The extrapolated interval global optimization algorithm

This paper presents a new approach based on extrapolation to accelerate the linear convergence process of Vectorized Moore–Skelboe (VMS) algorithm. The VMS is a modified version of basic Moore–Skelboe (MS) algorithm, where the vectorization is used as a means to speed up the basic MS algorithm. We propose to further accelerate the converging process of VMS from linear to quadratic by combining the Richardson extrapolation technique with VMS. The effectiveness of the proposed algorithm is tested on various multivariate examples and compared with the unaccelerated conventional method, i.e., MS and well-known optimization software GlobSol. The test results show that the proposed extrapolation-based VMS offer considerable speed improvements over both the existing algorithms.     

Ion solvation in biologically active magnesium salt with lactose–water mixed solvent system at different temperatures: a thermo-acoustics study

This paper presents the ion-solvations in biologically important metal ion like magnesium in lactose–water mixed solvent systems at different temperatures. The investigation involves the measurement of ultrasonic velocity, density and viscosity of different concentration of magnesium sulphate in various proportions of lactose–water mixed solvents at temperature 303.15, 308.15, 313.15 K and at atmospheric pressure. Different thermo-acoustic parameters have been calculated from the measured values and have been discussed in the light of ion–solvent interactions.     

A new mixed finite element method for Burgers’ equation

In this paper, anH ¹-Galerkin mixed finite element method is used to approximate the solution as well as the flux of Burgers’ equation. Error estimates have been derived. The results of the numerical experiment show the efficacy of the mixed method and justifies the theoretical results obtained in the paper.     

A mixed finite element method for fourth order eigenvalue problems

A mixed finite element method for approximating eigenpairs of IV order elliptic eigenvalue problems with Dirichlet boundary conditions has been given. The method can be applied to the vibration analysis of anisotropic/orthotropic/isotropic/biharmonic plates. Computer implementation procedures for this mixed method are given along with the results of numerical experiments.     

Mathematical simulation of combined trajectory paths of a seven link biped robot

The following article focuses on biped robot simulation and control over combined trajectory paths with the aid of mathematical modeling methods focusing on the effects of hip height over torso’s modified motion. The mathematical simulation has been exploited to interpolate the combined trajectory of the robot path with the given breakpoints using inverse kinematic and dynamic methods to determine ZMP and stability treatments. After the robot’s combined path determination, a third-order spline is utilized because of its high precision and ability to calculate the kinematic, dynamic and control parameters. With the aid of this software, common parameters such as joint angles and inertial forces for the given specifications and nominal conditions are calculated and simulated.     

Enhanced super-hydrophobic and switching behavior of ZnO nanostructured surfaces prepared by simple solution--immersion successive ionic layer adsorption and reaction process

A simple and cost-effective successive ionic layer adsorption and reaction (SILAR) method was adopted to fabricate hydrophobic ZnO nanostructured surfaces on transparent indium-tin oxide (ITO), glass and polyethylene terephthalate (PET) substrates. ZnO films deposited on different substrates show hierarchical structures like spindle, flower and spherical shape with diameters ranging from 30 to 300 nm. The photo-induced switching behaviors of ZnO film surfaces between hydrophobic and hydrophilic states were examined by water contact angle and X-ray photoelectron spectroscopy (XPS) analysis. ZnO nanostructured films had contact angles of ~140° and 160°±2 on glass and PET substrates, respectively, exhibiting hydrophobic behavior without any surface modification or treatment. Upon exposure to ultraviolet (UV) illumination, the films showed hydrophilic behavior (contact angle: 15°±2), which upon low thermal stimuli revert back to its original hydrophobic nature. Such reversible and repeatable switching behaviors were observed upon cyclical exposure to ultraviolet radiation. These biomimetic ZnO surfaces exhibit good anti-reflective properties with lower reflectance of 9% for PET substrates. Thus, the present work is significant in terms of its potential application in switching devices, solar coatings and self-cleaning smart windows.     

A posteriori error estimates for an optimal control problem of laser surface hardening of steel

The main focus of this article is on the development of a posteriori error estimates for an optimal control problem of laser surface hardening of steel, governed by a dynamical system consisting of a semi-linear parabolic equation and an ordinary differential equation. A posteriori error estimators are developed for the variables representing temperature, formation of austenite, and laser energy using residual method when a continuous piecewise linear discretization has been used for the finite element approximation of space variables and a discontinuous Galerkin method has been used for time and control discretizations. The error indicators are used in the implementation and numerical results are obtained.