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Electron backscatter diffraction is a widely used technique for nano- to micro-scale analysis of crystal structure and orientation. Backscatter patterns produced by an alloy solid solution matrix and its ordered superlattice exhibit only…
We study the properties of superclusters detected in the Abell/ACO cluster catalogue. We identify the superclusters utilizing the `friend-of-friend' procedure, and then determine supercluster shapes by using the differential geometry…
Soft gels, formed via the self-assembly of particulate organic materials, exhibit intricate multi-scale structures that provides them with flexibility and resilience when subjected to external stresses. This work combines molecular…
Interplay between structure and function in atomically thin crystalline nanoribbons is sensitive to their conformations yet the ability to prescribe them is a formidable challenge. Here, we report a novel paradigm for controlled nucleation…
We demonstrate a novel approach to the reconstruction of scanning probe x-ray diffraction tomography data with anisotropic poly crystalline samples. The method involves reconstructing a voxel map containing an orientation distribution…
An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual Fourier-space formulations of atomicity. The new algorithm implements atomicity constraints in real-space, as well as…
In this paper I propose a new model for representing the formation energies of multicomponent crystalline alloys as a function of atom types. In the cases when displacements of atoms from their equilibrium positions are not large, the…
In the study of nanobubbles, nanodroplets or nanolenses immobilised on a substrate, a cross-section of a spherical-cap is widely applied to extract geometrical information from atomic force microscopy (AFM) topographic images. In this…
We demonstrate an atomic force microscopy based method for estimation of defect density by identification of threading dislocations on a non-flat surface resulting from metamorphic growth. The discussed technique can be applied as an…
We introduce a general method which allows reconstruction of electronic band structure of nanocrystals from ordinary real-space electronic structure calculations. A comprehensive study of band structure of a realistic nanocrystal is given…
Quantum phase is not a direct observable and is usually determined by interferometric methods. We present a method to map complete electron wave functions, including internal quantum phase information, from measured single-state probability…
Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in…
Methods for the statistical characterization of the large-scale structure in the Universe will be the main topic of the present text. The focus is on geometrical methods, mainly Minkowski functionals and the J-function. Their relations to…
The annealing of sub-critical Ge wetting layers (WL<3.5 ML) initiates the formation of 3D nanostructures, whose shape and orientation is determined by the WL thickness and thus directly related to the strain energy. The emergence of these…
We study semilinear wave equations with Ginzburg-Landau type nonlinearities multiplied by a factor $\epsilon^{-2}$, where $\epsilon>0$ is a small parameter. We prove that for suitable initial data, solutions exhibit energy concentration…
In the field of data-driven 3D shape analysis and generation, the estimation of global topological features from localized representations such as point clouds, voxels, and neural implicit fields is a longstanding challenge. This paper…
Any object on earth has two fundamental properties: it is finite, and it is made of atoms. Structural information about an object can be obtained from diffraction amplitude measurements that account for either one of these traits.…
A voxelization based post-processing algorithm is proposed to analyze the packing of non-spherical particle assemblies simulated using the Discrete Element Method. Voxelization of the particle data allows for isolating the geometric…
We present a novel approach for finding and evaluating structural models of small metallic nanoparticles. Rather than fitting a single model with many degrees of freedom, the approach algorithmically builds libraries of nanoparticle…
Multipolar plasmon oscillation frequencies and corresponding damping rates for nanospheres formed of the simplest free-electron metals are studied. The possibility of controlling plasmon features by choosing the size and dielectric…