Stationary superstatistics distributions of trapped run-and-tumble particles

Sevilla, Francisco J.; Arzola, Alejandro V.; Cital, Enrique Puga

doi:10.1103/physreve.99.012145

Cited by 66 publications

(70 citation statements)

References 66 publications

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“…From Eqs. (33) and (35) and using the relation (16) between P (x) and R(x) we can also calculate P i (x) individually in a straightforward manner. However, we do not give explicit expressions for them here.…”

Section: Position Distribution For β =mentioning

confidence: 99%

Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap

Basu¹,

Majumdar²,

Rosso³

et al. 2020

J. Phys. A: Math. Theor.

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We study the motion of a one-dimensional run-and-tumble particle with three discrete internal states in the presence of a harmonic trap of stiffness µ. The three internal states, corresponding to positive, negative and zero velocities respectively, evolve following a jump process with rate γ. We compute the stationary position distribution exactly for arbitrary values of µ and γ which turns out to have a finite support on the real line. We show that the distribution undergoes a shape-transition as β = γ/µ is changed. For β < 1, the distribution has a double-concave shape and shows algebraic divergences with an exponent (β − 1) both at the origin and at the boundaries. For β > 1, the position distribution becomes convex, vanishing at the boundaries and with a single, finite, peak at the origin. We also show that for the special case β = 1, the distribution shows a logarithmic divergence near the origin while saturating to a constant value at the boundaries.Exact stationary state of a three-state run-and-tumble particle

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Section: Position Distribution For β =mentioning

confidence: 99%

Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap

Basu¹,

Majumdar²,

Rosso³

et al. 2020

J. Phys. A: Math. Theor.

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show abstract

“…Setting b ± = 1/2 in Eq. (27), inverting the (2 × 2) matrix explicitly and adding the two equations for P + (p, s) and P − (p, s), we get…”

Section: A Single Rtp In the Presence Of An Absorbing Wall At Thementioning

confidence: 99%

Noncrossing run-and-tumble particles on a line

2019

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We study active particles performing independent run and tumble motion on an infinite line with velocities v0σ(t), where σ(t) = ±1 is a dichotomous telegraphic noise with constant flipping rate γ. We first consider one particle in the presence of an absorbing wall at x = 0 and calculate the probability that it has survived up to time t and is at position x at time t. We then consider two particles with independent telegraphic noises and compute exactly the probability that they do not cross up to time t. Contrarily to the case of passive (Brownian) particles this two-RTP problem can not be reduced to a single RTP with an absorbing wall. Nevertheless, we are able to compute exactly the probability of no-crossing of two independent RTP's up to time t and find that it decays at large time as t −1/2 with an amplitude that depends on the initial condition. The latter allows to define an effective length scale, analogous to the so called " Milne extrapolation length" in neutron scattering, which we demonstrate to be a fingerprint of the active dynamics.arXiv:1902.06176v2 [cond-mat.stat-mech]

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“…Starting from the Langevin equations (45), it is easy to write down the corresponding Fokker-Planck equation,…”

Section: Abp In a Harmonic Trapmentioning

confidence: 99%

“…Very recently, in Ref. [41], the same Langevin equation (45) was studied, but in the presence of an additive translational noise in the x and y directions with a nonzero translational diffusion constant D T . The stationary distribution P stat (x, y) was computed from the associated Fokker-Planck equation as a power series expansion in terms of the param-…”

Section: Abp In a Harmonic Trapmentioning

confidence: 99%

Long-time position distribution of an active Brownian particle in two dimensions

et al. 2019

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We study the late time dynamics of a single active Brownian particle in two dimensions with speed v0 and rotation diffusion constant DR. We show that at late times t D −1 R , while the position probability distribution P (x, y, t) in the x-y plane approaches a Gaussian form near its peak describing the typical diffusive fluctuations, it has non-Gaussian tails describing atypical rare fluctuations when x 2 + y 2 ∼ v0t. In this regime, the distribution admits a large deviation form,, where we compute the rate function Φ(z) analytically and also numerically using an importance sampling method. We show that the rate function Φ(z), encoding the rare fluctuations, still carries the trace of activity even at late times. Another way of detecting activity at late times is to subject the active particle to an external harmonic potential.In this case we show that the stationary distribution Pstat(x, y) depends explicitly on the activity parameter D −1 R and undergoes a crossover, as DR increases, from a ring shape in the strongly active limit (DR → 0) to a Gaussian shape in the strongly passive limit (DR → ∞).

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Stationary superstatistics distributions of trapped run-and-tumble particles

Cited by 66 publications

References 66 publications

Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap

Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap

Noncrossing run-and-tumble particles on a line

Long-time position distribution of an active Brownian particle in two dimensions

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