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The full optimization of the design and operation of instruments whose functioning relies on the interaction of radiation with matter is a super-human task, given the large dimensionality of the space of possible choices for geometry,…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
A sparse modeling approach is proposed for analyzing scanning tunneling microscopy topography data, which contains numerous peaks corresponding to surface atoms. The method, based on the relevance vector machine with $\mathrm{L}_1$…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data,…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…
Modeling artificial scanning electron microscope (SEM) and scanning ion microscope images has recently become important. This is because of the need to provide repeatable images with a priori determined parameters. Modeled artificial images…
Atom probe tomography (APT) is often quoted to provide "atomic-scale" analysis of materials in three dimensions. Despite efforts to quantify APT's spatial resolution, misunderstanding remain regarding its true spatial performance. If the…
Scanning tunnelling microscopy (STM) is a powerful technique for imaging surfaces with atomic resolution, providing insight into physical and chemical processes at the level of single atoms and molecules. A regular task of STM image…
A reflection-asymmetric deformed oscillator potential is analysed from the classical and quantum mechanical point of view. The connection between occurrence of shell structures and classical periodic orbits is studied using the ''removal of…
Krylov subspace recycling is a powerful tool for solving long series of large, sparse linear systems that change slowly. In PDE constrained shape optimization, these appear naturally, as hundreds or more optimization steps are needed with…
Using numerical electron wave functions and state-of-the-art nuclear many-body methods, I evaluate the $\beta$-decay spectra for typical decay channels of spherical nuclei. I check errors brought by various approximations used for deriving…
We consider problems related to initial meshing and adaptive mesh refinement for the electromagnetic simulation of various structures. The quality of the initial mesh and the performance of the adaptive refinement are of great importance…
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…
The nuclear shell model is one of the prime many-body methods to study the structure of atomic nuclei, but it is hampered by an exponential scaling on the basis size as the number of particles increases. We present a shell-model quantum…
The deformability of soft condensed matter often requires modelling of hydrodynamical aspects to gain quantitative understanding. This, however, requires specialised methods that can resolve the multiscale nature of soft matter systems. We…
A widely used strategy to reduce the computational cost in quantum-chemical calculations is to partition the system into an active subsystem, which is the focus of the computational efforts and an environment that is treated at a lower…
Freestanding oxide films offer significant potential for integrating exotic quantum functionalities with semiconductor technologies. However, their performance is critically limited by surface roughness and interfacial imperfection caused…
Many proposals have already been made for realizing programmable matter, ranging from shape-changing molecules, DNA tiles, and synthetic cells to reconfigurable modular robotics. Envisioning systems of nano-sensors devices, we are…
A real-space formalism for density-functional perturbation theory (DFPT) is derived and applied for the computation of harmonic vibrational properties in molecules and solids. The practical implementation using numeric atom-centered…