Density Functional Calculation of the Photoelectron Emission Spectra of BiSCl Crystal and Molecular Clusters

The photoelectron emission spectra of BiSCl crystal and molecular clusters have been calculated by the Density Functional Theory (DFT) method. Molecular clusters consists from 2 to 20 molecules in one double chain along z(c) axis. Total and partial density of states of BiSCl crystal and clusters have been weighted with atomic photoemission emission cross-section. The molecular clusters have been investigated including all normal modes of vibration. Theoretical results of BiSCl crystal and molecular clusters have been compared with experimental X-ray photoelectron emission spectra (XPS) of BiSI crystal.     

Normalized Leonard pairs and Askey-Wilson relations

Let V denote a vector space with finite positive dimension, and let (A, A^∗) denote a Leonard pair on V. As is known, the linear transformations A, A^∗ satisfy the Askey-Wilson relations

     

Hyperfine structure operator in the tensorial form of second quantization

The general tensorial form of the hyperfine interaction operator in the formalism of second quantization is presented. Both diagonal and off-diagnonal matrix elements of the above-mentioned operator are found using an approach based on a combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin) and a generalised graphical technique. This methodology allows us to account for correlation effects efficiently and, therefore, to study the hyperfine interactions in complex many-electron atoms, those with openf-shells included, in a practical manner. All this will lead us to design an efficient program for large scale calculations of hyperfine structure and isotope shift.     

Theoretical investigation of the electronic structure of a ferroelectric SbSI cluster at a phase transition

This paper presents the theoretical investigation of energy levels of valence bands (VB) and core levels (CL) of the ferroelectric SbSl single crystals in antiferroelectric and ferroelectric phases. Since the best approximation for the deep VB levels is a calculation by the Hartree-Fock method, the molecular model of a SbSI crystal was used for calculations. This model of the crystal was also used for calculations of the total density of states. It was found that the VB and CL of this ferroelectric semiconductor are sensitive to the small lattice distortion at the phase transition, and that an average of the total density of states, when all atoms participate in oscillations of all normal modes, are more similar to the experimental X-ray photoelectron spectra (XPS). The experimental splitting of CL obtained by XPS was compared with the theoretically calculated one by two different methods. The cluster model calculations showed that the splitting of the CL in SbSI might be caused by photoelectron emission from the atoms, which have different valence state, at the surface.     

Composite genus one Belyi maps

Motivated by a demand for explicit genus 1 Belyi maps from theoretical physics, we give an efficient method of explicitly computing genus one Belyi maps by (1) composing covering maps from elliptic curves to the Riemann sphere with simpler (univariate) genus zero Belyi maps, as well as by (2) composing further with isogenies between elliptic curves. The computed examples of genus 1 Belyi maps has doubly-periodic dessins d’enfant that are listed in the physics literature as so-called brane-tilings in the context of quiver gauge theories.     

Single-molecule measurements of trapped and migrating circular DNA during electrophoresis in agarose gels

The effect of agarose gel concentration and field strength on the electrophoretic trapping of open (relaxed) circular DNA was investigated using microscopic measurements of individual molecules stained with a fluorescent dye. Three open circles with sizes of 52.5, 115, and 220 kbp were trapped by the electric field (6 V/cm) and found to be predominately fixed and stretched at a single point in the gel. The length of the stretched circles did not significantly change with agarose concentration of the gels (mass fractions of 0.0025, 0.01, and 0.02). The relaxation kinetics of the trapped circles was also measured in the gels. The relaxation of the large open circles was found to be a slow process, taking several seconds. The velocity and average length of the 52.5 kbp open circles and 48.5 kbp linear DNA were measured during electrophoresis in the agarose gels. The velocity increased when the agarose concentrations were lowered, but the average length of the open-circle DNA (during electrophoresis) did not significantly change with agarose gel concentrations. The circles move through the gels by cycles of stretching and relaxation during electrophoresis. Linear dichroism was also used to investigate the trapping and alignment of the 52.5 kbp open circles. The results in this study provide information that can be used to improve electrophoretic separations of circular DNA, an important form of genetic material and commonly used to clone DNA.