Memory-encoding vibrations in a disconnecting air bubble

Abstract

Conventional wisdom suggests that it should be impossible for information to pass across a singularity. A study of the behaviour of air bubbles as they disconnect from a submerged nozzle suggests that this isn’t always the case. Many nonlinear processes, such as the propagation of waves over an ocean or the transmission of light pulses down an optical fibre1, are integrable in the sense that the dynamics has as many conserved quantities as there are independent variables. The result is a time evolution that retains a complete memory of the initial state. In contrast, the nonlinear dynamics near a finite-time singularity, in which physical quantities such as pressure or velocity diverge at a point in time, is believed to evolve towards a universal form, one independent of the initial state2. The break-up of a water drop in air3 or a viscous liquid inside an immiscible oil4,5 are processes that conform to this second scenario. These opposing scenarios collide in the nonlinearity produced by the formation of a finite-time singularity that is also integrable. We demonstrate here that the result is a novel dynamics with a dual character.

Cite this article

Schmidt, L., Keim, N., Zhang, W. et al. Memory-encoding vibrations in a disconnecting air bubble. Nature Phys 5, 343–346 (2009). https://doi.org/10.1038/nphys1233

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