Nuclear quantum effects in calculated NMR shieldings of benzene; a Feynman path integral study

The Feynman path integral Monte Carlo approach has been coupled to the gauge including atomic orbital formalism in order to analyse the absolute magnetic shieldings of the benzene nuclei under the conditions of thermal equilibrium. The Hamiltonian employed in the derivation of ensemble averaged NMR quantities is of the Hartree-Fock type. The basis set used is of 6–31G quality. The spatial delocalization of the atoms leads to a deshielding of both types of benzene nuclei relative to the shieldings experienced at the minimum of the potential energy surface. This deshielding has to be traced back to bond length elongations in thermal equilibrium. The influence of the nuclear fluctuations on the NMR parameters of benzene is quantum driven up to temperatures of 400 K; classical fluctuations are of minor importance in this low-temperature window.     

Influence of air pollution and site conditions on trends of carbon and oxygen isotope ratios in tree ring cellulose

Oxygen and carbon isotopic compositions of tree ring cellulose (δ¹³C_cell and δ¹⁸O_cell) were measured for pines growing at four sites in east Germany. Three sites differed markedly in soil water availability within a short distance and the fourth site served as a reference. The choice of the sites was guided by the desire to detect effects of air pollution on the long-term trend of isotopic compositions and to examine the influence of soil water availability on the relationship between the carbon and oxygen isotope ratios. Locations in east Germany are particularly well suited for the study of pollution effects because there was a steady increase in environmental contamination until the German Reunification in 1990, followed by a sharp decline due to the implementation of stricter environmental standards.

The long-term trend of δ¹³C_cell showed an extraordinary increase in the period 1945–1990 and a rapid decrease after 1990, whereas δ¹⁸O_cell remained nearly constant. The increase of δ¹³C_cell is explained by secondary fractionation caused by phytotoxicity of SO₂. Two effects are mainly responsible for the secondary fractionation under SO₂ exposure: increase of dark respiration, and changes in photosynthate allocation and partitioning. Both effects do not influence δ¹⁸O_cell. Furthermore, a significant positive correlation between the year-to-year variations of carbon and oxygen isotope ratios (δ¹³C_resid and δ¹⁸O_resid) has been found for all sites. The slopes of the relationship between δ¹³C_resid and δ¹⁸O_resid differ insignificantly. It is concluded that this relationship is not influenced by soil water availability but by climatic variables.     

Temperature derivatives of the bulk modulus of ZrB2 calculated by using the pressure derivative of the bulk modulus

The temperature dependence of the bulk modulus of ZrB₂ above room temperature was calculated by using the equations by Garai and Laugier (J. Appl. Phys. 101 (2007) p.023514) and Lawson and Ledbetter (Philos Mag. 91 (2011) p.1425). The present calculations involve the accurate data for pressure derivative of the bulk modulus for the Anderson–Grüneisen parameter in addition to the other experimental parameters involved. It is interesting to note that the cited equations derived by different thermodynamic approaches give almost equivalent values for the temperature dependencies of the bulk modulus of ZrB₂. The present results for the temperature derivatives of the bulk modulus of ZrB₂ vary from ?0.016?GPa/K at 300–400?K to ?0.022?GPa/K at 1500–1600?K, being in good agreements with the corresponding experimental values.     

Cogenerators for convex spaces

We give cogenerators for the categories of convex (= finitely superconvex), finitely positively convex, and absolute convex (= finitely totally convex) spaces introduced by Pumplün and Röhrl.Dedicated to our academic teacher Dieter Pumplün on the occasion of his sixtieth birthday.     

On input/output stabilization of singular integrodifferential systems

In this paper we consider a class of systems described by singular integrodifferential equations. This type of systems appear, for example, in the modeling of certain aeroelastic control problems. We study these systems in frequency domain framework and show the existence of finite-dimensional stabilizing controllers. An algorithmic procedure is outlined for the construction of such controllers. In order to illustrate the numerical aspects of this algorithm, we present an example involving the classical Theodorsen model of an airfoil, which fits in the class of systems considered here.This work was supported in part by the National Science Foundation under Grants DMS-8907019 and MSS-9203418.     

Calculation of wavefunctions and frequencies for noninfinitesimal vibrations: Comparison of various methods using ab initio CI potential curves

Three computational methods employing different means of representing molecular potentials are used to obtain wavefunctions and energy levels for noninfinitesimal vibrations. An interpolation scheme based on a cubic spline fitting procedure is introduced to supplement the CI energy results obtained explicitly in actual calculations. As long as a representative set of potential points is available it is found that the results of all three methods (two of variational and one of numerical integration type) are quite consistent, for both bending and stretching vibrations of ground and electronically excited states (examples for HCN and O₂ are considered). In addition a comparison of one- and two-dimensional bending vibrational treatments is made.     

250 W end-pumped Nd:YAG laser with direct pumping into the upper laser level

A high-power longitudinally pumped Nd:YAG laser using direct pumping into the upper laser level is demonstrated. With an absorbed pump power of 438 W an output power of 250 W was realized, which results in an optical-to-optical efficiency of 57%. To the best of our knowledge, this is the first demonstration of a high-output power 885 nm pumped laser design.