The analysis of rigid pavements is a complex mission for many reasons. First, the loading conditions include the repetition of parts of the applied loads (cyclic loads), which produce fatigue in the pavement materials. Additionally, the climatic conditions reveal an important role in the performance of the pavement since the expansion or contraction induced by temperature differences may significantly change the supporting conditions of the pavement. There is an extra difficulty because the pavement structure is made of completely different materials, such as concrete, steel, and soil, with problems related to their interfaces like contact or friction. Because of the problem's difficulty, the finite element simulation is

This paper is attempt to study the nonlinear second order delay multi-value problems. We want to say that the properties of such kind of problems are the same as the properties of those with out delay just more technically involved. Our results discuss several known properties, introduce some notations and definitions. We also give an approximate solution to the coined problems using the Galerkin's method.

Solutions of dyes Rhodamine 6G (Rh6G) and Coumarin480(C480) were prepared at five concentrations (1x10-3, 5x10-4, 1x10-4, 5x10-5 and1x10-5) mol/l, the mixing was stirred to obtain on a homogenous solution, the(poly methyl-methacrylate) (PMMA) was solved by chloroform solvent with certain ratio, afterward (PMMA+Rh6G) and (PMMA+C480) thin films were prepared by casting method on glass block which has substrate with dimensions (7.5 x2.5)cm2, the prepared samples were left in dark place at room temperature for 24 hours to obtain uniform and homogenous thin films. UV-VIS absorption spectra, transmission spectra and fluorescence spectra were done to measure linear refractive index and linear absorption coefficient. The nonlinear optical proper

A huge potential from researchers was presented for enhancing the nonlinear optical response for materials that interacts by light. In this work, we study the nonlinear optical response for chemically prepared nano- fluid of silver nanoparticles in de-ionized water with TSC (Tri-sodium citrate) protecting agent. By the means of self-defocusing technique and under CW 473 nm blue laser, the reflected diffraction pattern were observed and recorded by CCD camera. The results demonstrate that, the Ag nano-fluid shows a good third order nonlinear response and the magnitude of the nonlinear refractive index was in the order of 10−7 cm2/W. We determine the maximum change of the nonlinear refractive index and the related phase shift for the mat

Colloidal crystals (opals) made of close-packed polymethylmethacrylate (PMMA) were fabricated and grown by Template-Directed methods to obtain porous materials with well-ordered periodicity and interconnected pore systems to manufacture photonic crystals. Opals were made from aqueous suspensions of monodisperse PMMA spheres with diameters between 280 and 415 nm. SEM confirmed the PMMA spheres crystallized uniformly in a face-centered cubic (FCC) array. Optical properties of synthesized pores PMMA were characterized by UV–Visible spectroscopy. It shows that the colloidal crystals possess pseudo photonic band gaps in the visible region. A combination of Bragg’s law of diffraction and Snell’s law of refraction were used to calculate t

Magnetic levitation (Maglev) systems are employed in a wide range of applications and are therefore of significant practical importance, which has led to growing research interest. This paper presents the design of a terminal synergetic control (TSC) and feedback linearization-based proportional-integral-derivative plus second-order derivative (FL-PIDD2) controller for the Maglev system. For developing the control law of both controllers, the mathematical model of the Maglev system is converted into a canonical system where the expression of the nonlinearity is displayed in the last differential dynamic equation of the system. The determination of the TSC and FL-PIDD2 gains for achieving the desired dynamic response is carried out using the