Scaling dependence and synchronization of forced mercury beating heart systems

We perform experiments on a nonautonomous Mercury beating heart system, which is forced to pulsate using an external square wave potential. At suitable frequencies and volumes, the drop exhibits pulsation with polygonal shapes having n corners. We find the scaling dependence of the forcing frequency ν_{n} on the volume V of the drop and establish the relationship ν_{n}∝n/sqrt[V]. It is shown that the geometrical shape of substrate is important for obtaining closer match to these scaling relationships. Furthermore, we study synchronization of two nonidentical drops driven by the same frequency and establish that synchrony happens when the relationship n_{2}/n_{1}=sqrt[V_{2}/V_{1}] is satisfied.