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Regular Seminar Alejandro Jenkins (Costa Rica U.)
room G.O. Jones 610
A self-oscillator generates and maintains a periodic motion at the expense of an energy source with no corresponding periodicity. Small perturbations about equilibrium are amplified. Non-linearity accounts for steady-state oscillations and for the ability of coupled self-oscillators to exhibit both spontaneous synchronisation (“entrainment”) and chaos. The theory of self-oscillators has achieved its greatest sophistication in mathematical control theory and in the study of ordinary differential equations. I shall explain in this talk how an understanding better suited to physicists can be founded on considerations of energy, efficiency, and thermodynamic irreversibility. After reviewing the key differences between forced a parametric resonances on the one hand and self-oscillators on the other, I will comment on how a physical approach to the theory of self-oscillators throws new light on flow instabilities. I will close by describing mechanical and hydrodynamic analogs of the Zel’dovich superradiance of rotating black holes, a subject of considerable interest in high-energy physics today.