Optimal protocol for a collective flashing ratchet
1 Departamento de Física Aplicada I, Universidad Complutense de Madrid - 28040 Madrid, Spain
2 Departamento de Física Atómica, Molecular y Nuclear, Universidad Complutense de Madrid - 28040 Madrid, Spain
Received: 11 February 2014
Accepted: 12 June 2014
We study a system of independent Brownian particles in a flashing ratchet potential that can be turned on or off depending on the position of the particles, with the aim of maximising the speed of the center of mass in the long run. First, an explanation of how to find the optimal protocol using Bellman's principle of optimality for any number of particles is given. Then the problem is numerically solved for a system of 2 particles. Simulations show that the optimal protocol performs better than the maximisation of instantaneous center-of-mass speed, a protocol known to give better results for 2 particles than any open-loop protocol.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.30.Yy – Control theory
© EPLA, 2014