Shodhganga Collection:
http://hdl.handle.net/10603/14184
2020-04-07T22:56:51ZMathematical Modeling and Analysis of Various Flow Characteristics of Blood Through Stenosed Artery
http://hdl.handle.net/10603/277570
Title: Mathematical Modeling and Analysis of Various Flow Characteristics of Blood Through Stenosed Artery
Abstract: In this thesis, physiological problems related to blood flow from the field of Bio- fluid dynamics are investigated and the behavior of blood in cosine shaped and overlapping atherosclerotic artery using Herschel- Bulkley and Power- law non- Newtonian fluid model is studied. In this study, the constitutive equations of the models are solved analytically using the initial and boundary conditions to get expressions for different flow characteristics of blood such as flow rate, resistance to flow and wall shear stress and its variation are analyzed graphically. The graphs for these flow parameters are drawn using the MATLAB software and results are then discussed with the help of these graphs.
newlineTime Minimizing Solution Procedures for the Transportation Problem with Mixed Constraints
http://hdl.handle.net/10603/240039
Title: Time Minimizing Solution Procedures for the Transportation Problem with Mixed Constraints
Abstract: The present thesis focuses on the development of methodologies to find an optimal solution of Time Minimizing Transportation Problem with Mixed Constraints (TMTP-MC). To obtain an optimum transportation time of TMTP-MC, four methods are developed along with their algorithms.
newlineIn the first method, greatest time cells are avoided for allotment, one by one, in decreasing order of time till the feasibility sustains in the absence of avoided cells. Then, assignment of cells along with objective value, is the optimal solution.
newlineSecond method starts with a basic infeasible solution and moving towards a basic feasible solution by updating the basis iteratively. This basic feasible solution is an optimal solution of TMTP-MC.
newlineThird approach initiates with a basic feasible solution. A method for finding it, is exclusively developed. To improve that basic feasible solution, allotment of a basic cell with highest time, is shifted to a cell with lesser time than that. In this way, that cell is vacated to reduce the time of transportation. Shifting is made through an open loop initiated with that basic cell and terminated at the cell having lower time. After termination of shifting process, the solution in the transportation table is the optimal solution with corresponding shipment time.
newlineIn fourth method, some parameters are introduced to equality constraints of TMTP-MC to analyze the More-for-Less (MFL) paradoxical situation in it. Treating these parameters also as basic variables, a basic infeasible solution is obtained. By updating the basis of the solution iteratively, a basic solution is improved to obtain a basic feasible solution. This solution is the MFL solution, if at least one of the parameters remain in the basis at positive level. Otherwise, the MFL situation does not exist in the problem and the solution obtained is an optimal solution. Through MFL solution, an optimal solution of the problem can also be obtained.
newlineOptimizing Solution Procedures for the Transshipment Problem with Mixed Constraints
http://hdl.handle.net/10603/239967
Title: Optimizing Solution Procedures for the Transshipment Problem with Mixed Constraints
Abstract: The whole thesis is divided into six chapters
newlineIn the first chapter we have introduced the problem starting with classical transportation problem and shaped it in Mathematical model. It is shown that the model helps us to reduce the optimal transportation time of transportation problem with mixed constraints by allowing all the sources and destinations to act as trans-shippers in the transportation problem with mixed constraints. All the related problems which help directly or indirectly in solving it are also introduced together with its existence in the literature.
newlineIn the second chapter a primal method has been developed for solving the transshipment problem with mixed constraints. Methodology adopted here is to create an equivalent transportation problem with mixed constraints, then it is reconverted into a classical transportation problem. A span method has been developed for getting its solution. Through the solution of classical transportation problem, an optimal solution of the transshipment problem with mixed constraints is obtained.
newlineThird chapter is devoted to develop a method for the optimal solution of transshipment problem with mixed constraints .Transshipment problem is converted into an equivalent transportation problem with mixed constraints. Since the transportation problem with mixed constraints is a linear programming problem and every linear programming problem have their dual linear programming problem, so it is then converted into an equivalent dual transportation problem with mixed constraints. Its basic solution is obtained and improved to reach optimality. With the help of this optimal solution, the optimal solution of transshipment problem with mixed constraints is achieved.
newlineChapter four focuses on the development of a tabular method for solving the problem via converting its constraints into required constraints of Fourier Elimination Method form. The
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newlineobjective value is obtained by eliminating all the variables one by one using Fourier Elimination Method, values of the variables are obtained by back substitution method. Iterations are performed from table to table instead of set of equation to equation.
newlineIn chapter five, a zero suffix method has been developed for transshipment problem with mixed constraints. Transshipment problem with mixed constraints is directly converted into classical transportation problem. In the method, basic cells of classical transportation problem are located through the possible minimum cost cell for allotment. Minimum cost cell is located by subtracting the least element of all the rows and columns from all the elements of the corresponding rows and columns of the transportation table. At least one cells with zeros entries are created in each row and each column of transportation table. Suffix value of each zero is obtained. The cell with greatest suffix value is assigned and the row/column having exhausted rim requirements are deleted to get the reduced table. Continuing this process, optimal solution of classical transportation table is obtained. With the help of this optimal solution, the optimal solution of transshipment problem is achieved.
newlineChapter six deals with searching the possibility of reducing the optimal cost of transshipment problem with mixed constraints by increasing the rim requirements. If possible, then the corresponding solution is termed as more-for-less (more-for-same) solution. The situation is termed as more-for-less paradoxical situation. A method has been developed for finding more-for-less solution. In the process parameters corresponding to equal to type constraints are added on RHS and all the other constraints are converted into less than equal to type constraints, if needed multiplying by - sign. Introducing slack variables corresponding to each less than equal to type constraints and performing dual simplex iteration through simplex table gives the more-for- less (more-for-same) solution.
newlineStudy and Development of Hybrid Evolutionary Algorithms with Application to Socio Economic Systems
http://hdl.handle.net/10603/238941
Title: Study and Development of Hybrid Evolutionary Algorithms with Application to Socio Economic Systems
Abstract: newline