Cages and Anomalous Diffusion in Vibrated Dense Granular Media

Abstract

A vertically shaken granular medium hosts a blade rotating around a fixed vertical axis, which acts as a mesorheological probe. At high densities, independently from the shaking intensity, the blade's dynamics show strong caging effects, marked by transient sub-diffusion and a maximum in the velocity power density spectrum (vpds), at a resonant frequency ∼ 10 Hz. Interpreting the data through a diffusing harmonic cage model allows us to retrieve the elastic constant of the granular medium and its collective diffusion coefficient. For high frequencies f , a tail ∼ 1/f in the vpds reveals non-trivial correlations in the intra-cage micro-dynamics. At very long times (larger than 10 s), a super-diffusive behavior emerges, ballistic in the most extreme cases. Consistently, the distribution of slow velocity inversion times τ displays a power-law decay, likely due to persistent collective fluctuations of the host medium.

Dynamical Collective Memory in Fluidized Granular Materials

“…The probe for diffusion is a blade (dimensions 35 × 6 × 15 mm, momentum of inertia I = 353 g mm 2 ) mechanically isolated from the container, that can rotate around a centered vertical axis and takes energy only from collisions with the granular medium. The angular velocity ω(t) of the blade and its absolute angle of rotation θ(t) = t 0 ω(t )dt are measured in the experiment by an encoder with high spatial and temporal resolution (see Supplemental Materials in [16]). The numerical simulations are performed with a discrete-elements model implemented by LAMMPS package [20] with interactions obeying a nonlinear visco-elastic Hertzian model that takes into account the relative deformation of the grains.…”

Nonlinear response and emerging nonequilibrium microstructures for biased diffusion in confined crowded environments

“…The study of the system response to a local perturbation is particularly relevant to complex and heterogeneous media, such as glasses, gels, and many biological systems. Experimentally, the microscopic probe can be driven externally by using magnetic or optical tweezers; such an experimental technique, called active micro-rheology, (where the term "active" emphasizes that the tracer is not in equilibrium with the environment but rather induces some micro-structural changes in the host medium), has been successfully applied to probe the micro-rheological properties of a variety of different systems (see, e.g., [1,2] for recent reviews), including living cells [3], colloidal suspensions [4], soft glassy materials [5,6], and granular media [7][8][9][10], to name but a few.…”

Effective equations in complex systems: from Langevin to machine learning

“…Therefore if we want to build an effective Langevin equation, it is necessary to introduce (at least) another variable. [35]. The system is composed of a large number of beads immersed in a cylindrical container, which is shaken from below with a fixed frequency.…”