Matching Items (90)
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
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
Consideration of both biological and human-use dynamics in coupled social-ecological systems is essential for the success of interventions such as marine reserves. As purely human institutions, marine reserves have no direct effects on ecological systems. Consequently, the success of a marine reserve depends on managers` ability to alter human behavior in the direction and magnitude that supports reserve objectives. Further, a marine reserve is just one component in a larger coupled social-ecological system. The social, economic, political, and biological landscape all determine the social acceptability of a reserve, conflicts that arise, how the reserve interacts with existing fisheries management, accuracy of reserve monitoring, and whether the reserve is ultimately able to meet conservation and fishery enhancement goals. Just as the social-ecological landscape is critical at all stages for marine reserve, from initial establishment to maintenance, the reserve in turn interacts with biological and human use dynamics beyond its borders. Those interactions can lead to the failure of a reserve to meet management goals, or compromise management goals outside the reserve. I use a bio-economic model of a fishery in a spatially patchy environment to demonstrate how the pre-reserve fisheries management strategy determines the pattern of fishing effort displacement once the reserve is established, and discuss the social, political, and biological consequences of different patterns for the reserve and the fishery. Using a stochastic bio-economic model, I demonstrate how biological and human use connectivity can confound the accurate detection of reserve effects by violating assumptions in the quasi-experimental framework. Finally, I examine data on recreational fishing site selection to investigate changes in response to the announcement of enforcement of a marine reserve in the Gulf of California, Mexico. I generate a scale of fines that would fully or partially protect the reserve, providing a data-driven way for managers to balance biological and socio-economic goals. I suggest that natural resource managers consider human use dynamics with the same frequency, rigor, and tools as they do biological stocks.
ContributorsFujitani, Marie (Author) / Abbott, Joshua (Thesis advisor) / Fenichel, Eli (Thesis advisor) / Gerber, Leah (Committee member) / Anderies, John (Committee member) / Arizona State University (Publisher)
Created2014
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
Globally, many species of shark are facing rapid population decline. This is due to increasing fishing pressures, primarily from the booming demand in China for shark fins for soup. In recent years there has also been an increase in international shark conservation efforts, but there is still a long way to go in gathering support for those efforts. Public perception of sharks in America has been greatly influenced by negative media representations of them, Jaws being one of the most influential. Many of these representations are based on inaccurate information that has been disproven by science, but still lingers in popular culture. Symbolic Interactionism Theory proved to be a useful framework for unpacking the connections between public perception, mainstream culture and media, and conservation regarding sharks. A social psychological theory, Symbolic Interactionism describes the ways that people construct meaning about a topic through direct and indirect interactions, and how this meaning can change on individual, social, and cultural levels. By changing the way sharks are perceived and represented to the public, these important and incredible animals may gather the support they need to continue living in the world's oceans.
ContributorsCressler, Christina Nancy (Author) / Minteer, Ben (Thesis director) / Gerber, Leah (Committee member) / Ellison, Karin (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2014-05
Description
Consumption of seafood poses a substantial threat to global biodiversity. Chemical contamination found in both wild-caught and farmed seafood also presents significant health risks to consumers. Flame retardants, used in upholstery, plastics, clothing, and other products to reduce fire danger, are of particular concern as they are commonly found in the marine environment and permeate the tissues of fish that are sold for consumption via multiple pathways. By summarizing various metrics of sustainability and the mercury content in consumed species of fish and shellfish, researchers have found that high levels of chemical contamination was linked with lesser fishery sustainability. I conducted a literature review of flame retardant content in seafood to further compare contamination and sustainability in addition to the initial analysis with mercury. My review suggests that the widespread issue of fishery collapse could be alleviated by demonstrating to stakeholders that many unsustainable fish stocks are mutually disadvantageous for both human consumers and the environment. Future research should address the need for the collection of data that better represent actual global contaminant concentrations in seafood.
ContributorsNoziglia, Andrea Joyce (Author) / Gerber, Leah (Thesis director) / Smith, Andrew (Committee member) / Pratt, Stephen (Committee member) / Barrett, The Honors College (Contributor) / Herberger Institute for Design and the Arts (Contributor) / School of International Letters and Cultures (Contributor) / School of Life Sciences (Contributor)
Created2014-05
Description
Protein is an essential macronutrient in the human diet, but the source of this protein has both human health and environmental impacts. Health complications can result from protein deficiency, but the practices by which protein sources are raised, grown, or harvested have environmental consequences, potentially reducing biodiversity, essential habitat, and crucial stocks of natural resources. Terrestrial cultivation encroaches on natural habitats and consumes resources inefficiently, while overfishing has greatly depleted wild fishery stocks. These environmental factors, along with concerns about nutrients, contaminants and the ethics of animal protein has led to confusion about weighing the risks and benefits associated with alternative sources of protein. Providing consumers \u2014 and policy makers \u2014 with a comprehensive account of major protein sources and their impacts in an understandable form is crucial to reducing environmental degradation and improving human health. Here I provide a general framework to compare the health and environmental impacts of livestock, seafood, and plant protein, and illustrate the application of this framework with case studies for each of these categories.
ContributorsGeren, Sarah Lindsey (Author) / Gerber, Leah (Thesis director) / Smith, Andrew (Committee member) / Minteer, Ben (Committee member) / Barrett, The Honors College (Contributor) / School of Human Evolution and Social Change (Contributor) / School of Life Sciences (Contributor)
Created2014-05
DescriptionThis paper provides an analysis of the differences in impacts made by companies that promote their sustainability efforts. A comparison of companies reveals that the ones with greater supply chain influence and larger consumer bases can make more concrete progress in terms of accomplishment for the sustainability realm.
ContributorsBeaubien, Courtney Lynn (Author) / Anderies, John (Thesis director) / Allenby, Brad (Committee member) / Janssen, Marco (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2013-05
Description
Abstract This thesis is derived from the conservation biology field of study and seeks to chronicle and characterize the history of wolf conservation in the US, with a focus on post-ESA listing and present day events. The compelling question this thesis seeks to address is how to make long-term wolf conservation effective and feasible in the United States. An overview of wolf life history is provided, as well as a brief overview of early wolf-human interactions in Europe and the US, before reviewing the following regions in the US: Yellowstone, Idaho/Montana/Wyoming, Alaska, and Arizona. The trend identified in all regions is described as a hostile political atmosphere with particular resentment by some stakeholders towards the federal enforcement of wolf conservation via the ESA. A comparative section on Italy is provided in contrast to this US theme, as Italy tends to have a much more relaxed attitude towards wolf conservation. For success in the future of wolf conservation three suggestions are made. First, efforts to protect wolves through federal regulation are to be dismissed. Second, efforts should instead focus on education of key demographics regarding responsible environmental management and wolf management specifically. Thirdly, conservationists must actively strive to remarket the wolf as a symbol of the freedom of the west as opposed to the symbol of Washington's encroachment on state's rights.
ContributorsCampini, Conner Pennington (Author) / Smith, Andrew (Thesis director) / Gerber, Leah (Committee member) / Minteer, Ben (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2014-12
Description
Because of a projected surge of several billion urban inhabitants by mid-century, a rising urgency exists to advance local and strategically deployed measures intended to ameliorate negative consequences on urban climate (e.g., heat stress, poor air quality, energy/water availability). Here we highlight the importance of incorporating scale-dependent built environment induced solutions within the broader umbrella of urban sustainability outcomes, thereby accounting for fundamental physical principles. Contemporary and future design of settlements demands cooperative participation between planners, architects, and relevant stakeholders, with the urban and global climate community, which recognizes the complexity of the physical systems involved and is ideally fit to quantitatively examine the viability of proposed solutions. Such participatory efforts can aid the development of locally sensible approaches by integrating across the socioeconomic and climatic continuum, therefore providing opportunities facilitating comprehensive solutions that maximize benefits and limit unintended consequences.
ContributorsGeorgescu, Matei (Author) / Chow, Winston, 1951- (Author) / Brazel, Anthony J. (Author) / Trapido-Lurie, B (Author) / Roth, M (Author) / Benson-Lira, V (Author)
Created2015-06-09