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Heat unit accumulation and computer mapping for use in phenological modeling of Arizona insects
AuthorNelson, Alan Kent
KeywordsInsects -- Behavior -- Arizona -- Mathematical models.
Insect populations -- Mathematical models.
Phenology -- Arizona -- Maps.
Crops and climate -- Arizona -- Mathematical models.
Insect-plant relationships -- Mathematical models.
MetadataShow full item record
PublisherThe University of Arizona.
RightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Degree GrantorUniversity of Arizona
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Model identification and parameter estimation of stochastic linear models.Vazirinejad, Shamsedin. (The University of Arizona., 1990)It is well known that when the input variables of the linear regression model are subject to noise contamination, the model parameters can not be estimated uniquely. This, in the statistical literature, is referred to as the identifiability problem of the errors-in-variables models. Further, in linear regression there is an explicit assumption of the existence of a single linear relationship. The statistical properties of the errors-in-variables models under the assumption that the noise variances are either known or that they can be estimated are well documented. In many situations, however, such information is neither available nor obtainable. Although under such circumstances one can not obtain a unique vector of parameters, the space, Ω, of the feasible solutions can be computed. Additionally, assumption of existence of a single linear relationship may be presumptuous as well. A multi-equation model similar to the simultaneous-equations models of econometrics may be more appropriate. The goals of this dissertation are the following: (1) To present analytical techniques or algorithms to reduce the solution space, Ω, when any type of prior information, exact or relative, is available; (2) The data covariance matrix, Σ, can be examined to determine whether or not Ω is bounded. If Ω is not bounded a multi-equation model is more appropriate. The methodology for identifying the subsets of variables within which linear relations can feasibly exist is presented; (3) Ridge regression technique is commonly employed in order to reduce the ills caused by collinearity. This is achieved by perturbing the diagonal elements of Σ. In certain situations, applying ridge regression causes some of the coefficients to change signs. An analytical technique is presented to measure the amount of perturbation required to render such variables ineffective. This information can assist the analyst in variable selection as well as deciding on the appropriate model; (4) For the situations when Ω is bounded, a new weighted regression technique based on the computed upper bounds on the noise variances is presented. This technique will result in identification of a unique estimate of the model parameters.
The effects of surface roughness and stress on lattice gas models using kinetic Monte Carlo modelingBentz, Daniel N. (The University of Arizona., 2003)This thesis reports kinetic Monte Carlo computer simulations using a lattice gas model conducted on a variety of systems. These studies may be divided into two main categories: rod eutectics and related surface roughening, and surface morphology changes due to local stresses. The first grouping is a study of irregular rod eutectic systems. Simulations of directional solidification of rod eutectic systems were conducted using a model similar to the spin one Ising model. Growth of the rods was initiated from columns of pure A atoms embedded in a matrix of B atoms. The growth characteristics of the eutectic depend on the location of the surface roughening transition for the two phases. The surface roughening transition was determined using fluctuation dissipation theory, where the kinetic behavior of the interface is related to a characteristic time of fluctuations about an equilibrium position. These times were determined by time correlations. Results show a sharp transition in the kinetic behavior of the interface as a function of Jackson's alpha factor. This is the first time this method has been used to locate the surface roughening transition. An applied temperature gradient supplied the restoring force for the interface. The roughening behavior of binary alloys was also examined and compared to pure component systems. The second set of simulations reported here examine the effects of local stress on surface morphology. The weakening of bonds due to the dislocation stress field was studied as the origin of the formation of etch-pits at dislocations. Atoms from a diamond cubic lattice were irreversibly removed with a probability which depends on an local surface configuration as well as on the local stress developed from its physical location with respect to a dislocation in the lattice. In accordance with experimental observations, both faceted and non-faceted dislocation etch-pits have been observed. Simulations of crystal surfaces near equilibrium have reproduced direct experimental results using atomic force microscopy (AFM). The probe tip interacts with the shape and the motion of step edges, and the motion of a step is retarded in the vicinity of the tip.