Thesis (M.S.)--University of Wyoming, 2007. / Title from PDF title page (viewed on Oct. 31, 2008). Includes bibliographical references (p. 81-82).

In this dissertation, we examine an advection diffusion model for insects inhabiting a spatially heterogeneous environment and moving toward a more favorable environment. We first study the effects of adding a term describing drift or advection toward a favorable environment to diffusion models for population dynamics. The diffusion model is a basic linear two-dimensional diffusion equation describing local dispersal of species. The mathematical advection terms are taken to be Fickian and describe directed movement of the population toward the favorable environment. For this model, the landscape is composed of one homogeneous habitat patch embedded in a spatially heterogeneous environment and the boundary of the habitat inhabited by the population acts as a lethal edge. We also derived the mean occupancy time and the boundary flux of the habitat patch. The diffusion rate and advection parameters of the advection diffusion model are estimated based on mean occupancy time and boundary flux. We then introduce two methods for the identification of these coefficients in the model as well as the capture rate. These two new methods have some advantages over other methods of estimating those parameters, including reduced computational cost and ease of use in the field. We further examine the statistical properties of new methods through simulation, and discuss how mean occupancy time and boundary flux could be estimated in field experiments.

Die Surface Renewal Analysis wurde zur Bestimmung sensibler Wärmeflußdichten im bodennahen Bereich der atmosphärischen Grenzschicht genutzt und mit der Eddy - Korrelations - Methode verglichen. Dazu wurden beide Berechnungsmethoden auf Temperatur - und Vertikalwinddaten angewandt, die unter Verwendung von Strukturfunktionen simuliert wurden. Zur Überprüfung der Resultate wurden über zwei verschiedenen Unterlagen (Wiese und Düne) hochfrequente Zeitreihen von Temperatur und Vertikalwind gemessen und mit der Surface Renewal Analysis und der Eddy - Korrelations - Methode analysiert. / The Surface Renewal Analysis was used to estimate the sensible heat flux density in the ground near area of the boundary layer. The results were compared with eddy correlation method. For it both methods were used to analyse temperature- and vertical velocity-data, which were simulated by the application of structure functions. Time series of high frequency temperature- and vertical velocity-data over two different canopies (meadow and dune) were measured to examine the results. The data were analysed with surface renewal analysis and eddy correlation.

Reaction-diffusion equations have been used to study various phenomena across different fields. These equations can be posed on the whole real line, or on a subinterval, depending on the situation being studied. For finite intervals, we also impose diverse boundary conditions on the system. In the present thesis, we solely focus on the bistable reaction-diffusion equation while working on a bounded interval of the form $[0,L]$ ($L>0$). Furthermore, we consider both mixed and no-flux boundary conditions, where we extend the former to Dirichlet boundary conditions once our analysis of that system is complete. We first use phase-plane analysis to set up our initial investigation of both systems. This gives us an integral describing the transit time of orbits within the phase-plane. This allows us to determine the bifurcation diagram of both systems. We then transform the integral to ease numerical calculations. Finally, we determine the stability of the steady states of each system.

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