Cubic or 3-regular graphs are (simple) graphs where each vertex has degree 3. The class of cubic graphs is especially interesting for mathematical applications because for various important open problems in graph theory cubic graphs are the smallest or simplest possible potential counterexamples. In chemistry, cubic graphs serve as models for the Nobel Prize winning fullerenes [14] or, more gen...

In this thesis, quantum-mechanical calculations within density-functional theory on metallic systems are presented. The overarching goal has been to investigate effects of disorder. In particular, one of the properties investigated is the bindingenergy shifts for core electrons in binary alloys using different theoretical methods. These methods are compared with each other and with experimental...

Complex transition-metal oxides are important functional materials in areas such as energy and information storage. The cubic ABO3 perovskite is an archetypal example of this class, formed by the occupation of small octahedral B-sites within an AO3 network defined by larger A cations. We show that introduction of chemically mismatched octahedral cations into a cubic perovskite oxide parent phas...

We present our recent results on the growth of cubic AlN (001) layers by plasma assisted molecular beam epitaxy (PAMBE) using freestanding 3C-SiC (001) substrate. For high-quality c-AlN layers reflection high-electron energy diffraction (RHEED) patterns in all azimuths show RHEED patterns of the cubic lattice, hexagonal reflections are absent. Highresolution X-ray diffraction (HRXRD) measuremen...

One of the most important open problems in computational biology is the prediction of the conformation of a protein based on its amino acid sequence. In this paper, we design approximation algorithms for protein structure prediction in the so-called HP side chain model. The major drawback of the standard HP side chain model is the bipartiteness of the cubic lattice. To eliminate this drawback, ...

We report an ab initio study of the effect of hydrostatic pressure and uniaxial strain on electronic properties of KNa2Bi, a cubic bialkali bismuthide. It is found that this zero-gap semimetal with an inverted band structure at the Brillouin zone center can be driven into various topological phases under proper external pressure. We show that upon hydrostatic compression KNa2Bi turns into a tri...

The crystal structures of ordered b.c.c. (body-centered cubic), f.c. c. (face-centered cubic) or primitive cubic alloys AxBy and related NaCl, ZnS or CaF(2) derivative structures are characterized by the self-coordination numbers T(1), T(2) of the A atoms with A atoms. Structures with identical T(1) and T(2) values for all A atoms are at the corners of T(1) and T(2) structure maps, and can be a...

The phase stability of group VB (V, Nb, and Ta) transition metals is explored by first-principles electronic-structure calculations. Alloying with a small amount of a neighboring metal can either stabilize or destabilize the body-centered-cubic phase relative to low-symmetry rhombohedral phases. We show that band-structure effects determine phase stability when a particular group VB metal is al...

Low-temperature structures of the lithium manganese spinels were determined using TOF neutron Rietveld analysis. The spinels LiMn2O4 with different values, (0.016, 0.040, and 0.132) showed the cubic-orthorhombic phase transitions, and the lattice distortion decreased with decreasing . Although no anomaly corresponding to the cubic-orthorhombic phase transition was observed in the DSC curve for ...

Traditionally, ice I was considered to exist in two well-defined crystalline forms at ambient pressure: stable hexagonal ice (ice Ih) and metastable cubic ice (ice Ic). However, it is becoming increasingly evident that what has been called cubic ice in the past does not have a structure consistent with the cubic crystal system. Instead, it is a stacking-disordered material containing cubic sequ...