Description of the smooth rms charge radius surface R(N, Z) and prediction of neutron skin by a two-liquid drop model

The smooth N and Z dependence of nuclear rms charge radii is interpereted by a two-liquid drop model with ?_p+?_n=?₀=const. Proton and neutron radii R _p and R _n are given in closed form. In addition to rms charge radii, the model yields the nucleon number dependence of the skin thickness, s, e.g. ds=0.00124×dA for Sn isotopes, in agreement with experimental results and theoretical calculations. A strong correlation between the two global parameters of the model — including s _stthe skin thickness of the stable isotope — is established. If s _stis taken from experiment, the other parameter is also fixed; this parameter (m) characterizes the restoring force responsible for the skin thickness. Its value m=2.2 suggests that — in addition to the number of nucleons in the skin — the skin thickness also influences the distribution of “surplus” nucleons between volume and skin.     

Theoretical framework and experimental procedure for modelling mesoscopic volume fraction stochastic fluctuations in fiber reinforced composites

Many engineering materials exhibit fluctuations and uncertainties on their macroscopic mechanical properties. This randomness results from random fluctuations observed at a lower scale, especially at the meso-scale where microstructural uncertainties generally occur. In the present paper, we first propose a complete theoretical stochastic framework (that is, a relevant probabilistic model as well as a non-intrusive stochastic solver) in which the volume fraction at the microscale is modelled as a random field whose statistical reduction is performed using a Karhunen–Loeve expansion. Then, an experimental procedure dedicated to the identification of the parameters involved in the probabilistic model is presented and relies on a non-destructive ultrasonic method. The combination of the experimental results with a micromechanical analysis provides realizations of the volume fraction random field. In particular, it is shown that the volume fraction can be modelled by a homogeneous random field whose spatial correlation lengths are determined and may provide conditions on the size of the meso-volumes to be considered.     

Planetenbewegungen des Flaggenraumes

In [8] the author gave a report on some properties of flag space motions, especially of the composition of screw motions or rotations in flag space. Planet motions more generally are motions which can be composed by two one-parameter-groups. These motions are investigated with respect to their orbits, their multiple ways of construction and the tubular surfaces they can determine. Some of them yield tubular screw surfaces, some others move every sphere the way that it again envellopes a sphere. These motions, which have no Euclidean counterpart, determine non-trivial, kinematically generated LIE-transformations in flag space.     

Ansa macrolides as molecular workbenches for stereoselective additions to achiral (E) olefins

Highly stereocontrolled additions to achiral acyclic (E) olefins are achieved via incorporation into an ansa macrolide with a non-racemic stilbene diol (molecular workbench approach).