Local time for run and tumble particle

Singh, Prashant; Kundu, Anupam

doi:10.1103/physreve.103.042119

Cited by 18 publications

(28 citation statements)

References 49 publications

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“…Two of these conditions come from the behaviour of Q(p, x 0 ) as x 0 → 0 + and x 0 → ∞ which are, respectively, written in Eqs. (10) and (11). In addition, we use two matching conditions.…”

Section: Local Timementioning

confidence: 99%

“…To compute them, we use the boundary conditions in Eqs. (10) and (11) along with the continuity conditions for Q(p, x 0 ) and ∂Q(p,x 0 )…”

Section: Residence Timementioning

confidence: 99%

“…We next use the boundary conditions in Eqs. (10) and (11) to evaluate these constants. Finally taking…”

Section: N =mentioning

confidence: 99%

“…A well-studied Brownian functional in the literature is the local time for which Z(x) = δ(x − x ). It measures the total time that the particle spends in the vicinity of a desired location x in space [1,[5][6][7][8][9][10]. As such, the local time provides interesting information with regard to the spatio-temporal properties of the particle's trajectory and is thus a useful measure with various applications in chemical reactions and catalytic processes [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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First-passage Brownian functionals with stochastic resetting

Singh,

Pal

2022

Preprint

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We study the statistical properties of first-passage time functionals of a one dimensional Brownian motion in the presence of stochastic resetting. A firstpassage functional is defined aswhere t f is the first-passage time of a reset Brownian process x(τ ), i.e., the first time the process crosses zero. In here, the particle is reset to x R > 0 at a constant rate r starting from x 0 > 0 and we focus on the following functionals:, and (iii) functionals of the form A n = ´tf 0 dτ [x(τ )] n with n > −2. For first two functionals, we analytically derive the exact expressions for the moments and distributions. Interestingly, the residence time moments reach minima at some optimal resetting rates. A similar phenomena is also observed for the moments of the functional A n . Finally, we show that the distribution of A n for large A n decays exponentially as ∼ exp (−A n /a n ) for all values of n and the corresponding decay length a n is also estimated. In particular, exact distribution for the first passage time under resetting (which corresponds to the n = 0 case) is derived and shown to be exponential at large time limit in accordance with the generic observation. This behavioural drift from the underlying process can be understood as a ramification due to the resetting mechanism which curtails the undesired long Brownian first passage trajectories and leads to an accelerated completion. We confirm our results to high precision by numerical simulations.

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Section: Local Timementioning

confidence: 99%

“…To compute them, we use the boundary conditions in Eqs. (10) and (11) along with the continuity conditions for Q(p, x 0 ) and ∂Q(p,x 0 )…”

Section: Residence Timementioning

confidence: 99%

“…We next use the boundary conditions in Eqs. (10) and (11) to evaluate these constants. Finally taking…”

Section: N =mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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First-passage Brownian functionals with stochastic resetting

Singh,

Pal

2022

Preprint

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“…We remark that telegraph processes have been extensively studied in the literature, where they are referred to alternatively as persistent Brownian motion processes [12,46], velocity-jump processes [37], correlated random walks [55,12,51], run-and-tumble particles (RTP) [3,4,29,49], and more generally, non-Markovian random walks [16,30]. Recently, the telegraph process has seen increased interest due to its biological application to the motion of bacteria [29,49,47,48,33] Many existing studies on the telegraph process consider a one-dimensional domain with absorbing boundaries [42,25], but mean first passage time calculations often involve computing the exit time out of the entire interval [55,16,30,31,56,4,29,12,46,51,49]. In contrast, we wish to compute the mean first exit time through a particular end of the interval given an initial positive velocity and initial position z 0 ∈ [0, L].…”

Section: Mean First Passage Time To Translocationmentioning

confidence: 99%

Coarse-grained Stochastic Model of Myosin-Driven Vesicles into Dendritic Spines

Park,

Singh,

Fai

2021

Preprint

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We study the dynamics of membrane vesicle motor transport into dendritic spines, which are bulbous intracellular compartments in neurons that play a key role in transmitting signals between neurons. We consider the stochastic analog of the vesicle transport model in [Park and Fai, The Dynamics of Vesicles Driven Into Closed Constrictions by Molecular Motors. Bull. Math. Biol. 82, 141 (2020)]. The stochastic version, which may be considered as an agent-based model, relies mostly on the action of individual myosin motors to produce vesicle motion. To aid in our analysis, we coarse-grain this agent-based model using a master equation combined with a partial differential equation describing the probability of local motor positions. We confirm through convergence studies that the coarse-graining captures the essential features of bistability in velocity (observed in experiments) and waiting-time distributions to switch between steady-state velocities. Interestingly, these results allow us to reformulate the translocation problem in terms of the mean first passage time for a run-and-tumble particle moving on a finite domain with absorbing boundaries at the two ends. We conclude by presenting numerical and analytical calculations of vesicle translocation.

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Spectral density of individual trajectories of an active Brownian particle

2022

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We study analytically the single-trajectory spectral density (STSD) of an active Brownian motion as exhibited, for example, by the dynamics of a chemically-active Janus colloid. We evaluate the standardly-defined spectral density, {\it i.e.} the STSD averaged over a statistical ensemble of trajectories in the limit of an infinitely long observation time $T$, and also go beyond the standard analysis by considering the coefficient of variation $\gamma$ of the distribution of the STSD. Moreover, we analyse the finite-$T$ behaviour of the STSD and $\gamma$, determine the cross-correlations between spatial components of the STSD, and address the effects of translational diffusion on the functional forms of spectral densities. The exact expressions that we obtain unveil many distinctive features of active Brownian motion compared to its passive counterpart, which allow to distinguish between these two classes based solely on the spectral content of individual trajectories.

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Local time for run and tumble particle

Cited by 18 publications

References 49 publications

First-passage Brownian functionals with stochastic resetting

First-passage Brownian functionals with stochastic resetting

Coarse-grained Stochastic Model of Myosin-Driven Vesicles into Dendritic Spines

Spectral density of individual trajectories of an active Brownian particle

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