Detecting cold gas at intermediate redshifts: GMRT survey using Mg II systems

Intervening HI 21-cm absorption systems at z > 1.0 are very rare and only 4 confirmed detections have been reported in the literature. Despite their scarcity, they provide interesting and unique insights into the physical conditions in the interstellar medium of high-z galaxies. Moreover, they can provide independent constraints on the variation of fundamental constants. We report 3 new detections based on our ongoing Giant Metrewave Radio Telescope (GMRT) survey for 21-cm absorbers at 1.10< z_abs< 1.45 from candidate damped Lyman_alpha systems. The 21-cm lines are narrow for the z_abs = 1.3710 system towards SDSS J0108-0037 and z_abs = 1.1726 system toward SDSS J2358-1020. Based on line full-width at half maximum, the kinetic temperatures are <= 5200 K and <=800 K, respectively. The 21-cm absorption profile of the third system, z_abs =1.1908 system towards SDSS J0804+3012, is shallow, broad and complex, extending up to 100 km/s. The centroids of the 21-cm lines are found to be shifted with respect to the corresponding centroids of the metal lines derived from SDSS spectra. This may mean that the 21-cm absorption is not associated with the strongest metal line component.Comment: 13 pages with 5 figures. Accepted for publication in ApJ

Linear Superposition in Nonlinear Equations

Even though the KdV and modified KdV equations are nonlinear, we show that suitable linear combinations of known periodic solutions involving Jacobi elliptic functions yield a large class of additional solutions. This procedure works by virtue of some remarkable new identities satisfied by the elliptic functions.Comment: 7 pages, 1 figur

Exact Solutions of the Saturable Discrete Nonlinear Schrodinger Equation

Exact solutions to a nonlinear Schr{\"o}dinger lattice with a saturable nonlinearity are reported. For finite lattices we find two different standing-wave-like solutions, and for an infinite lattice we find a localized soliton-like solution. The existence requirements and stability of these solutions are discussed, and we find that our solutions are linearly stable in most cases. We also show that the effective Peierls-Nabarro barrier potential is nonzero thereby indicating that this discrete model is quite likely nonintegrable

Element Abundances at High-redshift: Magellan MIKE Observations of sub-Damped Lyman-alpha Absorbers at 1.7 < z <2.4

We present chemical abundance measurements from high-resolution observations of 5 sub-damped Lyman-alpha absorbers at 1.7 < z < 2.4 observed with the Magellan Inamori Kyocera Echelle (MIKE) spectrograph on the 6.5-m Magellan II Clay telescope. Lines of Zn II, Mg I, Mg II, Al II, Al III, S II, Si II, Si IV, C II, C II*, C IV, Ni II, Mn II and Fe II were detected and column densities were determined. The metallicity of the absorbing gas, inferred from the nearly undepleted element Zn, is in the range of < -0.95 to +0.25 dex for the five absorbers in our sample, with three of the systems being near-solar or super-solar. We also investigate the effect of ionisation on the observed abundances using photoionisation modelling. Combining our data with other sub-DLA and DLA data from the literature, we report the most complete existing determination of the metallicity vs. redshift relation for sub-DLAs and DLAs. We confirm the suggestion from previous investigations that sub-DLAs are, on average, more metal-rich than DLAs and evolve faster. We also discuss relative abundances and abundance ratios in these absorbers. The more metal-rich systems show significant dust depletion levels, as suggested by the ratios [Zn/Cr] and [Zn/Fe]. For the majority of the systems in our sample, the [Mn/Fe] vs. [Zn/H] trend is consistent with that seen previously for lower-redshift sub-DLAs. We also measure the velocity width values for the sub-DLAs in our sample from unsaturated absorption lines of Fe II 2344, 2374, 2600 A, and examine where these systems lie in a plot of metallicity vs. velocity dispersion. Finally, we examine cooling rate vs. H I column density in these sub-DLAs, and compare this with the data from DLAs and the Milky Way ISM. We find that most of the systems in our sample show higher cooling rate values compared to those seen in the DLAs.Comment: Accepted for publication in the Monthly Notices of The Royal Astronomical Societ

Superposition in nonlinear wave and evolution equations

Real and bounded elliptic solutions suitable for applying the Khare-Sukhatme superposition procedure are presented and used to generate superposition solutions of the generalized modified Kadomtsev-Petviashvili equation (gmKPE) and the nonlinear cubic-quintic Schroedinger equation (NLCQSE).Comment: submitted to International Journal of Theoretical Physics, 23 pages, 2 figures, style change

Stability Check of Escarpment Using Finite Element Method

The valve house of the Tons Hydel Project, Madhya Pradesh, India is located just adjacent to a steep escarpment. The stability analysis of scarp near the valve house was made by the Central Water and Power Research Station, using finite element method. The problem was treated as a plain strain case. The analysis under self weight and with seepage forces indicated tensile stresses less than 4 kg/cm2 in the scarp. A proposal by the project authorities namely removing rock in the area above R.L.230 m at 74 degrees and filling lean concrete below the overhang was found to provide a stable condition. The state of stress in the scarp near the valve house was obtained under different conditions. The finite element method thus proved to be a very useful tool in analysing problem

Barrier Penetration for Supersymmetric Shape-Invariant Potentials

Exact reflection and transmission coefficients for supersymmetric shape-invariant potentials barriers are calculated by an analytical continuation of the asymptotic wave functions obtained via the introduction of new generalized ladder operators. The general form of the wave function is obtained by the use of the F-matrix formalism of Froman and Froman which is related to the evolution of asymptotic wave function coefficients