Some aspects of measured and estimated evaporation in the Sudan

The present work analyses, for the Sudan, the methods of evaporation measurement by Piche evaporimeter and Clas ‘A' pan, together with the estimation of open-water evaporation (EO) from Penman's formula (1948) and potential evapotranspiration (PE) by Thornthwaite's method (1948). Measured Class 'A' pan and Piche evaporation tend to follow similar fluctuations during the various seasons. Monthly and seasonal fluctuations of the measured water loss are large compared with the computed evaporation which displays limited variations. During the dry season, measured evaporation is greater than the computed, but, in the wet season, the measured values are slightly exceeded by the (PE) and even more so by the (EO). Regression analysis shows a close correlation between measured and computed evaporation at some stations in northern Sudan where the correlation coefficients are large (over 0.70). At some stations in central and southern Sudan the correlation coefficients are low (under 0.50), and the correlation is rather poor and may not be statistically significant. In a comparative study between Penman's (EO) and Thornthwaite's (PE), the former usually gives larger values than the latter. But the disparity between them is relatively small in the dry season. The final aspect of the thesis discusses the distribution of average annual, seasonal and monthly Piche evaporation over the Sudan. Annual values reveal a steady decrease from north to south, and evaporation isolines seem to run roughly along latitudes from east to west. This pattern of isolines is interrupted by the uplands of Jebel Marra, the Red Sea hills, and Nuba mountains where evaporation tends to decrease with high altitudes

Numerical approximation of the Boltzmann equation : moment closure

This work applies the moment method onto a generic form of kinetic equations to simplify kinetic models of particle systems. This leads to the moment closure problem which is addressed using entropy-based moment closure techniques utilizing entropy minimization. The resulting moment closure system forms a system of partial differential equations that retain structural features of the kinetic system in question. This system of partial differential equations generate balance laws for velocity moments of a kinetic density that are symmetric hyperbolic, implying well-posedness in finite time. In addition, the resulting moment closure system satisfies an analog of Boltzmann's H-Theorem, i.e. solutions of the moment closure system are entropy dissipative. Such a model provides a promising alternative to particle methods, such as the Monte Carlo approaches, which can be prohibitive with regard to computational costs and inefficient with regard to error decay. However, several challenges pertaining to the analytical formulation and computational implementation of the moment closure system arise that are addressed in this work. The entropy minimization problem is studied in light of the classical results by Junk [18] showing that this technique suffers from a realizability problem, i.e. there exists realizable moments such that the entropy minimizer does not exist. Recent results by Hauck [17], Schneider [31] and Pavan [29] are used to investigate and circumvent this issue. The resulting moment closure system involves moments of exponentials of polynomials of, in principle, arbitrary order. In the context of numerical approximations, this is regarded as a complication. A novel and mathematically tractable moment system is developed that is based on approximating the entropy minimizing distribution. It will be shown that the resulting system retains the same structural features of the kinetic system in question. This system can be seen as a refinement of Grad's original moment system [15, 32]. Finally, a numerical approximation of the resulting moment systems is devised using discontinuous Galerkin (DG) finite elements method. Energy analysis based on the work of Barth [1, 2] is employed to investigate energy stable numerical flux functions to be used for the DG discretization of the moment systems. In contrast to the work of Barth [1], the numerical flux function suggested for the tractable system does not require a simplified construction since it is computable. In addition, higher order (approximated) moment systems, beyond the 10-moment system investigated by Barth [1], can be considered

Numerical approximation of the Boltzmann equation : moment closure

This work applies the moment method onto a generic form of kinetic equations to simplify kinetic models of particle systems. This leads to the moment closure problem which is addressed using entropy-based moment closure techniques utilizing entropy minimization. The resulting moment closure system forms a system of partial differential equations that retain structural features of the kinetic system in question. This system of partial differential equations generate balance laws for velocity moments of a kinetic density that are symmetric hyperbolic, implying well-posedness in finite time. In addition, the resulting moment closure system satisfies an analog of Boltzmann's H-Theorem, i.e. solutions of the moment closure system are entropy dissipative. Such a model provides a promising alternative to particle methods, such as the Monte Carlo approaches, which can be prohibitive with regard to computational costs and inefficient with regard to error decay. However, several challenges pertaining to the analytical formulation and computational implementation of the moment closure system arise that are addressed in this work. The entropy minimization problem is studied in light of the classical results by Junk [18] showing that this technique suffers from a realizability problem, i.e. there exists realizable moments such that the entropy minimizer does not exist. Recent results by Hauck [17], Schneider [31] and Pavan [29] are used to investigate and circumvent this issue. The resulting moment closure system involves moments of exponentials of polynomials of, in principle, arbitrary order. In the context of numerical approximations, this is regarded as a complication. A novel and mathematically tractable moment system is developed that is based on approximating the entropy minimizing distribution. It will be shown that the resulting system retains the same structural features of the kinetic system in question. This system can be seen as a refinement of Grad's original moment system [15, 32]. Finally, a numerical approximation of the resulting moment systems is devised using discontinuous Galerkin (DG) finite elements method. Energy analysis based on the work of Barth [1, 2] is employed to investigate energy stable numerical flux functions to be used for the DG discretization of the moment systems. In contrast to the work of Barth [1], the numerical flux function suggested for the tractable system does not require a simplified construction since it is computable. In addition, higher order (approximated) moment systems, beyond the 10-moment system investigated by Barth [1], can be considered

New representations for weighted Drazin inverse of matrices

In this paper, the result are established in the following four ways: First, we present a general representation for the weighted Drazin inverse Ad,W of an arbitrary rectangular matrix A ∈ Mm,n involving Moore-Penrose inverse, which reduces to the well-known result if the matrix A is a square and W = In . Second, we find represenations for the weighted Drazin inverse of the Tracy-Singh product A B of the two matrices A ∈ Mm,n and B ∈ Mp,q by using our approach. Third,the results are extended to the case of Tracy-Singh product of any finite number of matrices.The result lead to equalities involving Kronecker product, Drazin inverse and group inverse, as a special case. Finally,We apply our result to present the solution of restricted singular matrix equations

Isothermal and Thermal Analyses of Elastohydrodynamic Lubrication of Hard Rolling Contact

In the field of industrial tribology, elastohydrodynamic lubrication (EHL) is a comparatively recent area of research. It only became properly established in the early 1960s. EHL of rolling contact is mainly divided to two phases (soft and hard), depending on the elasticity modulus of the material in contact. Hard rolling which relates to materials of high modulus of elasticity e.g. metal, is the part of interesting the present study. The f1rst objective of the research is to study the elastohydrodynamic rolling line contact. lubr1cat1on problem of hard Second is to investigate the isothermal and thermal conditions for EHL in hard rolling system. The contact geometry of the rolling process was specified as a line contact. An in compressible fluid flows in to the system. Under both isothermal and thermal conditions, a Newton1an lubricant was descr1bed. Two different widely used lubricants were tested. First, is a mineral Naphthenic (TN22) and the second is asynthetic Cycloaliphatic (ST40). It is assumed that two rollers of equal radius are moving relatively with same speed on a plane of d1fferent velocity. Two coord1nate axe s were considered (x and y). The parameters and conditions of controlling the system of contact are theoretically selected to match the practical field situations. Newton-Raphson and the finite difference methods were represented in the mathematical technique used for computations

Role of Interactive infographics in the Interior design of contemporary museums

This research is an interdisciplinary study exploring the role of infographics and interactive displays in the interior design of museums, showing the impact of new technologies on the process of delivering information and exploring newfangled ways to deliver the interactive experience in developing and promoting new learning techniques. With an intensive focus on the different types of infographics and interactive displays through the exposure to diverse applications and models supporting the creative design ideas, considering it a space for engagement, discovery, learning and playing. Finally, the study emphasized the importance of linking the various disciplines in the design process leading to a successful and integrated design to contribute in sharing knowledge across the world

Official Political Institutions and Party System in the Kingdom of Belgium

استطاعت مملكة بلجيكا أن تحقق استقراراً سياسياً على الرغم من وجود تنوع وتعدد معقد جداً (ديني وثقافي وعرقي واثني ولغوي واقليمي)، إنّ أخذ المملكة بالنموذج الفيدرالي كأسلوب في الادارة  والعمل بالنظام اللا مركزي وتوزيع السلطات عزّز من مبدأ المشاركة في صنع القرار وتحقيق التوازنات بين الأقاليم والتجمعات والعمل ضمن كيان سياسي موحد، قضت من خلالها على الانشقاقات والصراعات التي عرفت بها بلجيكا منذ بداية نشأتها، فضلاً عن الأخذ بمبدأ الديمقراطية التوافقية الذي ساعد بشكل كبير في وجود تحالفات واسعة وتوازن سياسي أدى إلى احتواء الأزمات اللغوية والقومية التي طالما هدّدت استقرارها ووحدتها الوطنية، ومع الأخذ بمبدأ التمثيل النسبي للأقلّيات والعرقيات أسهم بشكل اساس على التداول السلمي للسلطة التي كانت أحد الأسس المهمة في الاستقرار السياسي للنظام السياسي في مملكة بلجيكا.The Kingdom of Belgium was able to achieve political stability despite the existence of a very complex diversity (religious, ethnic, and linguistic). The Kingdom's adoption of the federal model as a method of administration and the decentralization of the authorities strengthened the principle of participation in decision-making and balancing between regions, Political process, through which it resolved the splits and conflicts that have been known to Belgium since the beginning of its inception, as well as the principle of democratic consensus, which helped significantly in the existence of alliances and wide led to contain crises language and nationalism, which has long threatened the stability and unity And taking into account the principle of proportional representation of minorities and ethnic groups, was based mainly on the peaceful transfer of power, which was one of the important foundations for the political stability of the political system in the Kingdom of Belgium