This paper reviews the problem of a thin rigid rod sliding on a horizontal surface in the plane, which is commonly cited as an example of the inconsistency of planar rigid-body Newtonian mechanics. We demonstrate the existence of a consistent solution, using Routh's analysis of rigid-body impact. Copyright © 1987 Carnegie-Mel lon University This work was supported under grants from the System D...

Let C be a cone in R whose base B is a planar convex body in a horizontal plane π and whose tip is a point v / ∈ π. Let C be a packing formed by translates of C and −C in R. We exhibit an explicit constant c > 0 such that the density of any such C is is smaller than 1−c, answering a question of Wlodek Kuperberg.

We investigate the effect on the roughness of microcrack nucleation ahead of a propagating planar crack and study the structure of the damage zone. To this end we consider a quasi-two dimensional random fuse model, confining the crack between two horizontal plates. The two-dimensional geometry introduces a characteristic length in the problem, limiting the crack roughness. The damage ahead of t...

To successfully execute large-scale algorithms, a quantum computer will need to perform its elementary operations near perfectly. This is fundamental challenge since all physical qubits suffer considerable level of noise. Moreover, real systems are likely have finite yield, i.e., some nonzero proportion the components in complex device may be irredeemably broken at fabrication stage. We present...

In conventional planar growth of bulk III-V materials, a slow growth rate favors high crystallographic quality, optical quality, and purity of the resulting material. Surprisingly, we observe exactly the opposite effect for Au-assisted GaAs nanowire growth. By employing a rapid growth rate, the resulting nanowires are markedly less tapered, are free of planar crystallographic defects, and have ...

We investigate theoretically the wetting properties of cholesteric liquid crystals at a planar substrate. If the properties of substrate and of the interface are such that the cholesteric layers are not distorted, the wetting properties are similar to those of a nematic liquid crystal. If, on the other hand, the anchoring conditions force the distortion of the liquid crystal layers the wetting ...

A plane graph is a planar graph with a fixed planar embedding in the plane. In a boxrectangular drawing of a plane graph, every vertex is drawn as a rectangle, called a box, each edge is drawn as either a horizontal line segment or a vertical line segment, and the contour of each face is drawn as a rectangle. A planar graph is said to have a box-rectangular drawing if at least one of its plane ...

The design and fabrication process for a high performance manipulation stage for nanometer resolution TEM sample positioning over a 20 m range is presented. A two level, planar stage is moved in three translational and three rotational directions by just two types of actuators; three horizontal and three vertical combdrives. The vertical combdrives are suspended by optimally designed torsion-be...

The synthesis of a conformal three-dimensional nanostructure based on porous anodic alumina with transversal nanopores on wires is herein presented. The resulting three-dimensional network exhibits the same nanostructure as that obtained on planar geometries, but with a macroscopic cylindrical geometry. The morphological analysis of the nanostructure revealed the effects of the initial defects ...

Many biological materials are polymerized analogues of cholesteric liquid crystals. The same types of defect occur both in cholesteric liquids and in these more or less solid biological systems. However, their distribution and therefore the textures are different, owing to certain growth mechanisms in biological analogues. I . Introduction. -In a previous work 111, a comparison was made between...