28,592 research outputs found
Non-Universality of Density and Disorder in Jammed Sphere Packings
We show for the first time that collectively jammed disordered packings of
three-dimensional monodisperse frictionless hard spheres can be produced and
tuned using a novel numerical protocol with packing density as low as
0.6. This is well below the value of 0.64 associated with the maximally random
jammed state and entirely unrelated to the ill-defined ``random loose packing''
state density. Specifically, collectively jammed packings are generated with a
very narrow distribution centered at any density over a wide density
range with variable disorder. Our results
support the view that there is no universal jamming point that is
distinguishable based on the packing density and frequency of occurence. Our
jammed packings are mapped onto a density-order-metric plane, which provides a
broader characterization of packings than density alone. Other packing
characteristics, such as the pair correlation function, average contact number
and fraction of rattlers are quantified and discussed.Comment: 19 pages, 4 figure
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
Market partitioning and the geometry of the resource space
Operations such as integration or modularization of databases can be considered as operations on database universes. This paper describes some operations on database universes. Formally, a database universe is a special kind of table. It turns out that various operations on tables constitute interesting operations on database universes as well.
Cavity method for force transmission in jammed disordered packings of hard particles
The force distribution of jammed disordered packings has always been
considered a central object in the physics of granular materials. However, many
of its features are poorly understood. In particular, analytic relations to
other key macroscopic properties of jammed matter, such as the contact network
and its coordination number, are still lacking. Here we develop a mean-field
theory for this problem, based on the consideration of the contact network as a
random graph where the force transmission becomes a constraint optimization
problem. We can thus use the cavity method developed in the last decades within
the statistical physics of spin glasses and hard computer science problems.
This method allows us to compute the force distribution for random
packings of hard particles of any shape, with or without friction. We find a
new signature of jamming in the small force behavior , whose exponent has attracted recent active interest: we find a
finite value for , along with . Furthermore, we relate
the force distribution to a lower bound of the average coordination number of jammed packings of frictional spheres with
coefficient . This bridges the gap between the two known isostatic limits
(in dimension ) and by extending the naive Maxwell's counting argument to
frictional spheres. The theoretical framework describes different types of
systems, such as non-spherical objects in arbitrary dimensions, providing a
common mean-field scenario to investigate force transmission, contact networks
and coordination numbers of jammed disordered packings
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