The phenomenon of drag reduction by polymers in turbulent flow has beenstudied over the last 60 years. New insight have been recently gained by meansof numerical simulation of dilute polymer solution at moderate values of theturbulent Reynolds number and elasticity. In this thesis, we track elastic parti-cles in Lagrangian frame in turbulent channel flow at Reτ = 180, by tracking,where the single particle obeys the FENE (finite extendible nonlinear elastic)formulation for dumbbel model. The feedback from polymers to the flow is notconsidered, while the Lagrangian approach enables us to consider high valuesof polymer elasticity. In addition, the finite time Lyapunov exponent (FTLE)of the flow is computed tracking infinitesimal material elements advected bythe flow. Following the large deviation theory, the Cramer’s function of theprobability density function of the FTLE for large values of time intervals isstudied at different wall-normal positions. The one-way effect of the turbulentflow on polymers is investigated by looking at the elongation and orientation ofthe polymers, with different relaxation times, across the channel. The confor-mation tensor of the polymers deformation which is an important contributionin the momentum balance equation is calculated by averaging in wall-parallelplanes and compared to theories available in the literature. / QC 20100706

An appropriate accounting for thinning effects on growth rate and wood quality requires a clear understanding and quantification of these effects. In this regard, four basic interrelated issues were addressed in this study: 1) thinning effects on ring specific gravity 2) thinning effects on ring width distribution 3) thinning effects on stem form, and 4) prediction models for these quantities. The study showed that thinning does not significantly affect ring specific gravity, whereas its effects on ring width distribution and stem form were significant. Thinning increases ring width significantly over most of the tree bole and increases the earlywood and latewood components proportionally maintaining an approximately constant latewood proportion. As a consequence, thinning effects on latewood proportion is not significant; confirming the results obtained in the specific gravity study and further dispelling the concern that thinning may substantially reduce wood specific gravity. Thinning affects stem form by increasing the form exponent especially near the tree base accentuating the neiloid form expected in that area. High up in the stem, the form exponent changes little within a tree and among thinning treatments, with a general tendency towards a paraboloid shape. Differences due to thinning intensities, in general, were not significant indicating the applicability of results within a wide range of densities. Prediction models for ring specific gravity, ring width, latewood proportion and stem profile based on ring, tree, stand and site factors were developed Influences of stand level factors, density measures in particular, in prediction models are minor probably because tree level factors such as, stem diameter at breast height, crown ratio, etc. themselves manifest stand conditions. The mixed-effects analysis technique was used in data analysis to account for correlation among observations from the same subject. Direct covariance modeling yielded better fits than accounting for correlation indirectly using random effects covariates in many cases; however, both could not be accommodated simultaneously. Structures which assume decreasing correlation with increasing distance between observations, such as the first-order autoregressive structure, performed better than alternative specifications. Results consistently showed that accounting for correlation among observations substantially improves the fits over ignoring correlation; effectively addressing the issue of bias in the standard errors of estimates. / Ph. D.

The main goal of this thesis is to test the ability of the Hurst exponent to recognise some processes with deterministic signal as nonrandom and to test the randomness of daily stock returns of three stocks traded in BCPP. Critical values to determine the critical region of a randomness hypothesis test were set for this purpose. Another goal of the thesis is the description of the Hurst exponent estimation by means of Rescaled Range Analysis and outline some problems accompanying this estimation if the Hurst exponent would be used as a randomness indicator. Within the frame of Rescaled Range Analysis was constructed another method that showed to be successful in recognising some series that contain deterministic signal.

Estimation of the self-similarity exponent has attracted growing interest in recent decades and became a research subject in various fields and disciplines. Real-world data exhibiting self-similar behavior and/or parametrized by self-similarity exponent (in particular Hurst exponent) have been collected in different fields ranging from finance and human sciencies to hydrologic and traffic networks. Such rich classes of possible applications obligates researchers to investigate qualitatively new methods for estimation of the self-similarity exponent as well as identification of long-range dependencies (or long memory). In this thesis I present the Bayesian estimation of the Hurst exponent. In contrast to previous methods, the Bayesian approach allows the possibility to calculate the point estimator and confidence intervals at the same time, bringing significant advantages in data-analysis as discussed in this thesis. Moreover, it is also applicable to short data and unevenly sampled data, thus broadening the range of systems where the estimation of the Hurst exponent is possible. Taking into account that one of the substantial classes of great interest in modeling is the class of Gaussian self-similar processes, this thesis considers the realizations of the processes of fractional Brownian motion and fractional Gaussian noise. Additionally, applications to real-world data, such as the data of water level of the Nile River and fixational eye movements are also discussed. / Die Abschätzung des Selbstähnlichkeitsexponenten hat in den letzten Jahr-zehnten an Aufmerksamkeit gewonnen und ist in vielen wissenschaftlichen Gebieten und Disziplinen zu einem intensiven Forschungsthema geworden. Reelle Daten, die selbsähnliches Verhalten zeigen und/oder durch den Selbstähnlichkeitsexponenten (insbesondere durch den Hurst-Exponenten) parametrisiert werden, wurden in verschiedenen Gebieten gesammelt, die von Finanzwissenschaften über Humanwissenschaften bis zu Netzwerken in der Hydrologie und dem Verkehr reichen. Diese reiche Anzahl an möglichen Anwendungen verlangt von Forschern, neue Methoden zu entwickeln, um den Selbstähnlichkeitsexponenten abzuschätzen, sowie großskalige Abhängigkeiten zu erkennen. In dieser Arbeit stelle ich die Bayessche Schätzung des Hurst-Exponenten vor. Im Unterschied zu früheren Methoden, erlaubt die Bayessche Herangehensweise die Berechnung von Punktschätzungen zusammen mit Konfidenzintervallen, was von bedeutendem Vorteil in der Datenanalyse ist, wie in der Arbeit diskutiert wird. Zudem ist diese Methode anwendbar auf kurze und unregelmäßig verteilte Datensätze, wodurch die Auswahl der möglichen Anwendung, wo der Hurst-Exponent geschätzt werden soll, stark erweitert wird. Unter Berücksichtigung der Tatsache, dass der Gauß'sche selbstähnliche Prozess von bedeutender Interesse in der Modellierung ist, werden in dieser Arbeit Realisierungen der Prozesse der fraktionalen Brown'schen Bewegung und des fraktionalen Gauß'schen Rauschens untersucht. Zusätzlich werden Anwendungen auf reelle Daten, wie Wasserstände des Nil und fixierte Augenbewegungen, diskutiert.

The goal of the thesis is to evaluate the degree of efficiency of the particular markets and to apply the methods of fundamental and technical analysis on them in order to assess their efficiency in terms of profitablity. The thesis analyses the degree of long-term memory of the particular commodities and stock indices via Hurst coefficient. Afterwards fundamental and technical methods are applied to the market with the highest degree of long-term memory, which is the feeder cattle market. Indidivual methods from both disciplines are being applied at first, after wich a combnation of both is appleid as well. The result is the discovery, whether combining the two approaches leads to a higher profitability of the trading strategy. At the end the effect of transacton costs is also evalauted and a final conclusion is made regarding the profit potential of both methods for the case of individual Czech investor.

We study one-parameter families of quasi-periodically forced monotone interval maps and provide sufficient conditions for the existence of a parameter at which the respective system possesses a non-uniformly hyperbolic attractor. This is equivalent to the existence of a sink-source orbit, that is, an orbit with positive Lyapunov exponent both forwards and backwards in time. The attractor itself is a non-continuous invariant graph with negative Lyapunov exponent, often referred to as ‘SNA’. In contrast to former results in this direction, our conditions are C² -open in the fibre maps. By applying a general result about saddle-node bifurcations in skew-products, we obtain a conclusion on the occurrence of non-smooth bifurcations in the respective families. Explicit examples show the applicability of the derived statements.

This master thesis deals with cluster analysis, more specifically with clustering methods that use fuzzy sets. Basic clustering algorithms and necessary multivariate transformations are described in the first chapter. In the practical part, which is in the third chapter we apply fuzzy c-means clustering and k-means clustering on real data. Data used for clustering are the inputs of chemical transport model CMAQ. Model CMAQ is used to approximate concentration of air pollutants in the atmosphere. To the data we will apply two different clustering methods. We have used two different methods to select optimal weighting exponent to find data structure in our data. We have compared all 3 created data structures. The structures resembled each other but with fuzzy c-means clustering, one of the clusters did not resemble any of the clustering inputs. The end of the third chapter is dedicated to an attempt to find a regression model that finds the relationship between inputs and outputs of model CMAQ.

This thesis tests the ability of the Lorenz's (2005) chaotic model to simulate predictability curve of the ECMWF model calculated from data over the 1986 to 2011 period and demonstrates similarity of the predictability curves for the Lorenz's model with N = 90 variables. This thesis also tests approximations of predictability curves and their differentials, aiming to correct the ECMWF model estimated parameters and thus allow for estimation of the largest Lyapunov exponent, model error and limit value of the predictability curve. The correction is based on comparing the parameters estimated for the Lorenz's and ECMWF and on comparison with the largest Lyapunov exponent (λ=0,35 day-1 ) and limit value of the predictability curve (E∞=8,2) of the Lorenz's model. Parameters are calculated from approximations made by the Quadratic hypothesis with and without model error, as well as by Logarithmic and General hypotheses and by hyperbolic tangent employing corrections with and without model error. Average value of the largest Lyapunov exponent is estimated to be λ=0,37 day-1 for the ECMWF model, limit values of the predictability curves are estimated with lower theoretically derived values and new approach of calculation of model error based on comparison of models is presented.

Turbochargers are used on many automotive internal combustion engines to increase power density. The broad operating range of the engine also requires a wide range of the turbocharger compressor. At low mass flows, however, turbo compressor operation becomes unstable and eventually enters surge. Surge is characterized by large oscillations in mass flow and pressure. Due to the associated noise, control problems, and possibility of mechanical component damage, this has to be avoided. Different indicators exist to classify compressor operation as stable or unstable on a gas stand. They are based on pressure oscillations, speed oscillations, or inlet temperature increase. In this thesis, a new stability indicator is proposed based on the Hurst exponent of the pressure signal. The Hurst exponent is a number between zero and one that describes what kind of long-term correlations are present in a time series. Data from three cold gas stand experiments are analyzed using this criterion. Results show that the Hurst exponent of the compressor outlet pressure signal has good characteristics. Stable operation is being indicated by values larger than 0.5. As compressor operation moves towards the surge line, the Hurst exponent decreases towards zero. An additional distinction between the long-term correlations of small and large amplitude fluctuations by means of higher order Hurst exponents can be used as an early warning indicator. Further tests using compressor housing accelerometers show that the Hurst exponent is not a good choice for real-time surge detection on the engine. Reasons are the long required sampling time compared to competing methods, and the fact that other periodically repeating oscillations lead to Hurst exponents close to zero independent of compressor operation. / Turboladdare används ofta på förbränningsmotorer för att öka motorns effekttäthet. Motorns breda driftområde ställer krav på ett brett driftområde för turboladdarens kompressor. Vid låga massflöden blir kompressordriften dock mindre stabil, och surge kan uppträda. Surge innebär stora oscillationer i tryck och massflöde genom kompressorn. På grund av oljud, reglerproblem och risken för mekaniska skador vill man undvika surge. Det finns indikatorer för att bedöma kompressorns stabilitet på ett gas stand. Indikatorerna är baserade på tryckoscillationer, varvtalsoscillationer, eller temperaturökning i gasen i kompressorinloppet. I denna avhandling presenteras en ny indikator baserad på Hurst-exponenten, beräknad på trycksignalen. Hurst-exponenten är ett tal mellan noll och ett som beskriver vilka typer av långtidskorrelationer det finns i signalen. Mätningar från tre gas-stand-experiment har analyserats på detta sätt. Analyserna visar att Hurst-exponenten baserad på kompressorutloppstrycket fungerar bra som som surgeindikator. Stabil drift av kompressorn indikeras av att Hurst-exponenten är större än 0.5. När kompressordriftpunkten närmar sig surgelinjen faller Hurst-exponenten mot noll. En distinktion mellan oscillationer med små och stora amplituder kan används för att få en tidig varning. Analyser av vibrationsmätningar på kompressorhuset vid motorapplikation visar att Hurst-exponenten inte är lämplig som realtidsindikator på en motor. Detta kommer sig dels av att data behöver samlas in under en längre tid än med andra tänkbara indikatorer, dels av att andra periodiska oscillationer i signalen kopplade till motorns naturliga beteende leder till Hurst-exponenter nära noll även vid stabil kompressordrift. / <p>QC 20170510</p> / CCGEx - Compressor off-Design

Det är ofta användbart att beräkna eller uppskatta kapaciteter för olika parametrar och mängder. Det kan vara till exempel vid hantering av sobolevfunktioner eller vid undersökning av partiella dierentialekvationer. För ringområden i det vanliga rummet går detta att göra exakt, men för att kunna uppskatta kapacitet i viktade rum behöver man fyra exponentmängder Q, S, Q och S till hjälp. Med dessa kan man i princip redogöra för beteendet hos kapaciteten av olika ringområden kring en x punkt. Det nns många möjliga kombinationer av hur de fyra exponentmängderna kan se ut, men det är oklart precis vilka kombinationer som är möjliga. Genom att ta fram nya exempel på kombinationer av mängderna kan vi få större kännedom om vilka kombinationer som är möjliga, och på så sätt kunna dra större nytta av dem. För att hitta nya sammansättningar utgår vi från önskade exponentmängder och undersöker om det går att ta fram bakomliggande vikter som genererar dem. Sedan tidigare nns nio exempel på kombinationer av exponentmängder. Dessa skiljer sig åt vad gäller längden på intervallen som utgör dem och om ändpunkterna tillhör intervallen eller ej. I den här rapporten har tre nya exempel på kombinationer av exponentmängder tagits fram. I alla tre exempel skiljer sig Q och S bara i ändpunkten, och vi har visat att det är möjligt att konstruera ett exempel där alla fyra mängder delar ändpunkt, men där alla mängder utom S är öppna. / It is often useful to calculate or estimate capacities for dierent parameters and sets. This is the case for example when working with Sobolev functions or when studying partial dierential equations. For annuli i Rn this can be done exactly, but when estimating capacity in weighted spaces you need four exponent sets Q, S, Q and S. With these sets it is possible to describe how the capacity of dierent annuli around a given point behaves. There are many possible combinations of the four exponent sets, and it is not clear which combinations are possible. By generating new examples of combinations of the exponent sets we obtain a larger understanding of which combinations are possible, and are thus able to use them more eciently. To nd new examples we start from the desired exponent sets and investigate if one can produce an underlying weight that generates them. Earlier, there were nine examples of combinations of exponent sets. These dier in terms of the length of the intervals that constitute them and whether the endpoints belong to the sets or not. In this thesis three new examples of combinations of exponent sets have been constructed. In all three of them, Q and S dier only in the endpoint, and we have shown that it is possible to construct an example where all four sets share the same endpoint, but all sets except S are open.