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Dislocations are the main carriers of the permanent deformation of crystals. For simulations of engineering applications, continuum models where material microstructures are represented by continuous density distributions of dislocations…
Clean Hoag-like ring galaxies are often characterized by an old compact central component, a depleted gap, and a detached outer ring. We identify a boundary-supported radial-layering mechanism in a shell-deformed Kepler control model. A…
We use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions; in particular the case of a Bernoulli distribution is covered. The…
Frequency-dependent acoustical loss due to a multitude of physical mechanisms is commonly modeled by multiple relaxations. For discrete relaxation distributions, such models correspond with causal wave equations of integer-order temporal…
We study the real-time dynamics of a two-dimensional Anderson--Hubbard model using nonequilibrium self-consistent perturbation theory within the second-Born approximation. When compared with exact diagonalization performed on small…
A simple algorithm is presented for the calculation of the projected line-of-sight velocity profiles (VPs) of non-rotating anisotropic spherical stellar dynamical models with a phase-space distribution function of the Osipkov-Merritt type.…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
We present a method to perform fully selfconsistent density-functional calculations, which scales linearly with the system size and which is well suited for very large systems. It uses strictly localized pseudoatomic orbitals as basis…
Mode separation, namely how sharply a distribution fragments into barrier-separated clusters, is a fundamental geometric property of densities, difficult to quantify in high dimensions. It is structurally distinct from dispersion, yet…
We develop the scattering theory of general conformally compact metrics. For low frequencies, the domain of the scattering matrix is shown to be frequency dependent. In particular, generalized eigenfunctions exhibit L^2 decay in directions…
Recent years have seen a great deal of progress in our understanding of bootstrap percolation models, a particular class of monotone cellular automata. In the two dimensional lattice there is now a quite satisfactory understanding of their…
We study how finite-window sampling (random spatial truncation) and reciprocal-space radial binning influence the detection of hyperuniformity in disordered systems. Using thirteen representative two-dimensional simulation systems (two…
Typical Wannier-function downfolding starts with a mean-field or density functional set of bands to construct the Wannier functions. Here we carry out a controlled approach, using DMRG-computed natural orbital bands, to downfold the…
Data-driven methods of model identification are able to discern governing dynamics of a system from data. Such methods are well suited to help us learn about systems with unpredictable evolution or systems with ambiguous governing dynamics…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
Granular flows down inclined channels with smooth boundaries are common in nature and in the industry. Nevertheless, the common setup of flat boundaries has comparatively been much less investigated than the bumpy boundaries one, which is…
The time-dependent Ginzburg-Landau equation and the Swift-Hohenberg equation, both added with a stochastic term, are proposed to describe cloud pattern formation and cloud regime phase transitions of shallow convective clouds organized in…
Isotropic positive definite functions on spheres play important roles in spatial statistics, where they occur as the correlation functions of homogeneous random fields and star-shaped random particles. In approximation theory, strictly…
Under the weak interaction regime, we prove the one and the two volumes Wegner type bounds for one dimensional multi-particle models on the lattice and for very singular probability distribution functions such as the Bernoulli measures. The…
This work justifies the paradigmatic importance of viscoelastic subdiffusion in random environments for cellular biological systems. This model displays several remarkable features, which makes it an attractive paradigm to explain the…