1,267 research outputs found

    Toward mixed-element meshing based on restricted Voronoi diagrams

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    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

    Scutoids unveil the three-dimensional packing in curved epithelia

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    As animals develop, the initial simple planar epithelia of the early embryos must acquire complex three-dimensional architectures to form the final functional tissues of the organism. Epithelial bending is, therefore, a general principle of all developing systems. Scholarly publications depict epithelial cells as prisms where their basal and apical faces resemble polygons with the same number of sides. The accepted view is that, when a tissue bend, the cells of the epithelia modify their shape from columnar to what has been traditionally called “bottle shape”. However, the morphology and packing of curved epithelia remain largely unknown. Here, through mathematical and computational modelling, we show that cells in bent epithelia necessarily undergo intercalations along the apico-basal axis. This event forces cells to exchange their neighbours between their basal and apical surfaces. Therefore, the traditional view of epithelial cells as simple prisms is incompatible with this phenomenon. Consequently, epithelial cells are compelled to adopt a novel geometrical shape that we have named “scutoid”. The in-depth analysis of diverse epithelial tissues and organs confirm the generation of apico-basal transitions among cell during morphogenesis. Using biophysics arguments, we determine that scutoids support the energetic minimization on the tissue and conclude that the transitions along the apico-basal axis stabilize the threedimensional packing of the tissue. Altogether, we argue that scutoids are nature’s solution to bend efficiently epithelia, and the missing piece for developing a unifying and realistic model of epithelial architecture

    Subset Warping: Rubber Sheeting with Cuts

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    Image warping, often referred to as "rubber sheeting" represents the deformation of a domain image space into a range image space. In this paper, a technique is described which extends the definition of a rubber-sheet transformation to allow a polygonal region to be warped into one or more subsets of itself, where the subsets may be multiply connected. To do this, it constructs a set of "slits" in the domain image, which correspond to discontinuities in the range image, using a technique based on generalized Voronoi diagrams. The concept of medial axis is extended to describe inner and outer medial contours of a polygon. Polygonal regions are decomposed into annular subregions, and path homotopies are introduced to describe the annular subregions. These constructions motivate the definition of a ladder, which guides the construction of grid point pairs necessary to effect the warp itself

    A feature extracting and meshing approach for sheet-like structures in rocks

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    Meshing rock samples with sheet-like structures based their CT scanned volumetric images, is a crucial component for both visualization and numerical simulation. In rocks, fractures and veins commonly exist in the form of sheet-like objects (e.g. thin layers and distinct flat shapes), which are much smaller than the rock mass dimensions. The representations of such objects require high-resolution 3D images with a huge dataset, which are difficult and even impossible to visualize or analyze by numerical methods. Therefore, we develop a microscopic image based meshing approach to extract major sheet-like structures and then preserve their major geometric features at the macroscale. This is achieved by the following four major steps: (1) extracting major objects through extending, separation and recovering operations based on the CT scanned data/microscopic images; (2) simplifying and constructing a simplified centroidal Voronoi diagram on the extracted structures; (3) generating triangular meshes to represent the structure; (4) generating volume tetrahedron meshes constrained with the above surface mesh as the internal surfaces. Moreover, a shape similarity approach is proposed to measure and evaluate how similar the generated mesh models to the original rock samples. It is applied as criteria for further mesh generation to better describe the rock features with fewer elements. Finally, a practical CT scanned rock is taken as an application example to demonstrate the usefulness and capability of the proposed approach

    Performances of the mixed virtual element method on complex grids for underground flow

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    The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults, while the latter are connected to the properties of the rock matrix which might vary abruptly in space. The development of approximation schemes has recently focused on the overcoming of such difficulties with the objective of obtaining numerical schemes with good approximation properties. In this work we carry out a numerical study on the performances of the Mixed Virtual Element Method (MVEM) for the solution of a single-phase flow model in fractured porous media. This method is able to handle grid cells of polytopal type and treat hybrid dimensional problems. It has been proven to be robust with respect to the variation of the permeability field and of the shape of the elements. Our numerical experiments focus on two test cases that cover several of the aforementioned critical aspects

    The investigation of a method to generate conformal lattice structures for additive manufacturing

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    Additive manufacturing (AM) allows a geometric complexity in products not seen in conventional manufacturing. This geometric freedom facilitates the design and fabrication of conformal hierarchical structures. Entire parts or regions of a part can be populated with lattice structure, designed to exhibit properties that differ from the solid material used in fabrication. Current computer aided design (CAD) software used to design products is not suitable for the generation of lattice structure models. Although conceptually simple, the memory requirements to store a virtual CAD model of a lattice structure are prohibitively high. Conventional CAD software defines geometry through boundary representation (B-rep); shapes are described by the connectivity of faces, edges and vertices. While useful for representing accurate models of complex shape, the sheer quantity of individual surfaces required to represent each of the relatively simple individual struts that comprise a lattice structure ensure that memory limitations are soon reached. Additionally, the conventional data flow from CAD to manufactured part is arduous, involving several conversions between file formats. As well as a lengthy process, each conversion risks the generation of geometric errors that must be fixed before manufacture. A method was developed to specifically generate large arrays of lattice structures, based on a general voxel modelling method identified in the literature review. The method is much less sensitive to geometric complexity than conventional methods and thus facilitates the design of considerably more complex structures. The ability to grade structure designs across regions of a part (termed functional grading ) was also investigated, as well as a method to retain connectivity between boundary struts of a conformal structure. In addition, the method streamlines the data flow from design to manufacture: earlier steps of the data conversion process are bypassed entirely. The effect of the modelling method on surface roughness of parts produced was investigated, as voxel models define boundaries with discrete, stepped blocks. It was concluded that the effect of this stepping on surface roughness was minimal. This thesis concludes with suggestions for further work to improve the efficiency, capability and usability of the conformal structure method developed in this work

    Large-area biomolecule nanopatterns on diblock copolymer surfaces for cell adhesion studies

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    Cell membrane receptors bind to extracellular ligands, triggering intracellular signal transduction pathways that result in specific cell function. Some receptors require to be associated forming clusters for effective signaling. Increasing evidences suggest that receptor clustering is subjected to spatially controlled ligand distribution at the nanoscale. Herein we present a method to produce in an easy, straightforward process, nanopatterns of biomolecular ligands to study ligand–receptor processes involving multivalent interactions. We based our platform in self-assembled diblock copolymers composed of poly(styrene) (PS) and poly(methyl methacrylate) (PMMA) that form PMMA nanodomains in a closed-packed hexagonal arrangement. Upon PMMA selective functionalization, biomolecular nanopatterns over large areas are produced. Nanopattern size and spacing can be controlled by the composition of the block-copolymer selected. Nanopatterns of cell adhesive peptides of different size and spacing were produced, and their impact in integrin receptor clustering and the formation of cell focal adhesions was studied. Cells on ligand nanopatterns showed an increased number of focal contacts, which were, in turn, more matured than those found in cells cultured on randomly presenting ligands. These findings suggest that our methodology is a suitable, versatile tool to study and control receptor clustering signaling and downstream cell behavior through a surface-based ligand patterning technique

    Boosting Heterogeneous Catalyst Discovery by Structurally Constrained Deep Learning Models

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    The discovery of new catalysts is one of the significant topics of computational chemistry as it has the potential to accelerate the adoption of renewable energy sources. Recently developed deep learning approaches such as graph neural networks (GNNs) open new opportunity to significantly extend scope for modelling novel high-performance catalysts. Nevertheless, the graph representation of particular crystal structure is not a straightforward task due to the ambiguous connectivity schemes and numerous embeddings of nodes and edges. Here we present embedding improvement for GNN that has been modified by Voronoi tesselation and is able to predict the energy of catalytic systems within Open Catalyst Project dataset. Enrichment of the graph was calculated via Voronoi tessellation and the corresponding contact solid angles and types (direct or indirect) were considered as features of edges and Voronoi volumes were used as node characteristics. The auxiliary approach was enriching node representation by intrinsic atomic properties (electronegativity, period and group position). Proposed modifications allowed us to improve the mean absolute error of the original model and the final error equals to 651 meV per atom on the Open Catalyst Project dataset and 6 meV per atom on the intermetallics dataset. Also, by consideration of additional dataset, we show that a sensible choice of data can decrease the error to values above physically-based 20 meV per atom threshold

    VoroNoodles: Topological Interlocking with Helical Layered 2‐Honeycombs

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    Fundamental physical cellular constraints drive self-organization of tissues

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    Morphogenesis is driven by small cell shape changes that modulate tissue organization. Apical surfaces of proliferating epithelial sheets have been particularly well studied. Currently, it is accepted that a stereotyped distribution of cellular polygons is conserved in proliferating tissues among metazoans. In this work, we challenge these previous findings showing that diverse natural packed tissues have very different polygon distributions. We use Voronoi tessellations as a mathematical framework that predicts this diversity. We demonstrate that Voronoi tessellations and the very different tissues analysed share an overriding restriction: the frequency of polygon types correlates with the distribution of cell areas. By altering the balance of tensions and pressures within the packed tissues using disease, genetic or computer model perturbations, we show that as long as packed cells present a balance of forces within tissue, they will be under a physical constraint that limits its organization. Our discoveries establish a new framework to understand tissue architecture in development and disease. Synopsis Cell shapes in naturally packed tissues have different polygon distributions. Voronoi tessellations-based analysis suggests that polygon frequencies are restricted by the distribution of cell areas, and that this restriction emanates from the balance of forces within the tissue. Cell shapes in natural packed tissues present very different polygon distributions. These patterns can be reproduced by Voronoi tessellations. Natural tissues and Voronoi diagrams share some geometrical properties. There is a physical constraint that limits the organization of natural tissues. Unbalance of forces within the natural tissue breaks this restriction. Cell shapes in naturally packed tissues have different polygon distributions. Voronoi tessellations-based analysis suggests that polygon frequencies are restricted by the distribution of cell areas, and that this restriction emanates from the balance of forces within the tissue.Ministerio de Ciencia e Innovación BFU2011-2573
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