Topological Microstructure Analysis Using Persistence Landscapes

International audiencePhase separation mechanisms can produce a variety of complicated and intricate microstructures, which often can be difficult to characterize in a quantitative way. In recent years, a number of novel topological metrics for microstructures have been proposed, which measure essential connectivity information and are based on techniques from algebraic topology. Such metrics are inherently computable using computational homology, provided the microstructures are discretized using a thresholding process. However, while in many cases the thresholding is straightforward, noise and measurement errors can lead to misleading metric values. In such situations, persistence landscapes have been proposed as a natural topology metric. Common to all of these approaches is the enormous data reduction, which passes from complicated patterns to discrete information. It is therefore natural to wonder what type of information is actually retained by the topology. In the present paper, we demonstrate that averaged persistence landscapes can be used to recover central system information in the Cahn-Hilliard theory of phase separation. More precisely, we show that topological information of evolving microstructures alone suffices to accurately detect both concentration information and the actual decomposition stage of a data snapshot. Considering that persistent homology only measures discrete connectivity information, regardless of the size of the topological features, these results indicate that the system parameters in a phase separation process affect the topology considerably more than anticipated. We believe that the methods discussed in this paper could provide a valuable tool for relating experimental data to model simulations

How soft materials control harder ones: routes to bioorganization

Ordered structures are remarkably common, even without direct human guidance or direction. The ordering can be at the atomic scale or on the macroscopic scale or at the mesoscale. The term 'self-organization' is often used, but this description is facile, giving no hint as to the range or variety of mechanisms. Ordering can occur in circumstances commonly associated with disorder, as in the irradiation of metals to high doses; it can also occur when soft, flexible materials organize structures of harder, rigid structures. My review attempts to analyse some of these widely varying behaviours, both to seek evidence of common underlying principles and to assess how organization might be controlled, and with what level of accuracy

Mesoscale modelling of steel processing

Numerical methods are utilised to reproduce the evolution of a system observed in natural phenomena. Within the area of materials science there is an increase of interest in modelling techniques that can accurately predict the microstructure of a material subject to various processing conditions. Recently, there is a requirement of techniques that have the ability to be applied to systems involving microstructural change in the presence of fluid flow. This presents a challenge since the forces governing these processes involve those predominately influenced by thermodynamics as well as those influenced by hydrodynamics. The phase-field method, a popular technique used in this area, has been shown to have the ability to cope with phase transformation dynamics such as solidification and solid-state phase transformations. However, its predictive capabilities mainly apply to a flow free environment where flow effects are minimal compared to other effects. Other techniques such as smoothed particle hydrodynamics exist that are more than capable of describing the mechanisms of flow demonstrating superiority in many complex flow problems. The thermodynamic quantities related to the evolution of a system to which this method is applied must then be consistent in order to be translated between models. This thesis develops the tools necessary to deal with phase growth and microstructural change within the presence of flow. This is done by developing phase-field models that can efficiently deal with displacive transformations in steels as well as diffusive, and SPH models with the ability to be coupled with thermodynamics. The phase-field models are developed to be applied to structure growth observed at relatively low temperatures within steels, namely martensite and bainite growth. The SPH method is analysed in order to assess and provide solutions for consistency when considered for coupling with models mainly dependent on thermodynamics.Open Acces