Matching Items (103)
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
Much like neighboring nations, living in close proximity can often lead to conflict over limited resources for social insect colonies. As with warring nations, conflicts among insect societies can also result in one colony attempting to invade the other. Though emigrations are common and well understood in social insects, the process of emigration in the context of conflict is not known. During emigrations of the ant Temnothorax rugatulus, colonies first employ the use of scouts, who search for new nest locations. These scouts then recruit naïve workers to these nests resulting in a ‘voting’ process through which colonies can collectively choose the best nest site. Once the decision is made, the selected nest is rapidly populated by workers who physically carry the queen(s), brood, and remaining naïve ants to the new nest. Invasions occurring during inter-colony conflicts bear a striking resemblance to this process. The state of the final nest suggested merged colonies, and statistical models were used to test for the likelihood of this. Here we test whether colonies of T. rugatulus use the same mechanisms during invasions as those used in emigrations by observing conflicts between colonies of T. rugatulus ants and tracking instances of scouting and recruitment, transport and changes in populations in each nest. Our results support the predicted order of behaviors starting with scouting, followed by recruitment and transport last. In addition, presence of the quorum rule, which determines the switch from recruitment to transport, is confirmed. Furthermore, evidence showed that the colonies were merged at the time of transport. While ant emigration patterns are well understood, there is a gap in understanding conflict driven emigrations/invasions. Our results serve to better understand conflict in social insects by further understanding the mechanisms used during conflicts.
ContributorsWalrod, Nicholas W (Author) / Pratt, Stephen (Thesis director) / Charbonneau, Daniel (Committee member) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
The repression of reproductive competition and the enforcement of altruism are key components to the success of animal societies. Eusocial insects are defined by having a reproductive division of labor, in which reproduction is relegated to one or few individuals while the rest of the group members maintain the colony and help raise offspring. However, workers have retained the ability to reproduce in most insect societies. In the social Hymenoptera, due to haplodiploidy, workers can lay unfertilized male destined eggs without mating. Potential conflict between workers and queens can arise over male production, and policing behaviors performed by nestmate workers and queens are a means of repressing worker reproduction. This work describes the means and results of the regulation of worker reproduction in the ant species Aphaenogaster cockerelli. Through manipulative laboratory studies on mature colonies, the lack of egg policing and the presence of physical policing by both workers and queens of this species are described. Through chemical analysis and artificial chemical treatments, the role of cuticular hydrocarbons as indicators of fertility status and the informational basis of policing in this species is demonstrated. An additional queen-specific chemical signal in the Dufour's gland is discovered to be used to direct nestmate aggression towards reproductive competitors. Finally, the level of actual worker-derived males in field colonies is measured. Together, these studies demonstrate the effectiveness of policing behaviors on the suppression of worker reproduction in a social insect species, and provide an example of how punishment and the threat of punishment is a powerful force in maintaining cooperative societies.
ContributorsSmith, Adrian A. (Author) / Liebig, Juergen (Thesis advisor) / Hoelldobler, Bert (Thesis advisor) / Gadau, Juergen (Committee member) / Johnson, Robert A. (Committee member) / Pratt, Stephen (Committee member) / Arizona State University (Publisher)
Created2011
Description
Speciation is the fundamental process that has generated the vast diversity of life on earth. The hallmark of speciation is the evolution of barriers to gene flow. These barriers may reduce gene flow either by keeping incipient species from hybridizing at all (pre-zygotic), or by reducing the fitness of hybrids (post-zygotic). To understand the genetic architecture of these barriers and how they evolve, I studied a genus of wasps that exhibits barriers to gene flow that act both pre- and post-zygotically. Nasonia is a genus of four species of parasitoid wasps that can be hybridized in the laboratory. When two of these species, N. vitripennis and N. giraulti are mated, their offspring suffer, depending on the generation and cross examined, up to 80% mortality during larval development due to incompatible genic interactions between their nuclear and mitochondrial genomes. These species also exhibit pre-zygotic isolation, meaning they are more likely to mate with their own species when given the choice. I examined these two species and their hybrids to determine the genetic and physiological bases of both speciation mechanisms and to understand the evolutionary forces leading to them. I present results that indicate that the oxidative phosphorylation (OXPHOS) pathway, an essential pathway that is responsible for mitochondrial energy generation, is impaired in hybrids of these two species. These results indicate that this impairment is due to the unique evolutionary dynamics of the combined nuclear and mitochondrial origin of this pathway. I also present results showing that, as larvae, these hybrids experience retarded growth linked to the previously observed mortality and I explore possible physiological mechanisms for this. Finally, I show that the pre-mating isolation is due to a change in a single pheromone component in N. vitripennis males, that this change is under simple genetic control, and that it evolved neutrally before being co-opted as a species recognition signal. These results are an important addition to our overall understanding of the mechanisms of speciation and showcase Nasonia as an emerging model for the study of the genetics of speciation.
ContributorsGibson, Joshua D (Author) / Gadau, Jürgen (Thesis advisor) / Harrison, Jon (Committee member) / Pratt, Stephen (Committee member) / Verrelli, Brian (Committee member) / Willis, Wayne (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
Of all the signals and cues that orchestrate the activities of a social insect colony, the reproductives' fertility pheromones are perhaps the most fundamental. These pheromones regulate reproductive division of labor, a defining characteristic of eusociality. Despite their critical role, reproductive fertility pheromones are not evenly expressed across the development of a social insect colony and may even be absent in the earliest colony stages. In the ant Camponotus floridanus, queens of incipient colonies do not produce the cuticular hydrocarbons that serve as fertility and egg-marking signals in this species. My dissertation investigates the consequences of the dramatic change in the quantity of these pheromones that occurs as the colony grows. C. floridanus workers from large, established colonies use egg surface hydrocarbons to discriminate among eggs. Eggs with surface hydrocarbons typical of eggs laid by established queens are nurtured, whereas eggs lacking these signals (i.e., eggs laid by workers and incipient queens) are destroyed. I characterized how workers from incipient colonies responded to eggs lacking queen fertility hydrocarbons. I found that established-queen-laid eggs, incipient-queen-laid eggs, and worker-laid eggs were not destroyed by workers at this colony stage. Destruction of worker-laid eggs is a form of policing, and theoretical models predict that policing should be strongest in incipient colonies. Since there was no evidence of policing by egg-eating in incipient C. floridanus colonies, I searched for evidence of another policing mechanism at this colony stage. Finding none, I discuss reasons why policing behavior may not be expressed in incipient colonies. I then considered the mechanism that accounts for the change in workers' response to eggs. By manipulating ants' egg experience and testing their egg-policing decisions, I found that ants use a combination of learned and innate criteria to discriminate between targets of care and destruction. Finally, I investigated how the increasing strength of queen-fertility hydrocarbons affects nestmate recognition, which also relies on cuticular hydrocarbons. I found that queens with strong fertility hydrocarbons can be transferred between established colonies without aggression, but they cannot be introduced into incipient colonies. Queens from incipient colonies cannot be transferred into incipient or established colonies.
ContributorsMoore, Dani (Author) / Liebig, Juergen (Thesis advisor) / Gadau, Juergen (Committee member) / Pratt, Stephen (Committee member) / Smith, Brian (Committee member) / Rutowski, Ronald (Committee member) / Arizona State University (Publisher)
Created2012
Description
Gene-centric theories of evolution by natural selection have been popularized and remain generally accepted in both scientific and public paradigms. While gene-centrism is certainly parsimonious, its explanations fall short of describing two patterns of evolutionary and social phenomena: the evolution of sex and the evolution of social altruism. I review and analyze current theories on the evolution of sex. I then introduce the conflict presented to gene-centric evolution by social phenomena such as altruism and caste sterility in eusocial insects. I review gene-centric models of inclusive fitness and kin selection proposed by Hamilton and Maynard Smith. Based their assumptions, that relatedness should be equal between sterile workers and reproductives, I present several empirical examples that conflict with their models. Following that, I introduce a unique system of genetic caste determination (GCD) observed in hybrid populations of two sister-species of seed harvester ants, Pogonomyrmex rugosus and Pogonomyrmex barbatus. I review the evidence for GCD in those species, followed by a critique of the current gene-centric models used to explain it. In chapter two I present my own theoretical model that is both simple and extricable in nature to explain the origin, evolution, and maintenance of GCD in Pogonomyrmex. Furthermore, I use that model to fill in the gaps left behind by the contributing authors of the other GCD models. As both populations in my study system formed from inter-specific hybridization, I review modern discussions of heterosis (also called hybrid vigor) and use those to help explain the ecological competitiveness of GCD. I empirically address the inbreeding depression the lineages of GCD must overcome in order to remain ecologically stable, demonstrating that as a result of their unique system of caste determination, GCD lineages have elevated recombination frequencies. I summarize and conclude with an argument for why GCD evolved under selective mechanisms which cannot be considered gene-centric, providing evidence that natural selection can effectively operate on non-heritable genotypes appearing in groups and other social contexts.
ContributorsJacobson, Neal (Author) / Gadau, Juergen (Thesis advisor) / Laubichler, Manfred (Committee member) / Pratt, Stephen (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
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
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