Active Brownian and inertial particles in disordered environments: Short-time expansion of the mean-square displacement

Breoni, Davide; Schmiedeberg, Michael; Löwen, Hartmut

doi:10.1103/physreve.102.062604

Cited by 30 publications

(25 citation statements)

References 82 publications

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“…The small-time regime of both observables is strongly affected by the details of the motility landscape, in agreement with Ref. [88]. Instead, in the large-time regime, the spatial variation of the swim velocity plays a less importnat role since the only relevant time-scale is the persistence time.…”

Section: Discussionsupporting

confidence: 88%

Dynamics of active particles with space-dependent swim velocity

Caprini,

Marconi,

Wittmann

et al. 2021

Preprint

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We study the dynamical properties of an active particle subject to a swimming speed explicitly depending on the particle position. The oscillating spatial profile of the swim velocity considered in this paper takes inspiration from experimental studies based on Janus particles whose speed can be modulated by an external source of light. We suggest and apply an appropriate model of an active Ornstein Uhlenbeck particle (AOUP) to the present case. This allows us to predict the stationary properties, by finding the exact solution of the steady-state probability distribution of particle position and velocity. From this, we obtain the spatial density profile and show that its form is consistent with the one found in the framework of other popular models. The reduced velocity distribution highlights the emergence of non-Gaussianity in our generalized AOUP model which becomes more evident as the spatial dependence of the velocity profile becomes more pronounced. Then, we focus on the time-dependent properties of the system. Velocity autocorrelation functions are studied in the steady-state combining numerical and analytical methods derived under suitable approximations. We observe a non-monotonic decay in the temporal shape of the velocity autocorrelation function which depends on the ratio between the persistence length and the spatial period of the swim velocity. Finally, we numerically and analytically study the mean square displacement and the long-time diffusion coefficient. The ballistic regime, observed in the small-time region, is deeply affected by the properties of the swim velocity landscape which induces also a crossover to a sub-ballistic but superdiffusive regime for intermediate times. Finally, the long-time diffusion coefficient decreases as the amplitude of the swim velocity oscillations increases because the diffusion is mainly determined by those regions where the particles are slow.

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Section: Discussionsupporting

confidence: 88%

Dynamics of active particles with space-dependent swim velocity

Caprini,

Marconi,

Wittmann

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The small-time regime of both observables is strongly affected by the details of the motility landscape, in agreement with ref. 91. Instead, in the large-time regime, the spatial variation of the swim velocity plays a less importnat role since the only relevant time-scale is the persistence time.…”

Section: Discussionmentioning

confidence: 99%

Dynamics of active particles with space-dependent swim velocity

et al. 2022

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“…Future work should generalize the present model to external potentials like optical fields, disorder and confinement [39,[100][101][102][103] and to motion in noninertial rotating frames [104,105]. Furthermore, anisotropic particles which show out-of-plane orientations and positions relevant for active complex plasmas [106] should be considered in the future.…”

Section: Discussionmentioning

confidence: 99%

Time-dependent inertia of self-propelled particles: the Langevin rocket

Sprenger,

Jahanshahi,

Ivlev

et al. 2021

Preprint

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Many self-propelled objects are large enough to exhibit inertial effects but still suffer from environmental fluctuations. The corresponding basic equations of motion are governed by active Langevin dynamics which involve inertia, friction and stochastic noise for both the translational and orientational degrees of freedom coupled via the self-propulsion along the particle orientation. In this paper, we generalize the active Langevin model to time-dependent parameters and explicitly discuss the effect of time-dependent inertia for achiral and chiral particles. Realizations of this situation are manifold ranging from minirockets which are self-propelled by burning their own mass, dust particles in plasma which lose mass by evaporating material to walkers with expiring activity. Here we present analytical solutions for several dynamical correlation functions such as the mean-square displacement and the orientational and velocity autocorrelation functions. If the parameters exhibit a slow power-law in time, we obtain anomalous superdiffusion with a non-trivial dynamical exponent. Finally we constitute the "Langevin rocket" model by including orientational fluctuations in the traditional Tsiolkovsky rocket equation. We calculate the mean reach of the Langevin rocket and discuss different mass ejection strategies to maximize it. Our results can be tested in experiments on macroscopic robotic or living particles or in self-propelled mesoscopic objects moving in media of low viscosity such as complex plasma.

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Active Brownian and inertial particles in disordered environments: Short-time expansion of the mean-square displacement

Cited by 30 publications

References 82 publications

Dynamics of active particles with space-dependent swim velocity

Dynamics of active particles with space-dependent swim velocity

Dynamics of active particles with space-dependent swim velocity

Time-dependent inertia of self-propelled particles: the Langevin rocket

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