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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)
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)
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 –(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)
Swarm robotics, active self-assembly, and amorphous computing are fields that focus on designing systems of large numbers of small, simple components that can cooperate to complete complex tasks. Many of these systems are inspired by biological systems, and all attempt to use the simplest components and environments possible, while still being capable of(More)
We describe an Intelligent Precision Jigging Robot (IPJR), which allows high precision assembly of commodity parts with low-precision bonding. We present preliminary experiments in 2D that are motivated by the problem of assembling a space telescope optical bench on orbit using inexpensive, stock hardware and low-precision welding. An IPJR is a robot that(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)
The fields of molecular electronics and self-assembly have the potential to revolutionize the way electronic devices are constructed. There are many high-level designs of self-assembling systems that, given the proper components, could be used to construct such devices, and there are many low-level components that have been experimentally validated and(More)