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- ItemOn Indecomposable Polyhedra and the Number of Steiner Points(Amsterdam [u.a.] : Elsevier, 2015) Goerigk, Nadja; Si, HangThe existence of indecomposable polyhedra, that is, the interior of every such polyhedron cannot be decomposed into a set of tetrahedra whose vertices are all of the given polyhedron, is well-known. However, the geometry and combinatorial structure of such polyhedra are much less studied. In this article, we investigate the structure of some well-known examples, the so-called Schönhardt polyhedron [10] and the Bagemihl's generalization of it [1], which will be called Bagemihl's polyhedra. We provide a construction of an additional point, so-called Steiner point, which can be used to decompose the Schönhardt and the Bagemihl's polyhedra. We then provide a construction of a larger class of three-dimensional indecomposable polyhedra which often appear in grid generation problems. We show that such polyhedra have the same combinatorial structure as the Schönhardt's and Bagemihl's polyhedra, but they may need more than one Steiner point to be decomposed. Given such a polyhedron with n ≥ 6 vertices, we show that it can be decomposed by adding at most interior Steiner points. We also show that this number is optimal in theworst case.
- ItemPulsed-field Invasion to HTS Bulk Magnets Grown from Two Seeds with Varied Seed-crystal Positions and Numbers(Amsterdam [u.a.] : Elsevier, 2014) Oka, T.; Yamada, Y.; Horiuchi, T.; Ogawa, J.; Fukui, S.; Sato, T.; Yokoyama, K.; Langer, M.The flux-invasion behavior into the melt-processed Y-Ba-Cu-O bulk magnets were precisely measured and analyzed during and after their pulsed-field magnetization processes operated at 30.6 K. The materials were fabricated as the bulk monoliths grown by adopting two seed-crystals, or shifting the seed-crystal positions from the centre of the sample surface, which exhibited the magnetically single-domain distributions. Although the performances of the trapped flux density after activations showed no obvious differences, the flux started invading into the sample bearing two seeds obviously at lower fields than those of normally-grown isotropic crystal. Since the flux penetration behavior were thus clearly different between the samples with the structure grown from two seeds and uniformly grown samples with a seed crystal, it is suggested that the structure results in an effective magnetizing method with less heating than those of conventional samples, which results in the higher performance of field trapping in the bulk magnets than usual.
- ItemOn Tetrahedralisations Containing Knotted and Linked Line Segments(Amsterdam [u.a.] : Elsevier, 2017) Si, Hang; Ren, Yuxue; Lei, Na; Gu, XianfengThis paper considers a set of twisted line segments in 3d such that they form a knot (a closed curve) or a link of two closed curves. Such line segments appear on the boundary of a family of 3d indecomposable polyhedra (like the Schönhardt polyhedron) whose interior cannot be tetrahedralised without additional vertices added. On the other hand, a 3d (non-convex) polyhedron whose boundary contains such line segments may still be decomposable as long as the twist is not too large. It is therefore interesting to consider the question: when there exists a tetrahedralisation contains a given set of knotted or linked line segments? In this paper, we studied a simplified question with the assumption that all vertices of the line segments are in convex position. It is straightforward to show that no tetrahedralisation of 6 vertices (the three-line-segments case) can contain a trefoil knot. Things become interesting when the number of line segments increases. Since it is necessary to create new interior edges to form a tetrahedralisation. We provided a detailed analysis for the case of a set of 4 line segments. This leads to a crucial condition on the orientation of pairs of new interior edges which determines whether this set is decomposable or not. We then prove a new theorem about the decomposability for a set of n (n ≥ 3) knotted or linked line segments. This theorem implies that the family of polyhedra generalised from the Schonhardt polyhedron by Rambau [1] are all indecomposable.
- ItemFormation dynamics of ultra-short laser induced micro-dots in the bulk of transparent materials(Amsterdam [u.a.] : Elsevier, 2013) Mermillod-Blondin, A.; Ashkenasi, D.; Lemke, A.; Schwagmeier, M.; Rosenfeld, A.In this paper, we study the formation dynamics of ultra-short laser-induced micro dots under the surface of transparent materials. Laser-induced micro dots find their application in direct part marking, to address full life cycle traceability. We first demonstrate the possibility of direct laser part marking into the cladding of an optical fiber. Then, we monitor the laser affected zone with the help of a time-resolved phase contrast microscopy setup in a fused silica substrate. We show that the transient energy relaxation processes affect the host material over a region that exceeds the micro dot size by several micrometers.
- ItemMeasurements of Streams Agitated by Fluid Loaded SAW-devices Using a Volumetric 3-component Measurement Technique (V3V)(Amsterdam [u.a.] : Elsevier, 2015) Kiebert, Florian; König, Jörg; Kykal, Carsten; Schmidt, HagenUtilizing surface acoustic waves (SAW) to induce tailored fluid motion via the acoustic streaming requires detailed knowledge about the acoustic bulk wave excitation. For the first time, the Defocus Digital Particle Image Velocimetry is used to measure the fluid motion originating from a fluid loaded SAW-device. With this flow measurement technique, the acoustic streaming-induced fluid motion can be observed volumetrically, which is attractive not only for application, but also for simulation in order to gain deeper insights regarding three-dimensional acoustic effects.
- ItemOn Tetrahedralisations of Reduced Chazelle Polyhedra with Interior Steiner Points(Amsterdam [u.a.] : Elsevier, 2016) Si, Hang; Goerigk, NadjaThe non-convex polyhedron constructed by Chazelle, known as the Chazelle polyhedron [4], establishes a quadratic lower bound on the minimum number of convex pieces for the 3d polyhedron partitioning problem. In this paper, we study the problem of tetrahedralising the Chazelle polyhedron without modifying its exterior boundary. It is motivated by a crucial step in tetrahedral mesh generation in which a set of arbitrary constraints (edges or faces) need to be entirely preserved. The goal of this study is to gain more knowledge about the family of 3d indecomposable polyhedra which needs additional points, so-called Steiner points, to be tetrahedralised. The requirement of only using interior Steiner points for the Chazelle polyhedron is extremely challenging. We first “cut off” the volume of the Chazelle polyhedron by removing the regions that are tetrahedralisable. This leads to a 3d non-convex polyhedron whose vertices are all in the two slightly shifted saddle surfaces which are used to construct the Chazelle polyhedron. We call it the reduced Chazelle polyhedron. It is an indecomposable polyhedron. We then give a set of (N + 1)2 interior Steiner points that ensures the existence of a tetrahedralisation of the reduced Chazelle polyhedron with 4(N + 1) vertices. The proof is done by transforming a 3d tetrahedralisation problem into a 2d edge flip problem. In particular, we design an edge splitting and flipping algorithm and prove that it gives to a tetrahedralisation of the reduced Chazelle polyhedron.
- ItemModelling of a radio frequency plasma bridge neutralizer (RFPBN)(Amsterdam [u.a.] : Elsevier, 2017) Scholze, F.; Eichhorn, C.; Bundesmann, C.; Spemann, D.; Neumann, H.; Bulit, A.; Feili, D.; Gonzalez del Amo, J.A performance model of a radio frequency plasma bridge neutralizer was developed to calculate the electrical parameters and optimize the neutralizer design. Minimization of power losses and gas consumption, and a maximization of the neutralizer lifetime and the reliability of the system are requirements of all electric propulsion concepts and strongly determine their future application. The requirements of the neutralizer depend on mission profiles.
- ItemOptimization of the energy deposition in glasses with temporally-shaped femtosecond laser pulses(Amsterdam [u.a.] : Elsevier, 2011) Mauclair, C.; Mishchik, K.; Mermillod-Blondin, A.; Rosenfeld, A.; Hertel, I.V.; Audouard, E.; Stoian, R.Bulk machining of glasses with femtosecond laser pulses enables the fabrication of embedded optical functions. Due to the nonlinear character of the laser-matter interaction, structural modifications can occur within the focal region. To reach a full control of the process, ways of controlling the deposition of the laser energy inside the material have to be unveiled. From static and time-resolved pictures of bulk-excitation of a-SiO2 and borosilicate glass, we show that particular laser temporal shapes such as picosecond sequences can better confine the energy deposition than the femtosecond sequence by reducing the propagation artifacts.
- ItemLaser Embossing of Micro-and Submicrometer Surface Structures in Copper(Amsterdam [u.a.] : Elsevier, 2012) Ehrhardt, M.; Lorenz, P.; Frost, F.; Zimmer, K.Micro- and submicrometer structures have been transferred from nickel foils into solid copper surfaces by laser microembossing. The developed arrangement for laser microembossing allows a large-area replication using multi- pulse laser scanning scheme, guaranties a low contamination of the embossed surface and enables the utilization of thick workpieces. In the micrometer range the replicated patterns feature a high accuracy regarding the shape. A significant difference between the master and the replication pattern could be observed for the laser embossing of submicrometer patterns. In conclusion, the results show that the proposed laser embossing process is a promising method with a number of applications in microengineering.
- ItemFrom statistic to deterministic nanostructures in fused silica induced by nanosecond laser radiation(Amsterdam [u.a.] : Elsevier, 2018) Lorenz, Pierre; Klöppel, Michael; Zagoranskiy, Igor; Zimmer, KlausThe production of structures by laser machining below the diffraction limit is still a challenge. However, self-organization processes can be useful. The laser-induced self-organized modification of the shape of photolithographic produced chromium structures on fused silica as well as the structuring of the fused silica surface by nanosecond UV laser radiation was studied, respectively. Low fluence single pulse laser irradiation (□ > 300 mJ/cm2) cause the formation from chromium squares to droplets due to the mass transport in the molten chromium film. This process is governed by the instability of the molten metal due to the surface tension driven liquid phase mass transport. For a chromium pattern size similar to the instability length two specific droplet distributions were found which are single droplets with a determined position near the centre of the original pattern or random distributed smaller droplets arranged circularly. Each of the metal patterns can be transferred into the fused silica by a multi-pulse irradiation. The experimental results can be simulated well for low fluences by sequential solving the heat and Navier-Stokes equation.