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Wang Jun. / "February 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 116-124). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Animal group formation has often been studied by mathematical biologists through PDE models, producing classical results like traveling and stationary waves. Recently, Eftimie et al. introduced a 1-D PDE model that considers three social interactions between individuals in the relevant neighborhoods, specifically re- pulsion, alignment, and attraction. It takes into account the orientation of the neighbors when consider- ing if they can communicate. This has resulted in exciting new movement behaviors like zig-zag pulses, breathers, and feathers. In this work, we translate the Eftimie model into a Lagrangian implementation. Currently, the results from the Lagrangian formulations show many of the results displayed by Eftimie’s original PDE model, producing patterns like the zig-zag, breather traveling, and stationary pulses. In addi- tion, we model animal movement with an ODE approach to complete the investigation regarding the role of direction-dependent communication mechanism in discrete-space. / Applied Mathematics

A quantitative climatology of atmospheric transport in Texas is developed using previously described Lagrangian trajectory methods (Rogers and Bowman, 2001; Bowman and Carrie, 2002). The trajectories are computed using winds from 1979-2001 from the National Center for Environmental Prediction (NCEP) Reanalysis Project data set. Probability distributions are created for particle transport using trajectories from urban areas, making six-hourly particle distributions available from four urban areas in Texas. These probability distributions represent a quantitative understanding of regional air transport. Time-dependent Green's functions are calculated given initial conditions such as urban areas weighted with respect to population. The Green's functions describe how air from urban areas is transported through the atmosphere as a function of time. Summertime backward Lagrangian trajectories initialized at 5 Texas Commission on Environmental Quality (TCEQ) monitoring stations are grouped according to the ozone value recorded at the station at the initialization time of the trajectory. The directions of the trajectories in each group are used to determine the relationship between the transport characteristics of the circulation over Texas and regional-scale observations of pollutants. Synoptic conditions occurring at the time of summertime ozone exceedances at the 5 TCEQ stations are investigated in order to resolve what conditions are likely to coincide with ozone exceedances.

Thesis (M.S.)--Naval Postgraduate School, 2002. / Thesis advisor(s): R. Kevin Wood, Kelly J. Cormican. Includes bibliographical references (p. 45-46). Also available online.

It is generally accepted that models of the deep ocean must assimilate observations in order to make realistic forecasts in regions dominated by mesoscale variability (i.e., “ocean weather”). The present study is an attempt to quantify the information on ocean weather that is contained in Lagrangian trajectories, and the best way to extract it. Following a review of ocean data assimilation in a Bayesian framework, including the Ensemble Kalman Filter and the Particle Filter, a new class of idealized models of self advecting vortices is introduced. Through a large number of carefully designed Monte Carlo experiments it is shown when, where and why the Ensemble Kalman Filter will fail. The study concludes with a discussion of a hybrid scheme that takes advantage of the lower computational cost of the Ensemble Kalman Filter and the ability of the Particle Filter to handle highly non-Gaussian probability density functions. / MSc Thesis

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