论文标题
薄粘性膜的弯曲驱动趋于弯曲的平均水平的通用自相似吸引子
Universal Self-Similar Attractor in the Bending-Driven Leveling of Thin Viscous Films
论文作者
论文摘要
我们从理论和数字上研究润滑近似中薄粘性膜的弯曲驱动的水平。我们得出线性化薄膜方程的绿色功能，并进一步表明它长期代表了通用的自相似吸引子。因此，对于任何可总结的初始扰动曲线，胶片曲线的重新摄动将及时地趋向于重新缩放的绿色功能。此外，对于跨轴对称初始条件，我们证明了另一个短期和一维的自相似度状态的存在。此外，我们将收敛时间与相关的物理和几何参数有关，并在通用状态下提供局部流体动力领域和全球弹性能量作为时间的函数。最后，我们通过数值模拟将分析扩展到非线性薄膜方程。
We study theoretically and numerically the bending-driven leveling of thin viscous films within the lubrication approximation. We derive the Green's function of the linearized thin-film equation and further show that it represents a universal self-similar attractor at long times. As such, the rescaled perturbation of the film profile converges in time towards the rescaled Green's function, for any summable initial perturbation profile. In addition, for stepped axisymmetric initial conditions, we demonstrate the existence of another, short-term and one-dimensional-like self-similar regime. Besides, we characterize the convergence time towards the long-term universal attractor in terms of the relevant physical and geometrical parameters, and provide the local hydrodynamic fields and global elastic energy in the universal regime as functions of time. Finally, we extend our analysis to the non-linear thin-film equation through numerical simulations.
