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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 use of synthetic cathinones or "bath salts" has risen dramatically in recent years with one of the most popular being Methylendioxypyrovalerone (MDPV). Following the temporary legislative ban on the sale and distribution of this compound , a multitude of other cathinone derivatives have been synthesized. The current study seeks to compare the abuse potential of MDPV with one of the emergent synthetic cathinones 4-methylethcathinone (4-MEC), based on their respective ability to lower current thresholds in an intracranial self-stimulation (ICSS) paradigm. Following acute administration (0.1, 0.5, 1 and 2 mg/kg i.p.) MDPV was found to significantly lower ICSS thresholds at all doses tested (F4,35=11.549, p<0.001). However, following acute administration (0.3,1,3,10,30 mg/kg i.p) 4-MEC produced no significant ICSS threshold depression (F5,135= 0.622, p = 0.684). Together these findings suggest that while MDPV may possess significant abuse potential, other synthetic cathinones such as 4-MEC may have a drastically reduced potential for abuse.
ContributorsWegner, Scott Andrew (Author) / Olive, M. Foster (Thesis director) / Presson, Clark (Committee member) / Sanabria, Federico (Committee member) / Barrett, The Honors College (Contributor) / Department of Chemistry and Biochemistry (Contributor) / Department of Psychology (Contributor)
Created2013-05
Description
Chronic restraint stress impairs hippocampal-mediated spatial learning and memory, which improves following a post-stress recovery period. Here, we investigated whether brain derived neurotrophic factor (BDNF), a protein important for hippocampal function, would alter the recovery from chronic stress-induced spatial memory deficits. Adult male Sprague-Dawley rats were infused into the hippocampus with adeno- associated viral vectors containing the coding sequence for short interfering (si)RNA directed against BDNF or a scrambled sequence (Scr), with both containing the coding information for green fluorescent protein to aid in anatomical localization. Rats were then chronically restrained (wire mesh, 6h/d/21d) and assessed for spatial learning and memory using a radial arm water maze (RAWM) either immediately after stressor cessation (Str-Imm) or following a 21-day post-stress recovery period (Str-Rec). All groups learned the RAWM task similarly, but differed on the memory retention trial. Rats in the Str-Imm group, regardless of viral vector contents, committed more errors in the spatial reference memory domain than did non-stressed controls. Importantly, the typical improvement in spatial memory following recovery from chronic stress was blocked with the siRNA against BDNF, as Str-Rec-siRNA performed worse on the RAWM compared to the non-stressed controls or Str-Rec-Scr. These effects were specific for the reference memory domain as repeated entry errors that reflect spatial working memory were unaffected by stress condition or viral vector contents. These results demonstrate that hippocampal BDNF is necessary for the recovery from stress-induced hippocampal dependent spatial memory deficits in the reference memory domain.
ContributorsOrtiz, J. Bryce (Author) / Conrad, Cheryl D. (Thesis advisor) / Olive, M. Foster (Committee member) / Taylor, Sara (Committee member) / Bimonte-Nelson, Heather A. (Committee member) / Arizona State University (Publisher)
Created2013
Description
The brain is a fundamental target of the stress response that promotes adaptation and survival but the repeated activation of the stress response has the potential alter cognition, emotion, and motivation, key functions of the limbic system. Three structures of the limbic system in particular, the hippocampus, medial prefrontal cortex (mPFC), and amygdala, are of special interest due to documented structural changes and their implication in post-traumatic stress disorder (PTSD). One of many notable chronic stress-induced changes include dendritic arbor restructuring, which reflect plasticity patterns in parallel with the direction of alterations observed in functional imaging studies in PTSD patients. For instance, chronic stress produces dendritic retraction in the hippocampus and mPFC, but dendritic hypertrophy in the amygdala, consistent with functional imaging in patients with PTSD. Some have hypothesized that these limbic region's modifications contribute to one's susceptibility to develop PTSD following a traumatic event. Consequently, we used a familiar chronic stress procedure in a rat model to create a vulnerable brain that might develop traits consistent with PTSD when presented with a challenge. In adult male rats, chronic stress by wire mesh restraint (6h/d/21d) was followed by a variety of behavioral tasks including radial arm water maze (RAWM), fear conditioning and extinction, and fear memory reconsolidation to determine chronic stress effects on behaviors mediated by these limbic structures. In chapter 2, we corroborated past findings that chronic stress caused hippocampal CA3 dendritic retraction. Importantly, we present new findings that CA3 dendritic retraction corresponded with poor spatial memory in the RAWM and that these outcomes reversed after a recovery period. In chapter 3, we also showed that chronic stress impaired mPFC-mediated extinction memory, findings that others have reported. Using carefully assessed behavior, we present new findings that chronic stress impacted nonassociative fear by enhancing contextual fear during extinction that generalized to a new context. Moreover, the generalization behavior corresponded with enhanced functional activation in the hippocampus and amygdala during fear extinction memory retrieval. In chapter 5, we showed for the first time that chronic stress enhanced amygdala functional activation during fear memory retrieval, i.e., reactivation. Moreover, these enhanced fear memories were resistant to protein synthesis interference to disrupt a previously formed memory, called reconsolidation in a novel attempt to weaken chronic stress enhanced traumatic memory. Collectively, these studies demonstrated the plastic and dynamic effects of chronic stress on limbic neurocircuitry implicated in PTSD. We showed that chronic stress created a structural and functional imbalance across the hippocampus, mPFC, and amygdala, which lead to a PTSD-like phenotype with persistent and exaggerated fear following fear conditioning. These behavioral disruptions in conjunction with morphological and functional imaging data reflect a chronic stress-induced imbalance between hippocampal and mPFC regulation in favor of amygdala function overdrive, and supports a novel approach for traumatic memory processing in PTSD.
ContributorsHoffman, Ann (Author) / Conrad, Cheryl D. (Thesis advisor) / Olive, M. Foster (Committee member) / Hammer, Jr., Ronald P. (Committee member) / Sanabria, Federico (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
A general continuum model for simulating the flow of ions in the salt baths that surround and fill excitable neurons is developed and presented. The ion densities and electric potential are computed using the drift-diffusion equations. In addition, a detailed model is given for handling the electrical dynamics on interior membrane boundaries, including a model for ion channels in the membranes that facilitate the transfer of ions in and out of cells. The model is applied to the triad synapse found in the outer plexiform layer of the retina in most species. Experimental evidence suggests the existence of a negative feedback pathway between horizontal cells and cone photoreceptors that modulates the flow of calcium ions into the synaptic terminals of cones. However, the underlying mechanism for this feedback is controversial and there are currently three competing hypotheses: the ephaptic hypothesis, the pH hypothesis and the GABA hypothesis. The goal of this work is to test some features of the ephaptic hypothesis using detailed simulations that employ rigorous numerical methods. The model is first applied in a simple rectangular geometry to demonstrate the effects of feedback for different extracellular gap widths. The model is then applied to a more complex and realistic geometry to demonstrate the existence of strictly electrical feedback, as predicted by the ephaptic hypothesis. Lastly, the effects of electrical feedback in regards to the behavior of the bipolar cell membrane potential is explored. Figures for the ion densities and electric potential are presented to verify key features of the model. The computed steady state IV curves for several cases are presented, which can be compared to experimental data. The results provide convincing evidence in favor of the ephaptic hypothesis since the existence of feedback that is strictly electrical in nature is shown, without any dependence on pH effects or chemical transmitters.
ContributorsJones, Jeremiah (Author) / Gardner, Carl (Committee member) / Baer, Steven (Committee member) / Crook, Sharon (Committee member) / Kostelich, Eric (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2013
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
Mortality of 1918 influenza virus was high, partly due to bacteria coinfections. We characterize pandemic mortality in Arizona, which had high prevalence of tuberculosis. We applied regressions to over 35,000 data points to estimate the basic reproduction number and excess mortality. Age-specific mortality curves show elevated mortality for all age groups, especially the young, and senior sparing effects. The low value for reproduction number indicates that transmissibility was moderately low.
ContributorsJenner, Melinda Eva (Author) / Chowell-Puente, Gerardo (Thesis director) / Kostelich, Eric (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Life Sciences (Contributor)
Created2015-05
Description
Females are highly vulnerable to the effects of methamphetamine, and understanding the mechanisms of this is critical to addressing methamphetamine use as a public health issue. Hormones may play a role in methamphetamine sensitivity; thus, the fluctuation of various endogenous peptides during the postpartum experience is of interest. This honors thesis project explored the relation between anxiety-like behavior, as measured by activity in an open field, and conditioned place preference to methamphetamine in female versus male rats. The behavior of postpartum as well as virgin female rats was compared to that of male rats. There was not a significant difference between males and females in conditioned place preference to methamphetamine, yet females showed higher locomotor activity in response to the drug as well as increased anxiety-like behavior in open field testing as compared to males. Further study is vital to comprehending the complex mechanisms of sex differences in methamphetamine addiction.
ContributorsBaker, Allison Nicole (Author) / Olive, M. Foster (Thesis director) / Presson, Clark (Committee member) / Hansen, Whitney (Committee member) / Department of Psychology (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Glioblastoma Multiforme (GBM) is an aggressive and deadly form of brain cancer with a median survival time of about a year with treatment. Due to the aggressive nature of these tumors and the tendency of gliomas to follow white matter tracks in the brain, each tumor mass has a unique growth pattern. Consequently it is difficult for neurosurgeons to anticipate where the tumor will spread in the brain, making treatment planning difficult. Archival patient data including MRI scans depicting the progress of tumors have been helpful in developing a model to predict Glioblastoma proliferation, but limited scans per patient make the tumor growth rate difficult to determine. Furthermore, patient treatment between scan points can significantly compound the challenge of accurately predicting the tumor growth. A partnership with Barrow Neurological Institute has allowed murine studies to be conducted in order to closely observe tumor growth and potentially improve the current model to more closely resemble intermittent stages of GBM growth without treatment effects.
ContributorsSnyder, Lena Haley (Author) / Kostelich, Eric (Thesis director) / Frakes, David (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Harrington Bioengineering Program (Contributor)
Created2014-05