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. ^

Tom Stoppard: Humanizing chaos

The purpose of this study was to critically evaluate Tom Stoppard’s application of chaos theory and quantum science in ROSENCRANTZ AND GUILDENSTERN ARE DEAD, HAPGOOD and ARCADIA; and determine the extent to which Stoppard argues for the importance of human action and choice. ^ Through critical analysis this study examined how Stoppard applies the quantum aspects of: (1) indeterminacy to human epistemology in ROSENCRANTZ AND GUILDENSTERN ARE DEAD; (2) complementarity to human identity in HAPGOOD; and (3) recursive symmetry to human history in ARCADIA. It also examined how Stoppard excavates the complexities of human action, choice and identity through the lens of chaos theory and quantum science. ^ These findings demonstrated that Tom Stoppard is not merely juxtaposing quantum science and human interactions for the sake of drama; rather, by excavating the complexities of human action, choice and identity through the lens of chaos theory and quantum science, Stoppard demonstrates the fundamental connection between individuals and the post-Newtonian universe.^

Spatiotemporal variation of the abundance of calcareous green macroalgae in the Florida Keys: A study of synchrony within a macroalgal functional-form group

The abundance of calcareous green algae was recorded quarterly at 28 sites within the Florida Keys National Marine Sanctuary (FKNMS) for a period of 7 years as part of a sea grass monitoring program. To evaluate the validity of using the functional-form group approach, we designed a sampling method that included the functional-form group and the component genera. This strategy enabled us to analyze the spatiotemporal patterns in the abundance of calcareous green algae as a group and to describe synchronous behavior among its genera through the application of a nonlinear regression model to both categories of data. Spatial analyses revealed that, in general, all genera displayed long-term trends of increasing abundance at most sites; however, at some sites the long-term trends for genera opposed one another. Strong synchrony in the timing of seasonal changes was found among all genera, possibly reflecting similar reproductive and seasonal growth pattern, but the variability in the magnitude of seasonal changes was very high among genera and sites. No spatial patterns were found in long-term or seasonal changes; the only significant relation detected was for slope, with sites closer to land showing higher values, suggesting that some factors associated with land proximity are affecting this increase. We conclude that the abundances of genera behaved differently from the functional-form group, indicating that the use of the functionalform group approach may be unsuitable to detect changes in sea grass community structure in the FKNMS at the existing temporal and spatial scale of the monitoring program.

Spatiotemporal patterns in community structure of macroinvertebrates inhabiting calcareous periphyton mats

Calcareous floating periphyton mats in the southern Everglades provide habitat for a diverse macroinvertebrate community that has not been well characterized. Our study described this community in an oligotrophic marsh, compared it with the macroinvertebrate community associated with adjacent epiphytic algae attached to macrophytes in the water column, and detected spatial patterns in density and community structure. The floating periphyton mat (floating mat) and epiphytic algae in the water column (submerged epiphyton) were sampled at 4 sites (1 km apart) in northern Shark River Slough, Everglades National Park (ENP), in the early (July) and late (November) wet season. Two perpendicular 90-m transects were established at each site and 100 samples were taken in a nested design. Sites were located in wet-prairie spikerush-dominated sloughs with similar water depths and emergent macrophyte communities. Floating mats were sampled by taking cores (6-cm diameter) that were sorted under magnification to enumerate infauna retained on a 250-μm-mesh sieve and with a maximum dimension >1 mm. Our results showed that floating mats provide habitat for a macroinvertebrate community with higher densities (no. animals/g ash-free dry mass) of Hyalella azteca, Dasyhelea spp., and Cladocera, and lower densities of Chironomidae and Planorbella spp. than communities associated with submerged epiphyton. Densities of the most common taxa increased 3× to 15× from early to late wet season, and community differences between the 2 habitat types became more pronounced. Floating-mat coverage and estimated floating-mat biomass increased 20 to 30% and 30 to 110%, respectively, at most sites in the late wet season. Some intersite variation was observed in individual taxa, but no consistent spatial pattern in any taxon was detected at any scale (from 0.2 m to 3 km). Floating mats and their resident macroinvertebrate communities are important components in the Everglades food web. This community should be included in environmental monitoring programs because degradation and eventual loss of the calcareous periphyton mat is associated with P enrichment in this ecosystem.

Theoretical Investigation of Intra- and Inter-cellular Spatiotemporal Calcium Patterns in Microcirculation

Microcirculatory vessels are lined by endothelial cells (ECs) which are surrounded by a single or multiple layer of smooth muscle cells (SMCs). Spontaneous and agonist induced spatiotemporal calcium (Ca2+) events are generated in ECs and SMCs, and regulated by complex bi-directional signaling between the two layers which ultimately determines the vessel tone. The contractile state of microcirculatory vessels is an important factor in the determination of vascular resistance, blood flow and blood pressure. This dissertation presents theoretical insights into some of the important and currently unresolved phenomena in microvascular tone regulation. Compartmental and continuum models of isolated EC and SMC, coupled EC-SMC and a multi-cellular vessel segment with deterministic and stochastic descriptions of the cellular components were developed, and the intra- and inter-cellular spatiotemporal Ca2+ mobilization was examined. Coupled EC-SMC model simulations captured the experimentally observed localized subcellular EC Ca2+ events arising from the opening of EC transient receptor vanilloid 4 (TRPV4) channels and inositol triphosphate receptors (IP3Rs). These localized EC Ca2+ events result in endothelium-derived hyperpolarization (EDH) and Nitric Oxide (NO) production which transmit to the adjacent SMCs to ultimately result in vasodilation. The model examined the effect of heterogeneous distribution of cellular components and channel gating kinetics in determination of the amplitude and spread of the Ca2+ events. The simulations suggested the necessity of co-localization of certain cellular components for modulation of EDH and NO responses. Isolated EC and SMC models captured intracellular Ca2+ wave like activity and predicted the necessity of non-uniform distribution of cellular components for the generation of Ca2+ waves. The simulations also suggested the role of membrane potential dynamics in regulating Ca2+ wave velocity. The multi-cellular vessel segment model examined the underlying mechanisms for the intercellular synchronization of spontaneous oscillatory Ca2+ waves in individual SMC. From local subcellular events to integrated macro-scale behavior at the vessel level, the developed multi-scale models captured basic features of vascular Ca2+ signaling and provide insights for their physiological relevance. The models provide a theoretical framework for assisting investigations on the regulation of vascular tone in health and disease.

Spatiotemporal Variation in Abundance and Social Structure of Bottlenose Dolphins in the Florida Coastal Everglades

Bottlenose dolphins (Tursiops truncatus) are large-bodied predators that are locally abundant in the coastal Everglades. Because of their potential to exert strong top-down effects on their communities, it is important to understand how spatiotemporal variation in biotic and abiotic factors affects the abundance and behavior of dolphins. This study combined two years of transect surveys with photographic identification methods to assess spatiotemporal variation in the abundance and group sizes of bottlenose dolphins across four large regions of the coastal Everglades including the Shark and Harney Rivers, Whitewater Bay, and coastal oceans of the Gulf of Mexico and Florida Bay. Dolphin abundance was similar across wet and dry seasons, except in river habitats where abundances were higher during the dry season. Group sizes were largest in Florida Bay and open water. Dolphins may be relatively resilient to abiotic changes in the coastal Everglades, with the possible exception of river habitats.

Zoroastrianism, Cosmology, and Chaos: A Detailed Analysis of the Musical Composition, Druj Aeterni

Druj Aeterni is a large chamber ensemble piece for flute, clarinet, French horn, two trumpets, piano, two percussionists, string quintet, and electric bass. My composition integrates three intellectual pursuits and interests, ancient mythology, cosmology, and mathematics. The title of the piece uses Latin and the language of the Avesta, the holy book of Zoroastrianism, and comments upon a philosophical perspective based in string theory. I abstract the cosmological implications of string theory, apply them to the terminology and theology of Zoroastrianism, and then structure the composition in consideration of a possible reconciliation. The analysis that follows incorporates analytical techniques similar to David Cope’s style of Vectoral Analysis.

Theoretical investigation of intra- and inter-cellular spatiotemporal calcium patterns in microcirculation

Microcirculatory vessels are lined by endothelial cells (ECs) which are surrounded by a single or multiple layer of smooth muscle cells (SMCs). Spontaneous and agonist induced spatiotemporal calcium (Ca2+) events are generated in ECs and SMCs, and regulated by complex bi-directional signaling between the two layers which ultimately determines the vessel tone. The contractile state of microcirculatory vessels is an important factor in the determination of vascular resistance, blood flow and blood pressure. This dissertation presents theoretical insights into some of the important and currently unresolved phenomena in microvascular tone regulation. Compartmental and continuum models of isolated EC and SMC, coupled EC-SMC and a multi-cellular vessel segment with deterministic and stochastic descriptions of the cellular components were developed, and the intra- and inter-cellular spatiotemporal Ca2+ mobilization was examined.^ Coupled EC-SMC model simulations captured the experimentally observed localized subcellular EC Ca2+ events arising from the opening of EC transient receptor vanilloid 4 (TRPV4) channels and inositol triphosphate receptors (IP3Rs). These localized EC Ca2+ events result in endothelium-derived hyperpolarization (EDH) and Nitric Oxide (NO) production which transmit to the adjacent SMCs to ultimately result in vasodilation. The model examined the effect of heterogeneous distribution of cellular components and channel gating kinetics in determination of the amplitude and spread of the Ca2+ events. The simulations suggested the necessity of co-localization of certain cellular components for modulation of EDH and NO responses. Isolated EC and SMC models captured intracellular Ca2+ wave like activity and predicted the necessity of non-uniform distribution of cellular components for the generation of Ca2+ waves. The simulations also suggested the role of membrane potential dynamics in regulating Ca2+ wave velocity. The multi-cellular vessel segment model examined the underlying mechanisms for the intercellular synchronization of spontaneous oscillatory Ca2+ waves in individual SMC. ^ From local subcellular events to integrated macro-scale behavior at the vessel level, the developed multi-scale models captured basic features of vascular Ca2+ signaling and provide insights for their physiological relevance. The models provide a theoretical framework for assisting investigations on the regulation of vascular tone in health and disease.^