@article{yin_fitzpatrick_yin_1999, title={Empirical distribution for linear system identification}, volume={17}, ISSN={["0736-2994"]}, DOI={10.1080/07362999908809601}, abstractNote={Asymptotic properties of empirical distributions of approximate errors for least squares identification are developed in this work. As a preparation, it is first shown that a law of large numbers type of result holds for the empirical distribution. Then a scaled sequence is proved to converge to a Gaussian process with a Brownian bridge component. These results are useful for carrying out statistical inference tasks, goodness of fit tests, and related matters}, number={2}, journal={STOCHASTIC ANALYSIS AND APPLICATIONS}, author={Yin, G and Fitzpatrick, BG and Yin, K}, year={1999}, month={Mar}, pages={295–313} }
@article{butera_fitzpatrick_wypasek_1998, title={Dispersion modeling and simulation in subsurface contaminant transport}, volume={8}, ISSN={["0218-2025"]}, DOI={10.1142/S0218202598000548}, abstractNote={ In this paper, we examine three separate approaches to analyze the spatial dispersion of a subsurface contaminant. These methods are contrasted against traditional models to demonstrate their feasibility and usefulness. Lastly, numerical simulations illustrate the effectiveness of these approaches. }, number={7}, journal={MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES}, author={Butera, JV and Fitzpatrick, BG and Wypasek, CJ}, year={1998}, month={Nov}, pages={1183–1197} }
@article{ackleh_fitzpatrick_1997, title={Modeling aggregation and growth processes in an algal population model: Analysis and computations}, volume={35}, ISSN={["0303-6812"]}, DOI={10.1007/s002850050062}, abstractNote={Aggregation, the formation of large particles through multiple collision of smaller ones is a highly visible phenomena in oceanic waters which can control material flux to the deep sea. Oceanic aggregates more than 1 cm in diameter have been observed and are frequently described to consist of phytoplankton cells as well as other organic matter such as fecel pellets and mucus nets from pteropods. Division of live phytoplankton cells within an aggregate can also increase the size of aggregate (assuming some daughter cells stay in the aggregate) and hence could be a significant factor in speeding up the formation process of larger aggregate. Due to the difficulty of modeling cell division within aggregates, few efforts have been made in this direction. In this paper, we propose a size structured approach that includes growth of aggregate size due to both cell division and aggregation. We first examine some basic mathematical issues associated with the development of a numerical simulation of the resulting algal aggregation model. The numerical algorithm is then used to examine the basic model behavior and present a comparison between aggregate distribution with and without division in aggregates. Results indicate that the inclusion of a growth term in aggregates, due to cell division, results in higher densities of larger aggregates; hence it has the impact to speed clearance of organic matter from the surface layer of the ocean.}, number={4}, journal={JOURNAL OF MATHEMATICAL BIOLOGY}, author={Ackleh, AS and Fitzpatrick, BG}, year={1997}, month={Mar}, pages={480–502} }
@article{fitzpatrick_1997, title={Shape matching with smart material structures using piezoceramic actuators}, volume={8}, ISSN={["1045-389X"]}, DOI={10.1177/1045389X9700801007}, abstractNote={ In this paper, we consider the problem of driving a flexible structure from an "unforced" equilibrium position to a given desired shape. Within the context of smart materials, we focus on piezoceramic actuators as controls. Our approach is to base the choice of input voltages on a physical model of the structure, with "good" voltage choices being those whose modelbased displacements "'closely" match the desired shape. This shape matching problem is posed as a least squares problem in a Hilbert space that represents the displacement component of the state space of the flexible structure model. Here we treat the structure as a distributed parameter system, so that the state space is infinite dimensional. Thus, we must examine questions of existence of solutions and convergence of approximations. To illustrate our techniques, we give some numerical examples. }, number={10}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Fitzpatrick, BG}, year={1997}, month={Oct}, pages={876–882} }