Statistically disordered short hydrogen bonds in (pipzH2)(cdoH)2 and a comparison with (pipzH2)(cdo)·H2O (pipz is piperazine and cdoH2 is chelidonic acid)

Two related proton‐transfer compounds, namely piperazine‐1,4‐diium 4‐oxo‐4H‐pyran‐2,6‐dicarboxylate monohydrate, C₄H₁₂N₂²⁺·C₇H₂O₆²⁻·H₂O or (pipzH₂)(cdo)·H₂O, (I), and piperazine‐1,4‐diium bis(6‐carboxy‐4‐oxo‐4H‐pyran‐2‐carboxylate), C₄H₁₂N₂²⁺·2C₇H₃O₆⁻ or (pipzH₂)(cdoH)₂, (II), were obtained by the reaction of 4‐oxo‐4H‐pyran‐2,6‐dicarboxylic acid (chelidonic acid, cdoH₂) and piperazine (pipz). In (I), both carboxyl H atoms of chelidonic acid have been transferred to piperazine to form the piperazine‐1,4‐diium ion. The structure is a monohydrate. All potential N—H donors are involved in N—H...O hydrogen bonds. The water molecule spans two anions via the 4‐oxo group of the pyranose ring and a carboxylate O atom. The hydrogen‐bonding motif is essentially two‐dimensional. The structure is a pseudomerohedral twin. In the asymmetric unit of (II), the anion consists of monodeprotonated chelidonic acid, while the piperazine‐1,4‐diium cation is located on an inversion centre. The single carboxyl H atom is disordered in two respects. Firstly, the disordered H atom is shared equally by both carboxylic acid groups. Secondly, the H atom is statistically disordered between two positions on either side of a centre of symmetry and is engaged in a very short hydrogen‐bonding interaction; the relevant O...O distances are 2.4549 (11) and 2.4395 (11) Å, and the O—H...O angles are 177 (6) and 177 (5)°, respectively. Further hydrogen bonding of the type N—H...O places the (pipzH₂)²⁺ cations in pockets formed by the chains of (cdoH)⁻ anions. In contrast with (I), the (pipzH₂)²⁺ cations form hydrogen‐bonding arrays that are perpendicular to the anions, yielding a three‐dimensional hydrogen‐bonding motif. The structures of both (I) and (II) also feature π–π stacking interactions between aromatic rings.     

Mode III fracture of an arbitrary oriented crack in two dimensional functionally graded material

In this paper, a two dimensional functionally graded material (2D-FGM) under an anti-plane load with an internal crack is considered. The crack is oriented in an arbitrary direction. The material properties are assumed to vary exponentially in two planar directions. The problem is analyzed and solved by two different methods namely Fourier integral transforms with singular integral equation technique, and then by the finite element method. The effects of crack orientation, material non-homogeneity, and other parameters on the value of stress intensity factor (SIF) are studied. Finally, the obtained results for Mode III stress intensity factor of different methods are compared.     

Adaptive finite-time stabilization of uncertain non-autonomous chaotic electromechanical gyrostat systems with unknown parameters

This paper deals with the problem of robust finite-time stabilization of non-autonomous chaotic gyrostat systems. It is assumed that the parameters of the gyrostat system are completely unknown in advance and the system is perturbed by unknown uncertainties and disturbances. Some update laws are proposed to estimate the unknown parameters. Based on the finite-time control idea and the update laws, appropriate control laws are designed to ensure the stabilization of the closed-loop system in a finite time. The finite-time stability and convergence of the closed-loop system are analytically proved. A numerical simulation is given to demonstrate the applicability and robustness of the proposed finite-time controller and to verify the theoretical results.     

Eulerian-Eulerian two-phase numerical simulation of nanofluid laminar forced convection in a microchannel

In this paper, laminar forced convection heat transfer of a copper-water nanofluid inside an isothermally heated microchannel is studied numerically. An Eulerian two-fluid model is considered to simulate the nanofluid flow inside the microchannel and the governing mass, momentum and energy equations for both phases are solved using the finite volume method. For the first time, the detailed study of the relative velocity and temperature of the phases are presented and it has been observed that the relative velocity and temperature between the phases is very small and negligible and the nanoparticle concentration distribution is uniform. However, the two-phase modeling results show higher heat transfer enhancement in comparison to the homogeneous single-phase model. Also, the heat transfer enhancement increases with increase in Reynolds number and nanoparticle volume concentration as well as with decrease in the nanoparticle diameter, while the pressure drop increases only slightly.     

Turbulent forced convection heat transfer of non-Newtonian nanofluids

Forced convection heat transfer of non-Newtonian nanofluids in a circular tube with constant wall temperature under turbulent flow conditions was investigated experimentally. Three types of nanofluids were prepared by dispersing homogeneously γ-Al₂O₃, TiO₂ and CuO nanoparticles into the base fluid. An aqueous solution of carboxymethyl cellulose (CMC) was used as the base fluid. Nanofluids as well as the base fluid show shear-thinning (pseudoplastic) rheological behavior. Results indicate that the convective heat transfer coefficient of nanofluids is higher than that of the base fluid. The enhancement of the convective heat transfer coefficient increases with an increase in the Peclet number and the nanoparticle concentration. The increase in the convective heat transfer coefficient of nanofluids is greater than the increase that would be observed considering strictly the increase in the effective thermal conductivity of nanofluids. Experimental data were compared to heat transfer coefficients predicted using available correlations for purely viscous non-Newtonian fluids. Results show poor agreement between experimental and predicted values. New correlation was proposed to predict successfully Nusselt numbers of non-Newtonian nanofluids as a function of Reynolds and Prandtl numbers.     

Non-fourier temperature field in a solid homogeneous finite hollow cylinder

Analytical solution of the non-Fourier Axisymmetric temperature field within a finite hollow cylinder is investigated considering the Cattaneo-Vernotte constitutive heat flux relation. The solution is found for the most general linear time-independent boundary conditions. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The standard method of separation of variables is used. The present solution can be reduced to special problems of interest by choosing appropriate boundary condition parameters. The solution is applied for two special cases including constant heat flux and the Gaussian distribution heating of a cylinder, and their respective non-Fourier thermal behavior is studied.     

Experimental analysis on vortex tube energy separation performance

The present study reports the effect of several operating parameters on the thermal performance of the vortex tube. The experimental results indicate that the inlet pressure and the cold fraction are the most significant parameters influencing the vortex tube performance. The experimental data point out that insulation has minimal effect on the vortex tube performance. The same inlet pressure tests show that energy separation increases as number of inlet nozzle increases.     

Accurate and approximate integrations of Drucker–Prager plasticity with linear isotropic and kinematic hardening

Up to now, some explicit approximate integration schemes based on exponential maps, for non-hardening material obeying Drucker–Prager’s criterion, have been presented. Two new exponential-based approximate formulations, for associative Drucker–Prager plasticity are developed in this article. Both are consistent and explicit algorithms. The linear isotropic and Prager’s kinematic hardening behavior are assumed. Furthermore, an accurate solution for the constitutive equations is derived. The accuracies of the suggested approximate algorithms are assessed by creating related iso-error maps. In addition, by using piecewise strain load histories, and calculating computation times, the robustness and efficiency of the formulations are demonstrated.     

Criteria for the solubility of finite groups by their centralizers

For any group G, let C(G){\mathcal{C}(G)} denote the set of centralizers of G. We say that a group G has n centralizers (G is a C_n{\mathcal{C}_n}-group) if |C(G)| = n{|\mathcal{C}(G)| = n}. In this note, we show that the derived length of a soluble C_n{\mathcal{C}_n}-group (not necessarily finite) is bounded by a function of n.     

A note on quasi-permutation representations of groups with two character degrees

In Behravesh (J. Lond. Math. Soc. (2) 55:251–260, 1997), we gave algorithms to calculate c(G), q(G) and p(G) for a finite group G. In this paper we will show that in groups with two character degrees we may have c(G)=q(G)≠p(G).