title: Gaussian theory for spatially distributed self-propelled particles.
abstract: Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting self-propelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model, we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatiotemporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement for a wide range of noise intensities. In particular, for low noise intensities the agreement with simulations is better as other approximations, making the GA to an acceptable candidates of describing spatially distributed self-propelled particles.
authors.affiliation: Department of Physics, Sharif University of Technology, P. O. Box 11155-9161, Tehran, Iran.
authors.forename: Hamid
authors.initials: H
authors.lastname: Seyed-Allaei
authors.affiliation: Department of Physics, Humboldt-Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany.
authors.forename: Lutz
authors.initials: L
authors.lastname: Schimansky-Geier
authors.affiliation: Department of Physics, Sharif University of Technology, P. O. Box 11155-9161, Tehran, Iran.|School of Nano Science, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5531, Tehran, Iran.
authors.forename: Mohammad Reza
authors.initials: MR
authors.lastname: Ejtehadi