Matching Items (139)
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 theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
ContributorsSanborn, Barbara (Author) / Suslov, Sergei K (Thesis advisor) / Suslov, Sergei (Committee member) / Spielberg, John (Committee member) / Quigg, John (Committee member) / Menéndez, Jose (Committee member) / Jones, Donald (Committee member) / Arizona State University (Publisher)
Created2011
Description
For over a century, researchers have been investigating collective cognition, in which a group of individuals together process information and act as a single cognitive unit. However, I still know little about circumstances under which groups achieve better (or worse) decisions than individuals. My dissertation research directly addressed this longstanding question, using the house-hunting ant Temnothorax rugatulus as a model system. Here I applied concepts and methods developed in psychology not only to individuals but also to colonies in order to investigate differences of their cognitive abilities. This approach is inspired by the superorganism concept, which sees a tightly integrated insect society as the analog of a single organism. I combined experimental manipulations and models to elucidate the emergent processes of collective cognition. My studies show that groups can achieve superior cognition by sharing the burden of option assessment among members and by integrating information from members using positive feedback. However, the same positive feedback can lock the group into a suboptimal choice in certain circumstances. Although ants are obligately social, my results show that they can be isolated and individually tested on cognitive tasks. In the future, this novel approach will help the field of animal behavior move towards better understanding of collective cognition.
ContributorsSasaki, Takao (Author) / Pratt, Stephen C (Thesis advisor) / Amazeen, Polemnia (Committee member) / Liebig, Jürgen (Committee member) / Janssen, Marco (Committee member) / Fewell, Jennifer (Committee member) / Hölldobler, Bert (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
The spread of invasive species may be greatly affected by human responses to prior species spread, but models and estimation methods seldom explicitly consider human responses. I investigate the effects of management responses on estimates of invasive species spread rates. To do this, I create an agent-based simulation model of an insect invasion across a county-level citrus landscape. My model provides an approximation of a complex spatial environment while allowing the "truth" to be known. The modeled environment consists of citrus orchards with insect pests dispersing among them. Insects move across the simulation environment infesting orchards, while orchard managers respond by administering insecticide according to analyst-selected behavior profiles and management responses may depend on prior invasion states. Dispersal data is generated in each simulation and used to calculate spread rate via a set of estimators selected for their predominance in the empirical literature. Spread rate is a mechanistic, emergent phenomenon measured at the population level caused by a suite of latent biological, environmental, and anthropogenic. I test the effectiveness of orchard behavior profiles on invasion suppression and evaluate the robustness of the estimators given orchard responses. I find that allowing growers to use future expectations of spread in management decisions leads to reduced spread rates. Acting in a preventative manner by applying insecticide before insects are actually present, orchards are able to lower spread rates more than by reactive behavior alone. Spread rates are highly sensitive to spatial configuration. Spatial configuration is hardly a random process, consisting of many latent factors often not accounted for in spread rate estimation. Not considering these factors may lead to an omitted variables bias and skew estimation results. The ability of spread rate estimators to predict future spread varies considerably between estimators, and with spatial configuration, invader biological parameters, and orchard behavior profile. The model suggests that understanding the latent factors inherent to dispersal is important for selecting phenomenological models of spread and interpreting estimation results. This indicates a need for caution when evaluating spread. Although standard practice, current empirical estimators may both over- and underestimate spread rate in the simulation.
ContributorsShanafelt, David William (Author) / Fenichel, Eli P (Thesis advisor) / Richards, Timothy (Committee member) / Janssen, Marco (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