Brownian noise a white noise signal: meaning that Brownian motion is the integral of the white noise formula_2, whose power spectral density is flat: Note that here formula_4 denotes the Fourier transform, and formula_5 is a constant. An important property of this transform is that the derivative of any distribution transforms as from which we can conclude that the power spectrum of Brownian noise is Brown noise can be produced by integrating white noise. That is, whereas (digital) white noise can be produced by randomly choosing each sample independently, Brown noise can be produced by adding a random offset to each sample
Brownian motor at the nanometer scale. The term "Brownian motor" was originally coined by Peter Hänggi in 1995: A distinct feature of a Brownian motor is—in contrast to a molecular motor—that the output response is typically coupled only loosely to the input perturbation and action of fluctuations. In biology, many protein-based molecular motors in the cell may in fact be Brownian motors. These molecular motors convert the chemical energy present in ATP into mechanical energy. One example of a Brownian motor would be an ATPase motor that hydrolyzes ATP to generate fluctuating anisotropic energetic potentials. The anisotropic potentials along the path would