论文标题
在柔性身体的捕捉动力学中，能量聚焦的异常曲率进化和几何正规化
Anomalous curvature evolution and geometric regularization of energy focusing in the snapping dynamics of a flexible body
论文作者
论文摘要
我们检查了动能的聚焦和在柔性结构的自由端的捕捉运动过程中的各种数量的扩增。这个简短但暴力的事件似乎是一个正规的有限时间奇异性，速度，加速度和张力很大，很容易由通用初始和边界条件引起。针对不可扩展的字符串方程的数值方案已针对降落链的可用实验数据进行了验证，并进一步用于探索现象。我们确定方程式的离散化等同于链的物理离散问题，不能提供正则长度尺度，在没有其他物理效果的情况下，必须由问题的几何形状产生。 An analytical solution for a geometrically singular limit, a falling perfectly-folded string, accounts surprisingly well for the scalings of several quantities in the numerics, but can only indirectly suggest a behavior for the curvature, one which seems to explain prior experimental data but does not correspond to the evolution of the curvature peak in our system, which instead displays a newly observed anomalously slow scaling.一个简单的模型，仅结合初始条件的知识以及异常和奇异限制量表，为相关数量的放大提供了合理的估计。这是预测和利用结构中的大型能量的第一步，其实际极限仅由离散机械系统或初始条件中的长度尺度设置。
We examine the focusing of kinetic energy and the amplification of various quantities during the snapping motion of the free end of a flexible structure. This brief but violent event appears to be a regularized finite-time singularity, with remarkably large spikes in velocity, acceleration, and tension easily induced by generic initial and boundary conditions. A numerical scheme for the inextensible string equations is validated against available experimental data for a falling chain and further employed to explore the phenomenon. We determine that the discretization of the equations, equivalent to the physically discrete problem of a chain, does not provide the regularizing length scale, which in the absence of other physical effects must then arise from the geometry of the problem. An analytical solution for a geometrically singular limit, a falling perfectly-folded string, accounts surprisingly well for the scalings of several quantities in the numerics, but can only indirectly suggest a behavior for the curvature, one which seems to explain prior experimental data but does not correspond to the evolution of the curvature peak in our system, which instead displays a newly observed anomalously slow scaling. A simple model, incorporating only knowledge of the initial conditions along with the anomalous and singular-limit scalings, provides reasonable estimates for the amplifications of relevant quantities. This is a first step to predict and harness arbitrarily large energy focusing in structures, with a practical limit set only by length scales present in the discrete mechanical system or the initial conditions.
