Function spaces and product topologies on powers of spaces

A study is made of two classes of product topologies on powers of spaces: the general box product topologies, and the general uniform product topologies. Some examples are given and some results are shown about the properties of these general product spaces. This is applied to show that certain spaces of continuous functions with the fine topology are homeomorphic to box product spaces, and certain spaces of continuous functions with the uniform topology are homeomorphic to uniform product spaces.     

Molecular flexibility effects upon liquid dynamics

Simulation results for the diffusive behavior of polymer chain/penetrant systems are analyzed. The attractive range and flexibility of simple chain molecules were varied in order to gauge the effect on dynamics. In all cases, the dimensionless diffusion coefficient, D*, is found to be a smooth, single-valued function of the packing fraction, eta. The functions D*(eta) are found to be power laws with exponents that are sensitive to both chain stiffness and particle type. For a specific system type, the D*'s for both penetrant and chain-center-of-mass extrapolate to zero at the same packing fraction, eta0. This limiting packing fraction is interpreted to be the location of the glass transition, and (eta0-eta), the distance to the glass transition.     

Oxidation of W(110) studied by LEED and STM

The oxidation of W(110) was studied over a temperature a range of 1000 K to 1600 K at 1 × 10^? 6 Torr oxygen. The subsequent oxide structure was then characterized using Low Energy Electron Diffraction (LEED) and Scanning Tunneling Microscopy (STM). It was found that the resulting structure was remarkably similar to that of Mo(110) oxidized under similar conditions. Using the Mo(110) oxide structure as our basis, along with atomic resolution STM images, we have constructed a model for the surface oxide of W(110).     

Bethe's Equation Is Incomplete for the XXZ Model at Roots of Unity

We demonstrate for the six vertex and XXZ model parameterized by = –(q+q^-1)/2±1 that when q^2N=1 for integer N2 the Bethe's ansatz equations determine only the eigenvectors which are the highest weights of the infinite dimensional sl₂ loop algebra symmetry group of the model. Therefore in this case the Bethe's ansatz equations are incomplete and further conditions need to be imposed in order to completely specify the wave function. We discuss how the evaluation parameters of the finite dimensional representations of the sl₂ loop algebra can be used to complete this specification.     

Optical and resonant X-ray diffraction studies confirm a SmC*FI2-SmC* liquid crystal phase sequence reversal

Employing both null transmission ellipsometry and resonant x-ray diffraction, we confirmed the SmC*FI2-SmC* phase sequence reversal in one liquid crystal compound and specially prepared binary mixtures. This phase sequence reversal was predicted by two recent theoretical advances. Moreover, the temperature range for the SmC*FI2 phase increases significantly in the mixture suggesting that such a phase sequence may exist in other compounds.     

Moving average fields, macro-scale response measures, and homogenizing micro-scale variation

There are two critical issues when deriving a macro-scale prediction model starting from a more complete, underlying model. The first is the precise relationship of the fields predicted by the more complete model and the fields predicted by the macro-scale model. The second is the manner of solving a closure problem that is invariably encountered in all such derivations. The understanding that moving averages of the fields predicted by the more complete model are the fields predicted by the macro-scale model is challenged on the grounds that accomplishing a moving average does not eliminate micro-scale variation, it only appears to do so in one representation of the moving average field. The solution of a closure problem by assumption is challenged on the grounds that the most common assumptions are demonstrably invalid, even while leading to prediction models that can provide reasonable estimates of the macro-scale response in some scenarios. In presenting the challenges, it is further shown how a multiresolution analysis by an orthogonal wavelet system provides a framework for both precisely defining macro-scale response fields, i.e., fields from which all micro-scale variation has been eliminated, and presenting a formally exact solution for a precisely described closure problem.     

Spectroscopic characterization of peroxynitrous acid in cis-perp configurations

This paper presents experimental evidence, supported by two-dimensional theoretical calculations, that HOONO can be observed in cis-perp (cp) configurations in a pulsed supersonic expansion. The spectral properties (transition frequency, rotational constants, and transition type) of OH overtone transitions originating from a state with predominately cp character are predicted theoretically and compared with those associated with a weak feature at 6996.2 cm(-1) observed experimentally using infrared action spectroscopy. This spectral feature is attributed to HOONO in cp configurations based on its vibrational frequency, rotational band contour, and resultant OH product state distribution.