Discrete and periodic complex Ginzburg-Landau equation for a hydrodynamic active lattice
Discrete and periodic complex Ginzburg-Landau equation for a hydrodynamic active lattice
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流体动力活性晶格的离散周期复数 Ginzburg-Landau 方程
DOI：
10.1103/physreve.103.062215
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发表时间：
2021
影响因子：
2.4
通讯作者：
Rosales, Rodolfo R.
中科院分区：
文献类型：
--
作者：
Thomson, Stuart J.;Durey, Matthew;Rosales, Rodolfo R.
一个离散的和周期性的复杂的Ginzburg-Landau方程，耦合到一个平均方程，系统地来自一个驱动和耗散晶格振子模型，接近超临界Andronov-Hopf分岔的发病。振荡器模型的灵感来自最近的实验探索主动振动的准一维晶格的自推进毫米液滴弹跳在垂直振动的流体浴。我们的系统推导提供了一个直接的联系之间的晶格系统的本构性质和所得的振幅方程的系数，铺平了道路，比较新兴的非线性动力学，即发病和离散暗孤子，呼吸子，行波的形成，对实验。本文提出的框架预计将适用于更广泛的一类振荡器，其特征在于粒子之间的动态耦合电位的存在。更广泛地说，我们的结果指出了非线性振荡器与活性和驱动物质物理学之间更深层次的联系。
A discrete and periodic complex Ginzburg-Landau equation, coupled to a mean equation, is systematically derived from a driven and dissipative lattice oscillator model, close to the onset of a supercritical Andronov-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, the onset and formation of discrete dark solitons, breathers, and traveling waves—against experiments. 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.