TUHH Open Research (TORE)
https://tore.tuhh.de:443
TORE captures, stores, indexes, preserves, and distributes digital research material.Tue, 20 Oct 2020 04:04:34 GMT2020-10-20T04:04:34ZMicrostructure and mechanical behavior of TiO₂-MnO-doped alumina/alumina laminates
http://hdl.handle.net/11420/7616
Title: Microstructure and mechanical behavior of TiO₂-MnO-doped alumina/alumina laminates
Authors: Barros, Marcelo; Jelitto, Hans; Hotza, Dachamir; Janßen, Rolf
Abstract: Tapes of TiO2-MnO-doped alumina (d-Al2O3) and pure alumina (Al2O3) were shaped via tape casting. Laminates with three different layer numbers and respective thicknesses were produced and sintered at 1200°C. The microstructure and mechanical behavior of laminates were investigated and compared to the respective monolithic references (d-Al2O3 and Al2O3). The use of dopants in alumina decreased the initial sintering temperature, leading to higher densification at 1200°C (~98% theoretical density (TD)) when compared to Al2O3 (~73% TD). The higher density was reflected in a higher Young's modulus and hardness for doped alumina. A region of diffusion of dopants in pure alumina layers was observed along the interface with doped layers. The mechanical strength of d-Al2O3 samples sintered at 1200°C was not statistically different from Al2O3 samples sintered at 1350°C. The strength of laminates composed of doped layers with undoped, porous interlayers did not change. Nevertheless, as the thickness of these porous interlayers increases, a loss of strength was observed. Monolithic references showed constant values of fracture toughness (KIC), ~2 MPa·m1/2, and linear crack path. On the other hand, KIC of laminates increases when the crack propagates from weak Al2O3 layers to dense d-Al2O3 layers.Mon, 19 Oct 2020 13:52:15 GMThttp://hdl.handle.net/11420/76162020-10-19T13:52:15ZSmall-area orthogonal drawings of 3-connected graphs
http://hdl.handle.net/11420/7615
Title: Small-area orthogonal drawings of 3-connected graphs
Authors: Biedl, Therese; Schmidt, Jens M.
Abstract: It is well-known that every graph with maximum degree 4 has an orthogonal drawing with area at most 49/64 n2+O(n)≈0.76n2. In this paper, we show that if the graph is 3-connected, then the area can be reduced even further to9/16n2+O(n)≈0.56n2.Thedrawingusesthe 3-canonical order for (not necessarily planar) 3-connected graphs, which is a special Mondshein sequence and can hence be computed in linear time. To our knowledge, this is the first application of a Mondshein sequence in graph drawing.Mon, 19 Oct 2020 13:09:11 GMThttp://hdl.handle.net/11420/76152020-10-19T13:09:11ZMondshein sequences (A.K.A. (2; 1)-orders)
http://hdl.handle.net/11420/7614
Title: Mondshein sequences (A.K.A. (2; 1)-orders)
Authors: Schmidt, Jens M.
Abstract: Canonical orderings have been used as a key tool in graph drawing, graph encoding, and visibility representations for the last decades [H. de Fraysseix, J. Pach, and R. Pollack, Proceedings of the 20th Annual ACM Symposium on Theory of Computing (STOC '88), ACM, New York, 1988, pp. 426-433; G. Kant, Proceedings of the 33rd Annual Symposium on Foundations of Computer Science (FOCS '92), IEEE Press, Piscataway, NJ, 1992, pp. 101-110]. We study a far-reaching generalization of canonical orderings to nonplanar graphs that was published by Lee Mondshein in a Ph.D. thesis as early as 1971. Mondshein proposed to order the vertices of a graph in a sequence such that for any i, the vertices from 1 to i essentially induce a 2-connected graph, while the remaining vertices from i+1 to n induce a connected graph. Mondshein's sequence generalizes canonical orderings and later became independently known as nonseparating ear decomposition. Surprisingly, this fundamental link between canonical orderings and nonseparating ear decomposition had not been previously established. Currently, the fastest known algorithm for computing a Mondshein sequence achieves a running time of O(nm); the main open problem in Mondshein's and follow-up work is to improve this running time to subquadratic time. After putting Mondshein's work into context, we present an algorithm that computes a Mondshein sequence in optimal time and space O(m). This improves the previous best running time by a factor of n. We illustrate the impact of this result by deducing linear-time algorithms for five other problems-in four of these, the previous best running time was quadratic. In particular, we show how to compute three independent spanning trees in a 3-connected graph in time O(m), improving a result of Cheriyan and Maheshwari [J. Algorithms, 9 (1988), pp. 507-537]; improve the preprocessing time from O(n2) to O(m) for the output-sensitive data structure of Di Battista, Tamassia, and Vismara [Algorithmica, 23 (1999), pp. 302-340] that reports three internally disjoint paths between any given vertex pair; derive a very simple O(n)-time planarity test once a Mondshein sequence is computed; compute a nested family of contractible subgraphs of 3-connected graphs in time O(m); and compute a 3-partition in time O(m) (the previous best running time is O(n2) due to Suzuki et al. [Information Processing Society of Japan (IPSJ), 31 (1990), pp. 584-592 (in Japanese)]).Mon, 19 Oct 2020 13:03:52 GMThttp://hdl.handle.net/11420/76142020-10-19T13:03:52ZThe Mondshein sequence
http://hdl.handle.net/11420/7613
Title: The Mondshein sequence
Authors: Schmidt, Jens M.
Abstract: Canonical orderings [STOC'88, FOCS'92] have been used as a key tool in graph drawing, graph encoding and visibility representations for the last decades. We study a far-reaching generalization of canonical orderings to non-planar graphs that was published by Lee Mondshein in a PhD-thesis at M.I.T. as early as 1971. Mondshein proposed to order the vertices of a graph in a sequence such that, for any i, the vertices from 1 to i induce essentially a 2-connected graph while the remaining vertices from i + 1 to n induce a connected graph. Mondshein's sequence generalizes canonical orderings and became later and independently known under the name non-separating ear decomposition. Currently, the best known algorithm for computing this sequence achieves a running time of O(nm); the main open problem in Mondshein's and follow-up work is to improve this running time to a subquadratic time. In this paper, we present the first algorithm that computes a Mondshein sequence in time and space O(m), improving the previous best running time by a factor of n. In addition, we illustrate the impact of this result by deducing linear-time algorithms for several other problems, for which the previous best running times have been quadratic. In particular, we show how to compute three independent spanning trees in a 3-connected graph in linear time, improving a result of Cheriyan and Maheshwari [J. Algorithms 9(4)]. Secondly, we improve the preprocessing time for the output-sensitive data structure by Di Battista, Tamassia and Vismara [Algorithmica 23(4)] that reports three internally disjoint paths between any given vertex pair from O(n2) to O(m). Thirdly, we improve the computation of 3-partitioning of a 3-connected graph to linear time. Finally, we show how a very simple linear-time planarity test can be derived once a Mondshein sequence is computed.Mon, 19 Oct 2020 12:53:12 GMThttp://hdl.handle.net/11420/76132020-10-19T12:53:12Z