Generalized Ornstein-Uhlenbeck Model for Active Motion

Abstract

We investigate a one-dimensional model of active motion, which takes into account the effects of persistent self-propulsion through a memory function in a dissipative-like term of the generalized Langevin equation for particle swimming velocity. The proposed model is a generalization of the active Ornstein-Uhlenbeck model introduced by G. Szamel [Phys. Rev. E {\bf 90}, 012111 (2014)]. We focus on two different kinds of memory which arise in many natural systems: an exponential decay and a power law, supplemented with additive colored noise. We provide analytical expressions for the velocity autocorrelation function and the mean-squared displacement, which are in excellent agreement with numerical simulations. For both models, damped oscillatory solutions emerge due to the competition between the memory of the system and the persistence of velocity fluctuations. In particular, for a power-law model with fractional Brownian noise, we show that long-time active subdiffusion occurs with increasing long-term memory.

14 pages, 3 figures, published version

References in corpus (14)

• Self-motile colloidal particles: from directed propulsion to random walk
• Sedimentation, trapping, and rectification of dilute bacteria
• A self-propelled particle in an external potential: is there an effective temperature?
• Effective Interactions in Active Brownian Suspensions
• Towards a 'Thermodynamics' of Active Matter
• Power laws in microrheology experiments on living cells: comparative analysis and modelling
• Nonequilibrium equation of state in suspensions of active colloids
• Self-propelled particles with fluctuating speed and direction of motion
• Effective Temperature of Red Blood Cell Membrane Fluctuations
• Glassy dynamics of athermal self-propelled particles: Computer simulations and a nonequilibrium microscopic theory
• Tuning the motility and directionality of self-propelled colloids
• Stationary superstatistics distributions of trapped run-and-tumble particles
• Clausius relation for active particles: what can we learn from fluctuations?
• Probing the Fluctuation-Dissipation Theorem in a Perrin-like Experiment

Cited by in corpus (23)

• The active trap model
• Effective temperatures in inhomogeneous passive and active bidimensional Brownian particle systems
• Condensation transition in the late-time position of a Run-and-Tumble particle
• Dynamics of active particles with translational and rotational inertia
• Irreversibility in active matter: General framework for active Ornstein-Uhlenbeck particles
• Active particles with fractional rotational Brownian motion
• Two-dimensional active motion
• Work extraction and performance of colloidal heat engines in viscoelastic baths
• First passage time distribution of active thermal particles in potentials
• Entropy production of active particles in underdamped regime
• Inertial active Ornstein-Uhlenbeck particle in the presence of magnetic field
• Nonequilibrium diffusion of active particles bound to a semi-flexible polymer network: simulations and fractional Langevin equation
• Orbital Magnetism of Active Viscoelastic Suspension
• Active noise-driven particles under space-dependent friction in one dimension
• Statistical mechanics of passive Brownian particles in a fluctuating harmonic trap
• Generalized persistence dynamics for active motion
• Premelting controlled active matter in ice
• Steady state correlations and induced trapping of an inertial AOUP particle
• Mean first passage time of active Brownian particles in two dimensions
• Biolocomotion and premelting in ice
• Field theory of survival probabilities, extreme values, first passage times, and mean span of non-Markovian stochastic processes
• Nonequilibrium dynamical structure of a dilute suspension of active particles in a viscoelastic fluid
• Beyond the Markovian limit: Exact solutions for active motion in a power-law viscoelastic bath