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The flashing ratchet and unidirectional transport of matter
Vorotnikov, DmitryWe study the ashing ratchet model of a Brownian motor, which consists in cyclical switching between the Fokker-Planck equation with an asymmetric ratchet-like potential and the pure di usion equation. We show that the motor really performs unidirectional transport of mass, for proper parameters of the model, by analyzing the attractor of the problem and the stationary vector of a related Markov chain
On the well-posedness of a two-phase minimization problem
Urbano, José Miguel; Vorotnikov, DmitryWe prove a series of results concerning the emptiness and non-emptiness of a certain set of Sobolev functions related to the well-posedness of a two-phase minimization problem, involving both the p(x)-norm and the in nity norm. The results, although interesting in their own right, hold the promise of a wider applicability since they can be relevant in the context of other problems where minimization of the p-en...
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