Browsing by Subject "Mathematical analysis"
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Item A comparison of simulation methods with finite-difference and finite element methods for solving Vlasov-Poisson systems(Texas Tech University, 1986-08) Ho, Wai HungWe consider the one dimensional periodic Vlasov-Poisson equation and discuss various approximations. These include the particle-in-cell method, the upstream-downstream method (a finite element method) and the Lax-Wendroff method (a finite-difference method). The model considered as a test problem numerically simulates electrons moving over a fixed, uniform positive background when, as an initial condition for the electron distribution, a Maxwellian beam is imposed. Landau damping phenomena are observed for all approximation methods. Good agreements on charge conservation have been observed for both finite element and finite-difference methods for up to 12.5 plasma periods. Numerical experiments show that for very short plasma periods (e.g., 2 plasma periods) the total energy of a Vlasov plasma system is conserved with finite element methods; however, it is not well conserved at all for longer plasma periods. Nevertheless, with finite - difference methods energy conservation of the system satisfactorily holds for up to 10 plasma periods. Modification of mesh sizes and time steps shows that fine mesh sizes and small time steps can be used for reducing numerical diffusion effects. Based on different numerical results, we make a comparative study of finite element and finite-difference methods with particle - in - cell methods.Item A mathematical analysis of the musculo-skeletal system of the human shoulder joint(Texas Tech University, 1977-05) Park, Young-PilThe purpose of this study has been to formulate a mathematical model capable of predicting muscular tension characteristics for muscles in the human shoulder joint. This was done by using the data that were collected through dissection of a cadaver and through physiological information about human skeletal muscles and anatomical characteristics of the human shoulder joint. By using this method, the explicit characterization of the shoulder joint was described in terms of a three dimensional coordinate system. The mathematical equations for the relationships between the electrical signal intensities that are generated from the muscles, and muscular tensions that are exerted by muscles at various postures during abduction of the upper extremity were investigated. General equations that can be applied to various individual persons who have different anthropometric dimensions were developed by using scale factors. Computer programs were developed to determine the muscular tension in muscles in the shoulder joint of various persons and to predict the linear coefficients between electromyographic electrical signal intensities and the muscular tensions of the skeletal muscles. According to the results and the techniques of this study, it was determined that most of the complicated human musculo-skeletal systems can be analyzed mathematically without invasion of the living body.Item Mathematical analysis of equations in plasma physics(2009-12) White, Ryan Lee, 1982-; Hazeltine, R. D. (Richard D.); Morrison, PhilIn this paper, two equations from plasma physics are analyzed using two different mathematical procedures to yield information of interest for fusion energy. In the first case, Lie’s technique of computing symmetries of differential equations is applied to a specific case of the Grad-Shafranov equation. The case considered contains the majority of exact solutions from the literature. The full symmetry group is computed and new group-invariant solutions are obtained from these symmetries. The basic results and methods behind this technique are given along with several plots of the level sets or flux surfaces of the new solutions. In addition, a mathematical technique which was first used to prove the non-existence of solitons in quantum field theory is employed to derive an integral relation for any solution of the Sinh-Poisson equation. The original technique is modified to allow for a finite boundary and results are computed for two different boundary geometries.Item Properties of partial sums of certain special functions in complex variables(Texas Tech University, 1995-12) Wheeler, William AnthonyNOT AVAILABLE