Matching Items (64)
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
In this thesis I introduce a new direction to computing using nonlinear chaotic dynamics. The main idea is rich dynamics of a chaotic system enables us to (1) build better computers that have a flexible instruction set, and (2) carry out computation that conventional computers are not good at it. Here I start from the theory, explaining how one can build a computing logic block using a chaotic system, and then I introduce a new theoretical analysis for chaos computing. Specifically, I demonstrate how unstable periodic orbits and a model based on them explains and predicts how and how well a chaotic system can do computation. Furthermore, since unstable periodic orbits and their stability measures in terms of eigenvalues are extractable from experimental times series, I develop a time series technique for modeling and predicting chaos computing from a given time series of a chaotic system. After building a theoretical framework for chaos computing I proceed to architecture of these chaos-computing blocks to build a sophisticated computing system out of them. I describe how one can arrange and organize these chaos-based blocks to build a computer. I propose a brand new computer architecture using chaos computing, which shifts the limits of conventional computers by introducing flexible instruction set. Our new chaos based computer has a flexible instruction set, meaning that the user can load its desired instruction set to the computer to reconfigure the computer to be an implementation for the desired instruction set. Apart from direct application of chaos theory in generic computation, the application of chaos theory to speech processing is explained and a novel application for chaos theory in speech coding and synthesizing is introduced. More specifically it is demonstrated how a chaotic system can model the natural turbulent flow of the air in the human speech production system and how chaotic orbits can be used to excite a vocal tract model. Also as another approach to build computing system based on nonlinear system, the idea of Logical Stochastic Resonance is studied and adapted to an autoregulatory gene network in the bacteriophage λ.
ContributorsKia, Behnam (Author) / Ditto, William (Thesis advisor) / Huang, Liang (Committee member) / Lai, Ying-Cheng (Committee member) / Helms Tillery, Stephen (Committee member) / Arizona State University (Publisher)
Created2011
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
Complex dynamical systems consisting interacting dynamical units are ubiquitous in nature and society. Predicting and reconstructing nonlinear dynamics of units and the complex interacting networks among them serves the base for the understanding of a variety of collective dynamical phenomena. I present a general method to address the two outstanding problems as a whole based solely on time-series measurements. The method is implemented by incorporating compressive sensing approach that enables an accurate reconstruction of complex dynamical systems in terms of both nodal equations that determines the self-dynamics of units and detailed coupling patterns among units. The representative advantages of the approach are (i) the sparse data requirement which allows for a successful reconstruction from limited measurements, and (ii) general applicability to identical and nonidentical nodal dynamics, and to networks with arbitrary interacting structure, strength and sizes. Another two challenging problem of significant interest in nonlinear dynamics: (i) predicting catastrophes in nonlinear dynamical systems in advance of their occurrences and (ii) predicting the future state for time-varying nonlinear dynamical systems, can be formulated and solved in the framework of compressive sensing using only limited measurements. Once the network structure can be inferred, the dynamics behavior on them can be investigated, for example optimize information spreading dynamics, suppress cascading dynamics and traffic congestion, enhance synchronization, game dynamics, etc. The results can yield insights to control strategies design in the real-world social and natural systems. Since 2004, there has been a tremendous amount of interest in graphene. The most amazing feature of graphene is that there exists linear energy-momentum relationship when energy is low. The quasi-particles inside the system can be treated as chiral, massless Dirac fermions obeying relativistic quantum mechanics. Therefore, the graphene provides one perfect test bed to investigate relativistic quantum phenomena, such as relativistic quantum chaotic scattering and abnormal electron paths induced by klein tunneling. This phenomenon has profound implications to the development of graphene based devices that require stable electronic properties.
ContributorsYang, Rui (Author) / Lai, Ying-Cheng (Thesis advisor) / Duman, Tolga M. (Committee member) / Akis, Richard (Committee member) / Huang, Liang (Committee member) / Arizona State University (Publisher)
Created2012
Description
What can classical chaos do to quantum systems is a fundamental issue highly relevant to a number of branches in physics. The field of quantum chaos has been active for three decades, where the focus was on non-relativistic quantumsystems described by the Schr¨odinger equation. By developing an efficient method to solve the Dirac equation in the setting where relativistic particles can tunnel between two symmetric cavities through a potential barrier, chaotic cavities are found to suppress the spread in the tunneling rate. Tunneling rate for any given energy assumes a wide range that increases with the energy for integrable classical dynamics. However, for chaotic underlying dynamics, the spread is greatly reduced. A remarkable feature, which is a consequence of Klein tunneling, arise only in relativistc quantum systems that substantial tunneling exists even for particle energy approaching zero. Similar results are found in graphene tunneling devices, implying high relevance of relativistic quantum chaos to the development of such devices. Wave propagation through random media occurs in many physical systems, where interesting phenomena such as branched, fracal-like wave patterns can arise. The generic origin of these wave structures is currently a matter of active debate. It is of fundamental interest to develop a minimal, paradigmaticmodel that can generate robust branched wave structures. In so doing, a general observation in all situations where branched structures emerge is non-Gaussian statistics of wave intensity with an algebraic tail in the probability density function. Thus, a universal algebraic wave-intensity distribution becomes the criterion for the validity of any minimal model of branched wave patterns. Coexistence of competing species in spatially extended ecosystems is key to biodiversity in nature. Understanding the dynamical mechanisms of coexistence is a fundamental problem of continuous interest not only in evolutionary biology but also in nonlinear science. A continuous model is proposed for cyclically competing species and the effect of the interplay between the interaction range and mobility on coexistence is investigated. A transition from coexistence to extinction is uncovered with a non-monotonic behavior in the coexistence probability and switches between spiral and plane-wave patterns arise. Strong mobility can either promote or hamper coexistence, while absent in lattice-based models, can be explained in terms of nonlinear partial differential equations.
ContributorsNi, Xuan (Author) / Lai, Ying-Cheng (Thesis advisor) / Huang, Liang (Committee member) / Yu, Hongbin (Committee member) / Akis, Richard (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
Honey bee workers display remarkable flexibility in the aging process. This plasticity is closely tied to behavioral maturation. Workers who initiate foraging behavior at earlier ages have shorter lifespans, and much of the variation in total lifespan can be explained by differences in pre-foraging lifespan. Vitellogenin (Vg), a yolk precursor protein, influences worker lifespan both as a regulator of behavioral maturation and through anti-oxidant and immune functions. Experimental reduction of Vg mRNA, and thus Vg protein levels, in wild-type bees results in precocious foraging behavior, decreased lifespan, and increased susceptibility to oxidative damage. We sought to separate the effects of Vg on lifespan due to behavioral maturation from those due to immune and antioxidant function using two selected strains of honey bees that differ in their phenotypic responsiveness to Vg gene knockdown. Surprisingly, we found that lifespans lengthen in the strain described as behaviorally and hormonally insensitive to Vg reduction. We then performed targeted gene expression analyses on genes hypothesized to mediate aging and lifespan: the insulin-like peptides (Ilp1 and 2) and manganese superoxide dismutase (mnSOD). The two honey bee Ilps are the most upstream components in the insulin-signaling pathway, which influences lifespan in Drosophila melanogaster and other organisms, while manganese superoxide dismutase encodes an enzyme with antioxidant functions in animals. We found expression differences in the llps in fat body related to behavior (llp1 and 2) and genetic background (Ilp2), but did not find strain by treatment effects. Expression of mnSOD was also affected by behavior and genetic background. Additionally, we observed a differential response to Vg knockdown in fat body expression of mnSOD, suggesting that antioxidant pathways may partially explain the strain-specific lifespan responses to Vg knockdown.
ContributorsIhle, Kate (Author) / Fondrk, M. Kim (Author) / Page, Robert (Author) / Amdam, Gro (Author) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor)
Created2015-01-01
Description
The brain is considered the crux of identity, yet human behavior may be influenced by bacteria in gut microbiomes. Honeybees can exchange bacteria through their many social behaviors, making their microbiomes, and the effect they have on honeybee behavior, of interest. There is recent evidence suggesting the presence of bacteria existing in human brains, which can be investigated in honeybee brains due to their well-documented structure. The purpose of this study is to establish if lipopolysaccharide—a molecule on bacteria membranes—is present in the honeybee brain and if it colocalizes with vitellogenin—an immune mediator. Additionally, this study also seeks to establish the efficacy of embedding tissue samples in resin and performing immunohistochemistry for vitellogenin and lipopolysaccharide on sections.
ContributorsStrange, Amalie Sofie (Co-author) / Strange, Amalie (Co-author) / Amdam, Gro (Thesis director) / Baluch, Page (Committee member) / School of International Letters and Cultures (Contributor) / School of Life Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
Background
The reproductive ground plan hypothesis of social evolution suggests that reproductive controls of a solitary ancestor have been co-opted during social evolution, facilitating the division of labor among social insect workers. Despite substantial empirical support, the generality of this hypothesis is not universally accepted. Thus, we investigated the prediction of particular genes with pleiotropic effects on ovarian traits and social behavior in worker honey bees as a stringent test of the reproductive ground plan hypothesis. We complemented these tests with a comprehensive genome scan for additional quantitative trait loci (QTL) to gain a better understanding of the genetic architecture of the ovary size of honey bee workers, a morphological trait that is significant for understanding social insect caste evolution and general insect biology.
Results
Back-crossing hybrid European x Africanized honey bee queens to the Africanized parent colony generated two study populations with extraordinarily large worker ovaries. Despite the transgressive ovary phenotypes, several previously mapped QTL for social foraging behavior demonstrated ovary size effects, confirming the prediction of pleiotropic genetic effects on reproductive traits and social behavior. One major QTL for ovary size was detected in each backcross, along with several smaller effects and two QTL for ovary asymmetry. One of the main ovary size QTL coincided with a major QTL for ovary activation, explaining 3/4 of the phenotypic variance, although no simple positive correlation between ovary size and activation was observed.
Conclusions
Our results provide strong support for the reproductive ground plan hypothesis of evolution in study populations that are independent of the genetic stocks that originally led to the formulation of this hypothesis. As predicted, worker ovary size is genetically linked to multiple correlated traits of the complex division of labor in worker honey bees, known as the pollen hoarding syndrome. The genetic architecture of worker ovary size presumably consists of a combination of trait-specific loci and general regulators that affect the whole behavioral syndrome and may even play a role in caste determination. Several promising candidate genes in the QTL intervals await further study to clarify their potential role in social insect evolution and the regulation of insect fertility in general.
The reproductive ground plan hypothesis of social evolution suggests that reproductive controls of a solitary ancestor have been co-opted during social evolution, facilitating the division of labor among social insect workers. Despite substantial empirical support, the generality of this hypothesis is not universally accepted. Thus, we investigated the prediction of particular genes with pleiotropic effects on ovarian traits and social behavior in worker honey bees as a stringent test of the reproductive ground plan hypothesis. We complemented these tests with a comprehensive genome scan for additional quantitative trait loci (QTL) to gain a better understanding of the genetic architecture of the ovary size of honey bee workers, a morphological trait that is significant for understanding social insect caste evolution and general insect biology.
Results
Back-crossing hybrid European x Africanized honey bee queens to the Africanized parent colony generated two study populations with extraordinarily large worker ovaries. Despite the transgressive ovary phenotypes, several previously mapped QTL for social foraging behavior demonstrated ovary size effects, confirming the prediction of pleiotropic genetic effects on reproductive traits and social behavior. One major QTL for ovary size was detected in each backcross, along with several smaller effects and two QTL for ovary asymmetry. One of the main ovary size QTL coincided with a major QTL for ovary activation, explaining 3/4 of the phenotypic variance, although no simple positive correlation between ovary size and activation was observed.
Conclusions
Our results provide strong support for the reproductive ground plan hypothesis of evolution in study populations that are independent of the genetic stocks that originally led to the formulation of this hypothesis. As predicted, worker ovary size is genetically linked to multiple correlated traits of the complex division of labor in worker honey bees, known as the pollen hoarding syndrome. The genetic architecture of worker ovary size presumably consists of a combination of trait-specific loci and general regulators that affect the whole behavioral syndrome and may even play a role in caste determination. Several promising candidate genes in the QTL intervals await further study to clarify their potential role in social insect evolution and the regulation of insect fertility in general.
ContributorsGraham, Allie M. (Author) / Munday, Michael D. (Author) / Kaftanoglu, Osman (Author) / Page, Robert (Author) / Amdam, Gro (Author) / Rueppell, Olav (Author) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor)
Created2011-04-13
Description
As a biology major, many of my classes have included studying the fundamentals of genetics or investigating the way genetics influence heritability of certain diseases. When I began taking upper-division psychology courses, the genetic factors of psychological disorders became an important part of the material. I was exposed to a new idea: that genes were equally important in studying somatic diseases as they were to psychological disorders. As important as genetics are to psychology, they are not part of the required courses for the major; I found many of my peers in psychology courses did not have a grasp on genetic fundamentals in the same way biology majors did. This was a disconnect that I also found in my own life outside the classroom. Growing up, my mother consistently reminded me to limit my carbs and watch my sugars. Diabetes was very prevalent in my family and I was also at risk. I was repeatedly reminded of my own genes and the risk I faced in having this biological disorder. However, my friend whose father was an alcoholic did not warn her in the same way. While she did know of her father's history, she was not warned of the potential for her to become an alcoholic. While my behavior was altered due to my mother's warning and my own knowledge of the genetic risk of diabetes, I wondered if other people at genetic risk of psychological disorders also altered their behavior. Through my thesis, I hope to answer if students have the same perceived genetic knowledge of psychological diseases as they do for biological ones. In my experience, it is not as well known that psychological disorders have genetic factors. For example, alcohol is commonly used by college students. Alcohol use disorder is present in 16.2% of college aged students and "40-60% of the variance of risk explained by genetic influences." (DSM V, 2013) Compare this to diabetes that has "several common genetic variants that account for about 10% of the total genetic effects," but is much more openly discussed even though it is less genetically linked. (McVay, 2015)This stems from the stigma/taboo surrounding many psychological disorders. If students do know that psychological disorder are genetically influenced, I expect their knowledge to be skewed or inaccurate. As part of a survey, I hope to see how strong they believe the genetic risk of certain diseases are as well as where they gained this knowledge. I hypothesize that only students with a background in psychology will be able to correctly assign the genetic risk of the four presented diseases. Completing this thesis will require in-depth study of the genetic factors, an understanding of the way each disease is perceived and understood by the general population, and a statistical analysis of the survey responses. If the survey data turns out as I expect where students do not have a strong grasp of diseases that could potentially influence their own health, I hope to find a way to educate students on biological and psychological diseases, their genetic risk, and how to speak openly about them.
ContributorsParasher, Nisha (Author) / Amdam, Gro (Thesis director) / Toft, Carolyn Cavaugh (Committee member) / Ostwald, Madeleine (Committee member) / Department of Psychology (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05