Matching Items (45)
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
The dynamics of urban water use are characterized by spatial and temporal variability that is influenced by associated factors at different scales. Thus it is important to capture the relationship between urban water use and its determinants in a spatio-temporal framework in order to enhance understanding and management of urban water demand. This dissertation aims to contribute to understanding the spatio-temporal relationships between single-family residential (SFR) water use and its determinants in a desert city. The dissertation has three distinct papers to support this goal. In the first paper, I demonstrate that aggregated scale data can be reliably used to study the relationship between SFR water use and its determinants without leading to significant ecological fallacy. The usability of aggregated scale data facilitates scientific inquiry about SFR water use with more available aggregated scale data. The second paper advances understanding of the relationship between SFR water use and its associated factors by accounting for the spatial and temporal dependence in a panel data setting. The third paper of this dissertation studies the historical contingency, spatial heterogeneity, and spatial connectivity in the relationship of SFR water use and its determinants by comparing three different regression models. This dissertation demonstrates the importance and necessity of incorporating spatio-temporal components, such as scale, dependence, and heterogeneity, into SFR water use research. Spatial statistical models should be used to understand the effects of associated factors on water use and test the effectiveness of certain management policies since spatial effects probably will significantly influence the estimates if only non-spatial statistical models are used. Urban water demand management should pay attention to the spatial heterogeneity in predicting the future water demand to achieve more accurate estimates, and spatial statistical models provide a promising method to do this job.
ContributorsOuyang, Yun (Author) / Wentz, Elizabeth (Thesis advisor) / Ruddell, Benjamin (Thesis advisor) / Harlan, Sharon (Committee member) / Janssen, Marcus (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
Ponderosa pine forests are a dominant land cover type in semiarid montane areas. Water supplies in major rivers of the southwestern United States depend on ponderosa pine forests since these ecosystems: (1) receive a significant amount of rainfall and snowfall, (2) intercept precipitation and transpire water, and (3) indirectly influence runoff by impacting the infiltration rate. However, the hydrologic patterns in these ecosystems with strong seasonality are poorly understood. In this study, we used a distributed hydrologic model evaluated against field observations to improve our understandings on spatial controls of hydrologic patterns, appropriate model resolution to simulate ponderosa pine ecosystems and hydrologic responses in the context of contrasting winter to summer transitions. Our modeling effort is focused on the hydrologic responses during the North American Monsoon (NAM), winter and spring periods. In Chapter 2, we utilized a distributed model explore the spatial controls on simulated soil moisture and temporal evolution of these spatial controls as a function of seasonal wetness. Our findings indicate that vegetation and topographic curvature are spatial controls. Vegetation controlled patterns during dry summer period switch to fine-scale terrain curvature controlled patterns during persistently wet NAM period. Thus, a climatic threshold involving rainfall and weather conditions during the NAM is identified when high rainfall amount (such as 146 mm rain in August, 1997) activates lateral flux of soil moisture and frequent cloudy cover (such as 42% cloud cover during daytime of August, 1997) lowers evapotranspiration. In Chapter 3, we investigate the impacts of model coarsening on simulated soil moisture patterns during the NAM. Results indicate that model aggregation quickly eradicates curvature features and its spatial control on hydrologic patterns. A threshold resolution of ~10% of the original terrain is identified through analyses of homogeneity indices, correlation coefficients and spatial errors beyond which the fidelity of simulated soil moisture is no longer reliable. Based on spatial error analyses, we detected that the concave areas (~28% of hillslope) are very sensitive to model coarsening and root mean square error (RMSE) is higher than residual soil moisture content (~0.07 m3/m3 soil moisture) for concave areas. Thus, concave areas need to be sampled for capturing appropriate hillslope response for this hillslope. In Chapter 4, we investigate the impacts of contrasting winter to summer transitions on hillslope hydrologic responses. We use a distributed hydrologic model to generate a consistent set of high-resolution hydrologic estimates. Our model is evaluated against the snow depth, soil moisture and runoff observations over two water years yielding reliable spatial distributions during the winter to summer transitions. We find that a wet winter followed by a dry summer promotes evapotranspiration losses (spatial averaged ~193 mm spring ET and ~ 600 mm summer ET) that dry the soil and disconnect lateral fluxes in the forested hillslope, leading to soil moisture patterns resembling vegetation patches. Conversely, a dry winter prior to a wet summer results in soil moisture increases due to high rainfall and low ET during the spring (spatially averaged 78 mm ET and 232 mm rainfall) and summer period (spatially averaged 147 mm ET and 247 mm rainfall) which promote lateral connectivity and soil moisture patterns with the signature of terrain curvature. An opposing temporal switch between infiltration and saturation excess runoff is also identified. These contrasting responses indicate that the inverse relation has significant consequences on hillslope water availability and its spatial distribution with implications on other ecohydrological processes including vegetation phenology, groundwater recharge and geomorphic development. Results from this work have implications on the design of hillslope experiments, the resolution of hillslope scale models, and the prediction of hydrologic conditions in ponderosa pine ecosystems. In addition, our findings can be used to select future hillslope sites for detailed ecohydrological investigations. Further, the proposed methodology can be useful for predicting responses to climate and land cover changes that are anticipated for the southwestern United States.
ContributorsMahmood, Taufique Hasan (Author) / Vivoni, Enrique R. (Thesis advisor) / Whipple, Kelin X. (Committee member) / Shock, Everett (Committee member) / Heimsath, Arjun M. (Committee member) / Ruddell, Benjamin (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
In this project, I investigated the ecosystem services, or lack thereof, that landscape designs created in terms of microclimate modification at 11 residential homes throughout the Phoenix Metro Area. I also created an article for the homeowners who participated, explaining what I did and how they could apply my research. My research question was how a person can achieve a comfortable outdoor climate in their yard without over-using scarce water resources. I hypothesized that there would be a negative correlation between the maximum air temperature and the percent shade in each yard, regardless of the percent grass. I analyzed the data I collected using the program, R, and discovered that my hypothesis was supported for the month of July. These results are in line with previous studies on the subject and can help homeowners make informed decisions about the effects their landscaping choices might have.
ContributorsBarton, Erin Michaela (Author) / Hall, Sharon (Thesis director) / Ruddell, Benjamin (Committee member) / Spielmann, Katherine (Committee member) / Barrett, The Honors College (Contributor) / School of Sustainability (Contributor)
Created2014-05
Description
There is an interest in citizen scientist networks such as CoCoRaHS to develop an air temperature sensor with a solar shield that is both extremely low cost and user friendly for use in widespread data collection in order to analyze urban microclimates. This paper outlines work done to develop a low cost micrometeorology instrument to fulfill the design requirements set by CoCoRaHS. While the first two revisions of this technology had significant changes in development, a third revision was created as a proof of concept that low cost temperature sensors could be used in an array to accurately measure air temperature without solar radiation interference. Another technology, described as revision four, called the iButton was also evaluated and displayed promising ability to log temperatures, but costs too much for the ultra-low cost design goal. Additionally, work was done to design a radiation shield that will be prototyped and tested alongside commercial radiation shields. This controlled experiment will also include further evaluation of the iButton and the next revision of a custom microclimate temperature sensing unit to determine the best option for widespread field testing.
ContributorsMarshall, Travis Keith (Author) / Jordan, Shawn (Thesis director) / Ruddell, Benjamin (Committee member) / Barrett, The Honors College (Contributor) / Department of Engineering (Contributor)
Created2014-05
Description
Thirty six percent of Americans are obese and thirty three percent are overweight; obesity has become a known killer in the U.S. yet its prevalence has maintained a firm grasp on the U.S. population and continues to spread across the globe as other countries slowly adopt the American lifestyle. A survey was compiled collecting demographic and body mass index (BMI) information, as well as Tanofsky-Kraff’s (2009) “Assess Eating in the Absence of Hunger” survey questions. The survey used for this study was emailed out to Arizona State University students in Barrett, The Honors College, and the ASU School of Nutrition and Health Promotion listservs. A total of 457 participants completed the survey, 72 males and 385 females (mean age, 24.5±7.7 y; average body mass index (BMI), 23.4 ± 4.8 [a BMI of 25-29.9 is classified as overweight]). When comparing BMI with the living situation, 71% of obese students were living at home with family versus off campus with friends or alone. For comparison, 45% of normal weight students lived at home with family. These data could help structure prevention plans targeting college students by focusing on weight gain prevention at the family level. Results from the Tanofsky-Kraff (2009) survey revealed there was not a significant relationship between external or physical cues and BMI in men or women, but there was a significant positive correlation between emotional cues and BMI in women only. Anger and sadness were the emotional cues in women related to initiating consumption past satiation and consumption following several hours of fasting. Although BMI was inversely related to physical activity in this sample (r = -0.132; p=0.005), controlling for physical activity did not impact the significant associations of BMI with anger or sadness (P>0.05). This information is important in targeting prevention programs to address behavioral change and cognitive awareness of the effects of emotion on over-consumption.
ContributorsGarza, Andrea Marie (Author) / Johnston, Carol (Thesis director) / Jacobs, Mark (Committee member) / Coletta, Dawn (Committee member) / Barrett, The Honors College (Contributor) / Department of Psychology (Contributor) / School of Life Sciences (Contributor)
Created2013-05
Description
New-onset diabetes after kidney transplantation (NODAT) occurs in 20% of kidney transplant patients. In 5 patients who are at risk for new-onset diabetes after kidney transplantation, skeletal muscle gene expression profiling was performed both before and after kidney transplant. The differences in gene expression before and after transplant were compared in order to identify specific genes that could be linked to developing NODAT. These findings could open new avenues for future research.
ContributorsLowery, Clint Curtis (Author) / Coletta, Dawn (Thesis director) / Katsanos, Christos (Committee member) / Willis, Wayne (Committee member) / Barrett, The Honors College (Contributor) / Department of Chemistry and Biochemistry (Contributor) / W. P. Carey School of Business (Contributor)
Created2014-05
Description
DNA methylation, a subset of epigenetics, has been found to be a significant marker associated with variations in gene expression and activity across the entire human genome. As of now, however, there is little to no information about how DNA methylation varies between different tissues inside a singular person's body. By using research data from a preliminary study of lean and obese clinical subjects, this study attempts to put together a profile of the differences in DNA methylation that can be observed between two particular body tissues from this subject group: blood and skeletal muscle. This study allows us to start describing the changes that occur at the epigenetic level that influence how differently these two tissues operate, along with seeing how these tissues change between individuals of different weight classes, especially in the context of the development of symptoms of Type 2 Diabetes.
ContributorsRappazzo, Micah Gabriel (Author) / Coletta, Dawn (Thesis director) / Katsanos, Christos (Committee member) / Dinu, Valentin (Committee member) / Barrett, The Honors College (Contributor) / Harrington Bioengineering Program (Contributor) / Department of Psychology (Contributor)
Created2013-12