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The purpose of this project is to test and, if necessary, refine a model of the public sphere known as the circulation of power model. The model faces several criticisms and was applied in a case study only once. It has not yet been applied to an American context.

This study uses the circulation of power model as a framework in a historical case study of a regional public library system in the United States. The temporal boundaries of the case are from 1924 to 2016.

This study resulted in a new and modified model called the tessellation model. New concepts in the tessellation model include circuits, tessellations, formal decisions and decision cycles. New distinctions in the model include narrowcast/broadcast and coalesced public/diffuse public.

The tessellation model and its associated concepts offer a new way to describe and analyze deliberative systems over time. The model requires further testing in other contexts.

The tessellation model is a new and validated way to describe the public sphere in an American political context.

The “chiralisation” of Euclidean polygonal tessellations is a novel, recent method which has been used to design new auxetic metamaterials with complex topologies and improved geometric versatility over traditional chiral honeycombs. This paper aims to design and manufacture chiral honeycombs representative of four distinct classes of 2D Euclidean tessellations with hexagonal rotational symmetry using fused-deposition additive manufacturing and experimentally analysed the mechanical properties and failure modes of these metamaterials.

Finite Element simulations were also used to study the high-strain compressive performance of these systems under both periodic boundary conditions and realistic, finite conditions. Experimental uniaxial compressive loading tests were applied to additively manufactured prototypes and digital image correlation was used to measure the Poisson’s ratio and analyse the deformation behaviour of these systems.

The results obtained demonstrate that these systems have the ability to exhibit a wide range of Poisson’s ratios (positive, quasi-zero and negative values) and stiffnesses as well as unusual failure modes characterised by a sequential layer-by-layer collapse of specific, non-adjacent ligaments. These findings provide useful insights on the mechanical properties and deformation behaviours of this new class of metamaterials and indicate that these chiral honeycombs could potentially possess anomalous characteristics which are not commonly found in traditional chiral metamaterials based on regular monohedral tilings.

To the best of the authors’ knowledge, the authors have analysed for the first time the high strain behaviour and failure modes of chiral metamaterials based on Euclidean multi-polygonal tessellations.

We describe a novel mathematical approach to deriving and solving covolume models of the incompressible 2‐D Navier‐Stokes flow equations. The approach integrates three technical components into a single modelling algorithm: 1. Automatic Grid Generation. An algorithm is described and used to automatically discretize the flow domain into a Delaunay triangulation and a dual Voronoi polygonal tessellation. 2. Covolume Finite Difference Equation Generation. Three covolume discretizations of the Navier‐Stokes equations are presented. The first scheme conserves mass over triangular control volumes, the second scheme over polygonal control volumes and the third scheme conserves mass over both. Simple consistent finite difference equations are derived in terms of the primitive variables of velocity and pressure. 3. Dual Variable Reduction. A network theoretic technique is used to transform each of the finite difference systems into equivalent systems which are considerably smaller than the original primitive finite difference system.

We describe a new mathematical approach for deriving and solving covolume models of the three‐dimensional, incompressible Navier—Stokes flow equations. The approach integrates three technical components into a single modelling algorothm: automatic grid generation; covolume equation generation; dual variable reduction.

Virtual assembly (VA) based on virtual reality (VR) is a key technique of virtual manufacturing. It provides not only an intuitive and interactive interface for virtual product design, but also an efficient method to analyze or verify assembly performance of these products. Preliminary investigations of constructing a VA system were implemented in this paper. There were three key techniques in constructing a VA system, which were data transformation from CAD system to VA system, collision detection, and virtual manipulation with a virtual hand. These key techniques were analyzed further and their concrete algorithms were given. At last an experimental VA system was set‐up to verify these algorithms. It is proved that the transformed data are sufficient, which can satisfy the VA system's requirement; the collision detection algorithm is efficient as it assures the system to be real time; and the virtual manipulation algorithm guarantees the system's reality and maneuverability.

Sizing functions are crucial inputs for unstructured mesh generation since they determine the element distributions of resulting meshes to a large extent. Meanwhile, automating the procedure of creating a sizing function is a prerequisite to set up a fully automatic mesh generation pipeline. In this paper, an automatic algorithm is proposed to create a high-quality sizing function for an unstructured surface and volume mesh generation by using a triangular mesh as the background mesh.

A practically efficient and effective solution is developed by using local operators carefully to re-mesh the tessellation of the input Computer Aided Design (CAD) models. A nonlinear programming (NLP) problem has been formulated to limit the gradient of the sizing function, while in this study, the object function of this NLP is replaced by an analytical equation that predicts the number of elements. For the query of the sizing value, an improved algorithm is developed by using the axis-aligned bounding box (AABB) tree structure.

The local operations of re-meshing could effectively and efficiently resolve the banding issue caused by using the default tessellation of the model to define a sizing function. Experiments show that the solution of the revised NLP, in most cases, could provide a better solution at the lower cost of computational time. With the help of the AABB tree, the sizing function defined at a surface background mesh can be also used as the input of volume mesh generation.

Theoretical analysis reveals that the construction of the initial sizing function could be reduced to the solution of an optimization problem. The definitions of the banding elements and surface proximity are also given. Under the guidance of this theoretical analysis, re-meshing and ray-casting technologies are well-designed to initial the sizing function. Smoothing with the revised NLP and querying by the AABB tree, the paper provides an automatic method to get a high-quality sizing function for both surface and volume mesh generation.

Accurate presentation of the rock microstructure is critical to the grain-scale analysis of rock deformation and failure in numerical modelling. 3D granite microstructure modelling has only been used in limited studies with the mineral pattern often remaining poorly constructed. In this study, the authors developed a new approach for generating 2D and 3D granite microstructure models from a 2D image by combining a heterogeneous material reconstruction method (simulated annealing method) with Voronoi tessellation.

More specifically, the stochastic information in the 2D image is first extracted using the two-point correlation function (TPCF). Then an initial 2D or 3D Voronoi diagram with a random distribution of the minerals is generated and optimised using a simulated annealing method until the corresponding TPCF is consistent with that in the 2D image. The generated microstructure model accurately inherits the stochastic information (e.g. volume fraction and mineral pattern) from the 2D image. Lastly, the authors compared the topological characteristics and mechanical properties of the 2D and 3D reconstructed microstructure models with the model obtained by direct mapping from the 2D image of a real rock sample.

The good agreements between the mapped and reconstructed models indicate the accuracy of the reconstructed microstructure models on topological characteristics and mechanical properties.

The newly developed reconstruction method successfully transfers the mineral pattern from a granite sample into the 2D and 3D Voronoi-based microstructure models ready for use in grain-scale modelling.

This study aims to perform flow simulations inside the acinus with fine alveolar pores (Kohn pores) using hexagonal cells and bottom-up geometric modeling, which enabled the elimination of invalid voids using previous top-bottom methods and spherical or circular cells.

Regular hexagonal cells were used to construct alveoli with no gaps via tessellation. Some hexagonal cells were fused to eliminate the inner boundaries to represent the structure of the bronchial tree. For the remaining hexagonal cells, the side lengths of the shared walls were adjusted to construct alveolar pores. Periodic moving boundaries with the same phase were set for all walls to describe synchronous contraction and expansion of the bronchi and alveoli.

More realistic flow characteristics in the distal lung were obtained. The effects of pore size and the mechanism of auxiliary ventilation of alveolar pores were revealed.

To the best of the authors’ knowledge, this is the first numerical simulation study on the function of multiple alveolar pores at the level of pulmonary acini, which will be helpful for simulating the dynamic process of cough and sputum excretion in the future.

A set of algorithms has been developed and evaluated for 3D and 21/2D rapid prototyping replication of 3D reconstructions of cancellous bone samples. The algorithms replicate a voxel map without any loss of fidelity, so as to increase the validity of the comparison of mechanical tests on the 3D reconstructed models with those predicted by finite element analyses. The evaluation is both in terms of algorithmic complexity and the resultant data set size. The former determines the feasibility of the conversion process, whereas the latter the potential success of the manufacturing process. The algorithms and their implementation in PC software is presented.

The extended Delaunay tessellation (EDT) is presented in this paper as the unique partition of a node set into polyhedral regions defined by nodes lying on the nearby Voronoï spheres. Until recently, all the FEM mesh generators were limited to the generation of tetrahedral or hexahedral elements (or triangular and quadrangular in 2D problems). The reason for this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements. Nowadays, there are several acceptable shape functions for a very large class of polyhedra. These new shape functions, together with the EDT, gives an optimal combination and a powerful tool to solve a large variety of physical problems by numerical methods. The domain partition into polyhedra presented here does not introduce any new node nor change any node position. This makes this process suitable for Lagrangian problems and meshless methods in which only the connectivity information is used and there is no need for any expensive smoothing process.