Simulated annealing applied to the irregular rotational placement of shapes over containers with fixed dimensions

This work deals with the problem of minimizing the waste of space that occurs on a rotational placement of a set of irregular two dimensional polygons inside a two dimensional container. This problem is approached with an heuristic based on simulated annealing. Traditional 14 external penalization"" techniques are avoided through the application of the no-fit polygon, that determinates the collision free area for each polygon before its placement. The simulated annealing controls: the rotation applied, the placement and the sequence of placement of the polygons. For each non placed polygon, a limited depth binary search is performed to find a scale factor that when applied to the polygon, would allow it to be fitted in the container. It is proposed a crystallization heuristic, in order to increase the number of accepted solutions. The bottom left and larger first deterministic heuristics were also studied. The proposed process is suited for non convex polygons and containers, the containers can have holes inside. (C) 2009 Elsevier Ltd. All rights reserved.

GHASP: an H alpha kinematic survey of spiral and irregular galaxies - IX. The near-infrared, stellar and baryonic Tully-Fisher relations

We studied, for the first time, the near-infrared, stellar and baryonic Tully-Fisher relations for a sample of field galaxies taken from a homogeneous Fabry-Perot sample of galaxies [the Gassendi HAlpha survey of SPirals (GHASP) survey]. The main advantage of GHASP over other samples is that the maximum rotational velocities were estimated from 2D velocity fields, avoiding assumptions about the inclination and position angle of the galaxies. By combining these data with 2MASS photometry, optical colours, HI masses and different mass-to-light ratio estimators, we found a slope of 4.48 +/- 0.38 and 3.64 +/- 0.28 for the stellar and baryonic Tully-Fisher relation, respectively. We found that these values do not change significantly when different mass-to-light ratio recipes were used. We also point out, for the first time, that the rising rotation curves as well as asymmetric rotation curves show a larger dispersion in the Tully-Fisher relation than the flat ones or the symmetric ones. Using the baryonic mass and the optical radius of galaxies, we found that the surface baryonic mass density is almost constant for all the galaxies of this sample. In this study we also emphasize the presence of a break in the NIR Tully-Fisher relation at M(H,K) similar to -20 and we confirm that late-type galaxies present higher total-to-baryonic mass ratios than early-type spirals, suggesting that supernova feedback is actually an important issue in late-type spirals. Due to the well-defined sample selection criteria and the homogeneity of the data analysis, the Tully-Fisher relation for GHASP galaxies can be used as a reference for the study of this relation in other environments and at higher redshifts.