The Algebraic Theory of Matrix Polynomials

A matrix S is a solvent of the matrix polynomial M(X)=A₀Xᵐ +...+ Am if M(S)=O where A, X, and S are square matrices. In this paper we develop the algebraic theory of matrix polynomials and solvents. We define division and interpolation, investigate the properties of block Vandermonde matrices, and define and study the existence of a complete set of solvents. We study the relation between the matrix polynomial problem and the lambda-matrix problem, which is to find a scalar A₀λᵐ + A₁λᵐ⁻¹ +...+ Am is singular. In a future paper we extend Traub’s algorithm for calculating zeros of scalar polynomials to matrix polynomials and establish global convergence properties of this algorithm for a class of matrix polynomials

Algorithms for Solvents of Matrix Polynomials

In an earlier paper we developed the algebraic theory of matrix polynomials. Here we introduce two algorithms for computing "dominant" solvents. Global convergence of the algorithms under certain conditions is established

Impact of beam smoothing method on direct drive target performance for the NIF

The impact of smoothing method on the performance of a direct drive target is modeled and examined in terms of its 1-mode spectrum. In particular, two classes of smoothing methods are compared, smoothing by spectral dispersion (SSD) and the induced spatial incoherence (ISI) method. It is found that SSD using sinusoidal phase modulation (FM) results in poor smoothing at low 1-modes and therefore inferior target performance at both peak velocity and ignition. This disparity is most notable if the effective imprinting integration time of the target is small. However, using SSD with more generalized phase modulation can result in smoothing at low l-modes which is identical to that obtained with ISI. For either smoothing method, the calculations indicate that at peak velocity the surface perturbations are about 100 times larger than that which leads to nonlinear hydrodynamics. Modeling of the hydrodynamic nonlinearity shows that saturation can reduce the amplified nonuniformities to the level required to achieve ignition for either smoothing method. The low l- mode behavior at ignition is found to be strongly dependent on the induced divergence of the smoothing method. For the NIF parameters the target performance asymptotes for smoothing divergence larger than {approximately}100 {mu}rad

Impact of beam smoothing method on direct drive target performance for the NIF

The impact of smoothing method on the performance of a direct drive target is modeled and examined in terms of its l-mode spectrum. In particular, two classes of smoothing methods are compared, smoothing by spectral dispersion (SSD) and the induced spatial incoherence (ISI) method. It is found that SSD using sinusoidal phase modulation (FM) results in poor smoothing at low l-modes and therefore inferior target performance at both peak velocity and ignition. Modeling of the hydrodynamic nonlinearity shows that saturation tends to reduce the difference between target performance for the smoothing methods considered. However, using SSD with more generalized phase modulation results in a smoothed spatial spectrum, and therefore target performance, which is identical to that obtained with the ISI or similar method where random phase plates are present in both methods and identical beam divergence is assumed

Effect of annealing on glassy dynamics and non-Fermi liquid behavior in UCu_4Pd

Longitudinal-field muon spin relaxation (LF-muSR) experiments have been performed in unannealed and annealed samples of the heavy-fermion compound UCu_4Pd to study the effect of disorder on non-Fermi liquid behavior in this material. The muon spin relaxation functions G(t,H) obey the time-field scaling relation G(t,H) = G(t/H^gamma) previously observed in this compound. The observed scaling exponent gamma = 0.3 pm 0.1, independent of annealing. Fits of the stretched-exponential relaxation function G(t) = exp[-(Lambda t)^K] to the data yielded stretching exponentials K < 1 for all samples. Annealed samples exhibited a reduction of the relaxation rate at low temperatures, indicating that annealing shifts fluctuation noise power to higher frequencies. There was no tendency of the inhomogeneous spread in rates to decrease with annealing, which modifies but does not eliminate the glassy spin dynamics reported previously in this compound. The correlation with residual resistivity previously observed for a number of NFL heavy-electron materials is also found in the present work.Comment: 4 pages, 3 figures, submitted to 10th International Conference on Muon Spin Rotation, Relaxation, and Resonance, Oxford, UK, August 200

Change Mining in Adaptive Process Management Systems

The wide-spread adoption of process-aware information systems has resulted in a bulk of computerized information about real-world processes. This data can be utilized for process performance analysis as well as for process improvement. In this context process mining offers promising perspectives. So far, existing mining techniques have been applied to operational processes, i.e., knowledge is extracted from execution logs (process discovery), or execution logs are compared with some a-priori process model (conformance checking). However, execution logs only constitute one kind of data gathered during process enactment. In particular, adaptive processes provide additional information about process changes (e.g., ad-hoc changes of single process instances) which can be used to enable organizational learning. In this paper we present an approach for mining change logs in adaptive process management systems. The change process discovered through process mining provides an aggregated overview of all changes that happened so far. This, in turn, can serve as basis for all kinds of process improvement actions, e.g., it may trigger process redesign or better control mechanisms

A collision avoidance system for workpiece protection

This paper describes an application of Sandia`s non-contact capacitive sensing technology for collision avoidance during the manufacturing of rocket engine thrust chambers. The collision avoidance system consists of an octagon shaped collar with a capacitive proximity sensor mounted on each face. The sensors produced electric fields which extend several inches from the face of the collar and detect potential collisions between the robot and the workpiece. A signal conditioning system processes the sensor output and provides varying voltage signals to the robot controller for stopping the robot

Reduction of the Three Dimensional Schrodinger Equation for Multilayered Films

In this paper, we present a method for reducing the three dimensional Schrodinger equation to study confined metallic states, such as quantum well states, in a multilayer film geometry. While discussing some approximations that are employed when dealing with the three dimensionality of the problem, we derive a one dimensional equation suitable for studying such states using an envelope function approach. Some applications to the Cu/Co multilayer system with regard to spin tunneling/rotations and angle resolved photoemission are discussed.Comment: 14 pages, 1 figur

Influence of uncorrelated overlayers on the magnetism in thin itinerant-electron films

The influence of uncorrelated (nonmagnetic) overlayers on the magnetic properties of thin itinerant-electron films is investigated within the single-band Hubbard model. The Coulomb correlation between the electrons in the ferromagnetic layers is treated by using the spectral density approach (SDA). It is found that the presence of nonmagnetic layers has a strong effect on the magnetic properties of thin films. The Curie temperatures of very thin films are modified by the uncorrelated overlayers. The quasiparticle density of states is used to analyze the results. In addition, the coupling between the ferromagnetic layers and the nonmagnetic layers is discussed in detail. The coupling depends on the band occupation of the nonmagnetic layers, while it is almost independent of the number of the nonmagnetic layers. The induced polarization in the nonmagnetic layers shows a long-range decreasing oscillatory behavior and it depends on the coupling between ferromagnetic and nonmagnetic layers.Comment: 9 pages, RevTex, 6 figures, for related work see: http://orion.physik.hu-berlin.d

Penetration Depth Measurements in MgB_2: Evidence for Unconventional Superconductivity

We have measured the magnetic penetration depth of the recently discovered binary superconductor MgB_2 using muon spin rotation and low field $ac$-susceptibility. From the damping of the muon precession signal we find the penetration depth at zero temperature is about 85nm. The low temperature penetration depth shows a quadratic temperature dependence, indicating the presence of nodes in the superconducting energy gap.Comment: 4 pages 3 figure