nary differential equations, fictitious time integration method (FTIM), modified Newton method (MNM). The Newton algorithm based on the “continuation ” method may be written as being governed by the equation ()jx t + 1 ( ) 0,ij i jB F x − = where Fi (xj) = 0, i, j = 1, …n are nonlinear algebraic

on triangular elements. The time integration is based on backward difference formulas resulting in a nonlinear system of equations which is solved at each timestep. This is accomplished using Newton’s method. The resulting linear systems are solved using a preconditioned GMRES itera-tive algorithm. We consider

Dyson-Schwinger equations are important tools for non-perturbative analyses of quantum field theories. For example, they are very useful for investigations in quan-tum chromodynamics and related theories. However, sometimes progress is impeded by the complexity of the equations. Thus automatizing

The recent discovery of dark energy has prompted an investigation of ways in which the accelerated expansion of the universe can be realized. In this dissertation, we present two separate projects related to dark energy. The first project analyzes a class of braneworld models in which multiple branes float in a five-dimensional anti-de Sitter bulk, while the second investigates a class of dark energy models from an effective field theory perspective. Investigations of models including extra dimensions have led to modifications of gravity involving a number of interesting features. In particular, the Randall-Sundrum model is well-known for achieving an amelioration of the hierarchy problem. However, the basic model relies on Minkowski branes and is subject to solar system constraints in the absence of a radion stabilization mechanism. We present a method by which a four-dimensional low-energy description can be obtained for braneworld scenarios, allowing for a number of generalizations to the original models. This method is applied to orbifolded and uncompactified N-brane models, deriving an effective four-dimensional action. The parameter space of this theory is constrained using observational evidence, and it is found that the generalizations do not weaken solar system constraints on the original model. Furthermore, we find that general

This is a preliminary version of a Chapter on Algebraic Algorithms in the up-

Hamilton equation based symplectic nite element

the training of the ANNs, which is a feedforward and supervised learning algorithm. Adaptive gradient and Kalman’s learning rules were used to modify the artificial neural networks weights. Kalman’s learning rule was found superior for the estimation of diameter values at certain heights of the tree-bole. The

integrator wind-up and, therefore, it is recommended that separate weighting be used with a modified integrating component predictive controller. The separate weighting also improves the designers intuition with respect to tuning the controller, significantly reducing the time required to generate

was introduced for microwave imaging in 1997 and has since proven to be one of the most successful algorithms for nonlinear microwave tomography. In the CSI algorithm, the nonlinear integral equation, which must be solved to extract the constitutive electromagnetic parameters of the object under test from

Abstract not found