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- ItemNanometer-resolved mechanical properties around GaN crystal surface steps(Frankfurt, M. : Beilstein-Institut zur Förderung der Chemischen Wissenschaften, 2014) Buchwald, J.; Sarmanova, M.; Rauschenbach, B.; Mayr, S.G.The mechanical properties of surfaces and nanostructures deviate from their bulk counterparts due to surface stress and reduced dimensionality. Experimental indentation-based techniques present the challenge of measuring these effects, while avoiding artifacts caused by the measurement technique itself. We performed a molecular dynamics study to investigate the mechanical properties of a GaN step of only a few lattice constants step height and scrutinized its applicability to indentation experiments using a finite element approach (FEM). We show that the breakdown of half-space symmetry leads to an "artificial" reduction of the elastic properties of comparable lateral dimensions which overlays the effect of surface stress. Contact resonance atomic force microscopy (CR-AFM) was used to compare the simulation results with experiments.
- ItemEarth system data cubes unravel global multivariate dynamics(Göttingen : Copernicus Publ., 2020) Mahecha, Miguel D.; Gans, Fabian; Brandt, Gunnar; Christiansen, Rune; Cornell, Sarah E.; Fomferra, Normann; Kraemer, Guido; Peters, Jonas; Bodesheim, Paul; Camps-Valls, Gustau; Donges, Jonathan F.; Dorigo, Wouter; Estupinan-Suarez, Lina M.; Gutierrez-Velez, Victor H.; Gutwin, Martin; Jung, Martin; Londoño, Maria C.; Miralles, Diego G.; Papastefanou, Phillip; Reichstein, MarkusUnderstanding Earth system dynamics in light of ongoing human intervention and dependency remains a major scientific challenge. The unprecedented availability of data streams describing different facets of the Earth now offers fundamentally new avenues to address this quest. However, several practical hurdles, especially the lack of data interoperability, limit the joint potential of these data streams. Today, many initiatives within and beyond the Earth system sciences are exploring new approaches to overcome these hurdles and meet the growing interdisciplinary need for data-intensive research; using data cubes is one promising avenue. Here, we introduce the concept of Earth system data cubes and how to operate on them in a formal way. The idea is that treating multiple data dimensions, such as spatial, temporal, variable, frequency, and other grids alike, allows effective application of user-defined functions to co-interpret Earth observations and/or model-data integration. An implementation of this concept combines analysis-ready data cubes with a suitable analytic interface. In three case studies, we demonstrate how the concept and its implementation facilitate the execution of complex workflows for research across multiple variables, and spatial and temporal scales: (1) summary statistics for ecosystem and climate dynamics; (2) intrinsic dimensionality analysis on multiple timescales; and (3) model-data integration. We discuss the emerging perspectives for investigating global interacting and coupled phenomena in observed or simulated data. In particular, we see many emerging perspectives of this approach for interpreting large-scale model ensembles. The latest developments in machine learning, causal inference, and model-data integration can be seamlessly implemented in the proposed framework, supporting rapid progress in data-intensive research across disciplinary boundaries. © 2020 Institute of Electrical and Electronics Engineers Inc.. All rights reserved.
- ItemA numerical study on deformation of Newtonian droplets through converging cylindrical dies(Berlin : de Gruyter, 2013) Mostafaiyan, M.; Saeb, M.R.; Ahmadi, Z.; Khonakdar, H.A.; Wagenknecht, U.; Heinrich, G.In this work, the dynamic deformation of a viscose Newtonian droplet passing through cylindrical converging dies has been studied. The changes in the interfacial area between two immiscible Newtonian fluids have been considered as a variable representing the time-dependent deformation of a circular droplet along converging dies. To do so, a surface tracking method has been incorporated into a finite element code, developed by the authors, which quantifies the deformation of the droplet through the converging path, and where the surface area of the deformed drop has been consequently chosen as a criterion for a two-phase interface. In this study, it has been revealed that by changing both rheological and geometrical parameters it is possible to manage the value of interface area between two phases. Ultimately, a unique curve is developed for each droplet to primary phase viscosity ratio which can correlate drop deformation with geometrical parameters.
- ItemToward mixed-element meshing based on restricted Voronoi diagrams(Amsterdam [u.a.] : Elsevier, 2014) Pellerin, J.; Lévy, B.; Caumon, G.In this paper we propose a method to generate mixed-element meshes (tetrahedra, triangular prisms, square pyramids) for B-Rep models. The vertices, edges, facets, and cells of the final volumetric mesh are determined from the combinatorial analysis of the intersections between the model components and the Voronoi diagram of sites distributed to sample the model. Inside the volumetric regions, Delaunay tetrahedra dual of the Voronoi diagram are built. Where the intersections of the Voronoi cells with the model surfaces have a unique connected component, tetrahedra are modified to fit the input triangulated surfaces. Where these intersections are more complicated, a correspondence between the elements of the Voronoi diagram and the elements of the mixedelement mesh is used to build the final volumetric mesh. The method which was motivated by meshing challenges encountered in geological modeling is demonstrated on several 3D synthetic models of subsurface rock volumes.
- ItemTopology- and Geometry-Controlled Functionalization of Nanostructured Metamaterials(Basel : MDPI, 2023) Fomin, Vladimir M.; Marquardt, Oliver[No abstract available]
- ItemCoupling of chiralities in spin and physical spaces: The Möbius ring as a case study(College Park : American Physical Society, 2015) Pylypovskyi, Oleksandr V.; Kravchuk, Volodymyr P.; Sheka, Denis D.; Makarov, Denys; Schmidt, Oliver G.; Gaididei, YuriWe show that the interaction of the magnetic subsystem of a curved magnet with the magnet curvature results in the coupling of a topologically nontrivial magnetization pattern and topology of the object. The mechanism of this coupling is explored and illustrated by an example of a ferromagnetic Möbius ring, where a topologically induced domain wall appears as a ground state in the case of strong easy-normal anisotropy. For the Möbius geometry, the curvilinear form of the exchange interaction produces an additional effective Dzyaloshinskii-like term which leads to the coupling of the magnetochirality of the domain wall and chirality of the Möbius ring. Two types of domain walls are found, transversal and longitudinal, which are oriented across and along the Möbius ring, respectively. In both cases, the effect of magnetochirality symmetry breaking is established. The dependence of the ground state of the Möbius ring on its geometrical parameters and on the value of the easy-normal anisotropy is explored numerically.
- ItemTwo-dimensional numerical investigations on the termination of bilinear flow in fractures(Göttingen : Copernicus Publ., 2013) Ortiz R., A.E.; Jung, R.; Renner, J.Bilinear flow occurs when fluid is drained from a permeable matrix by producing it through an enclosed fracture of finite conductivity intersecting a well along its axis. The terminology reflects the combination of two approximately linear flow regimes: one in the matrix with flow essentially perpendicular to the fracture, and one along the fracture itself associated with the non-negligible pressure drop in it. We investigated the characteristics, in particular the termination, of bilinear flow by numerical modeling allowing for an examination of the entire flow field without prescribing the flow geometry in the matrix. Fracture storage capacity was neglected relying on previous findings that bilinear flow is associated with a quasi-steady flow in the fracture. Numerical results were generalized by dimensionless presentation. Definition of a dimensionless time that, other than in previous approaches, does not use geometrical parameters of the fracture permitted identifying the dimensionless well pressure for the infinitely long fracture as the master curve for type curves of all fractures with finite length from the beginning of bilinear flow up to fully developed radial flow. In log–log scale the master curve's logarithmic derivative initially follows a 1/4-slope straight line (characteristic for bilinear flow) and gradually bends into a horizontal line (characteristic for radial flow) for long times. During the bilinear flow period, isobars normalized to well pressure propagate with the fourth and second root of time in fracture and matrix, respectively. The width-to-length ratio of the pressure field increases proportional to the fourth root of time during the bilinear period, and starts to deviate from this relation close to the deviation of well pressure and its derivative from their fourth-root-of-time relations. At this time, isobars are already significantly inclined with respect to the fracture. The type curves of finite fractures all deviate counterclockwise from the master curve instead of clockwise or counterclockwise from the 1/4-slope straight line as previously proposed. The counterclockwise deviation from the master curve was identified as the arrival of a normalized isobar reflected at the fracture tip 16 times earlier. Nevertheless, two distinct regimes were found in regard to pressure at the fracture tip when bilinear flow ends. For dimensionless fracture conductivities TD < 1, a significant pressure increase is not observed at the fracture tip until bilinear flow is succeeded by radial flow at a fixed dimensionless time. For TD > 10, the pressure at the fracture tip has reached substantial fractions of the associated change in well pressure when the flow field transforms towards intermittent formation linear flow at times that scale inversely with the fourth power of dimensionless fracture conductivity. Our results suggest that semi-log plots of normalized well pressure provide a means for the determination of hydraulic parameters of fracture and matrix after shorter test duration than for conventional analysis.
- ItemDevelopment of a numerical workflow based on μ-CT imaging for the determination of capillary pressure–saturation-specific interfacial area relationship in 2-phase flow pore-scale porous-media systems: a case study on Heletz sandstone(Göttingen : Copernicus Publ., 2016) Peche, Aaron; Halisch, Matthias; Bogdan Tatomir, Alexandru; Sauter, MartinIn this case study, we present the implementation of a finite element method (FEM)-based numerical pore-scale model that is able to track and quantify the propagating fluid–fluid interfacial area on highly complex micro-computed tomography (μ-CT)-obtained geometries. Special focus is drawn to the relationship between reservoir-specific capillary pressure (pc), wetting phase saturation (Sw) and interfacial area (awn). The basis of this approach is high-resolution μ-CT images representing the geometrical characteristics of a georeservoir sample. The successfully validated 2-phase flow model is based on the Navier–Stokes equations, including the surface tension force, in order to consider capillary effects for the computation of flow and the phase-field method for the emulation of a sharp fluid–fluid interface. In combination with specialized software packages, a complex high-resolution modelling domain can be obtained. A numerical workflow based on representative elementary volume (REV)-scale pore-size distributions is introduced. This workflow aims at the successive modification of model and model set-up for simulating, such as a type of 2-phase problem on asymmetric μ-CT-based model domains. The geometrical complexity is gradually increased, starting from idealized pore geometries until complex μ-CT-based pore network domains, whereas all domains represent geostatistics of the REV-scale core sample pore-size distribution. Finally, the model can be applied to a complex μ-CT-based model domain and the pc–Sw–awn relationship can be computed.
- 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.