Force statistics and correlations in dense granular packings

Abstract

In dense, static, polydisperse granular media under isotropic pressure, the probability density and the correlations of particle-wall contact forces are studied.Furthermore, the probability density functions of the populations of pressures measured with different sized circular pressure cells is examined. The questions answered are: (i) What is the number of contacts that has to be considered so that the measured pressure lies within a certain error margin from its expectation value? (ii) What is the statistics of the pressure probability density as function of the size of the pressure cell? Astonishing non-random correlations between contact forces are evidenced that lead to a rapid decay of the width of the distribution and range at least 10 to 15 particle diameters. Finally, an experiment is proposed to tackle and better understand this issue.

Local Anisotropy in Globally Isotropic Granular Packings

“…figure 1 below), quantitative characterizations of them have only recently been reported. These recent approaches have focused on topological characterizations [3], 2-point correlations in the local hydrostatic pressure [4], and statistics of spatially averaged forces [5]. These works showed that there are some characteristics in the spatial structure of the stress field which are independent of density, but they left open the important question of whether one can define a characteristic lengthscale associated with the general visual impression one gets when observing the contact force network.…”

Slow dynamics near jamming

“…For different size ratios, we found different scaling prefactors of the average and maximum overlaps confirming their different behaviors and thus indicating different shapes of the overlap probability distribution functions [25].…”

“…The ratios A m (ρ)/B δ (ρ) are not constant (see Table 1), which means that the probability distribution functions of the overlap are not self-similar, but change shape with increasing ρ [25]. …”

Thermodynamics of a bouncer model: A simplified one-dimensional gas

“…Since the exponents β, α 1 and α 2 are known, the two scaling laws given by Eqs. (33) and (35) can be evaluated to obtain z 1 and z 2 . When we substitute the numerical values for β = 1/2, α 1 = 1 and α 2 = −2 we obtain that z 1 = 0 and z 2 = −1.…”