About the Algebraic Solutions of Smallest Enclosing Cylinders Problems

Given n points in Euclidean space E^d, we propose an algebraic algorithm to compute the best fitting (d-1)-cylinder. This algorithm computes the unknown direction of the axis of the cylinder. The location of the axis and the radius of the cylinder are deduced analytically from this direction. Special attention is paid to the case d=3 when n=4 and n=5. For the former, the minimal radius enclosing cylinder is computed algebrically from constrained minimization of a quartic form of the unknown direction of the axis. For the latter, an analytical condition of existence of the circumscribed cylinder is given, and the algorithm reduces to find the zeroes of an one unknown polynomial of degree at most 6. In both cases, the other parameters of the cylinder are deduced analytically. The minimal radius enclosing cylinder is computed analytically for the regular tetrahedron and for a trigonal bipyramids family with a symmetry axis of order 3.Comment: 13 pages, 0 figure; revised version submitted to publication (previous version is a copy of the original one of 2010

Testing Cosmological Models With A \lya Forest Statistic: The High End Of The Optical Depth Distribution

We pay particular attention to the high end of the \lya optical depth distribution of a quasar spectrum. Based on the flux distribution (Miralda-Escud\'e et al 1996), a simple yet seemingly cosmological model -differentiating statistic, $\Delta_{\tau_0}$ -- the cumulative probability of a quasar spectrum with \lya optical depth greater than a high value $\tau_0$ -- is emphasized. It is shown that two different models -- the cold dark matter model with a cosmological constant and the mixed hot and cold dark matter model, both normalized to COBE and local galaxy cluster abundance -- yield quite different values of $\Delta_{\tau_0}$: 0.13 of the former versus 0.058 of the latter for $\tau_0=3.0$ at $z=3$. Moreover, it is argued that $\Delta_{\tau_0}$ may be fairly robust to compute theoretically because it does not seem to depend sensitively on small variations of simulations parameters such as radiation field, cooling, feedback process, radiative transfer, resolution and simulation volume within the plausible ranges of the concerned quantities. Furthermore, it is illustrated that $\Delta_{\tau_0}$ can be obtained sufficiently accurately from currently available observed quasar spectra for $\tau_0\sim 3.0-4.0$, when observational noise is properly taken into account. We anticipate that analyses of observations of quasar \lya absorption spectra over a range of redshift may be able to constrain the redshift evolution of the amplitude of the density fluctuations on small-to-intermediate scales, therefore providing an independent constraint on $\Omega_0$, $\Omega_{0,HDM}$ and $\Lambda_0$.Comment: ApJ Letters, in press, substantial changes have been made from the last versio

Semiclassical approach to the ac-conductance of chaotic cavities

We address frequency-dependent quantum transport through mesoscopic conductors in the semiclassical limit. By generalizing the trajectory-based semiclassical theory of dc quantum transport to the ac case, we derive the average screened conductance as well as ac weak-localization corrections for chaotic conductors. Thereby we confirm respective random matrix results and generalize them by accounting for Ehrenfest time effects. We consider the case of a cavity connected through many leads to a macroscopic circuit which contains ac-sources. In addition to the reservoir the cavity itself is capacitively coupled to a gate. By incorporating tunnel barriers between cavity and leads we obtain results for arbitrary tunnel rates. Finally, based on our findings we investigate the effect of dephasing on the charge relaxation resistance of a mesoscopic capacitor in the linear low-frequency regime

Temperature and Kinematics of CIV Absorption Systems

We use Keck HIRES spectra of three intermediate redshift QSOs to study the physical state and kinematics of the individual components of CIV selected heavy element absorption systems. Fewer than 8 % of all CIV lines with column densities greater than 10^{12.5} cm^{-2} have Doppler parameters b < 6 km/s. A formal decomposition into thermal and non-thermal motion using the simultaneous presence of SiIV gives a mean thermal Doppler parameter b_{therm}(CIV) = 7.2 km/s, corresponding to a temperature of 38,000 K although temperatures possibly in excess of 300,000 K occur occasionally. We also find tentative evidence for a mild increase of temperature with HI column density. Non-thermal motions within components are typically small (< 10 km/s) for most systems, indicative of a quiescent environment. The two-point correlation function (TPCF) of CIV systems on scales up to 500 km/s suggests that there is more than one source of velocity dispersion. The shape of the TPCF can be understood if the CIV systems are caused by ensembles of objects with the kinematics of dwarf galaxies on a small scale, while following the Hubble flow on a larger scale. Individual high redshift CIV components may be the building blocks of future normal galaxies in a hierarchical structure formation scenario.Comment: submitted to the ApJ Letters, March 16, 1996 (in press); (13 Latex pages, 4 Postscript figures, and psfig.sty included

High resolution study of associated C IV absorption systems in NGC 5548

We present the results of a careful analysis of associated absorption systems toward NGC 5548. Most of the well resolved narrow components in the associated system, defined by the Lyman alpha, C IV and N V profiles, show velocity separation similar (to within 10~\kms) to the C IV doublet splitting. We estimate the chance probability of occurrence of such pairs with velocity separation equal to C IV doublet splitting to be $6\times10^{-3}$. Thus it is more likely that most of the narrow components are line-locked with C IV doublet splitting. This will mean that the radiative acceleration plays an important role in the kinematics of the absorbing clouds. We build grids of photoionization models and estimate the radiative acceleration due to all possible bound-bound transitions. We show that the clouds producing absorption have densities less than $10^9 cm^{-3}$, and are in the outer regions of the broad emission line region (BLR). We note that the clouds which are line-locked cannot produce appreciable optical depths of O VII and O VIII, and hence cannot be responsible for the observed ionized edges, in the soft X-ray. We discuss the implications of the presence of optically thin clouds in the outer regions of the BLR to the models of broad emission lines.Comment: 21 pages, latex (aasms4 style), incluedes 4 ps figures. To appear in Astrophysical Journa

A Multi-Species Model for Hydrogen and Helium Absorbers in Lyman-Alpha Forest Clouds

We have performed a multi-species hydrodynamical simulation of the formation and evolution of Lyman alpha clouds in a flat CDM dominated universe with an external flux of ionizing radiation. We solve the fully coupled non-equilibrium rate equations for the following species: H, H^+, H^-, H_2, H_2^+, He, He^+, He^{++}, and e^-. The statistical properties of the distribution and evolution of both hydrogen and helium absorption lines are extracted and compared to observed data. We find excellent agreement for the following neutral hydrogen data: the distribution of column densities is fit well by a power law with exponent beta=1.55 with a possible deficiency of lines above column density 10^{15} cm^{-2}; the integrated distribution matches observed data over a broad range of column densities 10^{13} to 10^{17} cm^{-2}; a Gaussian statistical fit to the Doppler parameter distribution yields a median of 35.6 km s^{-1}; the evolution of the number of clouds with column densities larger than 10^{14} cm^{-2} follows a power law with exponent gamma=2.22. Analogous calculations are presented for HeII absorption lines and we find the ratio of Doppler parameters b_{HeII}/b_{HI} = 0.87. Our data also suggests that Ly$\alpha$ clouds may belong to two morphologically different groups: small column density clouds which tend to reside in sheets or filamental structures and are very elongated and/or flattened, and the large column density clouds which are typically found at the intersections of these caustic structures and are quasi-spherical.Comment: 14 pages, 4 postscript figure

The Origin of C IV Absorption Systems at Redshifts z<1---Discovery of Extended C IV Envelopes Around Galaxies

(Abridged) We report the discovery of extended CIV gaseous envelopes around galaxies of a wide range of luminosity and morphological type. First, we show that CIV absorption systems are strongly clustered around galaxies on velocity scales of v < 250 km/s and impact parameter scales of rho < 100 h^{-1} kpc but not on larger velocity or impact parameter scales. Next, adopting measurements of galaxy properties presented in previous papers, we examine how properties of the CIV absorption systems depend on properties of the galaxies. On the basis of 14 galaxy and absorber pairs and 36 galaxies that do not produce corresponding CIV absorption lines to within sensitive upper limits, we find that: (1) Galaxies of a range of morphological type and luminosity appear to possess extended CIV gaseous envelopes of radius R ~ 100 h^{-1} kpc, with abrupt boundaries between the CIV absorbing and non-absorbing regions. (2) The extent of CIV-absorbing gas around galaxies scales with galaxy B-band luminosity as R \propto L_B^{0.5 +/- 0.1} but does not depend strongly on galaxy surface brightness, redshift, or morphological type. And (3) the covering factor of CIV clouds within ~ 100 h^{-1} kpc of galaxies is nearly unity, but there is a large scatter in the mean number of clouds encountered along the line of sight. The most significant implication of the study is that galaxies of a wide range of luminosity and morphological type are surrounded by chemically enriched gas that extends for at least ~ 100 h^{-1} kpc. We consider various scenarios that may have produced metals at large galactic distance and conclude that accreting satellites are most likely to be responsible for chemically enriched gas at large galactic distances to regular looking galaxies.Comment: 19 pages, 3 figures, to appear in ApJ, July 20 200