We apply local structure theory calculations 7 to the study of cellular automata on the two-dimensional hexagonal lattice. A particular hexagonal lattice rule denoted (3422) is considered in detail. This rule has many features in common with Conway's Life. The local struc-1 ture theory captures many of the statistical properties of this rule; this supports hypotheses raised by a study of Life i...

We characterize the macroscopic effective mechanical behavior of a graphene sheet modeled by a hexagonal lattice with twoand three-point atomic interactions, using Γ-convergence.

We characterize the macroscopic effective mechanical behavior of a graphene sheet modeled by a hexagonal lattice of elastic bars, using Γ-convergence.

Motivated by the frequency assignment problem we study the ddistant coloring of the vertices of an infinite plane hexagonal lattice H. Let d be a positive integer. A d-distant coloring of the lattice H is a coloring of the vertices of H such that each pair of vertices distance at most d apart have different colors. The d-distant chromatic number of H, denoted χd(H), is the minimum number of col...

Schmutz Schaller’s conjecture regarding the lengths of the hexagonal versus the lengths of the square lattice is shown to be true. The proof makes use of results from (computational) prime number theory. Using an identity due to Selberg, it is shown that, in principle, the conjecture can be resolved without using computational prime number theory. By our approach, however, this would require a ...

A simple and rapid procedure has been found for the preparation of highly pure alkaline form fructose-1,6-diphosphatase from turkey liver. The protein is tetrameric and is composed of subunits comprised of a 29,000 molecular weight core fragment and an associated 7,000-dalton Speptide. Large single crystals of the protein, suitable for xray diffraction analysis, are produced in the course of th...

Hexagonal population distributions of several sizes are shown to be selforganized from a uniformly inhabited state, which is modeled by a system of places (cities) on a hexagonal lattice. Microeconomic interactions among the places are expressed by a core–periphery model in new economic geography. Lösch’s ten smallest hexagonal distributions in central place theory are guaranteed to be existent...

We report that the flux-line lattice in the cubic superconductor Pr(Os4Sb12 is strongly distorted from an ideal hexagonal lattice at very low temperatures in a small applied field. We attribute this to the presence of gap nodes in the superconducting state on at least some Fermi-surface sheets.

A simple Ising-like model for the stacking thermodynamics of ice 1 is constructed for nuclei in supercooled water, and combined with classical nucleation theory. For relative stabilities of cubic and hexagonal ice I within the range of experimental estimates, this predicts critical nuclei are stacking disordered at strong sub-cooling, consistent with recent experiments. At higher temperatures n...

Lattice-Boltzmann models are also state-based models with update rules that are to be applied in a synchronous fashion. Although rectangular lattices are computationally convenient, they impose difficulties in achieving isotropic flow behavior. Therefore, we start with a hexagonal lattice of nodes in the plane: We assume a lattice spacing (the distance to the next node), λ, a time step, τ, unit...