Absolute transverse mobility and ratchet effect on periodic two-dimensional symmetric substrates

2013

Phys. Rev. E

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There are many examples of driven and active matter systems containing particles that exhibit circular motion with different chiralities, such as swimming bacteria near surfaces or certain types of self-driven colloidal particles. Circular motion of passive particles can also be induced with an external rotating drive. Here we examine particles that move in circles and interact with a periodic array of asymmetric L-shaped obstacles. We find a series of dynamical phases as a function of swimming radius, including regimes where the particle motion is rectified, producing a net dc motion. The direction of the rectification varies with the swimming radius, permitting the separation of particles with different swimming radii. Particles with the same swimming radius but different chirality can also move in different directions over the substrate and be separated. The rectification occurs for specific windows of swimming radii corresponding to periodic orbits in which the particles interact one or more times with the barriers per rotation cycle. The rectification effects are robust against the addition of thermal or diffusive effects, and are in some cases even enhanced by these effects.

Section: Rectification Effectsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics and separation of circularly moving particles in asymmetrically patterned arrays

2013

Phys. Rev. E

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“…These phase locking steps are distinct from Shapiro steps, and their widths grow quadratically with increasing ac amplitude rather than showing the oscillatory behavior associated with Shapiro steps. Phase locking effects can also occur for overdamped particle motion in 2D periodic systems under combinations of two perpendicular ac drives, producing localized and delocalized motion as well as rectification effects [30][31][32][33][34][35] .…”

Section: Introductionmentioning

confidence: 99%

Shapiro steps for skyrmion motion on a washboard potential with longitudinal and transverse ac drives

2015

Phys. Rev. B

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We numerically study the behavior of two-dimensional skyrmions in the presence of a quasi-onedimensional sinusoidal substrate under the influence of externally applied dc and ac drives. In the overdamped limit, when both dc and ac drives are aligned in the longitudinal direction parallel to the direction of the substrate modulation, the velocity-force curves exhibit classic Shapiro step features when the frequency of the ac drive matches the washboard frequency that is dynamically generated by the motion of the skyrmions over the substrate, similar to previous observations in superconducting vortex systems. In the case of skyrmions, the additional contribution to the skyrmion motion from a non-dissipative Magnus force shifts the location of the locking steps to higher dc drives, and we find that the skyrmions move at an angle with respect to the direction of the dc drive. For a longitudinal dc drive and a perpendicular or transverse ac drive, the overdamped system exhibits no Shapiro steps; however, when a finite Magnus force is present we find pronounced transverse Shapiro steps along with complex two-dimensional periodic orbits of the skyrmions in the phaselocked regimes. Both the longitudinal and transverse ac drives produce locking steps whose widths oscillate with increasing ac drive amplitude. We examine the role of collective skyrmion interactions and find that additional fractional locking steps occur for both longitudinal and transverse ac drives. At higher skyrmion densities, the system undergoes a series of dynamical order-disorder transitions, with the skyrmions forming a moving solid on the phase locking steps and a fluctuating dynamical liquid in regimes between the steps.

“…We have also considered the cases A = B and ω A = ω B , as well as the addition of a phase offset and driving with more complicated ac forms. These introduce a considerable number of new behaviors not found for the strictly circular case, and have been detailed in a separate publication [29].…”

Section: Simulationmentioning

confidence: 99%

Nonlinear dynamics, rectification, and phase locking for particles on symmetrical two-dimensional periodic substrates with dc and circular ac drives

Hastings

2004

Phys. Rev. E

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We investigate the dynamical motion of particles on a two-dimensional symmetric periodic substrate in the presence of both a dc drive along a symmetry direction of the periodic substrate and an additional circular ac drive. For large enough ac drives, the particle orbit encircles one or more potential maxima of the periodic substrate. In this case, when an additional increasing dc drive is applied in the longitudinal direction, the longitudinal velocity increases in a series of discrete steps that are integer multiples of aω/(2π), where a is the lattice constant of the substrate. Fractional steps can also occur. These integer and fractional steps correspond to distinct stable dynamical orbits. A number of these phases also show a rectification in the positive or negative transverse direction where a non-zero transverse velocity occurs in the absence of a dc transverse drive. We map out the phase diagrams of the regions of rectification as a function of ac amplitude, and find a series of tongues. Most of the features, including the steps in the longitudinal velocity and the transverse rectification, can be captured with a simple toy model and by arguments from nonlinear maps. We have also investigated the effects of thermal disorder and incommensuration on the rectification phenomena, and find that for increasing disorder, the rectification regions are gradually smeared and the longitudinal velocity steps are no longer flat but show a linearly increasing velocity.