Matching Items (358)
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
Underwater acoustic communications face significant challenges unprecedented in radio terrestrial communications including long multipath delay spreads, strong Doppler effects, and stringent bandwidth requirements. Recently, multi-carrier communications based on orthogonal frequency division multiplexing (OFDM) have seen significant growth in underwater acoustic (UWA) communications, thanks to their well well-known robustness against severely time-dispersive channels. However, the performance of OFDM systems over UWA channels significantly deteriorates due to severe intercarrier interference (ICI) resulting from rapid time variations of the channel. With the motivation of developing enabling techniques for OFDM over UWA channels, the major contributions of this thesis include (1) two effective frequencydomain equalizers that provide general means to counteract the ICI; (2) a family of multiple-resampling receiver designs dealing with distortions caused by user and/or path specific Doppler scaling effects; (3) proposal of using orthogonal frequency division multiple access (OFDMA) as an effective multiple access scheme for UWA communications; (4) the capacity evaluation for single-resampling versus multiple-resampling receiver designs. All of the proposed receiver designs have been verified both through simulations and emulations based on data collected in real-life UWA communications experiments. Particularly, the frequency domain equalizers are shown to be effective with significantly reduced pilot overhead and offer robustness against Doppler and timing estimation errors. The multiple-resampling designs, where each branch is tasked with the Doppler distortion of different paths and/or users, overcome the disadvantages of the commonly-used single-resampling receivers and yield significant performance gains. Multiple-resampling receivers are also demonstrated to be necessary for UWA OFDMA systems. The unique design effectively mitigates interuser interference (IUI), opening up the possibility to exploit advanced user subcarrier assignment schemes. Finally, the benefits of the multiple-resampling receivers are further demonstrated through channel capacity evaluation results.
ContributorsTu, Kai (Author) / Duman, Tolga M. (Thesis advisor) / Zhang, Junshan (Committee member) / Tepedelenlioğlu, Cihan (Committee member) / Papandreou-Suppappola, Antonia (Committee member) / Arizona State University (Publisher)
Created2011
Description
There are many wireless communication and networking applications that require high transmission rates and reliability with only limited resources in terms of bandwidth, power, hardware complexity etc.. Real-time video streaming, gaming and social networking are a few such examples. Over the years many problems have been addressed towards the goal of enabling such applications; however, significant challenges still remain, particularly, in the context of multi-user communications. With the motivation of addressing some of these challenges, the main focus of this dissertation is the design and analysis of capacity approaching coding schemes for several (wireless) multi-user communication scenarios. Specifically, three main themes are studied: superposition coding over broadcast channels, practical coding for binary-input binary-output broadcast channels, and signalling schemes for two-way relay channels. As the first contribution, we propose an analytical tool that allows for reliable comparison of different practical codes and decoding strategies over degraded broadcast channels, even for very low error rates for which simulations are impractical. The second contribution deals with binary-input binary-output degraded broadcast channels, for which an optimal encoding scheme that achieves the capacity boundary is found, and a practical coding scheme is given by concatenation of an outer low density parity check code and an inner (non-linear) mapper that induces desired distribution of "one" in a codeword. The third contribution considers two-way relay channels where the information exchange between two nodes takes place in two transmission phases using a coding scheme called physical-layer network coding. At the relay, a near optimal decoding strategy is derived using a list decoding algorithm, and an approximation is obtained by a joint decoding approach. For the latter scheme, an analytical approximation of the word error rate based on a union bounding technique is computed under the assumption that linear codes are employed at the two nodes exchanging data. Further, when the wireless channel is frequency selective, two decoding strategies at the relay are developed, namely, a near optimal decoding scheme implemented using list decoding, and a reduced complexity detection/decoding scheme utilizing a linear minimum mean squared error based detector followed by a network coded sequence decoder.
ContributorsBhat, Uttam (Author) / Duman, Tolga M. (Thesis advisor) / Tepedelenlioğlu, Cihan (Committee member) / Li, Baoxin (Committee member) / Zhang, Junshan (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
Pathogenic Gram-negative bacteria employ a variety of molecular mechanisms to combat host defenses. Two-component regulatory systems (TCR systems) are the most ubiquitous signal transduction systems which regulate many genes required for virulence and survival of bacteria. In this study, I analyzed different TCR systems in two clinically-relevant Gram-negative bacteria, i.e., oral pathogen Porphyromonas gingivalis and enterobacterial Escherichia coli. P. gingivalis is a major causative agent of periodontal disease as well as systemic illnesses, like cardiovascular disease. A microarray study found that the putative PorY-PorX TCR system controls the secretion and maturation of virulence factors, as well as loci involved in the PorSS secretion system, which secretes proteinases, i.e., gingipains, responsible for periodontal disease. Proteomic analysis (SILAC) was used to improve the microarray data, reverse-transcription PCR to verify the proteomic data, and primer extension assay to determine the promoter regions of specific PorX regulated loci. I was able to characterize multiple genetic loci regulated by this TCR system, many of which play an essential role in hemagglutination and host-cell adhesion, and likely contribute to virulence in this bacterium. Enteric Gram-negative bacteria must withstand many host defenses such as digestive enzymes, low pH, and antimicrobial peptides (AMPs). The CpxR-CpxA TCR system of E. coli has been extensively characterized and shown to be required for protection against AMPs. Most recently, this TCR system has been shown to up-regulate the rfe-rff operon which encodes genes involved in the production of enterobacterial common antigen (ECA), and confers protection against a variety of AMPs. In this study, I utilized primer extension and DNase I footprinting to determine how CpxR regulates the ECA operon. My findings suggest that CpxR modulates transcription by directly binding to the rfe promoter. Multiple genetic and biochemical approaches were used to demonstrate that specific TCR systems contribute to regulation of virulence factors and resistance to host defenses in P. gingivalis and E. coli, respectively. Understanding these genetic circuits provides insight into strategies for pathogenesis and resistance to host defenses in Gram negative bacterial pathogens. Finally, these data provide compelling potential molecular targets for therapeutics to treat P. gingivalis and E. coli infections.
ContributorsLeonetti, Cori (Author) / Shi, Yixin (Thesis advisor) / Stout, Valerie (Committee member) / Nickerson, Cheryl (Committee member) / Sandrin, Todd (Committee member) / Arizona State University (Publisher)
Created2013
Description
Practical communication systems are subject to errors due to imperfect time alignment among the communicating nodes. Timing errors can occur in different forms depending on the underlying communication scenario. This doctoral study considers two different classes of asynchronous systems; point-to-point (P2P) communication systems with synchronization errors, and asynchronous cooperative systems. In particular, the focus is on an information theoretic analysis for P2P systems with synchronization errors and developing new signaling solutions for several asynchronous cooperative communication systems. The first part of the dissertation presents several bounds on the capacity of the P2P systems with synchronization errors. First, binary insertion and deletion channels are considered where lower bounds on the mutual information between the input and output sequences are computed for independent uniformly distributed (i.u.d.) inputs. Then, a channel suffering from both synchronization errors and additive noise is considered as a serial concatenation of a synchronization error-only channel and an additive noise channel. It is proved that the capacity of the original channel is lower bounded in terms of the synchronization error-only channel capacity and the parameters of both channels. On a different front, to better characterize the deletion channel capacity, the capacity of three independent deletion channels with different deletion probabilities are related through an inequality resulting in the tightest upper bound on the deletion channel capacity for deletion probabilities larger than 0.65. Furthermore, the first non-trivial upper bound on the 2K-ary input deletion channel capacity is provided by relating the 2K-ary input deletion channel capacity with the binary deletion channel capacity through an inequality. The second part of the dissertation develops two new relaying schemes to alleviate asynchronism issues in cooperative communications. The first one is a single carrier (SC)-based scheme providing a spectrally efficient Alamouti code structure at the receiver under flat fading channel conditions by reducing the overhead needed to overcome the asynchronism and obtain spatial diversity. The second one is an orthogonal frequency division multiplexing (OFDM)-based approach useful for asynchronous cooperative systems experiencing excessive relative delays among the relays under frequency-selective channel conditions to achieve a delay diversity structure at the receiver and extract spatial diversity.
ContributorsRahmati, Mojtaba (Author) / Duman, Tolga M. (Thesis advisor) / Zhang, Junshan (Committee member) / Tepedelenlioğlu, Cihan (Committee member) / Reisslein, Martin (Committee member) / Arizona State University (Publisher)
Created2013
Description
The study of bacterial resistance to antimicrobial peptides (AMPs) is a significant area of interest as these peptides have the potential to be developed into alternative drug therapies to combat microbial pathogens. AMPs represent a class of host-mediated factors that function to prevent microbial infection of their host and serve as a first line of defense. To date, over 1,000 AMPs of various natures have been predicted or experimentally characterized. Their potent bactericidal activities and broad-based target repertoire make them a promising next-generation pharmaceutical therapy to combat bacterial pathogens. It is important to understand the molecular mechanisms, both genetic and physiological, that bacteria employ to circumvent the bactericidal activities of AMPs. These understandings will allow researchers to overcome challenges posed with the development of new drug therapies; as well as identify, at a fundamental level, how bacteria are able to adapt and survive within varied host environments. Here, results are presented from the first reported large scale, systematic screen in which the Keio collection of ~4,000 Escherichia coli deletion mutants were challenged against physiologically significant AMPs to identify genes required for resistance. Less than 3% of the total number of genes on the E. coli chromosome was determined to contribute to bacterial resistance to at least one AMP analyzed in the screen. Further, the screen implicated a single cellular component (enterobacterial common antigen, ECA) and a single transporter system (twin-arginine transporter, Tat) as being required for resistance to each AMP class. Using antimicrobial resistance as a tool to identify novel genetic mechanisms, subsequent analyses were able to identify a two-component system, CpxR/CpxA, as a global regulator in bacterial resistance to AMPs. Multiple previously characterized CpxR/A members, as well as members found in this study, were identified in the screen. Notably, CpxR/A was found to transcriptionally regulate the gene cluster responsible for the biosynthesis of the ECA. Thus, a novel genetic mechanism was uncovered that directly correlates with a physiologically significant cellular component that appears to globally contribute to bacterial resistance to AMPs.
ContributorsWeatherspoon-Griffin, Natasha (Author) / Shi, Yixin (Thesis advisor) / Clark-Curtiss, Josephine (Committee member) / Misra, Rajeev (Committee member) / Nickerson, Cheryl (Committee member) / Stout, Valerie (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
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