Markov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problems (IVPs) compared to other approaches found in the literature, which is verified by the obtained solutions. The determination of the transient solutions for Markov chains is presented using the proposed method. The results show better accuracy in solving the transient distribution in Markov chains, which implies that there is an improved assurance in adopting this approach in future studies of the Markov chain modeling process for predicting future events based on the current state of a process. Future studies on Markov chain modeling could adopt the introduced method to predict future events based on the current state of a process.
This paper presents a nonlinear finite element modeling and analysis of steel fiber reinforced concrete (SFRC) deep beams with and without openings in web subjected to two- point loading. In this study, the beams were modeled using ANSYS nonlinear finite element
software. The percentage of steel fiber was varied from 0 to 1.0%.The influence of fiber content in the concrete deep beams has been studied by measuring the deflection of the deep beams at mid- span and marking the cracking patterns, compute the failure loads for each deep beam, and also study the shearing and first principal stresses for the deep beams with and without openings and with different steel fiber ratios. The above study indicates that the location of openings an
In this work we used the environmentally friendly method to prepared ZrO2 nanoparticles utilizing the extract of Thyms plant In basic medium and at pH 12, the ZrO2 NPs was characterized by different techniques such as FTIR, ultraviolet visible, Atomic force microscope, Scanning Electron Microscopy, X-ray diffraction and Energy dispersive X-ray. The average crystalline size was calculated using the Debye Scherres equation in value 7.65 nm. Atomic force microscope results showed the size values for ZrO2 NPs were 45.11nm, and there are several distortions due to the presence of some large sizes. Atomic force microscope results showed the typical size values for ZrO2 NPs were 45.11 nm, and there are several distortions due to the presence of so
... Show MoreAccurate calculation of transient overvoltages and dielectric stresses from fast-front excitations is required to obtain an optimal dielectric design of power components subjected to these conditions, which are commonly due to switching and lightning, as well as utilization of power-electronic devices. Toroidal transformers are generally used at the low voltage level. However, recent investigations and developments have explored their use at the medium voltage level. This paper analyzes the model-based improvement of the insulation design of medium voltage toroidal transformers. Lumped and distributed parameter models are used and compared to predict the transient response and dielectric stress along the transformer winding. The parameters
... Show MoreThis article presents the results of an experimental investigation of using carbon fiber–reinforced polymer sheets to enhance the behavior of reinforced concrete deep beams with large web openings in shear spans. A set of 18 specimens were fabricated and tested up to a failure to evaluate the structural performance in terms of cracking, deformation, and load-carrying capacity. All tested specimens were with 1500-mm length, 500-mm cross-sectional deep, and 150-mm wide. Parameters that studied were opening size, opening location, and the strengthening factor. Two deep beams were implemented as control specimens without opening and without strengthening. Eight deep beams were fabricated with openings but without strengthening, while
... Show MoreThere is an interesting potential for the use of GFRP-pultruded profiles in hybrid GFRP-concrete structural elements, either for new constructions or for the rehabilitation of existing structures. This paper provides experimental and numerical investigations on the flexural performance of reinforced concrete (RC) specimens composite with encased pultruded GFRP I-sections. Five simply supported composite beams were tested in this experimental program to investigate the static flexural behavior of encased GFRP beams with high-strength concrete. Besides, the effect of using shear studs to improve the composite interaction between the GFRP beam and concrete as well as the effect of web stiffeners of GFRP were explored. Encasing the GFRP
... Show MoreIn the present study, the effectiveness of a procedure of electrocoagulation for removing chemical oxygen demand (COD) from the wastewater of petroleum refinery has been evaluated. Aluminum and stainless steel electrodes were used as a sacrificial anode and cathode respectively. The effect of current density (4-20mAcm−2), pH (3-11), and NaCl concentration (0-4g/l) on efficiency of removal of chemical oxygen demand was investigated. The results have shown that increasing of current density led to increase the efficiency of COD removal while increasing NaCl concentration resulted in decreasing of COD removal efficiency. Effect of pH was found to be lowering COD re