Matching Items (61)
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
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
Collective decision making in social organism societies involves a large network of communication systems. Studying the processes behind the transmission of information allows for greater understanding of the decision making capabilities of a group. For Temnothorax rugatulus colonies, information is commonly spread in the form of tandem running, a linear recruitment pattern where a leading ant uses a short-ranged pheromone to direct a following ant to a target location (in tandem).The observed phenomenon of reverse tandem running (RTR), where a follower is lead from a target back to the home nest, has not been as extensively studied as forward tandem running and transportation recruitment activities. This study seeks to explain a potential reason for the presence of the RTR behavior; more specifically, the study explores the idea that reverse tandem run followers are being shown a specific route to the home nest by a highly experienced and efficient leading ant. Ten colonies had migrations induced experimentally in order to generate some reverse tandem running activity. Once an RTR has been observed, the follower and leader were studied for behavior and their pathways were analyzed. It was seen that while RTR paths were quite efficient (1.4x a straight line distance), followers did not experience a statistically significant improvement in their pathways between the home and target nests (based on total distance traveled) when compared to similar non-RTR ants. Further, RTR leading ants were no more efficient than other non-RTR ants. It was observed that some followers began recruiting after completion of an RTR, but the number than changed their behavior was not significant. Thus, the results of this experiment cannot conclusively show that RTR followers are utilizing reverse tandem runs to improve their routes between the home and target nests.
ContributorsColling, Blake David (Author) / Pratt, Stephen (Thesis director) / Liebig, Juergen (Committee member) / Sasaki, Takao (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2014-12
Description
Evolutionary theory predicts that animal behavior is generally governed by decision rules (heuristics) which adhere to ecological rationality: the tendency to make decisions that maximize fitness in most situations the animal encounters. However, the particular heuristics used by ant colonies of the genus Temnothorax and their propensity towards ecological rationality are up for debate. These ants are adept at choosing a nest site, making a collective decision based on complex interactions between the many individual choices made by workers. Colonies will migrate between nests either upon the destruction of their current home or the discovery of a sufficiently superior nest. This study offers a descriptive analysis of the heuristics potentially used in nest-site decision-making. Colonies were offered a choice of nests characterized by the Ebbinghaus Illusion: a perceptual illusion which effectively causes the viewer to perceive a circle as larger when it is surrounded by small circles than when that same circle is surrounded by large circles. Colonies were separated into two conditions: in one, they were given the option to move to a high-quality nest surrounded by poor-quality nests, and in the other they were given the option to move to a high-quality nest surrounded by medium-quality nests. The colonies in the poor condition were found to be more likely to move to the good nest than were colonies in the medium condition at a statistically significant level. That is, they responded to the Ebbinghaus Effect in the way that is normally expected. This result was discussed in terms of its implications for the ecological rationality of the nest-site choice behavior of these ants.
ContributorsTalken, Lucas Warren (Author) / Pratt, Stephen (Thesis director) / Sasaki, Takao (Committee member) / Liebig, Juergen (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Psychology (Contributor) / Economics Program in CLAS (Contributor)
Created2014-05
Description
In the digital humanities, there is a constant need to turn images and PDF files into plain text to apply analyses such as topic modelling, named entity recognition, and other techniques. However, although there exist different solutions to extract text embedded in PDF files or run OCR on images, they typically require additional training (for example, scholars have to learn how to use the command line) or are difficult to automate without programming skills. The Giles Ecosystem is a distributed system based on Apache Kafka that allows users to upload documents for text and image extraction. The system components are implemented using Java and the Spring Framework and are available under an Open Source license on GitHub (https://github.com/diging/).
ContributorsLessios-Damerow, Julia (Contributor) / Peirson, Erick (Contributor) / Laubichler, Manfred (Contributor) / ASU-SFI Center for Biosocial Complex Systems (Contributor)
Created2017-09-28
Description
The evolution of cooperation is a fundamental problem in biology, especially for non-relatives, where indirect fitness benefits cannot counter within-group inequalities. Multilevel selection models show how cooperation can evolve if it generates a group-level advantage, even when cooperators are disadvantaged within their group. This allows the possibility of group selection, but few examples have been described in nature. Here we show that group selection can explain the evolution of cooperative nest founding in the harvester ant Pogonomyrmex californicus. Through most of this species’ range, colonies are founded by single queens, but in some populations nests are instead founded by cooperative groups of unrelated queens. In mixed groups of cooperative and single-founding queens, we found that aggressive individuals had a survival advantage within their nest, but foundress groups with such non-cooperators died out more often than those with only cooperative members. An agent-based model shows that the between-group advantage of the cooperative phenotype drives it to fixation, despite its within-group disadvantage, but only when population density is high enough to make between-group competition intense. Field data show higher nest density in a population where cooperative founding is common, consistent with greater density driving the evolution of cooperative foundation through group selection.
ContributorsShaffer, Zachary (Author) / Sasaki, Takao (Author) / Haney, Brian (Author) / Janssen, Marco (Author) / Pratt, Stephen (Author) / Fewell, Jennifer (Author) / College of Liberal Arts and Sciences (Contributor)
Created2016-07-28
Description
Because collective cognition emerges from local signaling among group members, deciphering communication systems is crucial to understanding the underlying mechanisms. Alarm signals are widespread in the social insects and can elicit a variety of behavioral responses to danger, but the functional plasticity of these signals has not been well studied. Here we report an alarm pheromone in the ant Temnothorax rugatulus that elicits two different behaviors depending on context. When an ant was tethered inside an unfamiliar nest site and unable to move freely, she released a pheromone from her mandibular gland that signaled other ants to reject this nest as a potential new home, presumably to avoid potential danger. When the same pheromone was presented near the ants' home nest, they were instead attracted to it, presumably to respond to a threat to the colony. We used coupled gas chromatography/mass spectrometry to identify candidate compounds from the mandibular gland and tested each one in a nest choice bioassay. We found that 2,5-dimethylpyrazine was sufficient to induce rejection of a marked new nest and also to attract ants when released at the home nest. This is the first detailed investigation of chemical communication in the leptothoracine ants. We discuss the possibility that this pheromone's deterrent function can improve an emigrating colony's nest site selection performance.
ContributorsSasaki, Takao (Author) / Hoelldobler, Bert (Author) / Millar, Jocelyn G. (Author) / Pratt, Stephen (Author) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor) / ASU-SFI Center for Biosocial Complex Systems (Contributor) / Center for Social Dynamics and Complexity (Contributor)
Created2014-09-01
Description
A numerical study of wave-induced momentum transport across the tropopause in the presence of a stably stratified thin inversion layer is presented and discussed. This layer consists of a sharp increase in static stability within the tropopause. The wave propagation is modeled by numerically solving the Taylor-Goldstein equation, which governs the dynamics of internal waves in stably stratified shear flows. The waves are forced by a flow over a bell shaped mountain placed at the lower boundary of the domain. A perfectly radiating condition based on the group velocity of mountain waves is imposed at the top to avoid artificial wave reflection. A validation for the numerical method through comparisons with the corresponding analytical solutions will be provided. Then, the method is applied to more realistic profiles of the stability to study the impact of these profiles on wave propagation through the tropopause.
ContributorsCole, Alexandra Shea (Author) / Moustaoui, Mohamed (Thesis director) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / School of International Letters and Cultures (Contributor) / School of Geographical Sciences and Urban Planning (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05