Abstract-We study scalable routing for a sensor network deployed in complicated 3D settings such as underground tunnels in gas system or water system. The nodes are in general 3D space but they are very sparsely located and the network has complex topology. We propose a routing scheme by first embedding the network on a surface with possibly non-zero genus. Then we compute a canonical hyperbolic metric of the embedded surface, and use geodesics to decompose the network into canonical components called pairs of 'pants' whose topology is simpler (with genus zero). The adjacency of the pants components is extracted as a high level routing map and stored at every node. With the hyperbolic metric one can use greedy routing to navigate within and across pants. Altogether this leads to a two-level routing scheme by first finding a sequence of pants and then realizing the route with greedy steps. We show by simulation that the number of pants is closely related to the true 'genus' of the network and that the routing scheme is efficient and scalable.
Abstract-In this paper we address the problem of scalable and load balanced routing for wireless sensor networks. Motivated by the analog of the continuous setting that geodesic routing on a sphere gives perfect load balancing, we embed sensor nodes on a convex polyhedron in 3D and use greedy routing to deliver messages between any pair of nodes with guaranteed success. This embedding is known to exist by the Koebe-Andreev-Thurston Theorem for any 3-connected planar graphs. In our paper we use discrete Ricci flow to develop a distributed algorithm to compute this embedding. Further, such an embedding is not unique and differs from one another by a Möbius transformation. We employ an optimization routine to look for the Möbius transformation such that the nodes are spread on the polyhedron as uniformly as possible. We evaluated the load balancing property of this greedy routing scheme and showed favorable comparison with previous schemes.
To solve the problem of zinc to the weld quality of galvanised sheet, alloy elements (Cu, Nb, Y) have been added to combine with zinc to form stable compounds during welding. The structure and properties of CuZn, NbZn3 and YZn compounds were calculated by first-principles. The calculation results show that all three elements form a stable alloy with Zn. Among the alloys formed, CuZn has the best mechanical properties. MIG welding experiments of galvanised sheet were conducted to verify the effects of Cu addition on the weld seam formation. The experimental results show that the addition of Cu powder has little influence on the macro-morphology of the weld. In the centre of the weld, ferrite structure is refined and micro-hardness is improved.
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