Combining 2D2D synchrosqueezed wave packet transform with optimization for crystal image analysis

We develop a variational optimization method for crystal analysis in atomic resolution images, which uses information from a 2D synchrosqueezed transform (SST) as input. The synchrosqueezed transform is applied to extract initial information from atomic crystal images: crystal defects, rotations and the gradient of elastic deformation. The deformation gradient estimate is then improved outside the identified defect region via a variational approach, to obtain more robust results agreeing better with the physical constraints. The variational model is optimized by a nonlinear projected conjugate gradient method. Both examples of images from computer simulations and imaging experiments are analyzed, with results demonstrating the effectiveness of the proposed method

Crystal image analysis using 2D2D synchrosqueezed transforms

We propose efficient algorithms based on a band-limited version of 2D synchrosqueezed transforms to extract mesoscopic and microscopic information from atomic crystal images. The methods analyze atomic crystal images as an assemblage of non-overlapping segments of 2D general intrinsic mode type functions, which are superpositions of non-linear wave-like components. In particular, crystal defects are interpreted as the irregularity of local energy; crystal rotations are described as the angle deviation of local wave vectors from their references; the gradient of a crystal elastic deformation can be obtained by a linear system generated by local wave vectors. Several numerical examples of synthetic and real crystal images are provided to illustrate the efficiency, robustness, and reliability of our methods.Comment: 27 pages, 17 figure

Joint methods in imaging based on diffuse image representations

This thesis deals with the application and the analysis of different variants of the Mumford-Shah model in the context of image processing. In this kind of models, a given function is approximated in a piecewise smooth or piecewise constant manner. Especially the numerical treatment of the discontinuities requires additional models that are also outlined in this work. The main part of this thesis is concerned with four different topics. Simultaneous edge detection and registration of two images: The image edges are detected with the Ambrosio-Tortorelli model, an approximation of the Mumford-Shah model that approximates the discontinuity set with a phase field, and the registration is based on these edges. The registration obtained by this model is fully symmetric in the sense that the same matching is obtained if the roles of the two input images are swapped. Detection of grain boundaries from atomic scale images of metals or metal alloys: This is an image processing problem from materials science where atomic scale images are obtained either experimentally for instance by transmission electron microscopy or by numerical simulation tools. Grains are homogenous material regions whose atomic lattice orientation differs from their surroundings. Based on a Mumford-Shah type functional, the grain boundaries are modeled as the discontinuity set of the lattice orientation. In addition to the grain boundaries, the model incorporates the extraction of a global elastic deformation of the atomic lattice. Numerically, the discontinuity set is modeled by a level set function following the approach by Chan and Vese. Joint motion estimation and restoration of motion-blurred video: A variational model for joint object detection, motion estimation and deblurring of consecutive video frames is proposed. For this purpose, a new motion blur model is developed that accurately describes the blur also close to the boundary of a moving object. Here, the video is assumed to consist of an object moving in front of a static background. The segmentation into object and background is handled by a Mumford-Shah type aspect of the proposed model. Convexification of the binary Mumford-Shah segmentation model: After considering the application of Mumford-Shah type models to tackle specific image processing problems in the previous topics, the Mumford-Shah model itself is studied more closely. Inspired by the work of Nikolova, Esedoglu and Chan, a method is developed that allows global minimization of the binary Mumford-Shah segmentation model by solving a convex, unconstrained optimization problem. In an outlook, segmentation of flowfields into piecewise affine regions using this convexification method is briefly discussed

Multiscale Modeling for the Analysis for Grain-Scale Fracture Within Aluminum Microstructures

Multiscale modeling methods for the analysis of metallic microstructures are discussed. Both molecular dynamics and the finite element method are used to analyze crack propagation and stress distribution in a nanoscale aluminum bicrystal model subjected to hydrostatic loading. Quantitative similarity is observed between the results from the two very different analysis methods. A bilinear traction-displacement relationship that may be embedded into cohesive zone finite elements is extracted from the nanoscale molecular dynamics results

Discovering the building blocks of atomic systems using machine learning: Application to grain boundaries

AbstractMachine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large data set in the first place. Here we present a description of atomic systems that generates machine learning representations with a direct path to physical interpretation. As an example, we demonstrate its usefulness as a universal descriptor of grain boundary systems. Grain boundaries in crystalline materials are a quintessential example of a complex, high-dimensional system with broad impact on many physical properties including strength, ductility, corrosion resistance, crack resistance, and conductivity. In addition to modeling such properties, the method also provides insight into the physical “building blocks” that influence them. This opens the way to discover the underlying physics behind behaviors by understanding which building blocks map to particular properties. Once the structures are understood, they can then be optimized for desirable behaviors.</jats:p

Experimental quantification of 3D deformations in sensitive clay during stress-probing

Unique four-dimensional (4D) deformation data are collected during drained triaxial tests on intact specimens of a natural sensitive clay. This requires the development of a miniature triaxial cell for advanced stress path testing, specifically designed for X-ray computed tomography. Salient features include the omission of a membrane, and a mounting procedure that minimises disturbance by the experimenter. Three distinct drained stress ratios are studied for pseudo-isotropic, K-0, and highly deviatoric loading paths. The results indicate that the K-0 path shows the most uniform deformation mechanism, where the measured ratio of deviatoric and volumetric strain increments reach the stress ratio applied at boundary value level for large magnitudes of total strain. The pseudo-isotropic test also reaches a strain ratio close to eta at large total strain levels; however, the deformation field is less uniform. Furthermore, the highly deviatoric stress path shows the most heterogeneous deformation fields commensurate with the applied stress ratio, although the ratio of deviatoric and volumetric strain increments falls above the eta applied. The mean value of the three-dimensional spatial fields of strain corresponds well with the changes observed at boundary level, supporting prior research on drained stress-probing on clays for which there are no 4D deformation data available