695 research outputs found
Iterative Universal Rigidity
A bar framework determined by a finite graph and configuration in
space is universally rigid if it is rigid in any . We provide a characterization of universally rigidity for any
graph and any configuration in terms of a sequence of affine
subsets of the space of configurations. This corresponds to a facial reduction
process for closed finite dimensional convex cones.Comment: 41 pages, 12 figure
Periodic Planar Disk Packings
Several conditions are given when a packing of equal disks in a torus is
locally maximally dense, where the torus is defined as the quotient of the
plane by a two-dimensional lattice. Conjectures are presented that claim that
the density of any strictly jammed packings, whose graph does not consist of
all triangles and the torus lattice is the standard triangular lattice, is at
most , where is the number of packing
disks. Several classes of collectively jammed packings are presented where the
conjecture holds.Comment: 26 pages, 13 figure
Straight Line motion with rigid sets
If one is given a rigid triangle in the plane or space, we show that the only
motion possible, where each vertex of the triangle moves along a straight line,
is given by a hypocycloid line drawer in the plane, and a natural extension in
three-space. Each point lies on a circle which rolls around, without slipping,
inside a larger circle of twice its diameter
Comment on "Jamming at zero temperature and zero applied stress: The epitome of disorder"
O'Hern, Silbert, Liu and Nagel [Phys. Rev. E. 68, 011306 (2003)] (OSLN) claim
that a special point of a "jamming phase diagram" (in density, temperature,
stress space) is related to random close packing of hard spheres, and that it
represents, for their suggested definitions of jammed and random, the recently
introduced maximally random jammed state. We point out several difficulties
with their definitions and question some of their claims. Furthermore, we
discuss the connections between their algorithm and other hard-sphere packing
algorithms in the literature.Comment: 4 pages of text, already publishe
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