Solution of the Synthesis Problem of Boundary Optimal Control of a Rod Cooling Process with a Heat Conductive Viscosity

The problem of synthesis of the boundary optimal control of the cooling process of media with heat conductive viscosity is investigated. In addition to the distributed parameters, the concentrated parameters act on the system. This is due to the fact that the temperature of the external environment is unknown and varies according to a given law. As a result, the process is described by a system of partial differential equations and ordinary differential equations. In this case, heat transfer occurs at the right end of the rod. This complicates the obtaining of a solution of this boundary-value problem in an explicit form. But it is possible to establish the existence and uniqueness of the solution of the corresponding boundary-value problem for concrete admissible controls.The criterion of quality is a quadratic functional and it is required to build control in the form of feedback. First by the Fourier method, the problem under consideration is formulated in an infinite-dimensional phase space. As a result, the problem of synthesis of optimal control in a functional space is obtained. To solve this problem, the dynamic programming method is used. To do this, let's introduce the Bellman functional and obtain the Bellman equation, which this functional satisfies. The solution of this equation allows to find the control parameter in the form of a functional defined on the set of the state function. Further, by introducing the corresponding functions, feedback control is constructed for the original problem. Unlike program control, this allows to influence the behavior of the system at any time, that is, to ensure the self-regulation of the process. However, let's note that the difficulties in solving this problem are connected with the justification of the proposed method. This is established by the investigation of a closed system

Essays in Socioeconomic Inequalities in Health and the Labor Market, with special Focus on Egypt

Inequalities in health are more worrying than disparities in most other spheres, as ill health hinders people from generating income and becoming part of daily life. This thesis is an attempt to gain a better understanding of socioeconomic inequalities in health in Egypt. It studies socioeconomic inequalities in health and education in Egypt from several angels. It consists of five research papers that contribute to the economic analysis of inequalities

A foundation for analytical developments in the logarithmic region of turbulent channels

An analytical framework for studying the logarithmic region of turbulent channels is formulated. We build on recent findings (Moarref et al., J. Fluid Mech., 734, 2013) that the velocity fluctuations in the logarithmic region can be decomposed into a weighted sum of geometrically self-similar resolvent modes. The resolvent modes and the weights represent the linear amplification mechanisms and the scaling influence of the nonlinear interactions in the Navier-Stokes equations (NSE), respectively (McKeon & Sharma, J. Fluid Mech., 658, 2010). Originating from the NSE, this framework provides an analytical support for Townsend's attached-eddy model. Our main result is that self-similarity enables order reduction in modeling the logarithmic region by establishing a quantitative link between the self-similar structures and the velocity spectra. Specifically, the energy intensities, the Reynolds stresses, and the energy budget are expressed in terms of the resolvent modes with speeds corresponding to the top of the logarithmic region. The weights of the triad modes -the modes that directly interact via the quadratic nonlinearity in the NSE- are coupled via the interaction coefficients that depend solely on the resolvent modes (McKeon et al., Phys. Fluids, 25, 2013). We use the hierarchies of self-similar modes in the logarithmic region to extend the notion of triad modes to triad hierarchies. It is shown that the interaction coefficients for the triad modes that belong to a triad hierarchy follow an exponential function. The combination of these findings can be used to better understand the dynamics and interaction of flow structures in the logarithmic region. The compatibility of the proposed model with theoretical and experimental results is further discussed.Comment: Submitted to J. Fluid Mec

Evaluation of a power driven residue manager for no-till drills

The main operational problem in direct drilling of paddy straw residue is the accumulation and wrapping of loose straw within/on the tines and frame of no-till drills and traction problems with the ground wheel. A residue management equipment (RME) is developed to cut and remove paddy straw away from furrow openers of the no-till drill. The equipment consisted of nine parts; each part consisted of two powered wheels, one wheel for cutting the residue and the other wheel for removing them away from no-till drill furrow openers. This equipment was attached with the no-till drill with inverted "T" type furrow opener and the experiments have been conducted to compare the no-till drill with RME and same no-till drill without RME. No-till drill with RME increased the fuel consumption and time required by 29.6 % and 13.14 %, respectively. Adding RME to the no-till drill decreased the amount of residue clogged by 33% and increased the percentage of cut hill from 14.9 to 63.7%. The average numbers of effective tiller, spike length and plant heights were more for no-till drill with RME. Furthermore, the grain yield was increased by 12.4% for fields with no-drill with RME