We perform a detailed analysis of the contact force network in a dense confined packing of pentagonal particles simulated by means of the contact dynamics method. The effect of particle shape is evidenced by comparing the data from pentagon packing and from a packing with identical characteristics, except for the circular shape of the particles. A counterintuitive finding of this work is that, ...

An empty pentagon in a point set P in the plane is a set of five points in P in strictly convex position with no other point of P in their convex hull. We prove that every finite set of at least 328` points in the plane contains an empty pentagon or ` collinear points. This is optimal up to a constant factor since the (` − 1) × (` − 1) grid contains no empty pentagon and no ` collinear points. ...

Submitted for the MAR09 Meeting of The American Physical Society Gap opening due to topological defects in graphene1 RICARDO NUNES, JOICE ARAÚJO, HELIO CHACHAM, UFMG Brazil — Stone-Wales defects (SWD = two adjacent pentagon-heptagon pairs) are common low-energy defects in carbon nanotubes. Previously, Crespi et al.[PRB, 53, 1996] have proposed a purely-carbon covalent metal sheet called “pentah...

Naive male Hooded Lister rats (Rattus norvegicus) were required to find a submerged platform in a right-angled corner between a long and a short wall of a pool in the shape of an irregular pentagon. Tests in a rectangular pool revealed a preference for the corners that corresponded with the correct corner in the pentagon. These findings indicate that rats identified the correct corner in the pe...

We prove that for any convex pentagon in the plane there are two disks, among the five disks having a side of the pentagon as diameter, that do not intersect. All our arguments are from classical Euclidean geometry.

In terms of density functional theory combined with statistic mechanics computations, we investigated a dimetallic sulfide endohedral fullerene Sc2S@C76 which has been synthesized without any characterization in experiments. Our theoretical study reveals that Sc2S@Td(19151)-C76 which satisfies the isolated-pentagon rule (IPR) possesses the lowest energy, followed by three non-IPR structures (Sc...

We show an equivalence of Drinfeld's pentagon equation and Hirose-Sato's confluence relations. As a corollary, we obtain `pentagon-free' presentation the Grothendieck-Teichm\"{u}ller group $GRT_1$ associators.

A bstract We present the leading-color two-loop QCD corrections for scattering of four partons and a W boson, including its leptonic decay. The amplitudes are assembled from planar helicity vector boson decaying to lepton pair, which also used determine Z / ? ? with analytic expressions obtained by setting up dedicated Ansatz constraining free parameters numerical samples within framework unita...

A molecular-dynamics simulation has been carried out for amorphous selenium. The simulation used 64 atoms in a constant volume simple cubic cell. The pair correlation function, g…r†, and structure factor, S…Q†, were computed and compared with experimental and previous theoretical studies. The average coordination number is exactly 2. Only one defect, an intimate valence alternation pair type de...