Matching Items (293)
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
Rabies disease remains enzootic among raccoons, skunks, foxes and bats in the United States. It is of primary concern for public-health agencies to control spatial spread of rabies in wildlife and its potential spillover infection of domestic animals and humans. Rabies is invariably fatal in wildlife if untreated, with a non-negligible incubation period. Understanding how this latency affects spatial spread of rabies in wildlife is the concern of chapter 2 and 3. Chapter 1 deals with the background of mathematical models for rabies and lists main objectives. In chapter 2, a reaction-diffusion susceptible-exposed-infected (SEI) model and a delayed diffusive susceptible-infected (SI) model are constructed to describe the same epidemic process -- rabies spread in foxes. For the delayed diffusive model a non-local infection term with delay is resulted from modeling the dispersal during incubation stage. Comparison is made regarding minimum traveling wave speeds of the two models, which are verified using numerical experiments. In chapter 3, starting with two Kermack and McKendrick's models where infectivity, death rate and diffusion rate of infected individuals can depend on the age of infection, the asymptotic speed of spread $c^\ast$ for the cumulated force of infection can be analyzed. For the special case of fixed incubation period, the asymptotic speed of spread is governed by the same integral equation for both models. Although explicit solutions for $c^\ast$ are difficult to obtain, assuming that diffusion coefficient of incubating animals is small, $c^\ast$ can be estimated in terms of model parameter values. Chapter 4 considers the implementation of realistic landscape in simulation of rabies spread in skunks and bats in northeast Texas. The Finite Element Method (FEM) is adopted because the irregular shapes of realistic landscape naturally lead to unstructured grids in the spatial domain. This implementation leads to a more accurate description of skunk rabies cases distributions.
ContributorsLiu, Hao (Author) / Kuang, Yang (Thesis advisor) / Jackiewicz, Zdzislaw (Committee member) / Lanchier, Nicolas (Committee member) / Smith, Hal (Committee member) / Thieme, Horst (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
Bacteriophage (phage) are viruses that infect bacteria. Typical laboratory experiments show that in a chemostat containing phage and susceptible bacteria species, a mutant bacteria species will evolve. This mutant species is usually resistant to the phage infection and less competitive compared to the susceptible bacteria species. In some experiments, both susceptible and resistant bacteria species, as well as phage, can coexist at an equilibrium for hundreds of hours. The current research is inspired by these observations, and the goal is to establish a mathematical model and explore sufficient and necessary conditions for the coexistence. In this dissertation a model with infinite distributed delay terms based on some existing work is established. A rigorous analysis of the well-posedness of this model is provided, and it is proved that the susceptible bacteria persist. To study the persistence of phage species, a "Phage Reproduction Number" (PRN) is defined. The mathematical analysis shows phage persist if PRN > 1 and vanish if PRN < 1. A sufficient condition and a necessary condition for persistence of resistant bacteria are given. The persistence of the phage is essential for the persistence of resistant bacteria. Also, the resistant bacteria persist if its fitness is the same as the susceptible bacteria and if PRN > 1. A special case of the general model leads to a system of ordinary differential equations, for which numerical simulation results are presented.
ContributorsHan, Zhun (Author) / Smith, Hal (Thesis advisor) / Armbruster, Dieter (Committee member) / Kawski, Matthias (Committee member) / Kuang, Yang (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2012
Description
In vertebrate outer retina, changes in the membrane potential of horizontal cells affect the calcium influx and glutamate release of cone photoreceptors via a negative feedback. This feedback has a number of important physiological consequences. One is called background-induced flicker enhancement (BIFE) in which the onset of dim background enhances the center flicker response of horizontal cells. The underlying mechanism for the feedback is still unclear but competing hypotheses have been proposed. One is the GABA hypothesis, which states that the feedback is mediated by gamma-aminobutyric acid (GABA), an inhibitory neurotransmitter released from horizontal cells. Another is the ephaptic hypothesis, which contends that the feedback is non-GABAergic and is achieved through the modulation of electrical potential in the intersynaptic cleft between cones and horizontal cells. In this study, a continuum spine model of the cone-horizontal cell synaptic circuitry is formulated. This model, a partial differential equation system, incorporates both the GABA and ephaptic feedback mechanisms. Simulation results, in comparison with experiments, indicate that the ephaptic mechanism is necessary in order for the model to capture the major spatial and temporal dynamics of the BIFE effect. In addition, simulations indicate that the GABA mechanism may play some minor modulation role.
ContributorsChang, Shaojie (Author) / Baer, Steven M. (Thesis advisor) / Gardner, Carl L (Thesis advisor) / Crook, Sharon M (Committee member) / Kuang, Yang (Committee member) / Ringhofer, Christian (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
I conducted a qualitative, comparative study on the nursing education systems in the United Kingdom and the United States, focusing on two universities—Arizona State University in Phoenix, Arizona and Leeds Beckett University in Leeds, England. The goals of my thesis included comparing the educational, economic, and cultural aspects of the countries and how those aspects impact nursing students on both sides of the pond. The educational and economic aspects were compared by utilizing existing literature and open data sources such as the university websites and publications from comparative education journals, while the cultural differences were evaluated by conducting short, one-on-one interviews with students enrolled in the Adult Health courses at both universities. The findings from the interviews were transcribed and coded, and findings from the sites were compared. While there is an extensive amount of research published regarding comparative education, there has not been much published comparing these developed countries. While there is a significant difference in the structure and cost of the nursing programs, there are more similarities than differences in culture between nursing students interviewed in the US and those interviewed in the UK.
ContributorsTahiliani, Shreja (Author) / Hagler, Debra (Thesis director) / Allen, Angela (Committee member) / Arizona State University. College of Nursing & Healthcare Innovation (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
The goal of this creative project is to explain the different roles of advanced practice nursing as well as the role of a registered nurse. Advanced practice nursing roles include Certified Nurse Practitioner, Certified Registered Nurse Anesthetist, Certified Clinical Nurse Specialist, and Certified Nurse Midwife. The role of the registered nurse is included in this website because this role is the foundation for becoming an advanced practice nurse and is an equally important role. The target audience for the website is potential nursing students, current nursing students, and licensed nurses who desire to advance their career and are looking for more information about each role. This comprehensive website includes the scope of practice, salary, educational programs, and an interview with a nurse in each role. The description of each advanced practice role includes audio and visual aids to appeal to different types of learners. In depth education regarding advanced practice nursing roles will make current and future nurses more aware of the endless possibilities of a career in nursing. Nurses provide education to patients every day, but there is rarely adequate education provided to nurses regarding their profession or professional advancement opportunities. Nursing is a patient-focused career and sometimes nurses forget to focus on their own personal growth while caring for others. This one-stop website promotes nurse to nurse education by thoroughly explaining each advanced practice role. All of the information in this website is publically available through the internet and this website is meant solely for educational purposes.
ContributorsThompson, Rachel (Co-author) / Banchik, Jennifer (Co-author) / Peterson, Katherine (Thesis director) / Kriz, Lindsey (Committee member) / Spahr, Nancy (Committee member) / School of Community Resources and Development (Contributor) / School of Social Transformation (Contributor) / Arizona State University. College of Nursing & Healthcare Innovation (Contributor) / T. Denny Sanford School of Social and Family Dynamics (Contributor) / Barrett, The Honors College (Contributor)
Created2015-12
Description
Colorectal cancer (CRC) is the third most prevalent form of cancer in both genders and second highest cause of cancer-related death in the United States. Despite the availability of preventative CRC screening, Latinos as a group are of particular concern for CRC as they tend to have a lower screening rate, contributing to the possibility of late-stage diagnosis or even death. However, little is known about the perceptions of CRC screening and factors which contribute to beliefs about CRC in Latinos. Most studies are quantitative and rarely include a qualitative approach focusing on cultural aspects and communication with physicians. The purpose of this study was to explore participants' perceived facilitators and barriers to CRC screening, as well as perspectives on physician recommendation and fatalism, using a qualitative approach. A convenience and snowball sampling were used to collect the data. Eight English-speaking Latino individuals (M age=56 years; 75% female) in the Phoenix, Arizona area were invited to 60-90 minute in-depth interviews on perceptions of the colorectal cancer screening process. Ten major themes emerged from the interviews: (1) lacking awareness and knowledge of CRC screening, (2) attitude toward CRC and screening, (3) availability of preventive care, (4) physician trust, (5) fear, (6) desire for increased information, (7) personal learning, (8) lifestyle factors, (9) cultural impact, and (10) willingness to change lifestyle. Results indicated varying levels of perceived knowledge of colorectal cancer, little perceived risk of diagnosis, desire for more information, and a high level of physician trust. Implications for nursing included increased need for CRC screening educational resources, as well as further investigation of the influence of fatalistic belief in CRC screening compliance for the Latino population.
ContributorsMagdaleno, Claire Rose (Author) / Kim, Sunny (Thesis director) / McNulty, Julie (Committee member) / Arizona State University. College of Nursing & Healthcare Innovation (Contributor) / Barrett, The Honors College (Contributor)
Created2015-12
Description
This past summer, I met a young lady named Ashley (name has been changed) who has been diagnosed with chronic Lyme disease. Upon researching this condition in greater detail, I learned that many medical providers who base their practice on the best evidence do not support treating patients for a chronic Lyme infection, the existence of which has not been substantially supported with research. I inquired about the process that led her to seek treatment for chronic Lyme disease at Jemsek Specialty Clinic. I learned that after many inaccurate diagnoses and years of unhelpful treatments, Ashley finally rejected the help offered by traditional medical doctors because she felt they were uncaring and inattentive, and went somewhere she felt heard. What she deserved, however, was both care that was based in scientific research and care that felt compassionate, as has been promoted by the nursing field. Despite the lack of a confirmed medical diagnosis, Ashley's day to day symptoms and struggles could be addressed with nursing care. I then constructed a nursing care plan to be implemented by Ashley's family and friends to help her feel her best and live a fulfilling life despite chronic disease. Patients should not have to choose between a healthcare provider who utilizes the strongest scientific evidence and one they feel understands them, though many do. Nursing can unite these mindsets by alleviating the daily challenges patients face. Please see the website http://careplanforashley.blogspot.com
ContributorsKnochel, Amanda Marie (Author) / Panchmatia, Bella (Thesis director) / Mishark, Kenneth (Committee member) / Barrett, The Honors College (Contributor) / Arizona State University. College of Nursing & Healthcare Innovation (Contributor)
Created2014-05