This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

Durability of hot mix asphalt (HMA) against moisture damage is mostly related to asphalt-aggregate adhesion. The objective of this work is to find the effect of nanoclay with montmorillonite (MMT) on Marshall properties and moisture susceptibility of asphalt mixture. Two types of asphalt cement, AC(40-50) and AC(60-70) were modified with 2%, 4% and 6% of Iraqi nanoclay with montmorillonite. The Marshall properties, Tensile strength ratio(TSR) and Index of retained strength(ISR) were determined in this work. The total number of specimens was 216 and the optimum asphalt content was 4.91% and 5% for asphalt cement (40-50) and (60-70) respectively. The results showed that the modification of asphalt cement with MMT led to increase Marsh

A polycrystalline CdTefilms have been prepared by thermal evaporation technique on glass substrate at room temperature. The films thickness was about700±50 nm. Some of these films were annealed at 573 K for different duration times (60, 120 and 180 minutes), and other CdTe films followed by a layer of CdCl₂ which has been deposited on them, and then the prepared CdTe films with CdCl₂ layer have been annealed for the same conditions. The structures of CdTe films without and with CdCl₂ layer have been investigated by X-ray diffraction. The as prepared and annealed films without and with CdCl₂ layer were polycrystalline structure with preferred orientation at (111) plane. The better structural pr

The structural, optical and electrical properties of ZnS films prepared by vacuum evaporation technique on glass substrate at room temperature and treated at different annealing temperatures (323, 373, 423)K of thickness (0.5)µm have been studied. The structure of these films is determined by X-ray diffraction (XRD). The X-ray diffraction studies show that the structure is polycrystalline with cubic structure, and there are strong peaks at the direction (111). The optical properties investigated which include the absorbance and transmittance spectra, energy band gab, absorption coefficient, and other optical constants. The results showed that films have direct optical transition. The optical band gab was found to be in the range t

     This work compares the changes in optical and structural properties of cerium oxide (CeO2) when doped with different concentrations (3%,5%,7%, and 9%) of two oxides, In2O3 and Eu2O3. X-ray diffraction and spectrophotometry were employed in the visible, ultraviolet, and near-infrared regions. The findings demonstrated that CeO2 doped with In2O3 and Eu2O3 thin films were polycrystalline and had a cubic structure. The crystal size increased from 20.5 to 32.15 when Eu2O3 doping ratio increased from 0% to 7% and then decreased to 28.46 nm at 9%. While the crystal size showed an increase from 20.5 to 21.42 nm with the increase of the In2O3 doping ratio, while the lattice constant measured for cubic CeO2 changed opposite to that

In this study, an unknown force function dependent on the space in the wave equation is investigated. Numerically wave equation splitting in two parts, part one using the finite-difference method (FDM). Part two using separating variables method. This is the continuation and changing technique for solving inverse problem part in (1,2). Instead, the boundary element method (BEM) in (1,2), the finite-difference method (FDM) has applied. Boundary data are in the role of overdetermination data. The second part of the problem is inverse and ill-posed, since small errors in the extra boundary data cause errors in the force solution. Zeroth order of Tikhonov regularization, and several parameters of regularization are employed to decrease error

In the present work, the focusing was on the study of the x-ray diffraction, dielectric constant, loses dielectric coefficient, tangent angle, alter- natively conductivity and morphology of PET/BaTio3. The PET/BaTio3 composite was prepared for polyethylene terephthalate PET polymer composite containing 0, 10, 20, 30, 40, 50, and 60 wt. % from Barium titanate BaTi03 powder. The composite of two materials leads to form mixing solution and hot-pressing method. The effect of BaTio3 on the structure and dielectric properties with morphology was studied on PET matrix polymer using XRD, LCR meter and SEM.

This research explores the integration of multi-walled carbon nanotubes (MWCNTs) into polyvinyl alcohol (PVA) matrices to enhance their structural, electrical and thermal properties. Fourier-transform infrared spectroscopy analysis confirms the formation of a PVA-MWCNT complex. The incorporation of MWCNTs, even at low concentrations, leads to increased electrical conductivity, making the composite material suitable for applications in flexible electronics and sensors. Dielectric studies reveal frequency-dependent electrical behavior, attributed to interfacial polarization, suggesting potential uses in capacitors and energy storage devices. The introduction of MWCNTs into PVA leads to N-type semiconductor behavior, as indicated by the Hall c

We study the physics of flow due to the interaction between a viscous dipole and boundaries that permit slip. This includes partial and free slip, and interactions near corners. The problem is investigated by using a two relaxation time lattice Boltzmann equation with moment-based boundary conditions. Navier-slip conditions, which involve gradients of the velocity, are formulated and applied locally. The implementation of free-slip conditions with the moment-based approach is discussed. Collision angles of 0°, 30°, and 45° are investigated. Stable simulations are shown for Reynolds numbers between 625 and 10 000 and various slip lengths. Vorticity generation on the wall is shown to be affected by slip length, angle of incidence,