Self-assembly of two-dimensional binary quasicrystals: A possible route to a DNA quasicrystal

We use Monte Carlo simulations and free-energy techniques to show that binary solutions of penta- and hexavalent two-dimensional patchy particles can form thermodynamically stable quasicrystals even at very narrow patch widths, provided their patch interactions are chosen in an appropriate way. Such patchy particles can be thought of as a coarse-grained representation of DNA multi-arm `star' motifs, which can be chosen to bond with one another very specifically by tuning the DNA sequences of the protruding arms. We explore several possible design strategies and conclude that DNA star tiles that are designed to interact with one another in a specific but not overly constrained way could potentially be used to construct soft quasicrystals in experiment. We verify that such star tiles can form stable dodecagonal motifs using oxDNA, a realistic coarse-grained model of DNA

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

An aperiodic hexagonal tile

We show that a single prototile can fill space uniformly but not admit a periodic tiling. A two-dimensional, hexagonal prototile with markings that enforce local matching rules is proven to be aperiodic by two independent methods. The space--filling tiling that can be built from copies of the prototile has the structure of a union of honeycombs with lattice constants of $2^n a$, where $a$ sets the scale of the most dense lattice and $n$ takes all positive integer values. There are two local isomorphism classes consistent with the matching rules and there is a nontrivial relation between these tilings and a previous construction by Penrose. Alternative forms of the prototile enforce the local matching rules by shape alone, one using a prototile that is not a connected region and the other using a three--dimensional prototile.Comment: 32 pages, 24 figures; submitted to Journal of Combinatorial Theory Series A. Version 2 is a major revision. Parts of Version 1 have been expanded and parts have been moved to a separate article (arXiv:1003.4279

Solvent Mediated Assembly of Nanoparticles Confined in Mesoporous Alumina

The controlled self-assembly of thiol stabilized gold nanocrystals in a mediating solvent and confined within mesoporous alumina was probed in situ with small angle x-ray scattering. The evolution of the self-assembly process was controlled reversibly via regulated changes in the amount of solvent condensed from an undersaturated vapor. Analysis indicated that the nanoparticles self-assembled into cylindrical monolayers within the porous template. Nanoparticle nearest-neighbor separation within the monolayer increased and the ordering decreased with the controlled addition of solvent. The process was reversible with the removal of solvent. Isotropic clusters of nanoparticles were also observed to form temporarily during desorption of the liquid solvent and disappeared upon complete removal of liquid. Measurements of the absorption and desorption of the solvent showed strong hysteresis upon thermal cycling. In addition, the capillary filling transition for the solvent in the nanoparticle-doped pores was shifted to larger chemical potential, relative to the liquid/vapor coexistence, by a factor of 4 as compared to the expected value for the same system without nanoparticles.Comment: 9 pages, 9 figures, appeared in Phys. Rev.

Forcing nonperiodicity with a single tile

An aperiodic prototile is a shape for which infinitely many copies can be arranged to fill Euclidean space completely with no overlaps, but not in a periodic pattern. Tiling theorists refer to such a prototile as an "einstein" (a German pun on "one stone"). The possible existence of an einstein has been pondered ever since Berger's discovery of large set of prototiles that in combination can tile the plane only in a nonperiodic way. In this article we review and clarify some features of a prototile we recently introduced that is an einstein according to a reasonable definition. [This abstract does not appear in the published article.]Comment: 18 pages, 10 figures. This article has been substantially revised and accepted for publication in the Mathematical Intelligencer and is scheduled to appear in Vol 33. Citations to and quotations from this work should reference that publication. If you cite this work, please check that the published form contains precisely the material to which you intend to refe

Structural performance of two aerobrake hexagonal heat shield panel concepts

Structural sizing and performance are presented for two structural concepts for an aerobrake hexagonal heat shield panel. One concept features a sandwich construction with an aluminum honeycomb core and thin quasi-isotropic graphite-epoxy face sheets. The other concept features a skin-rib isogrid construction with thin quasi-isotropic graphite-epoxy skins and graphite-epoxy ribs oriented at 0, +60, and -60 degs along the panel. Linear static, linear bifurcation buckling, and nonlinear static analyses were performed to compare the structural performance of the two panel concepts and assess their feasibility for a lunar transfer vehicle aerobrake application