Solving for Micro- and Macro- Scale Electrostatic Configurations Using the Robin Hood Algorithm

We present a novel technique by which highly-segmented electrostatic configurations can be solved. The Robin Hood method is a matrix-inversion algorithm optimized for solving high density boundary element method (BEM) problems. We illustrate the capabilities of this solver by studying two distinct geometry scales: (a) the electrostatic potential of a large volume beta-detector and (b) the field enhancement present at surface of electrode nano-structures. Geometries with elements numbering in the O(10^5) are easily modeled and solved without loss of accuracy. The technique has recently been expanded so as to include dielectrics and magnetic materials.Comment: 40 pages, 20 figure

Calibrating the Galaxy Halo - Black Hole Relation Based on the Clustering of Quasars

The observed number counts of quasars may be explained either by long-lived activity within rare massive hosts, or by short-lived activity within smaller, more common hosts. It has been argued that quasar lifetimes may therefore be inferred from their clustering length, which determines the typical mass of the quasar host. Here we point out that the relationship between the mass of the black-hole and the circular velocity of its host dark-matter halo is more fundamental to the determination of the clustering length. In particular, the clustering length observed in the 2dF quasar redshift survey is consistent with the galactic halo - black-hole relation observed in local galaxies, provided that quasars shine at ~10-100% of their Eddington luminosity. The slow evolution of the clustering length with redshift inferred in the 2dF quasar survey favors a black-hole mass whose redshift-independent scaling is with halo circular velocity, rather than halo mass. These results are independent from observations of the number counts of bright quasars which may be used to determine the quasar lifetime and its dependence on redshift. We show that if quasar activity results from galaxy mergers, then the number counts of quasars imply an episodic quasar lifetime that is set by the dynamical time of the host galaxy rather than by the Salpeter time. Our results imply that as the redshift increases, the central black-holes comprise a larger fraction of their host galaxy mass and the quasar lifetime gets shorter.Comment: 10 pages, 5 figures. Submitted to Ap

A Bayesian analysis of the 27 highest energy cosmic rays detected by the Pierre Auger Observatory

It is possible that ultra-high energy cosmic rays (UHECRs) are generated by active galactic nuclei (AGNs), but there is currently no conclusive evidence for this hypothesis. Several reports of correlations between the arrival directions of UHECRs and the positions of nearby AGNs have been made, the strongest detection coming from a sample of 27 UHECRs detected by the Pierre Auger Observatory (PAO). However, the PAO results were based on a statistical methodology that not only ignored some relevant information (most obviously the UHECR arrival energies but also some of the information in the arrival directions) but also involved some problematic fine-tuning of the correlation parameters. Here we present a fully Bayesian analysis of the PAO data (collected before 2007 September), which makes use of more of the available information, and find that a fraction F_AGN = 0.15^(+0.10)_(-0.07) of the UHECRs originate from known AGNs in the Veron-Cetty & Veron (VCV) catalogue. The hypothesis that all the UHECRs come from VCV AGNs is ruled out, although there remains a small possibility that the PAO-AGN correlation is coincidental (F_AGN = 0.15 is 200 times as probable as F_AGN = 0.00).Comment: MNRAS, accepted; 8 pages, 7 figure

Quantum corrections to the Larmor radiation formula in scalar electrodynamics

We use the semi-classical approximation in perturbative scalar quantum electrodynamics to calculate the quantum correction to the Larmor radiation formula to first order in Planck's constant in the non-relativistic approximation, choosing the initial state of the charged particle to be a momentum eigenstate. We calculate this correction in two cases: in the first case the charged particle is accelerated by a time-dependent but space-independent vector potential whereas in the second case it is accelerated by a time-independent vector potential which is a function of one spatial coordinate. We find that the corrections in these two cases are different even for a charged particle with the same classical motion. The correction in each case turns out to be non-local in time in contrast to the classical approximation.Comment: 19 page

Constraints on the Proper Motion of the Andromeda Galaxy Based on the Survival of Its Satellite M33

A major uncertainty in the dynamical history of the local group of galaxies originates from the unknown transverse speed of the Andromeda galaxy (M31) relative to the Milky Way. We show that the recent VLBA measurement of the proper motion of Andromeda's satellite, M33, severely constrains the possible values of M31's proper motion. The condition that M33's stellar disk will not be tidally disrupted by either M31 or the Milky Way over the past 10 billion years, favors a proper motion amplitude of 100+-20km/s for M31 with the quadrant of a negative velocity component along Right Ascension and a positive component along Declination strongly ruled-out. This inference can be tested by future astrometric measurements with SIM, GAIA, or the SKA. Our results imply that the dark halos of Andromeda and the Milky Way will pass through each other within the next 5-10 billion years.Comment: Accepted for publication in Ap

Descriptors for terpene esters from chromatographic and partition measurements: Estimation of human odor detection thresholds

We have used gas chromatographic retention data together with other data to obtain Abraham descriptors for 30 terpene esters. These include the air-water partition coefficient, as log Kw, for which no experimental values are available for any terpene ester. The other descriptors are the ester dipolarity, S, the hydrogen bond basicity, B, (the ester hydrogen bond acidity is zero for the esters studied), and L the logarithm of the air-hexadecane partition coefficient. Both S and B are larger than those for simple aliphatic esters, as expected from the terpene ester structures that include ring systems and ethylenic double bonds. These descriptors can then be used to obtain a large number of physicochemical and environmental properties of terpene esters. We have analyzed experimental results on human odor detection thresholds and have constructed another equation for the calculation of these thresholds, to go with a previous equation that we have reported. Then the descriptors for terpene esters can be used to estimate the important odor detection thresholds

Identifying the Environment and Redshift of GRB Afterglows from the Time-Dependence of Their Absorption Spectra

The discovery of Gamma-Ray Burst (GRB) afterglows revealed a new class of variable sources at optical and radio wavelengths. At present, the environment and precise redshift of the detected afterglows are still unknown. We show that if a GRB source resides in a compact (<100pc) gas-rich environment, the afterglow spectrum will show time-dependent absorption features due to the gradual ionization of the surrounding medium by the afterglow radiation. Detection of this time-dependence can be used to constrain the size and density of the surrounding gaseous system. For example, the MgII absorption line detected in GRB970508 should have weakened considerably during the first month if the absorption occurred in a gas cloud of size <100pc around the source. The time-dependent HI or metal absorption features provide a precise determination of the GRB redshift.Comment: 13 pages, 4 figures, submitted to ApJ

Self-energy of a scalar charge near higher-dimensional black holes

We study the problem of self-energy of charges in higher dimensional static spacetimes. Application of regularization methods of quantum field theory to calculation of the classical self-energy of charges leads to model-independent results. The correction to the self-energy of a scalar charge due to the gravitational field of black holes of the higher dimensional Majumdar-Papapetrou spacetime is calculated exactly. It proves to be zero in even dimensions, but it acquires non-zero value in odd dimensional spacetimes. The origin of the self-energy correction in odd dimensions is similar to the origin the conformal anomalies in quantum field theory in even dimensional spacetimes.Comment: 9 page

Spacetime Encodings II - Pictures of Integrability

I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are highlighted. The geodesic problem for these SAV spacetimes is rewritten as a two degree of freedom problem and the connection between current ideas in dynamical systems and the study of two manifolds sought. The relationship between the Hamilton-Jacobi equations, canonical transformations, constants of motion and Killing tensors are commented on. Wherever possible I illustrate the concepts by means of examples from general relativity. This investigation is designed to build the readers' intuition about how integrability arises, and to summarize some of the known facts about two degree of freedom systems. Evidence is given, in the form of orbit-crossing structure, that geodesics in SAV spacetimes might admit, a fourth constant of motion that is quartic in momentum (by contrast with Kerr spacetime, where Carter's fourth constant is quadratic).Comment: 11 pages, 10 figure

Neutrino Background Flux from Sources of Ultrahigh-Energy Cosmic-Ray Nuclei

Motivated by Pierre Auger Observatory results favoring a heavy nuclear composition for ultrahigh-energy (UHE) cosmic rays, we investigate implications for the cumulative neutrino background. The requirement that nuclei not be photodisintegrated constrains their interactions in sources, therefore limiting neutrino production via photomeson interactions. Assuming a $dN_{\rm CR}/dE_{\rm CR} \propto E_{\rm CR}^{-2}$ injection spectrum and photodisintegration via the giant dipole resonance, the background flux of neutrinos is lower than $E_\nu^2 \Phi_\nu \sim {10}^{-9} {\rm GeV} {\rm cm}^{-2} {\rm s}^{-1} {\rm sr}^{-1}$ if UHE nuclei ubiquitously survive in their sources. This is smaller than the analogous Waxman-Bahcall flux for UHE protons by about one order of magnitude, and is below the projected IceCube sensitivity. If IceCube detects a neutrino background, it could be due to other sources, e.g., hadronuclear interactions of lower-energy cosmic rays; if it does not, this supports our strong restrictions on the properties of sources of UHE nuclei.Comment: 7 pages, 3 figure