Periodic solutions for certain non-smooth oscillators by iterated homotopy perturbation method combined with modified Lindstedt-Poincaré technique

In this paper, a new technique is introduced by combining Homotopy perturbation method and modified Lindstedt-Poincaré technique to obtain the periodic solutions of certain non-smooth oscillators. In this technique, homotopy perturbation method is re-written in iterative form to linearize perturbation process by homotopy, and then, the modified Lindstedt-Poincaré method is utilized to obtain next approximation for each iteration step. We realize that this new technique works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been confirmed and discussed. Only one or two iterations lead to high accuracy of the solutions. The result obtained and comparison with analytical solution and different methods provide confirmation for the validity of the technique.     

Thermal analysis of two series <Emphasis Type="Italic">mono</Emphasis>- and <Emphasis Type="Italic">di</Emphasis>-azocalix[4]arene derivatives

In the present study, thermal decomposition of mono- and di-azocalix[4]arene derivatives (A1–A8 and B1–B8) was investigated by means of thermogravimetry (TG), differential thermal analysis (DTA) and derivative thermogravimetry (DTG). The exclusion of methanol, hydrolysis of benzoyl ester and methyl ketone groups in lower rim, and decomposition of azo groups in upper rim have occurred during thermal analysis, consecutively. The thermal decomposition degrees amount of volatile pyrolysis products were determined in air atmosphere using TG, DTA and DTG curves. In conclusion, the thermal analyses of azocalix[4]arenes demonstrated that its stability depends on the substituted groups and their positions in the calix[4]arene structure.     

Synthesis,Crystal Structure and Thermal Properties of <Emphasis Type="Italic">N</Emphasis>-Acetyl-3-(2-furyl)-5-ferrocenyl-2-pyrazoline and <Emphasis Type="Italic">N</Emphasis>-Acetyl-3-(2-thienyl)-5-ferrocenyl-2-pyrazoline

Abstract  

Two novel ferrocenyl substituted N-acetyl-2-pyrazolines, N-acetyl-3-(2-furyl)-5-ferrocenyl-2-pyrazoline (3) and N-acetyl-3-(2-thienyl)-5-ferrocenyl-2-pyrazoline (4), have been synthesized and characterized by FTIR, ¹H-NMR, ¹³C-NMR techniques, elemental analysis and X-ray structure analysis. Thermal properties of these compounds have been determined by TGA, DTA and DSC analysis. Compound 3 (C₁₉H₁₈N₂O₂Fe) crystallizes in the monoclinic space group P21/c and Z = 4, with a = 8.6970(4) ?, b = 18.4725(9) ?, c = 11.0041(5) ?, β = 110.942(3)°. Compound 4 (C₁₉H₁₈N₂OSFe) crystallizes in the orthorhombic space group Fdd2 and Z = 16, with a = 84.242(2) ?, b = 13.5416(5) ?, c = 5.9405(2) ?, β = 90°. In terms of crystal packing, each compound shows different molecular arrangement, which are stabilized by C–H···O intermolecular weak hydrogen bonds, and/or C–H···π interactions.     

On conformable double Laplace transform

In this study authors introduce the conformable double Laplace transform which can be used to solve fractional partial differential equations that represents many physical and engineering models. In these models the derivatives and integrals are in the sense of newly defined conformable type. Then some properties of conformable double Laplace transform are expressed. Finally fractional heat equation and fractional telegraph equation which is used in various applications in science and engineering investigated as an application of this new transform.     

Plasma Streamwise Vortex Generators for Flow Separation Control on Trucks

An experimental study of the effect of Dielectric Barrier Discharge plasma actuators on the flow separation on the A-pillar of a modern truck under cross-wind conditions has been carried out. The experiments were done in a wind tunnel with a 1:6 scale model of a tractor-trailer combination. The actuators were used as vortex generators positioned on the A-pillar on the leeward side of the tractor and the drag force was measured with a wind-tunnel balance. The results show that the effect at the largest yaw angle (9 degrees) can give a drag reduction of about 20% and that it results in a net power reduction. At lower yaw angles the reduction was smaller. The present results were obtained at a lower Reynolds number and a lower speed than for real driving conditions so it is still not yet confirmed if a similar positive result can be obtained in full scale.     

Analytical solutions in a cosmic string Born–Infeld-dilaton black hole geometry: quasinormal modes and quantization

Chargeless massive scalar fields are studied in the spacetime of Born–Infeld dilaton black holes (BIDBHs). We first separate the massive covariant Klein–Gordon equation into radial and angular parts and obtain the exact solution of the radial equation in terms of the confluent Heun functions. Using the obtained radial solution, we show how one gets the exact quasinormal modes for some particular cases. We also solve the Klein–Gordon equation solution in the spacetime of a BIDBHs with a cosmic string in which we point out the effect of the conical deficit on the BIDBHs. The analytical solutions of the radial and angular parts are obtained in terms of the confluent Heun functions. Finally, we study the quantization of the BIDBH. While doing this, we also discuss the Hawking radiation in terms of the effective temperature.     

A new constitutive analysis of hexagonal close-packed metal in equal channel angular pressing by crystal plasticity finite element method

Most of hexagonal close-packed (HCP) metals are lightweight metals. With the increasing application of light metal products, the production of light metal is increasingly attracting the attentions of researchers worldwide. To obtain a better understanding of the deformation mechanism of HCP metals (especially for Mg and its alloys), a new constitutive analysis was carried out based on previous research. In this study, combining the theories of strain gradient and continuum mechanics, the equal channel angular pressing process is analyzed and a HCP crystal plasticity constitutive model is developed especially for Mg and its alloys. The influence of elevated temperature on the deformation mechanism of the Mg alloy (slip and twin) is novelly introduced into a crystal plasticity constitutive model. The solution for the new developed constitutive model is established on the basis of the Lagrangian iterations and Newton Raphson simplification.     

Simulation of a Large-Eddy-Break-up Device (LEBU) in a Moderate Reynolds Number Turbulent Boundary Layer

A well-resolved large eddy simulation (LES) of a large-eddy break-up (LEBU) device in a spatially evolving turbulent boundary layer is performed with, Reynolds number, based on free-stream velocity and momentum-loss thickness, of R e _θ ≈ 4300. The implementation of the LEBU is via an immersed boundary method. The LEBU is positioned at a wall-normal distance of 0.8 δ (δ denoting the local boundary layer thickness at the location of the LEBU) from the wall. The LEBU acts to delay the growth of the turbulent boundary layer and produces global skin friction reduction beyond 180δ downstream of the LEBU, with a peak local skin friction reduction of approximately 12 %. However, no net drag reduction is found when accounting for the device drag of the LEBU in accordance with the towing tank experiments by Sahlin et al. (Phys. Fluids 31, 2814, 1988). Further investigation is performed on the interactions of high and low momentum bulges with the LEBU and the corresponding output is analysed, showing a ‘break-up’ of these large momentum bulges downstream of the LEBU. In addition, results from the spanwise energy spectra show consistent reduction in energy at spanwise length scales for \(\lambda _{z}^{+} > 1000\) independent of streamwise and wall-normal location when compared to the corresponding turbulent boundary layer without LEBU.     

Crystal and Molecular Structure of 3,5-Diphenyl-4,5-dihydro-2-phenylcarboxamide-1H-pyrazole

Crystal structure of the title compound C₂₂H₁₉N₃O is determined by single crystal X-ray diffraction (sp. gr. P2₁/c, Z = 4). The molecule as a whole, is not planar: phenyl cycles are rotated relative to the plane of pyrazole ring. N?H···N intramolecular hydrogen bond forms five-membered ring fused to pyrazole ring. There are also intramolecular C?H···O and C?H···π interactions. Intermolecular C?H···O hydrogen bond links the molecules into a C(7) chain along the a axis. The crystal structure is stabilized also by C–H···π and π···π intermolecular hydrogen bonds.     

Metal Complexation Properties of Schiff Bases Containing 1,3,5-Triazine Derived from 2-Hydroxy-1-Naphthaldehyde in Solution. A Simple Spectrofluorimetric Method to Determine Mercury (II)

Four new Schiff base ligands carrying naphthalene groups were prepared from the reaction of 2,4-diamino-6-methyl-1,3,5-triazine and 2,4-diamino-6-undecyl-1,3,5-triazine with 2-hydroxy-1-naphthaldehyde. The influence of a series of metal ions including Cu²⁺, Co²⁺, Hg²⁺, Al³⁺, Cr³⁺, Fe³⁺, Pb²⁺, Ni²⁺, Cd²⁺, Zn²⁺, Mn²⁺, Ag⁺, Ba²⁺, Ca²⁺ and Mg²⁺ on the spectroscopic properties of the ligands was investigated by means of absorption and emission spectrometry. The results of spectrophotometric and spectrofluorimetric titrations disclosed the complexation stoichiometry and complex stability constant of the ligands with metal ions. A simple spectrofluorimetric method was developed using the Schiff base derived from 2,4-diamino-6-undecyl-1,3,5-triazine to determine Hg²⁺ ion. No cleanup or enrichment of the tap water sample was required. A modified standard addition method was used to eliminate matrix effect. The standard addition graph was linear between 0.2 and 2.6 mg/L in determination of Hg²⁺. Detection and quantification limits were 0.08 and 0.23 mg/L, respectively. The simple and cost-effective method can be applied to water samples.