On the Balance Equation for Stresses Concentrated on Curves

Conditions of equilibrium of forces are formulated for a force system in a continuous body which consists of a bulk stress and a stress concentrated on a curve. The system of forces is interpreted as a tensor valued measure and the equilibrium of forces is interpreted in a weak sense. The divergence theorem is proved for bulk stress fields with the corresponding singularity. Examples of such stress fields are given.      

Converging shock on laser plasma: Density profiles by holographic interferometry

A double pulse ruby laser was used to obtained interference patterns from a laser produced plasma in helium. From patterns obtained at different times the electron density evolution was inferred by Abel inversion, with suitable approximations. There was a net evidence for electron density increase due to the action of a converging shock wave produced by reflection.     

Rotordynamic analysis of systems with a non-linear model of tilting pad bearings including turbulence effects

An analytical model of a tilting pad bearing was developed based on the short bearing assumption with the turbulence effect included. In order to determine its influence on the dynamic behavior of the rotor, this model was compared against one without the turbulence effect through a simulation of a Jeffcott/Laval rotor supported by a couple of bearings. Both models were also used to determine the influence of geometric parameters on tilting pad bearing making use of the aforementioned system at different rotor speeds. When analyzing the results, the parameters which presented the largest influence were: pad preload, number of segments, radial clearance, pad position, and pad pivoting angle. As the pad moment of inertia and the pivoting distance have changed the shaft motion only a few microns, their effects can be neglected. The bearing model with turbulent flow effect has generated higher hydrodynamic forces when compared to the one without this effect, which remarks the importance of considering such phenomenon during the analysis of the high speed hydrodynamic bearings.     

Ear Decompositions of Matching Covered Graphs

G different from and has at least Δ edge-disjoint removable ears, where Δ is the maximum degree of G. This shows that any matching covered graph G has at least Δ! different ear decompositions, and thus is a generalization of the fundamental theorem of Lovász and Plummer establishing the existence of ear decompositions. We also show that every brick G different from and has Δ− 2 edges, each of which is a removable edge in G, that is, an edge whose deletion from G results in a matching covered graph. This generalizes a well-known theorem of Lovász. We also give a simple proof of another theorem due to Lovász which says that every nonbipartite matching covered graph has a canonical ear decomposition, that is, one in which either the third graph in the sequence is an odd-subdivision of or the fourth graph in the sequence is an odd-subdivision of . Our method in fact shows that every nonbipartite matching covered graph has a canonical ear decomposition which is optimal, that is one which has as few double ears as possible. Most of these results appear in the Ph. D. thesis of the first author [1], written under the supervision of the second author. Received: November 3, 1997     

How to use the Sun–Earth Lagrange points for fundamental physics and navigation

We illustrate the proposal, nicknamed LAGRANGE, to use spacecraft, located at the Sun–Earth Lagrange points, as a physical reference frame. Performing time of flight measurements of electromagnetic signals traveling on closed paths between the points, we show that it would be possible: (a) to refine gravitational time delay knowledge due both to the Sun and the Earth; (b) to detect the gravito-magnetic frame dragging of the Sun, so deducing information about the interior of the star; (c) to check the possible existence of a galactic gravitomagnetic field, which would imply a revision of the properties of a dark matter halo; (d) to set up a relativistic positioning and navigation system at the scale of the inner solar system. The paper presents estimated values for the relevant quantities and discusses the feasibility of the project analyzing the behavior of the space devices close to the Lagrange points.     

The minimal section of a triangular masonry dam

Summary A masonry dam with triangular cross section is subjected to its own weight and to hydrostatic pressure in a state of plane strain. Under the constraint that the principal stresses be strictly negative in the interior, it is shown that there is a section of minimal area and, consequently, a dam of lowest weight.

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Sommario Una diga in muratura di sezione triangolare è soggetta al peso proprio e alla spinta idrostatica in condizioni di deformazione piana. Si dimostra che, sotto il vincolo che le tensioni principali siano entrambe negative in tutti i punti interni, esiste una sezione di minima area e, quindi, una diga di minimo peso.

     

Unravelling the detailed microstructure of a semiconducting (quasi‐metal) soluble polymer incorporating conjugated thienylene methine sequences

This article reports a thorough spectroscopic characterization and the complete microstructural unravelling of a novel soluble poly(thienylene methylene) recently obtained by a straightforward process based on the methanesulfonic acid‐catalyzed self‐condensation of 2‐acetoxymethyl‐3,4‐dimethylthiophene. These macromolecules were found to generate both in situ (in the acidic reaction medium) and ex situ (by the addition of appropriate dopants) conjugated sequences consisting of alternating aromatic‐ and quinoid‐like thiophene rings, that is, conjugated thienylene methine sequences. The effect of different types of dopants on the electronic features of these polymers was assessed by the extent of bathochromic shifts they induced in the macromolecule UV–vis spectra. Doped films obtained by solution casting were characterized by dielectric spectroscopy to evaluate their electronic conductivity. The observed low values of conductivity were explained on microscopic basis evidencing the presence of polymer branching. All the structures arising from side reactions responsible for branching were determined by an exhaustive NMR study, which led to the formulation of the corresponding mechanisms. Remarkably, all these polymers, irrespective of their specific structural features and molecular weights, retained complete solubility in common solvents. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011