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

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

The heat kernel on curvilinear polygonal domains in surfaces

We construct the heat kernel on curvilinear polygonal domains in arbitrary surfaces for Dirichlet, Neumann, and Robin boundary conditions as well as mixed problems, including those of Zaremba type. We compute the short time asymptotic expansion of the heat trace and apply this expansion to demonstrate a collection of results showing that corners are spectral invariants

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

Temperature effects on electrical resistivity of metallic strain gage material

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