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.
numerical study is applied to the mercury-argon mixture by solving the boltzman transport equation for different mixture percentage.
There is of great importance to know the values of the optical constants of materials due to their relationship with the optical properties and then with their practical applications. For this reason, it was proposed to study the optical constants of amorphous silicon nanostructures (quantum well, quantum wire, and quantum dot) because of their importance in the world of optical applications. In this study, it was adopted the Herve and Vandamme (HV) model of the refractive index because it was found that this model has very good optical properties for almost all semiconductors. Also, it was carried out by applying experimental results for the energy gaps of these three nanostructures, which makes the results of the theoretical calculations
... Show MoreIraq has a range of small and large marshes, which can be divided into two groups, a group of marshes feeding water from the Tigris and Euphrates rivers, and a group of marshes fed by the seasonal valleys coming from the desert plateau and the aljazera plateau.
The marshes have go through major changes, some of them turning into industrial lakes to store the flood waters of the Tigris and Euphrates rivers. Others have been dried up and turned into agricultural land. Others have dried up and the water has been returned to them in less quantities than before.
The purpose of this research is to but light on the changes that have occurred in these marshes, with the mention of marshes turned into industrial lakes or agricultur
... Show MoreCeremony of the Koran vocabulary animate different connotations unique style patch on
smth not any method of Arabs, has been used used vocabulary and special Madza, he put
every single in place of installation so that if you do not put in place misfire meaning and
became Rkika method. Our goal in this research study a range of vocabulary in terms of the
implications and documenting the trial of the Hadith and sayings of the beneficiaries of Arab
scholars have different attitudes, linguists and interpreters and speakers and fundamentalists,
philosophers, and others.
It has mixed views on the concept or the role (Portrait) carving human faces across historical periods. The counting and historical document recording profiles for individual, promised impression represents promised impression represents the importance and greatness of personal without attention logs features and individual features, and in all cases the (portrait) was working for celebrated personality, glorifying and out of respect for his role heroic or reputation or social status.
But if we intend carving human faces one varieties of art in sculpture became necessary for us to proceed from the statement which affirms "The requirement of art to be liberated from their recovery forms as they are in the outside world" and here we beg
Individual mobility is an outcome of the rapid changes in life; it is revealed in particular literary works within the end of the 19th century. Mobility is clearer in modern time as the individual has become physically freer in his movement. But the individual’s freedom is often conditioned by restrictions. Usually, change stimulates individuals to obtain new structure of feeling; the individual mocks or rages against institutions, or he would comply, suffering rapid personal deterioration as he faces effective stability or institutions. There is a continuous sense of “deadlock.” Sylvia Plath’s novel reflects the depression of an intellectual young woman who fails to find her right path muddled by an inconsistent, confusing
... Show MoreThe geomorphological importance of studying the alluvial fan derives from the fact that
in enables us to know the Origin and development of such a phenomenon which cover a vast
area in different regions.
This study tackles the geomorphological development of Badra alluvial fan through
knowing the factors of its origin, development, form and their present area, by using the
climate hydrological In formation besides using topographic Maps and changes detection for
different years (1973 - 2013) from satellite images
In order to get an idea about things closely, we should look at the role of social discipline
in the building of society from civilization cultural viewpoint. The real weigh of the societal
opinion is not measured by the number of its population or its area but the real value lies in its
civilization cultural accumulative experience inherited by the generations, which determine its
distinguished character. That is based upon the social construction in which the methods of
socialization and political, economic, cultural and religious stability and enhance the national
and ethical character of self-realization.
In this research, we try to give an analysis for the obstacles in political economic and
religious social