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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
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
Land management practices such as domestic animal grazing can alter plant communities via changes in soil structure and chemistry, species composition, and plant nutrient content. These changes can affect the abundance and quality of plants consumed by insect herbivores with consequent changes in population dynamics. These population changes can translate to massive crop damage and pest control costs. My dissertation focused on Oedaleus asiaticus, a dominant Asian locust, and had three main objectives. First, I identified morphological, physiological, and behavioral characteristics of the migratory ("brown") and non-migratory ("green") phenotypes. I found that brown morphs had longer wings, larger thoraxes and higher metabolic rates compared to green morphs, suggesting that developmental plasticity allows greater migratory capacity in the brown morph of this locust. Second, I tested the hypothesis of a causal link between livestock overgrazing and an increase in migratory swarms of O. asiaticus. Current paradigms generally assume that increased plant nitrogen (N) should enhance herbivore performance by relieving protein-limitation, increasing herbivorous insect populations. I showed, in contrast to this scenario, that host plant N-enrichment and high protein artificial diets decreased the size and viability of O. asiaticus. Plant N content was lowest and locust abundance highest in heavily livestock-grazed fields where soils were N-depleted, likely due to enhanced erosion and leaching. These results suggest that heavy livestock grazing promotes outbreaks of this locust by reducing plant protein content. Third, I tested for the influence of dietary imbalance, in conjunction with high population density, on migratory plasticity. While high population density has clearly been shown to induce the migratory morph in several locusts, the effect of diet has been unclear. I found that locusts reared at high population density and fed unfertilized plants (i.e. high quality plants for O. asiaticus) had the greatest migratory capacity, and maintained a high percent of brown locusts. These results did not support the hypothesis that poor-quality resources increased expression of migratory phenotypes. This highlights a need to develop new theoretical frameworks for predicting how environmental factors will regulate migratory plasticity in locusts and perhaps other insects.
ContributorsCease, Arianne (Author) / Harrison, Jon (Thesis advisor) / Elser, James (Thesis advisor) / DeNardo, Dale (Committee member) / Quinlan, Michael (Committee member) / Sabo, John (Committee member) / Arizona State University (Publisher)
Created2012
Description
Conditions during development can shape the expression of traits at adulthood, a phenomenon called developmental plasticity. In this context, factors such as nutrition or health state during development can affect current and subsequent physiology, body size, brain structure, ornamentation, and behavior. However, many of the links between developmental and adult phenotype are poorly understood. I performed a series of experiments using a common molecular currency - carotenoid pigments - to track somatic and reproductive investments through development and into adulthood. Carotenoids are red, orange, or yellow pigments that: (a) animals must acquire from their diets, (b) can be physiologically beneficial, acting as antioxidants or immunostimulants, and (c) color the sexually attractive features (e.g., feathers, scales) of many animals. I studied how carotenoid nutrition and immune challenges during ontogeny impacted ornamental coloration and immune function of adult male mallard ducks (Anas platyrhynchos). Male mallards use carotenoids to pigment their yellow beak, and males with more beaks that are more yellow are preferred as mates, have increased immune function, and have higher quality sperm. In my dissertation work, I established a natural context for the role that carotenoids and body condition play in the formation of the adult phenotype and examined how early-life experiences, including immune challenges and dietary access to carotenoids, affect adult immune function and ornamental coloration. Evidence from mallard ducklings in the field showed that variation in circulating carotenoid levels at hatch are likely driven by maternal allocation of carotenoids, but that carotenoid physiology shifts during the subsequent few weeks to reflect individual foraging habits. In the lab, adult beak color expression and immune function were more tightly correlated with body condition during growth than body condition during subsequent stages of development or adulthood. Immune challenges during development affected adult immune function and interacted with carotenoid physiology during adulthood, but did not affect adult beak coloration. Dietary access to carotenoids during development, but not adulthood, also affected adult immune function. Taken together, these results highlight the importance of the developmental stage in shaping certain survival-related traits (i.e., immune function), and lead to further questions regarding the development of ornamental traits.
ContributorsButler, Michael (Author) / McGraw, Kevin J. (Thesis advisor) / Chang, Yung (Committee member) / Deviche, Pierre (Committee member) / DeNardo, Dale (Committee member) / Rutowski, Ronald (Committee member) / Arizona State University (Publisher)
Created2012
Description
Parental care provides many benefits to offspring. One widely realized benefit is enhanced regulation of offspring's thermal environment. The developmental thermal environment during development can be optimized behaviorally through nest site selection and brooding, and it can be further enhanced by physiological heat production. In fact, enhancement of the developmental thermal environment has been proposed as the initial driving force for the evolution of endothermy in bird and mammals. I used pythons (Squamata: Pythonidae) to expand existing knowledge of behavioral and physiological parental tactics used to regulate offspring thermal environment. I first demonstrated that brooding behavior in the Children's python (Antaresia childreni) is largely driven by internal mechanisms, similar to solitary birds, suggesting that the early evolution of the parent-offspring association was probably hormonally driven. Two species of python are known to be facultatively thermogenic (i.e., are endothermic during reproduction). I expand current knowledge of thermogenesis in Burmese pythons (Python molurus) by demonstrating that females use their own body temperature to modulate thermogenesis. Although pythons are commonly cited as thermogenic, the actual extent of thermogenesis within the family Pythonidae is unknown. Thus, I assessed the thermogenic capability of five previously unstudied species of python to aid in understanding phylogenetic, morphological, and distributional influences on thermogenesis in pythons. Results suggest that facultative thermogenesis is likely rare among pythons. To understand why it is rare, I used an artificial model to demonstrate that energetic costs to the female likely outweigh thermal benefits to the clutch in species that do not inhabit cooler latitudes or lack large energy reserves. In combination with other studies, these results show that facultative thermogenesis during brooding in pythons likely requires particular ecological and physiological factors for its evolution.
ContributorsBrashears, Jake (Author) / DeNardo, Dale (Thesis advisor) / Harrison, Jon (Committee member) / Deviche, Pierre (Committee member) / McGraw, Kevin (Committee member) / Smith, Andrew (Committee member) / Arizona State University (Publisher)
Created2012
Description
An organism's ability to maintain optimal body temperature is extremely important for sustaining physiological and behavioral processes necessary for survival. However, like other physiological systems, thermobiology can be influenced by the availability of resources. Water is a vital resource that has profound implications on many aspects of biological function, including thermoregulatory pathways. However, water availability has a tendency fluctuate within any given ecosystem. While several studies have investigated the influence of water availability on a range of thermoregulatory pathways, very little attention has been given to its influence on Voluntary Maximum Temperature (VMT). We investigated the effects of dehydration on Voluntary Maximum Temperature in a captive population of Gila monsters (Heloderma suspectum). Gila monsters are large-bodied, desert dwelling lizards that experience periods of seasonal dehydration. Additionally, the effects of dehydration on their physiology and behavior have been extensively studied. We hypothesized that dehydration would reduce VMT. As expected, there was a significant decrease in exit temperature as blood osmolality increased. This is presumed to be in an effort to decrease water loss. Adaptations that allow desert dwelling organisms to conserve water are highly advantageous due to seasonal water constraints. Our findings offer insight on how the behavior of these organisms may change in response to changes in climate.
ContributorsHartson, Callie Elizabeth (Author) / DeNardo, Dale (Thesis director) / Angilletta, Michael (Committee member) / Camacho, Agus (Committee member) / School of Life Sciences (Contributor) / School of Human Evolution and Social Change (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Identifying disease biomarkers may aid in the early detection of breast cancer and improve patient outcomes. Recent evidence suggests that tumors are immunogenic and therefore patients may launch an autoantibody response to tumor associated antigens. Single-chain variable fragments of autoantibodies derived from regional lymph node B cells of breast cancer patients were used to discover these tumor associated biomarkers on protein microarrays. Six candidate biomarkers were discovered from 22 heavy chain-only variable region antibody fragments screened. Validation tests are necessary to confirm the tumorgenicity of these antigens. However, the use of single-chain variable autoantibody fragments presents a novel platform for diagnostics and cancer therapeutics.
ContributorsSharman, M. Camila (Author) / Magee, Dewey (Mitch) (Thesis director) / Wallstrom, Garrick (Committee member) / Petritis, Brianne (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor) / Virginia G. Piper Center for Personalized Diagnostics (Contributor) / Biodesign Institute (Contributor)
Created2012-12
Description
There are numerous strategies for determining an organism's metabolic rate, one of which is the heart rate method. The heart rate method is based on a relationship between an organism's heart rate and its oxygen consumption (V(O2)). Although validations of the heart rate method have focused on adult animals, researchers could benefit from applying this method to embryonic animals. In this study, the heart rate's reliability as an indicator of oxygen consumption in early stage embryos of reptiles (or more specifically, lizards) is evaluated. The focus is primarily on the earliest stages of cardiovascular detection. The results suggest that while it may be possible to use a reliable heart rate method to find an accurate value for oxygen consumption of a group of early embryos in lizards if the oxygen pulse can be accurately identified, it is more likely that in the earliest stages of cardiovascular development, the heart rate cannot serve as a reliable indicator of V(O2) because it may not be the primary manner in which oxygen is distributed in Sceloporus undulatus.
ContributorsHambsch, Zakary Jordan (Author) / Angilletta, Michael (Thesis director) / DeNardo, Dale (Committee member) / Condon, Catriona (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2013-05
Description
Attitudes toward animal welfare have been evolving in our society as we have developed from early agricultural roots to an increasingly urban and technologically advanced community. However, despite the growing societal appreciation and care for animals in our homes and backyards, veterinarians are still faced with cases of abuse and neglect. Although it may seem obvious for veterinarians, as animal welfare advocates, to confront this dilemma each time they are faced with it, that is not always the case. In order to assess the responsibilities of veterinarians in regard to neglect and abuse, an extensive literature review and analysis was performed and practicing veterinarians were interviewed to determine their attitudes regarding the responsibility to report suspected cases of animal neglect and abuse. Specifically, these interviews focused on such topics as the educational background of the practitioners, how empathy impacts their perception of animal welfare, their relationship with law enforcement agencies, and related questions. The study demonstrated that the most prominent factor in a veterinarian's understanding of violations of animal welfare stems from their educational background. Therefore, it is recommended that veterinary medicine programs alter their curricula to emphasize animal welfare training and the obligation of veterinarians to report suspected cases of neglect and abuse.
ContributorsMichael, Allison Therese (Author) / Minteer, Ben (Thesis director) / Ellison, Karin (Committee member) / DeNardo, Dale (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2013-12
Description
Suicide is one of the leading causes of death worldwide and statistical analysis of suicide by profession reveals that physicians and veterinarians experience abnormally high suicide rates. This paper seeks to provide a comprehensive literature review over what some general theories of suicide are, why these professions exhibit high suicide rates, what assistance is currently being provided, and where do these assistance efforts succeed or fail. Moreover, this paper addresses what advancements may be made within these fields to further combat suicide in physicians and veterinarians. To achieve this, general theories behind suicide, risk factors unique to or heavily prevalent in these professions, and current assistance efforts are read, organized, and summarized.<br/><br/>A summary of these risk factors includes stress and mental health disorders accumulated through school and work, personal and professional isolation, access to lethal substances, suicide contagion, exposure to euthanasia, and the role of perfectionism. There are several assistance efforts in place with the most successful ones being highly personalized, but many are still underutilized. Moreover, the stigma of suicide pervades these professions and is addressed by several researchers as something to combat or prevent. Going forward, it is hopeful that not only will more assistance efforts will be created and provided for physicians and veterinarians suffering from suicidal tendencies, but efforts to reduce the stigma of suicide be implemented and utilized as soon as possible.
ContributorsSinclair, Andrew (Author) / DeNardo, Dale (Thesis director) / Sterner, Beckett (Committee member) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05