Complex Singularity Of Stretch-Twist-Fold System And Mathematical Application Of Nuclear Reactor

The research is consisted primarily on constructing various plausible fast dynamosby employing approximate techniques where applicable, and testing them by numericalsimulation. The Stretch-Twist-Fold flow (STF) is a three-dimensional (3D) system ofordinary differential equations (ODE) with quadratic nonlinearities. This mathematicalsystem is related with aerospace engineering and its application is in satellite fuel tank.Due to the complex singularity of this system, limited literature is available. A naturalstarting point for a dynamo theory assumes the fluid motion to be a given vector field,without regard for the origin of the forces which drive it.During recent years, it has been realized that a very singular limit of smalldiffusion or large magnetic Reynolds number is the feasible choice for most of theproblems. The some big problems are, how fast dynamos might work? What would bethe stable and instable position of this system? Is there having any safety to protect thissystem? Is it possible to make new system with same characteristics? What is the bestmathematical modeling and method is perfect for this system? In this research, we havebeen successfully deal with these problems.In this dissertation, the modifiedAdomian’s decomposition method (ADM) andfifth order Runge-Kutta method (RK5) have been applied to the STF system. Acomputer based Matlab program has been developed in order to solve the chaotic andnon-chaotic behavior of this system. It depends upon the positive or not of Lyapunovexponent. Newton’s method was applied to show the best convergence. Furthermore,we investigate an external force that is applied on the STF system and analyze thebehavior of control parameter with theoretical details.The research is also conducted on the mathematical modeling of nuclear reactoranalysis by using specialized nuclear reactor codes. In this work, we have developed amathematical model for thermal hydraulic analysis of nuclear reactor core. Thismodified nuclear code is applicable to the thermal analysis of the reactor which is veryimportant to determine the design of the reactor. It can produce desired thermal powerwithout exceeding limitations on core components which may leads to fuel failure andradioactive release into the environment. THEATRe code can only work for thecylindrical type fuel reactor and cannot work for the plate type fuel nuclear reactor.Therefore, THEATRe code has been modified for the plate type fuel element and then utilize in the current research. The result obtained from modified code agrees well withother codes conforming the accuracy of simulation.