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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.
This Thesis was devoted to the study of the coupled system composed by El Niño/Southern Oscillation and the Annual Cycle. More precisely, the work was focused on two main problems: 1. How to separate both oscillations into an affordable model for understanding the behaviour of the whole system. 2. How to model the system in order to achieve a better understanding of the interaction, as well as to predict future states of the system. We focused our efforts in the Sea Surface Temperature equations, considering that atmospheric effects were secondary to the ocean dynamics. The results found may be summarised as follows: 1. Linear methods are not suitable for characterising the dimensionality of the sea surface temperature in the tropical Pacific Ocean. Therefore they do not help to separate the oscillations by themselves. Instead, nonlinear methods of dimensionality reduction are proven to be better in defining a lower limit for the dimensionality of the system as well as in explaining the statistical results in a more physical way [1]. In particular, Isomap, a nonlinear modification of Multidimensional Scaling methods, provides a physically appealing method of decomposing the data, as it substitutes the euclidean distances in the manifold by an approximation of the geodesic distances. We expect that this method could be successfully applied to other oscillatory extended systems and, in particular, to meteorological systems. 2. A three dimensional dynamical system could be modeled, using a backfitting algorithm, for describing the dynamics of the sea surface temperature in the tropical Pacific Ocean. We observed that, although there were few data points available, we could predict future behaviours of the coupled ENSO-Annual Cycle system with an accuracy of less than six months, although the constructed system presented several drawbacks: few data points to input in the backfitting algorithm, untrained model, lack of forcing with external data and simplification using a close system. Anyway, ensemble prediction techniques showed that the prediction skills of the three dimensional time series were as good as those found in much more complex models. This suggests that the climatological system in the tropics is mainly explained by ocean dynamics, while the atmosphere plays a secondary role in the physics of the process. Relevant predictions for short lead times can be made using a low dimensional system, despite its simplicity. The analysis of the SST data suggests that nonlinear interaction between the oscillations is small, and that noise plays a secondary role in the fundamental dynamics of the oscillations [2]. A global view of the work shows a general procedure to face modeling of climatological systems. First, we should find a suitable method of either linear or nonlinear dimensionality reduction. Then, low dimensional time series could be extracted out of the method applied. Finally, a low dimensional model could be found using a backfitting algorithm in order to predict future states of the system.
We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching, we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. Our discussion is based on experimental parameters for tau proteins in neuronal cells, but the results obtained here are expected to be of relevance for a broad class of processes in complex systems. Specifically, we obtain that, when the mean binding time is significantly longer than the mean mobile time, transient anomalous diffusion is observed at short and intermediate time scales, with a strong dependence on the fraction of initially mobile and immobile particles. We unveil a Laplace distribution of particle displacements at relevant intermediate time scales. For any initial fraction of mobile particles, the respective mean squared displacement (MSD) displays a plateau. Moreover, we demonstrate a short-time cubic time dependence of the MSD for immobile tracers when initially all particles are immobile.
Die Untersuchung mikrogelinster astronomischer Objekte ermöglicht es, Informationen über die Größe und Struktur dieser Objekte zu erhalten. Im ersten Teil dieser Arbeit werden die Spektren von drei gelinsten Quasare, die mit dem Potsdamer Multi Aperture Spectrophotometer (PMAS) erhalten wurden, auf Anzeichen für Mikrolensing untersucht. In den Spektren des Vierfachquasares HE 0435-1223 und des Doppelquasares HE 0047-1756 konnten Hinweise für Mikrolensing gefunden werden, während der Doppelquasar UM 673 (Q 0142--100) keine Anzeichen für Mikrolensing zeigt. Die Invertierung der Lichtkurve eines Mikrolensing-Kausik-Crossing-Ereignisses ermöglicht es, das eindimensionale Helligkeitsprofil der gelinsten Quelle zu rekonstruieren. Dies wird im zweiten Teil dieser Arbeit untersucht. Die mathematische Beschreibung dieser Aufgabe führt zu einer Volterra'schen Integralgleichung der ersten Art, deren Lösung ein schlecht gestelltes Problem ist. Zu ihrer Lösung wird in dieser Arbeit ein lokales Regularisierungsverfahren angewendet, das an die kausale Strukture der Volterra'schen Gleichung besser angepasst ist als die bisher verwendete Tikhonov-Phillips-Regularisierung. Es zeigt sich, dass mit dieser Methode eine bessere Rekonstruktion kleinerer Strukturen in der Quelle möglich ist. Weiterhin wird die Anwendbarkeit der Regularisierungsmethode auf realistische Lichtkurven mit irregulärem Sampling bzw. größeren Lücken in den Datenpunkten untersucht.
Rotating stellar convection transports angular momentum towards the equator, generating the characteristic equatorial acceleration of the solar rotation while the radial flux of angular momentum is always inwards. New numerical box simulations for the meridional cross-correlation < u(theta)u(phi)>, however, reveal the angular momentum transport towards the poles for slow rotation and towards the equator for fast rotation. The explanation is that for slow rotation a negative radial gradient of the angular velocity always appears, which in combination with a so-far neglected rotation-induced off-diagonal eddy viscosity term nu(perpendicular to) provides "antisolar rotation" laws with a decelerated equator Similarly, the simulations provided positive values for the rotation-induced correlation < u(r)u(theta)>, which is relevant for the resulting latitudinal temperature profiles (cool or warm poles) for slow rotation and negative values for fast rotation. Observations of the differential rotation of slowly rotating stars will therefore lead to a better understanding of the actual stress-strain relation, the heat transport, and the underlying model of the rotating convection.
Understanding the origin of inefficient photocurrent generation in organic solar cells with low energy offset remains key to realizing high-performance donor-acceptor systems. Here, we probe the origin of field-dependent free-charge generation and photoluminescence in wnon-fullereneacceptor (NFA)-based organic solar cells using the polymer PM6 and the NFA Y5-a non-halogenated sibling to Y6, with a smaller energetic offset to PM6. By performing time-delayed collection field (TDCF) measurements on a variety of samples with different electron transport layers and active layer thickness, we show that the fill factor and photocurrent are limited by field-dependent free charge generation in the bulk of the blend. We also introduce a new method of TDCF called m-TDCF to prove the absence of artifacts from non-geminate recombination of photogenerated and dark charge carriers near the electrodes. We then correlate free charge generation with steady-state photoluminescence intensity and find perfect anticorrelation between these two properties. Through this, we conclude that photocurrent generation in this low-offset system is entirely controlled by the field-dependent dissociation of local excitons into charge-transfer states. (c) 2023 Author(s).
Ocean-induced melting below ice shelves is one of the dominant drivers for mass loss from the Antarctic Ice Sheet at present. An appropriate representation of sub-shelf melt rates is therefore essential for model simulations of marine-based ice sheet evolution. Continental-scale ice sheet models often rely on simple melt-parameterizations, in particular for long-term simulations, when fully coupled ice-ocean interaction becomes computationally too expensive. Such parameterizations can account for the influence of the local depth of the ice-shelf draft or its slope on melting. However, they do not capture the effect of ocean circulation underneath the ice shelf. Here we present the Potsdam Ice-shelf Cavity mOdel (PICO), which simulates the vertical overturning circulation in ice-shelf cavities and thus enables the computation of sub-shelf melt rates consistent with this circulation. PICO is based on an ocean box model that coarsely resolves ice shelf cavities and uses a boundary layer melt formulation. We implement it as a module of the Parallel Ice Sheet Model (PISM) and evaluate its performance under present-day conditions of the Southern Ocean. We identify a set of parameters that yield two-dimensional melt rate fields that qualitatively reproduce the typical pattern of comparably high melting near the grounding line and lower melting or refreezing towards the calving front. PICO captures the wide range of melt rates observed for Antarctic ice shelves, with an average of about 0.1 ma(-1) for cold sub-shelf cavities, for example, underneath Ross or Ronne ice shelves, to 16 ma(-1) for warm cavities such as in the Amundsen Sea region. This makes PICO a computationally feasible and more physical alternative to melt parameterizations purely based on ice draft geometry.
The mobile-immobile model (MIM) has been established in geoscience in the context of contaminant transport in groundwater. Here the tracer particles effectively immobilise, e.g., due to diffusion into dead-end pores or sorption. The main idea of the MIM is to split the total particle density into a mobile and an immobile density. Individual tracers switch between the mobile and immobile state following a two-state telegraph process, i.e., the residence times in each state are distributed exponentially. In geoscience the focus lies on the breakthrough curve (BTC), which is the concentration at a fixed location over time. We apply the MIM to biological experiments with a special focus on anomalous scaling regimes of the mean squared displacement (MSD) and non-Gaussian displacement distributions. As an exemplary system, we have analysed the motion of tau proteins, that diffuse freely inside axons of neurons. Their free diffusion thereby corresponds to the mobile state of the MIM. Tau proteins stochastically bind to microtubules, which effectively immobilises the tau proteins until they unbind and continue diffusing. Long immobilisation durations compared to the mobile durations give rise to distinct non-Gaussian Laplace shaped distributions. It is accompanied by a plateau in the MSD for initially mobile tracer particles at relevant intermediate timescales. An equilibrium fraction of initially mobile tracers gives rise to non-Gaussian displacements at intermediate timescales, while the MSD remains linear at all times. In another setting bio molecules diffuse in a biosensor and transiently bind to specific receptors, where advection becomes relevant in the mobile state. The plateau in the MSD observed for the advection-free setting and long immobilisation durations persists also for the case with advection. We find a new clear regime of anomalous diffusion with non-Gaussian distributions and a cubic scaling of the MSD. This regime emerges for initially mobile and for initially immobile tracers. For an equilibrium fraction of initially mobile tracers we observe an intermittent ballistic scaling of the MSD. The long-time effective diffusion coefficient is enhanced by advection, which we physically explain with the variance of mobile durations. Finally, we generalize the MIM to incorporate arbitrary immobilisation time distributions and focus on a Mittag-Leffler immobilisation time distribution with power-law tail ~ t^(-1-mu) with 0<mu<1 and diverging mean immobilisation durations. A fit of our model to the BTC of experimental data from tracer particles in aquifers matches the BTC including the power-law tail. We use the fit parameters for plotting the displacement distributions and the MSD. We find Gaussian normal diffusion at short times and long-time power-law decay of mobile mass accompanied by anomalous diffusion at long times. The long-time diffusion is subdiffusive in the advection-free setting, while it is either subdiffusive for 0<mu<1/2 or superdiffusive for 1/2<mu<1 when advection is present. In the long-time limit we show equivalence of our model to a bi-fractional diffusion equation.
We investigate a diffusion process with a time-dependent diffusion coefficient, both exponentially increasing and decreasing in time, D(t)=D-0(e +/- 2 alpha t). For this (hypothetical) nonstationary diffusion process we compute-both analytically and from extensive stochastic simulations-the behavior of the ensemble- and time-averaged mean-squared displacements (MSDs) of the particles, both in the over- and underdamped limits. Simple asymptotic relations derived for the short- and long-time behaviors are shown to be in excellent agreement with the results of simulations. The diffusive characteristics in the presence of ageing are also considered, with dramatic differences of the over- versus underdamped regime. Our results for D(t)=D-0(e +/- 2 alpha t) extend and generalize the class of diffusive systems obeying scaled Brownian motion featuring a power-law-like variation of the diffusivity with time, D(t) similar to t(alpha-1). We also examine the logarithmically increasing diffusivity, D(t)=D(0)log[t/tau(0)], as another fundamental functional dependence (in addition to the power-law and exponential) and as an example of diffusivity slowly varying in time. One of the main conclusions is that the behavior of the massive particles is predominantly ergodic, while weak ergodicity breaking is repeatedly found for the time-dependent diffusion of the massless particles at short times. The latter manifests itself in the nonequivalence of the (both nonaged and aged) MSD and the mean time-averaged MSD. The current findings are potentially applicable to a class of physical systems out of thermal equilibrium where a rapid increase or decrease of the particles' diffusivity is inherently realized. One biological system potentially featuring all three types of time-dependent diffusion (power-law-like, exponential, and logarithmic) is water diffusion in the brain tissues, as we thoroughly discuss in the end.