Elastically coupled two-dimensional Brownian motors

Chaos in kicked ratchets

We present a minimal one-dimensional deterministic continuous dynamical system that exhibits chaotic behavior and complex transport properties. Our model is an overdamped rocking ratchet with finite dissipation, that is periodically kicked with a δ function driving force, without finite inertia terms or temporal or spatial stochastic forces. To our knowledge this is the simplest model reported in the literature for a ratchet, with this complex behavior. We develop an analytical approach that predicts many key features of the system, such as current reversals, as well as the presence of chaotic behavior and bifurcation. Our analytical approach allows us to study the transition from regular to chaotic motion as well as a tangent bifurcation associated with this transition. We show that our approach can be easily extended to other types of periodic driving forces. The square wave is shown as an example.

Collective dynamics of a network of ratchets coupled via a stochastic dynamical environment

We investigate the collective dynamics of a network of inertia particles diffusing in a ratchet potential and interacting indirectly through their stochastic dynamical environment. We obtain analytically the condition for the existence of a stable collective state, and we show that the number N of particles in the network, and the strength k of their interaction with the environment, play key roles in synchronization and transport processes. Synchronization is preceded by symmetry-breaking associated with double-resonance oscillations and is shown to be strongly dependent on the network size: convergence to the synchronization manifold occurs much faster with a large network. For small networks, increasing the noise level enhances synchronization in the weakly coupled regime, while particles in a large network are weakly synchronized. Similarly, in the strongly coupled regime, particles in a small network are weakly synchronized; whereas the synchronization is strong and robust against noise when the network-size is large. Small and moderate networks maximize and stabilize efficient transport. Although the dynamics for larger networks is highly correlated, the transport current is erratic.

Robust unidirectional rotation in three-tooth Brownian rotary ratchet systems

We apply a simple Brownian ratchet model to an artificial molecular rotary system mounted in a biological membrane, in which the rotor always maintains unidirectional rotation in response to a linearly polarized weak ac field. Because the rotor and stator compose a ratchet system, we describe the motion of the rotor tip with the Langevin equation for a particle in a two-dimensional three-tooth ratchet potential of threefold symmetry. Unidirectional rotation can be induced under the field and optimized by stochastic resonance, wherein the mean angular momentum (MAM) of the rotor exhibits a bell-shaped curve for the noise strength. We obtain analytical expressions for the MAM and power loss from the corresponding Fokker-Planck equation, via a Markov transition model for coarse-grained states (six-state model). The MAM expression reveals a significant effect depending on the chirality of the ratchet potential: in achiral cases, the MAM approximately vanishes with respect to the polarization angle φ of the field; in chiral cases, the MAM does not crucially depend on φ, but depends on the direction of the ratchet; i.e., the parity of the unidirectional rotation is inherent in the ratchet structure. This feature is useful for artificial rotary systems to maintain robust unidirectional rotation independent of the mounting condition.

Current reversals and synchronization in coupled ratchets

Current reversal is an intriguing phenomenon that has been central to recent experimental and theoretical investigations of transport based on ratchet mechanism. By considering a system of two interacting ratchets, we demonstrate how the coupling can be used to control the reversals. In particular, we find that current reversal that exists in a single driven ratchet system can ultimately be eliminated with the presence of a second ratchet. For specific coupling strengths a current-reversal free regime has been detected. Furthermore, in the fully synchronized state characterized by the coupling threshold k(th), a specific driving amplitude a(opt) is found for which the transport is optimum.

Mechanical coupling in flashing ratchets

We consider the transport of rigid objects with internal structure in a flashing ratchet potential by investigating the overdamped behavior of a rodlike chain of evenly spaced point particles. In one dimension, analytical arguments show that the velocity can reverse direction multiple times in response to changing the size of the chain or the temperature of the heat bath. The physical reason is that the effective potential experienced by the mechanically coupled objects can have a different symmetry than that of individual objects. All analytical predictions are confirmed by Brownian dynamics simulations. These results may provide a route to simple, coarse-grained models of molecular motor transport that incorporate an object's size and rotational degrees of freedom into the mechanism of transport.

Rotary motor powered by stochastic uncorrelated dipoles

It is demonstrated that the stochastic back-and-forth vibrations of uncorrelated dipoles may lead to rotation of their ambient dipoles. This peculiar phenomenon is clarified by considering spatial and temporal symmetry breakings. The former asymmetry is the result of the multiple biased Hamiltonian vector fields, which is a ratchet effect, and the latter, of the time sequence specified by a metastable state. Since this driving mechanism is simpler than that of F0F1ATPase, it could benefit the design of nanometer scale rotary devices.