Matching Items (117)
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 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
For over a century, researchers have been investigating collective cognition, in which a group of individuals together process information and act as a single cognitive unit. However, I still know little about circumstances under which groups achieve better (or worse) decisions than individuals. My dissertation research directly addressed this longstanding question, using the house-hunting ant Temnothorax rugatulus as a model system. Here I applied concepts and methods developed in psychology not only to individuals but also to colonies in order to investigate differences of their cognitive abilities. This approach is inspired by the superorganism concept, which sees a tightly integrated insect society as the analog of a single organism. I combined experimental manipulations and models to elucidate the emergent processes of collective cognition. My studies show that groups can achieve superior cognition by sharing the burden of option assessment among members and by integrating information from members using positive feedback. However, the same positive feedback can lock the group into a suboptimal choice in certain circumstances. Although ants are obligately social, my results show that they can be isolated and individually tested on cognitive tasks. In the future, this novel approach will help the field of animal behavior move towards better understanding of collective cognition.
ContributorsSasaki, Takao (Author) / Pratt, Stephen C (Thesis advisor) / Amazeen, Polemnia (Committee member) / Liebig, Jürgen (Committee member) / Janssen, Marco (Committee member) / Fewell, Jennifer (Committee member) / Hölldobler, Bert (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 spread of invasive species may be greatly affected by human responses to prior species spread, but models and estimation methods seldom explicitly consider human responses. I investigate the effects of management responses on estimates of invasive species spread rates. To do this, I create an agent-based simulation model of an insect invasion across a county-level citrus landscape. My model provides an approximation of a complex spatial environment while allowing the "truth" to be known. The modeled environment consists of citrus orchards with insect pests dispersing among them. Insects move across the simulation environment infesting orchards, while orchard managers respond by administering insecticide according to analyst-selected behavior profiles and management responses may depend on prior invasion states. Dispersal data is generated in each simulation and used to calculate spread rate via a set of estimators selected for their predominance in the empirical literature. Spread rate is a mechanistic, emergent phenomenon measured at the population level caused by a suite of latent biological, environmental, and anthropogenic. I test the effectiveness of orchard behavior profiles on invasion suppression and evaluate the robustness of the estimators given orchard responses. I find that allowing growers to use future expectations of spread in management decisions leads to reduced spread rates. Acting in a preventative manner by applying insecticide before insects are actually present, orchards are able to lower spread rates more than by reactive behavior alone. Spread rates are highly sensitive to spatial configuration. Spatial configuration is hardly a random process, consisting of many latent factors often not accounted for in spread rate estimation. Not considering these factors may lead to an omitted variables bias and skew estimation results. The ability of spread rate estimators to predict future spread varies considerably between estimators, and with spatial configuration, invader biological parameters, and orchard behavior profile. The model suggests that understanding the latent factors inherent to dispersal is important for selecting phenomenological models of spread and interpreting estimation results. This indicates a need for caution when evaluating spread. Although standard practice, current empirical estimators may both over- and underestimate spread rate in the simulation.
ContributorsShanafelt, David William (Author) / Fenichel, Eli P (Thesis advisor) / Richards, Timothy (Committee member) / Janssen, Marco (Committee member) / Arizona State University (Publisher)
Created2012
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
Sports related concussions, or mild traumatic brain injuries (mTBI), have recently increased in prevalence, and thus gained a great deal of recognition from the public and the media. While the acute symptoms associated with concussions are well known, which include headaches, dizziness, vomiting, and fatigue, recent research has indicated that there can be severe chronic consequences of multiple conditions. Most notably, a disease called Chronic Traumatic Encephalopathy (CTE) has been linked to multiple mTBIs, which produces symptoms similar to Alzheimer's disease and dementia, in addition to personality changes, increased suicidality, and in some cases death. This knowledge has led the NFL to take steps to protect their players, and increase both the understanding and awareness of the problems associated with multiple concussions. This comes with many problems, however, as players and fans alike are quick to resist any type of change to the rules or policies present in football, in fear that it may damage the integrity of the game. The NFL is thus forced into a difficult position, and must balance public opinion and player safety. There are things that can be done, however, that do not threaten the game itself, such as investing in concussion research and safety equipment design that will more effectively protect the brain from concussions.
ContributorsAiello, Mimi Elizabeth (Author) / Olive, M. Foster (Thesis director) / Bimonte-Nelson, Heather (Committee member) / Camp, Bryan (Committee member) / Barrett, The Honors College (Contributor) / Department of Psychology (Contributor)
Created2013-05