Electrochemical reduction of Bi2Sr2Ca1Cu2O8 superconductor single crystals

Single crystals and polycrystalline pellets of the high-temperature cuprate superconductor Bi₂Sr₂Ca₁Cu₂O₈ were doped at room temperature by electrochemical reduction at > 95% Coulombic efficiency using lithium dopant ions in propylene carbonate electrolyte. Cyclic voltammetry and potential step measurements on single crystals suggest an unusual reduction mechanism, with a diffusion coefficient for Li⁺ in the c-axis direction of bulk superconductor of ca. 3 × 10⁻¹¹ cm²s⁻¹. Sintered pellets of polycrystalline powder could be doped more rapidly, with an apparent diffusion coefficient of 7 × 10⁻⁸ cm²s⁻¹. X-ray susceptibility analysis show extensive disordering occurs on heavy Li doping, with a first-order transition from a crystalline/superconducting to an amorphous/non-superconducting phase. Single, crystals of Bi₂Sr₂Ca₁Cu₂O₈ exhibited a color change on reduction from metallic gray to golden bronze. The reduced material was highly air-sensitive, forming a hydroxide surface film on exposure to ambient atmosphere.     

Eikonal Approximation to 5D Wave Equations and the 4D Space-Time Metric

We apply a method analogous to the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold, using a method which identifies the symplectic structure of the corresponding mechanics, to the five dimensional generalization of Maxwell theory required by the gauge invariance of Stueckelberg's covariant classical and quantum dynamics. In this way, we demonstrate, in the eikonal approximation, the existence of geodesic motion for the flow of mass in a four dimensional pseudo-Riemannian manifold. These results provide a foundation for the geometrical optics of the five dimensional radiation theory and establish a model in which there is mass flow along geodesics. We then discuss the interesting case of relativistic quantum theory in an anisotropic medium as well. In this case the eikonal approximation to the relativistic quantum mechanical current coincides with the geodesic flow governed by the pseudo-Riemannian metric obtained from the eikonal approximation to solutions of the Stueckelberg–Schrödinger equation. The locally symplectic structure which emerges is that of a generally covariant form of Stueckelberg's mechanics on this manifold.     

Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting

In this paper we discuss Sobolev bounds on functions that vanish at scattered points in a bounded, Lipschitz domain that satisfies a uniform interior cone condition. The Sobolev spaces involved may have fractional as well as integer order. We then apply these results to obtain estimates for continuous and discrete least squares surface fits via radial basis functions (RBFs). These estimates include situations in which the target function does not belong to the native space of the RBF.

     

PDE with Random Coefficients and Euclidean Field Theory

In this paper a new proof of an identity of Giacomin, Olla, and Spohn is given. The identity relates the 2 point correlation function of a Euclidean field theory to the expectation of the Green's function for a pde with random coefficients. The Euclidean field theory is assumed to have convex potential. An inequality of Brascamp and Lieb therefore implies Gaussian bounds on the Fourier transform of the 2 point correlation function. By an application of results from random pde, the previously mentioned identity implies pointwise Gaussian bounds on the 2 point correlation function.     

A Bitangential Interpolation Problem on the Closed Unit Ball for Multipliers of the Arveson Space

We solve a bitangential interpolation problem for contractive multipliers on the Arveson space with an arbitrary interpolating set in the closed unit ball . The solvability criterion is established in terms of positive kernels. The set of all solutions is parametrized by a Redheffer transform. Submitted: February 2, 2002.