2016
DOI: 10.1103/physreve.94.062603
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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 selfpropelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. … Show more

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Cited by 3 publications
(6 citation statements)
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References 90 publications
(188 reference statements)
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“…The critical noise strength (38) predicted by the von Mises ansatz coincides with the one predicted by the Fourier analysis, see [10].…”
Section: Small Order Parametersupporting
confidence: 68%
See 1 more Smart Citation
“…The critical noise strength (38) predicted by the von Mises ansatz coincides with the one predicted by the Fourier analysis, see [10].…”
Section: Small Order Parametersupporting
confidence: 68%
“…After submitting this paper we became aware of [38], where the angular distribution was approximated by a wrapped Gaussian in real space. The distribution has, like the von Mises distribution, the advantage that it is described solely by a single parameter.…”
Section: Discussionmentioning
confidence: 99%
“…Our main purpose was to find an approach to an adiabatic elimination of the orientation of the velocity as a persistent variable, and to formulate a memoryless dynamics for the position of the particle in the diffusive regime. In analogy to the known theory of a normal Brownian particle which was revisited in Sec.2, we have derived in Sec.3 the overdamped dynamics of the projection of the motion onto a given direction (32) and also for the full two-dimensional case, Eq.(37). On the basis of stochastic differential equations we elaborated systematic elimination procedure.…”
Section: Discussionmentioning
confidence: 99%
“…Active particles are extensively studied from the experimental as well as from the theoretical point of view. Examples of corresponding studies range from investigations of the dynamical behavior of individual units like motile cells [6][7][8][9][10][11][12][13], over macroscopic animals [14,15] and artificial self-propelled particles [16][17][18][19][20][21][22][23], to many body interactions and collective phenomena in many-particle systems [2,[24][25][26][27][28][29][30][31][32][33].…”
Section: Introductionmentioning
confidence: 99%
“…An additional closure relation between Q α , v α and ρ α is required to yield a selfconsistent hydrodynamic description. Deep in the homogeneous phase, we make a wrapped Gaussian approximation for the orientational fluctuations in each population [24,36]. This hypothesis is equivalent to setting Q α = |v α | 4 (v α vα − 1 2 I) [24,37].…”
Section: Methodsmentioning
confidence: 99%