Improved convergence towards generalized Euler-Mascheroni constant

We propose new simple sequences approximating the Euler-Mascheroni constant and its generalization, which converge faster towards their limits than those considered by DeTemple [D.W. DeTemple, A quicker convergence to Euler’s constant, Am. Math. Monthly 100 (5) (1998) 468-470], Sînt?m?rian [A. Sînt?m?rian, A generalization of Euler’s constant, Numer. Algorithms 46 (2) (2007) 141-151] and Vernescu [A. Vernescu, A new accelerate convergence to the constant of Euler, Gazeta Matem., Ser. A, Bucharest XVII(XCVI) (4) (1999) 273-278].     

High Péclet number heat exchange between cocurrent streams

Summary  This paper concentrates on the analysis of the heat transfer between two cocurrent laminar flows in parallel channels. For high values of the Péclet number Pe, a boundary layer arises near the wall separating the streams. Matched asymptotic expansions (MAE) are used to obtain approximate solutions. We consider arbitrary inlet temperatures and derive higher-order corrections of the boundary problem. The separating wall is supposed to be sufficiently thin to neglect the heat conduction in it. Analyticity and adiabatic conditions at the outer walls impose restrictions on the inlet temperatures. It turns out, however, that only the inlet temperatures at the wall separating the two fluids enter the leading-order problem. The Nusselt numbers thus calculated are in the leading order proportional to (Pe/x)^1/3, where x is the stream-wise coordinate. An estimate of the thickness of the separating wall to validate the MAE approach is obtained. It is also demonstrated that the MAE analysis is unable to describe the heat exchange of counterflowing fluids. Received 9 June 1999; accepted for publication 17 November 1999     

Mn-based antiperovskite functional materials： Review of research

Our recent research on the Mn-based antiperovskite functional materials AXMn 3(A:metal or semiconducting elements;X:C or N) is outlined.Antiperovskite carbides(e.g.,AlCMn 3) show large magnetocaloric effect comparable to those of typical magnetic refrigerant materials.Enhanced giant magnetoresistance up to 70% at 50 kOe(1 Oe = 79.5775 A.m-1) over a wide temperature span was obtained in Ga1-xZnxCMn3 and GaCMn3-xNix.In Cu0.3Sn0.5NMn3.2,negative thermal expansion(NTE) was achieved in a wide temperature region covering room temperature(α =-6.8 ppm/K,150 K-400 K).Neutron pair distribution function analysis suggests the Cu/Sn-Mn bond fluctuation is the driving force for the NTE in Cu1-xSnxNMn3.In CuN1-xCx Mn3 and CuNMn3-yCoy,the temperature coefficient of resistivity(TCR) decreases monotonically from positive to negative as Co or C content increases.TCR is extremely low when the composition approaches the critical points.For example,TCR is ～ 1.29 ppm/K between 240K and 320K in CuN0.95C0.05Mn3,which is one twentieth of that in the typical low-TCR materials(～ 25 ppm/K).By studying the critical scaling behavior and X deficiency effect,some clues of localized-electron magnetism have been found against the background of electronic itinerant magnetism.     

Interactions Between Solitons and Cnoidal Periodic Waves of the(2+1)-Dimensional Konopelchenko–Dubrovsky Equation

The(2+1)-dimensional Konopelchenko–Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the(2+1)-dimensional Konopelchenko–Dubrovsky equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this paper, with the help of the Riccati equation, the(2+1)-dimensional Konopelchenko–Dubrovsky equation is solved by the consistent Riccati expansion(CRE). Furthermore, we obtain the soliton-cnoidal wave interaction solution of the(2+1)-dimensional Konopelchenko–Dubrovsky equation.     

Chemical expansion of solid oxide fuel cell materials: A brief overview

The importance of oxygen non-stoichiometry induced expansion, known as chemical expansion, for the mechanical properties of solid oxide fuel cells （SOFCs） is discussed. The methods used to measure chemical expansion and the defects responsible for its existence are introduced. Recent work demonstrating the origin of chemical expansion in fluorite structured oxides for SOFCs is presented. Models used to predict stress induced by chemical expansion in SOFCs, highlighting the necessity of considering electro-chemo-mechanical coupling relationships, are discussed.     

Deep punching PMMA

The authors performed deep punching experiments on PMMA (polymethyl methacrylate) using cylindrical-shaped punches with conical and hemispherical noses. The test samples cracked when no lateral confinement was provided. Application of proper lateral confinement suppressed the cracks. The punching force recorded from the experiments correlates very well with cavity expansion theory. Because the use of a single friction coefficient gives excellent agreement between theory and experiments for two different-shaped punches, the authors propose deep punching as a new technique to measure the friction coefficient.     

Applications of Floquet–Magnus expansion,average Hamiltonian theory and Fer expansion to study interactions in solid state NMR when irradiated with the magic-echo sequence

This work presents the possibility of applying the Floquet–Magnus expansion and the Fer expansion approaches to the most useful interactions known in solid-state nuclear magnetic resonance using the magic-echo scheme. The results of the effective Hamiltonians of these theories and average Hamiltonian theory are presented.     

Asymptotic profiles for the third grade fluids equations

We study the long time behaviour of the solutions of the third grade fluids equations in dimension 2. Introducing scaled variables and performing several energy estimates in weighted Sobolev spaces, we describe the first order of an asymptotic expansion of these solutions. It shows in particular that, under smallness assumptions on the data, the solutions of the third grade fluids equations converge to self-similar solutions of the heat equations, which can be computed explicitly from the data.     

Conformations and Structures of Ethoxycarbonyl Isothiocyanate Revealed by Rotational Spectroscopy

The ethoxycarbonyl isothiocyanate has been investigated by using supersonic jet Fourier transform microwave spectroscopy. Two sets of rotational spectra belonging to conformers TCC (with the backbone of C\begin{document}$ - $\end{document}C\begin{document}$ - $\end{document}O\begin{document}$ - $\end{document}C, C\begin{document}$ - $\end{document}O\begin{document}$ - $\end{document}C=O, and O\begin{document}$ - $\end{document}C(=O)\begin{document}$ - $\end{document}NCS being trans, cis, and cis arranged, respectively) and GCC (\begin{document}$ gauche $\end{document}, cis, and cis arrangement of the C\begin{document}$ - $\end{document}C\begin{document}$ - $\end{document}O\begin{document}$ - $\end{document}C, C\begin{document}$ - $\end{document}O\begin{document}$ - $\end{document}C=O, and O\begin{document}$ - $\end{document}C(=O)\begin{document}$ - $\end{document}NCS) have been measured and assigned. The measurements of \begin{document}$ ^{13} $\end{document}C, \begin{document}$ ^{15} $\end{document}N and \begin{document}$ ^{34} $\end{document}S mono-substituted species of the two conformers have also been performed. The comprehensive rotational spectroscopic investigations provide accurate values of rotational constants and \begin{document}$ ^{14} $\end{document}N quadrupole coupling constants, which lead to structural determinations of the two conformers of ethoxycarbonyl isothiocyanate. For conformer TCC, the values of \begin{document}$ P_{ \rm{cc}} $\end{document} keep constant upon isotopic substitution, indicating that the heavy atoms of TCC are effectively located in the \begin{document}$ ab $\end{document} plane.