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We investigate the dynamical motion of particles on a two-dimensionalsymmetric periodic substrate in the presence of both a dc drive along asymmetry direction of the periodic substrate and an additional circular acdrive. For large enough ac drives, the particle orbit encircles one or morepotential maxima of the periodic substrate. In this case, when an additionalincreasing dc drive is applied in the longitudinal direction, the longitudinalvelocity increases in a series of discrete steps that are integer multiples ofthe lattice constant of the substrate times the frequency. Fractional steps canalso occur. These integer and fractional steps correspond to distinct stabledynamical orbits. A number of these phases also show a rectification in thepositive or negative transverse direction where a non-zero transverse velocityoccurs in the absence of a dc transverse drive. We map out the phase diagramsof the regions of rectification as a function of ac amplitude, and find aseries of tongues. Most of the features, including the steps in thelongitudinal velocity and the transverse rectification, can be captured with asimple toy model and by arguments from nonlinear maps. We have alsoinvestigated the effects of thermal disorder and incommensuration on therectification phenomena, and find that for increasing disorder, therectification regions are gradually smeared and the longitudinal velocity stepsare no longer flat but show a linearly increasing velocity.Comment: 14 pages, 17 postscript figure

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