Related papers: A Classification Scheme for Toroidal Molecules
In this paper we treat in details a modular variety $\cal Y$ that has a Calabi-Yau model, $\tilde{\cal Y}$. We shall describe the structure of the ring of modular forms and its geometry. We shall illustrate two different methods of…
Chiral heteropolymers such as larger globular proteins can simultaneously support multiple length scales. The interplay between different scales brings about conformational diversity, and governs the structure of the energy landscape.…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
Electron microscopy techniques are instrumental in the characterization of energy storage materials, with atomic resolution images providing the detailed structural features that are needed to understand their properties. Atomically…
We classify edge-to-edge tilings of the sphere by congruent pentagons with the edge combination $a^4b$ and with rational angles in degree: they are a one-parameter family of symmetric $a^4b$-pentagonal subdivisions of the tetrahedron with…
We determine the structure of the Hodge ring, a natural object encoding the Hodge numbers of all compact Kaehler manifolds. As a consequence of this structure, there are no unexpected relations among the Hodge numbers, and no essential…
Predicting the structure of multi-protein complexes is a grand challenge in biochemistry, with major implications for basic science and drug discovery. Computational structure prediction methods generally leverage pre-defined structural…
We consider the interaction of electromagnetic radiation of arbitrary polarization with multi-level atoms in a self-consistent manner, taking into account both spatial and temporal dependencies of local fields. This is done by numerically…
A cluster consisting of many atoms or molecules may be considered, in some circustances, to be a single large molecule with a well defined polarizability. Once the polarizability of such a cluster is known, one can evaluate certain…
Models, describing relativistic particles, where Lagrangian densities depend linearly on both the curvature and the torsion of the trajectories, are revisited in D=3 space forms. The moduli spaces of trajectories are completely and…
The three-dimensional cranking model is used to investigate the microscopic aspects of the rotation of nuclei with the tetrahedral symmetry. Two classes of rotation axes are studied corresponding to two different discrete symmetries of the…
Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also the universal localisations of a hereditary ring, or…
We have derived orbital basis sets from scattering theory. They are expressed as polynomial approximations to the energy dependence of a set of partial waves, in quantized form. The corresponding matrices, as well as the Hamiltonian and…
Semi-empirical quantum chemistry has recently seen a renaissance with applications in high-throughput virtual screening and machine learning. The simplest semi-empirical model still in widespread use in chemistry is H\"uckel's…
A method has been recently proposed to establish the geometry of the alpha-cluster arrangement in $^{12}$C making use of polarized gamma-rays. The ratio of intensities of scattered radiation at 90 degrees along and perpendicular to the…
By studying the structures of clusters bound by a model potential that favours polytetrahedral order, we find a previously unknown series of `magic numbers' (i.e. sizes of special stability) whose polytetrahedral structures are…
We describe limits of line bundles on nodal curves in terms of toric arrangements associated to Voronoi tilings of Euclidean spaces. These tilings encode information on the relationship between the possibly infinitely many limits, and…
We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…
A central issue in molecular orbital theory is to compute the HOMO-LUMO gap of a molecule, which measures the excitability of the molecule. Thus it would be of interest to learn how to construct a molecule with the prescribed HOMO-LUMO gap.…
Despite being the main tool to visualize molecules at the atomic scale, AFM with CO-functionalized metal tips is unable to chemically identify the observed molecules. Here we present a strategy to address this challenging task using deep…