5,571 research outputs found

    Random Directional Nearest-Neighbour Graphs

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    We look at a class of random spatial graphs constructed on random points (points of a Poisson process) in Euclidean space with edges defined by a geometrical rule based on proximity. Specifically, each point is joined by an edge to its nearest neighbour in a given direction specified by a cone. The unrestricted case is the ordinary nearest-neighbour graph; the restricted case is a version of the minimal directed spanning forest (MDSF) introduced by Bhatt & Roy. These graphs have been widely used for modelling networks with spatial content, such as in the communications sector, social networks, and transportation networks. The large-sample asymptotic behaviour of the total edge length of these graphs is our main interest. For the ordinary nearest-neighbour graph, the appropriate central limit theorem is due to Avram & Bertsimas. For the MDSF, the limit theory is known (Penrose & Wade) in two special cases, namely the 'south' and 'south-west' versions: here the limit is not normal, due to the presence of long edges near to the boundary. In this thesis, we will extend the limit theory to the case of general cones; depending on the parameters, the limit distribution may be normal, or the convolution of a normal distribution with a non-normal element due to boundary effects whose distribution can be characterized by a fixed-point equation

    Discrete modelling of continuous dynamic recrystallisation by modified Metropolis algorithm

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    Continuous dynamic recrystallisation (CDRX) is often the primary mechanism for microstructure evolution during severe plastic deformation (SPD) of polycrystalline metals. Its physically realistic simulation remains challenging for the existing modelling approaches based on continuum mathematics because they do not capture important local interactions between microstructure elements and spatial inhomogeneities in plastic strain. An effective discrete method for simulating CDRX is developed in this work. It employs algebraic topology, graph theory and statistical physics tools to represent an evolution of grain boundary networks as a sequence of conversions between low-angle grain boundaries (LAGBs) and high-angle grain boundaries (HAGBs) governed by the principle of minimal energy increase, similar to the well-known Ising model. The energy is minimised by a modified Metropolis algorithm. The model is used to predict the equilibrium fractions of HAGBs in several SPD-processed copper alloys. The analysis captures non-equilibrium features of the transitions from sub-grain structures to new HAGB-dominated grain structures and provides estimations of critical values for HAGB fractions and accumulated strain at these transitions

    Evolution of polygonal crack patterns in mud when subjected to repeated wetting-drying cycles

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    The present paper demonstrates how a natural crack mosaic resembling a random tessellation evolves with repeated 'wetting followed by drying' cycles. The natural system here is a crack network in a drying colloidal material, for example, a layer of mud. A spring network model is used to simulate consecutive wetting and drying cycles in mud layers until the crack mosaic matures. The simulated results compare favourably with reported experimental findings. The evolution of these crack mosaics has been mapped as a trajectory of a 4-vector tuple in a geometry-topology domain. A phenomenological relation between energy and crack geometry as functions of time cycles is proposed based on principles of crack mechanics. We follow the crack pattern evolution to find that the pattern veers towards a Voronoi mosaic in order to minimize the system energy. Some examples of static crack mosaics in nature have also been explored to verify if nature prefers Voronoi patterns. In this context, the authors define new geometric measures of Voronoi-ness of crack mosaics to quantify how close a tessellation is to a Voronoi tessellation, or even, to a Centroidal Voronoi tessellation

    Accurate first-principle bandgap predictions in strain-engineered ternary III-V semiconductors

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    Tuning the bandgap in ternary III-V semiconductors via modification of the composition or the strain in the material is a major approach for the design of optoelectronic materials. Experimental approaches screening a large range of possible target structures are hampered by the tremendous effort to optimize the material synthesis for every target structure. We present an approach based on density functional theory efficiently capable of providing the bandgap as a function of composition and strain. Using a specific density functional designed for accurate bandgap computation (TB09) together with a band unfolding procedure and special quasirandom structures, we develop a computational protocol efficiently able to predict bandgaps. The approach's accuracy is validated by comparison to selected experimental data. We thus map the phase space of composition and strain (we call this the ``bandgap phase diagram'') for several important III-V compound semiconductors: GaAsP, GaAsN, GaPSb, GaAsSb, GaPBi, and GaAsBi. We show the application of these diagrams for identifying the most promising materials for device design. Furthermore, our computational protocol can easily be generalized to explore the vast chemical space of III-V materials with all other possible combinations of III- and V-elements.Comment: 13 pages, 7 figures, GitHub (https://bmondal94.github.io/Bandgap-Phase-Diagram/

    Investigating Lyman continuum escape fractions of high redshift galaxies during the era of reionization

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    Supporting Safety Analysis of Deep Neural Networks with Automated Debugging and Repair

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    Biomimicry green façade : integrating nature into building façades for enhanced building envelope efficiency

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    Incorporating natural elements into the design of building façades, such as green façades, has emerged as a promising strategy for achieving sustainable and energy-efficient buildings. Biomimicry has become a key inspiration for the development of innovative green façade systems. However, there is still progress to be made in maximising their aesthetic and structural performance, and the application of advanced and generative design methods is imperative for optimising green façade architecture. This research aims to present a generative design-based prototype of a biomimicry green façade substrate with photosynthetic microorganisms to enhance building façade efficiency. The concept of green façades offers numerous advantages, as it can be adapted to a wide range of building structures and implemented in various climates. To achieve this, Rhino and Grasshopper were utilized to design the generative and parametric substrate, optimizing the architectural form using a genetic algorithm. Consequently, a bio-façade prototype was developed, determining the optimal number and shape of coral envelopes to maintain cyanobacteria within a generative and parametric façade. Furthermore, the photosynthetic microorganism façade acted as an adaptive façade, effectively improving visual and thermal comfort, daylighting, and Indoor Environmental Quality performance

    Fluid dynamics and mass transfer in porous media: Modelling fluid flow and filtration inside open-cell foams

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    L'abstract è presente nell'allegato / the abstract is in the attachmen

    Small area analysis methods in an area of limited mapping : exploratory geospatial analysis of firearm injuries in Port-au-Prince, Haiti

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    Background: The city of Port-au-Prince, Haiti, is experiencing an epidemic of firearm injuries which has resulted in high burdens of morbidity and mortality. Despite this, little scientific literature exists on the topic. Geospatial research could inform stakeholders and aid in the response to the current firearm injury epidemic. However, traditional small-area geospatial methods are difficult to implement in Port-au-Prince, as the area has limited mapping penetration. Objectives of this study were to evaluate the feasibility of geospatial analysis in Port-au-Prince, to seek to understand specific limitations to geospatial research in this context, and to explore the geospatial epidemiology of firearm injuries in patients presenting to the largest public hospital in Port-au-Prince. Results: To overcome limited mapping penetration, multiple data sources were combined. Boundaries of informally developed neighborhoods were estimated from the crowd-sourced platform OpenStreetMap using Thiessen polygons. Population counts were obtained from previously published satellite-derived estimates and aggregated to the neighborhood level. Cases of firearm injuries presenting to the largest public hospital in Port-au-Prince from November 22nd, 2019, through December 31st, 2020, were geocoded and aggregated to the neighborhood level. Cluster analysis was performed using Global Moran’s I testing, local Moran’s I testing, and the SaTScan software. Results demonstrated significant geospatial autocorrelation in the risk of firearm injury within the city. Cluster analysis identified areas of the city with the highest burden of firearm injuries. Conclusions: By utilizing novel methodology in neighborhood estimation and combining multiple data sources, geospatial research was able to be conducted in Port-au-Prince. Geospatial clusters of firearm injuries were identified, and neighborhood level relative-risk estimates were obtained. While access to neighborhoods experiencing the largest burden of firearm injuries remains restricted, these geospatial methods could continue to inform stakeholder response to the growing burden of firearm injuries in Port-au-Prince

    Assessing the capacity of a denoising diffusion probabilistic model to reproduce spatial context

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    Diffusion models have emerged as a popular family of deep generative models (DGMs). In the literature, it has been claimed that one class of diffusion models -- denoising diffusion probabilistic models (DDPMs) -- demonstrate superior image synthesis performance as compared to generative adversarial networks (GANs). To date, these claims have been evaluated using either ensemble-based methods designed for natural images, or conventional measures of image quality such as structural similarity. However, there remains an important need to understand the extent to which DDPMs can reliably learn medical imaging domain-relevant information, which is referred to as `spatial context' in this work. To address this, a systematic assessment of the ability of DDPMs to learn spatial context relevant to medical imaging applications is reported for the first time. A key aspect of the studies is the use of stochastic context models (SCMs) to produce training data. In this way, the ability of the DDPMs to reliably reproduce spatial context can be quantitatively assessed by use of post-hoc image analyses. Error-rates in DDPM-generated ensembles are reported, and compared to those corresponding to a modern GAN. The studies reveal new and important insights regarding the capacity of DDPMs to learn spatial context. Notably, the results demonstrate that DDPMs hold significant capacity for generating contextually correct images that are `interpolated' between training samples, which may benefit data-augmentation tasks in ways that GANs cannot.Comment: This paper is under consideration at IEEE TM
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