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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
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 number of undergraduate students participating in short-term experiences in global health (STEGHs) abroad has increased dramatically in recent years (Eyler 2002, Drain et al. 2007). These experiences, in tandem with classroom learning, are designed to help students master skills related to global health competencies, including cultural humility and sensitivity, collaborating with community partners, and sociocultural and political awareness. Although STEGHs offer potential benefits to both students and to sending institutions, these experiences can sometimes be problematic and raise ethical challenges. As the number of students engaged in STEGHs continues to increase, it is important to better understand the impact of these programs on student learning. Current ethical and best practice guidelines for STEGHs state that programs should establish evaluation methods to solicit feedback from students both during and on completion of the program (Crump et al. 2010). However, there is currently no established method for gathering this feedback because of the many different global health competency frameworks, types and duration of programs, and different models of student engagement in such programs. Assessing the quality of a STEGH is a profoundly important and difficult question that cannot be answered as succinctly and quantitatively as classroom performance, which has more standard and established assessment metrics. The goal of this project is to identify the most appropriate and useful assessment metric(s) for determining educational quality and impact for STEGHs at ASU by comparing a typical quantitative evaluation tool (pre-post survey with brief open-ended questions) to a more in-depth qualitative method (key informant interviews). In performing my analysis I seek to examine if the latter can produce a richer narrative of student experiences to inform ongoing program evaluations. My research questions are: 1. What are the current qualitative and quantitative evaluation methods available to assess student learning during short-term experiences in global health? 2. How can current methodology for assessing student experiences with short-term experiences in global health be adapted to collect the most information from students? 3. How do student knowledge and attitudes change before and after their short-term experience in global health? Why is understanding those changes important for adapting programs? My end goal would be to use these new, optimal assessment methods for gathering student perspectives and experiences to adapt pre-departure trainings and post-experience debriefings for study abroad programs, both of which I believe will lead to more sustainable partnerships and a healthier understanding of global health work for students.
ContributorsHale, Brittany Ann (Author) / Jehn, Megan (Thesis director) / Wutich, Amber (Committee member) / School of Human Evolution and Social Change (Contributor) / School of Social Transformation (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Due to artificial selection, dogs have high levels of phenotypic diversity, yet, there appears to be low genetic diversity within individual breeds. Through their domestication from wolves, dogs have gone through a series of population bottlenecks, which has resulted in a reduction in genetic diversity, with a large amount of linkage disequilibrium and the persistence of deleterious mutations. This has led to an increased susceptibility to a multitude of diseases, including cancer. To study the effects of artificial selection and life history characteristics on the risk of cancer mortality, we collected cancer mortality data from four studies as well as the percent of heterozygosity, body size, lifespan and breed group for 201 dog breeds. We also collected specific types of cancer breeds were susceptible to and compared the dog cancer mortality patterns to the patterns observed in other mammals. We found a relationship between cancer mortality rate and heterozygosity, body size, lifespan as well as breed group. Higher levels of heterozygosity were also associated with longer lifespan. These results indicate larger breeds, such as Irish Water Spaniels, Flat-coated Retrievers and Bernese Mountain Dogs, are more susceptible to cancer, with lower heterozygosity and lifespan. These breeds are also more susceptible to sarcomas, as opposed to carcinomas in smaller breeds, such as Miniature Pinschers, Chihuahuas, and Pekingese. Other mammals show that larger and long-lived animals have decreased cancer mortality, however, within dog breeds, the opposite relationship is observed. These relationships could be due to the trade-off between cellular maintenance and growing fast and large, with higher expression of growth factors, such as IGF-1. This study further demonstrates the relationships between cancer mortality, heterozygosity, and life history traits and exhibits dogs as an important model organism for understanding the relationship between genetics and health.
ContributorsBalsley, Cassandra Sierra (Author) / Maley, Carlo (Thesis director) / Wynne, Clive (Committee member) / Tollis, Marc (Committee member) / School of Life Sciences (Contributor) / School of Human Evolution and Social Change (Contributor) / Barrett, The Honors College (Contributor)
Created2017-12
Description
Triops (Branchiopoda: Notostraca) and Streptocephalus (Branchiopoda: Anostraca) are two crustaceans which cohabitate in ephemeral freshwater pools. They both lay desiccation resistant eggs that disperse passively to new hydrologically isolated environments. The extent of genetic distance among regions and populations is of perennial interest in animals that live in such isolated habitats. Populations in six natural ephemeral pool habitats located in two different regions of the Sonoran Desert and a transition area between the Sonoran and Chihuahuan Deserts were sampled. Sequences from Genbank were used for reference points in the determination of species as well as to further identify regional genetic distance within species. This study estimated the amount of within and between genetic distance of individuals from each region and population through the use of a neutral marker, cytochrome oxidase I (COI). We concluded that, although the method of passive dispersal may differ between the two genera, the differences do not results in different patterns of genetic distances between regions and populations. Furthermore, we only found the putative species, Triops longicaudatus "short", with enough distinct speciation. Although Triops longicaudatus "long" and Triops newberryi may be in the early stages of speciation, this study does not find enough support to conclude that they have separated.
ContributorsMurphy Jr., Patrick Joseph (Author) / Rutowski, Ronald (Thesis director) / Cartwright, Reed (Committee member) / Lessios, Nikos (Committee member) / School of Life Sciences (Contributor) / School of Human Evolution and Social Change (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Volunteer motivation and satisfaction were assessed at Project CURE, a nonprofit that collects, sorts, tests, and ships donated medical supplies and equipment to healthcare facilities in developing countries. This research was the result of a yearlong partnership between the Community Action Research Experiences (CARE) program and Project CURE. Volunteers at Project CURE were surveyed (N=147) after completing a volunteer session to assess their motivation for volunteering, satisfaction with their experience, and any recommendations they had for improving the volunteer program. Five categories of motivating factors were assessed and it was found that the Values and Understanding categories were the strongest motivating factors. Overall, volunteers rated their experience highly, but the results indicated a number of small changes that Project CURE could make to better meet volunteers' needs, and better communicate the impact of volunteers' work, which could pave the way to increases in the numbers of volunteer hours Project CURE receives and increased quality of volunteer work.
ContributorsStepanek, Rachel (Author) / Reesing, Amy (Thesis director) / Dumka, Larry (Committee member) / School of Molecular Sciences (Contributor) / School of Human Evolution and Social Change (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
This purpose of this thesis study was to examine variables of the "War on Cancer" frame, loss-gain prime, and patient gender on treatment decision for advanced cancer patients. A total of 291 participants (141 females) participated in an online survey experiment and were randomly assigned to one of eight possible conditions, each of which were comprised of a combination of one of two levels for three total independent variables: war frame ("War on Cancer" frame or neutral frame), loss-gain prime (loss prime or gain prime), and patient gender (female or male). Each of the three variables were operationalized to determine whether or not the exposure to the war on cancer paradigm, loss-frame language, or male patient gender would increase the likelihood of a participant choosing a more aggressive cancer treatment. Participants read a patient scenario and were asked to respond to questions related to motivating factors. Participants were then asked to report preference for one of two treatment decisions. Participants were then asked to provide brief demographic information in addition to responding to questions about military history, war attitudes, and cancer history. The aforementioned manipulations sought to determine whether exposure to various factors would make a substantive difference in final treatment decision. Contrary to the predicted results, participants in the war frame condition (M = 3.85, SD = 1.48) were more likely to choose the pursuit of palliative care (as opposed to aggressive treatment) than participants in the neutral frame condition (M = 3.54, SD = 1.23). Ultimately, these significant findings suggest that there is practical information to be gained from treatment presentation manipulations. By arming healthcare providers with a more pointed understanding of the nuances of treatment presentation, we can hope to empower patients, their loved ones, and healthcare providers entrenched in the world of cancer treatment.
ContributorsKnowles, Madelyn Ann (Author) / Kwan, Virginia S. Y. (Thesis director) / Presson, Clark (Committee member) / Salamone, Damien (Committee member) / Department of Psychology (Contributor) / School of Human Evolution and Social Change (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
The purpose of this study was to create an evaluation plan for the Preventing Abusive Conduct (PAC/Peace) program, within the community-based organization Chrysalis. PAC/Peace is a program that provides treatment for domestic abuse offenders through psycho-educational counseling groups. This study analyzed evaluation methods used by similar programs to determine which methods were successful, as well as what criteria were used to evaluate these programs. A literature review was conducted on similar studies to find which measures should be used to determine whether a treatment program met the desired goals for its participants. The literature review, along with interviews with Chrysalis staff were used as resources to create a cost-effective evaluation plan for Chrysalis to measure the effectiveness of their offender treatment program. The results indicated a two part evaluation plan would be the most beneficial for Chrysalis at this time. The first part consists of official reports of recidivism collected at one year, and three years post-graduation from the program. The second is utilization of The Revised Conflict Tactics Scale as an offender self-reporting measure, administered at program intake and exit, as well as one year post-graduation. When implemented, the results of this evaluation will give Chrysalis insight to which aspects of the treatment are working, and which aspects might be improved upon. The results acquired from the evaluation may also help PAC/Peace to become an evidence-based program.
ContributorsScouras, Natasha Elexa (Author) / Low, Sabina (Thesis director) / Dumka, Larry (Committee member) / School of Social Transformation (Contributor) / School of Molecular Sciences (Contributor) / School of Human Evolution and Social Change (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Background: The purpose of this study was to determine the acceptability of a survey for MPN patients about: a) how patients with MPN cancer perceive information relayed from their healthcare providers in regards to integrative medicine and b) how patients use integrative medicine modalities to cope with their symptom burden (i.e. fatigue, headaches, abdominal discomfort). Additionally, we assessed what MPN patients thought about the survey (i.e., questions asked, how it could be modified, acceptability). This paper presents the patient's assessment of the survey. This information will be used to finalize the survey and distribute nationally to address integrative medicine and symptom burden in MPN patients. Methods: The survey was taken by 366, English speaking patients previously diagnosed with essential thrombocythemia, polycythemia vera, or myelofibrosis (primary and post polycythemia vera/post essential thrombocythemia) and ages 18 or older. The survey had XX questions and took approximately 20 minutes to complete. Acceptability questions were qualitatively analyzed and used to construct recurring themes and modifications for the final MPN Integrative Survey. Results: The following themes were recurrent in the acceptability responses; MPN symptom burden comments, views on healthcare, comments about demographics, and requests for survey modifications. When asked which Integrative Therapies have been used to treat symptom burden, participants most commonly named guidance therapy (i.e. counseling, prayer), physiotherapy ,and supplements administered orally, intravenously, intramuscularly, and topically. Conclusions: These results suggest this survey is an acceptable and feasible tool for MPN patients to assess how patients with MPN cancer perceive information relayed from their healthcare providers in regards to integrative medicine, and how patients use integrative medicine modalities to cope with their symptom burden. These findings also provide a better understanding of what facilitates and prevents MPN patients from using Integrative Medicine to treat MPN symptoms, as well as suggests useful survey modifications to inform the final MPN Integrative Survey.
ContributorsLebowitz, Nicole (Author) / Huberty, Jennifer (Thesis director) / Gowin, Krisstina (Committee member) / School of Nutrition and Health Promotion (Contributor) / School of Human Evolution and Social Change (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05