On Universal Tilers

A famous problem in discrete geometry is to find all monohedral plane tilers, which is still open to the best of our knowledge. This paper concerns with one of its variants that to determine all convex polyhedra whose every cross-section tiles the plane. We call such polyhedra universal tilers. We obtain that a convex polyhedron is a universal tiler only if it is a tetrahedron or a pentahedron.Comment: 10 pages, 2 figure

Multiscale Modeling of Amphibian Neurulation

This thesis presents a whole-embryo finite element model of neurulation -- the first of its kind. An advanced, multiscale finite element approach is used to capture the mechanical interactions that occur across cellular, tissue and whole-embryo scales. Cell-based simulations are used to construct a system of constitutive equations for embryonic tissue fabric evolution under different scenarios including bulk deformation, cell annealing, mitosis, and Lamellipodia effect. Experimental data are used to determine the parameters in these equations. Techniques for obtaining images of live embryos, serial sections of fixed embryo fabric parameters, and material properties of embryonic tissues are used. Also a spatial-temporal correlation system is introduced to organize and correlate the data and to construct the finite element model. Biological experiments have been conducted to verify the validity of this constitutive model. A full functional finite element analysis package has been written and is used to conduct computational simulations. A simplified contact algorithm is introduced to address the element permeability issue. Computational simulations of different cases have been conducted to investigate possible causes of neural tube defects. Defect cases including neural plate defect, non-neural epidermis defect, apical constriction defect, and convergent extension defect are compared with the case of normal embryonic development. Corresponding biological experiments are included to support these defect cases. A case with biomechanical feedbacks on non-neural epidermis is also discussed in detail with biological experiments and computational simulations. Its comparison with the normal case indicates that the introduction of biomechanical feedbacks can yield more realistic simulation results

Momentum transfer during the impact of granular matter with inclined sliding surfaces

© 2017 Elsevier Ltd Increasing the inclination of a rigid surface that is impacted by a collimated granular flow reduces the fraction of granular matter momentum transferred to the surface. Recent studies have shown that the momentum reduction depends upon a frictional interaction between the granular flow and the impacted surface. High coefficient of friction surfaces suffer significantly more momentum transfer than predicted by resolution of the incident momentum onto the inclined plane. This discovery has raised the possibility that inclined surfaces with very low friction coefficients might reduce the impulsive transferred by the impact of high velocity granular matter. Here the use of a lubricated sliding plate is investigated as a means for reducing interfacial friction and impulse transfer to an inclined surface. The study uses a combination of experimental testing and particle-based simulations to investigate impulse transfer to rigid aluminum surfaces inclined either perpendicular or at 53° to synthetic sand that was impulsively accelerated to a velocity of 350–500 m/s. The study shows that impact of this sand with lubricated plates attached to an inclined surface rapidly accelerates them to a velocity of about 55–70 m/s, and reduces the impulse transferred to the inclined surface below. The reduction of impulse by this approach is comparable to that achieved by changing the inclination of the surface.This research was funded by the Defense Advanced Research Projects Agency (DARPA) under grant number W91CRB-11-1-0005 (Program manager, Dr. J. Goldwasser)

At-Most-Hexa Meshes

AbstractVolumetric polyhedral meshes are required in many applications, especially for solving partial differential equations on finite element simulations. Still, their construction bears several additional challenges compared to boundary‐based representations. Tetrahedral meshes and (pure) hex‐meshes are two popular formats in scenarios like CAD applications, offering opposite advantages and disadvantages. Hex‐meshes are more intricate to construct due to the global structure of the meshing, but feature much better regularity, alignment, are more expressive, and offer the same simulation accuracy with fewer elements. Hex‐dominant meshes, where most but not all cell elements have a hexahedral structure, constitute an attractive compromise, potentially unlocking benefits from both structures, but their generality makes their employment in downstream applications difficult. In this work, we introduce a strict subset of general hex‐dominant meshes, which we term 'at‐most‐hexa meshes', in which most cells are still hexahedral, but no cell has more than six boundary faces, and no face has more than four sides. We exemplify the ease of construction of at‐most‐hexa meshes by proposing a frugal and straightforward method to generate high‐quality meshes of this kind, starting directly from hulls or point clouds, for example, from a 3D scan. In contrast to existing methods for (pure) hexahedral meshing, ours does not require an intermediate parameterization of other costly pre‐computations and can start directly from surfaces or samples. We leverage a Lloyd relaxation process to exploit the synergistic effects of aligning an orientation field in a modified 3D Voronoi diagram using the norm for cubical cells. The extracted geometry incorporates regularity as well as feature alignment, following sharp edges and curved boundary surfaces. We introduce specialized operations on the three‐dimensional graph structure to enforce consistency during the relaxation. The resulting algorithm allows for an efficient evaluation with parallel algorithms on GPU hardware and completes even large reconstructions within minutes

Fluid–structure interaction analysis of eccentricity and leaflet rigidity on thrombosis biomarkers in bioprosthetic aortic valve replacements

This work intends to study the effect of aortic annulus eccentricity and leaflet rigidity on the performance, thrombogenic risk and calcification risk in bioprosthetic aortic valve replacements (BAVRs). To address these questions, a two-way immersed fluid–structure interaction (FSI) computational model was implemented in a high-performance computing (HPC) multi-physics simulation software, and validated against a well-known FSI benchmark. The aortic valve bioprosthesis model is qualitatively contrasted against experimental data, showing good agreement in closed and open states. Regarding the performance of BAVRs, the model predicts that increasing eccentricities yield lower geometric orifice areas (GOAs) and higher normalized transvalvular pressure gradients (TPGs) for healthy cardiac outputs during systole, agreeing with in vitro experiments. Regions with peak values of residence time are observed to grow with eccentricity in the sinus of Valsalva, indicating an elevated risk of thrombus formation for eccentric configurations. In addition, the computational model is used to analyze the effect of varying leaflet rigidity on both performance, thrombogenic and calcification risks with applications to tissue-engineered prostheses. For more rigid leaflets it predicts an increase in systolic and diastolic TPGs, and decrease in systolic GOA, which translates to decreased valve performance. The peak shear rate and residence time regions increase with leaflet rigidity, but their volume-averaged values were not significantly affected. Peak solid stresses are also analyzed, and observed to increase with rigidity, elevating risk of valve calcification and structural failure. To the authors' knowledge this is the first computational FSI model to study the effect of eccentricity or leaflet rigidity on thrombogenic biomarkers, providing a novel tool to aid device manufacturers and clinical practitioners.This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 713673. The research leading to these results has also received funding from “la Caixa” Foundation, with fellowship ID: LCF/BQ/DI18/11660044, and has been co-funded by the project CompBioMed2 (H2020-EU.1.4.1.3. Grant No. 823712)Peer ReviewedPostprint (published version

Development of a coupling approach for multi-physics analyses of fusion reactors

An integrated multi-physics coupling system has been developed for fusion reactor systems analyses. This system has an advanced Monte Carlo (MC) modeling approach for converting complex CAD models to MC models with hybrid constructive solid and unstructured mesh geometries, and a high-fidelity coupling approach for data mapping from MC to thermal hydraulics and structural mechanics codes. The system was proven to be reliable, robust and efficient through verification calculations

Comparison of calculated and measured temperature fields in laser-heated thin film systems

Thermal modelling of the laser processing of nanoparticulate ITO films has been carried out with models of varying complexity. The results from a simple semi-analytical 1D model and numerical 1D, 2D and 2D-axisymmetric models are reported for continuous wave HeCd laser and nanosecond pulsed XeCl laser irradiation. These results are compared to thermal camera measurements to determine the validity of the models under the different laser regimes.For continuous wave laser heating, it is shown that heat flow out of the laser irradiated volume significantly affects the predicted peak temperature rise. Models with fewer dimensions overestimate the temperature change, by a factor of over 100 times in the worst cases, due to the lack of lateral heat conduction. Consequently, meaningful temperatures are only calculated with 2D-axisymmetric or 3D models. When considering nanosecond pulsed lasers, the energy absorbed does not have enough time during the pulse to diffuse away from the volume in which it was deposited. Because of this, lateral heat flow is less important during heating and all the numerical models converge to the same predicted peak temperature rise. This allows much less computationally taxing models to be solved whilst obtaining the same result.The optical properties of the film are shown to be significant in determining the rate of laser induced heating and resultant temperature rise. However, for continuous wave irradiation, the models were insensitive to changes in the thermal parameters of the film and the peak temperature is controlled by the thermal parameters of the substrate. The opposite is true for the nanosecond pulsed lasers, with the thermal parameters of the film drastically affecting the temperature rise and the substrate parameters only contributing to the cooling which occurred over longer timescales. The differing sensitivity of the models to these parameters has been attributed to the rates of heating under the different laser regimes