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Molecular crystals often exist in multiple competing polymorphs, showing significantly different physico-chemical properties. Computational crystal structure prediction is key to interpret and guide the search for the most stable or useful…
Crystal structure prediction is a long-standing challenge in materials science, with most data-driven methods developed for inorganic systems. This leaves an important gap for organic crystals, which are central to pharmaceuticals,…
Accurate molecular crystal structure prediction is a fundamental goal in academic and industrial condensed matter research and polymorphism is arguably the biggest obstacle on the way. We tackle this challenge in the difficult case of the…
In crystallography, a structure is typically represented by the arrangement of atoms in the direct space. Furthermore, space group symmetry and Wyckoff site notations are applied to characterize crystal structures with only a few variables.…
Metastable materials are abundant in nature and technology, showcasing remarkable properties that inspire innovative materials design. However, traditional crystal structure prediction methods, which rely solely on energetic factors to…
The large amount of powder diffraction data for which the corresponding crystal structures have not yet been identified suggests the existence of numerous undiscovered, physically relevant crystal structure prototypes. In this paper, we…
Multi-connected universe models with space identification scales smaller than the size of the observable universe produce topological images of cosmic sources. We generalise to locally hyperbolic spaces the crystallographic method, aimed to…
Accurate and precise astronomical distance determinations are crucial for derivations of, among others, the masses and luminosities of a large variety of distant objects. Astronomical distance determination has traditionally relied on the…
In this paper, we prove the existence of a crystallization transition for a family of hard-core particle models on periodic graphs in arbitrary dimensions. We establish a criterion under which crystallization occurs at sufficiently high…
Using numerical and analytical calculations we study the structure of vacancies and interstitials in two-dimensional colloidal crystals. In particular, we compare the displacement fields of the defect obtained numerically with the…
Crystal structure prediction is a central problem of theoretical crystallography and materials science, which until mid-2000s was considered intractable. Several methods, based on either energy landscape exploration$^{1,2}$ or, more…
Predicting crystal structures from chemical compositions is a fundamental challenge in materials discovery, complicated by complex 3D geometries that distinguish it from fields like protein folding. Here, we present Diffusion-based Crystal…
The purpose of continuum plasticity models is to efficiently predict the behavior of structures beyond their elastic limits. The purpose of multiscale materials science models, among them crystal plasticity models, is to understand the…
The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions), which are complete in general position and continuous under…
The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics,…
We have developed a software package CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) to predict the energetically stable/metastable crystal structures of materials at given chemical compositions and external conditions…
Crystal structure prediction is a fundamental problem in materials science. We present CrystalFormer-CSP, an efficient framework that unifies data-driven heuristic and physics-driven optimization approaches to predict stable crystal…
In the Hausdorff Voronoi diagram of a set of clusters of points in the plane, the distance between a point t and a cluster P is the maximum Euclidean distance between t and a point in P. This diagram has direct applications in VLSI design.…
Crystals are paradigms of ordered structures. While order was once seen as synonymous with lattice periodic arrangements, the discoveries of incommensurate crystals and quasicrystals led to a more general perception of crystalline order,…
Inspired by recent advances in the manipulation of atoms trapped near 1D waveguides and pro- posals to use surface acoustic waves on piezoelectric substrates for the same purpose, we show the potential of two-dimensional platforms. We…