4,110 research outputs found
Experimental evidence of ageing and slow restoration of the weak-contact configuration in tilted 3D granular packings
Granular packings slowly driven towards their instability threshold are
studied using a digital imaging technique as well as a nonlinear acoustic
method. The former method allows us to study grain rearrangements on the
surface during the tilting and the latter enables to selectively probe the
modifications of the weak-contact fraction in the material bulk. Gradual ageing
of both the surface activity and the weak-contact reconfigurations is observed
as a result of repeated tilt cycles up to a given angle smaller than the angle
of avalanche. For an aged configuration reached after several consecutive tilt
cycles, abrupt resumption of the on-surface activity and of the weak-contact
rearrangements occurs when the packing is subsequently inclined beyond the
previous maximal tilting angle. This behavior is compared with literature
results from numerical simulations of inclined 2D packings. It is also found
that the aged weak-contact configurations exhibit spontaneous restoration
towards the initial state if the packing remains at rest for tens of minutes.
When the packing is titled forth and back between zero and near-critical
angles, instead of ageing, the weak-contact configuration exhibits "internal
weak-contact avalanches" in the vicinity of both the near-critical and zero
angles. By contrast, the stronger-contact skeleton remains stable
The Behavior of Granular Materials under Cyclic Shear
The design and development of a parallel plate shear cell for the study of
large scale shear flows in granular materials is presented. The parallel plate
geometry allows for shear studies without the effects of curvature found in the
more common Couette experiments. A system of independently movable slats
creates a well with side walls that deform in response to the motions of grains
within the pack. This allows for true parallel plate shear with minimal
interference from the containing geometry. The motions of the side walls also
allow for a direct measurement of the velocity profile across the granular
pack. Results are presented for applying this system to the study of transients
in granular shear and for shear-induced crystallization. Initial shear profiles
are found to vary from packing to packing, ranging from a linear profile across
the entire system to an exponential decay with a width of approximately 6 bead
diameters. As the system is sheared, the velocity profile becomes much sharper,
resembling an exponential decay with a width of roughly 3 bead diameters.
Further shearing produces velocity profiles which can no longer be fit to an
exponential decay, but are better represented as a Gaussian decay or error
function profile. Cyclic shear is found to produce large scale ordering of the
granular pack, which has a profound impact on the shear profile. There exist
periods of time in which there is slipping between layers as well as periods of
time in which the layered particles lock together resulting in very little
relative motion.Comment: 10 pages including 12 figure
Embedding large subgraphs into dense graphs
What conditions ensure that a graph G contains some given spanning subgraph
H? The most famous examples of results of this kind are probably Dirac's
theorem on Hamilton cycles and Tutte's theorem on perfect matchings. Perfect
matchings are generalized by perfect F-packings, where instead of covering all
the vertices of G by disjoint edges, we want to cover G by disjoint copies of a
(small) graph F. It is unlikely that there is a characterization of all graphs
G which contain a perfect F-packing, so as in the case of Dirac's theorem it
makes sense to study conditions on the minimum degree of G which guarantee a
perfect F-packing.
The Regularity lemma of Szemeredi and the Blow-up lemma of Komlos, Sarkozy
and Szemeredi have proved to be powerful tools in attacking such problems and
quite recently, several long-standing problems and conjectures in the area have
been solved using these. In this survey, we give an outline of recent progress
(with our main emphasis on F-packings, Hamiltonicity problems and tree
embeddings) and describe some of the methods involved
Perfect packings with complete graphs minus an edge
Let K_r^- denote the graph obtained from K_r by deleting one edge. We show
that for every integer r\ge 4 there exists an integer n_0=n_0(r) such that
every graph G whose order n\ge n_0 is divisible by r and whose minimum degree
is at least (1-1/chi_{cr}(K_r^-))n contains a perfect K_r^- packing, i.e. a
collection of disjoint copies of K_r^- which covers all vertices of G. Here
chi_{cr}(K_r^-)=r(r-2)/(r-1) is the critical chromatic number of K_r^-. The
bound on the minimum degree is best possible and confirms a conjecture of
Kawarabayashi for large n
Compaction of a granular material under cyclic shear
In this paper we present experimental results concerning the compaction of a
granular assembly of spheres under periodic shear deformation. The dynamic of
the system is slow and continuous when the amplitude of the shear is constant,
but exhibits rapid evolution of the volume fraction when a sudden change in
shear amplitude is imposed. This rapid response is shown to be to be
uncorrelated with the slow compaction process.Comment: 7 pages, 9 figures, accepted for publication in European Physical
Journal
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