A 1/f Velocity Fluctuation Spectrum in One-Dimensional Random Walks

We developed a 1/f fluctuation model that is based on the random walks of several particles in a one-dimensional bar. We showed that the random walks in a bar of finite length could be treated as those in a bar of infinite length. This finding should explain what the lower limit of the frequency of 1/f fluctuations is. We also showed, using closed form analysis and computer simulations of random walks of many particles, that the velocity fluctuations of a group of several particles give the 1/f power spectrum. The computer simulations clearly demonstrate the generation of the 1/f fluctuation spectrum and the dynamics of the 1/f fluctuations.