Matching Items (44)
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
Accumulating evidence implicates exposure to adverse childhood experiences in the development of hypocortisolism in the long-term, and researchers are increasingly examining individual-level mechanisms that may underlie, exacerbate or attenuate this relation among at-risk populations. The current study takes a developmentally and theoretically informed approach to examining episodic childhood stressors, inherent and voluntary self-regulation, and physiological reactivity among a longitudinal sample of youth who experienced parental divorce. Participants were drawn from a larger randomized controlled trial of a preventive intervention for children of divorce between the ages of 9 and 12. The current sample included 159 young adults (mean age = 25.5 years; 53% male; 94% Caucasian) who participated in six waves of data collection, including a 15-year follow-up study. Participants reported on exposure to negative life events (four times over a 9-month period) during childhood, and mothers rated child temperament. Six years later, youth reported on the use of active and avoidant coping strategies, and 15 years later, they participated in a standardized psychosocial stress task and provided salivary cortisol samples prior to and following the task. Path analyses within a structural equation framework revealed that a multiple mediation model best fit the data. It was found that children with better mother-rated self-regulation (i.e. low impulsivity, low negative emotionality, and high attentional focus) exhibited lower total cortisol output 15 years later. In addition, greater self-regulation in childhood predicted greater use of active coping in adolescence, whereas a greater number of negative life events predicted increased use of avoidant coping in adolescence. Finally, a greater number of negative events in childhood predicted marginally lower total cortisol output, and higher levels of active coping in adolescence were associated with greater total cortisol output in young adulthood. Findings suggest that children of divorce who exhibit better self-regulation evidence lower cortisol output during a standardized psychosocial stress task relative to those who have higher impulsivity, lower attentional focus, and/or higher negative emotionality. The conceptual significance of the current findings, including the lack of evidence for hypothesized relations, methodological issues that arose, and issues in need of future research are discussed.
ContributorsHagan, Melissa (Author) / Luecken, Linda (Thesis advisor) / MacKinnon, David (Committee member) / Wolchik, Sharlene (Committee member) / Doane, Leah (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
In order to analyze data from an instrument administered at multiple time points it is a common practice to form composites of the items at each wave and to fit a longitudinal model to the composites. The advantage of using composites of items is that smaller sample sizes are required in contrast to second order models that include the measurement and the structural relationships among the variables. However, the use of composites assumes that longitudinal measurement invariance holds; that is, it is assumed that that the relationships among the items and the latent variables remain constant over time. Previous studies conducted on latent growth models (LGM) have shown that when longitudinal metric invariance is violated, the parameter estimates are biased and that mistaken conclusions about growth can be made. The purpose of the current study was to examine the impact of non-invariant loadings and non-invariant intercepts on two longitudinal models: the LGM and the autoregressive quasi-simplex model (AR quasi-simplex). A second purpose was to determine if there are conditions in which researchers can reach adequate conclusions about stability and growth even in the presence of violations of invariance. A Monte Carlo simulation study was conducted to achieve the purposes. The method consisted of generating items under a linear curve of factors model (COFM) or under the AR quasi-simplex. Composites of the items were formed at each time point and analyzed with a linear LGM or an AR quasi-simplex model. The results showed that AR quasi-simplex model yielded biased path coefficients only in the conditions with large violations of invariance. The fit of the AR quasi-simplex was not affected by violations of invariance. In general, the growth parameter estimates of the LGM were biased under violations of invariance. Further, in the presence of non-invariant loadings the rejection rates of the hypothesis of linear growth increased as the proportion of non-invariant items and as the magnitude of violations of invariance increased. A discussion of the results and limitations of the study are provided as well as general recommendations.
ContributorsOlivera-Aguilar, Margarita (Author) / Millsap, Roger E. (Thesis advisor) / Levy, Roy (Committee member) / MacKinnon, David (Committee member) / West, Stephen G. (Committee member) / Arizona State University (Publisher)
Created2013
Description
Research shows that general parenting practices (e.g., support and discipline), influence adolescent substance use. However, socialization theory suggests that parental socialization occurs not only through general parenting practices, but also through parents' attempts to influence specific behaviors and values. A growing literature supports links between substance-specific parenting and adolescent substance use. For adolescent alcohol use, there are considerable limitations and gaps within this literature. To address these limitations, the present study examined the factor structure of alcohol-specific parenting, investigated the determinants of alcohol-specific parenting, and explored its association with nondrinking adolescents' attitudes about alcohol use. Using a high-risk sample of nondrinking adolescents and their parents, the current study found three dimensions of alcohol-specific parenting using both adolescent and parent reports, but also found evidence of non-invariance across reporters. Results also revealed complex roles of parental alcohol use disorder (AUD; including recovered and current AUD), family history of AUD, and current drinking as determinants of the three dimensions of anti-alcohol parenting behaviors. Moreover, the current study showed that the effects of these determinants varied by the reporter of the parenting behavior. Finally, the current study found the dimensions of alcohol-specific parenting to be unique and significant predictors of nondrinking adolescents' attitudes about alcohol, over and above general parenting practices, parent AUD, and parent current drinking. Given its demonstrated distinctness from general parenting practices, its link with adolescent alcohol attitudes, and its potential malleability, alcohol-specific parenting may be an important complement to interventions targeting parents of adolescents.
ContributorsHandley, Elizabeth D (Author) / Chassin, Laurie (Thesis advisor) / MacKinnon, David (Committee member) / Crnic, Keith (Committee member) / Sandler, Irwin (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
The nature and correlates of emerging internalizing symptoms in young children are largely unknown. Maternal factors such as psychological symptoms and detached parenting style have been found to be present in children with anxiety and depression. Further, child attentional control in task completion has been associated with difficulty related to internalizing problems. This study tested hypotheses that child anxiety and depression at age five could be predicted by a combination of maternal distress and maternal detached behavior recorded at age three. An additional hypothesis was tested to determine if child attentional control at age four may be a partial mediator of the relation between maternal symptoms and parenting to child internalizing symptoms. Using structural equation modeling, no hypotheses were supported; child internalizing problems were not significantly predicted by maternal distress nor detached parenting. Further, child attentional control was not predicted by maternal distress or detached behavior, nor did attentional control predict internalizing problems. Findings indicate that over a two-year interval, childhood internalizing problems at age five are likely best predicted by early internalizing problems at age three. There was no support that the mother or child factors tested were predictive of child outcomes.
ContributorsSkelley, Shayna (Author) / Crnic, Keith A (Thesis advisor) / Eisenberg, Nancy (Committee member) / MacKinnon, David (Committee member) / Arizona State University (Publisher)
Created2010
Description
A numerical study of wave-induced momentum transport across the tropopause in the presence of a stably stratified thin inversion layer is presented and discussed. This layer consists of a sharp increase in static stability within the tropopause. The wave propagation is modeled by numerically solving the Taylor-Goldstein equation, which governs the dynamics of internal waves in stably stratified shear flows. The waves are forced by a flow over a bell shaped mountain placed at the lower boundary of the domain. A perfectly radiating condition based on the group velocity of mountain waves is imposed at the top to avoid artificial wave reflection. A validation for the numerical method through comparisons with the corresponding analytical solutions will be provided. Then, the method is applied to more realistic profiles of the stability to study the impact of these profiles on wave propagation through the tropopause.
ContributorsCole, Alexandra Shea (Author) / Moustaoui, Mohamed (Thesis director) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / School of International Letters and Cultures (Contributor) / School of Geographical Sciences and Urban Planning (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
Psychologists report effect sizes in randomized controlled trials to facilitate interpretation and inform clinical or policy guidance. Since commonly used effect size measures (e.g., standardized mean difference) are not sensitive to heterogeneous treatment effects, methodologists have suggested the use of an alternative effect size δ, a between-subjects causal parameter describing the probability that the outcome of a random participant in the treatment group is better than the outcome of another random participant in the control group. Although this effect size is useful, researchers could mistakenly use δ to describe its within-subject analogue, ψ, the probability that an individual will do better under the treatment than the control. Hand’s paradox describes the situation where ψ and δ are on opposing sides of 0.5: δ may imply most are helped whereas the (unknown) underlying ψ indicates that most are harmed by the treatment. The current study used Monte Carlo simulations to investigate plausible situations under which Hand’s paradox does and does not occur, tracked the magnitude of the discrepancy between ψ and δ, and explored whether the size of the discrepancy could be reduced with a relevant covariate. The findings suggested that although the paradox should not occur under bivariate normal data conditions in the population, there could be sample cases with the paradox. The magnitude of the discrepancy between ψ and δ depended on both the size of the average treatment effect and the underlying correlation between the potential outcomes, ρ. Smaller effects led to larger discrepancies when ρ < 0 and ρ = 1, whereas larger effects led to larger discrepancies when 0 < ρ < 1. It was useful to consider a relevant covariate when calculating ψ and δ. Although ψ and δ were still discrepant within covariate levels, results indicated that conditioning upon relevant covariates is still useful in describing heterogeneous treatment effects.
ContributorsLiu, Xinran (Author) / Anderson, Samantha F (Thesis advisor) / McNeish, Daniel (Committee member) / MacKinnon, David (Committee member) / Arizona State University (Publisher)
Created2023
Description
This work presents a thorough analysis of reconstruction of global wave fields (governed by the inhomogeneous wave equation and the Maxwell vector wave equation) from sensor time series data of the wave field. Three major problems are considered. First, an analysis of circumstances under which wave fields can be fully reconstructed from a network of fixed-location sensors is presented. It is proven that, in many cases, wave fields can be fully reconstructed from a single sensor, but that such reconstructions can be sensitive to small perturbations in sensor placement. Generally, multiple sensors are necessary. The next problem considered is how to obtain a global approximation of an electromagnetic wave field in the presence of an amplifying noisy current density from sensor time series data. This type of noise, described in terms of a cylindrical Wiener process, creates a nonequilibrium system, derived from Maxwell’s equations, where variance increases with time. In this noisy system, longer observation times do not generally provide more accurate estimates of the field coefficients. The mean squared error of the estimates can be decomposed into a sum of the squared bias and the variance. As the observation time $\tau$ increases, the bias decreases as $\mathcal{O}(1/\tau)$ but the variance increases as $\mathcal{O}(\tau)$. The contrasting time scales imply the existence of an ``optimal'' observing time (the bias-variance tradeoff). An iterative algorithm is developed to construct global approximations of the electric field using the optimal observing times. Lastly, the effect of sensor acceleration is considered. When the sensor location is fixed, measurements of wave fields composed of plane waves are almost periodic and so can be written in terms of a standard Fourier basis. When the sensor is accelerating, the resulting time series is no longer almost periodic. This phenomenon is related to the Doppler effect, where a time transformation must be performed to obtain the frequency and amplitude information from the time series data. To obtain frequency and amplitude information from accelerating sensor time series data in a general inhomogeneous medium, a randomized algorithm is presented. The algorithm is analyzed and example wave fields are reconstructed.
ContributorsBarclay, Bryce Matthew (Author) / Mahalov, Alex (Thesis advisor) / Kostelich, Eric J (Thesis advisor) / Moustaoui, Mohamed (Committee member) / Motsch, Sebastien (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2023