Localized defects in classical one-dimensional models

Several aspects of localized defects in the Frenkel-Kontorova, classicalXY chain and analogous models with a finite range of interactions are discussed from a general point of view. Precise definitions are given for defect phase shifts (charges) and for creation, pinning, and interaction energies. Corresponding definitions are also provided for interfaces (localized regions separating two phases). For the nearest-neighbor Frenkel-Kontorova model, the various defect energies are related to areas enclosed by contours joining heteroclinic points of the area-preserving map generated by the conditions of mechanical equilibrium.     

An approximately divergence-free 9-node velocity element (with variations) for incompressible flows

Explicit basis functions are constructed for 9-node biquadratic velocity fields which guarantee that a weak form of the continuity equation is satisfied. The corresponding pressure approximations are either piecewise constant, piecewise linear or piecewise bilinear. These results are extended to give bases for bilinear velocity/piecewise constant pressure elements and also to some three-dimensional brick elements.     

Inhibierung der Autoxydation von Polypropylenoxid durch KOH

Ohne Zusammenfassung     

Raman study of the O2F2 + VF5 reaction: Isolation and identification of an unstable reaction intermediate

The reaction of O₂F₂ with polymeric VF₅ in the temperature range -119 to -78°C leads first to the reaction intermediates

. On increasing the temperature of this intermediate, a new compound O⁺₂V₂F^-₁₁ is formed which in turn decomposes rapidly at room temperature. Raman studies of these species as well as of O₂F₂(solid), VF₅, KVF₆, KV₂F₁₁, CsVF₆ and CsV₂F₁₁ are reported and discussed.     

The collision of plane waves in general relativity

A number of exact solutions of Einstein's equations are obtained, which describe the collision and subsequent interaction of two plane parallel waves. Gravitational waves, null electromagnetic fields, and neutrino fields are all considered with collisions between any two types. It is shown that two such waves mutually focus each other with the focus usually appearing as a singularity in space-time. Further conclusions are made regarding the qualitative nature of the interactions, and it is argued that these also apply in more realistic physical situations.     

A Newman-Penrose-type formalism for space-times with torsion

The familiar Newman-Penrose formalism, in which the curvature of space-time is represented in terms of spin coefficients, is here extended to include the possibility of an asymmetric connection. It is hoped that this approach will be useful in dealing with certain problems in Einstein-Cartan theory, and also in other theories of gravitation that include torsion.     

Folded chain crystallization of poly(N-vinylcarbazole)

A study of the morphology of thermally induced crystallization in poly(N-vinylcarbazole) has shown the formation of folded chain lamellae. Diffraction analysis of multiple and single lamellae indicates a paracrystalline structure with hexagonal symmetry about the chain axis and an interchain spacing of 12.00 Å. No sharp reflections due to chain axis periodicity were observed and the chain axis period was calculated from the crystalline density extrapolated to 100% crystallinity. This gave a chain axis period/monomer unit of 2.16 Å consistent with an isotactic 3/1 screw axis and a basic trigonal structure with a = 12.00 Å and c = 6.47 Å.     

Convexity violations for noninteger parameters in certain lattice models

The convexity of the free energy is studied for several lattice models in situations in which a parameter which is normally a positive integer takes on noninteger real values. Examples include the numbern of components in then-vector model, the number of states in the Potts model, and the dimensionality of the lattice. In a typical case there is a critical value of the parameter such that convexity is preserved when the parameter exceeds the critical value, but can be violated for appropriate Hamiltonians whenever the parameter is less than the critical value, but not a positive integer. In several cases the critical value of the parameter increases with the size of the system, thus raising questions about the significance of a continuous variation of the parameter in the thermodynamic limit.     

Spectra of inert-gas matrices containing bismuth: ground-state frequency of Bi2

Bi, Bi₂, Bi₄, and possibly Bi₃ in inert-gas matrices were observed and characterized. Their spectra exhibit negligible shifts from matrix to matrix and, when known, from gas to matrix. The Bi₂ Raman frequency in Ne is measured at 173 ± 1 cm^?1, in excellent agreement with the gas phase.