Optimal Staged Self-Assembly of General Shapes
نویسندگان
چکیده
منابع مشابه
Optimal Results in Staged Self-Assembly of Wang Tiles
The subject of self-assembly deals with the spontaneous creation of ordered systems from simple units and is most often applied in the field of nanotechnology. The self-assembly model of Winfree describes the assembly of Wang tiles, simulating assembly in real-world systems. We use an extension of this model, known as the staged self-assembly model introduced by Demaine et al. that allows for d...
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We demonstrate sequential assembly of chemically patchy colloids such that their valence differs from stage to stage to produce hierarchical structures. For proof of concept, we employ ACB triblock spheres suspended in water, with the C middle band electrostatically repulsive. In the first assembly stage, only A-A hydrophobic attraction contributes, and discrete clusters form. They can be store...
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We consider staged self-assembly, in which squareshaped Wang tiles can be added to bins in several stages. Within these bins the tiles may connect to each other, depending on the glue types of their edges. In general, self-assembly constructs complex (polyomino-shaped) structures from a limited set of square tiles. Previous work by Demaine et al. considered a setting in which assembly proceeds ...
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We prove the unique assembly and unique shape verification problems, benchmark measures of self-assembly model power, are coNP-hard and contained in PSPACE (and in Πp2s for staged systems with s stages). En route, we prove that unique shape verification problem in the 2HAM is coNP-complete.
متن کاملSelf-Assembly of Squares and Scaled Shapes
The abstract Tile Assembly Model (aTAM) [3] is a mathematical model of self-assembly in which system components are four-sided Wang tiles with glue types assigned to each tile edge. Any pair of glue types are assigned some nonnegative interaction strength denoting how strongly the pair of glues bind. An aTAM system is an ordered triplet .T; ; / consisting of a set of tiles T , a positive intege...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2017
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-017-0318-0