15 research outputs found

    Fully Dynamic 3-Dimensional Orthogonal Graph Drawing

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    In a 3-dimensional orthogonal drawing of a graph, vertices are mapped to grid points on an integer lattice and edges are routed along integer grid lines. In this paper, we present a layout scheme that draws any graph with n vertices of maximum degree 6, using at most 6 bends per edge and in a volume of O(n^{2}). The advantage of our strategy over other drawing methods is that our method is fully dynamic, allowing both insertion and deletion of vertices and edges, while maintaining the volume and bend bounds. The drawing can be obtained in O(n) time and insertions/deletions can be performed in O(1) time. Multiple edges and self loops are permitted. A more elaborate construction that uses only 5 bends per edge, and a simpler, more balanced layout that requires at most 7 bends per edge are also described

    Microfluidics-mediated self-template synthesis of anisotropic hollow ellipsoidal mesoporous silica nanomaterials

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    Herein, a facile strategy was firstly developed to synthesize ellipsoidal mesoporous silica nanomaterials (MSNs) with well-ordered parallel channels along the short axis. A miniaturized microfluidic device with spiral-shaped channels was then chosen as a straightforward and general platform to produce the corresponding hollow counterparts of MSNs under mild conditions. Such reaction process carried out in a microfluidic system was further demonstrated to be more rapid and efficient than a conventional batch method under equivalent experimental conditions. The evolution of hollow structure can be well tuned by flow rates (i.e. etching time), providing a new paradigm for rational design and engineering of anisotropic nanostructures
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