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We analyse a generic bottom-up nutrient phytoplankton model to help understand the dynamics of seasonally recurring algae blooms. The deterministic model displays a wide spectrum of dynamical behaviours, from simple cyclical blooms which trigger annually, to irregular chaotic blooms in which both the time between outbreaks and their magnitudes are erratic. Unusually, despite the persistent seasonal forcing, it is extremely difficult to generate blooms that are both annually recurring and also chaotic or irregular (i.e. in amplitude) even though this characterizes many real time series. Instead the model has a tendency to `skip' with outbreaks often being suppressed from one year to the next. This behaviour is studied in detail and we develop an analytical expression to describe the model's flow in phase space, yielding insights into the mechanism of the bloom recurrence. We also discuss how modifications to the equations through the inclusion of appropriate functional forms can generate more realistic dynamics.
A package of programs written using the symbolic mathematics program, Mathematicatrademark, has been developed. Its principal usage is in teaching the LIMM method to students and demonstrating data analysis by means of the Polynomial Regularization Method (PRM). A large number of variables can be changed in the program and their effects can be shown graphically. Students at the University of Potsdam and Monash University have used the program successfully
We present a simple scheme for implementing an atomic phase gate using two degrees of freedom for each atom and discuss its realization with cold rubidium atoms on atom chips. We investigate the performance of this collisional phase gate and show that gate operations with high fidelity can be realized in magnetic traps that are currently available on atom chips
A set of d(2) vectors in a Hilbert space of dimension d is called equiangular if each pair of vectors encloses the same angle. The projection operators onto these vectors define a POVM which is distinguished by its high degree of symmetry. Measures of this kind are called symmetric informationally complete, or SIC POVMs for short, and could be applied for quantum state tomography. Despite its simple geometrical description, the problem of constructing SIC POVMs or even proving their existence seems to be very hard. It is our purpose to introduce two applications of discrete Wigner functions to the analysis of the problem at hand. First, we will present a method for identifying symmetries of SIC POVMs under Clifford operations. This constitutes an alternative approach to a structure described before by Zauner and Appleby. Further, a simple and geometrically motivated construction for an SIC POVM in dimensions two and three is given (which, unfortunately, allows no generalization). Even though no new structures are found, we hope that the re- formulation of the problem may prove useful for future inquiries
The spectrum of the quasar PHL 1226 is known to have a strong Mg II and sub-damped Lymanalpha (sub-DLA) absorption line system with N(H I) = (5 +/- 2) x 10(19) cm(-2) at z = 0.1602. Using integral field spectra from the Potsdam Multi Aperture Spectrophotometer (PMAS) we investigate a galaxy at an impact parameter of 6".4 which is most probably responsible for the absorption lines. A fainter galaxy at a similar redshift and a slightly larger distance from the QSO is known to exist, but we assume that the absorption is caused by the more nearby galaxy. From optical Balmer lines we estimate an intrinsic reddening consistent with 0, and a moderate star formation rate of 0.5 M-circle dot yr(-1) is inferred from the Ha luminosity. Using nebular emission line ratios we find a solar oxygen abundance 12 + log (O/H) = 8.7 +/- 0.1 and a solar nitrogen to oxygen abundance ratio log (N/O) = -1.0 +/- 0.2. This abundance is larger than those of all known sub-DLA systems derived from analyses of metal absorption lines in quasar spectra. On the other hand, the properties are compatible with the most metal rich galaxies responsible for strong Mg II absorption systems. These two categories can be reconciled if we assume an abundance gradient similar to local galaxies. Under that assumption we predict abundances 12 + log (O/H) = 7.1 and log (N/O) = -1.9 for the sub-DLA cloud, which is similar to high redshift DLA and sub-DLA systems. We find evidence for a rotational velocity of similar to200 km s(-1) over a length of similar to7 kpc. From the geometry and kinematics of the galaxy we estimate that the absorbing cloud does not belong to a rotating disk, but could originate in a rotating halo
We present a flashlamp-pumped Nd: YAG laser simultaneously emitting pulse structures on microsecond, nanosecond and picosecond time scales. Within a microsecond flashlamp pump pulse a nonlinear reflector based on stimulated Brillouin scattering (SBS) generates several Q-switch pulses. The phase-conjugating effect of the SBS reflector provides a compensation of phase distortions generated inside the laser rod, resulting in transverse fundamental mode operation. Additional acousto-optic loss modulation inside the resonator leads to mode locking. As a result, each Q-switch pulse is subdivided into several picosecond pulses. Energies of up to 2 mJ for the mode-locked pulses with durations between 220 and 800 ps are demonstrated. The wide variability of the laser's temporal output parameters as well as its high beam quality make it a splendid tool for fundamental research in laser materials processing
We present a nonparametric way to retrieve an additive system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long-term predictions. We apply our method to a modified chaotic Chua oscillator in order to demonstrate its potential
We show that realistic aftershock sequences with space-time characteristics compatible with observations are generated by a model consisting of brittle fault segments separated by creeping zones. The dynamics of the brittle regions is governed by static/kinetic friction, 3D elastic stress transfer and small creep deformation. The creeping parts are characterized by high ongoing creep velocities. These regions store stress during earthquake failures and then release it in the interseismic periods. The resulting postseismic deformation leads to aftershock sequences following the modified Omori law. The ratio of creep coefficients in the brittle and creeping sections determines the duration of the postseismic transients and the exponent p of the modified Omori law
Anomalous phase synchronization in two asymmetrically coupled oscillators in the presence of noise
(2005)
We study the route to synchronization in two noisy, nonisochronous oscillators. Anomalous phase synchronization arises if both oscillators differ in their respective value of nonisochronicity and it is characterized by a strong detuning of the oscillator frequencies with the onset of coupling. Here we show that anomalous synchronization, both in limit-cycle or chaotic oscillators, can considerably be enlarged under the influence of asymmetrical coupling and noise. In these systems we describe a number of noise induced effects, such as an inversion of the natural frequency difference and coupling induced desynchronization of two identical oscillators. Our results can be explained in terms of a noisy particle in a tilted washboard potential
Subject of this work is the study of applications of the Galactic Microlensing effect, where the light of a distant star (source) is bend according to Einstein's theory of gravity by the gravitational field of intervening compact mass objects (lenses), creating multiple (however not resolvable) images of the source. Relative motion of source, observer and lens leads to a variation of deflection/magnification and thus to a time dependant observable brightness change (lightcurve), a so-called microlensing event, lasting weeks to months. The focus lies on the modeling of binary-lens events, which provide a unique tool to fully characterize the lens-source system and to detect extra-solar planets around the lens star. Making use of the ability of genetic algorithms to efficiently explore large and intricate parameter spaces in the quest for the global best solution, a modeling software (Tango) for binary lenses is developed, presented and applied to data sets from the PLANET microlensing campaign. For the event OGLE-2002-BLG-069 the 2nd ever lens mass measurement has been achieved, leading to a scenario, where a G5III Bulge giant at 9.4 kpc is lensed by an M-dwarf binary with total mass of M=0.51 solar masses at distance 2.9 kpc. Furthermore a method is presented to use the absence of planetary lightcurve signatures to constrain the abundance of extra-solar planets.
We present an automatic control method for phase locking of regular and chaotic non-identical oscillations, when all subsystems interact via feedback. This method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering. In contrast to unidirectional and bidirectional coupling, the approach presented here supposes the existence of a special controller, which allows to change the parameters of the controlled systems. First we discuss general principles of automatic phase synchronization (PS) for arbitrary coupled systems with a controller whose input is given by a special quadratic form of coordinates of the individual systems and its output is a result of the application of a linear differential operator. We demonstrate the effectiveness of our approach for controlled PS on several examples: (i) two coupled regular oscillators, (ii) coupled regular and chaotic oscillators, (iii) two coupled chaotic R"ossler oscillators, (iv) two coupled foodweb models, (v) coupled chaotic R"ossler and Lorenz oscillators, (vi) ensembles of locally coupled regular oscillators, (vii) ensembles of locally coupled chaotic oscillators, and (viii) ensembles of globally coupled chaotic oscillators.
Bestimmung von Ozonabbauraten über der Arktis und Antarktis mittels Ozonsonden- und Satellitendaten
(2005)
Diese Arbeit beschäftigt sich mit der chemischen Ozonzerstörung im arktischen und antarktischen stratosphärischen Polarwirbel. Diese wird durch Abbauprodukte von anthropogen emittierten Fluorchlorkohlenwasserstoffen und Halonen, Chlor- und Bromradikale, verursacht. Studien in denen der gemessene und modellierte Ozonabbau verglichen wird zeigen, dass die Prozeße bekannt sind, der quantitative Verlauf allerdings nicht vollständig verstanden ist. Die Prozesse, die zur Ozonzerstörung führen sind in beiden Polarwirbeln ähnlich. Allerdings fällt als Konsequenz unterschiedlicher meteorologischer Bedingungen der chemische Ozonabbau im arktischen Polarwirbel weniger drastisch aus als über der Antarktis. Der arktische Polarwirbel ist im Mittel stärker dynamisch gestört als der antarktische und weist eine stärkere Jahr-zu-Jahr Variabilität auf. Das erschwert die Messung des chemischen Ozonabbaus. Zur Trennung des chemischen Ozonabbaus von der dynamischen Umverteilung des Ozons im arktischen Polarwirbel wurde die Matchmethode entwickelt. Bei dieser Methode werden Luftpakete innerhalb des Polarwirbels mehrfach beprobt, um den chemischen Anteil der Ozonänderung zu quantifizieren. Zur Identifizierung von doppelt beprobten Luftpaketen werden Trajektorien aus Windfeldern berechnet. Können zwei Messungen im Rahmen bestimmter Qualitätskriterien durch eine Trajektorie verbunden werden, kann die Ozondifferenz zwischen beiden Sondierungen berechnet und als chemischer Ozonabbau interpretiert werden. Eine solche Koinzidenz wird Match genannt. Der Matchmethode liegt ein statistischer Ansatz zugrunde, so dass eine Vielzahl solcher doppelt beprobter Luftmassen vorliegen muss, um gesicherte Aussagen über die Ozonzerstörung gewinnen zu können. So erhält man die Ozonzerstörung in einem bestimmten Zeitintervall, also Ozonabbauraten. Um die Anzahl an doppelt beprobten Luftpackten zu erhöhen wurde eine aktive Koordinierung der Ozonsondenaufstiege entwickelt. Im Rahmen dieser Arbeit wurden Matchkampagnen während des arktischen Winters 2002/2003 und zum ersten Mal während eines antarktischen Winter (2003) durchgeführt. Aus den gewonnenen Daten wurden Ozonabbauraten in beiden Polarwirbeln bestimmt. Diese Abbauraten dienen zum einen der Evaluierung von Modellen, ermöglichen aber auch den direkten Vergleich von Ozonabbauraten in beiden Polarwirbeln. Der Winter 2002/2003 war zu Beginn durch sehr tiefe Temperaturen in der mittleren und unteren Stratosphäre charakterisiert, so dass die Matchkampagne Ende November gestartet wurde. Ab Januar war der Polarwirbel zeitweise stark dynamisch gestört. Die Kampagne ging bis Mitte März. Für den Höhenbereich von 400 bis 550 K potentieller Temperatur (15-23 km) konnten Ozonabbauraten und der Verlust in der Gesamtsäule berechnet werden. Die Ozonabbauraten wurden in verschiedenen Tests auf ihre Stabilität überprüft. Der antarktische Polarwirbel war vom Beginn des Winters bis Mitte Oktober 2003 sehr kalt und stellte Ende September kurzzeitig den Rekord für die größte bisher aufgetretene Ozonloch-Fläche ein. Es konnten für den Kampagnenzeitraum, Anfang Juni bis Anfang Oktober, Ozonabbauraten im Höhenbereich von 400 bis 550 K potentieller Temperatur ermittelt werden. Der zeitliche Verlauf des Ozonabbaus war dabei auf fast allen Höhenniveaus identisch. Die Zunahme des Sonnenlichtes im Polarwirbel mit der Zeit führt zu einem starken Anwachsen der Ozonabbauraten. Ab Mitte September gingen die Ozonabbauraten auf Null zurück, da bis zu diesem Zeitpunkt das gesamte Ozon zwischen ca. 14 und 21 km zerstört wurde. Im letzten Teil der Arbeit wird ein neuer Algorithmus auf Basis der multivariaten Regression vorgestellt, mit dem Ozonabbauraten aus Ozonprofilen verschiedener Sensoren gleichzeitig berechnet werden können. Dabei können neben der Ozonabbaurate die systematischen Fehler zwischen den einzelnen Sensoren bestimmt werden. Dies wurde exemplarisch am antarktischen Winter 2003 für das 475 K potentielle Temperatur Niveau gezeigt. Neben den Ozonprofilen der Sonden wurden Daten von zwei Satellitenexperimenten verwendet. Die mit der multivariaten Matchtechnik berechneten Ozonabbauraten stimmen gut mit den Ozonabbauraten der Einzelsensor-Matchansätze überein.
We investigate the motion of a hard cylinder rolling down a soft, inclined plane. The cylinder is subjected to a viscous drag force and stochastic fluctuations due to the surrounding rnedium. In a wide range of parameters we observe bistability of the rolling velocity. In dependence on the parameters, increasing noise level may lead to increasing or decreasing average velocity of the cylinder. The approximative analytical theory agrees with numerical results
The formation of a Langmuir monolayer of an amphiphilic derivative of zinc phthalocyanine (Na[(ZnPcSO3)-S-t]) has been studied by means of surface potential technique and Brewster angle microscopy. The experiments were undertaken in order to understand the behaviour of this monolayer with a well-defined surface pressure isotherm. The floating film is described as a truly monomolecular layer formed by very rigid islands in which the phthalocyanine units tend to take on a preferential orientation with their planes perpendicular to the air-water interface, for high values of the surface pressure. (c) 2004 Elsevier B.V. All rights reserved
Complex dynamical systems with many degrees of freedom may exhibit a wealth of collective phenomena related to high-dimensional chaos. This paper focuses on a lattice of coupled logistic maps to investigate the relationship between the loss of chaos synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly non-hyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization manifold. This has been confirmed by numerical diagnostics of synchronization and non-hyperbolic behavior, the latter using the statistical properties of finite-time Lyapunov exponents. (c) 2005 Elsevier B.V. All rights reserved
Interaction of particles of dust with vortex convective flows is under theoretical consideration. It is assumed that the volume fraction of solid phase is small, variations of density due to nonuniform distribution of particles and those caused by temperature nonisothermality of medium are comparable. Equations for the description of thermal buoyancy convection of a dusty medium are developed in the framework of the generalized Boussinesq approximation taking into account finite velocity of particle sedimentation. The capture of a cloud of dust particles by a vortex convective flow is considered, general criterion for the formation of such a cloud is obtained. The peculiarities of a steady state in the form of a dust cloud and backward influence of the solid phase on the carrier flow are studied in detail for a vertical layer heated from the sidewalls. It is shown that in the case, when this backward influence is essential, a hysteresis behavior is possible. The stability analysis of the steady state is performed. It turns out that there is a narrow range of governing parameters, in which such a steady state is stable. (c) 2005 American Institute of Physics