A Numerical Method for Singular Two Point Boundary Value Problems

The numerical solution of boundary value problems for linear systems of first order equations with a regular singular point at one endpoint is considered. The standard procedure of expanding about the singularity to get a nonsingular problem over a reduced interval is justified in some detail. Quite general boundary conditions are included which permit unbounded solutions. Error estimates are given and some numerical calculations are presented to check the theory

Convergence Rates for Newton’s Method at Singular Points

If Newton’s method is employed to find a root of a map from a Banach space into itself and the derivative is singular at that root, the convergence of the Newton iterates to the root is linear rather than quadratic. In this paper we give a detailed analysis of the linear convergence rates for several types of singular problems. For some of these problems we describe modifications of Newton’s method which will restore quadratic convergence

The Flow of a Viscous Compressible Fluid Through a Very Narrow Gap

The effect of compressibility on the pressure distribution in the narrow gap between a rotating cylinder and a plane in a viscous fluid was studied by Taylor and Saffman [1] during an investigation of the centripetal pump effect discovered by Reiner [2]

Study of the in-plane magnetic penetration depth in the cuprate superconductor Ca_2-xNa_xCuO_2Cl_2: role of the apical sites

A study of the in-plane magnetic penetration depth \lambda_ab in a series of the cuprate superconductors Ca_2-xNa_xCuO_2Cl_2 (Na-CCOC) with Na content x=0.11, 0.12, 0.15, 0.18, and 0.19 is reported. The zero temperature values of \lambda_ab(0) were obtained by means of the muon-spin rotation technique, as well as from measurements of the intrinsic susceptibility \chi^int(0) by using the procedure developed by Kanigel et al. [Phys.Rev.B 71, 224511 (2005)]. \lambda_ab at T=0K was found to increase with decreasing doping from \lambda_ab(0)=316(19)nm for the x=0.19 sample to \lambda_ab(0)=430(26)nm for the x=0.11 one. From a comparison of the present Na-CCOC data with those of Bi2201 and La214 cuprate superconductors it is concluded that substitution of the apical oxygen by chlorine decreases the coupling between the superconducting CuO_2 planes, leading to an enhancement of the two-dimensional properties of Na-CCOC.Comment: 8 pages, 7 figure

Muon-Spin-Rotation Measurements of the Penetration Depth in the Infinite-Layer Electron-Doped Cuprate Superconductor Sr0.9La0.1CuO2

Muon spin rotation (mSR) measurements of the in-plane penetration depth lambda_ab have been performed in the electron-doped infinite layer high-Tc superconductor (HTS) Sr0.9La0.1CuO2. Absence of the magnetic rare-earth ions in this compound allowed to measure for the first time the absolute value of lambda_ab(0) in electron-doped HTS using mSR. We found lambda_ab(0)=116(2) nm. The zero-temperature depolarization rate sigma(0)?1/lambda_ab(0)^2=4.6(1) MHz is more than four times higher than expected from the Uemura line. Therefore this electron-doped HTS does not follow the Uemura relation found for hole-doped HTS.Comment: to be published in Physical Review Letter

A dynamical approximation for stochastic partial differential equations

Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the random invariant manifold is almost surely asymptotically complete. The asymptotic dynamical behavior is thus described by a stochastic ordinary differential system on the random invariant manifold, under suitable conditions. As an application, stationary states (invariant measures) is considered for one example of stochastic partial differential equations.Comment: 28 pages, no figure