Matching Items (85)
Description
Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears as a model in hydrodynamics, nonlinear optics, quantum condensates, heat pulses in solids and various other nonlinear instability phenomena. In mathematics, one of the interests is to look at the wave interaction: waves propagation with different speeds and/or different directions produces either small perturbations comparable with linear behavior, or creates solitary waves, or even leads to singular solutions. This dissertation studies the global behavior of finite energy solutions to the $d$-dimensional focusing NLS equation, $i partial _t u+Delta u+ |u|^{p-1}u=0, $ with initial data $u_0in H^1,; x in Rn$; the nonlinearity power $p$ and the dimension $d$ are chosen so that the scaling index $s=frac{d}{2}-frac{2}{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s<1).$ For solutions with $ME[u_0]<1$ ($ME[u_0]$ stands for an invariant and conserved quantity in terms of the mass and energy of $u_0$), a sharp threshold for scattering and blowup is given. Namely, if the renormalized gradient $g_u$ of a solution $u$ to NLS is initially less than 1, i.e., $g_u(0)<1,$ then the solution exists globally in time and scatters in $H^1$ (approaches some linear Schr"odinger evolution as $ttopminfty$); if the renormalized gradient $g_u(0)>1,$ then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle. One of the difficulties is fractional powers of nonlinearities which are overcome by considering Besov-Strichartz estimates and various fractional differentiation rules.
ContributorsGuevara, Cristi Darley (Author) / Roudenko, Svetlana (Thesis advisor) / Castillo_Chavez, Carlos (Committee member) / Jones, Donald (Committee member) / Mahalov, Alex (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2011
Description
For over a century, researchers have been investigating collective cognition, in which a group of individuals together process information and act as a single cognitive unit. However, I still know little about circumstances under which groups achieve better (or worse) decisions than individuals. My dissertation research directly addressed this longstanding question, using the house-hunting ant Temnothorax rugatulus as a model system. Here I applied concepts and methods developed in psychology not only to individuals but also to colonies in order to investigate differences of their cognitive abilities. This approach is inspired by the superorganism concept, which sees a tightly integrated insect society as the analog of a single organism. I combined experimental manipulations and models to elucidate the emergent processes of collective cognition. My studies show that groups can achieve superior cognition by sharing the burden of option assessment among members and by integrating information from members using positive feedback. However, the same positive feedback can lock the group into a suboptimal choice in certain circumstances. Although ants are obligately social, my results show that they can be isolated and individually tested on cognitive tasks. In the future, this novel approach will help the field of animal behavior move towards better understanding of collective cognition.
ContributorsSasaki, Takao (Author) / Pratt, Stephen C (Thesis advisor) / Amazeen, Polemnia (Committee member) / Liebig, Jürgen (Committee member) / Janssen, Marco (Committee member) / Fewell, Jennifer (Committee member) / Hölldobler, Bert (Committee member) / Arizona State University (Publisher)
Created2013
Description
This thesis outlines the development of a vector retrieval technique, based on data assimilation, for a coherent Doppler LIDAR (Light Detection and Ranging). A detailed analysis of the Optimal Interpolation (OI) technique for vector retrieval is presented. Through several modifications to the OI technique, it is shown that the modified technique results in significant improvement in velocity retrieval accuracy. These modifications include changes to innovation covariance portioning, covariance binning, and analysis increment calculation. It is observed that the modified technique is able to make retrievals with better accuracy, preserves local information better, and compares well with tower measurements. In order to study the error of representativeness and vector retrieval error, a lidar simulator was constructed. Using the lidar simulator a thorough sensitivity analysis of the lidar measurement process and vector retrieval is carried out. The error of representativeness as a function of scales of motion and sensitivity of vector retrieval to look angle is quantified. Using the modified OI technique, study of nocturnal flow in Owens' Valley, CA was carried out to identify and understand uncharacteristic events on the night of March 27th 2006. Observations from 1030 UTC to 1230 UTC (0230 hr local time to 0430 hr local time) on March 27 2006 are presented. Lidar observations show complex and uncharacteristic flows such as sudden bursts of westerly cross-valley wind mixing with the dominant up-valley wind. Model results from Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS®) and other in-situ instrumentations are used to corroborate and complement these observations. The modified OI technique is used to identify uncharacteristic and extreme flow events at a wind development site. Estimates of turbulence and shear from this technique are compared to tower measurements. A formulation for equivalent wind speed in the presence of variations in wind speed and direction, combined with shear is developed and used to determine wind energy content in presence of turbulence.
ContributorsChoukulkar, Aditya (Author) / Calhoun, Ronald (Thesis advisor) / Mahalov, Alex (Committee member) / Kostelich, Eric (Committee member) / Huang, Huei-Ping (Committee member) / Phelan, Patrick (Committee member) / Arizona State University (Publisher)
Created2013
Description
Here I present a phylogeographic study of at least six reproductively isolated lineages of harvester ants within the Pogonomyrmex barbatus and P. rugosus species group. The genetic and geographic relationships within this clade are complex: four of the identified lineages are divided into two pairs, and each pair has evolved under a mutualistic system that necessitates sympatry. These paired lineages are dependent upon one another because interlineage matings within each pair are the sole source of hybrid F1 workers; these workers build and sustain the colonies, facilitating the production of the reproductive caste, which results solely from intralineage fertilizations. This system of genetic caste determination (GCD) maintains genetic isolation among these closely related lineages, while simultaneously requiring co-expansion and emigration as their distributions have changed over time. Previous studies have also demonstrated that three of the four lineages displaying this unique genetic caste determination phenotype are of hybrid origin. Thus, reconstructing the phylogenetic and geographic history of this group allows us to evaluate past insights and plan future inquiries in a more complete historical biogeographic context. Using mitochondrial DNA sequences sampled across most of the morphospecies' ranges in the U.S. and Mexico, I employed several methods of phylogenetic and DNA sequence analysis, along with comparisons to geological, biogeographic, and phylogeographic studies throughout the sampled regions. These analyses on Pogonomyrmex harvester ants reveal a complex pattern of vicariance and dispersal that is largely concordant with models of late Miocene, Pliocene, and Pleistocene range shifts among various arid-adapted taxa in North America.
ContributorsMott, Brendon (Author) / Gadau, Juergen (Thesis advisor) / Fewell, Jennifer (Committee member) / Anderson, Kirk (Committee member) / Arizona State University (Publisher)
Created2012
Description
The spread of invasive species may be greatly affected by human responses to prior species spread, but models and estimation methods seldom explicitly consider human responses. I investigate the effects of management responses on estimates of invasive species spread rates. To do this, I create an agent-based simulation model of an insect invasion across a county-level citrus landscape. My model provides an approximation of a complex spatial environment while allowing the "truth" to be known. The modeled environment consists of citrus orchards with insect pests dispersing among them. Insects move across the simulation environment infesting orchards, while orchard managers respond by administering insecticide according to analyst-selected behavior profiles and management responses may depend on prior invasion states. Dispersal data is generated in each simulation and used to calculate spread rate via a set of estimators selected for their predominance in the empirical literature. Spread rate is a mechanistic, emergent phenomenon measured at the population level caused by a suite of latent biological, environmental, and anthropogenic. I test the effectiveness of orchard behavior profiles on invasion suppression and evaluate the robustness of the estimators given orchard responses. I find that allowing growers to use future expectations of spread in management decisions leads to reduced spread rates. Acting in a preventative manner by applying insecticide before insects are actually present, orchards are able to lower spread rates more than by reactive behavior alone. Spread rates are highly sensitive to spatial configuration. Spatial configuration is hardly a random process, consisting of many latent factors often not accounted for in spread rate estimation. Not considering these factors may lead to an omitted variables bias and skew estimation results. The ability of spread rate estimators to predict future spread varies considerably between estimators, and with spatial configuration, invader biological parameters, and orchard behavior profile. The model suggests that understanding the latent factors inherent to dispersal is important for selecting phenomenological models of spread and interpreting estimation results. This indicates a need for caution when evaluating spread. Although standard practice, current empirical estimators may both over- and underestimate spread rate in the simulation.
ContributorsShanafelt, David William (Author) / Fenichel, Eli P (Thesis advisor) / Richards, Timothy (Committee member) / Janssen, Marco (Committee member) / Arizona State University (Publisher)
Created2012
Description
It is possible in a properly controlled environment, such as industrial metrology, to make significant headway into the non-industrial constraints on image-based position measurement using the techniques of image registration and achieve repeatable feature measurements on the order of 0.3% of a pixel, or about an order of magnitude improvement on conventional real-world performance. These measurements are then used as inputs for a model optimal, model agnostic, smoothing for calibration of a laser scribe and online tracking of velocimeter using video input. Using appropriate smooth interpolation to increase effective sample density can reduce uncertainty and improve estimates. Use of the proper negative offset of the template function has the result of creating a convolution with higher local curvature than either template of target function which allows improved center-finding. Using the Akaike Information Criterion with a smoothing spline function it is possible to perform a model-optimal smooth on scalar measurements without knowing the underlying model and to determine the function describing the uncertainty in that optimal smooth. An example of empiric derivation of the parameters for a rudimentary Kalman Filter from this is then provided, and tested. Using the techniques of Exploratory Data Analysis and the "Formulize" genetic algorithm tool to convert the spline models into more accessible analytic forms resulted in stable, properly generalized, KF with performance and simplicity that exceeds "textbook" implementations thereof. Validation of the measurement includes that, in analytic case, it led to arbitrary precision in measurement of feature; in reasonable test case using the methods proposed, a reasonable and consistent maximum error of around 0.3% the length of a pixel was achieved and in practice using pixels that were 700nm in size feature position was located to within ± 2 nm. Robust applicability is demonstrated by the measurement of indicator position for a King model 2-32-G-042 rotameter.
ContributorsMunroe, Michael R (Author) / Phelan, Patrick (Thesis advisor) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / Arizona State University (Publisher)
Created2012
Description
Honey bee (Apis mellifera) colonies have experienced substantial losses due to colony collapse disorder (CCD) since the first officially reported cases in 2006. Many factors have been implicated in CCD, including pests, pathogens, malnutrition, and pesticide use, but no correlation has been found between a single factor and the occurrence of CCD. Fungicides have received less research attention compared to insecticides, despite the fact that fungicide application coincides with bloom and the presence of bees. Pristine fungicide is widely used in agriculture and is commonly found as a residue in hives. Several studies have concluded that Pristine can be used without harming bees, but reports of brood loss following Pristine application continue to surface across the country. The primary objectives of this study were to determine whether Pristine causes an aversive gustatory response in bees and whether consumption of an acute dose affects responsiveness to sucrose. An awareness of how foragers interact with contaminated food is useful to understand the likelihood that Pristine is ingested and how that may affect bees' ability to evaluate floral resources. Our results indicated that Pristine has no significant effect on gustatory response or sucrose responsiveness. There was no significant difference between bee responses to Pristine contaminated sucrose and sucrose alone, and no significant effect of Pristine on sucrose responsiveness. These results indicate that honey bees do not have a gustatory aversion to Pristine. A lack of aversion means that honey bees will continue collecting contaminated resources and dispersing them throughout the colony where it can affect brood and clean food stores.
ContributorsMcHugh, Cora Elizabeth (Co-author) / Jernigan, Christopher (Co-author, Committee member) / Burden, Christina (Co-author) / DeGrandi-Hoffman, Gloria (Co-author) / Smith, Brian (Thesis director) / Fewell, Jennifer (Committee member) / Barrett, The Honors College (Contributor) / School of Geographical Sciences and Urban Planning (Contributor) / School of Life Sciences (Contributor) / School of Art (Contributor)
Created2015-05
Description
We model communication among social insects as an interacting particle system in which individuals perform one of two tasks and neighboring sites anti-mimic one another. Parameters of our model are a probability of defection 2 (0; 1) and relative cost ci > 0 to the individual performing task i. We examine this process on complete graphs, bipartite graphs, and the integers, answering questions about the relationship between communication, defection rates and the division of labor. Assuming the division of labor is ideal when exactly half of the colony is performing each task, we nd that on some bipartite graphs and the integers it can eventually be made arbitrarily close to optimal if defection rates are sufficiently small. On complete graphs the fraction of individuals performing each task is also closest to one half when there is no defection, but is bounded by a constant dependent on the relative costs of each task.
ContributorsArcuri, Alesandro Antonio (Author) / Lanchier, Nicolas (Thesis director) / Kang, Yun (Committee member) / Fewell, Jennifer (Committee member) / Barrett, The Honors College (Contributor) / School of International Letters and Cultures (Contributor) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
Nutritional balance is a requirement for the survival of all species. This balance is important for complex eusocial organisms as it influences the growth and development of the colony. Leafcutter ants function as tri-trophic systems, harvesting mixed vegetation to cultivate a fungus garden that in return supplies the colony with food. Examining how the colony deals with nutrient balance is of particular interest because this species forages to provide nutrients for the fungus. There seems to be a feedback system between the fungus and the workers that influences how much of a particular macronutrient should be collected. The objective of this thesis study was to examine the foraging behavior of the desert leaf cutter ant, Acromyrmex versicolor. This study asked how nutrition, in particular the ratio of carbohydrates to proteins, influences the foraging behavior of the colony. It was hypothesized that given a choice of high protein and high carbohydrate diets the leafcutters would forage towards a balance ratio. The results from this experiment showed that A. versicolor forage towards a target ratio of protein to carbohydrate to based diets. This p:c ratio was calculated to be 1:6.2; 1 gram of protein to 6.2 grams of carbohydrate. When colonies were restricted to the high carbohydrate diet, they increased food consumption, consistent with the expectation that they would forage to reach their protein nutrient requirement, however, they reduced foraging on that diet. This suggests that ants avoid overconsuming protein, even when doing so provided more optimal carbohydrate intake. From this study I concluded that nutritional balance is a foraging goal for ant societies, similar to organisms. These results also open the question of how nutrient regulation by leafcutter ants is regulated around their mutualist relationship with another organism, the fungus.
ContributorsFarris, Megan Alexandra (Author) / Fewell, Jennifer (Thesis director) / Harrison, Jon (Committee member) / Smith, Nate (Committee member) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2015-12
Description
Division of labor among task specialists is a key feature of the organization of insect societies. Foraging and emigration are two distinct colony tasks that nonetheless depend on very similar behaviors, including searching outside the nest, evaluating discoveries, and recruiting nestmates. These subtasks are crucial to collective decisions about forager allocation and nest site selection. It remains unclear, however, whether the same ants are responsible for similar behavior in both contexts, and to what degree they show finer specializations among common subtasks. We are investigating these issues in the ant Temnothorax rugatulus, by making detailed behavioral descriptions of individually marked colonies as they forage and emigrate. There exists considerable heterogeneity among nest-movers, with a small proportion consistently responsible for a large share of recruitment. We found a similar pattern of heterogeneity amongst ants retrieving food during foraging, but had inconclusive results when examining recruitment to the food. It also appears that the ants that complete tasks during foraging are different from the ants that complete similar tasks during emigrations. These findings will shed light on the organization of division of labor and how it contributes to collective decision-making.
ContributorsSchaper, Gage (Contributor) / Pratt, Stephen (Thesis director) / Fewell, Jennifer (Committee member) / Shaffer, Zachary (Committee member) / Barrett, The Honors College (Contributor)
Created2013-05