Holographic Bjorken Flow at Large-D

We use gauge/gravity duality to study the dynamics of strongly coupled gauge theories undergoing boost invariant expansion in an arbitrary number of space-time dimensions (D). By keeping the scale of the late-time energy density fixed, we explore the infinite-D limit and study the first few corrections to this expansion. In agreement with other studies, we find that the large-D dynamics are controlled by hydrodynamics and we use our computation to constrain the leading large-D dependence of a certain combination of transport coefficients up to 6-th order in gradients. Going beyond late time physics, we discuss how non-hydrodynamic modes appear in the large-D expansion in the form of a trans-series in D, identical to the non-perturbative contributions to the gradient expansion. We discuss the consequence of this trans-series in the non-convergence of the large-D expansion.Comment: 38 pages, 3 figures. v2: Typos corrected, references adde

Mathematics and Thinking

Traditional textbook-centered, teacher-led instruction is based heavily on research about how students best learn mathematics, at what stages ideas can be introduced, and of what kinds of thinking students are capable. Application of student knowledge to tasks not explicitly taught enters a new domain relying on the emotional circuitry of the brain, as well as the cortex where reasoning and problem solving predominate. Cognitive science and neural science provide fascinating insights into non-content related considerations that govern how much of their intellectual resources students will commit to a task and how long they will persist before their knowledge is accessed. Information about how the brain works and how students address mathematics is complementary to more familiar mathematics education research

Investigation and Discovery

Investigation and discovery are how mathematics is applied outside the classroom. Richard Skemp, author of The Psychology of Learning Mathematics, says that gradually equipping students with the analytical skills to address mathematical situations without their aid is one of three tasks for mathematics teachers. This ability involves a different skill set than understanding the mathematics for solutions. The self-talk required to explore a non-routine situation to determine how to get started mimics questions the teacher uses to guide students through assisted learning. Discovery is the creative process of modifying existing schemas to accommodate the new situation. Whereas problem-solving is considered by students as narrowing to an answer, investigation and discovery are expansive to new learning

The prevention and treatment of C02 narcosis in a general medical unit

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Constipation in elderly patients attending a polyclinic

Objective. Tb determine the prevalence of and risk factors for constipation in the elderly. Differences between the white and black elderly populations in this regard were examined.Design. Cross-section hospital-based study.Setting. The family medicine cliriics at National and Pelonomi hospitals in greater Bloemfontein.Participants. 179 white and 188 black patients, born before 1930, visiting the clinics during December and January 1994/95 and seen by one doctor. Mizin outcome measures. Constipation.Results. In both the black and white population groups 29% of the participants were constipated according to the definition used in this study. Depression was a risk factor for constipation in both population groups. Age over 80 years was a risk factor in the black participants. The fibre and fluid contents of participants' diets were not found to be associated with constipation. Pain during defaecation was positively associated with constipation. Forty-three per cent of the white and 76.6% of the black participants used laxatives. Of the white and black laxative users 14.3% and 21.5%, respectively, used more than one laxative at a time.Conclusion. The prevalence of constipation was high in both groups. Laxative use and abuse are very common in the black elderly population

Metal abundances at z<1.5: new measurements in sub-Damped Lyman-alpha Absorbers

Damped Lyman-alpha systems (DLAs) and sub-DLAs seen toward background quasars provide the most detailed probes of elemental abundances. Somewhat paradoxically these measurements are more difficult at lower redshifts due to the atmospheric cut-off, and so a few years ago our group began a programme to study abundances at z < 1.5 in quasar absorbers. In this paper, we present new UVES observations of six additional quasar absorption line systems at z < 1.5, five of which are sub-DLAs. We find solar or above solar metallicity, as measured by the abundance of zinc, assumed not to be affected by dust, in two sub-DLAs: one, towards Q0138-0005 with [Zn/H]=+0.28 +/- 0.16; the other towards Q2335+1501 with [Zn/H]=+0.07 +/- 0.34. Relatively high metallicity was observed in another system: Q0123-0058 with [Zn/H]=-0.45 +/- 0.20. Only for the one DLA in our sample, in Q0449-1645, do we find a low metallicity, [Zn/H]=-0.96 +/- 0.08. We also note that in some of these systems large relative abundance variations from component to component are observed in Si, Mn, Cr and Zn.Comment: 7 figures and 10 tables. Accepted for publication in MNRA

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

Do Damped and Sub-damped Lyman-alpha Absorbers Arise in Galaxies of Different Masses?

We consider the questions of whether the damped Lyman-alpha (DLA) and sub-DLA absorbers in quasar spectra differ intrinsically in metallicity, and whether they could arise in galaxies of different masses. Using the recent measurements of the robust metallicity indicators Zn and S in DLAs and sub-DLAs, we confirm that sub-DLAs have higher mean metallicities than DLAs, especially at $z \lesssim 2$. We find that the intercept of the metallicity-redshift relation derived from Zn and S is higher than that derived from Fe by 0.5-0.6 dex. We also show that, while there is a correlation between the metallicity and the rest equivalent width of Mg II $\lambda 2796$ or Fe II $\lambda 2599$ for DLAs, no correlation is seen for sub-DLAs. Given this, and the similar Mg II or Fe II selection criteria employed in the discovery of both types of systems at lower redshifts, the difference between metallicities of DLAs and sub-DLAs appears to be real and not an artefact of selection. This conclusion is supported by our simulations of Mg II $\lambda 2796$ and Fe II $\lambda 2599$ lines for a wide range of physical conditions. On examining the velocity spreads of the absorbers, we find that sub-DLAs show somewhat higher mean and median velocity spreads ($\Delta v$), and an excess of systems with $\Delta v > 150$ km s$^{-1}$, than DLAs. Compared to DLAs, the [Mn/Fe] vs. [Zn/H] trend for sub-DLAs appears to be steeper and closer to the trend for Galactic bulge and thick disk stars, possibly suggesting different stellar populations. The absorber data appear to be consistent with galaxy down-sizing. The data are also consistent with the relative number densities of low-mass and high-mass galaxies. It is thus plausible that sub-DLAs arise in more massive galaxies on average than DLAs.Comment: 27 pages, 5 figures, 4 tables. Accepted for publication in New Astronom

Hubble Space Telescope Observations of Sub-Damped Lyman-alpha Absorbers at z < 0.5, and Implications for Galaxy Chemical Evolution

We report observations of four sub-damped Lyman-alpha (sub-DLA) quasar absorbers at z<0.5 obtained with the Hubble Space Telescope Cosmic Origins Spectrograph. We measure the available neutrals or ions of C, N, O, Si, P, S, Ar, Mn, Fe, and/or Ni. Our data have doubled the sub-DLA metallicity samples at z<0.5 and improved constraints on sub-DLA chemical evolution. All four of our sub-DLAs are consistent with near-solar or super-solar metallicities and relatively modest ionization corrections; observations of more lines and detailed modeling will help to verify this. Combining our data with measurements from the literature, we confirm previous suggestions that the N(HI)-weighted mean metallicity of sub-DLAs exceeds that of DLAs at all redshifts studied, even after making ionization corrections for sub-DLAs. The absorber toward PHL 1598 shows significant dust depletion. The absorbers toward PHL 1226 and PKS 0439-433 show the S/P ratio consistent with solar, i.e., they lack a profound odd-even effect. The absorber toward Q0439-433 shows super-solar Mn/Fe. For several sub-DLAs at z<0.5, [N/S] is below the level expected for secondary N production, suggesting a delay in the release of the secondary N or a tertiary N production mechanism. We constrain the electron density using Si II* and C II* absorption. We also report different metallicity vs. Delta V_90 relations for sub-DLAs and DLAs. For two sub-DLAs with detections of emission lines from the underlying galaxies, our measurements of the absorption-line metallicities are consistent with the emission-line metallicities, suggesting that metallicity gradients are not significant in these galaxies.Comment: 77 pages, 13 figures; accepted for publication in the Astrophysical Journal. Submitted (in the original form) May 26, 2014; accepted Apr. 15, 201