Matching Items (118)
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
In an effort to address the lack of literature in on-campus active travel, this study aims to investigate the following primary questions:<br/>• What are the modes that students use to travel on campus?<br/>• What are the motivations that underlie the mode choice of students on campus?<br/>My first stage of research involved a series of qualitative investigations. I held one-on-one virtual interviews with students in which I asked them questions about the mode they use and why they feel that their chosen mode works best for them. These interviews served two functions. First, they provided me with insight into the various motivations underlying student mode choice. Second, they provided me with an indication of what explanatory variables should be included in a model of mode choice on campus.<br/>The first half of the research project informed a quantitative survey that was released via the Honors Digest to attract student respondents. Data was gathered on travel behavior as well as relevant explanatory variables.<br/>My analysis involved developing a logit model to predict student mode choice on campus and presenting the model estimation in conjunction with a discussion of student travel motivations based on the qualitative interviews. I use this information to make a recommendation on how campus infrastructure could be modified to better support the needs of the student population.
ContributorsMirtich, Laura Christine (Author) / Salon, Deborah (Thesis director) / Fang, Kevin (Committee member) / School of Public Affairs (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Purpose: To examine: (1) whether Non-Hispanic Blacks (NHB) and Non-Hispanic Whites (NHW) with diagnosed arthritis differed in self-reported physical activity (PA) levels, (2) if NHB and NHW with arthritis differed on potential correlates of PA based on the Social Ecological Model (Mcleroy et al., 1988), and (3) if PA participation varied by race/ethnicity after controlling for age, gender, education, and BMI. Methods: This study was a secondary data analysis of data collected from 2006-2008 in Chicago, IL as part of the Midwest Roybal Center for Health Promotion. Bivariate analyses were used to assess potential differences between race in meeting either ACR or ACSM PA guidelines. Comparisons by race between potential socio-demographic correlates and meeting physical activity guidelines were assessed using Chi-squares. Potential differences by race in psychosocial, arthritis, and health-related and environmental correlates were assessed using T-tests. Finally, logistic regression analyses were used to examine if race was still associated with PA after controlling for socio-demographic characteristics. Results: A greater proportion of NHW (68.1% and 35.3%) than NHB (46.5% and 20.9%) met both the arthritis-specific and the American College of Sports Medicine (ACSM) recommendations for physical activity, respectively. NHB had significantly lower self-efficacy for exercise and reported greater impairments in physical function compared to NHW. Likewise, NHB reported more crime and less aesthetics within their neighborhood. NHW were 2.56 times more likely to meet arthritis-specific PA guidelines than NHB after controlling for age, gender, education, marital status, and BMI. In contrast, after controlling for sociodemographic characteristics, age and gender were the only significant predictors of meeting ACSM PA guidelines. Discussion: There were significant differences between NHB and NHW individuals with arthritis in meeting PA guidelines. After controlling for age, gender, education, and BMI non-Hispanic White individuals were still significantly more likely to meet PA guidelines. Interventions aimed at promoting higher levels of physical activity among individuals with arthritis need to consider neighborhood aesthetics and crime when designing programs. More arthritis-specific programs are needed in close proximity to neighborhoods in an effort to promote physical activity.
ContributorsChuran, Christopher (Author) / Der Ananian, Cheryl (Thesis advisor) / Adams, Marc (Committee member) / Campbell, Kathryn (Committee member) / Arizona State University (Publisher)
Created2013
Description
Food system and health characteristics were evaluated across the last Waorani hunter-gatherer group in Amazonian Ecuador and a remote neighboring Kichwa indigenous subsistence agriculture community. Hunter-gatherer food systems like the Waorani foragers may not only be nutritionally, but also pharmaceutically beneficial because of high dietary intake of varied plant phytochemical compounds. A modern diet that reduces these dietary plant defense phytochemicals below levels typical in human evolutionary history may leave humans vulnerable to diseases that were controlled through a foraging diet. Few studies consider the health impact of the recent drastic reduction of plant phytochemical content in the modern global food system, which has eliminated essential components of food because they are not considered "nutrients". The antimicrobial and anti-inflammatory nature of the food system may not only regulate infectious pathogens and inflammatory disease, but also support beneficial microbes in human hosts, reducing vulnerability to chronic diseases. Waorani foragers seem immune to certain infections with very low rates of chronic disease. Does returning to certain characteristics of a foraging food system begin to restore the human body microbe balance and inflammatory response to evolutionary norms, and if so, what implication does this have for the treatment of disease? Several years of data on dietary and health differences across the foragers and the farmers was gathered. There were major differences in health outcomes across the board. In the Waorani forager group there were no signs of infection in serious wounds such as 3rd degree burns and spear wounds. The foragers had one-degree lower body temperature than the farmers. The Waorani had an absence of signs of chronic diseases including vision and blood pressure that did not change markedly with age while Kichwa farmers suffered from both chronic diseases and physiological indicators of aging. In the Waorani forager population, there was an absence of many common regional infectious diseases, from helminthes to staphylococcus. Study design helped control for confounders (exercise, environment, genetic factors, non-phytochemical dietary intake). This study provides evidence of the major role total phytochemical dietary intake plays in human health, often not considered by policymakers and nutritional and agricultural scientists.
ContributorsLondon, Douglas (Author) / Tsuda, Takeyuki (Thesis advisor) / Beezhold, Bonnie L (Committee member) / Hruschka, Daniel (Committee member) / Eder, James (Committee member) / Arizona State University (Publisher)
Created2012
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
This dissertation is intended to tie together a body of work which utilizes a variety of methods to study applied mathematical models involving heterogeneity often omitted with classical modeling techniques. I posit three cogent classifications of heterogeneity: physiological, behavioral, and local (specifically connectivity in this work). I consider physiological heterogeneity using the method of transport equations to study heterogeneous susceptibility to diseases in open populations (those with births and deaths). I then present three separate models of behavioral heterogeneity. An SIS/SAS model of gonorrhea transmission in a population of highly active men-who-have-sex-with-men (MSM) is presented to study the impact of safe behavior (prevention and self-awareness) on the prevalence of this endemic disease. Behavior is modeled in this examples via static parameters describing consistent condom use and frequency of STD testing. In an example of behavioral heterogeneity, in the absence of underlying dynamics, I present a generalization to ``test theory without an answer key" (also known as cultural consensus modeling or CCM). CCM is commonly used to study the distribution of cultural knowledge within a population. The generalized framework presented allows for selecting the best model among various extensions of CCM: multiple subcultures, estimating the degree to which individuals guess yes, and making competence homogenous in the population. This permits model selection based on the principle of information criteria. The third behaviorally heterogeneous model studies adaptive behavioral response based on epidemiological-economic theory within an $SIR$ epidemic setting. Theorems used to analyze the stability of such models with a generalized, non-linear incidence structure are adapted and applied to the case of standard incidence and adaptive incidence. As an example of study in spatial heterogeneity I provide an explicit solution to a generalization of the continuous time approximation of the Albert-Barabasi scale-free network algorithm. The solution is found by recursively solving the differential equations via integrating factors, identifying a pattern for the coefficients and then proving this observed pattern is consistent using induction. An application to disease dynamics on such evolving structures is then studied.
ContributorsMorin, Benjamin (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Hiebeler, David (Thesis advisor) / Hruschka, Daniel (Committee member) / Suslov, Sergei (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
With an excessive amount of resources in the United States healthcare system being spent on the treatment of diseases that are largely preventable through lifestyle change, the need for successful physical activity interventions is apparent. Unfortunately an individual's physical activity and health goals are often not supported by the social context of their daily lives. This single-case design study, Walking Intervention through Text messaging for CoHabiting individuals (WalkIT CoHab), looks at the efficacy of a text based adaptive physical activity intervention to promote walking over a three month period and the effects of social support in intervention performance in three pairs of cohabiting pairs of individuals (n=6). Mean step increase from baseline to intervention ranged from 1300 to 3000 steps per day for all individuals, an average 45.87% increase in physical activity. Goal attainment during the intervention ranged from 43.96% to 71.43%, meaning all participants exceeded the 40% success rate predicted by 60th percentile goals. Social support scores for study partners, unlike social support scores for family and friends, were often in the high social support range and had a moderate increase from pre to post visits for most participants. Although there was variation amongst participants, there was a high correlation in physical activity trends and successful goal attainment in each pair of participants. Less ambitious percentile goals and more personalized motivational text messages might be beneficial to some participants. An extended intervention, something the majority of participants expressed interest in, would further support the efficacy of this behavioral intervention and allow for possible long term benefits of social support in the intervention to be investigated.
ContributorsFernandez, Jacqueline Alyssa (Author) / Adams, Marc (Thesis director) / Angadi, Siddhartha (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2015-05
Description
Due to persistent undernutrition in India and the increased demands placed on a woman’s body during childbearing and lactation, the Indian government has implemented a program to provide supplemental nutrition packets to women in rural India. This study examines the factors influencing uptake of nutritional packets by lactating mothers in southern, rural Rajasthan. Women were recruited from 65 villages in Rajasthan, India (n=149, minimum of 2 per village) to evaluate the relationship of nutrition packet uptake and two factors--education levels and distance to the health center.
Level of education had little impact on whether or not women received the nutrition packet. Of those women with no education, 63.1% received the packet. Of those with any education, 63.9% got the packet.
In contrast, distance was strongly correlated with whether or not women received the packet. For example, of the women living within 200 meters of the health center, 93.2% received a nutrition packet. Of the women living between 250 meters and one kilometer of the health center, 68.4% received a nutrition packet. Of the women living over one kilometer from the health center, only 25% received a nutrition packet. The relationship between uptake of packets and women’s perception of distance to the health center was also explored. Out of 50 women who did not receive the packet, all of the women who said there was no health center in their village did live more than one kilometer from a health center. Of the women who lived between 250 meters and one kilometer from the health center, 40% felt it was too far. Of the women who lived more than a kilometer from the health center, 66.7% felt it was too far and 29.6% said there was no health center in their village. Again, it does not appear that ‘too far’ is just a default reason for women, but that actual distance, more so than education, is a major contributing factor in their ability to take the nutrition packet. These findings suggest that improving access to supplemental nutrition packets at the village level may increase uptake by the women.
Level of education had little impact on whether or not women received the nutrition packet. Of those women with no education, 63.1% received the packet. Of those with any education, 63.9% got the packet.
In contrast, distance was strongly correlated with whether or not women received the packet. For example, of the women living within 200 meters of the health center, 93.2% received a nutrition packet. Of the women living between 250 meters and one kilometer of the health center, 68.4% received a nutrition packet. Of the women living over one kilometer from the health center, only 25% received a nutrition packet. The relationship between uptake of packets and women’s perception of distance to the health center was also explored. Out of 50 women who did not receive the packet, all of the women who said there was no health center in their village did live more than one kilometer from a health center. Of the women who lived between 250 meters and one kilometer from the health center, 40% felt it was too far. Of the women who lived more than a kilometer from the health center, 66.7% felt it was too far and 29.6% said there was no health center in their village. Again, it does not appear that ‘too far’ is just a default reason for women, but that actual distance, more so than education, is a major contributing factor in their ability to take the nutrition packet. These findings suggest that improving access to supplemental nutrition packets at the village level may increase uptake by the women.
ContributorsJeffers, Eva Marie (Author) / Hruschka, Daniel (Thesis director) / Maupin, Jonathan (Committee member) / Cook, Jeffrey (Committee member) / Barrett, The Honors College (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2015-05
Description
2015 marks the deadline for the UN Millennium Development Goal 5 to reduce global maternal mortality rate (MMR) by 75% since 1990. As of 2015, MMR has only been reduced by 45%. Many international organizations claim that more medically trained midwives can meet global maternal health care needs. This study investigates two major questions. What is the role of midwives in diverse international maternal healthcare contexts? How do midwives in these different contexts define their roles and the barriers to providing the best care for women? From May to August 2015, I conducted over 70 interviews with midwives in Netherlands, Sweden, Rwanda, Bangladesh, Australia and Guatemala, interviewing between 6 and 13 midwives from each country. The majority of midwives defined their roles as supporting women's individual capacities and power through normal birth, and knowing when to refer when high-risk complications arise. Although thematic barriers vary by country, midwives in all countries believed that maternal healthcare can be improved by increased collaboration between midwives and other health care professionals, better access to culturally appropriate services, and greater public awareness of the role of midwives.
ContributorsCarson, Anna Elizabeth (Author) / Hruschka, Daniel (Thesis director) / Maupin, Jonathan (Committee member) / School of International Letters and Cultures (Contributor) / School of Human Evolution and Social Change (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05