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Self-assembly, the process by which objects autonomously come together to form complex structures, is omnipresent in the physical world. A systematic study of self-assembly as a mathematical process has been initiated. The individual components are modelled as square tiles on the infinite two-dimensional plane. Each side of a tile is covered by a specific "(More)
In 1864, Waage and Guldberg formulated the " law of mass action. " Since that time, chemists, chemical engineers, physicists and mathematicians have amassed a great deal of knowledge on the topic. In our view, sufficient understanding has been acquired to warrant a formal mathematical consolidation. A major goal of this consolidation is to solidify the(More)
We consider the problem of fault-tolerance in nanoscale algorithmic self-assembly. We employ a standard variant of Winfree's abstract Tile Assembly Model (aTAM), the two-handed aTAM, in which square " tiles " – a model of molecules constructed from DNA for the purpose of engineering self-assembled nanostructures – aggregate according to specific binding(More)
Self-assembly, the process by which objects autonomously come together to form complex structures, is omnipresent in the physical world. Recent experiments in self-assembly demonstrate its potential for the parallel creation of a large number of nanostructures, including possibly computers. A systematic study of self-assembly as a mathematical process has(More)
We have designed and constructed DNA complexes in the form of triangles. We have created hexagonal planar tilings from these triangles via self-assembly. Unlike previously reported structures self-assembled from DNA, our structures appear to involve bending of double helices. Bending helices may be a useful design option in the creation of self-assembled(More)
We designed a molecular complex, the double-double crossover, consisting of four DNA double helices connected by six reciprocal exchanges. Atomic force micrographs suggest that double-double crossover complexes self-assemble into high-density, doubly connected, two-dimensional, planar structures. Such structures may be suitable as substrates for the(More)
DNA complexes, like the double crossover, are used as building blocks for the assembly of higher-order structures. Currently, the number of experimentally proven reliable complexes is small. We have begun work on expanding the collection of such complexes. Here we report on our design concepts and initial experiments. In particular, we present experimental(More)
We propose a novel method for object transport using granular convec-tion, in which the granular material is a robot swarm consisting of small robots with minimal sensors. Granular convection is commonly observed in the " Brazil Nut Effect ". In this work, we consider the transported object to be passive, however , and not actuated like the surrounding(More)