Approximate Euclidean Steiner Trees

An approximate Steiner tree is a Steiner tree on a given set of terminals in Euclidean space such that the angles at the Steiner points are within a specified error from \(120^{\circ }\). This notion arises in numerical approximations of minimum Steiner trees. We investigate the worst-case relative error of the length of an approximate Steiner tree compared to the shortest tree with the same topology. It has been conjectured that this relative error is at most linear in the maximum error at the angles, independent of the number of terminals. We verify this conjecture for the two-dimensional case as long as the maximum angle error is sufficiently small in terms of the number of terminals. In the two-dimensional case we derive a lower bound for the relative error in length. This bound is linear in terms of the maximum angle error when the angle error is sufficiently small in terms of the number of terminals. We find improved estimates of the relative error in length for larger values of the maximum angle error and calculate exact values in the plane for three and four terminals.     

MEASUREMENT OF ADHESION FORCES IN AIR WITH THE VIBRATION METHOD

The vibration method represents a practical method for the measurement of adhesion forces and adhesion force distributions. This method causes sinusoidally altemating stresses and yields detachment and contact forces between particles and substrate of the same order of magnitude. Alternating contact forces of the vibration method can cause an adhesion force intensification through flattening of asperities. The measuring principle of the vibration method and the analysis of experimental results are described in the article. Normal adhesion forces (pull-off forces) are measured using the vibration method and the colloidal probe technique. The results of both methods show good agreement for small particle sizes. The influence of the detachment force direction is shown by comparing tangential and normal adhesion forces measured using particle reentrainment in a turbulent air flow and the vibration method, respectively. The surface roughness of the substrate and the relative humidity are shown to significantly influence the measured adhesion forces. For the calculation of the adhesion forces, an approach by Rabinovich was combined with approximations of plastic micro asperity flattening. The Rabinovich approach accounts for roughness effects on the van der Waals force by incorporating the rms roughness of the interacting surfaces. rms-values of the particles and substrates were measured with atomic force microscopy at different scanning areas.     

Weak intermolecular interactions in gas-phase nuclear magnetic resonance

Gas-phase nuclear magnetic resonance (NMR) spectra demonstrating the effect of weak intermolecular forces on the NMR shielding constants of the interacting species are reported. We analyse the interaction of the molecular hydrogen isotopomers with He, Ne, and Ar, and the interaction in the He-CO(2) dimer. The same effects are studied for all these systems in the ab initio calculations. The comparison of the experimental and computed shielding constants is shown to depend strongly on the treatment of the bulk susceptibility effects, which determine in practice the pressure dependence of the experimental values. Best agreement of the results is obtained when the bulk susceptibility correction in rare gas solvents is evaluated from the analysis of the He-rare gas interactions, and when the shielding of deuterium in D(2)-rare gas systems is considered.     

Chemical tailoring of fullerene acceptors: synthesis, structures and electrochemical properties of perfluoroisopropylfullerenes

High-temperature syntheses of the new C(60)(i-C(3)F(7))(2,4,6) and C(70)(i-C(3)F(7))(2,4) isomers and their characterization by spectroscopic methods, X-ray crystallography, cyclic voltammetry and density functional theory provide compelling evidence that they are superior electron acceptors than trifluoromethylfullerenes.     

Generation of potential energy surfaces in high dimensions and their haptic exploration

A method is proposed for the automated generation of potential energy surfaces in high dimensions. It combines the existing algorithm for the definition of new energy data points, based on the interpolating moving least-squares algorithm with a simulated annealing procedure. This method is then studied in a haptic quantum chemistry environment that requires a fast evaluation of gradients on a potential energy surface with automatic improvement of its accuracy. As an example we investigate the nitrogen binding pathway in the Schrock dinitrogen fixation complex with this set-up.     

A Monte Carlo calculation of thermodynamic properties for the liquid NaCl+KCl mixture

The mixing process NaCl+KCl →(Na, K)Cl in the liquid state at T=1083 K and zero pressure is simulated by means of Monte Carlo calculations. A cubic box with periodic boundary conditions containing 216 ions interacting according to a pair potential of the Huggins-Mayer form served as a model of the system. Thermodynamic properties are calculated for the mixture and the pure salt models and compared with experiments. Radial and angular distribution functions are obtained. A perturbation theory of the heats of mixing of molten salts and the ‘random mixture approximation’ are commented on in the light of the Monte Carlo results.     

Stability for a class of bilocal Hamiltonians

We introduce a method to establish stability of non-local interactions, and we apply this method to certain polynomial non-linear field theory. The non-local potential must satisfy the property ofslow decrease at infinity in Fourier space (SDI).Dedicated to Huzihiro ArakiSupported in part by the National Science Foundation under Grant PHY91-20626