This paper investigates an effective computational method (ECM) based on the standard polynomials used to solve some nonlinear initial and boundary value problems appeared in engineering and applied sciences. Moreover, the effective computational methods in this paper were improved by suitable orthogonal base functions, especially the Chebyshev, Bernoulli, and Laguerre polynomials, to obtain novel approximate solutions for some nonlinear problems. These base functions enable the nonlinear problem to be effectively converted into a nonlinear algebraic system of equations, which are then solved using Mathematica^®12. The improved effective computational methods (I-ECMs) have been implemented to solve three applications involving

The process of controlling a Flexible Joint Robot Manipulator (FJRM) requires additional sensors for measuring the state variables of flexible joints. Therefore, taking the elasticity into account adds a lot of complexity as all the additional sensors must be taken into account during the control process. This paper proposes a nonlinear observer that controls FJRM, without requiring equipment sensors for measuring the states. The nonlinear state equations are derived in detail for the FJRM where nonlinearity, of order three, is considered. The Takagi–Sugeno Fuzzy Model (T-SFM) technique is applied to linearize the FJRM system. The Luenberger observer is designed to estimate the unmeasured states using error correction. The develop

The goal of this paper is to design a robust controller for controlling a pendulum
system. The control of nonlinear systems is a common problem that is facing the researchers in control systems design. The Sliding Mode Controller (SMC) is the best solution for controlling a nonlinear system. The classical SMC consists from two phases. The first phase is the reaching phase and the second is the sliding phase. The SMC suffers from the chattering phenomenon which is considered as a severe problem and undesirable property. It is a zigzag motion along the switching surface. In this paper, the chattering is reduced by using a saturation function instead of sign function. In spite of SMC is a good method for controlling a nonlinear system b

A fast laser texturing technique has been utilized to produce micro/nano surface textures in Silicon by means of UV femtosecond laser. We have prepared good absorber surface for photovoltaic cells. The textured Silicon surface absorbs the incident light greater than the non-textured surface. The results show a photovoltaic current increase about 21.3% for photovoltaic cell with two-dimensional pattern as compared to the same cell without texturing.

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

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

This paper is concerned with the existence of a unique state vector solution of a couple nonlinear hyperbolic equations using the Galerkin method when the continuous classical control vector is given, the existence theorem of a continuous classical optimal control vector with equality and inequality vector state constraints is proved, the existence of a unique solution of the adjoint equations associated with the state equations is studied. The Frcéhet derivative of the Hamiltonian is obtained. Finally the theorems of the necessary conditions and the sufficient conditions of optimality of the constrained problem are proved.

Temporomandibular Disorders (TMD) refer to a group of symptoms where pain is the most leading cause to demand a treatment by the patient. Light therapies are of great importance at current times due to its biosafety and non-invasive quality when used for the management of TMD symptoms. This study aimed to evaluate the efficacy of red LED light with low-level LASER in treating TMD patients.