Manual of Quaternions

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Inelastic X-ray scattering from valence electrons near absorption edges of FeTe and TiSe2_2

We study resonant inelastic x-ray scattering (RIXS) peaks corresponding to low energy particle-hole excited states of metallic FeTe and semi-metallic TiSe$_2$ for photon incident energy tuned near the $L_{3}$ absorption edge of Fe and Ti respectively. We show that the cross section amplitudes are well described within a renormalization group theory where the effect of the core electrons is captured by effective dielectric functions expressed in terms of the the atomic scattering parameters $f_1$ of Fe and Ti. This method can be used to extract the dynamical structure factor from experimental RIXS spectra in metallic systems.Comment: 6 pages, 4 figure

Temperature-mediated transition from Dyakonov-Tamm surface waves to surface-plasmon-polariton waves

The effect of changing the temperature on the propagation of electromagnetic surface waves (ESWs), guided by the planar interface of a homogeneous isotropic temperature-sensitive material (namely, InSb) and a temperature-insensitive structurally chiral material (SCM) was numerically investigated in the terahertz frequency regime. As the temperature rises, InSb transforms from a dissipative dielectric material to a \blue{dissipative} plasmonic material. Correspondingly, the ESWs transmute from Dyakonov--Tamm surface waves into surface--plasmon--polariton waves. The effects of the temperature change are clearly observed in the phase speeds, propagation distances, angular existence domains, multiplicity, and spatial profiles of energy flow of the ESWs. Remarkably large propagation distances can be achieved; in such instances the energy of an ESW is confined almost entirely within the SCM. For certain propagation directions, simultaneous excitation of two ESWs with (i) the same phase speeds but different propagation distances or (ii) the same propagation distances but different phase speeds are also indicated by our results

Geometric optics and instability for semi-classical Schrodinger equations

We prove some instability phenomena for semi-classical (linear or) nonlinear Schrodinger equations. For some perturbations of the data, we show that for very small times, we can neglect the Laplacian, and the mechanism is the same as for the corresponding ordinary differential equation. Our approach allows smaller perturbations of the data, where the instability occurs for times such that the problem cannot be reduced to the study of an o.d.e.Comment: 22 pages. Corollary 1.7 adde

Predicted FeII Emission-Line Strengths from Active Galactic Nuclei

We present theoretical FeII emission line strengths for physical conditions typical of Active Galactic Nuclei with Broad-Line Regions. The FeII line strengths were computed with a precise treatment of radiative transfer using extensive and accurate atomic data from the Iron Project. Excitation mechanisms for the FeII emission included continuum fluorescence, collisional excitation, self-fluorescence amoung the FeII transitions, and fluorescent excitation by Lyman-alpha and Lyman-beta. A large FeII atomic model consisting of 827 fine structure levels (including states to E ~ 15 eV) was used to predict fluxes for approximately 23,000 FeII transitions, covering most of the UV, optical, and IR wavelengths of astrophysical interest. Spectral synthesis for wavelengths from 1600 Angstroms to 1.2 microns is presented. Applications of present theoretical templates to the analysis of observations are described. In particular, we discuss recent observations of near-IR FeII lines in the 8500 Angstrom -- 1 micron region which are predicted by the Lyman-alpha fluorescence mechanism. We also compare our UV spectral synthesis with an empirical iron template for the prototypical, narrow-line Seyfert galaxy I Zw 1. The theoretical FeII template presented in this work should also applicable to a variety of objects with FeII spectra formed under similar excitation conditions, such as supernovae and symbiotic stars.Comment: 33 pages, 15 postscript figure

The Origin of Fe II Emission in AGN

We used a very large set of models of broad emission line (BEL) clouds in AGN to investigate the formation of the observed Fe II emission lines. We show that photoionized BEL clouds cannot produce both the observed shape and observed equivalent width of the 2200-2800A Fe II UV bump unless there is considerable velocity structure corresponding to a microturbulent velocity parameter v_turb > 100 km/s for the LOC models used here. This could be either microturbulence in gas that is confined by some phenomenon such as MHD waves, or a velocity shear such as in the various models of winds flowing off the surfaces of accretion disks. The alternative way that we can find to simultaneously match both the observed shape and equivalent width of the Fe II UV bump is for the Fe II emission to be the result of collisional excitation in a warm, dense gas. Such gas would emit very few lines other than Fe II. However, since the collisionally excited gas would constitute yet another component in an already complicated picture of the BELR, we prefer the model involving turbulence. In either model, the strength of Fe II emission relative to the emission lines of other ions such as Mg II depends as much on other parameters (either v_turb or the surface area of the collisionally excited gas) as it does on the iron abundance. Therefore, the measurement of the iron abundance from the FeII emission in quasars becomes a more difficult problem.Comment: 23 pages. Accepted by Ap

Diffusion in pores and its dependence on boundary conditions

We study the influence of the boundary conditions at the solid liquid interface on diffusion in a confined fluid. Using an hydrodynamic approach, we compute numerical estimates for the diffusion of a particle confined between two planes. Partial slip is shown to significantly influence the diffusion coefficient near a wall. Analytical expressions are derived in the low and high confinement limits, and are in good agreement with numerical results. These calculations indicate that diffusion of tagged particles could be used as a sensitive probe of the solid-liquid boundary conditions.Comment: soumis \`a J.Phys. Cond. Matt. special issue on "Diffusion in Liquids, Polymers, Biophysics and Chemical Dynamics