Current fluctuations in noninteracting run-and-tumble particles in one dimension

Banerjee, Tirthankar; Majumdar, Satya N.; Rosso, Alberto; Schehr, Grégory

doi:10.1103/physreve.101.052101

Cited by 51 publications

(101 citation statements)

References 37 publications

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“…Now we phrase the probability distribution of the sediment flux in terms of these particle dynamics. The method we present is very similar to the one developed by Banerjee et al (2020) to describe current fluctuations in condensed matter physics. The basic idea, as depicted in Fig.…”

Section: Mechanistic Formulation Of the Sediment Fluxmentioning

confidence: 99%

Stochastic description of the bedload sediment flux

Pierce

Hassan

Ferreira

2022

Preprint

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Abstract. We present a new formulation of the bedload sediment flux probability distribution. Individual particles obey Langevin equations which are switched on and off by particle entrainment and deposition. The flux is calculated as the rate of many such particles crossing a control surface within a specified observation time. Flux distributions inherit observation-time dependence from the on-off motions of particles. At the longest observation times, distributions converge to sharp peaks around classically-expected values, but at short times, fluctuations are erratic. We relate this scale dependence of bedload transport rates to the movement characteristics of individual grains. This work provides a statistical mechanics description for the fluctuations and observation-scale dependence of sediment transport rates.

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Section: Mechanistic Formulation Of the Sediment Fluxmentioning

confidence: 99%

Stochastic description of the bedload sediment flux

Pierce

Hassan

Ferreira

2022

Preprint

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“…( 43) is actually the Fourier transform of the marginal distribution P (Y, k * ) of the y-coordinate at step k * as can be easily seen from Eq. (37). Hence, performing inverse Fourier transform on both sides of Eq.…”

Section: Computation Ofmentioning

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%

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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“…Properties of non-interacting active particles, such as run-and-tumble particles (RTPs) [14,15,16], typically become indistinguishable from those of non-interacting passive Brownian particles at long times, for suitably chosen parameters [17]. A free RTP runs ballistically at speed v in a certain direction, tumbles and chooses a new random direction for the next run; this motion approximates that of E. coli bacteria [14].…”

Section: Introductionmentioning

confidence: 99%

“…A free RTP runs ballistically at speed v in a certain direction, tumbles and chooses a new random direction for the next run; this motion approximates that of E. coli bacteria [14]. This leads to temporal correlations in the particle velocity, with a range of the order of the flip time γ −1 [17]. This finite persistence time leads to several interesting features.…”

Section: Introductionmentioning

confidence: 99%

Tracer dynamics in one dimensional gases of active or passive particles

Banerjee,

Jack,

Cates

2021

Preprint

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We consider one-dimensional systems comprising either active runand-tumble particles (RTPs) or passive Brownian random walkers. These particles are either noninteracting or have hardcore exclusions. We study the dynamics of a single tracer particle embedded in such a system -this tracer may be either active or passive, with hardcore exclusion from environmental particles. In an active hardcore environment, both active and passive tracers show longtime subdiffusion: displacements scale as t 1/4 with a density-dependent prefactor that is independent of tracer type, and differs from the corresponding result for passive-in-passive subdiffusion. In an environment of noninteracting active particles, the passive-in-passive results are recovered at low densities for both active and passive tracers, but transient caging effects slow the tracer motion at higher densities, delaying the onset of any t 1/4 regime. For an active tracer in a passive environment, we find more complex outcomes, which depend on details of the dynamical discretization scheme. We interpret these results by studying the density distribution of environmental particles around the tracer. In particular, sticking of environment particles to the tracer cause it to move more slowly in noninteracting than in interacting active environments, while the anomalous behaviour of the active-in-passive cases stems from a 'snowplough' effect whereby a large pile of diffusive environmental particles accumulates in front of a RTP tracer during a ballistic run.

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Current fluctuations in noninteracting run-and-tumble particles in one dimension

Cited by 51 publications

References 37 publications

Stochastic description of the bedload sediment flux

Stochastic description of the bedload sediment flux

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

Tracer dynamics in one dimensional gases of active or passive particles

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