7 research outputs found
Critical scaling in linear response of frictionless granular packings near jamming
We study the origin of the scaling behavior in frictionless granular media
above the jamming transition by analyzing their linear response. The response
to local forcing is non-self-averaging and fluctuates over a length scale that
diverges at the jamming transition. The response to global forcing becomes
increasingly non-affine near the jamming transition. This is due to the
proximity of floppy modes, the influence of which we characterize by the local
linear response. We show that the local response also governs the anomalous
scaling of elastic constants and contact number.Comment: 4 pages, 3 figures. v2: Added new results; removed part of
discussion; changed Fig.
Non-affine response: jammed packings versus spring networks
We compare the elastic response of spring networks whose contact geometry is
derived from real packings of frictionless discs, to networks obtained by
randomly cutting bonds in a highly connected network derived from a
well-compressed packing. We find that the shear response of packing-derived
networks, and both the shear and compression response of randomly cut networks,
are all similar: the elastic moduli vanish linearly near jamming, and
distributions characterizing the local geometry of the response scale with
distance to jamming. Compression of packing-derived networks is exceptional:
the elastic modulus remains constant and the geometrical distributions do not
exhibit simple scaling. We conclude that the compression response of jammed
packings is anomalous, rather than the shear response.Comment: 6 pages, 6 figures, submitted to ep
Bounds on the shear load of cohesionless granular matter
We characterize the force state of shear-loaded granular matter by relating
the macroscopic stress to statistical properties of the force network. The
purely repulsive nature of the interaction between grains naturally provides an
upper bound for the sustainable shear stress, which we analyze using an
optimization procedure inspired by the so-called force network ensemble. We
establish a relation between the maximum possible shear resistance and the
friction coefficient between individual grains, and find that anisotropies of
the contact network (or the fabric tensor) only have a subdominant effect.
These results can be considered the hyperstatic limit of the force network
ensemble and we discuss possible implications for real systems. Finally, we
argue how force anisotropies can be related quantitatively to experimental
measurements of the effective elastic constants.Comment: 17 pages, 6 figures. v2: slightly rearranged, introduction and
discussion rewritte
Localization behavior of vibrational modes in granular packings
We study the localization of vibrational modes of frictionless granular
media. We introduce a new method, motivated by earlier work on non-Hermitian
quantum problems, which works well both in the localized regime where the
localization length is much less than the linear size and in the
regime grater or of order when modes are extended throughout our
finite system. Our very lowest frequency modes show "quasi-localized"
resonances away from the jamming point; the spatial extent of these regions
increases as the jamming point is approached, as expected theoretically.
Throughout the remaining frequency range, our data show no signature of the
nearness of the jamming point and collapse well when properly rescaled with the
system size. Using Random Matrix Theory we derive the scaling relation ~
for the regime >> in dimensions.Comment: 6 pages, 7 figure
Non-affine response: Jammed packings vs. spring networks
We compare the elastic response of spring networks whose contact geometry is derived from real packings of frictionless discs, to networks obtained by randomly cutting bonds in a highly connected network derived from a well-compressed packing. We find that the shear response of packing-derived networks, and both the shear and compression response of randomly cut networks, are all similar: the elastic moduli vanish linearly near jamming, and distributions characterizing the local geometry of the response scale with distance to jamming. Compression of packing-derived networks is exceptional: the elastic modulus remains constant and the geometrical distributions do not exhibit simple scaling. We conclude that the compression response of jammed packings is anomalous, rather than the shear response