The leaking elastic capacitor as a model for active matter

The leaking elastic capacitor (LEC) is a non-conservative dynamical system that combines electrical and mechanical degrees of freedom. We show analytically that a LEC connected to an external voltage source can become dynamically unstable (Hopf bifurcation) due to positive feedback between the mechanical separation of the plates and their electrical charging. Numerical simulation of the fully non-linear system allow us to identify regimes in which the LEC exhibits limit cycles (regular self-oscillations) or strange attractors (chaotic behavior). This thermodynamically irreversible process generates a non-conservative force that can be used to pump current or to sustain waves propagating along flexible plates. The LEC therefore acts as an engine, cyclically performing work at the expense of the constant voltage source. We argue that this model can offer a qualitatively new and more realistic description of some important properties of active matter in condensed-matter physics, chemistry, and biology.

This work has been submitted to PRE. The full manuscript is available at arXiv:2010.05534