Related papers: Migration-Driven Hierarchical Crystal Defect Aggre…
Crystal structure prediction has been a subject of topical interest, but remains a substantial challenge, especially for complex structures as it deals with the global minimization of the extremely rugged high-dimensional potential energy…
A large sample of young stellar groups is analysed aiming to investigate their clustering properties and dynamical evolution. A comparison of the Q statistical parameter, measured for the clusters, with the fractal dimension estimated for…
Mixtures of bare atomic nuclei on a nearly uniform degenerate electron background are a realistic model of matter in the interior of white dwarfs. Despite tremendous progress in understanding their phase diagrams achieved mainly via…
Elucidating the interplay of defect and stress at the microscopic level is a fundamental physical problem that has strong connection with materials science. Here, based on the two-dimensional crystal model, we show that the instability mode…
Topological defects -- locations of local mismatch of order -- are a universal concept playing important roles in diverse systems studied in physics and beyond, including the universe, various condensed matter systems, and recently, even…
Understanding the growth of quasicrystals poses a challenging problem, not the least because the quasiperiodic order present in idealized mathematical models of quasicrystals prohibit simple local growth algorithms. This can only be…
Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in $R^d$. It is shown that natural parametrizations provide affine section…
The mass assembly of a whole population of sub-Milky Way galaxies is studied by means of hydrodynamical simulations within the $\Lambda$-CDM cosmology. Our results show that while dark halos assemble hierarchically, in stellar mass this…
Dynamic recrystallization is one of the main phenomena responsible for microstructure evolutions during hot forming. Consequently, getting a better understanding of DRX mechanisms and being able to predict them is crucial. This paper…
Depending on the pH value and salt concentration of Al2O3 suspensions different microstructures can form. Especially the clustered one is of major interest for industrial purposes as found in the production of ceramics. In this paper we…
Hierarchical clustering is a popular method for analyzing data which associates a tree to a dataset. Hartigan consistency has been used extensively as a framework to analyze such clustering algorithms from a statistical point of view.…
We discuss the relevance of methods of graph theory for the study of damage in simple model materials described by the random fuse model. While such methods are not commonly used when dealing with regular random lattices, which mimic…
We sketch a procedure to capture general non-invertible symmetries of a d-dimensional quantum field theory in the data of a higher-category, which captures the local properties of topological defects associated to the symmetries. We also…
The scaling behavior of cyclical growth (e.g. cycles of alternating deposition and desorption primary processes) is investigated theoretically and probed experimentally. The scaling approach to kinetic roughening is generalized to cyclical…
We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the…
Hierarchical (first-order) structured deformations are studied from the variational point of view. The main contributions of the present research are the first steps, at the theoretical level, to establish a variational framework to…
What characterises a solid is its way to respond to external stresses. Ordered solids, such crystals, display an elastic regime followed by a plastic one, both well understood microscopically in terms of lattice distortion and dislocations.…
We study the finite-size scaling behaviour at the critical point, resulting from the addition of a homogeneous size-dependent perturbation, decaying as an inverse power of the system size. The scaling theory is first formulated in a general…
The paper outlines the principles of construction of a broad class of hierarchical aggregation algorithms of cluster analysis, essentially based on minimum distance mergers, which are derived from the general bi-partial objective function.…
Alloying metals with other elements is often done to improve the material strength or hardness. A key microscopic mechanism is precipitation hardening, where precipitates impede dislocation motion, but the role of such obstacles in…