Matching Items (106)
Filtering by
- Language: English
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
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
Mathematical epidemiology, one of the oldest and richest areas in mathematical biology, has significantly enhanced our understanding of how pathogens emerge, evolve, and spread. Classical epidemiological models, the standard for predicting and managing the spread of infectious disease, assume that contacts between susceptible and infectious individuals depend on their relative frequency in the population. The behavioral factors that underpin contact rates are not generally addressed. There is, however, an emerging a class of models that addresses the feedbacks between infectious disease dynamics and the behavioral decisions driving host contact. Referred to as “economic epidemiology” or “epidemiological economics,” the approach explores the determinants of decisions about the number and type of contacts made by individuals, using insights and methods from economics. We show how the approach has the potential both to improve predictions of the course of infectious disease, and to support development of novel approaches to infectious disease management.
ContributorsPerrings, Charles (Author) / Castillo-Chavez, Carlos (Author) / Chowell-Puente, Gerardo (Author) / Daszak, Peter (Author) / Fenichel, Eli P. (Author) / Finnoff, David (Author) / Horan, Richard D. (Author) / Kilpatrick, A. Marm (Author) / Kinzig, Ann (Author) / Kuminoff, Nicolai (Author) / Levin, Simon (Author) / Morin, Benjamin (Author) / Smith, Katherine F. (Author) / Springborn, Michael (Author) / Simon M. Levin Mathematical, Computational and Modeling Sciences Center (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor) / School of Human Evolution and Social Change (Contributor) / W.P. Carey School of Business (Contributor) / Economics (Contributor) / Julie Ann Wrigley Global Institute of Sustainability (Contributor)
Created2015-12-01
Description
Nutrient recycling by fish can be an important part of nutrient cycles in both freshwater and marine ecosystems. As a result, understanding the mechanisms that influence excretion elemental ratios of fish is of great importance to a complete understanding of aquatic nutrient cycles. As fish consume a wide range of diets that differ in elemental composition, stoichiometric theory can inform predictions about dietary effects on excretion ratios.
We conducted a meta-analysis to test the effects of diet elemental composition on consumption and nutrient excretion by fish. We examined the relationship between consumption rate and diet N : P across all laboratory studies and calculated effect sizes for each excretion metric to test for significant effects.
Consumption rate of N, but not P, was significantly negatively affected by diet N : P. Effect sizes of diet elemental composition on consumption-specific excretion N, P and N : P in laboratory studies were all significantly different from 0, but effect size for raw excretion N : P was not significantly different from zero in laboratory or field surveys.
Our results highlight the importance of having a mechanistic understanding of the drivers of consumer excretion rates and ratios. We suggest that more research is needed on how consumption and assimilation efficiency vary with N : P and in natural ecosystems in order to further understand mechanistic processes in consumer-driven nutrient recycling.
ContributorsMoody, Eric (Author) / Corman, Jessica (Author) / Elser, James (Author) / Sabo, John (Author) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor) / Julie Ann Wrigley Global Institute of Sustainability (Contributor)
Created2015-03-01
Description
Preserving a system’s viability in the presence of diversity erosion is critical if the goal is to sustainably support biodiversity. Reduction in population heterogeneity, whether inter- or intraspecies, may increase population fragility, either decreasing its ability to adapt effectively to environmental changes or facilitating the survival and success of ordinarily rare phenotypes. The latter may result in over-representation of individuals who may participate in resource utilization patterns that can lead to over-exploitation, exhaustion, and, ultimately, collapse of both the resource and the population that depends on it. Here, we aim to identify regimes that can signal whether a consumer–resource system is capable of supporting viable degrees of heterogeneity. The framework used here is an expansion of a previously introduced consumer–resource type system of a population of individuals classified by their resource consumption. Application of the Reduction Theorem to the system enables us to evaluate the health of the system through tracking both the mean value of the parameter of resource (over)consumption, and the population variance, as both change over time. The article concludes with a discussion that highlights applicability of the proposed system to investigation of systems that are affected by particularly devastating overly adapted populations, namely cancerous cells. Potential intervention approaches for system management are discussed in the context of cancer therapies.
ContributorsKareva, Irina (Author) / Morin, Benjamin (Author) / Castillo-Chavez, Carlos (Author) / Simon M. Levin Mathematical, Computational and Modeling Sciences Center (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Human Evolution and Social Change (Contributor) / Julie Ann Wrigley Global Institute of Sustainability (Contributor)
Created2015-02-01
Description
Evolving Earth observation and change detection techniques enable the automatic identification of Land Use and Land Cover Change (LULCC) over a large extent from massive amounts of remote sensing data. It at the same time poses a major challenge in effective organization, representation and modeling of such information. This study proposes and implements an integrated computational framework to support the modeling, semantic and spatial reasoning of change information with regard to space, time and topology. We first proposed a conceptual model to formally represent the spatiotemporal variation of change data, which is essential knowledge to support various environmental and social studies, such as deforestation and urbanization studies. Then, a spatial ontology was created to encode these semantic spatiotemporal data in a machine-understandable format. Based on the knowledge defined in the ontology and related reasoning rules, a semantic platform was developed to support the semantic query and change trajectory reasoning of areas with LULCC. This semantic platform is innovative, as it integrates semantic and spatial reasoning into a coherent computational and operational software framework to support automated semantic analysis of time series data that can go beyond LULC datasets. In addition, this system scales well as the amount of data increases, validated by a number of experimental results. This work contributes significantly to both the geospatial Semantic Web and GIScience communities in terms of the establishment of the (web-based) semantic platform for collaborative question answering and decision-making.
ContributorsVadjunec, Jacqueline M. (Author) / Radel, Claudia (Author) / Turner II, B. L. (Author) / College of Liberal Arts and Sciences (Contributor) / School of Geographical Sciences and Urban Planning (Contributor) / Julie Ann Wrigley Global Institute of Sustainability (Contributor) / School of Sustainability (Contributor)
Created2016-10-25
Description
The growth rate hypothesis (GRH) proposes that higher growth rate (the rate of change in biomass per unit biomass, μ) is associated with higher P concentration and lower C∶P and N∶P ratios. However, the applicability of the GRH to vascular plants is not well-studied and few studies have been done on belowground biomass. Here we showed that, for aboveground, belowground and total biomass of three study species, μ was positively correlated with N∶C under N limitation and positively correlated with P∶C under P limitation. However, the N∶P ratio was a unimodal function of μ, increasing for small values of μ, reaching a maximum, and then decreasing. The range of variations in μ was positively correlated with variation in C∶N∶P stoichiometry. Furthermore, μ and C∶N∶P ranges for aboveground biomass were negatively correlated with those for belowground. Our results confirm the well-known association of growth rate with tissue concentration of the limiting nutrient and provide empirical support for recent theoretical formulations.
ContributorsYu, Qiang (Author) / Wu, Honghui (Author) / He, Nianpeng (Author) / Lu, Xiaotao (Author) / Wang, Zhiping (Author) / Elser, James (Author) / Wu, Jianguo (Author) / Han, Xingguo (Author) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor) / Julie Ann Wrigley Global Institute of Sustainability (Contributor) / School of Sustainability (Contributor)
Created2012-03-13
Grasshoppers Regulate N: P Stoichiometric Homeostasis by Changing Phosphorus Contents in Their Frass
Description
Nitrogen (N) and phosphorus (P) are important limiting nutrients for plant production and consumer performance in a variety of ecosystems. As a result, the N:P stoichiometry of herbivores has received increased attention in ecology. However, the mechanisms by which herbivores maintain N:P stoichiometric homeostasis are poorly understood. Here, using a field manipulation experiment we show that the grasshopper Oedaleus asiaticus maintains strong N:P stoichiometric homeostasis regardless of whether grasshoppers were reared at low or high density. Grasshoppers maintained homeostasis by increasing P excretion when eating plants with higher P contents. However, while grasshoppers also maintained constant body N contents, we found no changes in N excretion in response to changing plant N content over the range measured. These results suggest that O. asiaticus maintains P homeostasis primarily by changing P absorption and excretion rates, but that other mechanisms may be more important for regulating N homeostasis. Our findings improve our understanding of consumer-driven P recycling and may help in understanding the factors affecting plant-herbivore interactions and ecosystem processes in grasslands.
ContributorsZhang, Zijia (Author) / Elser, James (Author) / Cease, Arianne (Author) / Zhang, Ximei (Author) / Yu, Qiang (Author) / Han, Xingguo (Author) / Zhang, Guangming (Author) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor) / Julie Ann Wrigley Global Institute of Sustainability (Contributor) / School of Sustainability (Contributor)
Created2014-08-04
Description
A large fraction of the world grasslands and savannas are undergoing a rapid shift from herbaceous to woody-plant dominance. This land-cover change is expected to lead to a loss in livestock production (LP), but the impacts of woody-plant encroachment on this crucial ecosystem service have not been assessed. We evaluate how tree cover (TC) has affected LP at large spatial scales in rangelands of contrasting social–economic characteristics in the United States and Argentina. Our models indicate that in areas of high productivity, a 1% increase in TC results in a reduction in LP ranging from 0.6 to 1.6 reproductive cows (Rc) per km[superscript 2]. Mean LP in the United States is 27 Rc per km[superscript 2], so a 1% increase in TC results in a 2.5% decrease in mean LP. This effect is large considering that woody-plant cover has been described as increasing at 0.5% to 2% per y. On the contrary, in areas of low productivity, increased TC had a positive effect on LP. Our results also show that ecological factors account for a larger fraction of LP variability in Argentinean than in US rangelands. Differences in the relative importance of ecological versus nonecological drivers of LP in Argentina and the United States suggest that the valuation of ecosystem services between these two rangelands might be different. Current management strategies in Argentina are likely designed to maximize LP for various reasons we are unable to explore in this effort, whereas land managers in the United States may be optimizing multiple ecosystem services, including conservation or recreation, alongside LP.
ContributorsAnadon, Jose Daniel (Author) / Sala, Osvaldo (Author) / Turner II, B. L. (Author) / Bennett, Elena M. (Author) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor) / Julie Ann Wrigley Global Institute of Sustainability (Contributor) / School of Sustainability (Contributor) / School of Geographical Sciences and Urban Planning (Contributor)
Created2014-09-02