Statistical analysis of random trajectories of vibrated disks: towards a macroscopic realization of Brownian motion

Abstract

We propose a macroscopic realization of planar Brownian motion by vertically vibrated disks. We perform a systematic statistical analysis of many random trajectories of individual disks. The distribution of increments is shown to be almost Gaussian, with slight deviations at large increments caused by inter-disk collisions. The velocity auto-correlation function takes both positive and negative values at short lag times but rapidly vanishes. We compare the empirical and theoretical distributions of time averaged mean square displacements and discuss distinctions between its mean and mode. These well-controlled experimental data can serve for validating statistical tools developed for the analysis of single-particle trajectories in microbiology.

References in corpus (9)

• Diffusion and mixing in gravity-driven dense granular flows
• Irreversible dynamics of a massive intruder in dense granular fluids
• Certain uncertainty: using pointwise error estimates in super-resolution microscopy
• Cages and anomalous diffusion in vibrated dense granular media
• Flow, Ordering and Jamming of Sheared Granular Suspensions
• Unravelling intermittent features in single particle trajectories by a local convex hull method
• Time-averaged MSD of Brownian motion
• Estimation of the Diffusion Constant from Intermittent Trajectories with Variable Position Uncertainties
• Optimal and sub-optimal quadratic forms for non-centered Gaussian processes

Cited by in corpus (12)

• Inertial effects of self-propelled particles: from active Brownian to active Langevin motion
• Inertial delay of self-propelled particles
• Classification of diffusion modes in single-particle tracking data: Feature-based versus deep-learning approach
• Role of rotational inertia for collective phenomena in active matter
• Surface Tensions between Active Fluids and Solid Interfaces: bare vs dressed
• Active particles in non-inertial frames: how to self-propel on a carousel
• Polymer-Chain Configurations in Active and Passive Baths
• The pseudo-two-dimensional dynamics in a system of macroscopic rolling spheres
• Orbital Magnetism of Active Viscoelastic Suspension
• Stochastic motion under nonlinear friction representing shear thinning
• Statistics for an object actively driven by spontaneous symmetry breaking into reversible directions
• Statistical properties of a granular gas fluidized by turbulent air wakes