74,512 research outputs found
Slow dynamics and aging of a confined granular flow
We present experimental results on slow flow properties of a granular
assembly confined in a vertical column and driven upwards at a constant
velocity V. For monodisperse assemblies this study evidences at low velocities
() a stiffening behaviour i.e. the stress necessary to obtain
a steady sate velocity increases roughly logarithmically with velocity. On the
other hand, at very low driving velocity (), we evidence a
discontinuous and hysteretic transition to a stick-slip regime characterized by
a strong divergence of the maximal blockage force when the velocity goes to
zero. We show that all this phenomenology is strongly influenced by surrounding
humidity. We also present a tentative to establish a link between the granular
rheology and the solid friction forces between the wall and the grains. We base
our discussions on a simple theoretical model and independent grain/wall
tribology measurements. We also use finite elements numerical simulations to
confront experimental results to isotropic elasticity. A second system made of
polydisperse assemblies of glass beads is investigated. We emphasize the onset
of a new dynamical behavior, i.e. the large distribution of blockage forces
evidenced in the stick-slip regime
Cubic Polyhedra
A cubic polyhedron is a polyhedral surface whose edges are exactly all the
edges of the cubic lattice. Every such polyhedron is a discrete minimal
surface, and it appears that many (but not all) of them can be relaxed to
smooth minimal surfaces (under an appropriate smoothing flow, keeping their
symmetries). Here we give a complete classification of the cubic polyhedra.
Among these are five new infinite uniform polyhedra and an uncountable
collection of new infinite semi-regular polyhedra. We also consider the
somewhat larger class of all discrete minimal surfaces in the cubic lattice.Comment: 18 pages, many figure
Filling loops at infinity in the mapping class group
We study the Dehn function at infinity in the mapping class group, finding a
polynomial upper bound of degree four. This is the same upper bound that holds
for arbitrary right-angled Artin groups.Comment: 7 pages, 2 figures; this note presents a result which was contained
in an earlier version of "Pushing fillings in right-angled Artin groups"
(arXiv:1004.4253) but is independent of the techniques in that pape
Rheology of a confined granular material
We study the rheology of a granular material slowly driven in a confined
geometry. The motion is characterized by a steady sliding with a resistance
force increasing with the driving velocity and the surrounding relative
humidity. For lower driving velocities a transition to stick-slip motion
occurs, exhibiting a blocking enhancement whith decreasing velocity. We propose
a model to explain this behavior pointing out the leading role of friction
properties between the grains and the container's boundary.Comment: 9 pages, 3 .eps figures, submitted to PR
PushPush is NP-hard in 2D
We prove that a particular pushing-blocks puzzle is intractable in 2D,
improving an earlier result that established intractability in 3D [OS99]. The
puzzle, inspired by the game *PushPush*, consists of unit square blocks on an
integer lattice. An agent may push blocks (but never pull them) in attempting
to move between given start and goal positions. In the PushPush version, the
agent can only push one block at a time, and moreover, each block, when pushed,
slides the maximal extent of its free range. We prove this version is NP-hard
in 2D by reduction from SAT.Comment: 18 pages, 13 figures, 1 table. Improves cs.CG/991101
A combinatorial description of the Heegaard Floer contact invariant
In this short note, we observe that the Heegaard Floer contact invariant is
combinatorial by applying the algorithm of Sarkar--Wang to the description of
the contact invariant due to Honda--Kazez--Matic. We include an example of this
combinatorial calculation.Comment: 6 page
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