Development and Implementation of NURBS Models of Quadratic Curves and Surfaces

This article goes into the development of NURBS models of quadratic curves and surfaces. Curves and surfaces which could be represented by one general equation (one for the curves and one for the surfaces) are addressed. The research examines the curves: ellipse, parabola and hyperbola, the surfaces: ellipsoid, paraboloid, hyperboloid, double hyperboloid, hyperbolic paraboloid and cone, and the cylinders: elliptic, parabolic and hyperbolic. Many real objects which have to be modeled in 3D applications possess specific features. Because of this these geometric objects have been chosen. Using the NURBS models presented here, specialized software modules (plug-ins) have been developed for a 3D graphic system. An analysis of their implementation and the primitives they create has been performed

Spectral shift function for operators with crossed magnetic and electric fields

We obtain a representation formula for the derivative of the spectral shift function $\xi(\lambda; B, \epsilon)$ related to the operators $H_0(B,\epsilon) = (D_x - By)^2 + D_y^2 + \epsilon x$ and $H(B, \epsilon) = H_0(B, \epsilon) + V(x,y), \: B > 0, \epsilon > 0$. We establish a limiting absorption principle for $H(B, \epsilon)$ and an estimate ${\mathcal O}(\epsilon^{n-2})$ for $\xi'(\lambda; B, \epsilon)$, provided $\lambda \notin \sigma(Q)$, where $Q = (D_x - By)^2 + D_y^2 + V(x,y).

Polyhedral units and network connectivity in calcium aluminosilicate glasses from high-energy x-ray diffraction

Structure factors for Cax/2AlxSi1-xO2 glasses (x=0,0.25,0.5,0.67) extended to a wave vector of magnitude Q= 40 1/A have been obtained by high-energy x-ray diffraction. For the first time, it is possible to resolve the contributions of Si-O, Al-O and Ca-O coordination polyhedra to the experimental atomic pair distribution functions (PDF). It has been found that both Si and Al are four-fold coordinated and so participate in a continuous tetrahedral network at low values of x. The number of network breaking defects in the form of non-bridging oxygens (NBO's) increases slowly with x until x=0.5 (NBO's ~ 10% at x=0.5). By x=0.67 the network breaking defects become significant as evidenced by the significant drop in the average coordination number of Si. By contrast, Al-O tetrahedra remain free of NBO's and fully integrated in the Al/Si-O network for all values of x. Calcium maintains a rather uniform coordination sphere of approximately 5 oxygen atoms for all values of x. The results suggest that not only Si/Al-O tetrahedra but Ca-O polyhedra, too, play a role in determining the glassy structure

Transition rates and nuclear structure changes in mirror nuclei 47Cr and 47V

Lifetime measurements in the mirror nuclei 47Cr and 47V were performed by means of the Doppler-shift attenuation method using the multidetector array EUROBALL, in conjunction with the ancillary detectors ISIS and the Neutron Wall. The determined transition strengths in the yrast cascades are well described by full pf shell model calculations.Comment: Latex2e, 11 pages, 3 figure

Lifetime measurement of excited low-spin states via the (p,p′γ(p,p^{\prime}\gamma) reaction

In this article a method for lifetime measurements in the sub-picosecond regime via the Doppler-shift attenuation method (DSAM) following the inelastic proton scattering reaction is presented. In a pioneering experiment we extracted the lifetimes of 30 excited low-spin states of $^{96}$Ru, taking advantage of the coincident detection of scattered protons and de-exciting $\gamma$-rays as well as the large number of particle and $\gamma$-ray detectors provided by the SONIC@HORUS setup at the University of Cologne. The large amount of new experimental data shows that this technique is suited for the measurement of lifetimes of excited low-spin states, especially for isotopes with a low isotopic abundance, where $(n,n^{\prime}\gamma$) or - in case of investigating dipole excitations - ($\gamma,\gamma^{\prime}$) experiments are not feasible due to the lack of sufficient isotopically enriched target material

Parallel computing and molecular dynamics of biological membranes

In this talk I discuss the general question of the portability of Molecular Dynamics codes for diffusive systems on parallel computers of the APE family. The intrinsic single precision arithmetics of the today available APE platforms does not seem to affect the numerical accuracy of the simulations, while the absence of integer addressing from CPU to individual nodes puts strong constraints on the possible programming strategies. Liquids can be very satisfactorily simulated using the "systolic" method. For more complex systems, like the biological ones at which we are ultimately interested in, the "domain decomposition" approach is best suited to beat the quadratic growth of the inter-molecular computational time with the number of elementary components of the system. The promising perspectives of using this strategy for extensive simulations of lipid bilayers are briefly reviewed.Comment: 4 pages LaTeX, 2 figures included, espcrc2.sty require