This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-linear optimization problem and use the lsqnonlin non-linear least-square solver from the MATLAB optimization toolbox. Through examples and discussions, we determine the optimal values of the regulation parameters to ensure accurate, convergent, and stable reconstructions. The direct problem is well-posed, and the Crank–Nicolson method provides accurate solutions with relative errors below 0.006% when the discretization elements are M=N=80. The accuracy of the forward solutions helps to obtain sensible solutions for the inverse problem. Although the inverse problem is ill-posed, we determine the optimal regularization parameter values to obtain satisfactory solutions. We also investigate the existence of inverse solutions to the considered problems and verify their uniqueness based on established definitions and theorems.
This survey investigates the thermal evaporation of Ag2Se on glass substrates at various thermal annealing temperatures (300, 348, 398, and 448) °K. To ascertain the effect of annealing temperature on the structural, surface morphology, and optical properties of Ag2Se films, investigations and research were carried out. The crystal structure of the film was described by Xray diffraction and other methods.The physical structure and characteristics of the Ag2Se thin films were examined using X-ray and atomic force microscopy (AFM) based techniques. The Ag2Se films surface morphology was examined by AFM techniques; the investigation gave average diameter, surface roughness, and grain size mutation values with increasing annealing temperature
... Show MoreBuckling analysis of a laminated composite thin plate with different boundary conditions subjected to in-plane uniform load are studied depending on classical laminated plate theory; analytically using (Rayleigh-Ritz method). Equation of motion of the plates was derived using the principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. The eigenvalue problem generated by using Ritz method, the set of linear algebraic equations can be solved using MATLAB for symmetric and anti-symmetric, cross and angle-ply laminated plate considering some design parameters such as aspect ratios, number of layers, lamination type and orthotropic ratio. The results obtained g
... Show MoreCritical buckling and natural frequencies behavior of laminated composite thin plates subjected to in-plane uniform load is obtained using classical laminated plate theory (CLPT). Analytical investigation is presented using Ritz- method for eigenvalue problems of buckling load solutions for laminated symmetric and anti-symmetric, angle and cross ply composite plate with different elastic supports along its edges. Equation of motion of the plate was derived using principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. Various numerical investigation were studied to exhibit a convergence and accuracy of the present solution for considering some design parameters such as edge
... Show MoreIn this paper, we present new algorithm for the solution of the nonlinear high order multi-point boundary value problem with suitable multi boundary conditions. The algorithm is based on the semi-analytic technique and the solutions are calculated in the form of a rapid convergent series. It is observed that the method gives more realistic series solution that converges very rapidly in physical problems. Illustrative examples are provided to demonstrate the efficiency and simplicity of the proposed method in solving this type of multi- point boundary value problems.
The purposes of this study are to measure masculine's identification among secondary school students, and to examine the significant differences among secondary school students in respect of students age (16-18) year. The researcher has prepared a questionnaire comprised (25) item to measure masculine identification among students: this scale was applied on (100) student who were selected as a sample from four different school at al-rusafa side in Baghdad. The scale then modified to (23) item to be more consistent. The results revealed that there were no significant differences among students based on the variable of age, and the mean of masculine identification showed a high level than the hypothesized mean.
The compressive residual stresses generated by shot peening, is increased in a direct proportional way with shot peening time (SPT). For each metal, there is an optimum shot peening time (O.S.T) which gives the optimum fatigue life. This paper experimentally studied to optimize shot peening time of aluminium alloy 6061-T651 as well as using of and analysis of variance (ANOVA).
Two types of fatigue test specimens’ configuration were used, one without notch (smooth) and the other with a notch radius (1,25mm), each type was shot peened at different time. The (O.S.T) was experimentally estimated to be 8 minutes reaching the surface stresses at maximum peak of -184.94 MPa.
A response surface methodology (RSM) is presen
... Show MoreIn this research study the effect of fish on the properties optical films thickness 1200-1800 and calculated energy gap Basra direct transport permitted and forbidden to membranes and urged decreasing values ??of Optical Energy Gap increase fish included accounts optical also calculate the constants visual as factories winding down and the refractive index and reflectivity membranes also by real part and imaginarythe dielectric constant