Walking droplets are millimetric fluid drops that propel themselves across a vibrated liquid bath through interaction with their self-generated waves. They constitute classical active wave-particle entities and exhibit a range of hydrodynamic quantum analogs. We investigate an \emph{active soft-impact oscillator} as a minimal model for a walking droplet moving within a piecewise-smooth external potential, analogous to classical mass-spring soft-impact oscillators and recently explored quantum soft-impact oscillators. Our active soft-impact oscillator model couples a non-smooth soft-impact force to the Lorenz-like dynamics arising from the wave-particle entity. Theoretical and numerical exploration of the full parameter space reveals a wide variety of nonlinear behaviors and bifurcations driven by impact and grazing events. These include grazing-induced and impact-induced transitions between periodic and chaotic motion, as well as grazing-mediated attractor switching and impact-free (invisible) attractor switching. The active soft-impact oscillator thus provides a versatile platform for probing nonlinear impact dynamics in active systems and exploring hydrodynamic quantum analogs in non-smooth potentials.
Diffraction of walking drops by a standing Faraday wave
Department of Mathematics, MIT（麻省理工学院数学系）；Department of Mechanical Engineering, Boston University（波士顿大学机械工程系）；Department of Mathematics, UNC, Chapel Hill（北卡罗来纳大学教堂山分校数学系）
Phase and frequency entrainment in locally coupled phase oscillators with repulsive interactions
最近在含有Belousov-Zhabotinsky反应物的液滴的一维和二维微流体阵列中的实验显示了丰富多样的空间图案[J. Phys. Chem. Lett. 1，1241-1246（2010）]。这些液滴之间的主要偶联是抑制性的。受这个实验系统的启发，我们研究了具有最近邻相互作用的排斥耦合Kuramoto振荡器，一维线性链和环，以及二维三角晶格。在一维，我们使用线性稳定性分析以及数值研究，稳定的相位图案取决于晶格的几何形状。我们表明，过渡到有序状态不存在的热力学极限。在两个维度上，我们表明，晶格的几何形状约束两个相邻的振荡器之间的相位差为120度。我们报告存在的域与顺时针或逆时针螺旋，导致缺陷的晶格。我们研究了这些域的时间依赖性，并表明，在大的耦合强度，域冻结由于频率同步。上述现象的特征可以在空间关联函数中看到。
