Vaporization and caloric studies on sodium niobate

Thermodynamic studies of a polycrystalline sodium niobate (NaNbO₃) under equilibrium conditions by the method of Knudsen effusion mass spectrometry (KEMS) were conducted in the temperature range 1250–1485 K. The vaporization of pure Na₂O(c) was investigated at temperatures of 900–1165 K. Thermodynamic quantities of sublimation enthalpy, activity, and entropy were derived from the partial pressures of gaseous Na, Na₂O, and O₂ over the sodium niobate and pure sodium oxide reference samples. The sublimation enthalpy of Na from NaNbO₃(c) at T=1370 K was ${\mathrm{\Delta }}_{\mathrm{sub}}{H}_{1370K}^0(\mathrm{Na})=465\pm 9\mathrm{kJ}{\mathrm{mol}}^{-1}$. Heat capacity measurements under constant pressure ($C_{\mathrm{p}\left(T\right)}^0$) by Dynamic Scanning Calorimetry (DSC) in the temperature range 298–1450 K resulted in six polynomial equations for each branch of the five transitions. Below the first phase transition at 639 K the $C_{\mathrm{p}\left(T\right)}^0$ values increased from 97 to 123 J mol⁻¹ K⁻¹. Beyond this transition and up to the third one at 792 K, $C_{\mathrm{p}\left(T\right)}^0$ gently inclined from about 120 to a maximum value of 123 J mol⁻¹ K⁻¹. Finally, beyond the fifth transition at 907 K it approximated to an almost constant value of 115 J mol⁻¹ K⁻¹. The enthalpy and the entropy values were calculated from the $C_{p\left(T\right)}^0$ polynomials and from the vaporization studies. The enthalpy of the five transitions in sodium niobate, ${\mathrm{\Delta }}_{\mathrm{trs}}{H}_{298}^0\left({\mathrm{NaNbO}}_3(\mathrm{c})\right)$ were measured by drop calorimetry. Deduced from empirical and experimental approaches, the heat of reaction for oxides was ${\mathrm{\Delta }}_{\mathrm{r}}{H}_{298}^0\left({\mathrm{NaNbO}}_3(\mathrm{c})\right)$=$-94.3\pm 7$ kJ mol⁻¹ and the heat of formation was ${\mathrm{\Delta }}_{\mathrm{f}}{H}_{298}^0\left({\mathrm{NaNbO}}_3\left(\mathrm{c}\right)\right)$=$-1250.8\pm 7$ kJ mol⁻¹. The thermodynamic activity of Na₂O in sodium niobate was temperature dependent, and its values varied from 2.6×10⁻³ to 8.3×10⁻⁴ in the range 1100–1250 K. NaNbO₃(c) has a long-term stability in the temperature range including the transition to cubic phase at 907 K.     

Application of ANN techniques for estimating modal damping of impact-damped flexible beams

A comprehensive laboratory work relating impact damping phenomenon of a flexible beam was carried out by Butt and Akl [Butt AS, Akl FA. Experimental analysis of impact-damped flexible beams. J Eng Mech ASCE 1997;123(4):376–83] to investigate the relation between system’s modal damping ratio $(\zeta )$ and system parameters, namely gap (c, mm), mass (m, kg), modal amplitude $({\Phi }_d)$, frequency (f, Hz), and peak value of the imaginary part of the frequency response functions $(F_I)$. Using a multiple nonlinear regression technique (MNLR), they established a relation between these system parameters and the resulting damping ratio, based on 60 steady-state vibration tests of a flexible beam. In current work, three different artificial neural network approaches (ANNs), namely FFBP (Feed-Forward Back Propagation), RBNN (Radial Basis Function Based Neural Network), and GRNN (Generalized Regression Neural Networks), for estimating modal damping ratio $(\zeta )$ were developed using the data collected by Butt and Akl (1997) and compared with MNLR. The results showed that the RBNN produced slightly better estimations than those of the FFBP and was significantly superior to the MNLR and GRNN.     

The complexity of approximately counting stable roommate assignments

We investigate the complexity of approximately counting stable roommate assignments in two models: (i) the k-attribute model, in which the preference lists are determined by dot products of “preference vectors” with “attribute vectors” and (ii) the k-Euclidean model, in which the preference lists are determined by the closeness of the “positions” of the people to their “preferred positions”. Exactly counting the number of assignments is #P-complete, since Irving and Leather demonstrated #P-completeness for the special case of the stable marriage problem (Irving and Leather, 1986 [11]). We show that counting the number of stable roommate assignments in the k-attribute model (#k-attribute SR, $k?4$) and the 3-Euclidean model (#k-Euclidean SR, $k?3$) is interreducible, in an approximation-preserving sense, with counting independent sets (of all sizes) ($\mathrm{\#}\mathit{IS}$) in a graph, or counting the number of satisfying assignments of a Boolean formula ($\mathrm{\#}\mathit{SAT}$). This means that there can be no FPRAS for any of these problems unless NP = RP. As a consequence, we infer that there is no FPRAS for counting stable roommate assignments ($\mathrm{\#}\mathit{SR}$) unless NP = RP. Utilizing previous results by Chebolu, Goldberg and Martin (2010) [3], we give an approximation-preserving reduction from counting the number of independent sets in a bipartite graph ($\mathrm{\#}\mathit{BIS}$) to counting the number of stable roommate assignments both in the 3-attribute model and in the 2-Euclidean model. $\mathrm{\#}\mathit{BIS}$ is complete with respect to approximation-preserving reductions in the logically-defined complexity class $\mathrm{\#}\mathrm{RH}{\mathrm{\Pi }}_1$. Hence, our result shows that an FPRAS for counting stable roommate assignments in the 3-attribute model would give an FPRAS for all $\mathrm{\#}\mathrm{RH}{\mathrm{\Pi }}_1$. We also show that the 1-attribute stable roommate problem always has either one or two stable roommate assignments, so the number of assignments can be determined exactly in polynomial time.     

Composition-dependent interdiffusivity matrices in face centered cubic Ni–Al–X (X = Rh and W) alloys at 1423, 1473 and 1523 K: A high-throughput experimental measurement

Based on 18 face centered cubic (fcc) single-phase diffusion couples in ternary Ni–Al–X (X = Rh and W) systems together with the recently developed numerical inverse method, high-throughput measurements of the composition-dependent interdiffusivity matrices in fcc Ni–Al–X (X = Rh and W) alloys at 1423, 1473 and 1523 K were performed in the present work. Their reliability was comprehensively validated through comparison between the model-predicted composition/interdiffusion flux profiles for each diffusion couple and the corresponding experimental data. Moreover, the direct comparison with the interdiffusivities evaluated from traditional Matano-Kirkaldy method as well as those from the literature and in the boundary binary systems was also made. The errors for the determined interdiffusivities were evaluated by a scientific method considering the error propagation. The three-dimensional main interdiffusivity planes for fcc Ni–Al–X (X = Rh and W) systems over the investigated concentration ranges at 1423, 1473 and 1523 K were subsequently constructed. It was then found that ${\tilde{D}}_{AlAl}^{Ni}$ is generally larger than ${\tilde{D}}_{R\mathrm{h}Rh}^{Ni}$, while ${\tilde{D}}_{WW}^{Ni}$ is the smallest.