Run-and-tumble particles in two dimensions: Marginal position distributions

Santra, Ion; Basu, Urna; Sabhapandit, Sanjib

doi:10.1103/physreve.101.062120

Cited by 89 publications

(107 citation statements)

References 46 publications

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“…( 69) can be derived using the Pollaczek-Spitzer formula in Eq. (26). We first recall that Q s (M, n) in Eq.…”

Section: Discussionmentioning

confidence: 99%

“…Over the recent few years, this model has been substantially studied and a variety of results are known. Examples include -position distribution in free space as well as in confining potential [21][22][23][24][25][26][27], condensation transition [28][29][30], persistent properties [31][32][33], extremal properties [34,35], path functionals [34,36], current fluctuations [37], interacting multiple RTPs [27,[38][39][40][41], etc.…”

Section: Introductionmentioning

confidence: 99%

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Mean area of the convex hull of a run and tumble particle in two dimensions

Singh,

Kundu,

Majumdar

et al. 2021

Preprint

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We investigate the statistics of the convex hull for a single run-and-tumble particle in two dimensions. Run-and-tumble particle (RTP), also known as persistent random walker, has gained significant interest in the recent years due to its biological application in modelling the motion of bacteria. We consider two different statistical ensembles depending on whether (i) the total number of tumbles n or (ii) the total observation time t is kept fixed. Benchmarking the results on perimeter, we study the statistical properties of the area of the convex hull for RTP. Exploiting the connections to extreme value statistics, we obtain exact analytical expressions for the mean area for both ensembles. For fixed-t ensemble, we show that the mean possesses a scaling form in γt (with γ being the tumbling rate) and the corresponding scaling function is exactly computed. Interestingly, we find that it exhibits crossover from ∼ t 3 scaling at small times t γ −1 to ∼ t scaling at large times t γ −1 . On the other hand, for fixed-n ensemble, the mean expectedly grows linearly with n for n 1. All our analytical findings are supported with numerical simulations.

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“…( 69) can be derived using the Pollaczek-Spitzer formula in Eq. (26). We first recall that Q s (M, n) in Eq.…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mean area of the convex hull of a run and tumble particle in two dimensions

Singh,

Kundu,

Majumdar

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The expansion in Eq. (22) shows that at short time the scaling r 4 (t) ∼ t 2 can cross over to r 4 (t) ∼ t 3 at…”

Section: Fourth Moment and Kurtosismentioning

confidence: 98%

“…In this context, studies of simple models have been crucial. They displayed several ballistic-diffusive crossovers, non-Boltzmann steady-state, localization away from potential minima, and associated re-entrant transition for steadystate properties of trapped particles [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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

Shee,

Chaudhuri

2021

Preprint

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We consider the influence of active speed fluctuations on the dynamics of a d-dimensional active Brownian particle performing a persistent stochastic motion. We use the Laplace transform of the Fokker-Planck equation to obtain exact expressions for time-dependent dynamical moments. Our results agree with direct numerical simulations and show several dynamical crossovers determined by the activity, persistence, and speed fluctuation. The persistence in the motion leads to anisotropy, with the parallel component of displacement fluctuation showing sub-diffusive behavior and non-monotonic variation. The kurtosis remains positive at short times determined by the speed fluctuation, crossing over to a negative minimum at intermediate times governed by the persistence before vanishing asymptotically. The probability distribution of particle displacement obtained from numerical simulations in two-dimension shows two crossovers between contracted and expanded trajectories via two bimodal distributions at intervening times. While the speed fluctuation dominates the first crossover, the second crossover is controlled by persistence like in the worm-like chain model of semiflexible polymers.

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“…In two dimensions, the RTP "runs" at constant speed in a fixed direction and then instantaneously "tumbles", i.e. reorients itself by choosing an angle randomly and isotropically [23,24]. Such RTPs undergo ballistic motion over short times, while diffusive motion emerges at long times [20].…”

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confidence: 99%

Attractor-driven matter

Valani¹,

Paganin²

2021

Preprint

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Strange attractors are induced by governing differential or integro-differential equations associated with non-linear dynamical systems, but they can also drive such dynamics. When the governing equations contain stochastic forcing, they may also be replaced by deterministic chaotic driving via a governing strange attractor. We outline a flexible deterministic means for such chaotic strangeattractor driven dynamics, and illustrate its utility for modeling active matter. Several active-matter phenomena may be modeled in this manner, such as run-and-tumble particles, run-reverse-flick motion, clustering, jamming and flocking.

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Run-and-tumble particles in two dimensions: Marginal position distributions

Cited by 89 publications

References 46 publications

Mean area of the convex hull of a run and tumble particle in two dimensions

Mean area of the convex hull of a run and tumble particle in two dimensions

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

Attractor-driven matter

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