Spectral Theory of Time Dispersive and Dissipative Systems

We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system -- which we show is essentially unique. We illustrate the method by applying it to the spectral analysis of time dispersive dielectrics and the damped oscillator with retarded friction. In particular, we obtain a conservative extension of the Maxwell equations which is equivalent to the original Maxwell equations for a dispersive and lossy dielectric medium.Comment: LaTeX, 57 Pages, incorporated revisions corresponding with published versio

Ultracold, radiative charge transfer in hybrid Yb ion - Rb atom traps

Ultracold hybrid ion-atom traps offer the possibility of microscopic manipulation of quantum coherences in the gas using the ion as a probe. However, inelastic processes, particularly charge transfer can be a significant process of ion loss and has been measured experimentally for the Yb$^{+}$ ion immersed in a Rb vapour. We use first-principles quantum chemistry codes to obtain the potential energy curves and dipole moments for the lowest-lying energy states of this complex. Calculations for the radiative decay processes cross sections and rate coefficients are presented for the total decay processes. Comparing the semi-classical Langevin approximation with the quantum approach, we find it provides a very good estimate of the background at higher energies. The results demonstrate that radiative decay mechanisms are important over the energy and temperature region considered. In fact, the Langevin process of ion-atom collisions dominates cold ion-atom collisions. For spin dependent processes \cite{kohl13} the anisotropic magnetic dipole-dipole interaction and the second-order spin-orbit coupling can play important roles, inducing couplingbetween the spin and the orbital motion. They measured the spin-relaxing collision rate to be approximately 5 orders of magnitude higher than the charge-exchange collision rate \cite{kohl13}. Regarding the measured radiative charge transfer collision rate, we find that our calculation is in very good agreement with experiment and with previous calculations. Nonetheless, we find no broad resonances features that might underly a strong isotope effect. In conclusion, we find, in agreement with previous theory that the isotope anomaly observed in experiment remains an open question.Comment: 7 figures, 1 table accepted for publication in J. Phys. B: At. Mol. Opt. Phys. arXiv admin note: text overlap with arXiv:1107.114

Three New Long Period X-ray Pulsars Discovered in the Small Magellanic Cloud

The Small Magellanic Cloud is increasingly an invaluable laboratory for studying accreting and isolated X-ray pulsars. We add to the class of compact SMC objects by reporting the discovery of three new long period X-ray pulsars detected with the {\it Chandra X-ray Observatory}. The pulsars, with periods of 152, 304 and 565 seconds, all show hard X-ray spectra over the range from 0.6 - 7.5 keV. The source positions of the three pulsars are consistent with known H-alpha emission sources, indicating they are likely to be Be type X-ray binary star systems.Comment: Accepted for publication in the Astrophysical Journa

Vortices, circumfluence, symmetry groups and Darboux transformations of the (2+1)-dimensional Euler equation

The Euler equation (EE) is one of the basic equations in many physical fields such as fluids, plasmas, condensed matter, astrophysics, oceanic and atmospheric dynamics. A symmetry group theorem of the (2+1)-dimensional EE is obtained via a simple direct method which is thus utilized to find \em exact analytical \rm vortex and circumfluence solutions. A weak Darboux transformation theorem of the (2+1)-dimensional EE can be obtained for \em arbitrary spectral parameter \rm from the general symmetry group theorem. \rm Possible applications of the vortex and circumfluence solutions to tropical cyclones, especially Hurricane Katrina 2005, are demonstrated.Comment: 25 pages, 9 figure

Progressive Star Bursts and High Velocities in the Infrared Luminous, Colliding Galaxy Arp 118

In this paper we demonstrate for the first time the connection between the spatial and temporal progression of star formation and the changing locations of the very dense regions in the gas of a massive disk galaxy (NGC 1144) in the aftermath of its collision with a massive elliptical (NGC 1143). These two galaxies form the combined object Arp 118, a collisional ring galaxy system. The results of 3D, time-dependent, numerical simulations of the behavior of the gas, stars, and dark matter of a disk galaxy and the stars and dark matter in an elliptical during a collision are compared with multiwavelength observations of Arp 118. The collision that took place approximately 22 Myr ago generated a strong, non-linear density wave in the stars and gas in the disk of NGC 1144, causing the gas to became clumped on a large scale. This wave produced a series of superstarclusters along arcs and rings that emanate from the central point of impact in the disk. The locations of these star forming regions match those of the regions of increased gas density predicted the time sequence of models. The models also predict the large velocity gradients observed across the disk of NGC 1144. These are due to the rapid radial outflow of gas coupled to large azimuthal velocities in the expanding ring, caused by the impact of the massive intruder.Comment: 12 pages in document, and 8 figures (figures are separate from the document's file); Submitted to Astrophysical Journal Letter

Influence of Internode Length on Degradability of Lucerne Stems

Lignification of plant tissues restricts degradation of forages by ruminants. The undegradable lignified middle lamella/primary cell wall prevents rumen microbes from accessing undamaged adjacent plant cells. In contrast, walls of non-lignified tissues are completely degradable. Preliminary observations of how deeply rumen microbes could degrade different tissues within 20- to 30-mm long lucerne (Medicago sativa L.) stem pieces indicated a two-fold range in depth of degradation among stem samples. Studies were undertaken to determine if extent of cell wall degradation in lucerne was influenced by length of stem internodes

Cross-sections of Andreev scattering by quantized vortex rings in 3He-B

We studied numerically the Andreev scattering cross-sections of three-dimensional isolated quantized vortex rings in superfluid 3He-B at ultra-low temperatures. We calculated the dependence of the cross-section on the ring's size and on the angle between the beam of incident thermal quasiparticle excitations and the direction of the ring's motion. We also introduced, and investigated numerically, the cross-section averaged over all possible orientations of the vortex ring; such a cross-section may be particularly relevant for the analysis of experimental data. We also analyzed the role of screening effects for Andreev reflection of quasiparticles by systems of vortex rings. Using the results obtained for isolated rings we found that the screening factor for a system of unlinked rings depends strongly on the average radius of the vortex ring, and that the screening effects increase with decreasing the rings' size.Comment: 11 pages, 8 figures ; submitted to Physical Review

The role of inertia for the rotation of a nearly spherical particle in a general linear flow

We analyse the angular dynamics of a neutrally buoyant nearly spherical particle immersed in a steady general linear flow. The hydrodynamic torque acting on the particle is obtained by means of a reciprocal theorem, regular perturbation theory exploiting the small eccentricity of the nearly spherical particle, and assuming that inertial effects are small, but finite.Comment: 7 pages, 1 figur

Capillary-Gravity Waves on Depth-Dependent Currents: Consequences for the Wave Resistance

We study theoretically the capillary-gravity waves created at the water-air interface by a small two-dimensional perturbation when a depth-dependent current is initially present in the fluid. Assuming linear wave theory, we derive a general expression of the wave resistance experienced by the perturbation as a function of the current profile in the case of an inviscid fluid. We then analyze and discuss in details the behavior of the wave resistance in the particular case of a linear current, a valid approximation for some wind generated currents.Comment: Submitted to EP