New methods to solve the resonant nonlinear Schrödinger’s equation with time-dependent coefficients

In this study, the generalized \(\tan (\phi /2)\)-expansion method and He’s semi-inverse variational method (HSIVM) are applied to seek the exact solitary wave solutions for the resonant nonlinear Schrödinger equation with time-dependent coefficients. Using these methods, we investigate exact solutions for the nonlinear resonant Schrödinger equation with time-dependent coefficients two forms of nonlinearity, including power and dual-power law nonlinearity. Moreover, many new analytical exact solutions are obtained which are expressed by hyperbolic solutions, trigonometric solutions, and rational solutions. In addition, we obtained the bright soliton by HSIVM. These methods are powerful, efficient and those can be used as an alternative to establishing new solutions of different types of differential equations in mathematical physics and engineering.     

FE analysis of the in-plane mechanical properties of a novel Voronoi-type lattice with positive and negative Poisson’s ratio configurations

This work presents a novel formulation for a Voronoi-type cellular material with in-plane anisotropic behaviour, showing global positive and negative Poisson’s ratio effects under uniaxial tensile loading. The effects of the cell geometry and relative density over the global stiffness, equivalent in-plane Poisson’s ratios and shear modulus of the Voronoi-type structure are evaluated with a parametric analysis. Empirical formulas are identified to reproduce the mechanical trends of the equivalent homogeneous orthotropic material representing the Voronoi-type structure and its geometry parameters.     

Unsteady Two-Dimensional Blood Flow in Porous Artery with Multi-Irregular Stenoses

The flow characteristics of an unsteady axisymmetric two-dimensional (2D) blood flow in a diseased porous arterial segment with flexible walls are investigated. The arterial walls mimic the irregular constrictions whereas the lumen containing the thrombus, cholesterol, and fatty plaques represents the porous medium. The governing equations with appropriate initial and boundary conditions are solved numerically using MAC method. The discretization is done on staggered grid with non-uniform grid size and pressure-poisson equation is solved following SOR method. The pressure and velocity corrections are made cyclically until the steady state is achieved. It is observed that for decreasing permeability, flow is highly decelerated while pressure drop and wall shear stress increases. The separation zones and re-circulation regions are found for severe stenoses. Flow separation and re-circulation diminishes for decreasing permeability of the porous medium. Comparisons are provided with published experimental and numerical results.     

Two-dimensional dopant profiling of silicon with submicron resolution using near field optics on silicon/electrolyte contacts

We demonstrate the possibility to use near field optics to perform two-dimensional dopant profiling on silicon surface, with deep submicron spatial resolution. The sample surface is contacted by an aqueous electrolyte giving a reverse biased junction that is illuminated by a subwavelength optical source, in near filed conditions. A staircase calibration structure was used with several boron-doped layers with either 4 μm or 0.4 μm thickness and doping between 10¹⁷ and 10²⁰ at/cm³. Measurements were performed on the sample cross section. It is shown that photocurrent surface mapping shows up the doped areas with a lateral resolution better than 100 nm.     

Towards Understanding the Anticorrosive Mechanism of Novel Surfactant Based on Mentha pulegium Oil as Eco-friendly Bio-source of Mild Steel in Acid Medium:a Combined DFT and Molecular Dynamics Investigation

Today,due to the increasingly stringent European directives concerning the use of molecules with certain toxicities towards the environment or their users,the essential oils,extracts,and molecules derived from plants exhibiting the characteristic of being biodegradable can be considered as a source of green corrosion inhibitors instead of harmful synthetic chemicals.The present work was devoted to testing the essential oil extracted from Mentha pulegium leaves(M1) as a corrosion inhibitor for C-steel in 1mol/L HCl solution using both electrochemical techniques and gravimetric measurements for the evaluation of the inhibition efficiencies at different temperatures.The results obtained showed that the inhibition efficiency increased with an increase in Ml concentration to reach a maximum value of 92.21%.We sought to determine the molecule responsible for this high efficiency,starting with the analysis of oil chemical composition by gas chromatography coupled with mass spectrometry.This analysis revealed that menthol(M2)and isomenthol(M3)were the principal constituents.In order to identify the molecule responsible for the inhibition and explain the protection mechanism involved,quantum chemical calculations and Monte Carlo simulations were used to explain the interaction of menthol,the major constituent of M1 with the Fe-surface.To practically confirm these results,we studied the action of 1mol/L HCl on steel with and without the addition of M2 by both methods(gravimetric and electrochemical study).A very high efficiency was obtained,an efficiency of 94.90% at 10^-3 mol/L,which was retained for a long exposure time,and slightly decreased in function of temperature.Finally,a good correlation between the experimental data,theoretical calculations,and SEM studies was obtained,which denied that the Ml efficiency was only a result of a synergy effect and confirmed the high efficiency of Mentha oil and its main component(menthol)as a strong ecological inhibitor of corrosion.     

Phase diagrams of poly(siloxane)/liquid crystal blends

Phase diagrams of blends of poly(methylphenylsiloxane) in short PMPS and two low molecular weight liquid crystals (4‐cyano‐4′‐n‐pentyl‐biphenyl and an eutectic mixture of paraphenylenes) are reported. Two polymers with very different weight‐average molar masses are considered in an evaluation of the loss of miscibility resulting from a known increase in the weight‐average molar mass. The experimental diagrams have been constructed via polarized optical microscopy and are rationalized in terms of the Flory–Huggins theory of isotropic mixtures and the Maier–Saupe theory of nematic order. The results show a good agreement between the theory and experiments and reveal a remarkable enhancement of miscibility with respect to similar systems involving poly(dimethylsiloxane). Variations of the interaction parameter with the temperature are compared for different systems of polysiloxanes. The effects of the nature of the liquid crystal and the polymer molar mass on the χ parameter are evaluated. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 39–43, 2003     

A Petrov-Galerkin method with quadrature for elliptic boundary value problems

We propose and analyse a fully discrete Petrov–Galerkinmethod with quadrature, for solving second-order, variable coefficient,elliptic boundary value problems on rectangular domains. Inour scheme, the trial space consists of C² splines of degreer 3, the test space consists of C⁰ splines of degree r –2, and we use composite (r – 1)-point Gauss quadrature.We show existence and uniqueness of the approximate solutionand establish optimal order error bounds in H², H¹ and L² norms.     

Rational surfaces having only a finite number of exceptional curves

We characterize the rational surfaces X which have a finite number of (-1)-curves under the assumption that -K_X is nef and having self-intersection zero.