Directed molecular transport in an oscillating symmetric channel

Numerical model of the locomotion of oscillating 'robots' with frictional anisotropy on differently-structured surfaces

In engineering materials, surface anisotropy is known in certain textured patterns that appear during the manufacturing process. In biology, there are numerous examples of mechanical systems which combine anisotropic surfaces with the motion, elicited due to some actuation using muscles or stimuli-responsive materials, such as highly ordered cellulose fiber arrays of plant seeds. The systems supplemented by the muscles are rather fast actuators, because of the relatively high speed of muscle contraction, whereas the latter ones are very slow, because they generate actuation depending on the daily changes in the environmental air humidity. If the substrate has ordered surface profile, one can expect certain statistical order of potential trajectories (depending on the order of the spatial distribution of the surface asperities). If not, the expected trajectories can be statistically rather random. The same presumably holds true for the artificial miniature robots that use actuation in combination with frictional anisotropy. In order to prove this hypothesis, we developed numerical model helping us to study abovementioned cases of locomotion in 2D space on an uneven terrain. We show that at extremely long times, these systems tends to behave according to the rules of ballistic diffusion. Physically, it means that their motion tends to be associated with the "channels" of the patterned substrate. Such a motion is more or less the same as it should be in the uniform space. Such asymptotic behavior is specific for the motion in model regular potential and would be impossible on more realistic (and complex) fractal reliefs. However, one can expect that in any kind of the potential with certain symmetry (hexagonal or rhombic, for example), where it is still possible to find the ways, the motion along fixed direction during long (or even almost infinite) time intervals is possible.

Motion periodicity and bifurcation of a wave excited hopping ball

We consider the problem of a hopping ball excited by a travelling harmonic wave on an elastic surface. The ball, considered as a particle, is assumed to interact with the surface through inelastic collisions. The surface motion due to the wave induces a horizontal drift in the ball. The problem is treated analytically under certain approximations. The phase space of the hopping motion is captured by constructing a phase-velocity return map. The fixed points of the return map and its compositions represent periodic hopping solutions. The linear stability of the obtained periodic solution is studied in detail. The minimum frequency for the onset of periodic hops, and the subsequent loss of stability at the bifurcation frequency, have been determined analytically. Interestingly, for small values of wave amplitude, the analytical solutions reveal striking similarities with the results of the classical bouncing ball problem.

Particle current on flexible surfaces excited by harmonic waves

In this paper, a study on the directed particle current on flexible surfaces excited by a harmonic wave is reported. The proposed theory considers three different models for the kinematics of the surface, namely the Euler-Bernoulli, Timoshenko, and Rayleigh surface wave models. The particle-surface interaction terms in the theory incorporate Coulomb friction and inelastic collision between the particle and the surface. Three possible phases of motion, namely sticking, sliding, and jumping, are considered, and the phase transition boundaries are estimated analytically for a general surface model. The effect of various parameters on the particle current and certain statistical features of the particle motion are then studied numerically. Remarkably, the particle current spectra exhibit, in addition to resonance modes, antiresonance and secondary resonance modes and transversal zero crossings. These features have interesting implications for the particle dynamics in terms of dynamic jamming states and particle eddies, which are pointed out. Under certain restricted conditions, averaging calculations are also performed and compared with the corresponding numerical simulations.

Frictional-anisotropy-based systems in biology: structural diversity and numerical model

There is a huge variety in biological surfaces covered with micro- and nanostructures oriented at some angle to the supporting surface. Such structures, for example snake skin, burr-covered plant leaves, cleaning devices and many others cause mechanical anisotropy due to different friction or/and mechanical interlocking during sliding in contact with another surface in different directions. Such surfaces serve propulsion generation on the substrate (or within the substrate) for the purpose of locomotion or for transporting items. We have theoretically studied the dependence of anisotropic friction efficiency in these systems on (1) the slope of the surface structures, (2) rigidity of their joints, and (3) sliding speed. Based on the proposed model, we suggest the generalized optimal set of variables for maximizing functional efficiency of anisotropic systems of this type. Finally, we discuss the optimal set of such parameters from the perspective of biological systems.

Directed molecular transport in an oscillating channel with randomness

Stability of directed transport and molecular separation in a symmetric channel is analyzed. The original mechanism is based on harmonic spatial oscillations of the channel, under which the system exhibits multiple regimes of a directed transport. The particles may be forced to move with different velocities and directions as the amplitude and/or frequency of the oscillations are adjusted to a proper resonance. The advantage of this mechanism in contrast to the ratchet systems is that the average particle velocity is larger than the velocity of the growing of the width of the particle spatial distribution. We have studied the stability of the directed transport with regard to random impacts to the channel parameters and oscillation frequency. Here we present the results of the simulations which show that the ability of the combined longitudinally and transversally vibrating randomized dynamic channel to perform directed molecular transport remains resilient to quite intensive random channel structure fluctuations (50-60%) and relatively strong random impacts to its oscillations (15-20%).

Unidirectional drift of bistable front under asymmetrically oscillating zero-mean force

The unidirectional drift of bistable fronts (BFs) that separate two stable uniform states of a bistable system under the action of an asymmetrically oscillating zero-mean force (driver) is considered within the "pseudolinear" (piecewise-linear) model of the system. The particular case of the symmetrical (symmetrically shaped) rate functions is studied. To perform a rigorous analytic treatment for arbitrary strengths of the driving force we assume that the applied ac force is quasistatically slow. Both cases of the initially static and the initially propagating BFs are examined; various types of the "unforced" dc motion are found. We show that the unforced transport of BF takes place in any case of the asymmetric driver, whether Maxwellian construction of the rate function was balanced or not. In particular, progressive (accelerated) dc drift of the initially static BFs occurred. In contrast, both progressive and regressive (decelerated) types of unforced dc drift of the initially propagating BFs take place. Moreover, reversal of the directed motion of the initially propagating BF occurred, if the deviation of Maxwellian construction from the strictly balanced situation was relatively small; by tuning the strength of the driving force the dc drift of BF exhibits the reversal. The symmetry properties of the biharmonic driver are discussed. The biharmonic ac force consisting of a superposition of the fundamental mode and its even (odd) superharmonics is an asymmetrically (symmetrically) oscillating one. The reversal type of the unforced dc drift occurred only in the case of the even superharmonic "mixing," when the superharmonic mode of the biharmonic driver was even.

Brownian motors: current fluctuations and rectification efficiency

With this work, we investigate an often neglected aspect of Brownian motor transport, namely, the role of fluctuations of the noise-induced current and its consequences for the efficiency of rectifying noise. In doing so, we consider a Brownian inertial motor that is driven by an unbiased monochromatic, time-periodic force and thermal noise. Typically, we find that the asymptotic, time-, and noise-averaged transport velocities are small, possessing rather broad velocity fluctuations. This implies a corresponding poor performance for the rectification power. However, for tailored profiles of the ratchet potential and appropriate drive parameters, we can identify a drastic enhancement of the rectification efficiency. This regime is marked by persistent, unidirectional motion of the Brownian motor with few back-turns only. The corresponding asymmetric velocity distribution is then rather narrow, with a support that predominantly favors only one sign for the velocity.