Matching Items (143)
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
Filtration for microfluidic sample-collection devices is desirable for sample selection, concentration, preprocessing, and downstream manipulation, but microfabricating the required sub-micrometer filtration structure is an elaborate process. This thesis presents a simple method to fabricate polydimethylsiloxane (PDMS) devices with an integrated membrane filter that will sample, lyse, and extract the DNA from microorganisms in aqueous environments. An off-the-shelf membrane filter disc was embedded in a PDMS layer and sequentially bound with other PDMS channel layers. No leakage was observed during filtration. This device was validated by concentrating a large amount of cyanobacterium Synechocystis in simulated sample water with consistent performance across devices. After accumulating sufficient biomass on the filter, a sequential electrochemical lysing process was performed by applying 5VDC across the filter. This device was further evaluated by delivering several samples of differing concentrations of cyanobacterium Synechocystis then quantifying the DNA using real-time PCR. Lastly, an environmental sample was run through the device and the amount of photosynthetic microorganisms present in the water was determined. The major breakthroughs in this design are low energy demand, cheap materials, simple design, straightforward fabrication, and robust performance, together enabling wide-utility of similar chip-based devices for field-deployable operations in environmental micro-biotechnology.
ContributorsLecluse, Aurelie (Author) / Meldrum, Deirdre (Thesis advisor) / Chao, Joseph (Thesis advisor) / Westerhoff, Paul (Committee member) / Arizona State University (Publisher)
Created2011
Description
Single cell phenotypic heterogeneity studies reveal more information about the pathogenesis process than conventional bulk methods. Furthermore, investigation of the individual cellular response mechanism during rapid environmental changes can only be achieved at single cell level. By enabling the study of cellular morphology, a single cell three-dimensional (3D) imaging system can be used to diagnose fatal diseases, such as cancer, at an early stage. One proven method, CellCT, accomplishes 3D imaging by rotating a single cell around a fixed axis. However, some existing cell rotating mechanisms require either intricate microfabrication, and some fail to provide a suitable environment for living cells. This thesis develops a microvorterx chamber that allows living cells to be rotated by hydrodynamic alone while facilitating imaging access. In this thesis work, 1) the new chamber design was developed through numerical simulation. Simulations revealed that in order to form a microvortex in the side chamber, the ratio of the chamber opening to the channel width must be smaller than one. After comparing different chamber designs, the trapezoidal side chamber was selected because it demonstrated controllable circulation and met the imaging requirements. Microvortex properties were not sensitive to the chambers with interface angles ranging from 0.32 to 0.64. A similar trend was observed when chamber heights were larger than chamber opening. 2) Micro-particle image velocimetry was used to characterize microvortices and validate simulation results. Agreement between experimentation and simulation confirmed that numerical simulation was an effective method for chamber design. 3) Finally, cell rotation experiments were performed in the trapezoidal side chamber. The experimental results demonstrated cell rotational rates ranging from 12 to 29 rpm for regular cells. With a volumetric flow rate of 0.5 µL/s, an irregular cell rotated at a mean rate of 97 ± 3 rpm. Rotational rates can be changed by altering inlet flow rates.
ContributorsZhang, Wenjie (Author) / Frakes, David (Thesis advisor) / Meldrum, Deirdre (Thesis advisor) / Chao, Shih-hui (Committee member) / Wang, Xiao (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
Laboratory automation systems have seen a lot of technological advances in recent times. As a result, the software that is written for them are becoming increasingly sophisticated. Existing software architectures and standards are targeted to a wider domain of software development and need to be customized in order to use them for developing software for laboratory automation systems. This thesis proposes an architecture that is based on existing software architectural paradigms and is specifically tailored to developing software for a laboratory automation system. The architecture is based on fairly autonomous software components that can be distributed across multiple computers. The components in the architecture make use of asynchronous communication methodologies that are facilitated by passing messages between one another. The architecture can be used to develop software that is distributed, responsive and thread-safe. The thesis also proposes a framework that has been developed to implement the ideas proposed by the architecture. The framework is used to develop software that is scalable, distributed, responsive and thread-safe. The framework currently has components to control very commonly used laboratory automation devices such as mechanical stages, cameras, and also to do common laboratory automation functionalities such as imaging.
ContributorsKuppuswamy, Venkataramanan (Author) / Meldrum, Deirdre (Thesis advisor) / Collofello, James (Thesis advisor) / Sarjoughian, Hessam S. (Committee member) / Johnson, Roger (Committee member) / Arizona State University (Publisher)
Created2012
Description
Single cell analysis has become increasingly important in understanding disease onset, progression, treatment and prognosis, especially when applied to cancer where cellular responses are highly heterogeneous. Through the advent of single cell computerized tomography (Cell-CT), researchers and clinicians now have the ability to obtain high resolution three-dimensional (3D) reconstructions of single cells. Yet to date, no live-cell compatible version of the technology exists. In this thesis, a microfluidic chip with the ability to rotate live single cells in hydrodynamic microvortices about an axis parallel to the optical focal plane has been demonstrated. The chip utilizes a novel 3D microchamber design arranged beneath a main channel creating flow detachment into the chamber, producing recirculating flow conditions. Single cells are flowed through the main channel, held in the center of the microvortex by an optical trap, and rotated by the forces induced by the recirculating fluid flow. Computational fluid dynamics (CFD) was employed to optimize the geometry of the microchamber. Two methods for the fabrication of the 3D microchamber were devised: anisotropic etching of silicon and backside diffuser photolithography (BDPL). First, the optimization of the silicon etching conditions was demonstrated through design of experiment (DOE). In addition, a non-conventional method of soft-lithography was demonstrated which incorporates the use of two positive molds, one of the main channel and the other of the microchambers, compressed together during replication to produce a single ultra-thin (<200 µm) negative used for device assembly. Second, methods for using thick negative photoresists such as SU-8 with BDPL have been developed which include a new simple and effective method for promoting the adhesion of SU-8 to glass. An assembly method that bonds two individual ultra-thin (<100 µm) replications of the channel and the microfeatures has also been demonstrated. Finally, a pressure driven pumping system with nanoliter per minute flow rate regulation, sub-second response times, and < 3% flow variability has been designed and characterized. The fabrication and assembly of this device is inexpensive and utilizes simple variants of conventional microfluidic fabrication techniques, making it easily accessible to the single cell analysis community.
ContributorsMyers, Jakrey R (Author) / Meldrum, Deirdre (Thesis advisor) / Johnson, Roger (Committee member) / Frakes, David (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
Mathematical epidemiology, one of the oldest and richest areas in mathematical biology, has significantly enhanced our understanding of how pathogens emerge, evolve, and spread. Classical epidemiological models, the standard for predicting and managing the spread of infectious disease, assume that contacts between susceptible and infectious individuals depend on their relative frequency in the population. The behavioral factors that underpin contact rates are not generally addressed. There is, however, an emerging a class of models that addresses the feedbacks between infectious disease dynamics and the behavioral decisions driving host contact. Referred to as “economic epidemiology” or “epidemiological economics,” the approach explores the determinants of decisions about the number and type of contacts made by individuals, using insights and methods from economics. We show how the approach has the potential both to improve predictions of the course of infectious disease, and to support development of novel approaches to infectious disease management.
ContributorsPerrings, Charles (Author) / Castillo-Chavez, Carlos (Author) / Chowell-Puente, Gerardo (Author) / Daszak, Peter (Author) / Fenichel, Eli P. (Author) / Finnoff, David (Author) / Horan, Richard D. (Author) / Kilpatrick, A. Marm (Author) / Kinzig, Ann (Author) / Kuminoff, Nicolai (Author) / Levin, Simon (Author) / Morin, Benjamin (Author) / Smith, Katherine F. (Author) / Springborn, Michael (Author) / Simon M. Levin Mathematical, Computational and Modeling Sciences Center (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor) / School of Human Evolution and Social Change (Contributor) / W.P. Carey School of Business (Contributor) / Economics (Contributor) / Julie Ann Wrigley Global Institute of Sustainability (Contributor)
Created2015-12-01
Description
Nutrient recycling by fish can be an important part of nutrient cycles in both freshwater and marine ecosystems. As a result, understanding the mechanisms that influence excretion elemental ratios of fish is of great importance to a complete understanding of aquatic nutrient cycles. As fish consume a wide range of diets that differ in elemental composition, stoichiometric theory can inform predictions about dietary effects on excretion ratios.
We conducted a meta-analysis to test the effects of diet elemental composition on consumption and nutrient excretion by fish. We examined the relationship between consumption rate and diet N : P across all laboratory studies and calculated effect sizes for each excretion metric to test for significant effects.
Consumption rate of N, but not P, was significantly negatively affected by diet N : P. Effect sizes of diet elemental composition on consumption-specific excretion N, P and N : P in laboratory studies were all significantly different from 0, but effect size for raw excretion N : P was not significantly different from zero in laboratory or field surveys.
Our results highlight the importance of having a mechanistic understanding of the drivers of consumer excretion rates and ratios. We suggest that more research is needed on how consumption and assimilation efficiency vary with N : P and in natural ecosystems in order to further understand mechanistic processes in consumer-driven nutrient recycling.
ContributorsMoody, Eric (Author) / Corman, Jessica (Author) / Elser, James (Author) / Sabo, John (Author) / College of Liberal Arts and Sciences (Contributor) / School of Life Sciences (Contributor) / Julie Ann Wrigley Global Institute of Sustainability (Contributor)
Created2015-03-01
Description
Preserving a system’s viability in the presence of diversity erosion is critical if the goal is to sustainably support biodiversity. Reduction in population heterogeneity, whether inter- or intraspecies, may increase population fragility, either decreasing its ability to adapt effectively to environmental changes or facilitating the survival and success of ordinarily rare phenotypes. The latter may result in over-representation of individuals who may participate in resource utilization patterns that can lead to over-exploitation, exhaustion, and, ultimately, collapse of both the resource and the population that depends on it. Here, we aim to identify regimes that can signal whether a consumer–resource system is capable of supporting viable degrees of heterogeneity. The framework used here is an expansion of a previously introduced consumer–resource type system of a population of individuals classified by their resource consumption. Application of the Reduction Theorem to the system enables us to evaluate the health of the system through tracking both the mean value of the parameter of resource (over)consumption, and the population variance, as both change over time. The article concludes with a discussion that highlights applicability of the proposed system to investigation of systems that are affected by particularly devastating overly adapted populations, namely cancerous cells. Potential intervention approaches for system management are discussed in the context of cancer therapies.
ContributorsKareva, Irina (Author) / Morin, Benjamin (Author) / Castillo-Chavez, Carlos (Author) / Simon M. Levin Mathematical, Computational and Modeling Sciences Center (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Human Evolution and Social Change (Contributor) / Julie Ann Wrigley Global Institute of Sustainability (Contributor)
Created2015-02-01