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Abstract In many situations, the combined effect of advection and diffusion greatly increases the rate of convergence to equilibrium—a phenomenon known asenhanced dissipation. Here we study the situation where the advecting velocity field generates a random dynamical system satisfying certainHarris conditions. Ifκdenotes the strength of the diffusion, then we show that with probability at least $1-o\left({\kappa }^N\right)$enhanced dissipation occurs on time scales of order $|\ln \kappa |$, a bound which is known to be optimal. Moreover, on long time scales, we show that the rate of convergence to equilibrium is almost surelyindependentof diffusivity. As a consequence we obtain enhanced dissipation for the randomly shifted alternating shears introduced by Pierrehumbert’94. 

Abstract This study investigates computationally the impact of particle size disparity and cohesion on force chain formation in granular media. The granular media considered in this study are bi-disperse systems under uniaxial compression, consisting of spherical, frictionless particles that interact through a modified Hookean model. Force chains in granular media are characterized as networks of particles that meet specific criteria for particle stress and inter-particle forces. The computational setup decouples the effects of particle packing on force chain formations, ensuring an independent assessment of particle size distribution and cohesion on force chain formation. The decoupling is achieved by characterizing particle packing through the radial density function, which enables the identification of systems with both regular and irregular packing. The fraction of particles in the force chains network is used to quantify the presence of the force chains. The findings show that particle size disparity promotes force chain formation in granular media with nearly-regular packing (i.e., an almost-ordered system). However, as particle size disparities grow, it promotes irregular packing (i.e., a disordered systems), leading to fewer force chains carrying larger loads than in ordered systems. Further, it is observed that the increased cohesion in granular systems leads to fewer force chains irrespective of particle size or packing.