Hard spheres on the gyroid surface

We find that 48/64 hard spheres per unit cell on the gyroid minimal surface are entropically self-organized. Striking evidence is obtained in terms of the acceptance ratio of Monte Carlo moves and order parameters. The regular tessellations of the spheres can be viewed as hyperbolic tilings on the Poincaré disc with a negative Gaussian curvature, one of which is, equivalently, the arrangement of angels and devils in Escher's Circle Limit IV .

Limit Circle/Limit Point Criteria for Second-Order Superlinear Differential Equations with a Damping Term

The purpose of the present paper is to establish some new criteria for the classifications of superlinear differential equations as being of the nonlinear limit circle type or of the nonlinear limit point type. The criteria presented here generalize some known results in literature.

Limit Circle/Limit Point Criteria for Second-Order Sublinear Differential Equations with Damping Term

The purpose of the present paper is to establish some new criteria for the classification of the sublinear differential equation as of the nonlinear limit circle type or of the nonlinear limit point type. The criteria presented here generalize some known results in the literature.

ESCHER, COXETER AND SYMMETRY

The Dutch graphic artist Escher was very much interested in plane symmetry. He was fascinated by the problem of infinity and the representation of infinity on a sheet of paper. An exchange of ideas with Coxeter was the origin of the series of works called "Circle Limit". This article also describes the animation technique, which by adding time and movement to the images of Escher try to contribute to Escher's dream of reaching infinity.

Isometries, Tessellations and Escher, Oh My!

Motivated to better understand the wonderful artistry and hyperbolic tessellations of M.C. Escher’s Circle Limit prints, we study the isometries of the hyperbolic plane and create tessellations of the Poincaré disk using the Euclidean tools of compass and straightedge.