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

Sprenger, Alexander R.; Jahanshahi, Soudeh; Ivlev, A. V.; Löwen, Hartmut

doi:10.1103/physreve.103.042601

Cited by 44 publications

(54 citation statements)

References 105 publications

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“…( 10 ) to obtain which yields As a result, the leading asymptotic behavior of is determined by the first term involving a scaling behavior of the MD in . This is remarkably slow compared to typical behavior of a Brownian particle in a harmonic potential or of active Brownian motion where the MD reaches its asymptotic value exponentially in time [ 57 – 59 ] thus constituting an example of a very slow relaxation as induced by space-dependent noise.…”

Section: Free Particle Casementioning

confidence: 99%

Brownian particles driven by spatially periodic noise

2022

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We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can be integrated formally exactly. We determine the short- and long-time behaviour of the mean displacement (MD) and mean-squared displacement (MSD). In particular, we find a very slow dynamics for the mean displacement, scaling as $$t^{-1/2}$$ t - 1 / 2 with time t. Placed under an additional external periodic force near the critical tilt value we compute the stationary current obtained from the corresponding Fokker–Planck equation and identify an essential singularity if the minimum of the noise strength is zero. Finally, in order to further elucidate the effect of the random periodic driving on the diffusion process, we introduce a phase factor in the spatial noise with respect to the external periodic force and identify the value of the phase shift for which the random force exerts its strongest effect on the long-time drift velocity and diffusion coefficient Graphical Abstract

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Section: Free Particle Casementioning

confidence: 99%

Brownian particles driven by spatially periodic noise

2022

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“…In Newtonian fluids, the effective selfpropulsion force is proportional and instantaneous in the orientation, and thus the delay function equates to zero for all time. In a similar manner, the inertial delay function was previously defined for macroscopic active particles which measured the mismatch between the particle velocity ṙ(t) and the particle orientation n(t) [5,70,71]. In our overdamped system, this inertial delay function is always zero since the average velocity is aligned with the orientation.…”

Section: General Resultsmentioning

confidence: 92%

“…Our model can be extended to higher spatial dimensions [69], to harmonic confinement [86][87][88][89], to external fields [90,91], and to include inertia [5,70,71,[92][93][94][95] where an analytical solution seems to be in reach as well. Moreover different combinations of friction and memory kernel as well as colored noise can be considered for future work [96][97][98][99][100], for instance, Mittag-Leffler noise [101,102] or power-law memory [103,104].…”

Section: Discussionmentioning

confidence: 99%

Active Brownian motion with memory delay induced by a viscoelastic medium

Sprenger¹,

Bair²,

Löwen³

2022

Preprint

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By now active Brownian motion is a well-established model to describe the motion of mesoscopic self-propelled particles in a Newtonian fluid. Here we use an extended model for swimming in a viscoelastic medium including memory effects of the solvent via a friction kernel for both translational and orientational degrees of freedom. We present an analytic framework for this extended model and evaluate it in particular for a Maxwell fluid characterized by a kernel which decays exponentially in time. We obtain analytical results for the mean displacement, the mean-square displacements and the orientational correlation function. We identify a memory induced delay between the effective self-propulsion force and the particle orientation which we quantify in terms of a special dynamical correlation function. In principle our predictions can be verified for an active colloidal particle in various viscoelastic environments such as a polymer solution.

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“…In conclusion, the PAM both unifies ABPs and AOUPs and provides a crucial step towards more realistic modeling of overdamped (dry) active motion in general, which should in future work be employed to provide an improved fit of experimental swim-velocity distributions. Investigating the effect of the swim-velocity fluctuations could represent an interesting perspective for circle swimming [92][93][94][95][96][97] , systems with spatial-dependent swim velocity [98][99][100][101][102][103] , and inertial dynamics [104][105][106][107][108] even affecting the orientational degrees of freedom 109,110 . The generalization of PAM to these cases could be responsible for new intriguing phenomena which will be investigated in future works.…”

Section: Parental Active Modelmentioning

confidence: 99%

The Parental Active Model: a unifying stochastic description of self-propulsion

Caprini,

Sprenger,

Löwen

et al. 2022

Preprint

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We propose a new overarching model for self-propelled particles that flexibly generates a full family of "descendants". The general dynamics introduced in this paper, which we denote as "parental" active model (PAM), unifies two special cases commonly used to describe active matter, namely active Brownian particles (ABPs) and active Ornstein-Uhlenbeck particles (AOUPs). We thereby document the existence of a deep and close stochastic relationship between them, resulting in the subtle balance between fluctuations in the magnitude and direction of the self-propulsion velocity. Besides illustrating the relation between these two common models, the PAM can generate additional offspring, interpolating between ABP and AOUP dynamics, that could provide more suitable models for a large class of living and inanimate active matter systems, possessing characteristic distributions of their self-propulsion velocity. Our general model is evaluated in the presence of a harmonic external confinement. For this reference example, we present a two-state phase diagram which sheds light on the transition in the shape of the positional density distribution, from a unimodal Gaussian for AOUPs to a Mexican-hat-like profile for ABPs.

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

Cited by 44 publications

References 105 publications

Brownian particles driven by spatially periodic noise

Brownian particles driven by spatially periodic noise

Active Brownian motion with memory delay induced by a viscoelastic medium

The Parental Active Model: a unifying stochastic description of self-propulsion

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