Mathematics Copyright (c) 2013 California Polytechnic State University All rights reserved. http://digitalcommons.calpoly.edu/mathsp Recent documents in Mathematics en-us Fri, 25 Jan 2013 18:33:18 PST 3600 Analysis of ROMS Estimated Posterior Error Utilizing 4DVAR Data Assimilation http://digitalcommons.calpoly.edu/mathsp/4 http://digitalcommons.calpoly.edu/mathsp/4 Mon, 13 Jun 2011 16:39:33 PDT The appropriateness of the approximate error calculated by the Regional Ocean Modeling System (ROMS) is analyzed using Four-Dimensional Data Assimilation (4DVAR) performed on a numerical model of the San Luis Obispo Bay. An effective method of sampling data to minimize the actual error associated with the assimilated numerical model is explored by using different data sampling methods. An idealized state of the SLO bay region ("Real Run") is created to be used as the real ocean, then a numerical model of this region is created approximating this Real Run; this is known as the "Simulated State". By taking samples from the Real Run then running 4DVAR on the Simulated State using this input, the exact error of the assimilation step is compared directly with the Real Run using the Assimilated State. Once the exact errors are determined, comparison between the exact error and the estimated error calculated by ROMS is used to evaluate the appropriateness of 4DVAR on the sample region.

]]> Joseph Patrick Horton Completeness of Ordered Fields http://digitalcommons.calpoly.edu/mathsp/3 http://digitalcommons.calpoly.edu/mathsp/3 Thu, 20 Jan 2011 10:56:55 PST The main goal of this project is to prove the equivalency of several characterizations of completeness of Archimedean ordered fields; some of which appear in most modern literature as theorems following from the Dedekind completeness of the real numbers, while a couple are not as well known and have to do with other areas of mathematics, such as nonstandard analysis.

Continuing, we study the completeness of non-Archimedean fields, and provide several examples of such fields with varying degrees of properties, using nonstandard analysis to produce some relatively "nice" (in particular, they are Cantor complete) final examples.

As a small detour, we present a short construction of the real numbers using methods from nonstandard analysis.

]]> James Forsythe Hall Exact Solutions for Wind-Driven Coastal Upwelling and Downwelling over Sloping Bathymetry http://digitalcommons.calpoly.edu/mathsp/2 http://digitalcommons.calpoly.edu/mathsp/2 Wed, 29 Sep 2010 14:57:23 PDT The dynamics of wind-driven coastal upwelling and downwelling are studied using a simpli fied dynamical model. Exact solutions are examined as a function of time and over a family of sloping bathymetries. Assumptions in the two-dimensional model include a frictionless ocean interior below the surface Ekman layer, and no alongshore dependence of the variables; however, dependence in the cross-shore and vertical directions is retained. Additionally, density and alongshore momentum are advected by the cross-shore velocity in order to maintain thermal wind. The time-dependent initial-value problem is solved with constant initial strati cation and no initial alongshore flow. An alongshore pressure gradient is added to allow the cross-shore flow to be geostrophically balanced far from shore. Previously, this model has been used to study upwelling over flat-bottom and sloping bathymetry, but the novel feature in this work is the discovery of exact solutions for downwelling. These exact solutions are compared to numerical solutions from a primitive-equation ocean model, based on the Princeton Ocean Model, confi gured in a similar two-dimensional geometry. Many typical features of the evolution of density and velocity during downwelling are displayed by the analytical model

]]> Dana Lynn Duke et al. Knowing When to Say When: An Expanded Description of Stopping Problems and Their Solutions http://digitalcommons.calpoly.edu/mathsp/1 http://digitalcommons.calpoly.edu/mathsp/1 Thu, 06 May 2010 08:11:21 PDT Eric C. Bauer