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.
The eff ect of partial substitution for lanthanum (La) on the structural properties of the compound Y1-xLaxBa4Cu7O15+δ were studied. The variation of (x) are x=0.1, 0.2 and 0.3, which was synthesized by solid state reaction method. The mixed powder was pressed with pressure (7 ton / cm2) as a disc (1.5 cm) diameter and a thickness of (0.25 to 0.3 cm). The samples were sintering by 120 °C / hour with a changing rate from room temperature to 850 ° C through 72 hours. XRD analysis using to calculate crystal size, strain and degree of crystallinity. It was found all samples have orthorhombic structure and change of structure with increasing lanthanum concentration. It was shown that the change lanthanum concentrations of all our samp
... Show MoreWe have studied theoretically the response of atomic three- level cascade scheme
of rubidium vapor to a strong laser under conditions in which electromagnetically
induced transparency would be induced on a weak probe beam. We show that the
medium that is an opaque to a probe laser can, by applying both lasers
simultaneously, be made transparent.
Ismailism is of great importance in Islamic history and Islamic political thought. In different countries of the Muslim world today their presence exists and is active but is confused with mystery and secrecy. The most important characteristic of their political ideology is their dependence on the esoteric exegesis, which they have made an intellectual basis for which their most ideas relate, when they make for everything visible and exposed a hidden matter, not only aware of the esoteric exegesis, which only God knows and entrenched in science, and they mean imams or whoever They are called "(esoteric)" as a result of the Ismaili belief in esoteric interpretation and that everything is apparent inward, as well as they called the ((seven
... Show MoreFlexible pavement design and analysis were carried out in the past with semi-experimental methods, using elastic characteristics of pavement layers. Due to the complex interferences between various layers and their time consumption, the traditional pavement analysis, and design methods were replaced with fast and powerful methods including the Finite Element Method (FEM) and the Discrete Element Method (DEM). FEM requires less computational power and is more appropriate for continuous environments. In this study, flexible pavement consisting of 5 layers (surface, binder, base, subbase, and subgrade) had been analyzed using FEM. The ABAQUS (6.14-2) software had been utilized to investigate the influence of the base layer depth on ver
... Show MoreThe dynamic response of foundation rest on collapsible soil in dry and soaked states is studied through wide experimental programmed. Gypseous soil from Tikrit governorate area was obtained and subjected to various physical and chemical analysis to determine its properties. Steel rectangular footing (400x200x20) mm is manufactured. The machine is fitted to the footing, then the model machine foundation is placed centrally over the prepared soil layer in steel container (1200x 1000x1000)mm with proper care to maintain the center of gravity of whole system lie in the same vertical line with container.Then, the footing is subjected to vertical harmonic loading using a rotating mass type mechanical oscillator to simulate different dynamic lo
... Show MoreResults: it was found that labelled cells participated in the formation of myotubes, which formed mature muscle fibers, and possibly new satellite cells. The results of this experiment may eventually revolutionized therapeutic procedures for some form of muscle diseases
For cleaner air and unpolluted continue assessment study air pollution the city of
Baghdad by measuring the concentrations of air pollutants, which included TSP, Pb, where
the adoption of three stations (Andalus Square, Jadiriya, Allawi) are distributed in the city of
Baghdad in order to compare the concentrations of these pollutants with previous studies.
Study pointed out that the city's air contaminant, especially in minutes outstanding after
deducting the amount of atmospheric dust thick mechanism city this year where the highest
concentration of minutes outstanding (9895) micrograms / m 3 at the station Alawi and lower
concentration of 157 micrograms / m 3 at the station Alawi and this was higher than the
det
The research aims to identify the reasons that lead to asymmetry of information between economic unity administration and the parties that use accounting information such as shareholders, So, the ability to reach to the solutions that would reduce this problem, these factors have been divided into two types: the first one is the internal factors which represent the administration's desire in order to expand the self-interest of getting the profits and increase the value and competitive entity and investors to obtaining greater returns for their shares, so the second type is the external factors, which represent the failer that occurs in the laws and regula
... Show Moreof the research is one of the poetic purposes that expresses the philosophy of the intellectual poet who experienced life and learned the tendencies and the gulf of the human soul and the fact that an intellectual attitude towards them, intensified within the poems do not need to be frequently narrated and elaborated, but based on the few words in the rich meanings and expressed the point of view he wanted to convey to the recipient without taking the position of disorientation and retreat to himself expressing his rejection of this reality, but faced this reality different manifestations and reflections and the conditions of human beings in it detailed His opinion is constructive criticism, and accurate observations reveal the culture o
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