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.

Additional scaled solutions to Richards' equation for infiltration and drainage

Warrick and Hussen developed in the nineties of the last century a method to scale Richards' equation (RE) for similar soils. In this paper, new scaled solutions are added to the method of Warrick and Hussen considering a wider range of soils regardless of their dissimilarity. Gardner-Kozeny hydraulic functions are adopted instead of Brooks-Corey functions used originally by Warrick and Hussen. These functions allow to reduce the dependence of the scaled RE on the soil properties. To evaluate the proposed method (PM), the scaled RE was solved numerically using a finite difference method with a fully implicit scheme. Three cases were considered: constant-head infiltration, constant-flux infiltration, and drainage of an initially uniform wet soil. The results for five texturally different soils ranging from sand to clay (adopted from the literature) showed that the scaled solutions were invariant to a satisfactory degree. However, slight deviations were observed mainly for the sandy soil. Moreover, the scaled solutions deviated when the soil profile was initially wet in the infiltration case or when deeply wet in the drainage condition. Based on the PM, a Philip-type model was also developed to approximate RE solutions for the constant-head infiltration. The model showed a good agreement with the scaled RE for the same range of soils and conditions, however only for Gardner-Kozeny soils. Such a procedure reduces numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils. (C) 2011 Elsevier B.V. All rights reserved.

Consistency of the mass variation formula for black holes accreting cosmological fluids

We address the spherical accretion of generic fluids onto black holes. We show that, if the black hole metric satisfies certain conditions, in the presence of a test fluid it is possible to derive a fully relativistic prescription for the black hole mass variation. Although the resulting equation may seem obvious due to a form of it appearing as a step in the derivation of the Schwarzschild metric, this geometrical argument is necessary to fix the added degree of freedom one gets for allowing the mass to vary with time. This result has applications on cosmological accretion models and provides a derivation from first principles to serve as a basis to the accretion equations already in use in the literature.

Determination of degree of ionization of poly(allylamine hydrochloride) (PAH) and poly[1-[4-(3-carboxy‑4 hydroxyphenylazo)benzene sulfonamido]-1,2-ethanediyl, sodium salt] (PAZO) in layer-by-layer films using vacuum photoabsorption spectroscopy

Electrostatic and hydrophobic interactions govern most of the properties of supramolecular systems, which is the reason determining the degree of ionization of macromolecules has become crucial for many applications. In this paper, we show that highresolution ultraviolet spectroscopy (VUV) can be used to determine the degree of ionization and its effect on the electronic excitation energies of layer-by-layer (LbL) films of poly(allylamine hydrochloride) (PAH) and poly[1-[4-(3-carboxy-4 hydroxyphenylazo)- benzene sulfonamido]-1,2-ethanediyl, sodium salt] (PAZO). A full assignment of the VUV peaks of these polyelectrolytes in solution and in cast or LbL films could be made, with their pH dependence allowing us to determine the p'K IND. a' using the Henderson-Hasselbach equation. The p'K IND. a' for PAZO increased from ca. 6 in solution to ca. 7.3 in LbL films owing to the charge transfer from PAH. Significantly, even using solutions at a fixed pH for PAH, the amount adsorbed on the LbL films still varied with the pH of the PAZO solutions due to these molecular-level interactions. Therefore, the procedure based on a comparison of VUV spectra from solutions and films obtained under distinct conditions is useful to determine the degree of dissociation of macromolecules, in addition to permitting interrogation of interface effects in multilayer films.