Equation of Motion Governing the Dynamics of Vertically Collapsing Buildings

The present paper aims at contributing to a discussion, opened by several authors, on the proper equation of motion that governs the vertical collapse of buildings. The most striking and tragic example is that of the World Trade Center Twin Towers, in New York City, about 10 years ago. This is a very complex problem and, besides dynamics, the analysis involves several areas of knowledge in mechanics, such as structural engineering, materials sciences, and thermodynamics, among others. Therefore, the goal of this work is far from claiming to deal with the problem in its completeness, leaving aside discussions about the modeling of the resistive load to collapse, for example. However, the following analysis, restricted to the study of motion, shows that the problem in question holds great similarity to the classic falling-chain problem, very much addressed in a number of different versions as the pioneering one, by von Buquoy or the one by Cayley. Following previous works, a simple single-degree-of-freedom model was readdressed and conceptually discussed. The form of Lagrange's equation, which leads to a proper equation of motion for the collapsing building, is a general and extended dissipative form, which is proper for systems with mass varying explicitly with position. The additional dissipative generalized force term, which was present in the extended form of the Lagrange equation, was shown to be derivable from a Rayleigh-like energy function. DOI: 10.1061/(ASCE)EM.1943-7889.0000453. (C) 2012 American Society of Civil Engineers.

The complexity of motion in the Aristotelian Physics

The intention of this paper is to present some Aristotelian arguments regarding the motion on local terrestrial region. Because it is a highly sophisticated and complex explanation dealt with, briefly, the principles and causes that based theoretic sciences in general and in particular physics. Subdivided into eight topics this article in order to facilitate the understanding of these concepts for the reader not familiar with the Aristotelian texts. With intent to avoid an innocent view, anachronistic and linear the citations are of primary sources or commentators of Aristotle's works.

Drag force in a strongly coupled anisotropic plasma

We calculate the drag force experienced by an in finitely massive quark propagating at constant velocity through an anisotropic, strongly coupled N = 4 plasma by means of its gravity dual. We find that the gluon cloud trailing behind the quark is generally misaligned with the quark velocity, and that the latter is also misaligned with the force. The drag coefficient mu can be larger or smaller than the corresponding isotropic value depending on the velocity and the direction of motion. In the ultra-relativistic limit we find that generically mu proportional to p. We discuss the conditions under which this behaviour may extend to more general situations.

Jet quenching in a strongly coupled anisotropic plasma

The jet quenching parameter of an anisotropic plasma depends on the relative orientation between the anisotropic direction, the direction of motion of the parton, and the direction along which the momentum broadening is measured. We calculate the jet quenching parameter of an anisotropic, strongly coupled N = 4 plasma by means of its gravity dual. We present the results for arbitrary orientations and arbitrary values of the anisotropy. The anisotropic value can be larger or smaller than the isotropic one, and this depends on whether the comparison is made at equal temperatures or at equal entropy densities. We compare our results to analogous calculations for the real-world quark-gluon plasma and find agreement in some cases and disagreement in others.

Characterisation of young stellar clusters

Aims. Several embedded clusters are found in the Galaxy. Depending on the formation scenario, most of them can evolve to unbounded groups that are dissolved within 10 Myr to 20 Myr. A systematic study of young stellar clusters that show distinct characteristics provides interesting information on the evolutionary phases during the pre-main sequence. To identify and to understand these phases we performed a comparative study of 21 young stellar clusters. Methods. Near-infrared data from 2MASS were used to determine the structural and fundamental parameters based on surface stellar density maps, radial density profile, and colour-magnitude diagrams. The cluster members were selected according to their membership probability, which is based on the statistical comparison with the cluster proper motion. Additional members were selected on the basis of a decontamination procedure that was adopted to distinguish field stars found in the direction of the cluster area. Results. We obtained age and mass distributions by comparing pre-main sequence models with the position of cluster members in the colour-magnitude diagram. The mean age of our sample is similar to 5 Myr, where 57% of the objects is found in the 4-10 Myr range of age, while 43% is <4 Myr old. Their low E(B - V) indicate that the members are not suffering high extinction (AV <1 mag), which means they are more likely young stellar groups than embedded clusters. Relations between structural and fundamental parameters were used to verify differences and similarities that could be found among the clusters. The parameters of most of the objects show the same trends or correlations. Comparisons with other young clusters show similar relations among mass, radius, and density. Our sample tends to have larger radius and lower volumetric density than embedded clusters. These differences are compatible with the mean age of our sample, which we consider intermediate between the embedded and the exposed phases of the stellar clusters evolution.