Experimental observation of a chaos-to-chaos transition in laser droplet generation

TL;DR

This paper investigates the chaotic dynamics of laser droplet generation, revealing a transition from spontaneous chaos to triggered chaos with an intermediate phase, using Lyapunov exponents and recurrence plots.

Contribution

It provides the first detailed analysis of the chaos-to-chaos transition in laser droplet generation, combining experimental observations with dynamical systems characterization.

Findings

Spontaneous droplet dripping is deterministically chaotic.

Detachment pulse influences droplet dynamics, inducing amplitude chaos.

Transition involves an intermittent period-doubling to chaos, with a nonstationary phase.

Abstract

We examine the dynamics of laser droplet generation in dependence on the detachment pulse power. In the absence of the detachment pulse, undulating pendant droplets are formed at the end of a properly fed metal wire due to the impact of the primary laser pulse that induces melting. Eventually, these droplets detach, i.e. overcome the surface tension, because of their increasing mass. We show that this spontaneous dripping is deterministically chaotic by means of a positive largest Lyapunov exponent and a negative divergence. In the presence of the detachment pulse, however, the generation of droplets is fastened depending on the pulse power. At high powers, the spontaneity of dripping is completely overshadowed by the impact of the detachment pulse. Still, amplitude chaos can be detected, which similarly as the spontaneous dripping, is characterized by a positive largest Lyapunov exponent and a negative divergence, thus indicating that the observed dynamics is deterministically chaotic with an attractor as solution in the phase space. In the intermediate regime, i.e. for low and medium detachment pulse powers, the two chaotic states compete for supremacy, yielding an intermittent period-doubling to amplitude chaos transition, which we characterize by means of recurrence plots and their properties. Altogether, the transition from spontaneous to triggered laser droplet generation is characterized by a chaos-to-chaos transition with an intermediate dynamically nonstationary phase in-between. Since metal droplets can be used in various industrial applications, we hope that the accurate determination of the dynamical properties underlying their formation will facilitate their use and guide future attempts at mathematical modeling.