Run-and-tumble particle in inhomogeneous media in one dimension

Singh, Prashant; Sabhapandit, Sanjib; Kundu, Anupam

doi:10.1088/1742-5468/aba7b1

Cited by 28 publications

(48 citation statements)

References 77 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The distribution of an RnT particle is captured by the propagator P (x, t) = (φ(x, t) + ψ(x, t)) φ(x 0 , 0) , where the system is initialised at t 0 = 0 with a right-moving particle at x 0 [27,60]. Diagrammatically, the particle distribution is (D.1)…”

Section: Appendix C Some Propagators In Closed Formmentioning

confidence: 99%

Run-and-tumble motion in a harmonic potential: field theory and entropy production

Garcia-Millan¹,

Pruessner²

2021

J. Stat. Mech.

View full text Add to dashboard Cite

Run-and-tumble (RnT) motion is an example of active motility where particles move at constant speed and change direction at random times. In this work we study RnT motion with diffusion in a harmonic potential in one dimension via a path integral approach. We derive a Doi-Peliti field theory and use it to calculate the entropy production and other observables in closed form. All our results are exact.

show abstract

Section: Appendix C Some Propagators In Closed Formmentioning

confidence: 99%

Run-and-tumble motion in a harmonic potential: field theory and entropy production

Garcia-Millan¹,

Pruessner²

2021

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

“…where the notation L s→t denoted the inverse Laplace transformation as indicated in Eq. (18). Using the inverse Laplace transformations…”

Section: Small Z Behaviour Of Fα(z)mentioning

confidence: 99%

“…Several studies on heterogeneous diffusive processes (HDPs) have revealed anomalous scaling of the mean squared displacement (MSD) and weak ergodicity breaking between time averaged and ensemble averaged MSDs [10][11][12][13][14][15][16]. Persistent properties of HDPs have also been investigated in [17,18].…”

Section: Introductionmentioning

confidence: 99%

Extreme value statistics and arcsine laws for heterogeneous diffusion processes

Singh

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Heterogeneous diffusion with spatially changing diffusion coefficient arises in many experimental systems like protein dynamics in the cell cytoplasm, mobility of cajal bodies and confined hardsphere fluids. Here, we showcase a simple model of heterogeneous diffusion where the diffusion coefficient D(x) varies in power-law way, i.e. D(x) ∼ |x| −α with the exponent α > −1. This model exhibits anomalous scaling of the mean squared displacement (MSD) of the form ∼ t 2 2+α and weak ergodicity breaking in the sense that ensemble averaged and time averaged MSDs do not converge. In this paper, we look at the extreme value statistics of this model and derive, for all α, the exact probability distributions of the maximum spatial displacement M (t) and arg-maximum tm(t) (i.e. the time at which this maximum is reached) till duration t. In the second part of our paper, we analyze the statistical properties of the residence time tr(t) and the last-passage time t (t) and compute their distributions exactly for all values of α. Our study unravels that the heterogeneous version (α = 0) displays many rich and contrasting features compared to that of the standard Brownian motion (SBm). For example, while for SBm (α = 0), the distributions of tm(t), tr(t) and t (t) are all identical (á la "arcsine laws" due to Lévy), they turn out to be significantly different for non-zero α. Another interesting property of tr(t) is the existence of a critical α (which we denote by αc = −0.3182) such that the distribution exhibits a local maximum at tr = t/2 for α < αc whereas it has minima at tr = t/2 for α ≥ αc. The underlying reasoning for this difference hints at the very contrasting natures of the process for α ≥ αc and α < αc which we thoroughly examine in our paper. All our analytical results are backed by extensive numerical simulations.

show abstract

“…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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Run-and-tumble particle in inhomogeneous media in one dimension

Cited by 28 publications

References 77 publications

Run-and-tumble motion in a harmonic potential: field theory and entropy production

Run-and-tumble motion in a harmonic potential: field theory and entropy production

Extreme value statistics and arcsine laws for heterogeneous diffusion processes

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

Contact Info

Product

Resources

About