Active Brownian particles: mapping to equilibrium polymers and exact computation of moments
arXiv:2002.01815 · doi:10.1039/D0SM00367k
Abstract
It is well known that path probabilities of Brownian motion correspond to the equilibrium configurational probabilities of flexible Gaussian polymers, while those of active Brownian motion correspond to in-extensible semiflexible polymers. Here we investigate the properties of the equilibrium polymer that corresponds to the trajectories of particles acted on simultaneously by both Brownian as well as active noise. Through this mapping we can see interesting crossovers in mechanical properties of the polymer with changing contour length. The polymer end-to-end distribution exhibits Gaussian behaviour for short lengths, which changes to the form of semiflexible filaments at intermediate lengths, to finally go back to a Gaussian form for long contour lengths. By performing a Laplace transform of the governing Fokker-Planck equation of the active Brownian particle, we discuss a direct method to derive exact expressions for all the moments of the relevant dynamical variables, in arbitrary dimensions. These are verified via numerical simulations and used to describe interesting qualitative features such as, for example, dynamical crossovers. Finally we discuss the kurtosis of the ABP's position which we compute exactly and show that it can be used to differentiate between active Brownian particles and active Ornstein-Uhlenbeck process.
arXiv comment14 pages, 13 figures; modifications for better clarity
References in corpus (24)
- Active Particles in Complex and Crowded Environments
- Collective motion
- Self-motile colloidal particles: from directed propulsion to random walk
- Active Brownian Particles. From Individual to Collective Stochastic Dynamics
- How far from equilibrium is active matter?
- Sedimentation of active colloidal suspensions
- When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
- Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
- Run-and-tumble particle in one-dimensional confining potential: Steady state, relaxation and first passage properties
- Active Brownian Motion in Two Dimensions
- Probing the spatiotemporal dynamics of catalytic Janus particles with single-particle tracking and differential dynamic microscopy
- Intermediate scattering function of an anisotropic active Brownian particle
- Elasticity of semi-flexible polymers
- Steady State of an Active Brownian Particle in Two-Dimensional Harmonic Trap
- Long time position distribution of an active Brownian particle in two dimensions
- Triple minima in free energy of semiflexible polymers
- Active processes in one dimension
- Steady-state distributions of ideal active Brownian particles under confinement and forcing
- Smoluchowski Diffusion Equation for Active Brownian Swimmers
- Active Brownian particles near straight or curved walls: Pressure and boundary layers
- Intermediate scattering function of an anisotropic Brownian circle swimmer
- Semiflexible polymers: Dependence on ensemble and boundary orientations
- Stochastic curvature of enclosed semiflexible polymers
- Bimodal probability density characterizes the elastic behavior of a semiflexible polymer in 2D under compression
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- Active Brownian Motion in two-dimensions under Stochastic Resetting
- Active Brownian Motion with Directional Reversals
- Condensation transition in the late-time position of a Run-and-Tumble particle
- Active Brownian particle in harmonic trap: exact computation of moments, and re-entrant transition
- AOUP in the presence of Brownian noise: a perturbative approach
- Toward the full short-time statistics of an active Brownian particle on the plane
- Run-and-Tumble particle in inhomogeneous media in one dimension
- Gap statistics of two interacting run and tumble particles in one dimension
- Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles
- Impact of chirality on active Brownian particle: Exact moments in two and three dimensions
- Spectral density of individual trajectories of an active Brownian particle
- Active Brownian motion with speed fluctuations in arbitrary dimensions: exact calculation of moments and dynamical crossovers
- Emergent Mesoscale Correlations in Active Solids with Noisy Chiral Dynamics
- Self-propulsion with speed and orientation fluctuation: exact computation of moments and dynamical bistabilities in displacement
- Dynamical crossovers and correlations in a harmonic chain of active particles
- Inertial Dynamics of Run-and-Tumble Particle
- Diffusion dynamics of an overdamped active ellipsoidal particle in two dimensions
- Active Brownian particle under stochastic position and orientation resetting in a harmonic trap
- Field theory of survival probabilities, extreme values, first passage times, and mean span of non-Markovian stochastic processes
- Long time behavior of run-and-tumble particles in two dimensions
- Chirality, confinement and dimensionality govern re-entrant transitions in active matter
- Orientational Distribution of an Active Brownian Particle: an analytical study
- Inertia-chirality interplay in active Brownian motion: exact dynamics and phase maps
- Dynamical metastability and re-entrant localization of trapped active elements with speed and orientation fluctuations
- Extension and dynamical phases in random walkers depositing and following chemical trails