The Internal Dynamics of Globular Clusters

Galactic globular clusters are ancient building blocks of our Galaxy. They represent a very interesting family of stellar systems in which some fundamental dynamical processes have been taking place for more than 10 Gyr, but on time scales shorter than the age of the universe. In contrast with galaxies, these star clusters represent unique laboratories for learning about two-body relaxation, mass segregation from equipartition of energy, stellar collisions, stellar mergers, core collapse, and tidal disruption. This review briefly summarizes some of the tremendous developments that have taken place during the last two decades. It ends with some recent results on tidal tails around galactic globular clusters and on a very massive globular cluster in M31.Comment: An invited review (32 pages, 7 figures) in "The Chaotic Universe: Theory, Observations, Computer Experiments", Proceedings of the ICRA Rome-Pescara workshop, eds. V.G. Gurzadyan and R. Ruffini (Singapore: World Sci.), in pres

A variation equation for the wave forcing of floating thin plates

A variational equation is derived for a floating thin plate subject to wave forcing. This variational equation is derived from the thin plate equations of motion by including the forcing due to the wave through the integral equation derived using the free surface Green’s function. This equation combines the optimum method forsolving the motion of a thin plate (the variational equation) with the optimum method for solving the wave forcing of a floating body (the Green’s function method). Solutions of the variational equation are presented for some simple thin plate geometries using polynomial basis functions. The variational equation is extended to the case of plates of variable properties and to multiple plates and example solutions are presented

Partisipasi Perempuan Dalam Pengelolaan Lingkungan Hidup

Women have strong links with the environment. In his role as manager of the household, they are more interacting with the environment and natural resources. The era of globalization has indirectly resulted in increasing the development of environmental pollution and environmental damage. Women and children are part of the citizens who have a direct impact of pollution. Women's health impaired due to unhealthy living environment will result indirectly on the health of children as the future generation. Law No. 32 of 2009 on the Protection and Management of Living (UUPPLH) has given the changes that are democratic; give broad authority to local governments and community involvement in giving priority to control environmental damage. The role of women is implicitly described in article 70 of the role of the community. The role of women in environmental protection under the act protection and environmental management can be a social control and the role of women in environmental policy-making through the legislature

Approximation and convergence of formal CR-mappings

Let $M\subset C^N$ be a minimal real-analytic CR-submanifold and $M'\subset C^{N'}$ a real-algebraic subset through points $p\in M$ and $p'\in M'$. We show that that any formal (holomorphic) mapping $f\colon (C^N,p)\to (C^{N'},p')$, sending $M$ into $M'$, can be approximated up to any given order at $p$ by a convergent map sending $M$ into $M'$. If $M$ is furthermore generic, we also show that any such map $f$, that is not convergent, must send (in an appropriate sense) $M$ into the set $E'\subset M'$ of points of D'Angelo infinite type. Therefore, if $M'$ does not contain any nontrivial complex-analytic subvariety through $p'$, any formal map $f$ as above is necessarily convergent

The Stellar Dynamics of Omega Centauri

The stellar dynamics of Omega Centauri are inferred from the radial velocities of 469 stars measured with CORAVEL (Mayor et al. 1997). Rather than fit the data to a family of models, we generate estimates of all dynamical functions nonparametrically, by direct operation on the data. The cluster is assumed to be oblate and edge-on but mass is not assumed to follow light. The mean motions are consistent with axisymmetry but the rotation is not cylindrical. The peak rotational velocity is 7.9 km/s at 11 pc from the center. The apparent rotation of Omega Centauri is attributable in part to its proper motion. We reconstruct the stellar velocity ellipsoid as a function of position, assuming isotropy in the meridional plane. We find no significant evidence for a difference between the velocity dispersions parallel and perpendicular to the meridional plane. The mass distribution inferred from the kinematics is slightly more extended than, though not strongly inconsistent with, the luminosity distribution. We also derive the two-integral distribution function f(E,Lz) implied by the velocity data.Comment: 25 Latex pages, 12 Postscript figures, uses aastex, epsf.sty. Submitted to The Astronomical Journal, December 199

Interpolating point spread function anisotropy

Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit from that scaling effect and will require very accurate modeling and correction. While numerous methods have been devised to carry out the PSF correction itself, modeling of the PSF shape and its spatial variations across the instrument field of view has, so far, attracted much less attention. This step is nevertheless crucial because the PSF is only known at star positions while the correction has to be performed at any position on the sky. A reliable interpolation scheme is therefore mandatory and a popular approach has been to use low-order bivariate polynomials. In the present paper, we evaluate four other classical spatial interpolation methods based on splines (B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and ordinary Kriging (OK). These methods are tested on the Star-challenge part of the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and are compared with the classical polynomial fitting (Polyfit). We also test all our interpolation methods independently of the way the PSF is modeled, by interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are known exactly at star positions). We find in that case RBF to be the clear winner, closely followed by the other local methods, IDW and OK. The global methods, Polyfit and B-splines, are largely behind, especially in fields with (ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all interpolators reach a variance on PSF systematics $\sigma_{sys}^2$ better than the $1\times10^{-7}$ upper bound expected by future space-based surveys, with the local interpolators performing better than the global ones