Nonlinear dynamics and chaos simulation system analysis for improved design

Small errors proved catastrophic. Our purpose to remark that a very small cause which escapes our notice determined a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. Small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. When dealing with any kind of electrical device specification, it is important to note that there exists a pair of test conditions that define a test: the forcing function and the limit. Forcing functions define the external operating constraints placed upon the device tested. The actual test defines how well the device responds to these constraints. Forcing inputs to threshold for example, represents the most difficult testing because this put those inputs as close as possible to the actual switching critical points and guarantees that the device will meet the Input-Output specifications. ^ Prediction becomes impossible by classical analytical analysis bounded by Newton and Euclides. We have found that non linear dynamics characteristics is the natural state of being in all circuits and devices. Opportunities exist for effective error detection in a nonlinear dynamics and chaos environment. ^ Nowadays there are a set of linear limits established around every aspect of a digital or analog circuits out of which devices are consider bad after failing the test. Deterministic chaos circuit is a fact not a possibility as it has been revived by our Ph.D. research. In practice for linear standard informational methodologies, this chaotic data product is usually undesirable and we are educated to be interested in obtaining a more regular stream of output data. ^ This Ph.D. research explored the possibilities of taking the foundation of a very well known simulation and modeling methodology, introducing nonlinear dynamics and chaos precepts, to produce a new error detector instrument able to put together streams of data scattered in space and time. Therefore, mastering deterministic chaos and changing the bad reputation of chaotic data as a potential risk for practical system status determination. ^

Effects of hydrologic and water quality drivers on periphyton dynamics in the southern Everglades

Everglades periphyton mats are tightly-coupled autotrophic (algae and cyanobacteria) and heterotrophic (eubacteria, fungi and microinvertebrates) microbial assemblages. We investigated the effect of water column total phosphorus and nitrogen concentrations, water depth and hydroperiod on periphyton of net production, respiration, nutrient content, and biomass. Our study sites were located along four transects that extended southward with freshwater sheetflow through sawgrass-dominated marsh. The water source for two of the transects were canal-driven and anchored at canal inputs. The two other transects were rain-driven (ombrotrophic) and began in sawgrass-dominated marsh. Periphyton dynamics were examined for upstream and downstream effects within and across the four transects. Although all study sites were characterized as short hydroperiod and phosphorus-limited oligotrophic, they represent gradients of hydrologic regime, water source and water quality of the southern Everglades. Average periphyton net production of 1.08 mg C AFDW−1 h−1 and periphyton whole system respiration of 0.38 mg C AFDW−1 h−1 rates were net autotrophic. Biomass was generally highest at ombrotrophic sites and sites downstream of canal inputs. Mean biomass over all our study sites was high, 1517.30 g AFDW m−2. Periphyton was phosphorus-limited. Average periphyton total phosphorus content was 137.15 μg P g−1 and average periphyton total N:P ratio was 192:1. Periphyton N:P was a sensitive indicator of water source. Even at extremely low mean water total phosphorus concentrations ( ≤ 0.21 μmol l−1), we found canal source effects on periphyton dynamics at sites adjacent to canal inputs, but not downstream of inflows. These canal source effects were most pronounced at the onset of wet season with initial rewetting. Spatial and temporal variability in periphyton dynamics could not solely be ascribed to water quality, but was often associated with both hydrology and water source.

Combination of 16S rRNA variable regions provides a detailed analysis of bacterial community dynamics in the lungs of cystic fibrosis patients

Chronic bronchopulmonary bacterial infections remain the most common cause of morbidity and mortality among patients with cystic fibrosis (CF). Recent community sequencing work has now shown that the bacterial community in the CF lung is polymicrobial. Identifying bacteria in the CF lung through sequencing can be costly and is not practical for many laboratories. Molecular techniques such as terminal restriction fragment length polymorphism or amplicon length heterogeneity-polymerase chain reaction (LH-PCR) can provide many laboratories with the ability to study CF bacterial communities without costly sequencing. The aim of this study was to determine if the use of LH-PCR with multiple hypervariable regions of the 16S rRNA gene could be used to identify organisms found in sputum DNA. This work also determined if LH-PCR could be used to observe the dynamics of lung infections over a period of time. Nineteen samples were analysed with the V1 and the V1_V2 region of the 16S rRNA gene. Based on the amplicon size present in the V1_V2 region, Pseudomonas aeruginosa was confirmed to be in all 19 samples obtained from the patients. The V1 region provided a higher power of discrimination between bacterial profiles of patients. Both regions were able to identify trends in the bacterial population over a period of time. LH profiles showed that the CF lung community is dynamic and that changes in the community may in part be driven by the patient's antibiotic treatment. LH-PCR is a tool that is well suited for studying bacterial communities and their dynamics.

Dynamics of spatial heterogeneity in a landfill with interacting phase densities:a stochastic analysis

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density, that themselves are stochastically affected by fluctuations, coupled with diffusive relaxation of the individual densities, in ambient surroundings. Our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure is primarily determined by the solid and hydrolysed mass densities only rendering the other variables as statistically "irrelevant" in this (large time) asymptotic limit. The other major implication of incorporation of stochasticity in the landfill evolution dynamics is in the hugely reduced production times of the plants that are now approximately 20-30 years instead of the previous deterministic model predictions of 50 years and above. The predictions from this stochastic model are in conformity with available experimental observations.

The critical role of intracavity dynamics in high-power mode-locked fiber lasers

We present a theoretical description of the generation of ultra-short, high-energy pulses in two laser cavities driven by periodic spectral filtering or dispersion management. Critical in driving the intra-cavity dynamics is the nontrivial phase profiles generated and their periodic modification from either spectral filtering or dispersion management. For laser cavities with a spectral filter, the theory gives a simple geometrical description of the intra-cavity dynamics and provides a simple and efficient method for optimizing the laser cavity performance. In the dispersion managed cavity, analysis shows the generated self-similar behavior to be governed by the porous media equation with a rapidly-varying, mean-zero diffusion coefficient whose solution is the well-known Barenblatt similarity solution with parabolic profile. © 2010 Copyright SPIE - The International Society for Optical Engineering.

Generation of harmonic oscillations in ring resonator with high Q-factor

We report on generation of harmonic oscillations with frequencies of hundreds of MHz and radio-frequency linewidth of 13 Hz in unidirectional ring laser oscillator. This high stability makes these oscillators a suitable substitute for existing quartz resonators used in high frequency optoelectronics applications.

Intracavity dynamics in mode-locked lasers

We present a theoretical description of the generation of ultra-short, high-energy pulses in two laser cavities driven by periodic spectral filtering or dispersion management. Critical in driving the intra-cavity dynamics is the nontrivial phase profiles generated and their periodic modification from either spectral filtering or dispersion management. For laser cavities with a spectral filter, the theory gives a simple geometrical description of the intra-cavity dynamics and provides a simple and efficient method for optimizing the laser cavity performance. In the dispersion managed cavity, analysis shows the generated self-similar behavior to be governed by the porous media equation with a rapidly-varying, mean-zero diffusion coefficient whose solution is the well-known Barenblatt similarity solution with parabolic profile. © 2010 American Institute of Physics.

Intracavity dynamics for power and energy enhancement in mode-locked lasers

We present a theoretical description of the generation of ultra-short, high-energy pulses in two laser cavities driven by periodic spectral filtering or dispersion management. Critical in driving the intra-cavity dynamics is the nontrivial phase profiles generated and their periodic modification from either spectral filtering or dispersion management. For laser cavities with a spectral filter, the theory gives a simple geometrical description of the intra-cavity dynamics and provides a simple and efficient method for optimizing the laser cavity performance. In the dispersion managed cavity, analysis shows the generated self-similar behavior to be governed by the porous media equation with a rapidly-varying, mean-zero diffusion coefficient whose solution is the well-known Barenblatt similarity solution with parabolic profile.

The Effects of Organic Matter Amendments and Migratory Waterfowl on Greenhouse Gas and Nutrient Dynamics in Managed Coastal Plain Wetlands

Wetland ecosystems provide many valuable ecosystem services, including carbon (C) storage and improvement of water quality. Yet, restored and managed wetlands are not frequently evaluated for their capacity to function in order to deliver on these values. Specific restoration or management practices designed to meet one set of criteria may yield unrecognized biogeochemical costs or co-benefits. The goal of this dissertation is to improve scientific understanding of how wetland restoration practices and waterfowl habitat management affect critical wetland biogeochemical processes related to greenhouse gas emissions and nutrient cycling. I met this goal through field and laboratory research experiments in which I tested for relationships between management factors and the biogeochemical responses of wetland soil, water, plants and trace gas emissions. Specifically, I quantified: (1) the effect of organic matter amendments on the carbon balance of a restored wetland; (2) the effectiveness of two static chamber designs in measuring methane (CH4) emissions from wetlands; (3) the impact of waterfowl herbivory on the oxygen-sensitive processes of methane emission and coupled nitrification-denitrification; and (4) nitrogen (N) exports caused by prescribed draw down of a waterfowl impoundment.

The potency of CH4 emissions from wetlands raises the concern that widespread restoration and/or creation of freshwater wetlands may present a radiative forcing hazard. Yet data on greenhouse gas emissions from restored wetlands are sparse and there has been little investigation into the greenhouse gas effects of amending wetland soils with organic matter, a recent practice used to improve function of mitigation wetlands in the Eastern United States. I measured trace gas emissions across an organic matter gradient at a restored wetland in the coastal plain of Virginia to test the hypothesis that added C substrate would increase the emission of CH4. I found soils heavily loaded with organic matter emitted significantly more carbon dioxide than those that have received little or no organic matter. CH4 emissions from the wetland were low compared to reference wetlands and contrary to my hypothesis, showed no relationship with the loading rate of added organic matter or total soil C. The addition of moderate amounts of organic matter (< 11.2 kg m-2) to the wetland did not greatly increase greenhouse gas emissions, while the addition of high amounts produced additional carbon dioxide, but not CH4.

I found that the static chambers I used for sampling CH4 in wetlands were highly sensitive to soil disturbance. Temporary compression around chambers during sampling inflated the initial chamber CH4 headspace concentration and/or lead to generation of nonlinear, unreliable flux estimates that had to be discarded. I tested an often-used rubber-gasket sealed static chamber against a water-filled-gutter seal chamber I designed that could be set up and sampled from a distance of 2 m with a remote rod sampling system to reduce soil disturbance. Compared to the conventional design, the remotely-sampled static chambers reduced the chance of detecting inflated initial CH4 concentrations from 66 to 6%, and nearly doubled the proportion of robust linear regressions from 45 to 86%. The new system I developed allows for more accurate and reliable CH4 sampling without costly boardwalk construction.

I explored the relationship between CH4 emissions and aquatic herbivores, which are recognized for imposing top-down control on the structure of wetland ecosystems. The biogeochemical consequences of herbivore-driven disruption of plant growth, and in turn, mediated oxygen transport into wetland sediments, were not previously known. Two growing seasons of herbivore exclusion experiments in a major waterfowl overwintering wetland in the Southeastern U.S. demonstrate that waterfowl herbivory had a strong impact on the oxygen-sensitive processes of CH4 emission and nitrification. Denudation by herbivorous birds increased cumulative CH4 flux by 233% (a mean of 63 g CH4 m-2 y-1) and inhibited coupled nitrification-denitrification, as indicated by nitrate availability and emissions of nitrous oxide. The recognition that large populations of aquatic herbivores may influence the capacity for wetlands to emit greenhouse gases and cycle nitrogen is particularly salient in the context of climate change and nutrient pollution mitigation goals. For example, our results suggest that annual emissions of 23 Gg of CH4 y-1 from ~55,000 ha of publicly owned waterfowl impoundments in the Southeastern U.S. could be tripled by overgrazing.

Hydrologically controlled moist-soil impoundment wetlands provide critical habitat for high densities of migratory bird populations, thus their potential to export nitrogen (N) to downstream waters may contribute to the eutrophication of aquatic ecosystems. To investigate the relative importance of N export from these built and managed habitats, I conducted a field study at an impoundment wetland that drains into hypereutrophic Lake Mattamuskeet. I found that prescribed hydrologic drawdowns of the impoundment exported roughly the same amount of N (14 to 22 kg ha-1) as adjacent fertilized agricultural fields (16 to 31 kg ha-1), and contributed approximately one-fifth of total N load (~45 Mg N y-1) to Lake Mattamuskeet. Ironically, the prescribed drawdown regime, designed to maximize waterfowl production in impoundments, may be exacerbating the degradation of habitat quality in the downstream lake. Few studies of wetland N dynamics have targeted impoundments managed to provide wildlife habitat, but a similar phenomenon may occur in some of the 36,000 ha of similarly-managed moist-soil impoundments on National Wildlife Refuges in the southeastern U.S. I suggest early drawdown as a potential method to mitigate impoundment N pollution and estimate it could reduce N export from our study impoundment by more than 70%.

In this dissertation research I found direct relationships between wetland restoration and impoundment management practices, and biogeochemical responses of greenhouse gas emission and nutrient cycling. Elevated soil C at a restored wetland increased CO2 losses even ten years after the organic matter was originally added and intensive herbivory impact on emergent aquatic vegetation resulted in a ~230% increase in CH4 emissions and impaired N cycling and removal. These findings have important implications for the basic understanding of the biogeochemical functioning of wetlands and practical importance for wetland restoration and impoundment management in the face of pressure to mitigate the environmental challenges of global warming and aquatic eutrophication.

Essays on Job Search and Labor Market Dynamics

This dissertation consists of three separate essays on job search and labor market dynamics. In the first essay, “The Impact of Labor Market Conditions on Job Creation: Evidence from Firm Level Data”, I study how much changes in labor market conditions reduce employment fluctuations over the business cycle. Changes in labor market conditions make hiring more expensive during expansions and cheaper during recessions, creating counter-cyclical incentives for job creation. I estimate firm level elasticities of labor demand with respect to changes in labor market conditions, considering two margins: changes in labor market tightness and changes in wages. Using employer-employee matched data from Brazil, I find that all firms are more sensitive to changes in wages rather than labor market tightness, and there is substantial heterogeneity in labor demand elasticity across regions. Based on these results, I demonstrate that changes in labor market conditions reduce the variance of employment growth over the business cycle by 20% in a median region, and this effect is equally driven by changes along each margin. Moreover, I show that the magnitude of the effect of labor market conditions on employment growth can be significantly affected by economic policy. In particular, I document that the rapid growth of the national minimum wages in Brazil in 1997-2010 amplified the impact of the change in labor market conditions during local expansions and diminished this impact during local recessions.

In the second essay, “A Framework for Estimating Persistence of Local Labor

Demand Shocks”, I propose a decomposition which allows me to study the persistence of local labor demand shocks. Persistence of labor demand shocks varies across industries, and the incidence of shocks in a region depends on the regional industrial composition. As a result, less diverse regions are more likely to experience deeper shocks, but not necessarily more long lasting shocks. Building on this idea, I propose a decomposition of local labor demand shocks into idiosyncratic location shocks and nationwide industry shocks and estimate the variance and the persistence of these shocks using the Quarterly Census of Employment and Wages (QCEW) in 1990-2013.

In the third essay, “Conditional Choice Probability Estimation of Continuous- Time Job Search Models”, co-authored with Peter Arcidiacono and Arnaud Maurel, we propose a novel, computationally feasible method of estimating non-stationary job search models. Non-stationary job search models arise in many applications, where policy change can be anticipated by the workers. The most prominent example of such policy is the expiration of unemployment benefits. However, estimating these models still poses a considerable computational challenge, because of the need to solve a differential equation numerically at each step of the optimization routine. We overcome this challenge by adopting conditional choice probability methods, widely used in dynamic discrete choice literature, to job search models and show how the hazard rate out of unemployment and the distribution of the accepted wages, which can be estimated in many datasets, can be used to infer the value of unemployment. We demonstrate how to apply our method by analyzing the effect of the unemployment benefit expiration on duration of unemployment using the data from the Survey of Income and Program Participation (SIPP) in 1996-2007.

Dynamics of the Disk-Pendulum Coupled System With Vertical Excitation

This paper investigates the static and dynamic characteristics of the semi-elliptical rocking disk on which a pendulum pinned. This coupled system’s response is also analyzed analytically and numerically when a vertical harmonic excitation is applied to the bottom of the rocking disk. Lagrange’s Equation is used to derive the motion equations of the disk-pendulum coupled system. The second derivative test for the system’s potential energy shows how the location of the pendulum’s pivotal point affects the number and stability of equilibria, and the change of location presents different bifurcation diagrams for different geometries of the rocking disk. For both vertically excited and unforced cases, the coupled system shows chaos easily, but the proper chosen parameters can still help the system reach and keep the steady state. For the steady state of the vertically excited rocking disk without a pendulum, the variation of the excitation’s amplitude and frequency result in the hysteresis for the amplitude of the response. When a pendulum is pinned on the rocking disk, three major categories of steady states are presently in the numerical way.

Diameter-driven crossover in resistive behaviour of heavily doped self-seeded germanium nanowires

The dependence of the resistivity with changing diameter of heavily-doped self-seeded germanium nanowires was studied for the diameter range 40 to 11 nm. The experimental data reveal an initial strong reduction of the resistivity with diameter decrease. At about 20 nm a region of slowly varying resistivity emerges with a peak feature around 14 nm. For diameters above 20 nm, nanowires were found to be describable by classical means. For smaller diameters a quantum-based approach was required where we employed the 1D Kubo–Greenwood framework and also revealed the dominant charge carriers to be heavy holes. For both regimes the theoretical results and experimental data agree qualitatively well assuming a spatial spreading of the free holes towards the nanowire centre upon diameter reduction.

On the microstructure, growth pattern and original porosity of belemnite rostra: insights from calcitic Jurassic belemnites

Calcitic belemnite rostra are usually employed to perform paleoenvironmental studies based on geochemical data. However, several questions, such as their original porosity and microstructure, remain open, despite they are essential to make accurate interpretations based on geochemical analyses.This paper revisits and enlightens some of these questions. Petrographic data demonstrate that calcite crystals of the rostrum solidum of belemnites grow from spherulites that successively develop along the apical line, resulting in a “regular spherulithic prismatic” microstructure. Radially arranged calcite crystals emerge and diverge from the spherulites: towards the apex, crystals grow until a new spherulite is formed; towards the external walls of the rostrum, the crystals become progressively bigger and prismatic. Adjacent crystals slightly vary in their c-axis orientation, resulting in undulose extinction. Concentric growth layering develops at different scales and is superimposed and traversed by a radial pattern, which results in the micro-fibrous texture that is observed in the calcite crystals in the rostra.Petrographic data demonstrate that single calcite crystals in the rostra have a composite nature, which strongly suggests that the belemnite rostra were originally porous. Single crystals consistently comprise two distinct zones or sectors in optical continuity: 1) the inner zone is fluorescent, has relatively low optical relief under transmitted light (TL) microscopy, a dark-grey color under backscatter electron microscopy (BSEM), a commonly triangular shape, a “patchy” appearance and relatively high Mg and Na contents; 2) the outer sector is non-fluorescent, has relatively high optical relief under TL, a light-grey color under BSEM and low Mg and Na contents. The inner and fluorescent sectors are interpreted to have formed first as a product of biologically controlled mineralization during belemnite skeletal growth and the non-fluorescent outer sectors as overgrowths of the former, filling the intra- and inter-crystalline porosity. This question has important implications for making paleoenvironmental and/or paleoclimatic interpretations based on geochemical analyses of belemnite rostra.Finally, the petrographic features of composite calcite crystals in the rostra also suggest the non-classical crystallization of belemnite rostra, as previously suggested by other authors.

Is the Russell Cycle a true cycle? Multidecadal zooplankton and climate trends in the western English Channel

The Russell Cycle is one of the classical examples of climate influence on biological oceanography, represented as shifts in the marine plankton over several decades with warm and cool conditions. While the time-series data associated with the phenomenon indicate cyclical patterns, the question remains whether or not the Russell Cycle should be considered a “true cycle”. Zooplankton time-series data from 1924 to 2011 from the western English Channel were analysed with principal component (PC), correlation and spectral analyses to determine the dominant trends, and cyclic frequencies of the Russell Cycle indicators in relation to long-term hydroclimatic indices. PC1 accounted for 37.4% of the variability in the zooplankton data with the main contributions from non-clupeid fish larvae, southwestern zooplankton, and overall zooplankton biovolume. For PC2 (14.6% of data variance), the dominant groups were northern fish larvae, non-sardine eggs, and southern fish larvae. Sardine eggs were the major contributors to PC3 (representing 12.1% of data variance). No significant correlations were observed between the above three components and climate indices: Atlantic Multidecadal Oscillation, North Atlantic Oscillation, and local seawater temperature. Significant 44- and 29-year frequencies were observed for PC3, but the physical mechanisms driving the cycles are unclear. Harmonic analysis did not reveal any significant frequencies in the physical variables or in PCs 1 and 2. To a large extent, this is due to the dominant cycles in all datasets generally being long term (>50 years or so) and not readily resolved in the examined time frame of 88 years, hence restricting the ability to draw firm conclusions on the multidecadal relationship between zooplankton community dynamics in the western English Channel and environmental indices. Thus, the zooplankton time-series often associated and represented as the Russell Cycle cannot be concluded as being truly cyclical.

Is the Russell Cycle a true cycle? Multidecadal zooplankton and climate trends in the western English Channel

The Russell Cycle is one of the classical examples of climate influence on biological oceanography, represented as shifts in the marine plankton over several decades with warm and cool conditions. While the time-series data associated with the phenomenon indicate cyclical patterns, the question remains whether or not the Russell Cycle should be considered a “true cycle”. Zooplankton time-series data from 1924 to 2011 from the western English Channel were analysed with principal component (PC), correlation and spectral analyses to determine the dominant trends, and cyclic frequencies of the Russell Cycle indicators in relation to long-term hydroclimatic indices. PC1 accounted for 37.4% of the variability in the zooplankton data with the main contributions from non-clupeid fish larvae, southwestern zooplankton, and overall zooplankton biovolume. For PC2 (14.6% of data variance), the dominant groups were northern fish larvae, non-sardine eggs, and southern fish larvae. Sardine eggs were the major contributors to PC3 (representing 12.1% of data variance). No significant correlations were observed between the above three components and climate indices: Atlantic Multidecadal Oscillation, North Atlantic Oscillation, and local seawater temperature. Significant 44- and 29-year frequencies were observed for PC3, but the physical mechanisms driving the cycles are unclear. Harmonic analysis did not reveal any significant frequencies in the physical variables or in PCs 1 and 2. To a large extent, this is due to the dominant cycles in all datasets generally being long term (>50 years or so) and not readily resolved in the examined time frame of 88 years, hence restricting the ability to draw firm conclusions on the multidecadal relationship between zooplankton community dynamics in the western English Channel and environmental indices. Thus, the zooplankton time-series often associated and represented as the Russell Cycle cannot be concluded as being truly cyclical.