Matching Items (155)
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
The health benefits of physical activity are widely accepted. Emerging research also indicates that sedentary behaviors can carry negative health consequences regardless of physical activity level. This dissertation explored four projects that examined measurement properties of physical activity and sedentary behavior monitors. Project one identified the oxygen costs of four other care activities in seventeen adults. Pushing a wheelchair and pushing a stroller were identified as moderate-intensity activities. Minutes spent engaged in these activities contribute towards meeting the 2008 Physical Activity Guidelines. Project two identified the oxygen costs of common cleaning activities in sixteen adults. Mopping a floor was identified as moderate-intensity physical activity, while cleaning a kitchen and cleaning a bathtub were identified as light-intensity physical activity. Minutes spent engaged in mopping a floor contributes towards meeting the 2008 Physical Activity Guidelines. Project three evaluated the differences in number of minutes spent in activity levels when utilizing different epoch lengths in accelerometry. A shorter epoch length (1-second, 5-seconds) accumulated significantly more minutes of sedentary behaviors than a longer epoch length (60-seconds). The longer epoch length also identified significantly more time engaged in light-intensity activities than the shorter epoch lengths. Future research needs to account for epoch length selection when conducting physical activity and sedentary behavior assessment. Project four investigated the accuracy of four activity monitors in assessing activities that were either sedentary behaviors or light-intensity physical activities. The ActiGraph GT3X+ assessed the activities least accurately, while the SenseWear Armband and ActivPAL assessed activities equally accurately. The monitor used to assess physical activity and sedentary behaviors may influence the accuracy of the measurement of a construct.
ContributorsMeckes, Nathanael (Author) / Ainsworth, Barbara E (Thesis advisor) / Belyea, Michael (Committee member) / Buman, Matthew (Committee member) / Gaesser, Glenn (Committee member) / Wharton, Christopher (Christopher Mack), 1977- (Committee member) / Arizona State University (Publisher)
Created2012
Description
Cardiovascular disease (CVD) is the number one cause of death in the United States and type 2 diabetes (T2D) and obesity lead to cardiovascular disease. Obese adults are more susceptible to CVD compared to their non-obese counterparts. Exercise training leads to large reductions in the risk of CVD and T2D. Recent evidence suggests high-intensity interval training (HIT) may yield similar or superior benefits in a shorter amount of time compared to traditional continuous exercise training. The purpose of this study was to compare the effects of HIT to continuous (CONT) exercise training for the improvement of endothelial function, glucose control, and visceral adipose tissue. Seventeen obese men (N=9) and women (N=8) were randomized to eight weeks of either HIT (N=9, age=34 years, BMI=37.6 kg/m2) or CONT (N=8, age=34 years, BMI=34.6 kg/m2) exercise 3 days/week for 8 weeks. Endothelial function was assessed via flow-mediated dilation (FMD), glucose control was assessed via continuous glucose monitoring (CGM), and visceral adipose tissue and body composition was measured with an iDXA. Incremental exercise testing was performed at baseline, 4 weeks, and 8 weeks. There were no changes in weight, fat mass, or visceral adipose tissue measured by the iDXA, but there was a significant reduction in body fat that did not differ by group (46±6.3 to 45.4±6.6%, P=0.025). HIT led to a significantly greater improvement in FMD compared to CONT exercise (HIT: 5.1 to 9.0%; CONT: 5.0 to 2.6%, P=0.006). Average 24-hour glucose was not improved over the whole group and there were no group x time interactions for CGM data (HIT: 103.9 to 98.2 mg/dl; CONT: 99.9 to 100.2 mg/dl, P>0.05). When statistical analysis included only the subjects who started with an average glucose at baseline > 100 mg/dl, there was a significant improvement in glucose control overall, but no group x time interaction (107.8 to 94.2 mg/dl, P=0.027). Eight weeks of HIT led to superior improvements in endothelial function and similar improvements in glucose control in obese subjects at risk for T2D and CVD. HIT was shown to have comparable or superior health benefits in this obese sample with a 36% lower total exercise time commitment.
ContributorsSawyer, Brandon J (Author) / Gaesser, Glenn A (Thesis advisor) / Shaibi, Gabriel (Committee member) / Lee, Chong (Committee member) / Swan, Pamela (Committee member) / Buman, Matthew (Committee member) / Arizona State University (Publisher)
Created2013
Description
Purpose: The purpose of this study was to examine the acute effects of two novel intermittent exercise prescriptions on glucose regulation and ambulatory blood pressure. Methods: Ten subjects (5 men and 5 women, ages 31.5 ± 5.42 yr, height 170.38 ± 9.69 cm and weight 88.59 ± 18.91 kg) participated in this four-treatment crossover trial. All subjects participated in four trials, each taking place over three days. On the evening of the first day, subjects were fitted with a continuous glucose monitor (CGM). On the second day, subjects were fitted with an ambulatory blood pressure monitor (ABP) and underwent one of the following four conditions in a randomized order: 1) 30-min: 30 minutes of continuous exercise at 60 - 70% VO2peak; 2) Mod 2-min: twenty-one 2-min bouts of walking at 3 mph performed once every 20 minutes; 3) HI 2-min: eight 2-min bouts of walking at maximal incline performed once every hour; 4) Control: a no exercise control condition. On the morning of the third day, the CGM and ABP devices were removed. All meals were standardized during the study visits. Linear mixed models were used to compare mean differences in glucose and blood pressure regulation between the four trials. Results: Glucose concentrations were significantly lower following the 30-min (91.1 ± 14.9 mg/dl), Mod 2-min (93.7 ± 19.8 mg/dl) and HI 2-min (96.1 ± 16.4 mg/dl) trials as compared to the Control (101.1 ± 20 mg/dl) (P < 0.001 for all three comparisons). The 30-min trial was superior to the Mod 2-min, which was superior to the HI 2-min trial in lowering blood glucose levels (P < 0.001 and P = 0.003 respectively). Only the 30-min trial was effective in lowering systolic ABP (124 ± 12 mmHg) as compared to the Control trial (127 ± 14 mmHg; P < 0.001) for up to 11 hours post exercise. Conclusion: Performing frequent short (i.e., 2 minutes) bouts of moderate or high intensity exercise may be a viable alternative to traditional continuous exercise in improving glucose regulation. However, 2-min bouts of exercise are not effective in reducing ambulatory blood pressure in healthy adults.
ContributorsBhammar, Dharini Mukeshkumar (Author) / Gaesser, Glenn A (Thesis advisor) / Shaibi, Gabriel (Committee member) / Buman, Matthew (Committee member) / Swan, Pamela (Committee member) / Lee, Chong (Committee member) / Arizona State University (Publisher)
Created2013
Description
The purpose of this pilot randomized control trial was to test the initial efficacy of a 10 week social cognitive theory (SCT)-based intervention to reduce workplace sitting time (ST). Participants were currently employed adults with predominantly sedentary occupations (n=24) working in the Greater Phoenix area in 2012-2013. Participants wore an activPAL (AP) inclinometer to assess postural allocation (i.e., sitting vs. standing) and Actigraph accelerometer (AG) to assess sedentary time for one week prior to beginning and immediately following the completion of the 10 week intervention. Self-reported measures of sedentary time were obtained via two validated questionnaires for overall (International Physical Activity Questionnaire [IPAQ]) and domain specific sedentary behaviors (Sedentary Behavior Questionnaire [SBQ]). SCT constructs were also measured pre and post via adapted physical activity questionnaires. Participants were randomly assigned to receive either (a) 10 weekly social cognitive-based e-newsletters focused on reducing workplace ST; or (b) similarly formatted 10 weekly e-newsletters focusing on health education. Baseline adjusted Analysis of Covariance statistical analyses were used to examine differences between groups in time spent sitting (AP) and sedentary (AG) during self-reported work hours from pre- to post- intervention. Both groups decreased ST and AG sedentary time; however, no significant differences were observed. SCT constructs also did not change significantly between pretest and post test in either group. These results indicate that individualized educational approaches to decreasing workplace sitting time may not be sufficient for observing long term change in behaviors. Future research should utilize a larger sample, measure main outcomes more frequently, and incorporate more environmental factors throughout the intervention.
ContributorsGordon, Amanda (Author) / Buman, Matthew (Thesis advisor) / Der Ananian, Cheryl (Committee member) / Swan, Pamela (Committee member) / Arizona State University (Publisher)
Created2013
Description
INTRODUCTION: Exercise performed at moderate to vigorous intensities has been shown to generate a post exercise hypotensive response. Whether this response is observed with very low exercise intensities is unclear. PURPOSE: To compare post physical activity ambulatory blood pressure (ABP) response to a single worksite walking day and a normal sedentary work day in pre-hypertensive adults. METHODS: Participants were 7 pre-hypertensive (127 + 8 mmHg / 83 + 8 mmHg) adults (3 male, 4 female, age = 42 + 12 yr) who participated in a randomized, cross-over study that included a control and a walking treatment. Only those who indicated regularly sitting at least 8 hours/day and no structured physical activity were enrolled. Treatment days were randomly assigned and were performed one week apart. Walking treatment consisted of periodically increasing walk time up to 2.5 hours over the course of an 8 hour work day on a walking workstation (Steelcase Company, Grand Rapids, MI). Walk speed was set at 1 mph. Participants wore an ambulatory blood pressure cuff (Oscar 2, SunTech Medical, Morrisville, NC) for 24-hours on both treatment days. Participants maintained normal daily activities on the control day. ABP data collected from 9:00 am until 10:00 pm of the same day were included in statistical analyses. Linear mixed models were used to detect differences in systolic (SBP) and diastolic blood pressure (DBP) by treatment condition over the whole day and post workday for the time periods between 4 -10 pm when participants were no longer at work. RESULTS:BP was significantly lower in response to the walking treatment compared to the control day (Mean SBP 126 +7 mmHg vs.124 +7 mmHg, p=.043; DBP 80 + 3 mmHg vs. 77 + 3 mmHg, p = 0.001 respectively). Post workday (4:00 to 10:00 pm) SBP decreased 3 mmHg (p=.017) and DBP decreased 4 mmHg (p<.001) following walking. CONCLUSION: Even low intensity exercise such as walking on a walking workstation is effective for significantly reducing acute BP when compared to a normal work day.
ContributorsZeigler, Zachary (Author) / Swan, Pamela (Thesis advisor) / Buman, Matthew (Committee member) / Gaesser, Glenn (Committee member) / Arizona State University (Publisher)
Created2013
Description
Eccentric muscle action (ECC) occurs when the force exerted by a working muscle is less than that of an outside resistance. This is characterized by muscle lengthening, despite actin-myosin crossbridge formation. Research has indicated that muscles acting eccentrically are capable of producing more force when compared to muscles acting concentrically. Further, research has shown ECC muscle actions may have different fatigue patterns that CON actions. The purpose of this study was to determine if a) ECC bench press yields greater strength than concentric (CON) as measured by one-repetition maximum (1RM), b) there is a difference between the number of repetitions that can be completed concentrically and eccentrically under the same relative intensities of 1RM (90%, 80%, 70%, 60%), c) a prediction model may be able to predict ECC 1RM from CON 1RM or CON repetitions to fatigue. For this study, 30 healthy males (age = 24.63 + 5.6 years) were tested for 1RM in CON and ECC bench press, as well as the number of repetitions they were able to complete at various intensities of mode-specific 1RM. A mechanical hoist was affixed to a gantry crane and placed over a standard weightlifting bench. The hoist was connected to 45lb plates that were loaded on a standard barbell, which allowed for mechanical raising and lowering of the barbell. For CON repetitions, the weight was mechanically lowered to the chest and the participant pressed it up. For ECC repetitions, the weight was mechanically raised and the participant lowered it. Paired t-tests showed that ECC 1RM was significantly (p < 0.05) greater than CON 1RM (ECC =255.17 + 68.37lbs, CON = 205.83 + 58.43lbs). There was a significant difference (p < 0.05) between the number of repetitions completed at 90% 1RM (CON = 4.57 + 2.21 repetitions, ECC = 7.67 + 3.24 repetitions). There were no differences in repetitions completed at any other intensity 1RM. CON 1RM and the number of repetitions completed with two different absolute loads (130-150lbs and 155-175lbs) concentrically and eccentrically were valid predictors of ECC 1RM. These data indicate that ECC actions yield increased force capabilities than CON actions, there is no difference in the rate of the fatigue, and ECC 1RM may be predicted from various CON tests.
ContributorsKelly, Stephen B., Jr (Author) / Hooker, Steven (Thesis advisor) / Brown, Lee (Committee member) / Buman, Matthew (Committee member) / Gaesser, Glenn (Committee member) / Swan, Pamela (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 purpose of this study is to first investigate the role of political socialization on young men and women and what motivates them to become politically active and make the ultimate decision to run for elected office. These effects include parental attitudes, exposure to political shows and news sources, participation in voluntary organizations, and overall community involvement. After understanding these direct and indirect effects of political socialization, I can attempt to explain the causes for the gender gap in political ambition \u2014 meaning that significantly more men are running for elected office compared to women.
ContributorsOsgood, Shannon Marie (Author) / Woodall, Gina (Thesis director) / Herrera, Richard (Committee member) / Barrett, The Honors College (Contributor) / College of Public Service and Community Solutions (Contributor) / School of Public Affairs (Contributor) / School of Politics and Global Studies (Contributor)
Created2015-05