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Building blocks and tiles are an excellent way of learning about geometry and mathematics in general. There are several versions of tiles that are either snapped together or connected with magnets that can be used to introduce topics like…
Macroscopic properties of materials stem from fundamental atomic-scale details, yet for insulators, resolving surface structures remains a challenge. The basal (0001) plane of ${\alpha}$-Al$_{2}$O$_{3}$ was imaged with noncontact atomic…
We investigate the problem of assembling general shapes and patterns in a model in which particles move based on uniform external forces until they encounter an obstacle. While previous work within this model of assembly has focused on…
In spite of remarkable developments in the field of advanced materials, silicon remains one of the foremost semiconductors of the day. Of enduring relevance to science and technology is silicon's nanomechanical behaviour including phase…
Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show…
With the hypothesis that all independent degrees of freedom of basic building blocks should be treated equally on the same footing and correlated by a possible maximal symmetry, we arrive at an 4-dimensional space-time unification model. In…
This paper reports state-of-the-art electronic structure calculations on the deposition of strontium on the technologically relevant, (001) orientated silicon surface. We identified the surface reconstructions from zero to four thirds…
A clean Si(001) surface thermally purified in an ultrahigh vacuum molecular-beam epitaxy chamber has been investigated by means of scanning tunneling microscopy. The morphological peculiarities of the Si(001) surface have been explored in…
In this paper we apply our results on the geometry of polygons in Cartan subspaces, symmetric spaces and buildings to four problems in algebraic group theory. Two of these problems are generalizations of the problems of finding the…
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…
Recent photoemission experiments on the Si(553)-Au reconstruction show a one-dimensional band with a peculiar ~1/4 filling. This band could provide an opportunity for observing large spin-charge separation if electron-electron interactions…
Searches for low-energy tetrahedral polymorphs of carbon and silicon have been performed using density functional theory computations and the ab initio random structure searching (AIRSS) ap- proach. Several of the hypothetical phases…
The atomic structure of self-assembled quasi-one-dimensional Gd chains on Si(111) has been investigated by low-energy electron diffraction and scanning tunneling microscopy. Based on comparison between Gd and Ca chains we show that this Gd…
In this paper, we present a new module to predict the potential surface reconstruction configurations of given surface structures in the framework of our machine learning and graph theory assisted universal structure searcher (MAGUS). In…
We discuss the possibility of a 2D ordered structure formed upon deposition of Si on metal surfaces. We investigate the atomic and electronic structure of the Si-$(\sqrt{19}\times\sqrt{19})R23.4^{\circ}$/Pt(111) surface reconstruction by…
The structure of amorphous silicon is widely thought of as a fourfold-connected random network, and yet it is defective atoms, with fewer or more than four bonds, that make it particularly interesting. Despite many attempts to explain such…
The nature of the alpha-Sn/Ge(111) surface is still a matter of debate. In particular, two possible configurations have been proposed for the 3x3 ground state of this surface: one with two Sn adatoms in a lower position with respect to the…
In this article we show that the reconstructions of semiconductor surfaces can be determined using a genetic procedure. Coupled with highly optimized interatomic potentials, the present approach represents an efficient tool for finding and…
Creating materials with structure that is independently controllable at a range of scales requires breaking naturally occurring hierarchies. Breaking these hierarchies can be achieved via the decoupling of building block attributes from…
Silica or SiO$_2$, the main constituent of earth's rocks has several 3D complex crystalline and amorphous phases, but it does not have a graphite like layered structure in 3D. Our theoretical analysis and numerical calculations from the…