients of the resultant amplitude equations, paving the way to compare the emergent nonlinear dynamics---namely discrete bright and dark solitons, breathers, and traveling waves---against experiments. Further, the amplitude equations allow us to rationalize the successive bifurcations leading to these distinct dynamical states. The framework presented herein is expected to be applicable to a wider class of oscillators characterized by the presence of a dynamic coupling potential between particles. More broadly, our results point to deeper connections between nonlinear oscillators and the physics of active and driven matter.
