Dimension theory and nonstable K1 of quadratic modules

Employing Bak’s dimension theory, we investigate the nonstable quadratic K-group K1,2n(A, ) = G2n(A, )/E2n(A, ), n 3, where G2n(A, ) denotes the general quadratic group of rank n over a form ring (A, ) and E2n(A, ) its elementary subgroup. Considering form rings as a category with dimension in the sense of Bak, we obtain a dimension filtration G2n(A, ) G2n0(A, ) G2n1(A, ) E2n(A, ) of the general quadratic group G2n(A, ) such that G2n(A, )/G2n0(A, ) is Abelian, G2n0(A, ) G2n1(A, ) is a descending central series, and G2nd(A)(A, ) = E2n(A, ) whenever d(A) = (Bass–Serre dimension of A) is finite. In particular K1,2n(A, ) is solvable when d(A) <.

Emission-line ratios for [N II] in gaseous nebulae and a comparison between theory and observation

R-matrix calculations of electron impact excitation rates among the 2s(2)2p(2) P-3, D-1, S-1, and 2s2p(3) S-5 levels of N II are presented. These results are used in conjunction with other recent calculations of electron impact excitation rates and Einstein A-coefficients for N II to derive the emission-line ratio: ratio diagrams and where (R-1, R-2) (R-1, R-3), where R-1 = I(5756.2 Angstrom)/I(6549.9 + 6585.2 Angstrom), R-2 = I(2143.5 Angstrom)/I(6549.9 + 6585.2 Angstrom), and R-3 = I(2139.7 Angstrom)/I(6549.9 + 658.2 Angstrom), for a range of electron temperatures (T-e = 5000-20,000 K) and electron densities (N-e = 10(2)-10(7) cm(-3)) appropriate to gaseous nebulae. These diagrams should, in principle, allow the simultaneous determination of T-e and N-e from measurements of the [N II] lines in a spectrum. Plasma parameters deduced for a sample of gaseous nebulae, using observational data obtained from ground-based telescopes plus the International Ultraviolet Explorer and Hubble Space Telescope satellites, are found to show generally excellent internal consistency and to be in good agreement with the values of T-e and N-e estimated from other line ratios. These results provide observational support for the accuracy of the theoretical ratios and hence the atomic data adopted in their derivation. Theoretical ratios are also presented for the infrared line pair R-4 = I(122 mum)/I(205 mum), and the usefulness of R-4 as an electron density diagnostic is briefly discussed.

Semiclassical complex angular momentum theory and Pade reconstruction for resonances, rainbows, and reaction thresholds

A semiclassical complex angular momentum theory, used to analyze atom-diatom reactive angular distributions, is applied to several well-known potential (one-particle) problems. Examples include resonance scattering, rainbow scattering, and the Eckart threshold model. Pade reconstruction of the corresponding matrix elements from the values at physical (integral) angular momenta and properties of the Pade approximants are discussed in detail.

Structural and chemical embrittlement of grain boundaries by impurities: A general theory and first-principles calculations for copper

First-principles calculations of the Sigma 5(310)[001] symmetric tilt grain boundary in Cu with Bi, Na, and Ag substitutional impurities provide evidence that in the phenomenon of Bi embrittlement of Cu grain boundaries electronic effects do not play a major role; on the contrary, the embrittlement is mostly a structural or "size" effect. Na is predicted to be nearly as good an embrittler as Bi, whereas Ag does not embrittle the boundary in agreement with experiment. While we reject the prevailing view that "electronic" effects (i.e., charge transfer) are responsible for embrittlement, we do not exclude the role of chemistry. However, numerical results show a striking equivalence between the alkali metal Na and the semimetal Bi, small differences being accounted for by their contrasting "size" and "softness" (defined here). In order to separate structural and chemical effects unambiguously if not uniquely, we model the embrittlement process by taking the system of grain boundary and free surfaces through a sequence of precisely defined gedanken processes; each of these representing a putative mechanism. We thereby identify three mechanisms of embrittlement by substitutional impurities, two of which survive in the case of embrittlement or cohesion enhancement by interstitials. Two of the three are purely structural and the third contains both structural and chemical elements that by their very nature cannot be further unraveled. We are able to take the systems we study through each of these stages by explicit computer simulations and assess the contribution of each to the net reduction in intergranular cohesion. The conclusion we reach is that embrittlement by both Bi and Na is almost exclusively structural in origin; that is, the embrittlement is a size effect.