A spectral element method using the modal basis and its application in solving second‐order nonlinear partial differential equations

We present a high‐order spectral element method (SEM) using modal (or hierarchical) basis for modeling of some nonlinear second‐order partial differential equations in two‐dimensional spatial space. The discretization is based on the conforming spectral element technique in space and the semi‐implicit or the explicit finite difference formula in time. Unlike the nodal SEM, which is based on the Lagrange polynomials associated with the Gauss–Lobatto–Legendre or Chebyshev quadrature nodes, the Lobatto polynomials are used in this paper as modal basis. Using modal bases due to their orthogonal properties enables us to exactly obtain the elemental matrices provided that the element‐wise mapping has the constant Jacobian. The difficulty of implementation of modal approximations for nonlinear problems is treated in this paper by expanding the nonlinear terms in the weak form of differential equations in terms of the Lobatto polynomials on each element using the fast Fourier transform (FFT). Utilization of the Fourier interpolation on equidistant points in the FFT algorithm and the enough polynomial order of approximation of the nonlinear terms can lead to minimize the aliasing error. Also, this approach leads to finding numerical solution of a nonlinear differential equation through solving a system of linear algebraic equations. Numerical results for some famous nonlinear equations illustrate efficiency, stability and convergence properties of the approximation scheme, which is exponential in space and up to third‐order in time. Copyright © 2014 John Wiley & Sons, Ltd.     

Bis(methyltri‐o‐tolylphosphonium) octaiodide

In the crystal structure of the title compound, 2C₂₂H₂₄P⁺·I₈²⁻, the I₈²⁻ anion is located on a crystallographic inversion centre and consists of two tri‐iodide anions linked by di‐iodine at angles of 89.92 (4)° to form a planar `Z'‐shaped dianion. The octaiodides are linked via long‐range interactions [3.877 (11) Å] into infinite polyiodide ribbons. This is the first example of a structure containing an [(o‐tolyl)₃PMe]⁺ cation, and the C_Me—P—C—C_Me torsion angles of −54.0 (11), −51.3 (11) and −48.2 (11)° indicate that the configuration is exo₃.     

Hybrid finite element method applied to supersonic flutter of an empty or partially liquid-filled truncated conical shell

In this study, aeroelastic analysis of a truncated conical shell subjected to the external supersonic airflow is carried out. The structural model is based on a combination of linear Sanders thin shell theory and the classic finite element method. Linearized first-order potential (piston) theory with the curvature correction term is coupled with the structural model to account for pressure loading. The influence of stress stiffening due to internal or external pressure and axial compression is also taken into account. The fluid-filled effect is considered as a velocity potential variable at each node of the shell elements at the fluid-structure interface in terms of nodal elastic displacements. Aeroelastic equations using the hybrid finite element formulation are derived and solved numerically. The results are validated using numerical and theoretical data available in the literature. The analysis is accomplished for conical shells of different boundary conditions and cone angles. In all cases the conical shell loses its stability through coupled-mode flutter. This proposed hybrid finite element method can be used efficiently for design and analysis of conical shells employed in high speed aircraft structures.     

Classification of Plane Symmetric Static Space-Times According to Their Noether Symmetries

In this paper we give a classification of plane symmetric static space-times using symmetry method. For this purpose we consider the Lagrangian corresponding to the general plane symmetric static metric in the Noether symmetry equation. This provides a system of determining equations. Solutions of this system give us classification of the plane symmetric static space-times according to their Noether symmetries. During this classification we recover all the results listed in Feroze et al. (J. Math. Phys. 42:4947, 2001) and Bashir and Ehsan (Il Nuovo Cimento B 123:1, 2008).     

Ultrasound assisted the chemoselective 1,1-diacetate protection and deprotection of aldehydes catalyzed by poly(4-vinylpyridinium)hydrogen sulfate salt as a eco-benign,efficient and reusable solid acid catalyst

Poly(4-vinylpyridinium) hydrogen sulfate solid acid was found to be efficient catalyst for preparation of 1,1-diacetate using ultrasound irradiation at ambient temperature and neat condition. Deprotection of the resulting 1,1-diacetates were achieved using the same catalyst in methanol solvent under ultrasound irradiation at room temperature. This new method consistently has the advantage of excellent yields and short reaction times. Utilization of solvent free, simple reaction conditions, isolation, and purification makes this manipulation very interesting from an economic and environmental perspective. Further, the catalyst can be reused and recovered for several times.     

Application of copper oxide–thermal oil (CuO-HTO) nanofluid on convective heat transfer enhancement in inclined circular tube

Journal of Thermal Analysis and Calorimetry - The influence of using copper oxide–thermal oil on convective heat transfer and pressure drop in an upward flow in an inclined smooth tube is...     

Optimization and sensitivity analysis of magneto-hydrodynamic natural convection nanofluid flow inside a square enclosure using response surface methodology

This article studies buoyancy-driven natural convection of a nanofluid affected by a magnetic field within a square enclosure with an individual conductive pin fin. The effects of electromagnetic forces, thermal conductivity, and inclination angle of pin fin were investigated using non-dimensional parameters. An extensive sensitivity analysis was conducted seeking an optimal heat transfer setting. The novelty of this work lies in including different contributing factors in heat transfer analysis, rigorous analysis of design parameters, and comprehensive mathematical analysis of solution domain for optimization. Results showed that magnetic strength diminished the heat transfer efficacy, while higher relative thermal conductivity of pin fin improved it. Based on the problem settings, we also obtained the relative conductivity value in which the heat transfer is optimal. Higher sensitivity of heat transfer was, though, noticed for both magnetic strength and fin thermal conductivity in comparison to fin inclination angle. Further studies, specifically with realistic geometrical configurations and heat transfer settings, are urged to translate current findings to industrial applications.

     

Di- and Tetracyano-Substituted Pyrene-Fused Pyrazaacenes: Aggregation in the Solid State

Five di- and tetracyano-substituted pyrene-fused pyrazaacenes were synthesized and studied as potential electron acceptors in the solid state. Single crystals of all compounds were grown and the crystal packing studied by DFT calculations (transfer integrals and reorganization energies) to get insight into possible use for semiconducting charge transport.     

Nonlinear vibration of the spiral bevel gear with a novel tooth surface modification method

Meccanica - The issue of gear noise is fairly common in power transmission systems. This noise largely stems from the gear pairs vibration triggered by transmission error excitation. This is mainly...