A new approach to improve the order of approximation of the Bernstein operators: theory and applications

This paper presents a new approach to improve the order of approximation of the Bernstein operators. Three new operators of the Bernstein-type with the degree of approximations one, two, and three are obtained. Also, some theoretical results concerning the rate of convergence of the new operators are proved. Finally, some applications of the obtained operators such as approximation of functions and some new quadrature rules are introduced and the theoretical results are verified numerically.     

Sinc-collocation method for solving the Blasius equation

Sinc-collocation method is applied for solving Blasius equation which comes from boundary layer equations. It is well known that sinc procedure converges to the solution at an exponential rate. Comparison with Howarth and Asaithambi's numerical solutions reveals that the proposed method is of high accuracy and reduces the solution of Blasius' equation to the solution of a system of algebraic equations.     

Interaction between annular crack and rigid disc inclusion in a transversely isotropic solid

An analytical approach has been presented to analyze the asymmetric and axisymmetric interactions between an annular crack and a rigid disc inclusion embedded in a transversely isotropic full-space. With the aid of a method of potential functions, Hankel and Abel transforms, the solution of the problems is reduced to a system of Fredholm integral equations, which are solved by using a numerical method. In each case, the stiffness of the disc inclusion and the stress intensity factor at the tips of the annular crack for different degrees of material anisotropy and different ratios of the inner and outer radius of the crack are illustrated graphically. Several limiting cases such as penny-shaped crack and external crack along with some exact solutions are presented to demonstrate the efficiency of the method.     

Generalized frames and their redundancy

Let be a generalized frame in a separable Hilbert space indexed by a measure space , and assume its analysing operator is surjective. It is shown that is essentially discrete; that is, the corresponding index measure space can be decomposed into atoms such that is isometrically isomorphic to the weighted space of all sequences of complex numbers with , where This provides a new proof for the redundancy of the windowed Fourier transform as well as any wavelet family in .

     

Investigating the Fracture Network Effects on Sweep Efficiency during WAG Injection Process

In this study, the main recovery mechanisms behind oil/water/gas interactions during the water-alternating-gas (WAG) injection process, in a network of matrix/fracture, were fundamentally investigated. A visual micromodel was utilized to provide insights into the potential applications of WAG process in fractured oil-wet media as well as the possibility of observing microscopic displacement behavior of fluids in the model. The model was made of an oil-wet facture/matrix network system, comprised of four matrix blocks surrounded with fractures. Different WAG injection scenarios, such as slug arrangements and the effects of fluid injection rates on oil recovery were studied. A new equation representing the capillary number, considering the fracture viscous force and matrix capillary force, was developed to make the experimental results more similar to a real field. In general, WAG tests performed in the fractured model showed a higher oil recovery factor compared with the results of gas and water injection tests at their optimum rates. The results showed that the presence of an oil film, in all cases, was the main reason for co-current drainage and double displacement of oil under applied driving forces. Furthermore, the formation of oil liquid bridges improved the recovery efficiency, which was greatly influenced by the size of fracture connecting the two matrix blocks; these connecting paths were more stable when there was initial water remaining in the media. Analyzing different recovery curves and microscopic view of the three phases in the transparent model showed that starting an injection mode with gas (followed by repeated small slugs of water and gas), could considerably improve oil recovery by pushing water into the matrix zone and increasing the total sweep efficiency.     

Numerical evaluation of passive control of shock wave/boundary layer interaction on NACA0012 airfoil using jagged wall

Shock formation due to flow compressibility and its interaction with boundary layers has adverse effects on aerodynamic characteristics, such as drag increase and flow separation. The objective of this paper is to appraise the prac-ticability of weakening shock waves and, hence, reducing the wave drag in transonic flight regime using a two-dimensional jagged wall and thereby to gain an appropriate jagged wall shape for future empirical study. Different shapes of the jagged wall, including rectangular, circular, and triangular shapes, were employed. The numerical method was validated by experimental and numerical studies involving transonic flow over the NACA0012 airfoil, and the results presented here closely match previous experimental and numerical results. The impact of parameters, including shape and the length-to-spacing ratio of a jagged wall, was studied on aerodynamic forces and flow field. The results revealed that applying a jagged wall method on the upper surface of an airfoil changes the shock structure significantly and disinte-grates it, which in turn leads to a decrease in wave drag. It was also found that the maximum drag coefficient decrease of around 17%occurs with a triangular shape, while the max-imum increase in aerodynamic efficiency (lift-to-drag ratio) of around 10%happens with a rectangular shape at an angle of attack of 2.26?.     

Influence of seed layers on the vertical growth of ZnO nanowires by low-temperature wet chemical bath deposition on ITO-coated glass substrate

Experimental Techniques - Aligned ZnO nanowires (NWs) were synthesized by low-temperature wet chemical bath deposition (CBD) technique on indium tin oxide (ITO)-coated glass substrates using c-axis...     

Accelerated double-step scale splitting iteration method for solving a class of complex symmetric linear systems

Numerical Algorithms - In this paper, we introduce and study an accelerated double-step scale splitting (ADSS) iteration method for solving complex linear systems. The convergence of the ADSS...