Orientation and anisotropy of multi-component shapes

There are many situations in which several single objects are better considered as components of a multi-component shape (e.g. a shoal of fish), but there are also situations in which a single object is better segmented into natural components and considered as a multi-component shape (e.g. decomposition of cellular materials onto the corresponding cells). Interestingly, not much research has been done on multi-component shapes. Very recently, the orientation and anisotropy problems were considered and some solutions have been offered. Both problems have straightforward applications in different areas of research which are based on a use of image based technologies, from medicine to astrophysics.The object orientation problem is a recurrent problem in image processing and computer vision. It is usually an initial step or a part of data pre-processing, implying that an unsuitable solution could lead to a large cumulative error at the end of the vision system’s pipeline. An enormous amount of work has been done to develop different methods for a spectrum of applications. We review the new idea for the orientation of multi-component shapes, and also its relation to some of the methods for determining the orientation of single-component shapes. We also show how the anisotropy measure of multi-component shapes, as a quantity which indicates how consistently the shape components are oriented, can be obtained as a by-product of the approach used

Orientation and anisotropy of multi-component shapes from boundary information

We define a method for computing the orientation of compound shapes based on boundary information. The orientation of a given compound shape S is taken as the direction α that maximises the integral of the squared length of projections, of all the straight line segments whose end points belong to particular boundaries of components of S to a line that has the slope α. Just as the concept of orientation can be extended from single component shapes to multiple components, elongation can also be applied to multiple components, and we will see that it effectively produces a measure of anisotropy since it is maximised when all components are aligned in the same direction. The presented method enables a closed formula for an easy computation of both orientation and anisotropy

Phase-field modeling of equilibrium precipitate shapes under the influence of coherency stresses

Coherency misfit stresses and their related anisotropies are known to influence the equilibrium shapes of precipitates. Additionally, mechanical properties of the alloys are also dependent on the shapes of the precipitates. Therefore, in order to investigate the mechanical response of a material which undergoes precipitation during heat treatment, it is important to derive the range of precipitate shapes that evolve. In this regard, several studies have been conducted in the past using sharp interface approaches where the influence of elastic energy anisotropy on the precipitate shapes has been investigated. In this paper, we propose a diffuse interface approach which allows us to minimize grid-anisotropy related issues applicable in sharp-interface methods. In this context, we introduce a novel phase-field method where we minimize the functional consisting of the elastic and surface energy contributions while preserving the precipitate volume. Using this method we reproduce the shape-bifurcation diagrams for the cases of pure dilatational misfit that have been studied previously using sharp interface methods and then extend them to include interfacial energy anisotropy with different anisotropy strengths which has not been a part of previous sharp-interface models. While we restrict ourselves to cubic anisotropies in both elastic and interfacial energies in this study, the model is generic enough to handle any combination of anisotropies in both the bulk and interfacial terms. Further, we have examined the influence of asymmetry in dilatational misfit strains along with interfacial energy anisotropy on precipitate morphologies

The effect of realistic geometries on the susceptibility-weighted MR signal in white matter

Purpose: To investigate the effect of realistic microstructural geometry on the susceptibility-weighted magnetic resonance (MR) signal in white matter (WM), with application to demyelination. Methods: Previous work has modeled susceptibility-weighted signals under the assumption that axons are cylindrical. In this work, we explore the implications of this assumption by considering the effect of more realistic geometries. A three-compartment WM model incorporating relevant properties based on literature was used to predict the MR signal. Myelinated axons were modeled with several cross-sectional geometries of increasing realism: nested circles, warped/elliptical circles and measured axonal geometries from electron micrographs. Signal simulations from the different microstructural geometries were compared to measured signals from a Cuprizone mouse model with varying degrees of demyelination. Results: Results from simulation suggest that axonal geometry affects the MR signal. Predictions with realistic models were significantly different compared to circular models under the same microstructural tissue properties, for simulations with and without diffusion. Conclusion: The geometry of axons affects the MR signal significantly. Literature estimates of myelin susceptibility, which are based on fitting biophysical models to the MR signal, are likely to be biased by the assumed geometry, as will any derived microstructural properties.Comment: Accepted March 4 2017, in publication at Magnetic Resonance in Medicin

The influence of material anisotropy and spiral welding on tensile strain capacity of spiral welded pipes

The longitudinal strain capacity of spiral welded pipelines displays to some extents unexplained behaviour. Therefore, they are not (yet) used extensively in offshore applications and harsh conditions, demanding a strain based design. An important factor that influences the tensile strain capacity is the quantity of anisotropy in terms of strength and toughness. Starting from an anisotropic hot rolled highstrength steel skelp, the process of helical forming and post-treating of the pipe adds heterogeneity and changes the level of anisotropy of the product. A parameter that should be examined with respect to anisotropy is the crack driving force, a measure for the toughness of the pipeline steel. Additional to the mode I loading (opening of the crack), the mode III component drives the in-plane shear motion of a crack in the spiral weld when the pipe is subjected to longitudinal deformation. This action, not present in longitudinal welded pipes, shows a decreasing contribution with increasing plasticity. FE simulations have demonstrated a rise of crack driving force in anisotropic cases with respect to an isotropic reference. However, exact data and variation of various parameters, along with experimental testing need to be conducted. The outcome analysis of such simulations and tests can validate existing models, or help create a better understanding of anisotropic and heterogenic influences on the tensile strain capacity of spiral welded pipes