On the second cohomology group in semi-abelian categories

We develop some new aspects of cohomology in the context of semi-abelian categories: we establish a Hochschild-Serre 5-term exact sequence extending the classical one for groups and Lie algebras; we prove that an object is perfect if and only if it admits a universal central extension; we show how the second Barr-Beck cohomology group classifies isomorphism classes of central extensions; we prove a universal coefficient theorem to explain the relationship with homology.     

Time-resolved fluorescence measurements on Eu3+- and Eu2+-doped glasses

Various fluoride, phosphate and borosilicate glasses with known properties and global structure have been doped with Eu³⁺ (4f⁶) at doping concentrations between 10¹⁸ and 10²¹ cm^?3. By applying reductive melting conditions Eu³⁺ could partially be transformed to Eu²⁺ (4f⁷). Four fluoroaluminate glasses with varying phosphate content between 0 and 20 mol% (FPx), a pure phosphate glass (P100) and two borosilicate glasses with low (DURAN^®-like) and high optical basicity (NBS1) have been used for these investigations. The time-resolved fluorescence in the visible range has been studied for both ions. Although static and dynamic fluorescence of Eu³⁺ and Eu²⁺ are dramatically different (f–f-transitions for Eu³⁺; d–f-transitions for Eu²⁺), glass structure changes have a similar influence on the dynamic fluorescence behavior of both ions. A strongly ionic surrounding due to fluorine ligands as in fluoroaluminate glass samples provides the longest fluorescence lifetime (about 7 ms for Eu³⁺; about 1.3 μs for Eu²⁺). Increasing phosphate content decreases the fluorescence lifetime due to more oxygen ligands. Interesting differences have been found for the two borosilicate glasses due to the difference in their optical basicity (Na₂O/B₂O₃ ratio). Measurements indicate a homogeneous distribution of europium ions in most FP samples. NBS1 measurements suggest that two different local europium sites are formed. For Duran-like samples only one specific europium site was found, although these samples show phase separation at high doping concentrations into a SiO₂-rich phase and borate- and europium-rich droplets. Fluorescence quenching due to energy transfer from Eu²⁺ to Eu³⁺ could be found for co-doped samples; Eu³⁺-doped samples show no fluorescence quenching.     

Modeling slow deformation of polygonal particles using DEM

We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach improves efficiency and accuracy of the Discrete Element Method （DEM） when modeling the dynamics of the granular packing. We determine the proper upper limit for the integration step in the standard numerical scheme using a wide range of material parameters. To this end, we study the kinetic energy decay in a stress controlled test between two particles. Second, we show that the usual way of defining the contact plane between two polygonal particles is, in general, not unique which leads to discontinuities in the direction of the contact plane while particles move. To solve this drawback, we introduce an accurate definition for the contact plane based on the shape of the overlap area between touching particles, which evolves continuously in time.     

Multidimensional optimization of structural changes of molecules upon lonization in Franck-Condon factor calculations

Two different iterative methods, namely, the conjugate gradients method and the pattern search method, are applied to Franck-Condon factor calculations using the Coon et al. method (J. B. Coon, R. E. DeWames, and C. M. Loyd, J. Mol. Spectrosc.8, 235–299 (1962)) and the generating function method (T. E. Sharp and H. M. Rosenstock, J. Chem. Phys.41, 3453–3463 (1964); R. Botter, V. H. Dibeler, J. A. Walker, and H. M. Rosenstock, J. Chem. Phys.44, 1271–1278 (1966)). In such treatment, either the changes in normal coordinates or the changes in internal symmetry displacement coordinates are refined automatically until the weighted sum of square deviation between the calculated and the observed Franck-Condon factors is minimized. Some properties of the methods used are given and their applications to several cases are discussed in detail.     

Analysis of dynamic mixed mode stress fields in bimaterials by the method of caustics

The equations of caustics for dynamically extending curvilinear interface cracks are derived where optical isotropy and anisotropy of the material have been considered, respectively. The equations have been obtained by applying the method of generalized complex potentials. Moreover, an algorithm for the determination of stress intensity factors from experimentally obtained caustics is presented for the case of dynamic crack extension.     

Nuclear magnetic resonance of175Hf oriented in iron

Nuclear magnetic resonance of¹⁷⁵Hf oriented at low temperature in iron has been observed with a sample prepared by ion implantation. The centre frequency of the broad resonance line isv _L (B _ext = 0)=138.53(36)MHz. Possible origins of the large inhomogeneous line width of FWHM=11.0(1.1) MHz are discussed. A comparison with model calculations for combined magnetic and electric hyperfine interaction indicates that the centre frequency may be interpreted as the magnetic interaction frequency for¹⁷⁵Hf in unperturbed substitutional sites of the host iron. With theg-factor of¹⁷⁵Hf from literature the magnetic hyperfine field of Hf in Fe is derived asB _hf=?64.9(9.3) T fitting well into systematics.