Bouncing on thin air: how squeeze forces in the air film during non-wetting droplet bouncing lead to momentum transfer and dissipation

Millimetre-sized droplets are able to bounce multiple times on flat solid substrates irrespective of their wettability, provided that a micrometre-thick air layer is sustained below the droplet, limiting $\mathit{We}$ to ${\lesssim}4$. We study the energy conversion during a bounce series by analysing the droplet motion and its shape (decomposed into eigenmodes). Internal modes are excited during the bounce, yet the viscous dissipation associated with the in-flight oscillations accounts for less than 20 % of the total energy loss. This suggests a significant contribution from the bouncing process itself, despite the continuous presence of a lubricating air film below the droplet. To study the role of this air film we visualize it using reflection interference microscopy. We quantify its thickness (typically a few micrometres) with sub-millisecond time resolution and ${\sim}30~\text{nm}$ height resolution. Our measurements reveal strong asymmetry in the air film shape between the spreading and receding phases of the bouncing process. This asymmetry is crucial for effective momentum reversal of the droplet: lubrication theory shows that the dissipative force is repulsive throughout each bounce, even near lift-off, which leads to a high restitution coefficient. After multiple bounces the droplet eventually hovers on the air film, while continuously experiencing a lift force to sustain its weight. Only after a long time does the droplet finally wet the substrate. The observed bounce mechanism can be described with a single oscillation mode model that successfully captures the asymmetry of the air film evolution.

Synchronous Motor Pull-in Process Analysis

In this paper, simple approach to analyzing the starting procedure of synchronous motors (SMs) is presented with an emphasis on the pull-in process. Instead of the classical, mostly intuitive pulling-repelling torque approach, an analytical method based on the motor mechanical part swing equation is employed. Factors affecting starting and pull-in processes are clearly indicated and torque impulse balance leading to a pull into step is revealed. It is shown that if the motor fails to pull into step within a single oscillation, it can still be synchronized during one of the succeeding acceleration periods. The crucial role of the excitation winding energizing instant is demonstrated as well. Moreover, the revealed similarity between the SM and phase locked loop (PLL) operations, leads to the conclusion that the algorithms use for analyzing the operation of one may be employed for investigating the other. Experimental results are given to demonstrate the different scenarios, mentioned in the manuscript.

Host-parasite coevolution in populations of constant and variable size

The matching-allele and gene-for-gene models are widely used in math- ematical approaches that study the dynamics of host-parasite interactions. Agrawal and Lively (Evolutionary Ecology Research 4:79-90, 2002) captured these two models in a single framework and numerically explored the associated time discrete dynamics of allele frequencies. Here, we present a detailed analytical investigation of this unifying framework in continuous time and provide a generalization. We extend the model to take into account changing population sizes, which result from the antagonistic nature of the interaction and follow the Lotka-Volterra equations. Under this extension, the population dynamics become most complex as the model moves away from pure matching-allele and becomes more gene-for-gene-like. While the population densities oscillate with a single oscillation frequency in the pure matching-allele model, a second oscillation frequency arises under gene-for-gene-like conditions. These observations hold for general interaction parameters and allow to infer generic patterns of the dynamics. Our results suggest that experimentally inferred dynamical patterns of host-parasite coevolution should typically be much more complex than the popular illustrations of Red Queen dynamics. A single parasite that infects more than one host can substantially alter the cyclic dynamics.

Gain Scheduling Feedback Control for Tower Cranes

The objective of crane control is to build an algorithm to move a load from point to point in the shortest time without inducing large swings. We assume that this objective cannot be accomplished in less than a single oscillation cycle of the load. Therefore, the controller is built to move the load such that it completes only one oscillation cycle at the end of the motion. Consequently, the settling time of the system should be equal to the period of oscillation of the load. This criterion enables the calculation of the controller feedback gains for varying load weight and cable length. The controller is built first for overhead cranes and then modified for tower cranes. Two controllers are used, one for the rotational motion of the tower and the other for the translational motion of the trolley. Numerical simulations show that the controller is effective in reducing the load oscillations and transferring the load in a reasonable time compared with that of optimal control.

A Simple Adaptive Feedback Controller for Tower Cranes

The objective of crane control is to build an algorithm to move a load from point to point in the shortest time without inducing large swings. We assume that this objective cannot be accomplished in less than a single oscillation cycle of the load. Therefore, the controller is built to move the load such that it completes only one oscillation cycle at the end of the motion. Consequently, the settling time of the system should be equal to the period of oscillation of the load. This criterion enables the calculation of the controller feedback gains for varying load weight and cable length. The controller is built first for overhead cranes and then modified for tower cranes. Two controllers are used, one for the rotational motion of the tower and the other for the translational motion of the trolley. Numerical simulations show that the controller is effective in reducing the load oscillations and transferring the load in a reasonable time compared with that of optimal control.