Decay of the Maxwell field on the Schwarzschild manifold

We study solutions of the decoupled Maxwell equations in the exterior region of a Schwarzschild black hole. In stationary regions, where the Schwarzschild coordinate $r$ ranges over $2M < r_1 < r < r_2$, we obtain a decay rate of $t^{-1}$ for all components of the Maxwell field. We use vector field methods and do not require a spherical harmonic decomposition. In outgoing regions, where the Regge-Wheeler tortoise coordinate is large, $r_*>\epsilon t$, we obtain decay for the null components with rates of $|\phi_+| \sim |\alpha| < C r^{-5/2}$, $|\phi_0| \sim |\rho| + |\sigma| < C r^{-2} |t-r_*|^{-1/2}$, and $|\phi_{-1}| \sim |\underline{\alpha}| < C r^{-1} |t-r_*|^{-1}$. Along the event horizon and in ingoing regions, where $r_*<0$, and when $t+r_*1$, all components (normalized with respect to an ingoing null basis) decay at a rate of C \uout^{-1} with \uout=t+r_* in the exterior region.Comment: 37 pages, 5 figure

Comparative study of radio pulses from simulated hadron-, electron-, and neutrino-initiated showers in ice in the GeV-PeV range

High energy particle showers produce coherent Cherenkov radio emission in dense, radio-transparent media such as cold ice. Using PYTHIA and GEANT simulation tools, we make a comparative study among electromagnetic (EM) and hadronic showers initiated by single particles and neutrino showers initiated by multiple particles produced at the neutrino-nucleon event vertex. We include all the physics processes and do a complete 3-D simulation up to 100 TeV for all showers and to 1 PeV for electron and neutrino induced showers. We calculate the radio pulses for energies between 100 GeV and 1 PeV and find hadron showers, and consequently neutrino showers, are not as efficient below 1 PeV at producing radio pulses as the electromagnetic showers. The agreement improves as energy increases, however, and by a PeV and above the difference disappears. By looking at the 3-D structure of the showers in time, we show that the hadronic showers are not as compact as the EM showers and hence the radiation is not as coherent as EM shower emission at the same frequency. We show that the ratio of emitted pulse strength to shower tracklength is a function only of a single, coherence parameter, independent of species and energy of initiating particle.Comment: a few comments added, to bo published in PRD Nov. issue, 10 pages, 3 figures in tex file, 3 jpg figures in separate files, and 1 tabl

Efficient numerical diagonalization of hermitian 3x3 matrices

A very common problem in science is the numerical diagonalization of symmetric or hermitian 3x3 matrices. Since standard "black box" packages may be too inefficient if the number of matrices is large, we study several alternatives. We consider optimized implementations of the Jacobi, QL, and Cuppen algorithms and compare them with an analytical method relying on Cardano's formula for the eigenvalues and on vector cross products for the eigenvectors. Jacobi is the most accurate, but also the slowest method, while QL and Cuppen are good general purpose algorithms. The analytical algorithm outperforms the others by more than a factor of 2, but becomes inaccurate or may even fail completely if the matrix entries differ greatly in magnitude. This can mostly be circumvented by using a hybrid method, which falls back to QL if conditions are such that the analytical calculation might become too inaccurate. For all algorithms, we give an overview of the underlying mathematical ideas, and present detailed benchmark results. C and Fortran implementations of our code are available for download from http://www.mpi-hd.mpg.de/~globes/3x3/ .Comment: 13 pages, no figures, new hybrid algorithm added, matches published version, typo in Eq. (39) corrected; software library available at http://www.mpi-hd.mpg.de/~globes/3x3

Tablet PCs in schools: Case study report: A report for Becta by the Open University

The publication provides an analysis of twelve case studies involving schools in England that were using Tablet PCs. The analysis is complemented by brief individual reports describing aspects of how each of these schools was using Tablet PCs

Relativistic Magnetic Monopole Flux Constraints from RICE

We report an upper limit on the flux of relativistic monopoles based on the non-observation of in-ice showers by the Radio Ice Cherenkov Experiment (RICE) at the South Pole. We obtain a 95% C.L. limit of order 10^{-18}/(cm^2-s-sr) for intermediate mass monopoles of 10^7<gamma<10^{12} at the anticipated energy E=10^{16} GeV. This bound is over an order of magnitude stronger than all previously published experimental limits for this range of boost parameters gamma, and exceeds two orders of magnitude improvement over most of the range. We review the physics of radio detection, describe a Monte Carlo simulation including continuous and stochastic energy losses, and compare to previous experimental limits.Comment: 16 pages, 6 figures. Accepted for publication in Phys. Rev. D. Minor revisions, including expanded discussion of monopole energy uncertaint

Connection between the elastic GEp/GMp and P to Delta form factors

It is suggested that the falloff in Qsq of the P to Delta magnetic form factor GM* is related to the recently observed falloff of the elastic electric form factor GEp/GMp. Calculation is carried out in the framework of a GPD mechanism

Signatures of Pseudoscalar Photon Mixing in CMB Radiation

We model the effect of photon and ultra-light pseudoscalar mixing on the propagation of electromagnetic radiation through the extragalactic medium. The medium is modelled as a large number of magnetic domains, uncorrelated with one another. We obtain an analytic expression for the different Stokes parameters in the limit of small mixing angle. The different Stokes parameters are found to increase linearly with the number of domains. We also verify this result by direct numerical simulations. We use this formalism to estimate the effect of pseudoscalar-photon mixing on the Cosmic Microwave Background (CMB) polarization. We impose limits on the model parameters by the CMB observations. We find that the currently allowed parameter range admits a CMB circular polarization up to order $10^{-7}$.Comment: 17 pages, 5 figure