Extremal Cylinder Configurations II: Configuration O6

Extremal Configurations of Hinge Structures

We study body-and-hinge and panel-and-hinge chains in R, with two marked points: one on the first body, the other on the last. For a general chain, the squared distance between the marked points gives a Morse-Bott function on a torus configuration space. Maximal configurations, when the distance between the two marked points reaches a global maximum, have particularly simple geometrical charact...

Configurations of Extremal Even Unimodular Lattices

We extend the results of Ozeki on the configurations of extremal even unimodular lattices. Specifically, we show that if L is such a lattice of rank 56, 72, or 96, then L is generated by its minimal-norm vectors. Mathematics Subject Classification (2000). 11H06 (52C07, 05B30).

Extremal statistics on non-crossing configurations

We analyze extremal statistics in non-crossing configurations on the n vertices of a convex polygon.We prove that themaximumdegree and the largest component are of logarithmic order, and that, suitably scaled, they converge to a well-defined constant. We also prove that the diameter is of order √ n. The proofs are based on singularity analysis, an application of the first and second moment meth...

Extremal Configurations and Levels in Pseudoline Arrangements

Sub-Wavelength Resonances in Metamaterial-Based Multi-Cylinder Configurations

Sub-wavelength resonances known to exist in isolated metamaterial-based structures of circular cylindrical shape are investigated with the purpose of determining whether the individual resonances are retained when several of such resonant structures are grouped to form a new structure. To this end, structures consisting of 1, 2 and 4 sets of metamaterial-based concentric cylinders excited by an...