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Diffraction methods are at the heart of structure determination of solids. While Bragg-like scattering (pure point diffraction) is a characteristic feature of crystals and quasicrystals, it is not straightforward to interpret continuous…
The diffraction pattern of a single non-periodic compact object, such as a molecule, is continuous and is proportional to the square modulus of the Fourier transform of that object. When arrayed in a crystal, the coherent sum of the…
Many materials contain extended defects of nanosize scale, such as dislocations, cracks, pores, polymorphic inclusions, and other embryos of competing phases. When one is interested not in the precise internal structure of a sample with…
This paper presents a computational model to recover the most likely interpretation of the 3D scene structure from a planar image, where some objects may occlude others. The estimated scene interpretation is obtained by integrating some…
The present paper studies non-uniform plastic deformations of crystals undergoing anti-plane constrained shear. The asymptotically exact energy density of crystals containing a moderately large density of excess dislocations is found by the…
Vision foundation models trained on discretely sampled images achieve strong performance on classification benchmarks, yet whether their representations encode the continuous processes underlying their training data remains unclear. This…
Fracture processes in heterogeneous materials comprise a large number of disordered spatial degrees of freedom, representing the dynamical state of a sample over the entire domain of interest. This complexity is usually modeled directly,…
The interaction of crack fronts with asperities is central to the criteria of fracture in heterogeneous materials and for predicting fracture surface formation. It is known how dynamic crack fronts respond to small, 1st-order,…
Over the past few years, dictionary learning (DL)-based methods have been successfully used in various image reconstruction problems. However, traditional DL-based computed tomography (CT) reconstruction methods are patch-based and ignore…
The investigation reported in this document focuses on identifying systems with symmetries using equivariant autoregressive reservoir computers. General results in structured matrix approximation theory are presented, exploring a two-fold…
Dark-field X-ray Microscopy (DFXM) is a novel diffraction-based imaging technique that non-destructively maps the local deformation from crystalline defects in bulk materials. While studies have demonstrated that DFXM can spatially map 3D…
Diffusion models have gained prominence as powerful generative tools for solving inverse problems due to their ability to model complex data distributions. However, existing methods typically rely on complete knowledge of the forward…
Accurate description of crystal structures is a prerequisite for predicting the physicochemical properties of materials. However, conventional X-ray diffraction (XRD) characterization often encounters intrinsic bottlenecks when applied to…
We present a simple 'shift-and-add' based improvement in the angular resolution of single electron backscatter diffraction (EBSD) patterns. Sub-pixel image registration is used to measure the (sub-pixel) difference in projection parameters…
The low-density imaging performance of a zone plate based nano-resolution hard X-ray computed tomography (CT) system can be significantly improved by incorporating a grating-based Lau interferometer. Due to the diffraction, however, the…
Topological defects, such as disclination lines in nematic liquid crystals, are fundamental to many physical systems and applications. In this work, we study the behavior of nematic disclinations in thin parallel-plate geometries with…
Single-image piece-wise planar 3D reconstruction aims to simultaneously segment plane instances and recover 3D plane parameters from an image. Most recent approaches leverage convolutional neural networks (CNNs) and achieve promising…
High-energy X-ray diffraction methods can non-destructively map the 3D microstructure and associated attributes of metallic polycrystalline engineering materials in their bulk form. These methods are often combined with external stimuli…
We study the structure of representations, defined as approximations of minimal sufficient statistics that are maximal invariants to nuisance factors, for visual data subject to scaling and occlusion of line-of-sight. We derive analytical…
We demonstrate the effect of introducing controlled disorder in self-assembled three-dimensional photonic crystals. Disorders are induced through controlling the self-assembling process using an electrolyte of specific concentrations.…