Candidates to the least perimeter partition of an equilateral triangle into N planar connected regions are calculated for N ≤ 45. A Voronoi construction is used to randomly create the candidates and then the perimeter of each is found with the Surface Evolver. The optimal configuration for each N has no more than one defect pair, and its location is determined by the proximity of N to a triangu...

A new method is introduced to study three-body clusters. Triangular configurations with D 3h point-group symmetry are analyzed. The spectrum, transition form factors and B(Eλ) values of 12 C are investigated. It is concluded that the low-lying spectrum of 12 C can be described by three alpha-particles at the vertices of an equilateral triangle, but not as a rigid structure. Large rotation-vibra...

We consider square and equilateral triangular open acoustic resonators with the ${C}_{4v}$ ${C}_{3v}$ symmetries, respectively. There is a unique property of accidental number fourfold degeneracy eigenstates that gives rise to twofold-degenerate Friedrich-Wintgen (FW) bound states in continuum (BICs). Compared usual FW BICs, degenerate BICs maintain high $Q$ factor wide range size resonators. T...

We report on the formation of equilateral triangular clusters hollow inside with 5-6 atoms per side, self-assembled on Ni adislands grown on Rh(111). The observation of standing wave patterns on the Ni adislands and the Rh(111) indicates that the self-assembly is mediated by Friedel oscillations. In this context, we propose a model based on the energy of interaction between adsorbates, which ex...

In this paper, we present a study of tuneable equilateral triangular shaped spilt ring resonator (ETSRR). In this ETSRR we rotate the inner and outer rings by varying the position of the splits in rings. For this we used radio frequency microelectromechanical system (RF MEMS) switches. By making MEMS switches ON/OFF, the positions of splits in the rings were varied which can be considered as ro...

Consider an arrangement of equilateral non-overlapping translated triangles in the plane and two points S and T so that the segment ST is parallel to a side of each of the triangles. Assume one needs to navigate from point S to point T by evading the triangular obstacles without any previous knowledge of the location of the obstacles. The navigator becomes aware of a triangle once it is contact...