One-dimensional run-and-tumble motions with generic boundary conditions

Angelani, Luca

doi:10.1088/1751-8121/ad009e

Cited by 6 publications

(12 citation statements)

References 37 publications

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“…A first implementation might be to consider reversible trapping, that is, the possibility for the particle to reactivate itself after trapping [43]. Other possible extensions could be the analysis of planar motions [12,[44][45][46][47] or considering more complex environments, such as those described by a continuously variable trapping rate, by a periodic sequence of trapping intervals [4,5] or by the presence of generic boundaries [48]. A final possible direction of investigation might be to consider different combinations of particle motion in the two phases, before and after trapping.…”

Section: Discussionmentioning

confidence: 99%

Run-and-tumble motion in trapping environments

Angelani

2023

Phys. Scr.

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Complex or hostile environments can sometimes inhibit the movement capabilities of diffusive particles or active swimmers, who may thus become stuck in fixed positions. This occurs, for example, in the adhesion of bacteria to surfaces at the initial stage of biofilm formation. Here we analyze the dynamics of active particles in the presence of trapping regions, where irreversible particle immobilization occurs at a fixed rate. By solving the kinetic equations for run-and-tumble motion in one space dimension, we give expressions for probability distribution functions, focusing on stationary distributions of blocked particles, and mean trapping times in terms of physical and geometrical parameters. Different extensions of the trapping region are considered, from infinite to cases of semi-infinite and finite intervals. The mean trapping time turns out to be simply the inverse of the trapping rate for infinitely extended trapping zones, while it has a nontrivial form in the semi-infinite case and is undefined for finite domains, due to the appearance of long tails in the trapping time distribution. Finally, to account for the subdiffusive behavior observed in the adhesion processes of bacteria to surfaces, we extend the model to include anomalous diffusive motion in the trapping region, reporting the exact expression of the mean-square displacement.

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Section: Discussionmentioning

confidence: 99%

Run-and-tumble motion in trapping environments

Angelani

2023

Phys. Scr.

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“…For an illustration, see the left panel of figure 4. Now, let us consider the dual process y(t) defined in (40). At t = 0, the dual process begins at position y = b, and there are two hard walls at a and b.…”

Section: Comments On the Duality Relation Of An Rtp Subjected To A Ge...mentioning

confidence: 99%

“…Recently, the MFPT of a one-dimensional RTP in confining potentials has been explicitly calculated, revealing that the MFPT can be minimised with respect to the tumbling rate γ [39]. Other studies focus on a free RTP in confined domains with various boundary conditions, in one dimension [40][41][42] or higher [43][44][45]. A related quantity is the exit probability (or splitting/hitting probability [34,46,47]).…”

Section: Introductionmentioning

confidence: 99%

Relating absorbing and hard wall boundary conditions for a one-dimensional run-and-tumble particle

Guéneau,

Touzo

2024

J. Phys. A: Math. Theor.

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The connection between absorbing boundary conditions and hard walls is well established in the mathematical literature for a variety of stochastic models, including for instance the Brownian motion. In this paper we explore this duality for a different type of process which is of particular interest in physics and biology, namely the run-tumble-particle, a toy model of active particle. For a one-dimensional run-and-tumble particle subjected to an arbitrary external force, we provide a duality relation between the exit probability, i.e. the probability that the particle exits an interval from a given boundary before a certain time $t$, and the cumulative distribution of its position in the presence of hard walls at the same time $t$. We show this relation for a run-and-tumble particle in the stationary state by explicitly computing both quantities. At finite time, we provide a derivation using the Fokker-Planck equation. All the results are confirmed by numerical simulations.

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“…In particular, we will focus on one-dimensional and two-dimensional systems, studying different boundary conditions. For the one-dimensional case we will exploit recent analytical results obtained for the run-and-tumble equations in the presence of partially absorption [ 33 , 34 ], sticky boundaries [ 22 , 23 ] and generic boundary conditions [ 35 ]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Optimal escapes in active matter

Angelani

2024

Eur. Phys. J. E

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The out-of-equilibrium character of active particles, responsible for accumulation at boundaries in confining domains, determines not-trivial effects when considering escape processes. Non-monotonous behavior of exit times with respect to tumbling rate (inverse of mean persistent time) appears, as a consequence of the competing processes of exploring the bulk and accumulate at boundaries. By using both 1D analytical results and 2D numerical simulations of run-and-tumble particles with different behaviours at boundaries, we scrutinize this very general phenomenon of active matter, evidencing the role of accumulation at walls for the existence of optimal tumbling rates for fast escapes.

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One-dimensional run-and-tumble motions with generic boundary conditions

Cited by 6 publications

References 37 publications

Run-and-tumble motion in trapping environments

Run-and-tumble motion in trapping environments

Relating absorbing and hard wall boundary conditions for a one-dimensional run-and-tumble particle

Optimal escapes in active matter

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