The relative accuracy of solutions to chaotic systems was examined using the Lorenz
system as a case study. The classical fourth order Runge-Kutta method was employed to
generate solutions using various step sizes, and the resultant solutions were compared. A
second set of solutions was then computed using one of...
The complexity of numerical ocean circulation models requires careful checking with a variety of test problems. The purpose of this paper is to develop a test problem involving Rossby and gravity waves in a two-layer fluid in a channel. The goal is to compute very accurate solutions to this test...
In this paper, Fourier analysis is used to
investigate various approximation methods for the one- and
two-dimensional wave equations. The spatial derivatives
are approximated by the second order centered finite
difference method, the linear and quadratic finite element
methods, and the fourth order centered finite difference
method. The approximation schemes...
This paper addresses some issues involving the application of discontinuous Galerkin (DG) methods to ocean circulation models having a generalized vertical coordinate. These issues include the following. (1) Determine the pressure forcing at cell edges, where the dependent variables can be discontinuous. In principle, this could be accomplished by solving...
This paper is part of an effort to examine the application of discontinuous Galerkin (DG) methods to the numerical modeling of the general circulation of the ocean. One step performed here is to develop an integral weak formulation of the lateral pressure forcing that is suitable for usage with a...
While replacement of dietary saturated fat with unsaturated fat has been advocated
to reduce cardiovascular disease risk, diets high in polyunsaturated fatty acids
(PUFA) could increase low density lipoprotein (LDL) susceptibility to oxidation,
potentially contributing to the pathology of atherosclerosis. To assess in vivo lipid
peroxidation and susceptibility, of LDL...
This thesis advocates the use of maximum likelihood analysis for generalized
regression models with measurement error in a single explanatory variable. This will be
done first by presenting a computational algorithm and the numerical details for carrying
out this algorithm on a wide variety of models. The computational methods will...
Numerical model and assimilation experiments were conducted in the tropical Pacific Ocean to obtain a better understanding of the processes that control the cold tongue surface mixed layer temperature balance during August 1999 to July 2004. The numerical model was first applied to test two hypotheses (asymmetric background currents and...
This paper explores some optimization methods such as the gradient descent method, Gauss-Newton method, and stochastic gradient method. Some examples of minimizing objective functions are given to validate the theories. Then we introduce a simple example of artificial neural networks, define its structure, and apply the optimization methods to it....