Self-propulsion with speed and orientation fluctuation: exact computation of moments and dynamical bistabilities in displacement

Shee, Amir; Chaudhuri, Debasish

doi:10.48550/arxiv.2112.13415

Cited by 2 publications

(2 citation statements)

References 43 publications

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“…In fact, our framework is quite generic and expected to be applicable to any Fokker-Planck or master equation involving a small perturbative parameter. For example it would be interesting to study the signatures of activity in other variants of active particle models [27,39,[47][48][49] It would be also interesting to ask similar questions for the generalized run-and-tumble process, where the large time scaling of the position fluctuations is anomalous [50]. Another future direction is to extend the framework to systematically study the subleading corrections to the long-time t −3/2 behavior of the first-passage time probability distributions of active motions.…”

Section: Discussionmentioning

confidence: 99%

Universal framework for the long-time position distribution of free active particles

Santra

Basu

Sabhapandit

2022

J. Phys. A: Math. Theor.

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Active particles self-propel themselves with a stochastically evolving velocity, generating a persistent motion leading to a non-diffusive behavior of the position distribution. Nevertheless, an effective diffusive behavior emerges at times much larger than the persistence time. Here we develop a general framework for studying the long-time behaviour for a class of active particle dynamics and illustrate it using the examples of run-and-tumble particle, active Ornstein-Uhlenbeck particle, active Brownian particle, and direction reversing active Brownian particle. Treating the ratio of the persistence-time to the observation time as the small parameter, we show that the position distribution generically satisfies the diffusion equation at the leading order. We further show that the sub-leading contributions, at each order, satisfies an inhomogeneous diffusion equation, where the source term depends on the previous order solutions. We explicitly obtain a few sub-leading contributions to the Gaussian position distribution. As a part of our framework, we also prescribe a way to find the position moments recursively and compute the first few explicitly for each model.

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Section: Discussionmentioning

confidence: 99%

Universal framework for the long-time position distribution of free active particles

Santra

Basu

Sabhapandit

2022

J. Phys. A: Math. Theor.

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“…Also macroscopic agents like locusts 81 , whirligig beetles 82 or zebrafish 14,83,84 exhibit natural speed fluctuations. To realistically describe these systems, a theoretical approach should incorporate both fluctuations of the modulus and the direction of the self-propulsion velocity [83][84][85][86][87] . For this purpose, our description within the PAM is particularly convenient, because it is based on a single stochastic process n of unit standard deviation (i.e., v 0 is treated as a velocity scale and does not fluctuate itself), such that all descendant models with an intermediate value of the parameter µ can be evaluated with the same numerical effort as ABPs and AOUPs.…”

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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Self-propulsion with speed and orientation fluctuation: exact computation of moments and dynamical bistabilities in displacement

Cited by 2 publications

References 43 publications

Universal framework for the long-time position distribution of free active particles

Universal framework for the long-time position distribution of free active particles

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

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