2 research outputs found
Force balance in canonical ensembles of static granular packings
We investigate the role of local force balance in the transition from a
microcanonical ensemble of static granular packings, characterized by an
invariant stress, to a canonical ensemble. Packings in two dimensions admit a
reciprocal tiling, and a collective effect of force balance is that the area of
this tiling is also invariant in a microcanonical ensemble. We present
analytical relations between stress, tiling area and tiling area fluctuations,
and show that a canonical ensemble can be characterized by an intensive
thermodynamic parameter conjugate to one or the other. We test the equivalence
of different ensembles through the first canonical simulations of the force
network ensemble, a model system.Comment: 9 pages, 9 figures, submitted to JSTA
Angoricity and compactivity describe the jamming transition in soft particulate matter
The application of concepts from equilibrium statistical mechanics to
out-of-equilibrium systems has a long history of describing diverse systems
ranging from glasses to granular materials. For dissipative jammed systems--
particulate grains or droplets-- a key concept is to replace the energy
ensemble describing conservative systems by the volume-stress ensemble. Here,
we test the applicability of the volume-stress ensemble to describe the jamming
transition by comparing the jammed configurations obtained by dynamics with
those averaged over the ensemble as a probe of ergodicity. Agreement between
both methods suggests the idea of "thermalization" at a given angoricity and
compactivity. We elucidate the thermodynamic order of the jamming transition by
showing the absence of critical fluctuations in static observables like
pressure and volume. The approach allows to calculate observables such as the
entropy, volume, pressure, coordination number and distribution of forces to
characterize the scaling laws near the jamming transition from a statistical
mechanics viewpoint.Comment: 27 pages, 13 figure