Dynamic density functional theory versus kinetic theory of simple fluids.
We study the collective dynamics of colloidal suspensions in the presence of a time-dependent potential by means of dynamic density functional theory. We consider a nonlinear 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.