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Cellular structures are commonplace in engineering applications, such as aerospace and medical engineering, because material-air composites offer significant mechanical benefits, for example due to improved weight-to-strength ratio. Typically, cellular structures are based on patterns of periodically repeating unit cells, such as squares or hexagons, but the periodic nature and the available symmetries of the patterns give rise to anisotropic performance. This is where patterns with aperiodic order are a viable alternative. Patterns created with rotational symmetry, yet no translational repetition do not possess the orders of symmetry from which mechanical anisotropy originates and therefore have the potential to mitigate this issue. In this study, additive manufacturing was used to create 2.5D, 45% dense, honeycomb cuboids based on the Penrose P3 aperiodic tiling. These were then tested under compression loading. Honeycomb cuboids based on periodic patterns were also manufactured using identical processes for the purpose of comparison. The outcome shows a significant improvement in isotropy and notably different progression of strain localisation for the honeycombs based on Penrose P3 patterns compared to the periodic comparisons during both elastic and plastic deformation.

Under appropriate external conditions a semiconductor nanowire in proximity to an s-wave superconductor can be in a topological superconducting (TS) phase. This phase supports localized zero-energy Majorana fermions at the ends of the wire. However, the non-Abelian exchange statistics of Majorana fermions is difficult verify because of the one-dimensional topology of such wires. In this paper we propose a scheme to transport Majorana fermions between the ends of different wires using tunneling, which is shown to be controllable by gate voltages. Such tunneling-generated hops of Majorana fermions can be used to exchange the Majorana fermions. The exchange process thus obtained is described by a non-Abelian braid operator that is uniquely determined by the well-controlled microscopic tunneling parameters., Comment: Final version with 8 pages, 5 figures. A companion paper, arXiv:1012.0296, discusses Majorana exchange through a general junction of three wire segments