Memory as vibration in a disconnecting air bubble
Wendy W. Zhang
Physics and James Franck Institute, University of Chicago
Focusing a finite amount of energy dynamically into a vanishingly small amount of material requires that the initial condition be perfectly symmetric. In reality, imperfections are always present and cut-off the approach towards the focusing singularity. The disconnection of an underwater bubble provides a simple example of this competition between asymmetry and focusing. We use a combination of theory, simulation and experiments to show that the dynamics near disconnection contradicts the prevailing view that the disconnection dynamics converges towards a universal, cylindrically-symmetric singularity. Instead an initial asymmetry in the shape of the bubble neck excites vibrations that persist until disconnection. We argue that such memory-encoding vibrations may arise whenever initial asymmetries perturb the approach towards a singularity whose dynamics has an integrable form.