Mathmatical modeling for diffractive optics

We consider a 'diffractive optic' to be a biperiodic surface separating two half-spaces, each having constant constitutive parameters; within a unit cell of the periodic surface and across the transition zone between the two half-spaces, the constitutive parameters can be a continuous, complex-valued function. Mathematical models for diffractive optics have been developed, and implemented as numerical codes, both for the 'direct' problem and for the 'inverse' problem. In problems of the 'direct' class, the diffractive optic is specified, and the full set of Maxwell's equations is cast in a variational form and solved numerically by a finite element approach. This approach is well-posed in the sense that existence and uniqueness of the solution can be proved and specific convergence conditions can be derived. An example of a metallic grating at a Wood anomaly is presented as a case where other approaches are known to have convergence problems. In problems of the 'inverse' class, some information about the diffracted field (e.g., the far-field intensity) is given, and the problem is to find the periodic structure in some optimal sense. Two approaches are described: phase reconstruction in the far-field approximation; and relaxed optimal design based on the Helmholtz equation. Practical examples are discussed for each approach to the inverse problem, including array generators in the far-field case and antireflective structures for the relaxed optimal design

Unlocking the Keyhole - H2 and PAH emission from molecular clumps in the Keyhole Nebula

To better understand the environment surrounding CO emission clumps in the Keyhole Nebula, we have made images of the region in H2 1-0 S(1) (2.122 um) emission and polycyclic aromatic hydrocarbon (PAH) emission at 3.29 um. Our results show that the H2 and PAH emission regions are morphologically similar, existing as several clumps, all of which correspond to CO emission clumps and dark optical features. The emission confirms the existence of photodissociation regions (PDRs) on the surface of the clumps. By comparing the velocity range of the CO emission with the optical appearance of the H2 and PAH emission, we present a model of the Keyhole Nebula in which the most negative velocity clumps are in front of the ionization region, the clumps at intermediate velocities are in it, and those which have the least negative velocities are at the far side. It may be that these clumps, which appear to have been swept up from molecular gas by the stellar winds from eta Car, are now being over-run by the ionization region and forming PDRs on their surfaces. These clumps comprise the last remnants of the ambient molecular cloud around eta Car.Comment: 8 pages, 4 figures, to be published in MNRA

Small Energy Scale for Mixed-Valent Uranium Materials

We investigate a two-channel Anderson impurity model with a $5f^1$ magnetic and a $5f^2$ quadrupolar ground doublet, and a $5f^2$ excited triplet. Using the numerical renormalization group method, we find a crossover to a non-Fermi liquid state below a temperature $T^*$ varying as the $5f^2$ triplet-doublet splitting to the 7/2 power. To within numerical accuracy, the non-linear magnetic susceptibility and the $5f^1$ contribution to the linear susceptibility are given by universal one-parameter scaling functions. These results may explain UBe$_{13}$ as mixed valent with a small crossover scale $T^*$.Comment: 4 pages, 3 figures, REVTeX, to appear in Phys. Rev. Let

Theory of One-Channel vs. Multi-Channel Kondo Effects for Ce3+^{3+} Impurities

We introduce a model for Ce$^{3+}$ impurities in cubic metals which exhibits competition between the Fermi-liquid fixed point of the single channel Kondo model and the non-Fermi-liquid fixed point of the two- and three-channel Kondo models. Using the non-crossing approximation and scaling theory, we find: (i) A possible three-channel Kondo effect between the one- and two-channel regimes in parameter space. (ii) The sign of the thermopower is a fixed point diagnostic. (iii) Our results will likely survive the introduction of additional $f^2$ and conduction states. We apply this model to interpret the non-Fermi liquid alloy La$_{1-x}$Ce$_x$Cu$_{2.2}$Si$_2$.Comment: 13 pages, Revtex, To appear in Phys. Rev. Let

Cognitive Information Processing

Contains reports on three research projects.Joint Services Electronics Program (Contract DAAB07-74-C-0630)National Science Foundation (Grant GK-33736X2

Black Holes in Galaxy Mergers: Evolution of Quasars

Based on numerical simulations of gas-rich galaxy mergers, we discuss a model in which quasar activity is tied to the self-regulated growth of supermassive black holes in galaxies. Nuclear inflow of gas attending a galaxy collision triggers a starburst and feeds black hole growth, but for most of the duration of the starburst, the black hole is heavily obscured by surrounding gas and dust which limits the visibility of the quasar, especially at optical and UV wavelengths. Eventually, feedback energy from accretion heats the gas and expels it in a powerful wind, leaving a 'dead quasar'. Between buried and dead phases there is a window during which the galaxy would be seen as a luminous quasar. Because the black hole mass, radiative output, and distribution of obscuring gas and dust all evolve strongly with time, the duration of this phase of observable quasar activity depends on both the waveband and imposed luminosity threshold. We determine the observed and intrinsic lifetimes as a function of luminosity and frequency, and calculate observable lifetimes ~10 Myr for bright quasars in the optical B-band, in good agreement with empirical estimates and much smaller than the black hole growth timescales ~100 Myr, naturally producing a substantial population of 'buried' quasars. However, observed and intrinsic energy outputs converge in the IR and hard X-ray bands as attenuation becomes weaker and chances of observation greatly increase. We obtain the distribution of column densities along sightlines in which the quasar is seen above a given luminosity, and find that our result agrees remarkably well with observed estimates of the column density distribution from the SDSS for appropriate luminosity thresholds. (Abridged)Comment: 12 pages, 7 figures. Accepted for publication in ApJ (September 2005). Replacement with minor revisions from referee repor

Topological (Sliced) Doping of a 3D Peierls System: Predicted Structure of Doped BaBiO3

At hole concentrations below x=0.4, Ba_(1-x)K_xBiO_3 is non-metallic. At x=0, pure BaBiO3 is a Peierls insulator. Very dilute holes create bipolaronic point defects in the Peierls order parameter. Here we find that the Rice-Sneddon version of Peierls theory predicts that more concentrated holes should form stacking faults (two-dimensional topological defects, called slices) in the Peierls order parameter. However, the long-range Coulomb interaction, left out of the Rice-Sneddon model, destabilizes slices in favor of point bipolarons at low concentrations, leaving a window near 30% doping where the sliced state is marginally stable.Comment: 6 pages with 5 embedded postscript figure

Pu 4f XPS spectra analyzed in the Anderson impurity model

X-ray photoemission spectra of the {alpha},{beta},{gamma}, and {delta} phases of Pu have been analyzed using the Gunnarsson-Schonhammer implementation of the Anderson impurity model. Changes in the relative intensities of the two spectral features representing mixed f{sup 5} and f{sup 6} final states are in reasonable agreement with the model`s predictions. The coulomb terms, U{sub ff} and U{sub fc}, are quite consistent with those derived from atomic and LDA calculations. Multiplet structure, which agrees with atomic calculations for 4f{sup 13}5f{sup 5}, strongly suggests 5f localization in the final state

A Chandra study of particle acceleration in the multiple hotspots of nearby radio galaxies

We present Chandra observations of a small sample of nearby classical double radio galaxies which have more than one radio hotspot in at least one of their lobes. The X-ray emission from the hotspots of these comparatively low-power objects is expected to be synchrotron in origin, and therefore to provide information about the locations of high-energy particle acceleration. In some models of the relationship between the jet and hotspot the hotspots that are not the current jet termination point should be detached from the energy supply from the active nucleus and therefore not capable of accelerating particles to high energies. We find that in fact some secondary hotspots are X-ray sources, and thus probably locations for high-energy particle acceleration after the initial jet termination shock. In detail, though, we show that the spatial structures seen in X-ray are not consistent with naive expectations from a simple shock model: the current locations of the acceleration of the highest-energy observable particles in powerful radio galaxies need not be coincident with the peaks of radio or even optical emission.Comment: Accepted for ApJ. 33 pages, 8 figures inc. 2 in colo