Homotopy Method for the Large, Sparse, Real Nonsymmetric Eigenvalue Problem

A homotopy method to compute the eigenpairs, i.e., the eigenvectors and eigenvalues, of a given real matrix A1 is presented. From the eigenpairs of some real matrix A0, the eigenpairs of A(t) ≡ (1 − t)A0 + tA1 are followed at successive "times" from t = 0 to t = 1 using continuation. At t = 1, the eigenpairs of the desired matrix A1 are found. The following phenomena are present when following the eigenpairs of a general nonsymmetric matrix: • bifurcation, • ill conditioning due to nonorthogonal eigenvectors, • jumping of eigenpaths. These can present considerable computational difficulties. Since each eigenpair can be followed independently, this algorithm is ideal for concurrent computers. The homotopy method has the potential to compete with other algorithms for computing a few eigenvalues of large, sparse matrices. It may be a useful tool for determining the stability of a solution of a PDE. Some numerical results will be presented

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

Mechanisms of superconductivity investigated by nuclear radiation

Investigation focused on the behavior of superconducting magnet and its constituent materials during and after exposure to nuclear radiation. The results will indicate the feasibility of their use in diverse applications and various environments

Design guide for helicopter transmission seals

A detailed approach for the selection and design of seals for helicopter transmissions is presented. There are two major types of seals presently being used and they are lip type seals and mechanical type seals. Lip type seals can be divided in conventional lip seals and hydrodynamic lip seals. Conventional lip seals can be used for slow-speed, low-pressure, low-temperature sealing. Hydrodynamic lip seals although they are as pressure and temperature limited as conventional lip seals, can operate at a higher speed. Mechanical types seals are comprised of face seals and circumferential seals. Face seals are capable of high speed, high pressure, and high temperature. Circumferential seals can be used in high-speed and high-temperature applications, but will leak excessively at moderate pressures. The performance goals of transmission seals are a life that is at least equal to the scheduled overhaul interval of the gearbox component and a leakage rate of near zero

Finite-size and pressure effects in YBa_2Cu_4O_8 probed by magnetic field penetration depth measurements

We explore the combined pressure and finite-size effects on the in-plane penetration depth \lambda_{ab} in YBa_2Cu_4O_8. Even though this cuprate is stoichiometric the finite-size scaling analysis of \lambda_{ab}^{-2}(T) uncovers the granular nature and reveals domains with nanoscale size L_{c} along the c-axis. L_{c} ranges from 33.2 Angstrom to 28.9 Angstrom at pressures from 0.5 to 11.5 kbar. These observations raise serious doubts on the existence of a phase coherent macroscopic superconducting state in cuprate superconductors.Comment: 7 pages, 6 figure

Pressure effects on the superconducting properties of YBa_2Cu_4O_8

Measurements of the magnetization under high hydrostatic pressure (up to 10.2 kbar) in YBa_2Cu_4O_8 were carried out. From the scaling analysis of the magnetization data the pressure induced shifts of the transition temperature T_c, the volume V and the anisotropy \gamma have been obtained. It was shown that the pressure induced relative shift of T_c mirrors essentially that of the anisotropy. This observation uncovers a novel generic property of anisotropic type II superconductors, that inexistent in the isotropic case.Comment: 4 pages, 3 figure