Conic degeneration and the determinant of the Laplacian

We investigate the behavior of various spectral invariants, particularly the determinant of the Laplacian, on a family of smooth Riemannian manifolds which undergo conic degeneration; that is, which converge in a particular way to a manifold with a conical singularity. Our main result is an asymptotic formula for the determinant up to terms which vanish as the degeneration parameter goes to zero. The proof proceeds in two parts; we study the fine structure of the heat trace on the degenerating manifolds via a parametrix construction, and then use that fine structure to analyze the zeta function and determinant of the Laplacian.Comment: 41 pages, 7 figures. Version 2: bug fixed in Theorem 2 statement, other minor change

Experimentally Probing the Shape of Extra Dimensions

In brane world scenarios in which only gravity can propagate in the extra dimensions, effects on the gravitational force may be experimentally testable if there are two or three large extra dimensions. The strength of the force at distances smaller than the compactification radius will be sensitive to the volume of the extra dimensions, but the determination of the shape requires knowing the gravitational potential at intermediate scales. We determine the dependence of the potential vs. distance as a function of both the relative size of the extra dimensions and the possible angle between the extra dimensional unit vectors, and show that high precision measurements of the gravitational force will allow the determination of the shape of the extra dimensions.Comment: Much more pedagogical version. Version to be published in the American Journal of Physic

Two-electron bond-orbital model, 2

The two-electron bond-orbital model of tetrahedrally-coordinated solids is generalized and its application extended. All intrabond matrix elements entering the formalism are explicitly retained, including the direct overlap S between the anion and cation sp3 hybrid wavefunctions. Complete analytic results are obtained for the six two-electron eigenvalues and eigenstates of the anion-cation bond in terms of S, one-electron parameters V2 and V3, and two-electron correlation parameters V4, V5 and V6. Refined formulas for the dielectric constant and the nuclear exchange and pseudodipolar coefficients, as well as new expressions for the valence electron density, polarity of the bond and the cohesive energy, are then derived. The theory gives a good account of the experimentally observed trends in all properties considered and approximate quantitative agreement is achieved for the pseudodipolar coefficient

Structural properties of bismuth-bearing semiconductor alloys

The structural properties of bismuth-bearing III-V semiconductor alloys are addressed. Because the Bi compounds are not known to form zincblende structures, only the anion-substituted alloys InPBi, InAsBi, and InSbBi are considered candidates as narrow-gap semiconductors. Miscibility calculations indicate that InSbBi will be the most miscible, and InPBi, with the large lattice mismatch of the constituents, will be the most difficult to mix. Calculations of the hardness of the Bi compounds indicate that, once formed, the InPBi alloy will be harder than the other Bi alloys, and substantially harder than the currently favored narrow-gap semiconductor HgCdTe. Thus, although InSbBi may be an easier material to prepare, InPBi promises to be a harder material. Growth of the Bi compounds will require high effective growth temperatures, probably attainable only through the use of nonequilibrium energy-assisted epitaxial growth techniques

Temperature variation of the resistivity of metallic strain gauge materials Final report

Temperature effects on electrical resistivity of metallic strain gage material