The biogeochemical cycles of iron (Fe) and manganese (Mn) in lakes and reservoirs have predictable seasonal trends, largely governed by stratification dynamics and redox conditions in the hypolimnion. However, short-term (i.e., sub-weekly) trends in Fe and Mn cycling are less well-understood, as most monitoring efforts focus on longer-term (i.e., monthly to yearly) time scales. The potential for elevated Fe and Mn to degrade water quality and impact ecosystem functioning, coupled with increasing evidence for high spatiotemporal variability in other biogeochemical cycles, necessitates a closer evaluation of the short-term Fe and Mn cycling dynamics in lakes and reservoirs. We adapted a UV-visible spectrophotometer coupled with a multiplexor pumping system and PLSR modeling to generate high spatiotemporal resolution predictions of Fe and Mn concentrations in a drinking water reservoir (Falling Creek Reservoir, Vinton, VA, USA) equipped with a hypolimnetic oxygenation (HOx) system. We quantified hourly Fe and Mn concentrations during two distinct transitional periods: reservoir turnover (Fall 2020) and initiation of the HOx system (Summer 2021). Our sensor system was able to successfully predict mean Fe and Mn concentrations as well as capture sub-weekly variability, ground-truthed by traditional grab sampling and laboratory analysis. During fall turnover, hypolimnetic Fe and Mn concentrations began to decrease more than two weeks before complete mixing of the reservoir occurred, with rapid equalization of epilimnetic and hypolimnetic Fe and Mn concentrations in less than 48 hours after full water column mixing. During the initiation of hypolimnetic oxygenation in Summer 2021, we observed that Fe and Mn were similarly affected by physical mixing in the hypolimnion, but displayed distinctly different responses to oxygenation, as indicated by the rapid oxidation of soluble Fe but not soluble Mn. This study demonstrates that Fe and Mn concentrations are highly sensitive to shifting dissolved oxygen and stratification and that their dynamics can substantially change on hourly to daily time scales in response to these transitions. / Master of Science / Iron and manganese are chemical elements that occur in many freshwater systems. Although they are naturally-occurring, high concentrations of iron and manganese can have negative effects on drinking water quality as well as the health of aquatic ecosystems. In temperate regions, iron and manganese can accumulate in the bottom waters of lakes and reservoirs during the summer months, but generally remain at low levels during the fall through spring. This seasonal cycle has been previously documented, but few studies have investigated the ways in which iron and manganese concentrations in a lake or reservoir change over shorter periods of time, such as hours or days. Recent advances in technology to measure chemical elements in the environment have allowed scientists to observe chemical fluctuations of other elements over relatively short time periods, which suggests that iron and manganese could potentially exhibit similar trends. In this study, we used an advanced sensor system to make hourly measurements of iron and manganese concentrations in a drinking water reservoir and observe how they changed during two time periods: in the fall of 2020, as the reservoir was transitioning from summer to winter, and in the summer of 2021, when oxygen was added to the bottom waters to improve water quality. Our observations indicate that iron and manganese concentrations in the reservoir waters were highly variable over short time scales and that they can change dramatically in as little as 24 hours, especially during transitional periods. We also successfully demonstrated the ability of our advanced sensor system to monitor these hourly changes, which could have many benefits for drinking water management and understanding metals cycling in freshwater systems.

When two or more chaotic systems are coupled, they may exhibit synchronized chaotic oscillations. The synchronization of chaos is usually understood as the regime of chaotic oscillations in which the corresponding variables or coupled systems are equal to each other. This kind of synchronized chaos is most frequently observed in systems specifically designed to be able to produce this behaviour. In this thesis, one particular type of synchronization, called impulsive synchronization, is investigated and applied to low dimensional chaotic, hyperchaotic and spatiotemporal chaotic systems. This synchronization technique requires driving one chaotic system, called response system, by samples of the state variables of the other chaotic system, called drive system, at discrete moments. Equi-Lagrange stability and equi-attractivity in the large property of the synchronization error become our major concerns when discussing the dynamics of synchronization to guarantee the convergence of the error dynamics to zero. Sufficient conditions for equi-Lagrange stability and equi-attractivity in the large are obtained for the different types of chaos-generating systems used. The issue of robustness of synchronized chaotic oscillations with respect to parameter variations and time delay, is also addressed and investigated when dealing with impulsive synchronization of low dimensional chaotic and hyperchaotic systems. Due to the fact that it is impossible to design two identical chaotic systems and that transmission and sampling delays in impulsive synchronization are inevitable, robustness becomes a fundamental issue in the models considered. Therefore it is established, in this thesis, that under relatively large parameter perturbations and bounded delay, impulsive synchronization still shows very desired behaviour. In fact, criteria for robustness of this particular type of synchronization are derived for both cases, especially in the case of time delay, where sufficient conditions for the synchronization error to be equi-attractivity in the large, are derived and an upper bound on the delay terms is also obtained in terms of the other parameters of the systems involved. The theoretical results, described above, regarding impulsive synchronization, are reconfirmed numerically. This is done by analyzing the Lyapunov exponents of the error dynamics and by showing the simulations of the different models discussed in each case. The application of the theory of synchronization, in general, and impulsive synchronization, in particular, to communication security, is also presented in this thesis. A new impulsive cryptosystem, called induced-message cryptosystem, is proposed and its properties are investigated. It was established that this cryptosystem does not require the transmission of the encrypted signal but instead the impulses will carry the information needed for synchronization and for retrieving the message signal. Thus the security of transmission is increased and the time-frame congestion problem, discussed in the literature, is also solved. Several other impulsive cryptosystems are also proposed to accommodate more solutions to several security issues and to illustrate the different properties of impulsive synchronization. Finally, extending the applications of impulsive synchronization to employ spatiotemporal chaotic systems, generated by partial differential equations, is addressed. Several possible models implementing this approach are suggested in this thesis and few questions are raised towards possible future research work in this area.

When two or more chaotic systems are coupled, they may exhibit synchronized chaotic oscillations. The synchronization of chaos is usually understood as the regime of chaotic oscillations in which the corresponding variables or coupled systems are equal to each other. This kind of synchronized chaos is most frequently observed in systems specifically designed to be able to produce this behaviour. In this thesis, one particular type of synchronization, called impulsive synchronization, is investigated and applied to low dimensional chaotic, hyperchaotic and spatiotemporal chaotic systems. This synchronization technique requires driving one chaotic system, called response system, by samples of the state variables of the other chaotic system, called drive system, at discrete moments. Equi-Lagrange stability and equi-attractivity in the large property of the synchronization error become our major concerns when discussing the dynamics of synchronization to guarantee the convergence of the error dynamics to zero. Sufficient conditions for equi-Lagrange stability and equi-attractivity in the large are obtained for the different types of chaos-generating systems used. The issue of robustness of synchronized chaotic oscillations with respect to parameter variations and time delay, is also addressed and investigated when dealing with impulsive synchronization of low dimensional chaotic and hyperchaotic systems. Due to the fact that it is impossible to design two identical chaotic systems and that transmission and sampling delays in impulsive synchronization are inevitable, robustness becomes a fundamental issue in the models considered. Therefore it is established, in this thesis, that under relatively large parameter perturbations and bounded delay, impulsive synchronization still shows very desired behaviour. In fact, criteria for robustness of this particular type of synchronization are derived for both cases, especially in the case of time delay, where sufficient conditions for the synchronization error to be equi-attractivity in the large, are derived and an upper bound on the delay terms is also obtained in terms of the other parameters of the systems involved. The theoretical results, described above, regarding impulsive synchronization, are reconfirmed numerically. This is done by analyzing the Lyapunov exponents of the error dynamics and by showing the simulations of the different models discussed in each case. The application of the theory of synchronization, in general, and impulsive synchronization, in particular, to communication security, is also presented in this thesis. A new impulsive cryptosystem, called induced-message cryptosystem, is proposed and its properties are investigated. It was established that this cryptosystem does not require the transmission of the encrypted signal but instead the impulses will carry the information needed for synchronization and for retrieving the message signal. Thus the security of transmission is increased and the time-frame congestion problem, discussed in the literature, is also solved. Several other impulsive cryptosystems are also proposed to accommodate more solutions to several security issues and to illustrate the different properties of impulsive synchronization. Finally, extending the applications of impulsive synchronization to employ spatiotemporal chaotic systems, generated by partial differential equations, is addressed. Several possible models implementing this approach are suggested in this thesis and few questions are raised towards possible future research work in this area.

The term spatiotemporal chaos refers to physical phenomena that exhibit irregular oscillations in both space and time. Examples of such phenomena range from cardiac dynamics to fluid turbulence, where the motion is described by nonlinear partial differential equations. It is well known from the studies of low dimensional chaotic systems that the state space, the space of solutions to the governing dynamical equations, is shaped by the invariant sets such as equilibria, periodic orbits, and invariant tori. State space of partial differential equations is infinite dimensional, nevertheless, recent computational advancements allow us to find their invariant solutions (exact coherent structures) numerically. In this thesis, we try to elucidate the chaotic dynamics of nonlinear partial differential equations by studying their exact coherent structures and invariant manifolds. Specifically, we investigate the Kuramoto-Sivashinsky equation, which describes the velocity of a flame front, and the Navier-Stokes equation for an incompressible fluid in a circular pipe. We argue with examples that this approach can lead to a theory of turbulence with predictive power.

Emotional cues within the environment capture our attention and influence how we perceive our surroundings. Past research has shown that emotional cues presented before the detection of a perceptual gap can actually impair the perception of elementary visual features (e.g., the lack of detail creating a spatial gap) while simultaneously improving the perception of fast temporal features of vision (e.g., the rapid onset, offset, and re-emergence of a stimulus). This effect has been attributed to amygdalar enhancements of visual inputs conveying emotional features along magnocellular channels. The current study compared participants’ ability to detect spatial and temporal gaps in simple stimuli (a Landolt Circle) after first being exposed to a facial cue in the periphery. The study was an attempt to replicate past research using younger adult samples while also extending these findings to an older adult sample. Unlike younger adults, older adults generally display an attentional bias toward positive instead of negative emotional facial expressions. It is not clear if this positivity bias is strictly driven by cognitive control processes or if there is a change in the human visual system with age that reduces the amplification of negative emotive expressions by the amygdala. The current study used psychophysical data to determine if the rapid presentation of an emotional cue and subsequent perceptual target to older adults leads to the same benefit to temporal vision evinced by younger adults or if amygdalocortical enhancements to perception degrade with age. The current study was only able to partly replicate findings from past research. The negative facial cues that were presented in the periphery did not lead to an enhancement in temporal gap detection for the younger adult sample nor a reduction in spatial gap detection. In fact, the opposite was found. Younger adults’ spatial gap detection benefited from the negative emotional cues. The negative and neutral emotional cues had no effect on the older adult sample. The older adults’ performance on both gap detection tasks was not impacted by the emotional cues

Systems of globally coupled phase oscillators can have robust attractors that are heteroclinic networks. Such a heteroclinic network is generated, where the phases cluster into three groups, within a specific regime of parameters when the phase oscillators are globally coupled using the function $g(\varphi) = -\sin(\varphi + \alpha) + r \sin(2\varphi + \beta)$. The resulting network switches between 30 partially synchronised states for a system of $N=5$ oscillators. Considering the states that are visited and the time spent at those states a spatio-temporal code can be generated for a given navigation around the network. We explore this phenomenon further by investigating the effect that noise has on the system, how this system can be used to generate a spatio-temporal code derived from specific inputs and how observation of a spatio-temporal code can be used to determine the inputs that were presented to the system to generate a given coding. We show that it is possible to find chaotic attractors for certain parameters and that it is possible to detail a genetic algorithm that can find the parameters required to generate a specific spatio-temporal code, even in the presence of noise. In closing we briefly explore the dynamics where $N>5$ and discuss this work in relation to winnerless competition.

Spatiotemporal properties of classical coupled nonlinear oscillators are investigated in this thesis. Chapter 1 gives an introduction to nonlinear lattices and to the concept of breathers, that are spatially localized and temporally periodic excitation in nonlinear lattices. The concept of anti-continuous limit that provides the basic methodology in probing spatiotemporal breather properties is discussed. In Chapter 2, the general approach for finding exact breather solutions from the anti-continuous limit is examined, and the rotating wave approximation(RWA) is applied to probe the spatial structure of static breathers. Numerical evidence reveals that the RWA relates the spatial structure of stable multi-breathers to a single breather of the same frequency. Chapter 3 presents linear stability analysis of static breathers and gives a systematic way to construct mobile breathers. Formation and collision properties of this moving breathers are also studied. Chapter 4 discusses dynamics of kinks and anti-kinks in hydrogen-bonded chains in the context of two-component soliton model. From molecular dynamics simulations with finite temperature, it is observed that, in a real system (eg. ice), a pair of kink and anti-kink can evolve into a moving-breather-like excitation. Chapter 5 is devoted to the understand of the effects of disorder in the Holstein model. The summary is given in Chapter 6.

This diploma thesis studies the issue of spatiotemporal mobility of pensioners in the environment of the city of České Budějovice and its hinterland. This research uses a combination of two methods. The first method is a questionnaire survey in witch each respondent received two questionnaires. Journeys made were recorded into the first questionnaire and characteristics of respondents and their households into the second one. The second method uses GPS loggers to collect spatial data on mobility of people. The theoretical part of this thesis deals with concepts of time geography, mobility specifics of pensioners, the issue of retirement age in the Czechia and the potential use of modern geoinformation technologies for mobility research. The methodology part presents methodological procedures for evaluating the obtained data, criteria for selection of respondents and the process of research. Followed by evaluation of actual results of surveys and their interpretation with regard to sub-goals of this thesis. The results are in many cases formed using a combination of data from both research methods. The main results, that relate to the specified individual goals and their consequent hypotheses, deal with the daily rhythms of the spatiotemporal mobility, evaluate the use of vehicles with regard to...

The understanding of how different parts of a landscape contribute to streamflow by storing and releasing water has long been a central issue in hydrology. Knowledge about what controls streamflow dynamics across landscapes can further our understanding of how catchments store and release water, facilitate predictions for ungauged catchments, and improve the management of water quality and resources. This thesis makes use of data from the Krycklan catchment in northern Sweden. Streamflow data from 14 catchments (0.12 - 68 km2) with variable landscape characteristics such as topography, vegetation, wetland cover, glacial till soils and deeper sediment soils were used to investigate spatial patterns and controls on runoff. The differences in specific discharge (discharge per unit catchment area) between nearby catchments were large at the annual scale, and have the same magnitude as predicted effects of a century of climate change or the observed effects of major forestry operations. This variability is important to consider when studying the effects of climate change and land use changes on streamflow, as well as for our understanding of geochemical mass balances. Streamflow from different catchments was strongly related to landscape characteristics. The distribution of wetland areas had a particularly strong influence, with an annual specific discharge 40-80% higher than catchments with high tree volume on till soils. During drier periods, catchments with deeper sediment soils at the lower elevations of Krycklan had a higher base flow compared to both forested till and wetland catchments. This pattern was reversed at high flows. The storages releasing water to streams in downstream sediment areas were able to maintain base flow for longer periods and were less influenced by evapotranspiration compared to the more superficial till and wetland systems. The results of this thesis have led to a better understanding of the landscape wide patterns of streamflow during different seasons and time scales. The strong associations to landscape characteristics and variable spatial patterns with season and antecedent conditions form the basis for a conceptual understanding of the processes and spatial patterns that shape the heterogeneity of streamflow responses in boreal catchments. / Hur olika delar av landskapet påverkar vattenbalansen och bidrar till avrinning har länge varit en central fråga inom hydrologin. Kunskap om vad som styr avrinningsdynamiken i ett landskap kan öka vår förståelse av hur olika delar av landskapet bidrar till avrinning, hur avrinningsområden lagrar vatten och bildar avrinning, underlätta prognoser för avrinningsområden utan vattenföringsmätningar och förbättra hanteringen av vattenkvaliteten och vattenresurser. Denna avhandling använder data från Krycklans avrinningsområde i norra Sverige. Vattenföringsdata från 14 delavrinningsområden (0.12 - 68 km2) med olika landskapskarakteristik såsom topografi, vegetation och jordarter, användes för att undersöka rumsliga mönster hos avrinningen över olika tidsperioder samt hur landskapet påverkar variabiliteten. Skillnaderna i specifik avrinning (avrinning per areaenhet) mellan närliggande avrinningsområden var stor för årliga värden, och är i samma storleksordning som effekterna av stora skogsavverkningar samt av förutspådda effekter av det kommande seklets förväntade klimatförändringar. Denna variation är viktig att ta hänsyn till när man studerar hur klimatförändringar och ändrad markanvändning påverkar avrinningen, liksom för vår förståelse av geokemiska massbalanser. Avrinning från olika områden var starkt relaterad till deras landskapsegenskaper. Förekomsten av våtmarker hade ett särskilt starkt inflytande. Områden med en stor andel våtmarker hade 40-80% högre årlig specifik avrinning än områden med hög trädvolym på moränjordar. Under torrare perioder hade områden med djupare sedimentjordar hög avrinning jämfört med både områden med skog på morän och med våtmarker. Under höga flöden var detta mönster omvänt. De vattenlager som bidrar till avrinning i sedimentområden kan upprätthålla basflöde under längre tidsperioder och påverkas mindre av evapotranspirationen än de ytligare flödessystemen i morän och våtmarker. Avhandlingen har givit en bättre förståelse av avrinningens rumsliga variation under olika årstider och i olika tidsskalor. Det starka sambandet mellan landskapskarakteristik och avrinningens varierande mönster under olika årstider och lagringsförhållanden utgör en grund för en begreppsmässig förståelse av de processer och rumsliga mönster som skapar heterogeniteten i flödesrespons i boreala områden.

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