Theory of diffusion of active particles that move at constant speed in two dimensions

Sevilla, Francisco J.; Gómez-Nava, Luis

doi:10.1103/physreve.90.022130

Cited by 50 publications

(87 citation statements)

References 44 publications

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“…Notice that the discrepancy between the results given by our analytical approximation and the exact results lies on the wave-like effects given by the second-order-time-derivative term of Eq. (11) which, as shown in [9], gives 8/3 ≃ 2.6667 as the value for the kurtosis in the vanishing translational diffusion. For D B = 0.001, the minimum of the exact kurtosis is about 4.1352 at t ≈ 0.39D…”

Section: Kurtosismentioning

confidence: 99%

Smoluchowski diffusion equation for active Brownian swimmers

Sevilla

Sandoval

2015

Phys. Rev. E

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We study the free diffusion in two dimensions of active-Brownian swimmers subject to passive fluctuations on the translational motion and to active fluctuations on the rotational one. The Smoluchowski equation is derived from a Langevin-like model of active swimmers, and analytically solved in the long-time regime for arbitrary values of the Péclet number, this allows us to analyze the out-of-equilibrium evolution of the positions distribution of active particles at all time regimes. Explicit expressions for the mean-square displacement and for the kurtosis of the probability distribution function are presented, and the effects of persistence discussed. We show through Brownian dynamics simulations that our prescription for the mean-square displacement gives the exact time dependence at all times. The departure of the probability distribution from a Gaussian, measured by the kurtosis, is also analyzed both analytically and computationally. We find that for Péclet numbers 0.1, the distance from Gaussian increases as ∼ t −2 at short times, while it diminishes as ∼ t −1 in the asymptotic limit.

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Section: Kurtosismentioning

confidence: 99%

Smoluchowski diffusion equation for active Brownian swimmers

Sevilla

Sandoval

2015

Phys. Rev. E

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“…We now switch to the probability density description by deriving from Eqs. (1) and (2) the corresponding Smoluchowski or Fokker-Planck equation [4,6,37]. In dimensionless units, this dynamic equation for the probability density ψ(r, φ, t) to find a particle at time t and position r with orientation φ of the self-propulsion direction becomes…”

Section: Model Systemmentioning

confidence: 99%

Focusing by blocking: Repeatedly generating central density peaks in self-propelled particle systems by exploiting diffusive processes

Menzel¹

2015

EPL

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Over the past few years the displacement statistics of self-propelled particles has been intensely studied, revealing their long-time diffusive behavior. Here, we demonstrate that a concerted combination of boundary conditions and switching on and off the self-propelling drive can generate and afterwards arbitrarily often restore a non-stationary centered peak in their spatial distribution. This corresponds to a partial reversibility of their statistical behavior, in opposition to the abovementioned long-time diffusive nature. Interestingly, it is a diffusive process that mediates and makes possible this procedure. It should be straightforward to verify our predictions in a real experimental system.

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“…Thus, no wonder why the other main line of research focuses on developing the theoretical frameworks to describe such, most of the times complex, patterns of motion exhibited by single active particles [19][20][21][22][23][24][25]. One aspect of interest corresponds to those swimmers, either alive or passive, that show chiral motion, i.e., a well defined state (clockwise or anticlockwise) of the circular motion component of the particle trajectories.…”

Section: Introductionmentioning

confidence: 99%

“…This approach leads us directly to the time evolution of the probability distribution of the particle positions, and from it, to relevant information regarding the characteristic features of the pattern of motion as its non-Gaussian nature [23,25,63].…”

Section: Introductionmentioning

confidence: 99%

Diffusion of active chiral particles

Sevilla

2016

Phys. Rev. E

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The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the directionv at time t, and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around an uniformly-distributed random axis, it is found evidence of the so called effect "anomalous, yet Brownian, diffusion", for which particles follow a non-Gaussian distribution for the positions yet the mean squared displacement is a linear function of time.PACS numbers: 02.50.-r 05.40.-a 05.10.Gg

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Theory of diffusion of active particles that move at constant speed in two dimensions

Cited by 50 publications

References 44 publications

Smoluchowski diffusion equation for active Brownian swimmers

Smoluchowski diffusion equation for active Brownian swimmers

Focusing by blocking: Repeatedly generating central density peaks in self-propelled particle systems by exploiting diffusive processes

Diffusion of active chiral particles

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