RR Lyrae variables in the globular cluster M3 (NGC5272). I. BVI CCD photometry

New BVI CCD photometry is presented for 60 RR Lyrae variables in the globular cluster M3. Light curves have been constructed and ephemerides have been (re)-derived for all of them. Four stars (i.e. V29, V136, V155 and V209), although recognized as variables, had no previous period determinations. Also, the period derived for V129 is significantly different from the one published by Sawyer-Hogg (1973). Light curve parameters, i.e. mean magnitudes, amplitudes and rise-times, have been derived. The discussion of these results in the framework of the stellar evolution and pulsation theories will be presented in a forthcoming paper.Comment: 19 pages, latex, uses mn.sty, 12 encapsulated figures, to be published in MNRAS, text and figures also available at http://www.bo.astro.it/bap/BAPhome.html or via anonymous ftp at ftp://boas3.bo.astro.it/bap/files (bap98-12-textfig.ps

An empirical mass-loss law for Population II giants from the Spitzer-IRAC survey of Galactic globular clusters

The main aim of the present work is to derive an empirical mass-loss (ML) law for Population II stars in first and second ascent red giant branches. We used the Spitzer InfraRed Array Camera (IRAC) photometry obtained in the 3.6-8 micron range of a carefully chosen sample of 15 Galactic globular clusters spanning the entire metallicity range and sampling the vast zoology of horizontal branch (HB) morphologies. We complemented the IRAC photometry with near-infrared data to build suitable color-magnitude and color-color diagrams and identify mass-losing giant stars. We find that while the majority of stars show colors typical of cool giants, some stars show an excess of mid-infrared light that is larger than expected from their photospheric emission and that is plausibly due to dust formation in mass flowing from them. For these stars, we estimate dust and total (gas + dust) ML rates and timescales. We finally calibrate an empirical ML law for Population II red and asymptotic giant branch stars with varying metallicity. We find that at a given red giant branch luminosity only a fraction of the stars are losing mass. From this, we conclude that ML is episodic and is active only a fraction of the time, which we define as the duty cycle. The fraction of mass-losing stars increases by increasing the stellar luminosity and metallicity. The ML rate, as estimated from reasonable assumptions for the gas-to-dust ratio and expansion velocity, depends on metallicity and slowly increases with decreasing metallicity. In contrast, the duty cycle increases with increasing metallicity, with the net result that total ML increases moderately with increasing metallicity, about 0.1 Msun every dex in [Fe/H]. For Population II asymptotic giant branch stars, we estimate a total ML of <0.1 Msun, nearly constant with varying metallicity.Comment: 17 pages, 9 figures, in press on A&

BVI Photometry and the Luminosity Function of the Globular Cluster M92

We present new BVI ground-based photometry and VI space-based photometry for the globular cluster M92 (NGC 6341) and examine luminosity functions in B, V, and I containing over 50,000 stars ranging from the tip of the red giant branch to several magnitudes below the main sequence turn off. Once corrected for completeness, the observed luminosity functions agree very well with theoretical models and do not show stellar excesses in any region of the luminosity function. Using reduced chi squared fitting, the new M92 luminosity function is shown to be an excellent match to the previously published luminosity function for M30. These points combine to establish that the "subgiant excess" found in previously published luminosity functions of Galactic globular clusters are due to deficiencies in the stellar models used at that time. Using up to date stellar models results in good agreement between observations and theory. Several statistical methods are presented to best determine the age of M92. These methods prove to be insensitive to the exact choice of metallicity within the published range. Using [Fe/H]=-2.17 to match recent studies we find an age of 14.2 plus or minus 1.2 Gyr for the cluster.Comment: 22 pages, 13 figures, 3 tables, accepted for publication in A

Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks

In this paper, we investigate the application of penalty and relaxation methods to the problem of optimal placement and operation of control valves in water supply networks, where the minimization of average zone pressure is the objective. The optimization framework considers both the location and settings of control valves as decision variables. Hydraulic conservation laws are enforced as nonlinear constraints and binary variables are used to model the placement of control valves, resulting in a mixed-integer nonlinear program. We review and discuss theoretical and algorithmic properties of two solution approaches. These include penalty and relaxation methods that solve a sequence of nonlinear programs whose stationary points converge to a stationary point of the original mixed-integer program. We implement and evaluate the algorithms using a benchmarking water supply network. In addition, the performance of different update strategies for the penalty and relaxation parameters are investigated under multiple initial conditions. Practical recommendations on the numerical implementation are provided

Quadratic head loss approximations for optimisation problems in water supply networks

This paper presents a novel analysis on the accuracy of quadratic approximations for Hazen--Williams head loss formula, which enables the control of constraint violations in optimisation problems for water supply networks. The two smooth polynomial approximations considered here minimise the absolute and relative errors, respectively, from the original non-smooth Hazen--Williams head loss function over a range of flows. Since the quadratic approximations are used to formulate head loss constraints for different optimisation problems, we are interested in quantifying and controlling their absolute errors, which affect the degree of constraint violations of candidate feasible solutions. We derive new exact analytical formulae for the absolute errors as a function of the approximation domain, pipe roughness and relative error tolerance. We assess the efficacy of the quadratic approximations in mathematical optimisation for optimal pressure regulation in an operational water supply network. We propose a strategy on how to choose the approximation domain for each pipe such that the optimisation results are sufficiently close to the exact hydraulic feasibility region. By using simulations with multiple parameters, the approximation errors are shown to be consistent with our analytical predictions

Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach

In this paper, we study the multiobjective co-design problem of optimal valve placement and operation in water distribution networks, addressing the minimization of average pressure and pressure variability indices. The presented formulation considers nodal pressures, pipe flows and valve locations as decision variables, where binary variables are used to model the placement of control valves. The resulting optimization problem is a multiobjective mixed integer nonlinear optimization problem. As conflicting objectives, average zone pressure and pressure variability can not be simultaneously optimized. Therefore, we present the concept of Pareto optima sets to investigate the trade-offs between the two conflicting objectives and evaluate the best compromise. We focus on the approximation of the Pareto front, the image of the Pareto optima set through the objective functions, using the weighted sum, normal boundary intersection and normalized normal constraint scalarization techniques. Each of the three methods relies on the solution of a series of single-objective optimization problems, which are mixed integer nonlinear programs (MINLPs) in our case. For the solution of each single-objective optimization problem, we implement a relaxation method that solves a sequence of nonlinear programs (NLPs) whose stationary points converge to a stationary point of the original MINLP. The relaxed NLPs have a sparse structure that come from the sparse water network graph constraints. In solving the large number of relaxed NLPs, sparsity is exploited by tailored techniques to improve the performance of the algorithms further and render the approaches scalable for large scale networks. The features of the proposed scalarization approaches are evaluated using a published benchmarking network model

Globular Clusters in the Magellanic Clouds.I:BV CCD-Photometry for 11 Clusters

We present BV CCD-data for 11 intermediate-age LMC clusters; the main conclusions are: 1. in the (V_to, V_cl,m) and (V-to, (V_to-V_cl,m)) planes the models yield a good overall description of the data; 2. with the current sample, it is impossible to firmly choose between "classical" and "overshooting" models; 3. the separation in colour between the MS band and the Red He-burning Clump is smaller than predicted by theoretical tracks; 4. the existence of the so-called "RGB phase-transition (Renzini and Buzzoni 1986) seems to be confirmed.Comment: 62 pages, 37 figures and tables 6 to 16 available on request, uuencoded compressed postscript file with tables 1-5 and 17-18 included, BAP 08-1994-020-OA

Model reduction and outer approximation for optimising the placement of control valves in complex water networks

The optimal placement and operation of pressure control valves in water distribution networks is a challenging engineering problem. When formulated in a mathematical optimisation frame work, this problem results in a nonconvex mixed integer nonlinear program (MINLP), which has combinatorial computational complexity. As a result, the considered MINLP becomes particularly difficult to solve for large-scale looped operational networks. We extend and combine network model reduction techniques with the proposed optimisation framework in order to lower the computational burden and enable the optimal placement and operation of control valves in these complex water distribution networks. An outer approximation algorithm is used to solve the considered MINLPs on reduced hydraulic models. We demonstrate that the restriction of the considered optimisation problem on a reduced hydraulic model is not equivalent to solving the original larger MINLP, and its solution is therefore sub-optimal. Consequently, we investigate the trade-off between reducing computational complexity and the potential sub-optimality of the solutions that can be controlled with a parameter of the model reduction routine. The efficacy of the proposed method is evaluated using two large scale water distribution network models