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 article aims to study the crisis of political change from three Phases . The first focuses on the crises of political legitimacy and democratic postponement, as fundamental issues in analyzing the phenomenon of power struggle through the dialectic between the concept of historical legitimacy and institutional fragility from the beginning of statehood in 1962 to the stage of multi-partyism and the cessation of the electoral process in the 1990s. While the second focuses on the question of the monopoly of power in the post-terrorism and national reconciliation according to considerations Political, social and security measures to prolong the life of the regime and avoid the demands of political change brought about
... Show MoreAbstract Political power in Lebanon is a fundamental objective of any political organization, whether political party or political group. Thus, there is a conflict of power. There are two kinds of political conflict that are differentiated by the idea of legitimacy. The competition is in the political system when the agreement between the social forces is considered legitimate, and the conflict is on the political system when the agreement between these forces ceases to be legitimate and Are working to topple it and seek to establish an alternative system. Therefore, the succession of power in Lebanon is a result of the competition and political conflict, which is in turn a result of the large number of regional and international players
... Show MoreExperimental and numerical studies have been conducted for the effect of injected air bubbles on the heat transfer coefficient through the water flow in a vertical pipe under the influence of uniform heat flux. The investigated parameters were water flow rate of (10, 14 and 18) lit/min, air flow rate of (1.5, 3 and 4) lit/min for subjected heat fluxes of (27264, 36316 and 45398) W/m2. The energy, momentum and continuity equations were solved numerically to describe the motion of flow. Turbulence models k-ε was implemented. The mathematical model is using a CFD code Fluent (Ansys15). The water was used as continuous phase while the air was represented as dispersed. phase. The experimental work includes design, build and instrument a test
... Show MoreThe aim of this study is to compare the effects of three methods: problem-based learning (PBL), PBL with lecture method, and conventional teaching on self-directed learning skills among physics undergraduates. The actual sample size comprises of 122 students, who were selected randomly from the Physics Department, College of Education in Iraq. In this study, the pre- and post-test were done and the instruments were administered to the students for data collection. The data was analyzed and statistical results rejected null hypothesis of this study. This study revealed that there are no signifigant differences between PBL and PBL with lecture method, thus the PBL without or with lecture method enhances the self-directed learning skills bette
... Show MoreMethods of estimating statistical distribution have attracted many researchers when it comes to fitting a specific distribution to data. However, when the data belong to more than one component, a popular distribution cannot be fitted to such data. To tackle this issue, mixture models are fitted by choosing the correct number of components that represent the data. This can be obvious in lifetime processes that are involved in a wide range of engineering applications as well as biological systems. In this paper, we introduce an application of estimating a finite mixture of Inverse Rayleigh distribution by the use of the Bayesian framework when considering the model as Markov chain Monte Carlo (MCMC). We employed the Gibbs sampler and
... Show MoreThis work presents the study of the dark current density and the capacitance for porous silicon prepared by photo-electrochemical etching for n-type silicon with laser power density of 10mw/cm2 and wavelength (650nm) under different anodization time (30,40,50,60) minute. The results obtained from this study shows different chara that different characteristic of porous diffecteristics for the different porous Silicon layers.
This paper is concerned with the blow-up solutions of a system of two reaction-diffusion equations coupled in both equations and boundary conditions. In order to understand how the reaction terms and the boundary terms affect the blow-up properties, the lower and upper blow-up rate estimates are derived. Moreover, the blow-up set under some restricted assumptions is studied.