The scaling and skewness of optimally transported meshes on the sphere

In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of interest, without modifying the connectivity of the mesh. Key to the success of these methods is that the mesh should be sufficiently refined (locally) and flexible in order to resolve evolving solution features, but at the same time not introduce errors through skewness and lack of regularity. Some state-of-the-art methods are bottom-up in that they attempt to prescribe both the local cell size and the alignment to features of the solution. However, the resulting problem is overdetermined, necessitating a compromise between these conflicting requirements. An alternative approach, described in this paper, is to prescribe only the local cell size and augment this an optimal transport condition to provide global regularity. This leads to a robust and flexible algorithm for generating meshes fitted to an evolving solution, with minimal need for tuning parameters. Of particular interest for geophysical modelling are meshes constructed on the surface of the sphere. The purpose of this paper is to demonstrate that meshes generated on the sphere using this optimal transport approach have good a-priori regularity and that the meshes produced are naturally aligned to various simple features. It is further shown that the sphere's intrinsic curvature leads to more regular meshes than the plane. In addition to these general results, we provide a wide range of examples relevant to practical applications, to showcase the behaviour of optimally transported meshes on the sphere. These range from axisymmetric cases that can be solved analytically to more general examples that are tackled numerically. Evaluation of the singular values and singular vectors of the mesh transformation provides a quantitative measure of the mesh aniso...Comment: Updated following reviewer comment

Cartography

The terrestrial space is the place of interaction of natural and social systems. The cartography is an essential tool to understand the complexity of these systems, their interaction and evolution. This brings the cartography to an important place in the modern world. The book presents several contributions at different areas and activities showing the importance of the cartography to the perception and organization of the territory. Learning with the past or understanding the present the use of cartography is presented as a way of looking to almost all themes of the knowledge

Modeling and simulation in tribology across scales: An overview

This review summarizes recent advances in the area of tribology based on the outcome of a Lorentz Center workshop surveying various physical, chemical and mechanical phenomena across scales. Among the main themes discussed were those of rough surface representations, the breakdown of continuum theories at the nano- and micro-scales, as well as multiscale and multiphysics aspects for analytical and computational models relevant to applications spanning a variety of sectors, from automotive to biotribology and nanotechnology. Significant effort is still required to account for complementary nonlinear effects of plasticity, adhesion, friction, wear, lubrication and surface chemistry in tribological models. For each topic, we propose some research directions

Composing quadrilateral meshes for animation

The modeling-by-composition paradigm can be a powerful tool in modern animation pipelines. We propose two novel interactive techniques to compose 3D assets that enable the artists to freely remove, detach and combine components of organic models. The idea behind our methods is to preserve most of the original information in the input characters and blend accordingly where necessary. The first method, QuadMixer, provides a robust tool to compose the quad layouts of watertight pure quadrilateral meshes, exploiting the boolean operations defined on triangles. Quad Layout is a crucial property for many applications since it conveys important information that would otherwise be destroyed by techniques that aim only at preserving the shape. Our technique keeps untouched all the quads in the patches which are not involved in the blending. The resulting meshes preserve the originally designed edge flows that, by construction, are captured and incorporated into the new quads. SkinMixer extends this approach to compose skinned models, taking into account not only the surface but also the data structures for animating the character. We propose a new operation-based technique that preserves and smoothly merges meshes, skeletons, and skinning weights. The retopology approach of QuadMixer is extended to work on quad-dominant and arbitrary complex surfaces. Instead of relying on boolean operations on triangle meshes, we manipulate signed distance fields to generate an implicit surface. The results preserve most of the information in the input assets, blending accordingly in the intersection regions. The resulting characters are ready to be used in animation pipelines. Given the high quality of the results generated, we believe that our methods could have a huge impact on the entertainment industry. Integrated into current software for 3D modeling, they would certainly provide a powerful tool for the artists. Allowing them to automatically reuse parts of their well-designed characters could lead to a new approach for creating models, which would significantly reduce the cost of the process

Proceedings of the 2021 DigitalFUTURES

This open access book is a compilation of selected papers from 2021 DigitalFUTURES—The 3rd International Conference on Computational Design and Robotic Fabrication (CDRF 2021). The work focuses on novel techniques for computational design and robotic fabrication. The contents make valuable contributions to academic researchers, designers, and engineers in the industry. As well, readers encounter new ideas about understanding material intelligence in architecture

Design and Topology Optimisation of Tissue Scaffolds

Tissue restoration by tissue scaffolding is an emerging technique with many potential applications. While it is well-known that the structural properties of tissue scaffolds play a critical role in cell regrowth, it is usually unclear how optimal tissue regeneration can be achieved. This thesis hereby presents a computational investigation of tissue scaffold design and optimisation. This study proposes an isosurface-based characterisation and optimisation technique for the design of microscopic architecture, and a porosity-based approach for the design of macroscopic structure. The goal of this study is to physically define the optimal tissue scaffold construct, and to establish any link between cell viability and scaffold architecture. Single-objective and multi-objective topology optimisation was conducted at both microscopic and macroscopic scales to determine the ideal scaffold design. A high quality isosurface modelling technique was formulated and automated to define the microstructure in stereolithography format. Periodic structures with maximised permeability, and theoretically maximum diffusivity and bulk modulus were found using a modified level set method. Microstructures with specific effective diffusivity were also created by means of inverse homogenisation. Cell viability simulation was subsequently conducted to show that the optimised microstructures offered a more viable environment than those with random microstructure. The cell proliferation outcome in terms of cell number and survival rate was also improved through the optimisation of the macroscopic porosity profile. Additionally artificial vascular systems were created and optimised to enhance diffusive nutrient transport. The formation of vasculature in the optimisation process suggests that natural vascular systems acquire their fractal shapes through self-optimisation

COBE's search for structure in the Big Bang

The launch of Cosmic Background Explorer (COBE) and the definition of Earth Observing System (EOS) are two of the major events at NASA-Goddard. The three experiments contained in COBE (Differential Microwave Radiometer (DMR), Far Infrared Absolute Spectrophotometer (FIRAS), and Diffuse Infrared Background Experiment (DIRBE)) are very important in measuring the big bang. DMR measures the isotropy of the cosmic background (direction of the radiation). FIRAS looks at the spectrum over the whole sky, searching for deviations, and DIRBE operates in the infrared part of the spectrum gathering evidence of the earliest galaxy formation. By special techniques, the radiation coming from the solar system will be distinguished from that of extragalactic origin. Unique graphics will be used to represent the temperature of the emitting material. A cosmic event will be modeled of such importance that it will affect cosmological theory for generations to come. EOS will monitor changes in the Earth's geophysics during a whole solar color cycle

Design and Topology Optimisation of Tissue Scaffolds

Tissue restoration by tissue scaffolding is an emerging technique with many potential applications. While it is well-known that the structural properties of tissue scaffolds play a critical role in cell regrowth, it is usually unclear how optimal tissue regeneration can be achieved. This thesis hereby presents a computational investigation of tissue scaffold design and optimisation. This study proposes an isosurface-based characterisation and optimisation technique for the design of microscopic architecture, and a porosity-based approach for the design of macroscopic structure. The goal of this study is to physically define the optimal tissue scaffold construct, and to establish any link between cell viability and scaffold architecture. Single-objective and multi-objective topology optimisation was conducted at both microscopic and macroscopic scales to determine the ideal scaffold design. A high quality isosurface modelling technique was formulated and automated to define the microstructure in stereolithography format. Periodic structures with maximised permeability, and theoretically maximum diffusivity and bulk modulus were found using a modified level set method. Microstructures with specific effective diffusivity were also created by means of inverse homogenisation. Cell viability simulation was subsequently conducted to show that the optimised microstructures offered a more viable environment than those with random microstructure. The cell proliferation outcome in terms of cell number and survival rate was also improved through the optimisation of the macroscopic porosity profile. Additionally artificial vascular systems were created and optimised to enhance diffusive nutrient transport. The formation of vasculature in the optimisation process suggests that natural vascular systems acquire their fractal shapes through self-optimisation