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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
Surface plasmon resonance (SPR) has emerged as a popular technique for elucidating subtle signals from biological events in a label-free, high throughput environment. The efficacy of conventional SPR sensors, whose signals are mass-sensitive, diminishes rapidly with the size of the observed target molecules. The following work advances the current SPR sensor paradigm for the purpose of small molecule detection. The detection limits of two orthogonal components of SPR measurement are targeted: speed and sensitivity. In the context of this report, speed refers to the dynamic range of measured kinetic rate constants, while sensitivity refers to the target molecule mass limitation of conventional SPR measurement. A simple device for high-speed microfluidic delivery of liquid samples to a sensor surface is presented to address the temporal limitations of conventional SPR measurement. The time scale of buffer/sample switching is on the order of milliseconds, thereby minimizing the opportunity for sample plug dispersion. The high rates of mass transport to and from the central microfluidic sensing region allow for SPR-based kinetic analysis of binding events with dissociation rate constants (kd) up to 130 s-1. The required sample volume is only 1 μL, allowing for minimal sample consumption during high-speed kinetic binding measurement. Charge-based detection of small molecules is demonstrated by plasmonic-based electrochemical impedance microscopy (P-EIM). The dependence of surface plasmon resonance (SPR) on surface charge density is used to detect small molecules (60-120 Da) printed on a dextran-modified sensor surface. The SPR response to an applied ac potential is a function of the surface charge density. This optical signal is comprised of a dc and an ac component, and is measured with high spatial resolution. The amplitude and phase of local surface impedance is provided by the ac component. The phase signal of the small molecules is a function of their charge status, which is manipulated by the pH of a solution. This technique is used to detect and distinguish small molecules based on their charge status, thereby circumventing the mass limitation (~100 Da) of conventional SPR measurement.
ContributorsMacGriff, Christopher Assiff (Author) / Tao, Nongjian (Thesis advisor) / Wang, Shaopeng (Committee member) / LaBaer, Joshua (Committee member) / Chae, Junseok (Committee member) / Arizona State University (Publisher)
Created2013
Description
The dynamics of urban water use are characterized by spatial and temporal variability that is influenced by associated factors at different scales. Thus it is important to capture the relationship between urban water use and its determinants in a spatio-temporal framework in order to enhance understanding and management of urban water demand. This dissertation aims to contribute to understanding the spatio-temporal relationships between single-family residential (SFR) water use and its determinants in a desert city. The dissertation has three distinct papers to support this goal. In the first paper, I demonstrate that aggregated scale data can be reliably used to study the relationship between SFR water use and its determinants without leading to significant ecological fallacy. The usability of aggregated scale data facilitates scientific inquiry about SFR water use with more available aggregated scale data. The second paper advances understanding of the relationship between SFR water use and its associated factors by accounting for the spatial and temporal dependence in a panel data setting. The third paper of this dissertation studies the historical contingency, spatial heterogeneity, and spatial connectivity in the relationship of SFR water use and its determinants by comparing three different regression models. This dissertation demonstrates the importance and necessity of incorporating spatio-temporal components, such as scale, dependence, and heterogeneity, into SFR water use research. Spatial statistical models should be used to understand the effects of associated factors on water use and test the effectiveness of certain management policies since spatial effects probably will significantly influence the estimates if only non-spatial statistical models are used. Urban water demand management should pay attention to the spatial heterogeneity in predicting the future water demand to achieve more accurate estimates, and spatial statistical models provide a promising method to do this job.
ContributorsOuyang, Yun (Author) / Wentz, Elizabeth (Thesis advisor) / Ruddell, Benjamin (Thesis advisor) / Harlan, Sharon (Committee member) / Janssen, Marcus (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
This dissertation investigates the condition of skeletal muscle insulin resistance using bioinformatics and computational biology approaches. Drawing from several studies and numerous data sources, I have attempted to uncover molecular mechanisms at multiple levels. From the detailed atomistic simulations of a single protein, to datamining approaches applied at the systems biology level, I provide new targets to explore for the research community. Furthermore I present a new online web resource that unifies various bioinformatics databases to enable discovery of relevant features in 3D protein structures.
ContributorsMielke, Clinton (Author) / Mandarino, Lawrence (Committee member) / LaBaer, Joshua (Committee member) / Magee, D. Mitchell (Committee member) / Dinu, Valentin (Committee member) / Willis, Wayne (Committee member) / Arizona State University (Publisher)
Created2013
Description
Ponderosa pine forests are a dominant land cover type in semiarid montane areas. Water supplies in major rivers of the southwestern United States depend on ponderosa pine forests since these ecosystems: (1) receive a significant amount of rainfall and snowfall, (2) intercept precipitation and transpire water, and (3) indirectly influence runoff by impacting the infiltration rate. However, the hydrologic patterns in these ecosystems with strong seasonality are poorly understood. In this study, we used a distributed hydrologic model evaluated against field observations to improve our understandings on spatial controls of hydrologic patterns, appropriate model resolution to simulate ponderosa pine ecosystems and hydrologic responses in the context of contrasting winter to summer transitions. Our modeling effort is focused on the hydrologic responses during the North American Monsoon (NAM), winter and spring periods. In Chapter 2, we utilized a distributed model explore the spatial controls on simulated soil moisture and temporal evolution of these spatial controls as a function of seasonal wetness. Our findings indicate that vegetation and topographic curvature are spatial controls. Vegetation controlled patterns during dry summer period switch to fine-scale terrain curvature controlled patterns during persistently wet NAM period. Thus, a climatic threshold involving rainfall and weather conditions during the NAM is identified when high rainfall amount (such as 146 mm rain in August, 1997) activates lateral flux of soil moisture and frequent cloudy cover (such as 42% cloud cover during daytime of August, 1997) lowers evapotranspiration. In Chapter 3, we investigate the impacts of model coarsening on simulated soil moisture patterns during the NAM. Results indicate that model aggregation quickly eradicates curvature features and its spatial control on hydrologic patterns. A threshold resolution of ~10% of the original terrain is identified through analyses of homogeneity indices, correlation coefficients and spatial errors beyond which the fidelity of simulated soil moisture is no longer reliable. Based on spatial error analyses, we detected that the concave areas (~28% of hillslope) are very sensitive to model coarsening and root mean square error (RMSE) is higher than residual soil moisture content (~0.07 m3/m3 soil moisture) for concave areas. Thus, concave areas need to be sampled for capturing appropriate hillslope response for this hillslope. In Chapter 4, we investigate the impacts of contrasting winter to summer transitions on hillslope hydrologic responses. We use a distributed hydrologic model to generate a consistent set of high-resolution hydrologic estimates. Our model is evaluated against the snow depth, soil moisture and runoff observations over two water years yielding reliable spatial distributions during the winter to summer transitions. We find that a wet winter followed by a dry summer promotes evapotranspiration losses (spatial averaged ~193 mm spring ET and ~ 600 mm summer ET) that dry the soil and disconnect lateral fluxes in the forested hillslope, leading to soil moisture patterns resembling vegetation patches. Conversely, a dry winter prior to a wet summer results in soil moisture increases due to high rainfall and low ET during the spring (spatially averaged 78 mm ET and 232 mm rainfall) and summer period (spatially averaged 147 mm ET and 247 mm rainfall) which promote lateral connectivity and soil moisture patterns with the signature of terrain curvature. An opposing temporal switch between infiltration and saturation excess runoff is also identified. These contrasting responses indicate that the inverse relation has significant consequences on hillslope water availability and its spatial distribution with implications on other ecohydrological processes including vegetation phenology, groundwater recharge and geomorphic development. Results from this work have implications on the design of hillslope experiments, the resolution of hillslope scale models, and the prediction of hydrologic conditions in ponderosa pine ecosystems. In addition, our findings can be used to select future hillslope sites for detailed ecohydrological investigations. Further, the proposed methodology can be useful for predicting responses to climate and land cover changes that are anticipated for the southwestern United States.
ContributorsMahmood, Taufique Hasan (Author) / Vivoni, Enrique R. (Thesis advisor) / Whipple, Kelin X. (Committee member) / Shock, Everett (Committee member) / Heimsath, Arjun M. (Committee member) / Ruddell, Benjamin (Committee member) / Arizona State University (Publisher)
Created2012
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
Recombinant protein expression is essential to biotechnology and molecular medicine, but facile methods for obtaining significant quantities of folded and functional protein in mammalian cell culture have been lacking. Here I describe a novel 37-nucleotide in vitro selected sequence that promotes unusually high transgene expression in a vaccinia driven cytoplasmic expression system. Vectors carrying this sequence in a monocistronic reporter plasmid produce >1,000-fold more protein than equivalent vectors with conventional vaccinia promoters. Initial mechanistic studies indicate that high protein expression results from dual activity that impacts both transcription and translation. I suggest that this motif represents a powerful new tool in vaccinia-based protein expression and vaccine development technology.
ContributorsFlores, Julia Anne (Author) / Chaput, John C (Thesis advisor) / Jacobs, Bertram (Committee member) / LaBaer, Joshua (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