Euler's Problem Revisited: 222 Years Later

This paper furnishes several closed-form solutions for the buckling eigenvalue problem of the columns with variable flexural rigidity along the axis. The column is either under uniformly distributed axial load or under concentrated compressive load. Sommario. Questo lavoro fornisce diverse soluzioni in forma chiusa per il problema agli autovalori dell'instabilità di colonne con rigidezza flessionale variabile lungo l'asse. La colonna è soggetta ad un carico assiale unifor-memente distribuito oppure ad una forza di compressione concentrata.     

Relaxations in chitin: Evidence for a glass transition

Relaxations in chitin have been investigated in the temperature range 298–523 K using impedance spectroscopy in the frequency range 10⁻¹–10⁸ Hz. The objective was to detect a glass‐transition temperature for this naturally occurring, semicrystalline polysaccharide. The impedance study was complemented with X‐ray diffraction, thermogravimetric, and differential scanning calorimetry measurements. Preliminary impedance data treatment includes the subtraction of the dc conductivity contribution, the exclusion of contact and interfacial polarization effects, and obtaining a condition of minimum moisture content for further analysis. When all these aspects are taken into account, two relaxations are clearly revealed in the impedance data. For the first time, evidence is presented for a relaxation process, which exhibits a non‐Arrhenius temperature dependence, in dry α‐chitin (∼0.1% moisture content), and likely represents the primary α‐relaxation. This evidence suggests a glass transition temperature for chitin of 335 ± 10 K estimated on the basis of the temperature dependence of the conductivity and of the relaxation time. A second relaxation in dry α‐chitin, not previously reported in the literature, is observed from 353 K to the onset of thermal degradation (∼483 K) and is identified as the σ‐relaxation often associated with proton mobility. It exhibits a normal Arrhenius‐type temperature dependence with activation energy of 113 ± 3 kJ/mol. The latter has not been previously reported in the literature. A high frequency secondary β‐relaxation is also observed with Arrhenius activation energy of 45 ± 1 kJ/mol. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 932–943, 2009     

75th anniversary of Vladimir K. Baev

Anniversary Dates

75th anniversary of Vladimir K. Baev     

Tailoring mixed proton-electronic conductivity of BaZrO3 by Y and Pr co-doping for cathode application in protonic SOFCs

BaZr_0.8 − xPr_xY_0.2O_3 − δ (BZPYx, 0.1 ≤ x ≤ 0.4) perovskite oxides were investigated for application as cathode materials for intermediate temperature solid oxide fuel cells based on proton conducting electrolytes (protonic-SOFCs). The BZPYx reactivity with CO₂ and water vapor was evaluated by thermogravimetric and X-ray diffraction analyses, and good chemical stability was observed for each BZPYx composition. Conductivity measurements of BZPYx sintered pellets were performed as a function of temperature and p_O2 in humidified atmospheres, corresponding to cathode operating condition in protonic-SOFCs. Different conductivity values and activation energies were measured depending on the Pr content, suggesting the presence of different charge carriers. For all the compositions, the partial electronic conductivity, calculated from conductivity measurements at different p_O2, increased with increasing the temperature from 500 to 700 °C. Furthermore, the larger the Pr content, the larger the electronic conductivity. BaZr_0.7Pr_0.1Y_0.2O_3 − δ and BaZr_0.4Pr_0.4Y_0.2O_3 − δ showed mostly pure proton and electron conductivity, respectively, whereas the intermediate compositions showed mixed proton/electronic conductivity. Among the two mixed proton/electronic conductors, BaZr_0.6Pr_0.3Y_0.2O_3 − δ presented the larger conductivity, which coupled with its good chemical stability, makes this perovskite oxide a candidate cathode materials for protonic-SOFCs.     

Generalized Hopf Bifurcation for Planar Vector Fields via the Inverse Integrating Factor

In this paper we study the maximum number of limit cycles that can bifurcate from a focus singular point p ₀ of an analytic, autonomous differential system in the real plane under an analytic perturbation. We consider p ₀ being a focus singular point of the following three types: non-degenerate, degenerate without characteristic directions and nilpotent. In a neighborhood of p ₀ the differential system can always be brought, by means of a change to (generalized) polar coordinates (r, θ), to an equation over a cylinder in which the singular point p ₀ corresponds to a limit cycle γ ₀. This equation over the cylinder always has an inverse integrating factor which is smooth and non-flat in r in a neighborhood of γ ₀. We define the notion of vanishing multiplicity of the inverse integrating factor over γ ₀. This vanishing multiplicity determines the maximum number of limit cycles that bifurcate from the singular point p ₀ in the non-degenerate case and a lower bound for the cyclicity otherwise. Moreover, we prove the existence of an inverse integrating factor in a neighborhood of many types of singular points, namely for the three types of focus considered in the previous paragraph and for any isolated singular point with at least one non-zero eigenvalue.     

System Dynamics Modelling for Residential Energy Efficiency Analysis and Management

A System Dynamics model to simulate the substitution of installed household appliances by more efficient ones is presented. The model allows the construction of scenarios and also the analyses of several other issues such as: alternatives for technology penetration, electricity consumption growth, gas consumption growth and effects of pricing policies on various energy demands. The proposed methodology has been applied to assist the decision process in relation to gas penetration policies. The model also supports policy making on energy efficiency and it allows the calculation of total energy savings under different scenarios. Furthermore, government underpricing policies on tariffs and appliance acquisition (longer loan terms, lower interest rates and grace periods) may also be analysed.