Xiao Ke, Roichman Yael, Grier David G
Department of Physics and Center for Soft Matter Research, New York University, New York, New York 10003, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jul;84(1 Pt 1):011131. doi: 10.1103/PhysRevE.84.011131. Epub 2011 Jul 22.
An ensemble of symmetric potential energy wells arranged at the vertices of a Fibonacci spiral can serve as the basis for an irreducibly two-dimensional thermal ratchet. Periodic rotation of the potential energy landscape through a three-step cycle drives trapped Brownian particles along spiral trajectories through the pattern. Which spiral is selected depends on the angular displacement at each step, with transitions between selected spirals arising at rational proportions of the golden angle. Fibonacci spiral ratchets therefore display an exceptionally rich range of transport properties, including inhomogeneous states in which different parts of the pattern induce motion in different directions. Both the radial and angular components of these trajectories can undergo flux reversal as a function of the scale of the pattern or the rate of rotation.
