General approach for dealing with dynamical systems with spatiotemporal periodicities.

Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected in the properties of these systems through a dependence on the parameters of their periodic terms. In this paper we provide a general theoretical framework for dealing with these kinds of systems, regardless of whether they are classical or quantum, stochastic or deterministic, dissipative or nondissipative, linear or nonlinear, etc.

Comment on "Ratchet universality in the presence of thermal noise".

A recent paper [P. J. Martínez and R.

Propulsion efficiency of a dynamic self-assembled helical ribbon.

We study the dynamic self-assembly and propulsion of a ribbon formed from paramagnetic colloids in a dynamic magnetic field. The sedimented ribbon assembles due to time averaged dipolar interactions between the beads. The time dependence of the dipolar interactions together with hydrodynamic interactions cause a twisted ribbon conformation.

Symmetries shape the current in ratchets induced by a biharmonic driving force.

Equations describing the evolution of particles, solitons, or localized structures, driven by a zero-average, periodic, external force, and invariant under time reversal and a half-period time shift, exhibit a ratchet current when the driving force breaks these symmetries. The biharmonic force f(t)=1 cos(qomegat+phi1)+2 cospomegat+phi2) does it for almost any choice of vphi1 and phi2, provided p and q are two coprime integers such that p+q is odd. It has been widely observed, in experiments in semiconductors, in Josephson junctions, photonic crystals, etc.