Reconstruction of graded groupoids from graded Steinberg algebras

We show how to reconstruct a graded ample Hausdorff groupoid with topologically principal neutrally-graded component from the ring structure of its graded Steinberg algebra over any commutative integral domain with 1, together with the embedding of the canonical abelian subring of functions supported on the unit space. We deduce that diagonal-preserving ring isomorphism of Leavitt path algebras implies $C^*$-isomorphism of $C^*$-algebras for graphs $E$ and $F$ in which every cycle has an exit. This is a joint work with Joan Bosa, Roozbeh Hazrat and Aidan Sims.

A Pre-processing Moving Mesh Method for Discontinuous Galerkin Approximations of Advection-Diffusion-Reaction Problems

We propose a pre-processing mesh re-distribution algorithm based upon harmonic maps employed in conjunction with discontinuous Galerkin approximations of advection-diffusion-reaction problems. Extensive two-dimensional numerical experiments with different choices of monitor functions, including monitor functions derived from goal-oriented a posteriori error indicators are presented. The examples presented clearly demonstrate the capabilities and the benefits of combining our pre-processing mesh movement algorithm with both uniform, as well as, adaptive isotropic and anisotropic mesh refinement.

Inverse identification of the bending stiffness of a braided polyethylene twine subject to large deformation: application to the identification of the mesh opening rigidity of fishing nets.

The evaluation of the mesh opening stiffness of fishing nets is an important issue in assessing the selectivity of trawls. It appeared that a larger bending rigidity of twines decreases the mesh opening and could reduce the escapement of fish. Nevertheless, netting structure is complex. A netting is made up of braided twines made of polyethylene or polyamide. These twines are tied with non-symmetrical knots. Thus, these assemblies develop contact-friction interactions. Moreover, the netting can be subject to large deformation. In this study, we investigate the responses of netting samples to different types of solicitations. Samples are loaded and unloaded with creep and relaxation stages, with different boundary conditions. Then, two models have been developed: an analytical model and a finite element model. The last one was used to assess, with an inverse identification algorithm, the bending stiffness of twines. In this paper, experimental results and a model for netting structures made up of braided twines are presented. During dry forming of a composite, for example, the matrix is not present or not active, and relative sliding can occur between constitutive fibres. So an accurate modelling of the mechanical behaviour of fibrous material is necessary. This study offers experimental data which could permit to improve current models of contact-friction interactions [4], to validate models for large deformation analysis of fibrous materials [1] on a new experimental case, then to improve the evaluation of the mesh opening stiffness of a fishing net

Aplicación de redes Mesh en el área de videovigilancia y ampliación de zonas Wi-Fi en el municipio de San José las Flores, Chalatenango

El trabajo describe la aplicación de redes Mesh (tecnología inalámbrica) en campos de la videovigilancia y ampliación de zonas Wi-Fi, basado en la realización de una red prototipo capaz de soportar tales servicios, todo esto aplicado al caso de estudio del municipio de San José las Flores, Chalatenango, comunidad de escasos recursos, pues uno de los principales objetivo de este trabajo es hacer accesible esta tecnología a las municipalidades más pobres, para ello se utilizaron herramientas y software libres, dejando plasmado en el documento las factibilidades económicas, técnica y operativa, así como los resultados obtenidos durante la investigación

Mesh Adaption for Tracking Vortex Structures in OVERTURNS Simulation of the S-76 Rotor in Hover

The constant need to improve helicopter performance requires the optimization of existing and future rotor designs. A crucial indicator of rotor capability is hover performance, which depends on the near-body flow as well as the structure and strength of the tip vortices formed at the trailing edge of the blades. Computational Fluid Dynamics (CFD) solvers must balance computational expenses with preservation of the flow, and to limit computational expenses the mesh is often coarsened in the outer regions of the computational domain. This can lead to degradation of the vortex structures which compose the rotor wake. The current work conducts three-dimensional simulations using OVERTURNS, a three-dimensional structured grid solver that models the flow field using the Reynolds-Averaged Navier-Stokes equations. The S-76 rotor in hover was chosen as the test case for evaluating the OVERTURNS solver, focusing on methods to better preserve the rotor wake. Using the hover condition, various computational domains, spatial schemes, and boundary conditions were tested. Furthermore, a mesh adaption routine was implemented, allowing for the increased refinement of the mesh in areas of turbulent flow without the need to add points to the mesh. The adapted mesh was employed to conduct a sweep of collective pitch angles, comparing the resolved wake and integrated forces to existing computational and experimental results. The integrated thrust values saw very close agreement across all tested pitch angles, while the power was slightly over predicted, resulting in under prediction of the Figure of Merit. Meanwhile, the tip vortices have been preserved for multiple blade passages, indicating an improvement in vortex preservation when compared with previous work. Finally, further results from a single collective pitch case were presented to provide a more complete picture of the solver results.

Error estimation and adaptive mesh refinement for aerodynamic flows

This lecture course covers the theory of so-called duality-based a posteriori error estimation of DG finite element methods. In particular, we formulate consistent and adjoint consistent DG methods for the numerical approximation of both the compressible Euler and Navier-Stokes equations; in the latter case, the viscous terms are discretized based on employing an interior penalty method. By exploiting a duality argument, adjoint-based a posteriori error indicators will be established. Moreover, application of these computable bounds within automatic adaptive finite element algorithms will be developed. Here, a variety of isotropic and anisotropic adaptive strategies, as well as $hp$-mesh refinement will be investigated.

Spectral-based mesh segmentation

In design and manufacturing, mesh segmentation is required for FACE construction in boundary representation (BRep), which in turn is central for featurebased design, machining, parametric CAD and reverse engineering, among others -- Although mesh segmentation is dictated by geometry and topology, this article focuses on the topological aspect (graph spectrum), as we consider that this tool has not been fully exploited -- We preprocess the mesh to obtain a edgelength homogeneous triangle set and its Graph Laplacian is calculated -- We then produce a monotonically increasing permutation of the Fiedler vector (2nd eigenvector of Graph Laplacian) for encoding the connectivity among part feature submeshes -- Within the mutated vector, discontinuities larger than a threshold (interactively set by a human) determine the partition of the original mesh -- We present tests of our method on large complex meshes, which show results which mostly adjust to BRep FACE partition -- The achieved segmentations properly locate most manufacturing features, although it requires human interaction to avoid over segmentation -- Future work includes an iterative application of this algorithm to progressively sever features of the mesh left from previous submesh removals

Triangular mesh parameterization with trimmed surfaces

Given a 2manifold triangular mesh \(M \subset {\mathbb {R}}^3\), with border, a parameterization of \(M\) is a FACE or trimmed surface \(F=\{S,L_0,\ldots, L_m\}\) -- \(F\) is a connected subset or region of a parametric surface \(S\), bounded by a set of LOOPs \(L_0,\ldots ,L_m\) such that each \(L_i \subset S\) is a closed 1manifold having no intersection with the other \(L_j\) LOOPs -- The parametric surface \(S\) is a statistical fit of the mesh \(M\) -- \(L_0\) is the outermost LOOP bounding \(F\) and \(L_i\) is the LOOP of the ith hole in \(F\) (if any) -- The problem of parameterizing triangular meshes is relevant for reverse engineering, tool path planning, feature detection, redesign, etc -- Stateofart mesh procedures parameterize a rectangular mesh \(M\) -- To improve such procedures, we report here the implementation of an algorithm which parameterizes meshes \(M\) presenting holes and concavities -- We synthesize a parametric surface \(S \subset {\mathbb {R}}^3\) which approximates a superset of the mesh \(M\) -- Then, we compute a set of LOOPs trimming \(S\), and therefore completing the FACE \(F=\ {S,L_0,\ldots ,L_m\}\) -- Our algorithm gives satisfactory results for \(M\) having low Gaussian curvature (i.e., \(M\) being quasi-developable or developable) -- This assumption is a reasonable one, since \(M\) is the product of manifold segmentation preprocessing -- Our algorithm computes: (1) a manifold learning mapping \(\phi : M \rightarrow U \subset {\mathbb {R}}^2\), (2) an inverse mapping \(S: W \subset {\mathbb {R}}^2 \rightarrow {\mathbb {R}}^3\), with \ (W\) being a rectangular grid containing and surpassing \(U\) -- To compute \(\phi\) we test IsoMap, Laplacian Eigenmaps and Hessian local linear embedding (best results with HLLE) -- For the back mapping (NURBS) \(S\) the crucial step is to find a control polyhedron \(P\), which is an extrapolation of \(M\) -- We calculate \(P\) by extrapolating radial basis functions that interpolate points inside \(\phi (M)\) -- We successfully test our implementation with several datasets presenting concavities, holes, and are extremely nondevelopable -- Ongoing work is being devoted to manifold segmentation which facilitates mesh parameterization

The crash behaviour of hot stamped components – the effect of tailoring conditions

It is known that tailoring a hot stamping part, to achieve locally graded properties, can improve the crash behavior. Depending on the role of the structural part (carrying either bending or axial crash load), the best position for the local regions with lower strength and higher ductility can be different. The distribution of these local regions and their mechanical properties affects the crash behavior of the part in each loading case and therefore can be effectively designed to improve the crash performance. To investigate these effects and examine the improvement possibilities, a numerical thermalmechanical-metallurgical model of a hot stamping process and a representative side impact crash model were created and analysed. The hot stamping model was used to predict the consequent phase fractions and mechanical properties of tailored hot stamping parts produced with different tailoring scenarios. In the metallurgical model, a modified phase transformation model based on Scheil’s additive principle was incorporated. The geometry and mesh of the stamped part was exported to a crash numerical model with a 3-point bending configuration. A constitutive model was used to define the plastic behavior of the stamped part corresponding to different hardness values. Various possibilities in locally positioning the high strength or high ductility zones of material were examined. The results show that the positioning of the soft zones has a more significant effect on the crash performance than the variation in their mechanical properties of these soft zones.

Perceptual and cerebro-spinal responses to graded innocuous and noxious stimuli following aerobic exercise

The aim of this study was to evaluate the effect of aerobic exercise on perceptual and cerebro-spinal responses to graded electrocutaneous stimuli. The design comprised 2 x 30 min of cycling exercise at 30% and 70% of peak oxygen consumption (VO2 peak) on separate occasions in a counter-balanced order in 10 healthy participants. Assessment of nociceptive withdrawal reflex threshold (NWR-T), pain threshold (PT), and somatosensory evoked potentials (SEPs) to graded electrocutaneous stimuli were performed before and after exercise. Perceptual magnitude ratings and SEPs were compared at 30%PT, 60%PT, 100%PT before (Pre), 5 min after (Post1), and 15 min after (Post2) aerobic exercise. There was no difference in the NWR-T and the PT following exercise at 30% and 70% of VO2 peak. ANOVA for the perceptual response within pooled electrocutaneous stimuli show a significant main effect for time (F2,18=5.41, P=0.01) but no difference for exercise intensity (F1,9=0.02, P=0.88). Within-subject contrasts reveal trend differences between 30%PT and 100%PT for Pre-Post1 (P=0.09) and Pre-Post2 (P=0.02). ANOVA for the SEPs peak-to-peak signal amplitude (N1-P1) show significant main effect for time (F2,18=4.04, P=0.04) but no difference for exercise intensity (F1,9=1.83, P=0.21). Pairwise comparisons for time reveal differences between Pre-Post1 (P=0.06) and Pre-Post2 (P=0.01). There was a significant interaction for SEPs N1-P1 between exercise intensity and stimulus intensity (F2,18=3.56, P=0.05). These results indicate that aerobic exercise did not increase the electrocutaneous threshold for pain and the NWR-T. Aerobic exercise attenuated perceptual responses to innocuous stimuli and SEPs N1-P1 response to noxious stimuli.

Functionally graded porous scaffolds made of Ti-based agglomerates

Mono- and double-layer porous scaffolds were successfully fabricated using ball-milled agglomerates of Ti and Ti-10Nb-3Mo alloy. For selectively controlling the level of porosity and pore size, the agglomerates were sieved into two different size fractions of 100-300μm and 300-500μm. Compressive mechanical properties were measured on a series of cylindrical sintered compacts with different ratios of solid core diameter to porous layer width. The graded porous scaffolds exhibited stress-strain curves typical for metallic foams with a defined plateau region after yielding. The compressive strengths and elastic moduli ranged from 300 to 700MPa and 14 to 55GPa, respectively, depending on the core diameter and the material used. The obtained properties make these materials suitable for load-bearing implant applications.

Development of a Coupling Model for Fluid-Structure Interaction using the Mesh-free Finite Element Method and the Lattice Boltzmann Method

In the presented thesis work, the meshfree method with distance fields was coupled with the lattice Boltzmann method to obtain solutions of fluid-structure interaction problems. The thesis work involved development and implementation of numerical algorithms, data structure, and software. Numerical and computational properties of the coupling algorithm combining the meshfree method with distance fields and the lattice Boltzmann method were investigated. Convergence and accuracy of the methodology was validated by analytical solutions. The research was focused on fluid-structure interaction solutions in complex, mesh-resistant domains as both the lattice Boltzmann method and the meshfree method with distance fields are particularly adept in these situations. Furthermore, the fluid solution provided by the lattice Boltzmann method is massively scalable, allowing extensive use of cutting edge parallel computing resources to accelerate this phase of the solution process. The meshfree method with distance fields allows for exact satisfaction of boundary conditions making it possible to exactly capture the effects of the fluid field on the solid structure.

Investigating the mesh dependency and upscaling of 3D grain-based models for the simulation of brittle fracture processes in low-porosity crystalline rock

The application of 3D grain-based modelling techniques is investigated in both small and large scale 3DEC models, in order to simulate brittle fracture processes in low-porosity crystalline rock. Mesh dependency in 3D grain-based models (GBMs) is examined through a number of cases to compare Voronoi and tetrahedral grain assemblages. Various methods are used in the generation of tessellations, each with a number of issues and advantages. A number of comparative UCS test simulations capture the distinct failure mechanisms, strength profiles, and progressive damage development using various Voronoi and tetrahedral GBMs. Relative calibration requirements are outlined to generate similar macro-strength and damage profiles for all the models. The results confirmed a number of inherent model behaviors that arise due to mesh dependency. In Voronoi models, inherent tensile failure mechanisms are produced by internal wedging and rotation of Voronoi grains. This results in a combined dependence on frictional and cohesive strength. In tetrahedral models, increased kinematic freedom of grains and an abundance of straight, connected failure pathways causes a preference for shear failure. This results in an inability to develop significant normal stresses causing cohesional strength dependence. In general, Voronoi models require high relative contact tensile strength values, with lower contact stiffness and contact cohesional strength compared to tetrahedral tessellations. Upscaling of 3D GBMs is investigated for both Voronoi and tetrahedral tessellations using a case study from the AECL’s Mine-by-Experiment at the Underground Research Laboratory. An upscaled tetrahedral model was able to reasonably simulate damage development in the roof forming a notch geometry by adjusting the cohesive strength. An upscaled Voronoi model underestimated the damage development in the roof and floor, and overestimated the damage in the side-walls. This was attributed to the discretization resolution limitations.

Cobalt carbonate hydroxide nanowire array on ti mesh: an efficient and robust 3D catalyst for on-demand hydrogen generation from alkaline naBH4 solution.

In this work, for the first time, a cobalt carbonate hydroxide (Co(CO3 )0.5 (OH)⋅0.11 H2 O) nanowire array on Ti mesh (CHNA/Ti) was applied to drive the dehydrogenation of alkaline NaBH4 solution for on-demand hydrogen production. Compared with other nanostructured Co-based catalyst systems, CHNA/Ti can be activated more quickly and separated easily from fuel solutions. This self-supported cobalt salt nanowire array catalyst works as an efficient and robust 3D catalyst for the hydrolysis reaction of NaBH4 with a hydrogen generation rate of 4000 mL min(-1)  gCo (-1) and a low apparent activation energy of 39.78 kJ mol(-1) and offers an attractive system for on-demand hydrogen generation.