The problem of mutual exclusion has to be solved to prevent race condition and, as a result, prevent the possibility of a program producing an incorrect result. Providing deadlock-free distributed mutual exclusion algorithms is often difficult and it involves passing many messages. The two major types of these algorithms are token-based and permission-based algorithms. In this research, we propose a hybrid distributed mutual exclusion algorithm. By Hybrid, we mean that the algorithm uses both token-based and permission-based techniques. The best case and worst case number of messages passed for every critical region entry and exit is calculated, which are better than many other algorithms.

One-dimensional elastic wave propagation under quadratic impact loading in a rod with a variable cross section and material distribution is the subject of this study. The material distribution of the problem under investigation as well as the variations of the geometry was elucidated with non-uniform rational B-spline (NURBS). The problem was analyzed employing the isogeometric approach in order to ensure precise modeling of the geometry. The effects of impact loading, cross sectional area, material distribution, and radial inertia on elastic waves were examined in this study. In addition, propagation, reflections, and propagation speed along the axis were investigated. It was observed that the speed was not constant along the axial direction. Also, the cross sectional area had more effect on the amplitude of the elastic wave than the radial inertia. Furthermore, it was concluded that the material distribution and radial inertia may influence the wave propagation speed.

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Analysis of elastic wave propagation in a hollow cylinder with two-dimensional (2D) functionally graded material (FGM) and the curved outer surface under internal moving shock loading is the subject of this study. In the proposed method, there is no restriction on the distribution of material properties, the shape of the outer surface, and the applied shock loading. They are treated with non-uniform rational B-spline (NURBS). The isogeometric approach is developed for solving the problem to ensure precise modeling of the geometry. Also, the Newmark approach is used for full discretization of the isogeometric equations. The distributions of all elastic field quantities are determined for two types of material distributions and shock loadings. The effects of shock loadings, the shape of the outer surface, and the material distribution on the elastic wave are thoroughly examined. Propagation, reflections, and propagation speed inside the hollow cylinder are investigated. It is found that the propagation speeds of elastic waves have a distribution associated with the distribution of the material properties. Also, the shape of the outer surface can affect the amplitude of the elastic wave and the locations of concentration stress. It is concluded that the sonic boom phenomenon occurs in the solids as well as in the air.