laser液滴生成动力学
The dynamics of laser droplet generation
摘要：
我们提出了一个实验装置，允许激光液滴生成的基本动力学方面的表征，主要表明，后者是确定性的混沌通过非线性时间序列分析方法。特别地，我们使用激光脉冲来熔化适当进给的垂直放置的金属线的端部。由于表面张力、重力和轻金属相互作用的相互作用，在熔融端处形成起伏的悬垂液滴，由于其质量增加，这些液滴最终完全从线材分离。我们通过采用高速红外摄像机捕获这个过程的动态，从而间接测量线端和悬垂液滴的温度。时间序列随后被生成为每个红外快照的像素强度的平均值。最后，我们采用非线性时间序列分析的方法来重建相空间的观察变量和测试它对确定性和平稳性。在建立了所观察到的激光液滴生成是一个确定的和动态平稳的过程后，我们计算了李雅普诺夫指数的频谱。我们得到一个正的最大李雅普诺夫指数和一个负的发散，即，所有指数的总和，从而表明所观察到的动力学是确定性的混沌与吸引子作为相空间中的解决方案。除了表征激光液滴生成的动力学，我们概述了该过程的工业应用，并指出了我们的研究结果对未来数学建模尝试的意义。
英文摘要：
We propose an experimental setup allowing for the characterization of laser droplet generation in terms of the underlying dynamics, primarily showing that the latter is deterministically chaotic by means of nonlinear time series analysis methods. In particular, we use a laser pulse to melt the end of a properly fed vertically placed metal wire. Due to the interplay of surface tension, gravity force and light-metal interaction, undulating pendant droplets are formed at the molten end, which eventually completely detach from the wire as a consequence of their increasing mass. We capture the dynamics of this process by employing a high-speed infrared camera, thereby indirectly measuring the temperature of the wire end and the pendant droplets. The time series is subsequently generated as the mean value over the pixel intensity of every infrared snapshot. Finally, we employ methods of nonlinear time series analysis to reconstruct the phase space from the observed variable and test it against determinism and stationarity. After establishing that the observed laser droplet generation is a deterministic and dynamically stationary process, we calculate the spectra of Lyapunov exponents. We obtain a positive largest Lyapunov exponent and a negative divergence, i.e., sum of all the exponents, thus indicating that the observed dynamics is deterministically chaotic with an attractor as solution in the phase space. In addition to characterizing the dynamics of laser droplet generation, we outline industrial applications of the process and point out the significance of our findings for future attempts at mathematical modeling.
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