Related papers: Extended Configurational Polyhedra Based on Graph …
The prediction of energetically stable crystal structures formed by a given chemical composition is a central problem in solid-state physics. In principle, the crystalline state of assembled atoms can be determined by optimizing the energy…
Crystal Structure Prediction (CSP) remains a fundamental challenge with significant implications for the development of new materials and the advancement of various scientific disciplines. Recent developments have shown that generative…
Classical particle systems characterized by continuous size polydispersity, such as colloidal materials, are not straightforwardly described using statistical mechanics, since fundamental issues may arise from particle distinguishability.…
We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…
Crystal structure determines properties of materials. With the crystal structure of a chemical substance, many physical and chemical properties can be predicted by first-principles calculations or machine learning models. Since it is…
The number of distinguishable inherent structures of a liquid is the key component to understanding the thermodynamics of glass formers. In the case of hard potential systems such as hard discs, spheres and ellipsoids, an inherent structure…
We investigate an algebraic problem related to the determination of the fundamental group of a class of spaces of configurations on surfaces. The configuration spaces are spaces of points grouped into colors. Whether two points are allowed…
Ab initio prediction of the variation of properties in the configurational space of solid solutions is computationally very demanding. We present an approach to accelerate these predictions via a combination of density functional theory and…
The paper surveys highlights of the ongoing program to classify discrete polyhedral structures in Euclidean 3-space by distinguished transitivity properties of their symmetry groups, focussing in particular on various aspects of the…
The chosen tool of this thesis is an extremal type approach. The lesson drawn by the theorems proved in the thesis is that surprisingly small compromise is necessary on the efficacy of the solutions to make the approach work. The problems…
Recently, it has been shown that, when the dimension of a graph turns out to be infinite dimensional in a broad sense, the upper critical surface and the corresponding critical behavior of an arbitrary Ising spin glass model defined over…
A graph theoretic approach is proposed for object shape representation in a hierarchical compositional architecture called Compositional Hierarchy of Parts (CHOP). In the proposed approach, vocabulary learning is performed using a hybrid…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical…
We propose a novel analytical model for anisotropic multi-layer cylindrical structures containing graphene layers. The general structure is formed by an aperiodic repetition of a three-layer sub-structure, where a graphene layer, with an…
We consider a generalization of the quiver varieties of Lusztig and Nakajima to the case of all symmetrizable Kac-Moody Lie algebras. To deal with the non-simply laced case one considers admissible automorphisms of a quiver and the…
The edges of the characteristic imset polytope, $\operatorname{CIM}_p$, were recently shown to have strong connections to causal discovery as many algorithms could be interpreted as greedy restricted edge-walks, even though only a strict…
We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional $\pi$-conjugated chains as representative model…
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…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…