Curvature and closed trapped surfaces in 4-dimensional space-times

The way a spacelike surfaceH sits in a 4-dimensional space-timeM may be measured by the average null curvature function _H and the shape function _H ofH. Relations between the shape function _H of a spaceiike surfaceH and curvature of a 4-dimensional space-time obeying the Einstein equation are investigated. Some relations between the shape functions of compact spacelike surfaces and infinite curvature are obtained and discussed. Assuming some curvature conditions, some results concerning the evolution of closed trapped surfaces from a restricted type of marginally trapped surfaces diffeomorphic toS ² are obtained.Based on Chapter 4 of the author's Ph.D. thesis.     

A study on 3-D stress distributions in the bi-adhesively bonded T-joints

In this study, the normal (σ_x, σ_y, σ_z) and shear stress (τ_xy, τ_yz, τ_zx) distributions occurring in a bi-adhesively bonded T-joint with was investigated via a non-linear three dimensional finite element analysis. For this purpose, first of all, using 2024-T3 aluminum alloy as the adherend and the support, a two-part paste (DP 460) and a film type (SBT 9244) as adhesive, two different types of T-joint samples (single-adhesively bonded T-joint and bi-adhesively bonded T-joint) were produced for experimental studies. After experimental studies on the three different T-joint types were conducted, stress analyses in the T-joints were performed with a three-dimensional finite element analysis by considering the geometrical non-linearity and the material non-linearities of the adhesive (DP460 and SBT9244) and adherend (AA2024-T3). Finally, for a given adherend, the lower the stiffness of the adhesive used in the overlap, the lower the stress concentration, leading to potentially higher joint strength. The use of relatively low stiffness adhesives at the ends of the overlap in a bi-adhesive can decrease the stress concentration and, therefore, potentially lead to higher joint strength.     

Delay equations with fluctuating delay related to the regenerative chatter II: analysis of reduced bifurcation equation

In this article, we study the reduced bifurcation equations of the nonlinear delay differential equations with periodic delays, which models the machine tool chatter with continuously modulated spindle speed to determine the periodic solutions and analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions close to the new stability boundary.     

Delay equations with fluctuating delay related to the regenerative chatter I: reduced bifurcation equation

The mathematical models representing machine tool chatter dynamics have been cast as differential equations with delay. The suppression of regenerative chatter by spindle speed variation is attracting increasing attention. In this paper, we study nonlinear delay differential equations with periodic delays which models the machine tool chatter with continuously modulated spindle speed. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. The reduced bifurcation equation is obtained by making use of Lyapunov–Schmidt Reduction method.     

Electrochemically induced atom-by-atom growth of ZnS thin films: a new approach for ZnS co-deposition

Ultrathin films of ZnS were grown on Au (111) substrates using a novel, simple co-deposition method and characterized using X-ray diffraction (XRD), atomic force microscopy (AFM), X-ray photoelectron spectroscopy (XPS), and UV-visible spectroscopy. Cyclic voltammograms were used to determine approximate deposition potentials for co-deposition. XRD shows that the material growth is highly preferential with (111) orientation. Both AFM and XRD data indicate that the ZnS growth mechanism starts by the formation of rounded nanoparticles at the surface and then continues by lateral and vertical growth to form flat square crystallites of ZnS. UV-vis spectra taken for the ZnS thin films with various thicknesses, which is related to deposition time, shows that the band gap of the ZnS decreases as the film thickness increases.