Small Covers over Prisms

In this paper we calculate the number of equivariant diffeomorphism classes of small covers over a prism

Detecting, segmenting and tracking bio-medical objects

Studying the behavior patterns of biomedical objects helps scientists understand the underlying mechanisms. With computer vision techniques, automated monitoring can be implemented for efficient and effective analysis in biomedical studies. Promising applications have been carried out in various research topics, including insect group monitoring, malignant cell detection and segmentation, human organ segmentation and nano-particle tracking. In general, applications of computer vision techniques in monitoring biomedical objects include the following stages: detection, segmentation and tracking. Challenges in each stage will potentially lead to unsatisfactory results of automated monitoring. These challenges include different foreground-background contrast, fast motion blur, clutter, object overlap and etc. In this thesis, we investigate the challenges in each stage, and we propose novel solutions with computer vision methods to overcome these challenges and help automatically monitor biomedical objects with high accuracy in different cases --Abstract, page iii

Dynamic splitting tensile behaviour of engineered geopolymer composites with hybrid polyvinyl alcohol and recycled tyre polymer fibres

Partial replacement of the widely used polyvinyl alcohol (PVA) fibre in engineered geopolymer composites (EGC) with recycled fibres can reduce the material cost and improve sustainability. This study investigates the effect of hybrid PVA and recycled tyre polymer (RTP) fibre content on the quasi-static and dynamic splitting tensile behaviour and microstructure of ambient-cured fly ash-slag based EGC through split Hopkinson pressure bar, scanning electron microscopy and X-ray computed tomography tests. Results indicate that the presence of PVA or RTP fibres can considerably improve the quasi-static and dynamic splitting tensile behaviour of geopolymers. All investigated mixtures are characterised by remarkable strain rate sensitivity within the considered test range, which can be well described using the proposed relationship between dynamic increase factor and strain rate for predictions of dynamic properties. Replacing PVA fibre with 0.25–0.5% RTP fibre can lead to better dynamic splitting tensile properties of EGC compared to that with 2.0% PVA fibre, which can be mainly ascribed to the improved synergistic effect of hybrid fibres in controlling the cracks. The microscopic images reveal that the failure mode of RTP fibres is not sensitive to the strain rate due to its hydrophobic surface feature, which could benefit the energy absorption capacity of EGC under dynamic loading. EGC containing hybrid PVA and RTP fibres holds promise as a cost-effective and sustainable material for applications against dynamic loadings

Random strings and tt-degrees of Turing complete C.E. sets

We investigate the truth-table degrees of (co-)c.e.\ sets, in particular, sets of random strings. It is known that the set of random strings with respect to any universal prefix-free machine is Turing complete, but that truth-table completeness depends on the choice of universal machine. We show that for such sets of random strings, any finite set of their truth-table degrees do not meet to the degree~0, even within the c.e. truth-table degrees, but when taking the meet over all such truth-table degrees, the infinite meet is indeed~0. The latter result proves a conjecture of Allender, Friedman and Gasarch. We also show that there are two Turing complete c.e. sets whose truth-table degrees form a minimal pair.Comment: 25 page

Multiscale modelling of ionic diffusivity in unsaturated concrete accounting for its hierarchical microstructure

This study presents an integrated multiscale framework for modelling ionic diffusivity in unsaturated concrete accounting for its microstructural features and 3D moisture distribution. The hierarchical microstructure of concrete at multiscale from nano- to meso-scale is mimicked, based on which the fluid-solid interaction and moisture distribution in pore network of concrete with various saturation levels are simulated using a lattice Boltzmann multiphase model. A lattice Boltzmann-finite difference model for diffusion is developed to mimic the ionic diffusion and predict the ionic diffusivity in unsaturated concrete. Results indicate that ionic diffusivity in unsaturated concrete highly depends on moisture content and distribution, pore structure, and aggregate content. As the water saturation level drops to around 90%, interfacial transition zone starts to retard ionic diffusion. Voids have a great contribution to water saturation level but less effect on ionic diffusivity. The simulation results of ionic diffusivity at each scale agree well with experimental data

Micromechanical modelling of fracture processes in cement composites

Cement composites are the most popular and widely used construction material in the world. Understanding and predicting fracture processes in these materials is scientifically challenging but important for durability assessments and life extension decisions. A recently proposed microstructure-informed site-bond model with elasticbrittle spring bundles is developed further to predict the elastic properties and fracture process of cement paste. It accounts for microstructure characteristics obtained from high resolution X-ray computed microtomography (micro-CT). Volume fraction and size distribution of anhydrous cement grains are used to determine the model length scale and pore-less elasticity. Porosity and pore size distribution are used for tuning elastic and failure properties of individual bonds. The fracture process is simulated by consecutive removal of bonds subject to failure criterion. The stress-strain response and elastic properties of cement paste are obtained. The simulated Young’s modulus and deformation response prior to peak stress agree very well with the experimental data. The proposed model provides an effective tool to simulate micro-cracks initiation, propagation, coalescence and localization

3D meso-scale modelling of tensile and compressive fracture behaviour of steel fibre reinforced concrete

This paper presents a novel meso-scale modelling framework to investigate the fracture process in steel fibre reinforced concrete (SFRC) under uniaxial tension and compression considering its 3D mesostructural characteristics, including different types of fibres, realistic shaped aggregates, mortar, interfacial transition zone and voids. Based on a hybrid damage model consisting of cohesive element method and damage plasticity method, a cost-effective finite element approach was proposed to simulate the fracture behaviour of SFRC in terms of stress-strain response, energy dissipation and crack morphology. The results indicated that under given conditions, the straight and hooked-end fibres improved the compressive damage tolerances of concrete over 11.5% while the spiral fibres had a negligible effect of 2.6%. The tensile macro-damage level index introduced was reduced over 15% by all fibres. Compared to straight fibres, the higher anchoring capacity of spiral fibres reduced the reinforcement performance while hooked-end fibres did not exhibit a significant influence