Matching Items (134)
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
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
Some of the most talented, innovative, and experimental artists are students, but they are often discouraged by the price of higher education and lack of scholarship or funding opportunities. Additionally, the art industry has become stagnant. Traditional brick-and-mortar galleries are not willing to represent young, unknown artists. Their overhead is simply too high for risky choices.
The Student Art Project is art patronage for the 21st century—a curated online gallery featuring exceptional student artists. The Student Art Project is a highly curated experience for buyers. Only five artists are featured each month. Buyers are not bombarded with thousands of different products and separate artists “shops”. They can read artists bios and find art they connect with.
Student artists apply through an online form. Once accepted to the program, artists receive a $200 materials stipend to create an exclusive collection of 5-10 pieces. Original artwork and limited edition prints are sold through our website. These collections can potentially fund an entire year of college tuition, a life-changing amount for many students.
Brick-and-mortar galleries typically take 40-60% of the retail price of artwork. The Student Art Project will only take 30%, which we will use to reinvest in future artists. Other art websites, like Etsy, require the artists to ship, invoice, and communicate with customers. For students, this means less time spent in the classroom and less time developing their craft. The Student Art Project handles all business functions for our artists, allowing them to concentrate on what really matters, their education.
The Student Art Project is art patronage for the 21st century—a curated online gallery featuring exceptional student artists. The Student Art Project is a highly curated experience for buyers. Only five artists are featured each month. Buyers are not bombarded with thousands of different products and separate artists “shops”. They can read artists bios and find art they connect with.
Student artists apply through an online form. Once accepted to the program, artists receive a $200 materials stipend to create an exclusive collection of 5-10 pieces. Original artwork and limited edition prints are sold through our website. These collections can potentially fund an entire year of college tuition, a life-changing amount for many students.
Brick-and-mortar galleries typically take 40-60% of the retail price of artwork. The Student Art Project will only take 30%, which we will use to reinvest in future artists. Other art websites, like Etsy, require the artists to ship, invoice, and communicate with customers. For students, this means less time spent in the classroom and less time developing their craft. The Student Art Project handles all business functions for our artists, allowing them to concentrate on what really matters, their education.
ContributorsDangler, Rebecca Leigh (Author) / Trujillo, Rhett (Thesis director) / Coleman, Sean (Committee member) / Barrett, The Honors College (Contributor) / Herberger Institute for Design and the Arts (Contributor) / Department of Management (Contributor)
Created2015-05
Description
Drought is one of the most pressing issues affecting the future of the standard of living here in Phoenix. With the threat of water rationing and steep price hikes looming on the horizon for water customers in California, the desert southwest, and in drought-stricken communities worldwide, industrial designers are in a prime position to help improve the experience of water conservation so that consumers are willing to start taking conscious steps toward rethinking their relationship with water usage.
In a research group, several designers sought to understand the depth and complexity of this highly politicized issue by interviewing a wide variety of stakeholders, including sustainability experts, landscapers, water company executives, small business owners, reservoir forest rangers, and many more. Data synthesis led to the conclusion that residential water use is a lifestyle issue, and the only real way to conserve involves a significant shift in the collective idea of an “ideal” home—lawns, pools, and overwatered landscaping contribute to 70% of all water use by residences in the Phoenix area. The only real way to conserve involves increasing population density and creating communal green spaces.
DR. DISH is a dishwashing device that is meant to fit into the high-density living spaces that are rapidly being built in the face of the massive exodus of people into the world’s cities. To help busy apartment and condominium dwellers conserve water and time, DR. DISH converts a standard kitchen sink into a small dishwasher, which uses significantly less water than hand-washing dishes or rinsing dishes before putting them into a conventional dishwasher. Using advanced filtration technology and a powerful rinse cycle, a load dishes can be cleaned with about 2 gallons of water. Fully automating the dishwashing process also saves the user time and minimizes unpleasant contact with food residue and grease.
This device is meant to have a significant impact upon the water use of households that do not have a dishwasher, or simply do not use their dishwasher. With a low target price point and myriad convenient features, DR. DISH is a high-tech solution that promises water savings at a time when every effort toward conservation is absolutely critical. As we move toward a new era in determining water rights and imposing mandatory restrictions upon each and every person living in affected areas, creating conservation solutions that will be relevant for the lifestyles of the future is especially important, and the agility of designers in coming up with products that quickly cut consumer water consumption will be a key factor in determining whether humanity will be able to adapt to a new era in our relationship with natural resources.
In a research group, several designers sought to understand the depth and complexity of this highly politicized issue by interviewing a wide variety of stakeholders, including sustainability experts, landscapers, water company executives, small business owners, reservoir forest rangers, and many more. Data synthesis led to the conclusion that residential water use is a lifestyle issue, and the only real way to conserve involves a significant shift in the collective idea of an “ideal” home—lawns, pools, and overwatered landscaping contribute to 70% of all water use by residences in the Phoenix area. The only real way to conserve involves increasing population density and creating communal green spaces.
DR. DISH is a dishwashing device that is meant to fit into the high-density living spaces that are rapidly being built in the face of the massive exodus of people into the world’s cities. To help busy apartment and condominium dwellers conserve water and time, DR. DISH converts a standard kitchen sink into a small dishwasher, which uses significantly less water than hand-washing dishes or rinsing dishes before putting them into a conventional dishwasher. Using advanced filtration technology and a powerful rinse cycle, a load dishes can be cleaned with about 2 gallons of water. Fully automating the dishwashing process also saves the user time and minimizes unpleasant contact with food residue and grease.
This device is meant to have a significant impact upon the water use of households that do not have a dishwasher, or simply do not use their dishwasher. With a low target price point and myriad convenient features, DR. DISH is a high-tech solution that promises water savings at a time when every effort toward conservation is absolutely critical. As we move toward a new era in determining water rights and imposing mandatory restrictions upon each and every person living in affected areas, creating conservation solutions that will be relevant for the lifestyles of the future is especially important, and the agility of designers in coming up with products that quickly cut consumer water consumption will be a key factor in determining whether humanity will be able to adapt to a new era in our relationship with natural resources.
ContributorsMarcinkowski, Margaret Nicole (Author) / Shin, Dosun (Thesis director) / McDermott, Lauren (Committee member) / Barrett, The Honors College (Contributor) / The Design School (Contributor) / Herberger Institute for Design and the Arts (Contributor)
Created2015-05
Description
Fire Shelter Foam Assist is meant as a firefighter's last effort of survival when a wildfire threatens their position. When deployed, it will cover the firefighter as the fire blows over. By reducing the time of deployment and simplifying the process, firefighters will have more time to ensure the area around them is cleared. The Fire Shelter Foam Assist has features that allow it to auto deploy around the firefighter through the use of fire foam retardant. The fire foam retardant inflates the shelter as well as provides an extra layer of protection against the wildfire.
ContributorsSmith, Tori Elizabeth (Author) / Shin, Dosun (Thesis director) / McDermott, Lauren (Committee member) / Barrett, The Honors College (Contributor) / Herberger Institute for Design and the Arts (Contributor) / The Design School (Contributor)
Created2015-05
Description
After researching pediatric cancer experiences, an opportunity emerged creating a less intimidating environment for children undergoing chemotherapy. By means of adding a creative component to their IV pole and disguising machinery, children will be a part of an Imagination Voyage adventure. Creative themes allow for a journey on a pirate ship, or being in a fantasy castle by captivating children in playtime. The design allows for a frightening experience to become a positive one.
ContributorsHerold, Brittany Ann (Author) / Shin, Dosun (Thesis director) / McDermott, Lauren (Committee member) / Barrett, The Honors College (Contributor) / Herberger Institute for Design and the Arts (Contributor) / School of Sustainability (Contributor) / The Design School (Contributor)
Created2015-05
Description
I set out to better understand the issues, perceptions & solutions surrounding drought. The question that compelled my project was "What might be all the ways that we can improve the experience of conserving, reusing & educating on the topic of water." Through the process of design research I developed a system of products that improves the user experiences surrounding water. The result is IOW, an intelligent 3-product system that aims to make your water needs & wants smarter & less wasteful.
ContributorsShappee, Christian Kyle (Author) / Shin, Dosun (Thesis director) / McDermott, Lauren (Committee member) / Barrett, The Honors College (Contributor) / Herberger Institute for Design and the Arts (Contributor) / School of Sustainability (Contributor) / The Design School (Contributor)
Created2015-05