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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.
- 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.
- 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.
- ItemDevelopment and Implementation of a Guideline for the Combination of Additively Manufactured Joint Assemblies with Wire Actuators made of Shape Memory Alloys(Amsterdam [u.a.] : Elsevier, 2023) Löffler, Robin; Tremmel, Stephan; Hornfeck, RüdigerSmart Materials actuators in the form of wires made of shape memory alloys in combination with additively manufactured carrier components are used in a wide variety of prototype developments of innovative joint assemblies. This combination is relevant because of the same manufacturing costs of the additively manufactured components, which are independent of the quantity of parts, the free geometric design possibilities as well as the huge energy density of the aforementioned actuator technology. In particular, the focus is on the possibility of appropriately fitting large wire lengths on a compact part volume while taking into account acceptable force losses. Since there is no design guideline for such joint developments, each is individual, which results in unnecessarily long development times and a higher risk of errors. Based on selected in-house and third-party examples, integration possibilities of shape memory alloy wire actuators in additively manufactured carrier components are analysed and transferred into a universally applicable design guideline. These recommendations are brought into the framework of existing design guidelines of the VDI (Verein Deutscher Ingenieure – Association of German Engineers), namely VDI 2206 and VDI 2221 with extensions for additive manufacturing, for a better usability and integrability into existing processes. Finally, this results in a simplified access to the topic of the combination of additive manufacturing and shape memory alloys and a more efficient realisation of such joint developments.
- 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.
- ItemPreface(Amsterdam [u.a.] : Elsevier, 2016) Canann, Scott; Owen, Steven; Si, Hang[No abstract available]
- ItemSelf-cleaning stainless steel surfaces induced by laser processing and chemical engineering(Amsterdam [u.a.] : Elsevier, 2022) Lorenz, Pierre; Zajadacz, Joachim; Marquardt, Franka; Ehrhardt, Martin; Hommes, Gregor; Peter, Sebastian; Zimmer, KlausNanostructured surfaces show a variety of beneficial macroscopic effects. The combination of hierarchic nanostructures with a suitable chemical surface composition allows for the fabrication of surfaces with interesting fluidic properties beyond such effects. This approach enables the specification of nano/microstructure and chemical composition independent of each other. Various hierarchical micro- and nanostructures can be realized by laser texturing of stainless steel surfaces with infrared picosecond laser. Simultaneously, the surface is activated for chemical processing. The surface can now be tuned by bonding of a self-assembled monolayer on the laser-treated surface by chemical treatment. This two-step functionalization process allows the for separated adjusting of the surface topography and chemical composition and thus for the well-defined setting of the surface properties. The fabrication of superhydrophobic surfaces with self-cleaning properties are performed that can be functionalized further by subsequent laser-irradiation. Furthermore, the long-time stability of the surface functionalization in relation to the impact chemicals or radiation was investigated.
- ItemGeneralized Regular Quadrilateral Mesh Generation based on Surface Foliation(Amsterdam [u.a.] : Elsevier, 2017) Lei, Na; Zheng, Xiaopeng; Si, Hang; Luo, Zhongxuan; Gu, XianfengThis work introduces a novel algorithm for quad-mesh generation based on surface foliation theory. The algorithm is based on the equivalence among colorable quad-meshes, measure foliations and holomorphic differentials. The holomorphic differentials can be obtained by graph-valued harmonic maps. The algorithm has several merits: it can be applied for surfaces with general topologies; the resulting quad-meshes have global tensor product structure and the least number of singularities; the algorithmic pipeline is fully automatic. The experimental results demonstrate the efficiency and efficacy of the proposed method.
- ItemGas-discharge plasma-assisted functionalization of titanium implant surfaces(Baech : Trans Tech Publications Ltd., 2010) Schröder, Karsten; Finke, Birgit; Polak, Martin; Lüthen, Frank; Nebe, Barbara; Rychly, Joachim; Bader, Rainer; Lukowski, Gerold; Walschus, Uwe; Schlosser, Michael; Ohl, Andreas; Weltmann, Klaus DieterA crucial factor for in-growth of metallic implants in the bone stock is the rapid cellular acceptance whilst prevention of bacterial adhesion on the surface. Such contradictorily adhesion events could be triggered by surface properties. There already exists fundamental knowledge about the influence of physicochemical surface properties like roughness, titanium dioxide modifications, cleanness, and (mainly ceramic) coatings on cell and microbial behavior in vitro and in vivo. The titanium surface can be equipped with antimicrobial properties by plasma-based copper implantation, which allows the release and generation of small concentrations of copper ions during contact with water-based biological liquids. Additionally, the titanium surface was equipped with amino groups by the deposition of an ultrathin plasma polymer. This coating on the one hand does not significantly reduce the generation of copper ions, and on the other hand improves the adhesion and spreading of osteoblast cells. The process development was accompanied by physicochemical surface analyses like XPS, FTIR, contact angle, SEM, and AFM. Very thin modified layers were created, which are resistant to hydrolysis and delamination. These titanium surface functionalizations were found to have either an antimicrobial activity or cell-adhesive properties. Intramuscular implantation of titanium samples coated with the cell-adhesive plasma polymer in rats revealed a reduced inflammation reaction compared to uncoated titanium. © (2010) Trans Tech Publications.