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 research aims at studying each of the cold and hot thermal wavelengths affecting
Iraq for a minimum climatic course of 11 years beginning from 1992 till 2002. Three stations
were selected including the parts of Iraq surface: Mosul, Baghdad and Basrah.
The wave days were also connected with the related climatic elements represented by
the wind direction and speeds and the relative humidity. It was shown that Iraq is affected by
the rates of hot thermal wave lengths greatly compared to the rates of cold wavelengths. The
results suggested that the highest rate of hot and cold wavelengths recorded over Basra station
was (3.5) days for the cold and (5) days for the hot. While the lowest rates was at Mosul
station
The Iraqi houses flattening the roof by a concrete panel, and because of the panels on the top directly exposed to the solar radiation become unbearably hot and cold during the summer and winter. The traditional concrete panel components are cement, sand, and aggregate, which have a poor thermal property. The usage of materials with low thermal conductivity with no negative reflects on its mechanical properties gives good improvements to the thermal properties of the concrete panel. The practical part of this work was built on a multi-stage mixing plan. In the first stage the mixing ratio based on the ratios of the sand to cement. The second stage mixing ratios based on replacing the coarse aggregate quantities with the
... Show MoreCalculations and predication a theoretical formulas for the electron drift velocity in a gas medium are achieved to deduced the electron distribution function for different gas concentrations. The calculations are achieved by using the numerical solution for Boltzmann transport equation in two term approximation, using the NOMAD program for the drift velocity in a gas medium. It's necessary to note that the solution is essentially depending upon the elastic and inelastic collision cross section. In order to fixe a good accuracy for the using cross section it's necessary to calculate the electron distribution function and therefore study their behavior. Results about the electron drift velocity show that a decreasing pro
... Show MoreSupernova explosions are described as very violent events which transfer a significant amount of energy to interstellar media and are responsible for a large variety of physical processes. This study does not discuss the actual explosion mechanisms but follows the behavior of the dynamical evolution of some selected type I and type II supernova remnant and particularly after a thousand years from their explosion and shows how the density of the medium affects the evolution and the lifetime of each remnant. By studying such behaviors, a simplified model has been proposed here for the velocity and radius of the remnant after thousand years of explosion that depends only on the density of the medium and age of the remnant. It has been found th
... Show MoreIn this study, a new Azo ligand 5-((2-(1H-indol-2-yl)ethyl)diazinyl)-2-aminophenol is synthesized from a reaction of Tryptamine with 2-aminophenol. The ligand and their metal ion complexes Ni(II), Pd(II) , Pt(IV) and Au(III) have been synthesized and characterized by various analytical techniques, including elemental microanalysis, metal content, chloride-containing, measurement of electrical conductivity, magnetic susceptibility, 1H and 13C-NMR, FT-IR, UV-Vis, mass spectra (MS), and thermal analysis (TGA and DSC) curves. The DCS curve was used to calculate the thermodynamic parameters ΔH, ΔS, and ΔG. The characterization results promote the metal complexes of azo ligand structures. The results indicate that the
... Show MoreGiven a matrix, the Consecutive Ones Submatrix (C1S) problem which aims to find the permutation of columns that maximizes the number of columns having together only one block of consecutive ones in each row is considered here. A heuristic approach will be suggested to solve the problem. Also, the Consecutive Blocks Minimization (CBM) problem which is related to the consecutive ones submatrix will be considered. The new procedure is proposed to improve the column insertion approach. Then real world and random matrices from the set covering problem will be evaluated and computational results will be highlighted.
In this paper we introduce many different Methods of ridge regression to solve multicollinearity problem in linear regression model. These Methods include two types of ordinary ridge regression (ORR1), (ORR2) according to the choice of ridge parameter as well as generalized ridge regression (GRR). These methods were applied on a dataset suffers from a high degree of multicollinearity, then according to the criterion of mean square error (MSE) and coefficient of determination (R2) it was found that (GRR) method performs better than the other two methods.
In this research we solved numerically Boltzmann transport equation in order to calculate the transport parameters, such as, drift velocity, W, D/? (ratio of diffusion coefficient to the mobility) and momentum transfer collision frequency ?m, for purpose of determination of magnetic drift velocity WM and magnetic deflection coefficient ? for low energy electrons, that moves in the electric field E, crossed with magnetic field B, i.e; E×B, in the nitrogen, Argon, Helium and it's gases mixtures as a function of: E/N (ratio of electric field strength to the number density of gas), E/P300 (ratio of electric field strength to the gas pressure) and D/? which covered a different ranges for E/P300 at temperatures 300°k (Kelvin). The results show
... Show MoreResearch Hypothesis from the fact that kicks off the effect that agricultural production in Iraq plays an important role in overcoming the food problem and achieving food security, but he became far far away from the provision of sufficient quantities of food products and then securing the Iraqi consumer food basket by the challenges faced by the agricultural sector.
To prove the hypothesis research in its structure in three axes came, the first axis eating historical significance to the subject of food over time periods as well as to clarify the concept of food security, and the second axis touched on the most important challenges facing the agricultural sector in Iraq and prevent the achievement of food requirements for members of