Modeling martensitic phase transformation in dual phase steels based on a sharp interface theory

Martensite forms under rapid cooling of austenitic grains accompanied by a change of the crystal lattice. Large deformations are induced which lead to plastic dislocations. In this work a transformation model based on the sharp interface theory, set in a finite strain context is developed. Crystal plasticity effects, the kinetic of the singular surface as well as a simple model of the inheritance from austenite dislocations into martensite are accounted for

Optimization methods for electric power systems: An overview

Power systems optimization problems are very difficult to solve because power systems are very large, complex, geographically widely distributed and are influenced by many unexpected events. It is therefore necessary to employ most efficient optimization methods to take full advantages in simplifying the formulation and implementation of the problem. This article presents an overview of important mathematical optimization and artificial intelligence (AI) techniques used in power optimization problems. Applications of hybrid AI techniques have also been discussed in this article

Optimising Spatial and Tonal Data for PDE-based Inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. We also give an extensive literature survey on PDE-based image compression methods

A segregated finite element method for cardiac elastodynamics in a fully coupled human heart model

One key characterstic of the cardiac function is its complexity, i.e., the multitude of different phenomena acting on various temporal and spatial scales interacting with each other. Over the past decades, many models varying in complexity describing these interactions were presented and are used in current research. Despite the incredible progress made in describing and simulating cardiac function, most of the more detailed models are not properly embedded within mathematical theory. This work aims to give a precise and comprehensive mathematical formulation of coupled cardiac elastodynamics, including electrophysiology, elasticity and physiological boundary conditions developed in recent years. Focussing on the analysis of dynamic elasticity, the concept of anisotropy is applied to common cardiac tissue models, such as the models of Guccione et al. and Holzapfel and Ogden. Frequently used modeling approaches, such as incompressibility and the active strain decomposition, are integrated in one overarching framework, allowing for propositions on polyconvexity of the materials and solvability of the elastic system. The equations of elastodynamics are then complemented by the monodomain equations, describing the propagation of the excitation potential in cardiac tissue, and a surrogate model to simulate cardiovascular blood pressure. The full mathematical description of this coupled model allows a detailed formulation of a discretization scheme in space and time for the electro-elastodynamical system. The classification of the coupled model within the context of weak solutions is presented and a time-segregated numerical approximation method for the full system is derived. The formulated numerical method is then examined by application on coupled test cases, providing first convergence results in space for the displacement in coupled cardiac problems

A Hierarchical Shape Representation by Convexities and Concavities and Its Application to Shape Matching.

Shape contains information. The identification and extraction of this information is not straightforward and is the main problem of Shape Analysis. The current trend of manipulating visual information, makes this problem more important. The abundant work published about shape analysis can be classified into two main approaches: statistical shape analysis and structural shape analysis. The structural approach was proposed around thirty years ago by K. S. Fu. The large amount of works published since then, prove the difficulty of defining a universal set of primitives. The structural description of shape is based on the assumption that shape recognition is a hierarchical process. Nevertheless, no effective general mechanism that captures hierarchical description has been found, and the existing representations may be applied to restricted applications. We propose a new structural representation of shape using convexity. Instead of using a predefined set of primitives, we use two basic components to decompose any shape: convexity and concavity. The decomposition obtained results in a natural hierarchy, of these basic components. We represent the decomposition by a new shape descriptor: the Convexity-Concavity Tree (CCT), which is a binary tree. The CCT representation is used for matching the shapes of two objects. The matching of two CCTs is represented by a binary tree, that we call the Matching Tree (MT). The Matching Tree represents the location and magnitude of the mismatch between corresponding convexities-concavities of the two shapes. Two shapes match if their corresponding CCTs match. Some of the advantages of our representation method are: (1) it is information preserving, (2) it has the desired properties of a good description method: invariance, uniqueness and stability, (3) it is economical, (4) it is robust in the presence of noise. Our matching method, based on convexity representation is superior to other methods in terms of simplicity, ability to explain and measure mismatches and also it may be used with other well known methods

Linear Estimation in Interconnected Sensor Systems with Information Constraints

A ubiquitous challenge in many technical applications is to estimate an unknown state by means of data that stems from several, often heterogeneous sensor sources. In this book, information is interpreted stochastically, and techniques for the distributed processing of data are derived that minimize the error of estimates about the unknown state. Methods for the reconstruction of dependencies are proposed and novel approaches for the distributed processing of noisy data are developed