An error diffusion based method to generate functionally graded cellular structures

The spatial variation of cell size in a functionally graded cellular structure is achieved using error diffusion to convert a continuous tone image into binary form. Effects of two control parameters, greyscale value and resolution on the resulting cell size measures were investigated. Variation in cell edge length was greatest for the Voronoi connection scheme, particularly at certain parameter combinations. Relationships between these parameters and cell size were identified and applied to an example, where the target was to control the minimum and maximum cell size. In both cases there was an 8% underestimation of cell area for target regions

Emergence of fractal geometries in the evolution of a metabolic enzyme

Fractals are patterns that are self-similar across multiple length-scales. Macroscopic fractals are common in nature; however, so far, molecular assembly into fractals is restricted to synthetic systems. Here we report the discovery of a natural protein, citrate synthase from the cyanobacterium Synechococcus elongatus, which self-assembles into Sierpiński triangles. Using cryo-electron microscopy, we reveal how the fractal assembles from a hexameric building block. Although different stimuli modulate the formation of fractal complexes and these complexes can regulate the enzymatic activity of citrate synthase in vitro, the fractal may not serve a physiological function in vivo. We use ancestral sequence reconstruction to retrace how the citrate synthase fractal evolved from non-fractal precursors, and the results suggest it may have emerged as a harmless evolutionary accident. Our findings expand the space of possible protein complexes and demonstrate that intricate and regulatable assemblies can evolve in a single substitution

Structures ordonnées dans les systèmes avec des interactions à longue portée

The central paradigm in the emerging field of metamaterials is that the properties of a material are in certain cases governed rather by the well-ordered spatial arrangement of its constituent particles than by the properties of those particles themselves. Since such highly ordered patterns can act as waveguides for acoustic, elastic, or electromagnetic waves, they can give rise to novel material properties, opening up new avenues in materials design. The central problem of how to produce the required ordered particle arrangements, e.g., via self-assembly, has received significant attention both from the experimental and theoretical sides.In theoretical studies, the interactions between particles are modeled via potential functions, whose shape and range have a profound impact on the formed structures. These potentials are often short-ranged, i.e., they are characterized by a rapid decay with distance. In this thesis, we focus on systems featuring long-range interactions, where particles interact over significantly larger distances than the mean inter-particle separation. Typical examples for such potentials are charged or multipolar interactions.In our approach, we first determine the ordered structures formed by the particles at vanishing temperature by minimizing the relevant thermodynamic potential. We observe a surprising plethora of different structural archetypes as well as novel phase transition scenarios. Then, we investigate the stability of these structures at low temperatures using Monte Carlo simulations.L'un des concepts fondamentaux dans l'étude des métamatériaux est que, dans certains cas, les propriétés du milieu sont déterminées par l'arrangement structurel de ses composants plutôt que par les propriétés intrinsèques des particules. De telles structures hautement ordonnées peuvent servir de guide d'onde en acoustique, ainsi que pour des ondes élastiques ou électromagnétiques ; elles peuvent aussi induire de nouvelles propriétés, ouvrant ainsi de nouvelles perspectives dans la conception des matériaux. Dans ce champ de recherche, la question centrale est de trouver comment produire ces arrangements ordonnés de particules et de molécules ; par exemple, un grand nombre d'études expérimentales et théoriques s'appuient sur des mécanismes d'auto-assemblage.Dans les études théoriques, ainsi que dans les simulations numériques, les interactions entre les constituants sont déterminées par des potentiels modèles ou effectifs dont la portée et la forme déterminent les structures collectives. Les potentiels utilisés sont souvent à courte portée, c'est-à-dire qu'ils ont une décroissance très rapide avec la distance ; typiquement, des molécules séparées de quelques diamètres moléculaires n'interagissent pas directement. Dans cette thèse, nous nous intéressons à ces structures ordonnées qu'il est possible d'obtenir, non pas avec des interactions à courte portée, mais avec des interactions à très longue portée (Coulomb, etc.). Notre démarche consiste dans un premier temps à déterminer les structures optimales à température nulle (états fondamentaux) en minimisant le potentiel thermodynamique adéquat ; puis, nous étudions la stabilité thermique de ces structures à basse température à l'aide de simulations numériques de Monte-Carlo. Nous observons une pléthore de structures prototypes, ainsi que des transitions de phases entre elles

Automatic Mesh Repair and Optimization for Quality Mesh Generation

Ph.DDOCTOR OF PHILOSOPH

Analysing and Enhancing the Coarse Registration Pipeline

The current and continual development of sensors and imaging systems capable of acquiring three-dimensional data provides a novel form in which the world can be expressed and examined. The acquisition process, however, is often limited by imaging systems only being able to view a portion of a scene or object from a single pose at a given time. A full representation can still be produced by shifting the system and registering subsequent acquisitions together. While many solutions to the registration problem have been proposed, there is no quintessential approach appropriate for all situations. This dissertation aims to coarsely register range images or point-clouds of a priori unknown pose by matching their overlapping regions. Using spherical harmonics to correlate normals in a coarse registration pipeline has been shown previously to be an effective means for registering partially overlapping point-clouds. The advantage of normals is their translation invariance, which permits the rotation and translation to be decoupled and determined separately. Examining each step of this pipeline in depth allows its registration capability to be quantified and identifies aspects which can be enhanced to further improve registration performance. The pipeline consists of three primary steps: identifying the rotation using spherical harmonics, identifying the translation in the Fourier domain, and automatically verifying if alignment is correct. Having achieved coarse registration, a fine registration algorithm can be used to refine and complete the alignment. Major contributions to knowledge are provided by this dissertation at each step of the pipeline. Point-clouds with known ground-truth are used to examine the pipeline's capability, allowing its limitations to be determined; an analysis which has not been performed previously. This examination allowed modifications to individual components to be introduced and measured, establishing their provided benefit. The rotation step received the greatest attention as it is the primary weakness of the pipeline, especially as the nature of the overlap between point-clouds is unknown. Examining three schemes for binning normals found that equiangular binning, when appropriately normalised, only had a marginal decrease in accuracy with respect to the icosahedron and the introduced Fibonacci schemes. Overall, equiangular binning was the most appropriate due to its natural affinity for fast spherical-harmonic conversion. Weighting normals was found to provide the greatest benefit to registration performance. The introduction of a straightforward method of combining two different weighting schemes using the orthogonality of complex values increased correct alignments by approximately 80% with respect to the next best scheme; additionally, point-cloud pairs with overlap as low as 5% were able to be brought into correct alignment. Transform transitivity, one of two introduced verification strategies, correctly classified almost 100% of point-cloud pair registrations when there are sufficient correct alignments. The enhancements made to the coarse registration pipeline throughout this dissertation provide significant improvements to its performance. The result is a pipeline with state-of-the-art capabilities that allow it to register point-cloud with minimal overlap and correct for alignments that are classified as misaligned. Even with its exceptional performance, it is unlikely that this pipeline has yet reached its pinnacle, as the introduced enhancements have the potential for further development

A Virtual Grain Structure Representation System for Micromechanics Simulations

Representing a grain structure within a combined finite element computer aided engineering environment is essential for micromechanics simulations. Methods are required to effectively generate high-fidelity virtual grain structures for accurate studies. A high-fidelity virtual grain structure means a statistically equivalent structure in conjunction with desired grain size distribution features, and must be represented with realistic grain morphology. A family of controlled Poisson Voronoi tessellation (CPVT) models have been developed in this work for systematically generating virtual grain structures with the aforementioned properties. Three tasks have been accomplished in the development of the CPVT models: (i) defining the grain structure’s regularity that specifies the uniformity of a tessellation as well as deriving a control parameter based on the regularity; (ii) modelling the mapping from a grain structure’s regularity to its grain size distribution; and (iii) establishing the relation between a set of physical parameters and a distribution function. A one-gamma distribution function is used to describe a grain size distribution characteristic and a group of four physical parameters are employed to represent the metallographic measurements of a grain size distribution property. Mathematical proofs of the uniqueness of the determination of the distribution parameter from the proposed set of physical parameters have been studied, and an efficient numerical procedure is provided for computing the distribution parameter. Based on the general scheme, two- and three-dimensional CPVT models have been formulated, which respectively define the quantities of regularity and control parameters, and model the mapping between regularity and grain size distribution. For the 2D-CPVT model, statistical tests have been carried out to validate the accuracy and robustness of regularity and grain size distribution control. In addition, micrographs with different grain size distribution features are employed to examine the capability of the 2D-CPVT model to generate virtual grain structures that meet physical measurements. A crystal plasticity finite element (CPFE) simulation of plane strain uniaxial tension has been performed to show the effect of grain size distribution on local strain distribution. For the 3D-CPVT model, a set of CPFE analyses of micro-pillar compression have been run and the effects of both regularity and grain size on deformation responses investigated. Further to this, a multi-zone scheme is proposed for the CPVT models to generate virtual gradient grain structures. In conjunction with the CPVT model that controls the seed generating process within individual zones, the multi-zone CPVT model has been developed by incorporating a novel mechanism of controlling the seed generation for grains spanning different zones. This model has the flexibility of generating various gradient grain structures and the natural morphology for interfacial grains between adjacent zones. Both of the 2D- and 3D-CPVT models are capable of generating a virtual grain structure with a mean grain size gradient for the grain structure domain and grain size distribution control for individual zones. A true gradient grain structure, two simulated gradient grain structure, and a true gradient grain structure with an elongated zone have been used to examine the capability of the multi-zone CPVT model. To facilitate the CPFE analyses of inter-granular crack initiation and evolution using the cohesive zone models, a Voronoi tessellation model with non-zero thickness cohesive zone representation was developed. A grain boundary offsetting algorithm is proposed to efficiently produce the cohesive boundaries for a Voronoi tessellation. The most challenging issue of automatically meshing multiple junctions with quadrilateral elements has been resolved and a rule-based method is presented to perform the automatically partitioning of cohesive zone junctions, including data representation, edge event processing and cut-trim operations. In order to demonstrate the novelty of the proposed cohesive zone modelling and junction partitioning schemes, the CPFE simulations of plane strain uniaxial tension and three point bending have been studied. A software system, VGRAIN, was developed to implement the proposed virtual grain structure modelling methods. Via user-friendly interfaces and the well-organised functional modules a virtual grain structure can be automatically generated to a very large-scale with the desired grain morphology and grain size properties. As a pre-processing grain structure representation system, VGRAIN is also capable of defining crystallographic orientations and mechanical constants for a generated grain structure. A set of additional functions has also been developed for users to study a generated grain structure and verify the feasibility of the generated case for their simulation requirements. A well-built grain structure model in VGRAIN can be easily exported into the commercial FE/CAE platform, e.g. ABAQUS and DEFORM, via script input, whereby the VGRAIN system is seamlessly integrated into CPFE modelling and simulation processing

Тhe benefits of an additional practice in descriptive geometry course: non obligatory workshop at the Faculty of civil engineering in Belgrade

At the Faculty of Civil Engineering in Belgrade, in the Descriptive geometry (DG) course, non-obligatory workshops named “facultative task” are held for the three generations of freshman students with the aim to give students the opportunity to get higher final grade on the exam. The content of this workshop was a creative task, performed by a group of three students, offering free choice of a topic, i.e. the geometric structure associated with some real or imagery architectural/art-work object. After the workshops a questionnaire (composed by the professors at the course) is given to the students, in order to get their response on teaching/learning materials for the DG course and the workshop. During the workshop students performed one of the common tests for testing spatial abilities, named “paper folding". Based on the results of the questionnairethe investigation of the linkages between:students’ final achievements and spatial abilities, as well as students’ expectations of their performance on the exam, and how the students’ capacity to correctly estimate their grades were associated with expected and final grades, is provided. The goal was to give an evidence that a creative work, performed by a small group of students and self-assessment of their performances are a good way of helping students to maintain motivation and to accomplish their achievement. The final conclusion is addressed to the benefits of additional workshops employment in the course, which confirmhigherfinal scores-grades, achievement of creative results (facultative tasks) and confirmation of DG knowledge adaption

Optimization Based Coverage Path Planning for Autonomous 3D Data Acquisition

The demand for 3D models that represent real-world objects such as structures and buildings has increased in recent years. It is becoming increasingly important that the reconstructions are not only visually convincing but also feature high geometric accuracy. This includes, for example, the fields of civil engineering, terrestrial surveying and archeology, where precise measurements are made in the models for documentation and analysis purposes. There are different approaches to create such a reconstruction. The photogrammetric method Structure from Motion and laser scanning are among the most widely used methods here, as they do not require a complicated setup and can be used for scenarios at small to large scale. Recent developments are enabling unmanned robotic systems, especially sensor mounted UAVs, to assist in the recording of areas which are otherwise difficult to observe. The demand for a high geometric accuracy, however, comes at the expense of high computational complexity of up to several days. Hence, especially real-time reconstructions are unfeasible, such that recording and reconstruction procedure must be executed consecutively. The resulting model quality, i.e. completeness and accuracy, is only assessable afterwards. Since it is often difficult or even impossible to improve these models with additional measurements afterwards, methods that ensure a reliable acquisition of sufficient data is required. In this thesis we develop new methods and theory that address this problem for the mentioned sensor types. For both, a probabilistic description of the expected surface reconstruction error is maintained cost-efficiently as an estimate for the model quality during the recording procedure. For image sensors this is realized by incrementally constructing confidence ellipsoids that describe the information obtained from all views. With depth sensors the surface quality is described by the variance of a Gaussian process implicit surface regression fit to point cloud data using polyharmonic kernel functions. Sensor poses are then assessed by the information they add to the subsequent reconstruction up to a desired geometric accuracy using a formulation that is motivated from Optimal Experimental Design. This quantity is further used in an iterative next-best-view selection framework as a subproblem of a coverage path planning problem. The general formulations presented in this thesis enables a wide range of applications, such as offline and online view planning or various autonomous robot systems under consideration of dynamic and geometric constraints. We present the first multi-view coverage path planning approach, specifically targeted at autonomous Structure from Motion data acquisition. Its correctness is validated in simulation using the physics simulator Gazebo. Furthermore, we lay a foundation for similar applications with depth sensors. All presented algorithms were developed with scalability in mind and show promising results regarding real-time usability