  Residence times of a particle in both the wells of a double-well system,
under the action of zero-mean Gaussian white noise and zero-averaged but
temporally asymmetric periodic forcings, are recorded in a numerical
simulation. The difference between the relative mean residence times in the two
wells shows monotonic variation as a function of asymmetry in the periodic
forcing and for a given asymmetry the difference becomes largest at an optimum
value of the noise strength. Moreover, the passages from one well to the other
become less synchronous at small noise strength as the asymmetry parameter
(defined below) differs from zero, but at relatively larger noise strengths the
passages become more synchronous with asymmetry in the field sweep. We propose
that asymmetric periodic forcing (with zero mean) could provide a simple but
sensible physical model for unidirectional motion in a symmetric periodic
system aided by a symmetric Gaussian white noise.
