Active Brownian motion with speed fluctuations in arbitrary dimensions: exact calculation of moments and dynamical crossovers

Shee, Amir; Chaudhuri, Debasish

doi:10.1088/1742-5468/ac403f

Cited by 8 publications

(4 citation statements)

References 54 publications

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“…As mentioned in section 2, we need the 2nth moment y 2n (t) to determine the distribution uniquely at the order (ε 2 /t) n ; so in the following, we first discuss the computation of the moments recursively (see also [46]).…”

Section: Active Brownian Particlesmentioning

confidence: 99%

Universal framework for the long-time position distribution of free active particles

Santra

Basu

Sabhapandit

2022

J. Phys. A: Math. Theor.

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Active particles self-propel themselves with a stochastically evolving velocity, generating a persistent motion leading to a non-diffusive behavior of the position distribution. Nevertheless, an effective diffusive behavior emerges at times much larger than the persistence time. Here we develop a general framework for studying the long-time behaviour for a class of active particle dynamics and illustrate it using the examples of run-and-tumble particle, active Ornstein-Uhlenbeck particle, active Brownian particle, and direction reversing active Brownian particle. Treating the ratio of the persistence-time to the observation time as the small parameter, we show that the position distribution generically satisfies the diffusion equation at the leading order. We further show that the sub-leading contributions, at each order, satisfies an inhomogeneous diffusion equation, where the source term depends on the previous order solutions. We explicitly obtain a few sub-leading contributions to the Gaussian position distribution. As a part of our framework, we also prescribe a way to find the position moments recursively and compute the first few explicitly for each model.

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Section: Active Brownian Particlesmentioning

confidence: 99%

Universal framework for the long-time position distribution of free active particles

Santra

Basu

Sabhapandit

2022

J. Phys. A: Math. Theor.

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“…Through a Laplace transform of the governing Fokker-Planck equation, we demonstrate the precise time evolution of all moments of any desired dynamical variable in arbitrary d dimensions, a primary accomplishment of this work. This method, initially devised for investigating worm-like chains in 1952 [61], has been recently adapted to study ABP dynamics [16,[62][63][64][65]. We provide the exact expressions for the time evolution of various position and velocity moments, validating them against direct numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

Exact moments for trapped active particles: inertial impact on steady-state properties and re-entrance

Patel,

Chaudhuri

2024

New J. Phys.

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In this study, we investigate the behavior of inertial active Brownian particles in a d-dimensional harmonic trap in the presence of translational diffusion. While the solution of the Fokker-Planck equation is generally challenging, it can be utilized to compute the exact time evolution of all time- dependent dynamical moments using a Laplace transform approach. We present the explicit form for several moments of position and velocity in d-dimensions. An interplay of time scales assures that the effective diffusivity and steady-state kinetic temperature depend on both inertia and trap strength, unlike passive systems. The distance from equilibrium, measured by the violation of equilibrium fluctuation-dissipation and the amount of entropy production, decreases with increasing inertia and trap strength. We present detailed ‘phase diagrams’ using kurtosis of velocity and position, showing possibilities of re-entrance to equilibrium.

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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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Active Brownian motion with speed fluctuations in arbitrary dimensions: exact calculation of moments and dynamical crossovers

Cited by 8 publications

References 54 publications

Universal framework for the long-time position distribution of free active particles

Universal framework for the long-time position distribution of free active particles

Exact moments for trapped active particles: inertial impact on steady-state properties and re-entrance

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

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