by Lui Hung Ngai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 56-[59]). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Thesis Overview --- p.3 / Chapter 2 --- Background & Related work --- p.4 / Chapter 2.1 --- Scheduling problem in ATM switch --- p.4 / Chapter 2.2 --- Traffic Scheduling in output-buffered switch --- p.5 / Chapter 2.3 --- Traffic Scheduling in Input buffered Switch --- p.16 / Chapter 3 --- Deadline-ordered Parallel Iterative Matching (DLPIM) --- p.22 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Switch model --- p.23 / Chapter 3.3 --- Deadline-ordered Parallel Iterative Matching (DLPIM) --- p.24 / Chapter 3.3.1 --- Motivation --- p.24 / Chapter 3.3.2 --- Algorithm --- p.26 / Chapter 3.3.3 --- An example of DLPIM --- p.28 / Chapter 3.4 --- Simulation --- p.30 / Chapter 4 --- DLPIM with static scheduling algorithm --- p.41 / Chapter 4.1 --- Introduction --- p.41 / Chapter 4.2 --- Static scheduling algorithm --- p.42 / Chapter 4.3 --- DLPIM with static scheduling algorithm --- p.48 / Chapter 4.4 --- An example of DLPIM with static scheduling algorithm --- p.50 / Chapter 5 --- Conclusion --- p.54 / Bibliography --- p.56

by Wan-Lung Ng. / Thesis submitted in: November 1997. / On added t.p.: January 19, 1998. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 114-119). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview --- p.1 / Chapter 1.2 --- Organization Outline --- p.5 / Chapter 2 --- Literature Review --- p.7 / Chapter 2.1 --- Modern Portfolio Theory --- p.7 / Chapter 2.1.1 --- Mean-Variance Model --- p.9 / Chapter 2.1.2 --- Setting-up the relationship between the portfolio and its component securities --- p.11 / Chapter 2.1.3 --- Identifying the efficient frontier --- p.12 / Chapter 2.1.4 --- Selecting the best compromised portfolio --- p.13 / Chapter 2.2 --- Stochastic Optimal Control --- p.17 / Chapter 2.2.1 --- Dynamic Programming --- p.18 / Chapter 2.2.2 --- Dynamic Programming Decomposition --- p.21 / Chapter 3 --- Multiple Period Portfolio Analysis --- p.23 / Chapter 3.1 --- Maximization of Multi-period Consumptions --- p.24 / Chapter 3.2 --- Maximization of Utility of Terminal Wealth --- p.29 / Chapter 3.3 --- Maximization of Expected Average Compounded Return --- p.33 / Chapter 3.4 --- Minimization of Time to Reach Target --- p.35 / Chapter 3.5 --- Goal-Seeking Investment Model --- p.37 / Chapter 4 --- Multi-period Mean-Variance Analysis with a Riskless Asset --- p.40 / Chapter 4.1 --- Motivation --- p.40 / Chapter 4.2 --- Dynamic Mean-Variance Analysis Formulation --- p.43 / Chapter 4.3 --- Auxiliary Problem Formulation --- p.45 / Chapter 4.4 --- Efficient Frontier in Multi-period Portfolio Selection --- p.53 / Chapter 4.5 --- Obseravtions --- p.58 / Chapter 4.6 --- Solution Algorithm for Problem E (w) --- p.62 / Chapter 4.7 --- Illstrative Examples --- p.63 / Chapter 4.8 --- Verification with Single-period Efficient Frontier --- p.72 / Chapter 4.9 --- Generalization to Cases with Nonlinear Utility Function of E (xT) and Var (xT) --- p.75 / Chapter 5 --- Dynamic Portfolio Selection without Risk-less Assets --- p.84 / Chapter 5.1 --- Construction of Auxiliuary Problem --- p.88 / Chapter 5.2 --- Analytical Solution for Efficient Frontier --- p.89 / Chapter 5.3 --- Reduction to Investment Situations with One Risk-free Asset --- p.101 / Chapter 5.4 --- "Multi-period Portfolio Selection via Maximizing Utility function U(E {xT),Var (xT))" --- p.103 / Chapter 6 --- Conclusions and Recommendations --- p.108 / Chapter 6.1 --- Summaries and Achievements --- p.108 / Chapter 6.2 --- Future Studies --- p.110 / Chapter 6.2.1 --- Constrained Investment Situations --- p.110 / Chapter 6.2.2 --- Including Higher Moments --- p.111

Newton's method is at the core of many algorithms used for solving nonlinear equations. A globalized Newton method is an implementation of Newton's method augmented with ``globalization procedures' intended to enhance the likelihood of convergence to a solution from an arbitrary initial guess. A Newton-GMRES method is an implementation of Newton's method in which the iterative linear algebra method GMRES is used to solve approximately the linear system that characterizes the Newton step. A globalized Newton-GMRES method combines both globalization procedures and the GMRES scheme to develop robust and efficient algorithms for solving nonlinear equations. The aim of this project is to describe the development of some globalized Newton-GMRES methods and to compare their performances on a few benchmark fluid flow problems.

Thesis. 1976. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / Microfiche copy available in Archives and Aero. / Bibliography: leaf 90. / by Thomas J. Fill. / M.S.

Orientador: Denis Dalmazi / Coorientador: Álvaro de Souza Dutra / Banca: Julio Marny Hoff da Silva / Banca: Rafael Augusto Couceiro Corrêa / Resumo: Certos sistemas físicos podem ser descritos por uma classe de equações não-lineares. Essas equações descrevem pacotes de onda chamado de sólitons que tem aplicações em diversas áreas, por exemplo, Óptica, Cosmologia, Matéria Condensada e Física de Partículas. Alguns métodos foram desenvolvidos ao longo dos anos para encontrar as soluções dessas equações. Buscaremos essas soluções usando o que chamamos de Método Iterativo de Taylor (MIT), que fornece uma solução aproximada em polinômio de Taylor de forma distinta do que se tem na literatura. Usaremos o MIT para calcular soluções por aproximantes de Padé que são razões entre dois polinômios e fornecem soluções melhores que o polinômio de Taylor que o gerou. Inicialmente resolveremos a equação de um modelo de um campo denominado λφ4 . Em seguida resolveremos um modelo com dois campos escalares acoplados e encontraremos uma solução analítica aproximada em casos onde não existe solução analítica, explorando a diversidade das soluções do modelo. Usando essa abordagem por aproximantes de Padé veremos que há algumas vantagens em relação a outros métodos / Abstract: Certain physical systems can be described by a class of non-linear differential equations. Those equations describe wave packets called solitons which have applications in several areas, for example, Optics, Cosmology, Condensed Matter, and Particle Physics. Some methods have been developed over the years to find solutions to these equations. We will look for those solutions using what we call the Taylor Iterative Method (TIM), which provides an approximate solution in terms of a Taylor's polynomial in a unusual way, regarding the present literature. We will use TIM to calculate solutions by Padé approximants, which are ratios between two polynomials and provide better solutions than the Taylor polynomial itself. We first solve the field equation of a model called λφ4 . Then we will solve a model with two coupled scalar fields and find an approximate analytic solution in cases where there is no known analytical solution, exploring the diversity of the solutions of the model. We will see that there are some advantages in using the Padè approximants as compared to other methods / Mestre

For over 30 years, the Implicit Monte Carlo (IMC) method has been used to solve challenging problems in thermal radiative transfer. These problems are typically optically thick and di ffusive, as a consequence of the high degree of "pseudo-scattering" introduced to model the absorption and reemission of photons from a tightly-coupled, radiating material. IMC has several well-known features which could be improved: a) it can be prohibitively computationally expensive, b) it introduces statistical noise into the material and radiation temperatures, which may be problematic in multiphysics simulations, and c) under certain conditions, solutions can be unphysical and numerically unstable, in that they violate a maximum principle - IMC calculated temperatures can be greater than the maximum temperature used to drive the problem. We have developed a variant of IMC called "iterative thermal emission" IMC, which is designed to be more stable than IMC and have a reduced parameter space in which the maximum principle is violated. ITE IMC is a more implicit method version of the IMC in that it uses the information obtained from a series of IMC photon histories to improve the estimate for the end of time-step material temperature during a time step. A better estimate of the end of time-step material temperature allows for a more implicit estimate of other temperature dependent quantities: opacity, heat capacity, Fleck Factor (probability that a photon absorbed during a time step is not reemitted) and the Planckian emission source. The ITE IMC method is developed by using Taylor series expansions in material temperature in a similar manner as the IMC method. It can be implemented in a Monte Carlo computer code by running photon histories for several sub-steps in a given time-step and combining the resulting data in a thoughtful way. The ITE IMC method is then validated against 0-D and 1-D analytic solutions and compared with traditional IMC. We perform an in finite medium stability analysis of ITE IMC and show that it is slightly more numerically stable than traditional IMC. We find that significantly larger time-steps can be used with ITE IMC without violating the maximum principle, especially in problems with non-linear material properties. We also compare ITE IMC to IMC on a two-dimensional, orthogonal mesh, x-y geometry problem called the "crooked pipe" and show that our new method reproduces the IMC solution. The ITE IMC method yields results with larger variances; however, the accuracy of the solution is improved in comparison with IMC, for a given choice of spatial and temporal grid. / Graduation date: 2013

by Dimitri P. Bertsekas. / Bibliography: leaf 15. / "August 1981." / Partial support provided by the Defense Advanced Research Projects Agency under Grant no. ONR-N00014-75-C-1183

The solution of coupled neutronic/thermal hydraulic nuclear reactor calculations requires the treatment of the nonlinear feedback induced by the thermal hydraulic dependence of the neutron cross sections. As a result of these nonlinearities, current solution techniques often diverge during the iteration process. These instabilities arise due to the low level of coupling achieved by these methods between the neutronic and thermal hydraulic components. In this work, this solution method is labeled the Decoupled Iteration (DI) method, and this technique is examined in an effort to improve its efficiency and stability. An examination of the DI method also serves to provide insight into the development of more highly coupled iteration methods. After the examination of several possible iteration procedures, two techniques are developed which achieve both a higher degree of coupling and stability. One such procedure is the Outer Iteration Coupling (OIC) method, which combines the outer iteration of the multigroup diffusion calculation with the controlling iteration of the thermal hydraulic calculations. The OIC method appears to be stable for all cases, while maintaining a high level of efficiency. Another iteration procedure developed is the Modified Axial Coupling (MAC) procedure, which couples the neutronic and thermal hydraulic components at the level of the axial position within the coolant channel. While the MAC method does achieve the highest level of coupling and stability, the efficiency of this technique is less than that of the other methods examined. Several characteristics of these coupled calculation methods are examined during the investigation. All methods are shown to be relatively insensitive to thermal hydraulic operating conditions, while the dependence upon convergence criteria is quite significant. It is demonstrated that the DI method does not converge for arbitrarily small convergence criteria, which is a result of a non-asymptotic solution approximation by the DI method. This asymptotic quality is achieved in the coupled methods. Thus, not only do the OIC and MAC techniques converge for small values of the relevant convergence criteria, but the computational expense of these methods is a predictable function of these criteria. The degree of stability of the iterative techniques is enhanced by a higher level of coupling, but the efficiency of these methods tends to decrease as a higher degree of coupling is achieved. This is apparent in the diminished efficiency of the MAC procedure. Seeking an optimum balance of efficiency and stability, the OIC technique is demonstrated to be the optimum method for coupled neutronic/thermal hydraulic reactor calculations. / Graduation date: 1994

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 105-112). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2003. / Typescript. Vita. Includes bibliographical references (leaves 105-112). Also available on the Internet.