Constraints on galaxy formation from alpha-enhancement in luminous elliptical galaxies

We explore the formation of alpha-enhanced and metal-rich stellar populations in the nuclei of luminous ellipticals under the assumption of two extreme galaxy formation scenarios based on hierarchical clustering, namely a fast clumpy collapse and the merger of two spirals. We investigate the parameter space of star formation time-scale, IMF slope, and stellar yields. In particular, the latter add a huge uncertainty in constraining time-scales and IMF slopes. We find that -- for Thielemann, Nomoto & Hashimoto nucleosynthesis -- in a fast clumpy collapse scenario an [alpha/Fe] overabundance of approx. 0.2 dex in the high metallicity stars can be achieved with a Salpeter IMF and star formation time-scales of the order 10^9 yr. The scenario of two merging spirals which are similar to our Galaxy, instead, fails to reproduce alpha-enhanced abundance ratios in the metal-rich stars, unless the IMF is flattened during the burst ignited by the merger. This result is independent of the burst time-scale. We suggest that abundance gradients give hints to distinguish between the two extreme formation scenarios considered in this paper.Comment: Accepted for publication in MNRAS, LaTex 2.09 with mn.sty, 13 pages, 5 figure

TOPEX orbit determination using GPS signals plus a sidetone ranging system

The GPS orbit determination was studied to see how well the radial coordinate for altimeter satellites such as TOPEX could be found by on board measurements of GPS signals, including the reconstructed carrier phase. The inclusion on altimeter satellites of an additional high accuracy tracking system is recommended. It is suggested that a sidetone ranging system is used in conjunction with TRANET 2 beacons

Guidance, flight mechanics and trajectory optimization. Volume 12 - Relative motion, guidance equations for terminal rendezvous

Equations of relative motion and guidance for orbital transfer and docking maneuvers in spacecraft rendezvou

The structure of supersymmetry in PT{\cal PT} symmetric quantum mechanics

The structure of supersymmetry is analyzed systematically in ${\cal PT}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional ${\cal PT}$ symmetric quantum mechanical theories. We show that there is a richer structure present in these theories compared to the conventional theories associated with Hermitian Hamiltonians. We bring out various properties associated with these supersymmetric systems and generalize such quantum mechanical theories to higher dimensions as well as to the case of one dimensional shape invariant potentials.Comment: 15 pages, some explanations included, references adde

Comparison of LISA and Atom Interferometry for Gravitational Wave Astronomy in Space

One of the atom interferometer gravitational wave missions proposed by Dimopoulos et al.1 in 2008 was called AGIS-Sat. 2. It had a suggested gravitational wave sensitivity set by the atom state detection shot noise level that started at 1 mHz, was comparable to LISA sensitivity from 1 to about 20 mHz, and had better sensitivity from 20 to 500 mHz. The separation between the spacecraft was 1,000 km, with atom interferometers 200 m long and shades from sunlight used at each end. A careful analysis of many error sources was included, but requirements on the time-stability of both the laser wavefront aberrations and the atom temperatures in the atom clouds were not investigated. After including these considerations, the laser wavefront aberration stability requirement to meet the quoted sensitivity level is about 1\times10-8 wavelengths, and is far tighter than for LISA. Also, the temperature fluctuations between atom clouds have to be less than 1 pK. An alternate atom interferometer GW mission in Earth orbit called AGIS-LEO with 30 km satellite separation has been suggested recently. The reduction of wavefront aberration noise by sending the laser beam through a high-finesse mode-scrubbing optical cavity is discussed briefly, but the requirements on such a cavity are not given. Unfortunately, such an Earth-orbiting mission seems to be considerably more difficult to design than a non-geocentric mission and does not appear to have comparably attractive scientific goals.Comment: Submitted to Proc. 46th Rencontres de Moriond: Gravitational Waves and Experimental Gravity, March 20 - 27, 2011, La Thuile, Ital

Harmonic oscillator well with a screened Coulombic core is quasi-exactly solvable

In the quantization scheme which weakens the hermiticity of a Hamiltonian to its mere PT invariance the superposition V(x) = x^2+ Ze^2/x of the harmonic and Coulomb potentials is defined at the purely imaginary effective charges (Ze^2=if) and regularized by a purely imaginary shift of x. This model is quasi-exactly solvable: We show that at each excited, (N+1)-st harmonic-oscillator energy E=2N+3 there exists not only the well known harmonic oscillator bound state (at the vanishing charge f=0) but also a normalizable (N+1)-plet of the further elementary Sturmian eigenstates \psi_n(x) at eigencharges f=f_n > 0, n = 0, 1, ..., N. Beyond the first few smallest multiplicities N we recommend their perturbative construction.Comment: 13 pages, Latex file, to appear in J. Phys. A: Math. Ge

A preliminary evaluation of LANDSAT-4 thematic mapper data for their geometric and radiometric accuracies

Some LANDSAT thematic mapper data collected over the eastern United States were analyzed for their whole scene geometric accuracy, band to band registration and radiometric accuracy. Band ratio images were created for a part of one scene in order to assess the capability of mapping geologic units with contrasting spectral properties. Systematic errors were found in the geometric accuracy of whole scenes, part of which were attributable to the film writing device used to record the images to film. Band to band registration showed that bands 1 through 4 were registered to within one pixel. Likewise, bands 5 and 7 also were registered to within one pixel. However, bands 5 and 7 were misregistered with bands 1 through 4 by 1 to 2 pixels. Band 6 was misregistered by 4 pixels to bands 1 through 4. Radiometric analysis indicated two kinds of banding, a modulo-16 stripping and an alternate light dark group of 16 scanlines. A color ratio composite image consisting of TM band ratios 3/4, 5/2, and 5/7 showed limonitic clay rich soils, limonitic clay poor soils, and nonlimonitic materials as distinctly different colors on the image

PT-symmetry breaking in complex nonlinear wave equations and their deformations

We investigate complex versions of the Korteweg-deVries equations and an Ito type nonlinear system with two coupled nonlinear fields. We systematically construct rational, trigonometric/hyperbolic, elliptic and soliton solutions for these models and focus in particular on physically feasible systems, that is those with real energies. The reality of the energy is usually attributed to different realisations of an antilinear symmetry, as for instance PT-symmetry. It is shown that the symmetry can be spontaneously broken in two alternative ways either by specific choices of the domain or by manipulating the parameters in the solutions of the model, thus leading to complex energies. Surprisingly the reality of the energies can be regained in some cases by a further breaking of the symmetry on the level of the Hamiltonian. In many examples some of the fixed points in the complex solution for the field undergo a Hopf bifurcation in the PT-symmetry breaking process. By employing several different variants of the symmetries we propose many classes of new invariant extensions of these models and study their properties. The reduction of some of these models yields complex quantum mechanical models previously studied.Comment: 50 pages, 39 figures (compressed in order to comply with arXiv policy; higher resolutions maybe obtained from the authors upon request

An alternative to the conventional micro-canonical ensemble

Usual approach to the foundations of quantum statistical physics is based on conventional micro-canonical ensemble as a starting point for deriving Boltzmann-Gibbs (BG) equilibrium. It leaves, however, a number of conceptual and practical questions unanswered. Here we discuss these questions, thereby motivating the study of a natural alternative known as Quantum Micro-Canonical (QMC) ensemble. We present a detailed numerical study of the properties of the QMC ensemble for finite quantum systems revealing a good agreement with the existing analytical results for large quantum systems. We also propose the way to introduce analytical corrections accounting for finite-size effects. With the above corrections, the agreement between the analytical and the numerical results becomes very accurate. The QMC ensemble leads to an unconventional kind of equilibrium, which may be realizable after strong perturbations in small isolated quantum systems having large number of levels. We demonstrate that the variance of energy fluctuations can be used to discriminate the QMC equilibrium from the BG equilibrium. We further suggest that the reason, why BG equilibrium commonly occurs in nature rather than the QMC-type equilibrium, has something to do with the notion of quantum collapse.Comment: 25 pages, 6 figure

Deconfined quantum criticality and generalised exclusion statistics in a non-hermitian BCS model

We present a pairing Hamiltonian of the Bardeen-Cooper-Schrieffer form which exhibits two quantum critical lines of deconfined excitations. This conclusion is drawn using the exact Bethe ansatz equations of the model which admit a class of simple, analytic solutions. The deconfined excitations obey generalised exclusion statistics. A notable property of the Hamiltonian is that it is non-hermitian. Although it does not have a real spectrum for all choices of coupling parameters, we provide a rigorous argument to establish that real spectra occur on the critical lines. The critical lines are found to be invariant under a renormalisation group map.Comment: 7 pages, 1 figure. Stylistic changes, results unchange