“School of Nano-Sciences”

Back to Papers Home
Back to Papers of School of Nano-Sciences

Paper   IPM / Nano-Sciences / 14647
School of Nano Science
  Title:   Gaussian theory for spatially distributed self-propelled particles
1.  Hamid Seyed Allaei
2.  Lutz Schimansky-Geier
3.  Mohammad Reza Ejtehadi
  Status:   Published
  Journal: Phys. Rev. E
  No.:  6
  Vol.:  94
  Year:  2016
  Pages:   062303
  Publisher(s):   American Physical Society
  Supported by:  IPM
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.

Download TeX format
back to top
scroll left or right