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Intrinsic universality and the computational power of self-assembly
This short survey of recent work in tile self-assembly discusses the use of
simulation to classify and separate the computational and expressive power of
self-assembly models. The journey begins with the result that there is a single
universal tile set that, with proper initialization and scaling, simulates any
tile assembly system. This universal tile set exhibits something stronger than
Turing universality: it captures the geometry and dynamics of any simulated
system. From there we find that there is no such tile set in the
noncooperative, or temperature 1, model, proving it weaker than the full tile
assembly model. In the two-handed or hierarchal model, where large assemblies
can bind together on one step, we encounter an infinite set, of infinite
hierarchies, each with strictly increasing simulation power. Towards the end of
our trip, we find one tile to rule them all: a single rotatable flipable
polygonal tile that can simulate any tile assembly system. It seems this could
be the beginning of a much longer journey, so directions for future work are
suggested.Comment: In Proceedings MCU 2013, arXiv:1309.104
Effect of pentagons in sp3 systems on electronic, elastic, and vibrational properties: Case of chiral structures
We present first-principles calculations of carbon and silicon chiral framework structures (CFSs). In this system, proposed recently by Pickard and Needs [Phys. Rev. B 81, 014106 (2010)], atoms form only pentagonal cycles. This configuration enables unambiguous analysis of the effects of pentagons on electronic, vibrational, and thermodynamic properties. The local density approximation electronic band gaps in CFSs were found to be equal to or greater than those of clathrates using the same formalism, as confirmed by GW calculations: 1.8 and 5.5 eV for Si and C-CFS, respectively. We show that, as in clathrates, an increasing electronic band gap is correlated with the contraction of the valence bands, resulting from the frustration of the p shells. The electron localized function and Wannier analysis confirm the sp3 nature of the bonds. Finally, we discuss vibrational and related properties. We show that CFSs present singularities, in particular, that the higher frequencies are not located at the Γ point
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