Automatic editing of manuals

The documentation problem is discussed that arises in getting all the many items included in a computer program prepared in a timely fashion and keeping them all correct and mutually consistent during the life of the program. The proposed approach to the problem is to collect all the necessary information into a single document, which is maintained with computer assistance during the life of the program and from which the required subdocuments can be extracted as desired. Implementation of this approach requires a package of programs for computer editorial assistance and is facilitated by certain programming practices that are discussed

Reply to Comment on 'Critical behaviour in the relaminarization of localized turbulence in pipe flow'

This is a Reply to Comment arXiv:0707.2642 by Hof et al. on Letter arXiv:physics/0608292 which was subsequently published in Phys Rev Lett, 98, 014501 (2007). In our letter it was reported that in pipe flow the median time $\tau$ for relaminarisation of localised turbulent disturbances closely follows the scaling $\tau\sim 1/(Re_c-Re)$. This conclusion was based on data from collections of 40 to 60 independent simulations at each of six different Reynolds numbers, Re. In the Comment, Hof et al. estimate $\tau$ differently for the point at lowest Re. Although this point is the most uncertain, it forms the basis for their assertion that the data might then fit an exponential scaling $\tau\sim \exp(A Re)$, for some constant A, supporting Hof et al. (2006) Nature, 443, 59. The most certain point (at largest Re) does not fit their conclusion and is rejected. We clarify why their argument for rejecting this point is flawed. The median $\tau$ is estimated from the distribution of observations, and it is shown that the correct part of the distribution is used. The data is sufficiently well determined to show that the exponential scaling cannot be fit to the data over this range of Re, whereas the $\tau\sim 1/(Re_c-Re)$ fit is excellent, indicating critical behaviour and supporting experiments by Peixinho & Mullin 2006.Comment: 1 page, 1 figur

Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow

Motivated by recent success in the dynamical systems approach to transitional flow, we study the efficiency and effectiveness of extracting simple invariant sets (recurrent flows) directly from chaotic/turbulent flows and the potential of these sets for providing predictions of certain statistics of the flow. Two-dimensional Kolmogorov flow (the 2D Navier-Stokes equations with a sinusoidal body force) is studied both over a square [0, 2{\pi}]2 torus and a rectangular torus extended in the forcing direction. In the former case, an order of magnitude more recurrent flows are found than previously (Chandler & Kerswell 2013) and shown to give improved predictions for the dissipation and energy pdfs of the chaos via periodic orbit theory. Over the extended torus at low forcing amplitudes, some extracted states mimick the statistics of the spatially-localised chaos present surprisingly well recalling the striking finding of Kawahara & Kida (2001) in low-Reynolds-number plane Couette flow. At higher forcing amplitudes, however, success is limited highlighting the increased dimensionality of the chaos and the need for larger data sets. Algorithmic developments to improve the extraction procedure are discussed

A 20 Thousand Solar Mass Black Hole in the Stellar Cluster G1

We present the detection of a 2.0(+1.4,-0.8)x10^4 solar mass black hole (BH) in the stellar cluster G1 (Mayall II), based on data taken with the Space Telescope Imaging Spectrograph onboard the Hubble Space Telescope. G1 is one of the most massive stellar clusters in M31. The central velocity dispersion (25 kms) and the measured BH mass of G1 places it on a linear extrapolation of the correlation between BH mass and bulge velocity dispersion established for nearby galaxies. The detection of a BH in this low-mass stellar system suggests that (1) the most likely candidates for seed massive BHs come from stellar clusters, (2) there is a direct link between massive stellar clusters and normal galaxies, and (3) the formation process of both bulges and massive clusters is similar due to their concordance in the M_BH/sigma relation. Globular clusters in our Galaxy should be searched for central BHs.Comment: 4 pages, accepted in The Astrophysical Journal Letters, October 200

Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Benard convection

An alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Benard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the "background field" variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Benard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents alpha and beta in the presumed Nu similar to (PrRa beta)-Ra-alpha scaling relation. The computations clearly show that for Ra <= 10(10) at fixed L = 2 root 2, Nu <= 0.106Pr(0)Ra(5/12), which indicates that molecular transport cannot generally be neglected in the "ultimate" high-Ra regime.NSF DMS-0928098 DMS-1515161 DMS-0927587 PHY-1205219Simons FoundationNSFONRInstitute for Computational Engineering and Sciences (ICES

Proper motions in Terzan 5: membership of the multi-iron sub-populations and first constrain to the orbit

By exploiting two sets of high-resolution images obtained with HST ACS/WFC over a baseline of ~10 years we have measured relative proper motions of ~70,000 stars in the stellar system Terzan 5. The results confirm the membership of the three sub-populations with different iron abudances discovered in the system. The orbit of the system has been derived from a first estimate of its absolute proper motion, obtained by using bulge stars as reference. The results of the integration of this orbit within an axisymmetric Galactic model exclude any external accretion origin for this cluster. Terzan 5 is known to have chemistry similar to the Galactic bulge; our findings support a kinematic link between the cluster and the bulge, further strengthening the possibility that Terzan 5 is the fossil remnant of one of the pristine clumps that originated the bulge.Comment: 25 pages, 14 figures, accepted for publication by Ap

Alpha Enhancement and the Metallicity Distribution Function of Plaut's Window

We present Fe, Si, and Ca abundances for 61 giants in Plaut's Window (l=-1,b=-8.5) and Fe abundances for an additional 31 giants in a second, nearby field (l=0,b=-8) derived from high resolution (R~25,000) spectra obtained with the Blanco 4m telescope and Hydra multifiber spectrograph. The median metallicity of red giant branch (RGB) stars in the Plaut field is ~0.4 dex lower than those in Baade's Window, and confirms the presence of an iron abundance gradient along the bulge minor axis. The full metallicity range of our (biased) RGB sample spans -1.5<[Fe/H]<+0.3, which is similar to that found in other bulge fields. We also derive a photometric metallicity distribution function for RGB stars in the (l=-1,b=-8.5) field and find very good agreement with the spectroscopic metallicity distribution. The radial velocity and dispersion data for the bulge RGB stars are in agreement with previous results of the BRAVA survey, and we find evidence for a decreasing velocity dispersion with increasing [Fe/H]. The [alpha/Fe] enhancement in Plaut field stars is nearly identical to that observed in Baade's window, and suggests that an [alpha/Fe] gradient does not exist between b=-4 and -8. Additionally, a subset of our sample (23 stars) appear to be foreground red clump stars that are very metal--rich, exhibit small metallicity and radial velocity dispersions, and are enhanced in alpha elements. While these stars likely belong to the Galactic inner disk population, they exhibit [alpha/Fe] ratios that are enhanced above the thin and thick disk.Comment: Accepted for publication in ApJ. 38 pages, 11 figures, and 2 tables. Requests for higher resolution figures and electronic versions of tables 1 and/or 2 in advance of publication may be sent to cijohnson[at]astro.ucla.ed