Self-propulsion with speed and orientation fluctuation: Exact computation of moments and dynamical bistabilities in displacement

Shee, Amir; Chaudhuri, Debasish

doi:10.1103/physreve.105.054148

Cited by 6 publications

(6 citation statements)

References 54 publications

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“…We can now obtain the mean, the variance, the skewness, and the excess kurtosis of X from expressions ( 27)- (30), and the results of Section 3.1.1. Thus ⟨X⟩ = 𝜔𝜏⟨Y⟩ a (37) that is, the average of the position is directly proportional to the average of 𝜌 a and to the rate of kicks 𝜔.…”

Section: Mean Variance Skewness and Excess Kurtosis Of Xmentioning

confidence: 99%

“…of Langevin equations with active noise, with the exception of few examples for which such calculations becomes a formidable task. [28][29][30] A fundamental question in statistical physics is the interaction of thermal energy and confinement. At equilibrium, the particle displacement in a conservative force field is described by the Boltzmann distribution.…”

Section: Introductionmentioning

confidence: 99%

“…of Langevin equations with active noise, with the exception of few examples for which such calculations becomes a formidable task. [ 28–30 ]…”

Section: Introductionmentioning

confidence: 99%

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Brownian Particle in a Poisson‐Shot‐Noise Active Bath: Exact Statistics, Effective Temperature, and Inference

Di Bello,

Majumdar,

Marathe

et al. 2024

Annalen der Physik

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The dynamics of an overdamped Brownian particle in a thermal bath that contains a dilute solution of active particles is studied. The particle moves in a harmonic potential and experiences Poisson shot‐noise kicks with specified amplitude distribution due to moving active particles in the bath. From the Fokker–Planck equation for the particle dynamics, the stationary solution for the displacement distribution is derived along with the moments characterizing mean, variance, skewness, and kurtosis, as well as finite‐time first and second moments. An effective temperature is also computed through the fluctuation–dissipation theorem and show that equipartition theorem holds for all zero‐mean kick distributions, including those leading to non‐Gaussian stationary statistics. For the case of Gaussian‐distributed active kicks, a re‐entrant behavior from non‐Gaussian to Gaussian stationary states and a heavy‐tailed leptokurtic distribution across a wide range of parameters are found as seen in recent experimental studies. Further analysis reveals statistical signatures of the irreversible dynamics of the particle displacement in terms of the time asymmetry of cross‐correlation functions. Fruits of the work is the development of an compact inference scheme that may allow experimentalists to extract the rate and moments of underlying shot‐noise solely from the statistics the particle position.

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Section: Mean Variance Skewness and Excess Kurtosis Of Xmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Brownian Particle in a Poisson‐Shot‐Noise Active Bath: Exact Statistics, Effective Temperature, and Inference

Di Bello,

Majumdar,

Marathe

et al. 2024

Annalen der Physik

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“…Offering a unified approach for computing the precise time evolution of all conceivable dynamical variables in arbitrary dimensions, our method represents a noteworthy analytical advancement in investigating inertial effects in active matter. The technique was originally proposed back in 1952 to study equilibrium properties of worm-like chains [53] and was recently put in use to study the dynamics of overdamped ABPs in [31,[54][55][56].…”

Section: Introductionmentioning

confidence: 99%

Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles

Patel,

Chaudhuri

2023

New J. Phys.

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In this study, we investigate the behavior of free inertial active Brownian particles in the presence of thermal noise. While finding a closed-form solution for the joint distribution of positions, orientations, and velocities using the Fokker–Planck equation is generally challenging, we utilize a Laplace transform method to obtain the exact temporal evolution of all dynamical moments in arbitrary dimensions. Our expressions in d dimensions reveal that inertia significantly impacts steady-state kinetic temperature and swim pressure while leaving the late-time diffusivity unchanged. Notably, as a function of activity and inertia, the steady-state velocity distribution exhibits a remarkable re-entrant crossover from ‘passive’ Gaussian to ‘active’ non-Gaussian behaviors. We construct a corresponding ‘phase diagram’ using the exact expression of the d-dimensional kurtosis. Our analytic expressions describe steady states and offer insights into time-dependent crossovers observed in moments of velocity and displacement. Our calculations can be extended to predict up to second-order moments for run-and-tumble particles and the active Ornstein–Uhlenbeck process (AOUP). Additionally, the kurtosis shows differences from AOUP.

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“…The active particles show several counter-intuitive properties including multiple crossovers between ballistic and diffusive motion, accumulation near confining boundaries, etc. [23][24][25][26][27][28]. The other important aspect of their dynamics is their time-delayed but spatially local interaction achieved via signalling through autoinducers or pheromones.…”

mentioning

confidence: 99%

Extension and dynamical phases in random walkers depositing and following chemical trails

Khuntia¹,

Chaudhuri²,

Chaudhuri³

2022

EPL

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Active walker models have proved to be extremely effective in understanding the evolution of a large class of systems in biology like ant trail formation and pedestrian trails. We propose a simple model of a random walker which modifies its local environment that in turn influences the motion of the walker at a {\em later} time. We perform direct numerical simulations of the walker in a discrete lattice with the walker actively depositing a chemical which attracts the walker trajectory and also evaporates in time. We propose a method to look at the structural transitions of the trajectory using radius of gyration for finite time walks. The extension over a definite time-window shows a non-monotonic change with the deposition rate characteristic of a coil-globule transition. At certain regions of the parameter space of the chemical deposition and evaporation rates, the extensions of the walker shows a re-entrant behavior. The dynamics, characterised by the mean-squared displacement, shows deviation from diffusive scaling at intermediate time scales, returning to diffusive behavior asymptotically. A mean field theory captures the variation of the asymptotic diffusivity.

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Self-propulsion with speed and orientation fluctuation: Exact computation of moments and dynamical bistabilities in displacement

Cited by 6 publications

References 54 publications

Brownian Particle in a Poisson‐Shot‐Noise Active Bath: Exact Statistics, Effective Temperature, and Inference

Brownian Particle in a Poisson‐Shot‐Noise Active Bath: Exact Statistics, Effective Temperature, and Inference

Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles

Extension and dynamical phases in random walkers depositing and following chemical trails

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