The Stability of One-Step Schemes for First-Order Two-Point Boundary Value Problems

The stability of a finite difference scheme is related explicitly to the stability of the continuous problem being solved. At times, this gives materially better estimates for the stability constant than those obtained by the standard process of appealing to the stability of the numerical scheme for the associated initial value problem

A numerical study of two-photon ionization of helium using the Pyprop framework

Few-photon induced breakup of helium is studied using a newly developed ab initio numerical framework for solving the six-dimensional time-dependent Schroedinger equation. We present details of the method and calculate (generalized) cross sections for the process of two-photon nonsequential (direct) double ionization at photon energies ranging from 39.4 to 54.4 eV, a process that has been very much debated in recent years and is not yet fully understood. In particular, we have studied the convergence property of the total cross section in the vicinity of the upper threshold (54.4 eV), versus the pulse duration of the applied laser field. We find that the cross section exhibits an increasing trend near the threshold, as has also been observed by others, and show that this rise cannot solely be attributed to an unintended inclusion of the sequential two-photon double ionization process, caused by the bandwidth of the applied field.Comment: 7 pages, 3 figure

Functions preserving nonnegativity of matrices

The main goal of this work is to determine which entire functions preserve nonnegativity of matrices of a fixed order $n$ -- i.e., to characterize entire functions $f$ with the property that $f(A)$ is entrywise nonnegative for every entrywise nonnegative matrix $A$ of size $n\times n$. Towards this goal, we present a complete characterization of functions preserving nonnegativity of (block) upper-triangular matrices and those preserving nonnegativity of circulant matrices. We also derive necessary conditions and sufficient conditions for entire functions that preserve nonnegativity of symmetric matrices. We also show that some of these latter conditions characterize the even or odd functions that preserve nonnegativity of symmetric matrices.Comment: 20 pages; expanded and corrected to reflect referees' remarks; to appear in SIAM J. Matrix Anal. App

Lattice QCD study of a five-quark hadronic molecule

We compute the ground-state energies of a heavy-light K-Lambda like system as a function of the relative distance r of the hadrons. The heavy quarks, one in each hadron, are treated as static. Then, the energies give rise to an adiabatic potential Va(r) which we use to study the structure of the five-quark system. The simulation is based on an anisotropic and asymmetric lattice with Wilson fermions. Energies are extracted from spectral density functions obtained with the maximum entropy method. Our results are meant to give qualitative insight: Using the resulting adiabatic potential in a Schroedinger equation produces bound state wave functions which indicate that the ground state of the five-quark system resembles a hadronic molecule, whereas the first excited state, having a very small rms radius, is probably better described as a five-quark cluster, or a pentaquark. We hypothesize that an all light-quark pentaquark may not exist, but in the heavy-quark sector it might, albeit only as an excited state.Comment: 11 pages, 15 figures, 4 table

Fabrication and characterization of nickel contacts for magnesium silicide based thermoelectric generators

AbstractMagnesium silicide based solid solutions are highly attractive materials for thermoelectric energy harvesting due to their abundance and excellent thermoelectric properties. Identification and testing of suitable contacts is – besides material optimization – the major challenge in the development of thermoelectric modules. We have applied Ni contacts on doped Mg2Si samples using a simple one-step sintering technique. These contacts were analyzed by combining microstructural analysis with spatially resolved and temperature dependent contact resistance measurements. We observe very good adhesion, homogeneous and low contact resistances <10μΩcm2. as well as good stability with temperature. Three different approaches for determining the contact resistances are compared and the respective errors are discussed

Four-nucleon scattering: Ab initio calculations in momentum space

The four-body equations of Alt, Grassberger and Sandhas are solved for \nH scattering at energies below three-body breakup threshold using various realistic interactions including one derived from chiral perturbation theory. After partial wave decomposition the equations are three-variable integral equations that are solved numerically without any approximations beyond the usual discretization of continuum variables on a finite momentum mesh. Large number of two-, three- and four-nucleon partial waves are considered until the convergence of the observables is obtained. The total \nH cross section data in the resonance region is not described by the calculations which confirms previous findings by other groups. Nevertheless the numbers we get are slightly higher and closer to the data than previously found and depend on the choice of the two-nucleon potential. Correlations between the $A_y$ deficiency in \nd elastic scattering and the total \nH cross section are studied.Comment: Corrected Eq. (10

Diffusion Monte Carlo calculations for the ground states of atoms and ions in neutron star magnetic fields

The diffusion quantum Monte Carlo method is extended to solve the old theoretical physics problem of many-electron atoms and ions in intense magnetic fields. The feature of our approach is the use of adiabatic approximation wave functions augmented by a Jastrow factor as guiding functions to initialize the quantum Monte Carlo prodecure. We calcula te the ground state energies of atoms and ions with nuclear charges from Z= 2, 3, 4, ..., 26 for magnetic field strengths relevant for neutron stars.Comment: 6 pages, 1 figure, proceedings of the "9th International Conference on Path Integrals - New Trends and Perspectives", Max-Planck-Institut fur Physik komplexer Systeme, Dresden, Germany, September 23 - 28, 2007, to be published as a book by World Scientific, Singapore (2008

The Asymptotics of Wilkinson's Iteration: Loss of Cubic Convergence

One of the most widely used methods for eigenvalue computation is the $QR$ iteration with Wilkinson's shift: here the shift $s$ is the eigenvalue of the bottom $2\times 2$ principal minor closest to the corner entry. It has been a long-standing conjecture that the rate of convergence of the algorithm is cubic. In contrast, we show that there exist matrices for which the rate of convergence is strictly quadratic. More precisely, let $T_X$ be the $3 \times 3$ matrix having only two nonzero entries $(T_X)_{12} = (T_X)_{21} = 1$ and let $T_L$ be the set of real, symmetric tridiagonal matrices with the same spectrum as $T_X$. There exists a neighborhood $U \subset T_L$ of $T_X$ which is invariant under Wilkinson's shift strategy with the following properties. For $T_0 \in U$, the sequence of iterates $(T_k)$ exhibits either strictly quadratic or strictly cubic convergence to zero of the entry $(T_k)_{23}$. In fact, quadratic convergence occurs exactly when $\lim T_k = T_X$. Let $X$ be the union of such quadratically convergent sequences $(T_k)$: the set $X$ has Hausdorff dimension 1 and is a union of disjoint arcs $X^\sigma$ meeting at $T_X$, where $\sigma$ ranges over a Cantor set.Comment: 20 pages, 8 figures. Some passages rewritten for clarit

Three-neutron resonance trajectories for realistic interaction models

Three-neutron resonances are investigated using realistic nucleon-nucleon interaction models. The resonance pole trajectories are explored by first adding an additional interaction to artificially bind the three-neutron system and then gradually removing it. The pole positions for the three-neutron states up to J=5/2 are localized in the third energy quadrant-Im (E)<=0, Re (E)<=0-well before the additional interaction is removed. Our study shows that realistic nucleon-nucleon interaction models exclude any possible experimental signature of three-neutron resonances.Comment: 13 pages ; 8 figs ; 5 table

Data analysis of gravitational-wave signals from spinning neutron stars. V. A narrow-band all-sky search

We present theory and algorithms to perform an all-sky coherent search for periodic signals of gravitational waves in narrow-band data of a detector. Our search is based on a statistic, commonly called the $\mathcal{F}$-statistic, derived from the maximum-likelihood principle in Paper I of this series. We briefly review the response of a ground-based detector to the gravitational-wave signal from a rotating neuron star and the derivation of the $\mathcal{F}$-statistic. We present several algorithms to calculate efficiently this statistic. In particular our algorithms are such that one can take advantage of the speed of fast Fourier transform (FFT) in calculation of the $\mathcal{F}$-statistic. We construct a grid in the parameter space such that the nodes of the grid coincide with the Fourier frequencies. We present interpolation methods that approximately convert the two integrals in the $\mathcal{F}$-statistic into Fourier transforms so that the FFT algorithm can be applied in their evaluation. We have implemented our methods and algorithms into computer codes and we present results of the Monte Carlo simulations performed to test these codes.Comment: REVTeX, 20 pages, 8 figure