  We study the collective dynamics of colloidal suspensions in the presence of
a time-dependent potential, by means of dynamical density functional theory. We
consider a non-linear diffusion equation for the density and show that spatial
patterns emerge from a sinusoidal external potential with a time-dependent
wavelength. These patterns are characterized by a sinusoidal density with the
average wavelength and a Bessel-function envelope with an induced wavelength
that depends only on the amplitude of the temporal oscillations. As a
generalization of this result, we propose a design strategy to obtain a family
of spatial patterns using time-dependent potentials of practically arbitrary
shape.
