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The goal of this article is to develop a spectral collocation method for solving a distributed-order fractional Korteweg-de Vries equation using fractional Zigzag rising diagonal functions. To meet this target, we first introduce Zigzag and Jaiswal polynomials. Then, using a transformation, we find their fractional counterparts. As a linear combination of these functions, we seek a solution to the problem. We will generate operational matrices for fractional Zigzag raising diagonal functions and apply Simpson's rule to approximate the distributed fractional derivative. The resultant approximate equations are collocated to create a system of nonlinear equations. Error analysis of the numerical scheme is fully discussed. Numerical experiments have demonstrated the capability and efficiency of the method. We also demonstrate how the approach might be helpful for problems with non-smooth solutions. [ABSTRACT FROM AUTHOR]

In this study, the effect of hexamine, sodium nitrite, sodium benzoate, and trisodium phosphate corrosion inhibitors concentration on corrosion resistance of St37 carbon steel was studied (at 45 °C in closed-circuit cooling water) using weight loss, electrochemical impedance spectroscopy (EIS) and cyclic polarization tests. For hexamine and trisodium phosphate, with an increase in the concentration of the inhibitors, the corrosion rate decreased significantly. Therefore, the highest corrosion inhibition efficiency (IE%) of hexamine and trisodium phosphate was equal to 62% and 47% for concentrations of 400 ppm and 100 ppm, respectively. On the other hand, there was a critical concentration of sodium nitrite and sodium benzoate to protect carbon steel. For sodium nitrite and sodium benzoate, the highest IE% values were obtained at concentrations of 200 ppm and 5000 ppm, respectively, which were equal to 77% and 74%. According to the results, carbon steel was susceptible to pitting corrosion in the presence of different concentrations of the investigated inhibitors except sodium benzoate. The findings of EIS measurements were consistent with the results of polarization experiments. Overall, it was concluded that for the studied inhibitors, the corrosion control mechanism was charge transfer control in the electrical double layer. [ABSTRACT FROM AUTHOR]

This paper presents a difference scheme by considering cubic B-spline quasi-interpolation for the numerical solution of a fourth-order time-fractional integro-differential equation with a weakly singular kernel. The fractional derivative of the mentioned equation has been described in the Caputo sense. Time fractional derivative is approximated by a scheme of order O (τ 2 - α) and the Riemann–Liouville fractional integral term is discretized by the fractional trapezoidal formula. The spatial second derivative has been approximated using the second derivative of the cubic B-spline quasi-interpolation. The discrete scheme leads to the solution of a system of linear equations. We show that the proposed scheme is stable and convergent. In addition, we have shown that the order of convergence is O (τ 2 - α + h 2) . Finally, various numerical examples are presented to support the fruitfulness and validity of the numerical scheme. [ABSTRACT FROM AUTHOR]

In the present paper, we propose a spectral collocation method based on Pell polynomials to obtain the solution of a variable-order fractional integro-differential equation with a weakly singular kernel. Fractional integro-differential equations are used in many mathematical models, including heat conduction in memory materials, nuclear reactor dynamics, and chemical kinetics. To provide a numerical scheme, we consider Pell polynomials and use operational matrices to approximate variable-order Caputo fractional derivative as well as integral terms in the main equation. A linear system of equations is formed by collocating the resulting approximate equations. The existence and uniqueness of the solution to the main equation have been proved. The convergence of the approximation solution has been discussed. Several test problems are reported to demonstrate the validity of the method. [ABSTRACT FROM AUTHOR]

In this study, the cause of a severe failure and degradation of a nozzle in a secondary reformer unit in an ammonia plant was investigated. The nozzle was made of Incoloy 800H and exposed to harsh atmospheres containing H2, CO, and H2O vapor at a temperature close to 800 °C. Service life of this nozzle is approximately 20,000 h which is much less than its expected design lifetime (80,000 h). Visual inspections indicated that parts of the nozzle's surface have been degraded into fine black powders/dust. According to the X-ray diffraction (XRD) result, the dust formed on the surface mainly consisted of carbon, Cr7C3, MnCr2O4, MnFeCrO4, Cr23C6, Mn23C6, and Fe3O4 phases. SEM images from the nozzle's cross section showed that there are some pits on the surface which are filled with metal, oxide, and carbide particles. Micro-hardness test results showed that in areas adjacent to the surface of the pits, the hardness has decreased from 145 to 89 HV due to the depletion of alloying elements and formation of spinel oxide layers over these areas. Overall, metal dusting was diagnosed as the main cause of premature degradation of nozzles in this plant. A failure scenario and some mitigation strategies were proposed, based on the obtained results. [ABSTRACT FROM AUTHOR]

In the current study, oxidation and wear resistance of FeAl and (Fe,Cr)Al intermetallic compounds as well as (Fe,Cr)Al-5%vol Al2O3 and (Fe,Cr)Al-10%vol Al2O3 nanocomposites were investigated. Ball-milled powders were hot-pressed at 5.5 GPa and 1600 °C for 15 min in order to produce the bulk samples. The cyclic oxidation test was performed at 1100 °C for 100h. High-temperature wear tests were conducted at 400 °C with loads of 20 N in sliding speed and sliding distance of 0.1 m/s and 500 m, respectively. Furthermore, the nano-scratch tests were performed in single-direction as well as pass and return modes with a maximum load of 20 mN. Results showed that the (Fe,Cr)Al intermetallic compound had superior oxidation resistance with the lowest kp value at the same oxidation time. The improved oxidation performance of (Fe,Cr)Al intermetallic compound compared to (Fe,Cr)Al-Al2O3 composites can be due to the presence of more Al in (Fe,Cr)Al sample. According to the nano-scratch test, (Fe,Cr)Al-10%vol Al2O3 nanocomposite (with H/E ratio of 0.036) had the best wear resistance. On the other hand, nanocomposites containing 5% and 10% of Al2O3 had the lowest friction coefficient (≈ 0.6 and 0.3, respectively). The main wear mechanism for the FeAl compound was adhesive wear, while, delamination was the main mechanism for samples containing Al2O3 nanoparticles. Although the formation of Al2O3 reinforcement nanoparticles somewhat decreases the oxidation resistance, it also resulted in significant overall improvement in the wear behavior. [ABSTRACT FROM AUTHOR]

This paper presents a soft computing based artificial intelligent technique, adaptive neuro-fuzzy inference system (ANFIS) to predict the neutron production rate (NPR) of IR-IECF device in wide discharge current and voltage ranges. A hybrid learning algorithm consists of back-propagation and least-squares estimation is used for training the ANFIS model. The performance of the proposed ANFIS model is tested using the experimental data using four performance measures: correlation coefficient, mean absolute error, mean relative error percentage (MRE%) and root mean square error. The obtained results show that the proposed ANFIS model has achieved good agreement with the experimental results. In comparison to the experimental data the proposed ANFIS model has MRE% <1.53 and 2.85 % for training and testing data respectively. Therefore, this model can be used as an efficient tool to predict the NPR in the IR-IECF device. [ABSTRACT FROM AUTHOR]

Organic acid has been related to nutrient mobilization, mainly in phosphorus (P) insoluble utilization, and therefore enhances P bioavailability. In this study, we examined the effect of low-molecular-weight organic acids (malic, citric, and oxalic acids) on P release of some calcareous soils from western Iran. Fractionation and speciation of P in the soil solution were studied at the initial and final P release. Significantly different quantities of P were extracted by the organic acids. On average the maximum (1,554.9 mg kg) and the minimum (1,260.5 mg kg) P were extracted by 10 mM oxalic and malic acid, respectively. Power equation described well P release. In the initial stage of P release, the solution samples in soils were supersaturated with respect to hydroxyapatite and β-TCP. At the end of P release, all solutions were undersaturated with phosphate minerals. The percentage of Fe-Al oxide fraction generally increased after P release, while carbonate and residual P fractions were decreased in all organic acids. Compared with the native soils, adding malic and citric acids had no effect on Fe-Al oxide fraction, but oxalic acid significantly reduced this fraction. [ABSTRACT FROM AUTHOR]

Our goal is to propose a useful and effective method to determine optimal machining parameters in order to minimize surface roughness, resultant cutting forces and maximize tool life in the turning process. At first, three separate neural networks were used to estimate outputs of the process by varying input machining parameters. Then, these networks were used as optimization objective functions. Moreover, the proposed algorithm, namely, GA and PSO were utilized to optimize each of the outputs, while the other outputs would also be kept in the suitable range. The obtained results showed that by using trained neural networks with genetic algorithms as optimization objective functions, a powerful model would be obtained with high accuracy to analyze the effect of each parameter on the output(s) and optimally estimate machining conditions to reach minimum machining outputs. [ABSTRACT FROM AUTHOR]

We show with the results of a study conducted in the Hamadan Province, Iran as to how the use of composite sampling for estimating mean zinc concentration in the soil can help reduce analytical costs by reducing the number of analysis required. We also introduce post-stratification methodology in the composition step to take advantage of possible spatial dispersion. We speculate that the zinc concentration value depends on the sample location, we first stratified the sample set and then composite units from different strata randomly. The results of a simulation study show that the use of this approach not only reduces the total costs but also increases the precision of the estimator. [ABSTRACT FROM AUTHOR]

Intraosseous schwannoma of T12 with burst L1 fracture is extremely rare. Here we present a report of the successful treatment and 18-month follow-up of a 46-year-old man with this complication. [ABSTRACT FROM AUTHOR]

In this retrospective study, ten patients with lumbar iatrogenic instability are reported who were treated by pedicular fixation and bone grafting with an average follow-up of 18 months. Early results, which are mostly encouraging, show relief of symptoms, solid fusion of spine, and maintenance of lumbar curve with no major complications. [ABSTRACT FROM AUTHOR]

Intradural nerve root hematoma of the lumbar spine is extremely rare and can cause compression of the cauda equina. This case, which presented with low back pain and radiation to both lower extremities, diagnosed as an intradural hematoma of nerve root by magnetic resonance imaging (MRI) and was totally removed successfully. Intradural nerve root hematoma can present with or without a history of trauma or blood dyscrasia, where MRI is the best imaging modality, and can be well treated by surgery. [ABSTRACT FROM AUTHOR]