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We propose a new autonomous dynamical system of dimension N=4 that demonstrates the regime of stable two- frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The interaction of two generators is also analyzed. The phenomenon of external and mutual synchronization of two-frequency oscillations is observed, for which winding number locking on a two- dimensional torus takes place
What can we learn from climate data? : Methods for fluctuation, time/scale and phase analysis
(2006)
Since Galileo Galilei invented the first thermometer, researchers have tried to understand the complex dynamics of ocean and atmosphere by means of scientific methods. They observe nature and formulate theories about the climate system. Since some decades powerful computers are capable to simulate the past and future evolution of climate. Time series analysis tries to link the observed data to the computer models: Using statistical methods, one estimates characteristic properties of the underlying climatological processes that in turn can enter the models. The quality of an estimation is evaluated by means of error bars and significance testing. On the one hand, such a test should be capable to detect interesting features, i.e. be sensitive. On the other hand, it should be robust and sort out false positive results, i.e. be specific. This thesis mainly aims to contribute to methodological questions of time series analysis with a focus on sensitivity and specificity and to apply the investigated methods to recent climatological problems. First, the inference of long-range correlations by means of Detrended Fluctuation Analysis (DFA) is studied. It is argued that power-law scaling of the fluctuation function and thus long-memory may not be assumed a priori but have to be established. This requires to investigate the local slopes of the fluctuation function. The variability characteristic for stochastic processes is accounted for by calculating empirical confidence regions. The comparison of a long-memory with a short-memory model shows that the inference of long-range correlations from a finite amount of data by means of DFA is not specific. When aiming to infer short memory by means of DFA, a local slope larger than $\alpha=0.5$ for large scales does not necessarily imply long-memory. Also, a finite scaling of the autocorrelation function is shifted to larger scales in the fluctuation function. It turns out that long-range correlations cannot be concluded unambiguously from the DFA results for the Prague temperature data set. In the second part of the thesis, an equivalence class of nonstationary Gaussian stochastic processes is defined in the wavelet domain. These processes are characterized by means of wavelet multipliers and exhibit well defined time dependent spectral properties; they allow one to generate realizations of any nonstationary Gaussian process. The dependency of the realizations on the wavelets used for the generation is studied, bias and variance of the wavelet sample spectrum are calculated. To overcome the difficulties of multiple testing, an areawise significance test is developed and compared to the conventional pointwise test in terms of sensitivity and specificity. Applications to Climatological and Hydrological questions are presented. The thesis at hand mainly aims to contribute to methodological questions of time series analysis and to apply the investigated methods to recent climatological problems. In the last part, the coupling between El Nino/Southern Oscillation (ENSO) and the Indian Monsoon on inter-annual time scales is studied by means of Hilbert transformation and a curvature defined phase. This method allows one to investigate the relation of two oscillating systems with respect to their phases, independently of their amplitudes. The performance of the technique is evaluated using a toy model. From the data, distinct epochs are identified, especially two intervals of phase coherence, 1886-1908 and 1964-1980, confirming earlier findings from a new point of view. A significance test of high specificity corroborates these results. Also so far unknown periods of coupling invisible to linear methods are detected. These findings suggest that the decreasing correlation during the last decades might be partly inherent to the ENSO/Monsoon system. Finally, a possible interpretation of how volcanic radiative forcing could cause the coupling is outlined.
Wachsende Filamentbündel
(2006)
We present the results of phase-referenced VLBA+Effelsberg observations at five frequencies of the double-image gravitational lens WAS B0218+357, made to establish the precise registration of the A and B lensed image positions. The motivation behind these observations is to investigate the anomalous variation of the image flux-density ratio (A[B) with frequency - this ratio changes by almost a factor of two over a frequency range from 1.65 GHz to 15.35 GHz. We investigate whether frequency dependent image positions, combined with a magnification gradient across the image field, could give rise to the anomaly. Our observations confirm the variation of image flux-density ratio with frequency. The results from Our phase-reference astrometry, taken together with the lens mass model of Wucknitz et al. (2004, MNRAS, 349, 14), show that shifts of the image peaks and centroids are too small to account for the observed frequency- dependent ratio
We study the overdamped version of two coupled anharmonic oscillators under the influence of both low- and high-frequency forces respectively and a Gaussian noise term added to one of the two state variables of the system. The dynamics of the system is first studied in the presence of both forces separately without noise. In the presence of only one of the forces, no resonance behaviour is observed, however, hysteresis happens there. Then the influence of the high-frequency force in the presence of a low-frequency, i.e. biharmonic forcing, is studied. Vibrational resonance is found to occur when the amplitude of the high-frequency force is varied. The resonance curve resembles a stochastic resonance-like curve. It is maximum at the value of g at which the orbit lies in one well during one half of the drive cycle of the low-frequency force and in the other for the remaining half cycle. Vibrational resonance is characterized using the response amplitude and mean residence time. We show the occurrence of stochastic resonance behaviour in the overdamped system by replacing the high-frequency force by Gaussian noise. Similarities and differences between both types of resonance are presented. (c) 2006 Elsevier B.V. All rights reserved.
Variationen der stratosphärischen Residualzirkulation und ihr Einfluss auf die Ozonverteilung
(2006)
Die Residualzirkulation entspricht der mittleren Massenzirkulation und beschreibt die im zonalen Mittel stattfindenden meridionalen Transportprozesse. Die Variationen der Residualzirkulation bestimmen gemeinsam mit dem anthropogen verursachten Ozonabbau die jährlichen Schwankungen der Ozongesamtsäule im arktischen Frühling. In der vorliegenden Arbeit wird die Geschwindigkeit des arktischen Astes der Residualzirkulation aus atmosphärischen Daten gewonnen. Zu diesem Zweck wird das diabatische Absinken im Polarwirbel mit Hilfe von Trajektorienrechnungen bestimmt. Die vertikalen Bewegungen der Luftpakete können mit vertikalen Windfeldern oder entsprechend einem neuen Ansatz mit diabatischen Heizraten angetrieben werden. Die Eingabedaten stammen aus dem 45 Jahre langen Reanalyse-Datensatz des "European Centre for Medium Range Weather Forecast" (ECMWF). Außerdem kann für die Jahre ab 1984 die operationelle ECMWF-Analyse verwendet werden. Die Qualität und Robustheit der Heizraten- und Trajektorienrechnungen werden durch Sensitivitätsstudien und Vergleiche mit anderen Modellen untermauert. Anschließend werden umfangreiche Trajektorienensemble statistisch ausgewertet, um ein detailliertes, zeit- und höhenaufgelöstes Bild des diabatischen Absinkens zu ermitteln. In diesem Zusammenhang werden zwei Methoden entwickelt, um das Absinken gemittelt im Polarwirbel oder als Funktion der äquivalenten Breite zu bestimmen. Es wird gezeigt, dass es notwendig ist den Lagrangeschen auf Trajektorienrechnungen basierenden Ansatz zu verfolgen, da die einfachen Eulerschen Mittel Abweichungen zu den Lagrangeschen Vertikalgeschwindigkeiten aufweisen. Das wirbelgemittelte Absinken wird für einzelne Winter mit dem beobachteten Absinken langlebiger Spurengase und anderen Modellstudien verglichen. Der Vergleich zeigt, dass das Absinken basierend auf den vertikalen Windfeldern der ECMWF-Datensätze den Nettoluftmassentransport durch die Residualzirkulation sehr stark überschätzt. Der neue Ansatz basierend auf den Heizraten ergibt hingegen realistische Ergebnisse und wird aus diesem Grund für alle Rechnungen verwendet. Es wird erstmalig eine Klimatologie des diabatischen Absinkens über einen fast fünf Jahrzehnte umfassenden Zeitraum erstellt. Die Klimatologie beinhaltet das vertikal und zeitlich aufgelöste diabatische Absinken gemittelt über den gesamten Polarwirbel und Informationen über die räumliche Struktur des vertikalen Absinkens. Die natürliche Jahr-zu-Jahr Variabilität des diabatischen Absinkens ist sehr stark ausgeprägt. Es wird gezeigt, dass zwischen der ECMWF-Zeitreihe des diabatischen Absinkens und der Zeitreihe aus einem unabhängig analysierten Temperaturdatensatz hohe Korrelationen bestehen. Erstmals wird der Einfluss von Transportprozessen auf die Ozongesamtsäule im arktischen Frühling direkt quantifiziert. Es wird gezeigt, dass die Jahr-zu-Jahr Variabilität der Ozongesamtsäule im arktischen Frühling zu gleichen Anteilen durch die Variabilität der dynamischen Komponente und durch die Variabilität der chemischen Komponente beeinflusst wird. Die gefundenen Variabilitäten von diabatischem Absinken und Ozoneintrag in hohen Breiten werden mit der vertikalen Ausbreitung planetarer Wellen aus der Troposphäre in die Stratosphäre in Beziehung gesetzt.
An approach is presented for coupled chaotic systems with weak coherent motion, from which we estimate the upper bound value for the absolute phase difference in phase synchronous states. This approach shows that synchronicity in phase implies synchronicity in the time of events, a characteristic explored to derive an equation to detect phase synchronization, based on the absolute difference between the time of these events. We demonstrate the potential use of this approach for the phase coherent and the funnel attractor of the Rossler system, as well as for the spiking/bursting Rulkov map.
Experimental results show that the polymerization of pyrrole in the presence of beta-naphthalenesulfonic acid and different fluorosurfactants like perfluorooctanesulfonic acid, perfluorooctyldiethanolamide, and ammonium perfluorooctanoate leads to polypyrrole with special morphologies, such as rings or disks and rectangular frames or plates. The formation of these unusually shaped particles of polymer dispersions is explained by the chemical and colloidal peculiarities of the oxidative pyrrole polymerization with ammonium peroxodisulfate in aqueous medium.
Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the synchronizability of random networks with a large minimum degree is determined by two leading parameters: the mean degree and the heterogeneity of the distribution of node's intensity, where the intensity of a node, defined as the total strength of input connections, is a natural combination of topology and weights. Our results provide a possibility for the control of synchronization in complex networks by the manipulation of a few parameters
We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of R¨ossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems.
Triplet energy back transfer in conjugated polymers with pendant phosphorescent iridium complexes
(2006)
The nature of Dexter triplet energy transfer between bonded systems of a red phosphorescent iridium complex 13 and a conjugated polymer, polyfluorene, has been investigated in electrophosphorescent organic light-emitting diodes. Red- emitting phosphorescent iridium complexes based on the [Ir(btp)2(acac)]fragment (where btp is 2-(2 '- benzo[b]thienyl)pyridinato and acac is acetylacetonate) have been attached either directly (spacerless) or through a - (CH2)(8)-chain (octamethylene-tethered) at the 9-position of a 9-octylfluorene host. The resulting dibromo- functionalized spacerless (8) or octamethylene-tethered (12) fluorene monomers were chain extended by Suzuki polycondensations using the bis(boronate)-terminated fluorene macromonomers 16 in the presence of end-capping chlorobenzene solvent to produce the statistical spacerless (17) and octamethylene-tethered ( 18) copolymers containing an even dispersion of the pendant phosphorescent fragments. The spacerless monomer 12 adopts a face-to-face conformation with a separation of only 3.6 angstrom between the iridium complex and fluorenyl group, as shown by X-ray analysis of a single crystal, and this facilitates intramolecular triplet energy transfer in the spacerless copolymers 17. The photo- and electroluminescence efficiencies of the octamethylene-tethered copolymers 18 are double those of the spacerless copolymers 17, and this is consistent with suppression of the back transfer of triplets from the red phosphorescent iridium complex to the polyfluorene backbone in 18. The incorporation of a -(CH2)(8)- chain between the polymer host and phosphorescent guest is thus an important design principle for achieving higher efficiencies in those electrophosphorescent organic light-emitting diodes for which the triplet energy levels of the host and guest are similar
We investigate the effects of a time-delayed all-to-all coupling scheme in a large population of oscillators with natural frequencies following a bimodal distribution. The regions of parameter space corresponding to synchronized and incoherent solutions are obtained both numerically and analytically for particular frequency distributions. In particular, we find that bimodality introduces a new time scale that results in a quasiperiodic disposition of the regions of incoherence.
We study thermally induced birefringence in crystalline Nd:YAG zigzag slab lasers and the associated depolarization losses. The optimum crystallographic orientation of the zigzag slab within the Nd:YAG boule and photoelastic effects in crystalline Nd:YAG slabs are briefly discussed. The depolarization is evaluated using the temperature and stress distributions, calculated using a finite element model, for realistically pumped and cooled slabs of finite dimensions. Jones matrices are then used to calculate the depolarization of the zigzag laser mode. We compare the predictions with measurements of depolarization, and suggest useful criteria for the design of the gain media for such lasers.
Fast, three-dimensional polarization mapping in piezoelectric sensor cables was performed by means of the novel thermal-pulse tomography (TPT) technique with a lateral resolution of 200 mum. The active piezoelectric cable material (a copolymer of polyvinylidene fluoride with trifluoroethylene) was electrically poled with a point-to-cable corona discharge. A focused laser was employed to heat the opaque outer electrode, and the short-circuit current generated by the thermal pulse was used to obtain 3D polarization maps via the scale transformation method. The article describes the TPT technique as a fast non-destructive option for studying cylindrical geometries.
Ferroelectrets are thin films of polymer foams, exhibiting piezoelectric properties after electrical charging. Ferroelectret foams usually consist of a cellular polymer structure filled with air. Polymer-air composites are elastically soft due to their high air content as well as due to the size and shape of the polymer walls. Their elastically soft composite structure is one essential key for the working principle of ferroelectrets, besides the permanent trapping of electric charges inside the polymer voids. The elastic properties allow large deformations of the electrically charged voids. However, the composite structure can also possibly limit the stability and consequently the range of applications because of, e. g., penetration of gas and liquids accompanied by discharge phenomena or because of a mechanical pre-load which may be required during the application. Here, we discuss various stability aspects related to the piezoelectric properties of polypropylene ferroelectrets. Near and below room temperature, the piezoelectric effect and the stability of the trapped charges are practically independent from humidity during long-time storage in a humid atmosphere or water, or from operating conditions, such as continuous mechanical excitation. Thermal treatment of cellular polypropylene above -10 degrees C leads to a softening of the voided structure which is apparent from the decreasing values of the elastic modulus. This decrease results in an increase of the piezoelectric activity. Heating above 60 degrees C, however, leads to a decrease in piezoelectricity
In this paper a perturbation-theory study of vibrational lifetimes for the bending and stretching modes of hydrogen adsorbed on a Si(100) surface is presented. The hydrogen-silicon interaction is treated with a semiempirical bond-order potential. Calculations are performed for H-Si clusters of different sizes. The finite lifetime is due to vibration-phonon coupling, which is assumed to be linear or bilinear in the phonon and nonlinear in the H-Si stretching and bending modes. Lifetimes and vibrational transition rates are evaluated with one- and two-phonon processes taken into account. Temperature effects are also discussed. In agreement with the experiment and previous theoretical treatment it is found that the H-Si (upsilon(s)=1) stretching vibration decays on a nanosecond timescale, whereas for the H-Si (upsilon(b)=1) bending mode a picosecond decay is predicted. For higher-excited vibrations, simple scaling laws are found if the excitation energies are not too large. The relaxation mechanisms for the excited H-Si stretching and the H-Si bending modes are analyzed in detail.