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Diffusion of finite-size particles in two-dimensional channels with random wall configurations
(2014)
Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick–Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda [J. Chem. Phys., 2012, 137, 024107].
The atmosphere over the Arctic Ocean is strongly influenced by the distribution of sea ice and open water. Leads in the sea ice produce strong convective fluxes of sensible and latent heat and release aerosol particles into the atmosphere. They increase the occurrence of clouds and modify the structure and characteristics of the atmospheric boundary layer (ABL) and thereby influence the Arctic climate.
In the course of this study aircraft measurements were performed over the western Arctic Ocean as part of the campaign PAMARCMIP 2012 of the Alfred Wegener Institute for Polar and Marine Research (AWI). Backscatter from aerosols and clouds within the lower troposphere and the ABL were measured with the nadir pointing Airborne Mobile Aerosol Lidar (AMALi) and dropsondes were launched to obtain profiles of meteorological variables. Furthermore, in situ measurements of aerosol properties, meteorological variables and turbulence were part of the campaign. The measurements covered a broad range of atmospheric and sea ice conditions.
In this thesis, properties of the ABL over Arctic sea ice with a focus on the influence of open leads are studied based on the data from the PAMARCMIP campaign. The height of the ABL is determined by different methods that are applied to dropsonde and AMALi backscatter profiles. ABL heights are compared for different flights representing different conditions of the atmosphere and of sea ice and open water influence. The different criteria for ABL height that are applied show large variation in terms of agreement among each other, depending on the characteristics of the ABL and its history. It is shown that ABL height determination from lidar backscatter by methods commonly used under mid-latitude conditions is applicable to the Arctic ABL only under certain conditions. Aerosol or clouds within the ABL are needed as a tracer for ABL height detection from backscatter. Hence an aerosol source close to the surface is necessary, that is typically found under the present influence of open water and therefore convective conditions. However it is not always possible to distinguish residual layers from the actual ABL. Stable boundary layers are generally difficult to detect.
To illustrate the complexity of the Arctic ABL and processes therein, four case studies are analyzed each of which represents a snapshot of the interplay between atmosphere and underlying sea ice or water surface. Influences of leads and open water on the aerosol and clouds within the ABL are identified and discussed. Leads are observed to cause the formation of fog and cloud layers within the ABL by humidity emission. Furthermore they decrease the stability and increase the height of the ABL and consequently facilitate entrainment of air and aerosol layers from the free troposphere.
During this work I built a four wave mixing setup for the time-resolved femtosecond spectroscopy of Raman-active lattice modes. This setup enables to study the selective excitation of phonon polaritons. These quasi-particles arise from the coupling of electro-magnetic waves and transverse optical lattice modes, the so-called phonons. The phonon polaritons were investigated in the optically non-linear, ferroelectric crystals LiNbO₃ and LiTaO₃.
The direct observation of the frequency shift of the scattered narrow bandwidth probe pulses proofs the role of the Raman interaction during the probe and excitation process of phonon polaritons. I compare this experimental method with the measurement where ultra-short laser pulses are used. The frequency shift remains obscured by the relative broad bandwidth of these laser pulses. In an experiment with narrow bandwidth probe pulses, the Stokes and anti-Stokes intensities are spectrally separated. They are assigned to the corresponding counter-propagating wavepackets of phonon polaritons. Thus, the dynamics of these wavepackets was separately studied. Based on these findings, I develop the mathematical description of the so-called homodyne detection of light for the case of light scattering from counter propagating phonon polaritons.
Further, I modified the broad bandwidth of the ultra-short pump pulses using bandpass filters to generate two pump pulses with non-overlapping spectra. This enables the frequency-selective excitation of polariton modes in the sample, which allows me to observe even very weak polariton modes in LiNbO₃ or LiTaO₃ that belong to the higher branches of the dispersion relation of phonon polaritons. The experimentally determined dispersion relation of the phonon polaritons could therefore be extended and compared to theoretical models. In addition, I determined the frequency-dependent damping of phonon polaritons.
The characterization of exoplanets is a young and rapidly expanding field in astronomy.
It includes a method called transmission spectroscopy that searches for planetary spectral
fingerprints in the light received from the host star during the event of a transit. This
techniques allows for conclusions on the atmospheric composition at the terminator region,
the boundary between the day and night side of the planet. Observationally a big
challenge, first attempts in the community have been successful in the detection of several
absorption features in the optical wavelength range. These are for example a Rayleighscattering
slope and absorption by sodium and potassium. However, other objects show
a featureless spectrum indicative for a cloud or haze layer of condensates masking the
probable atmospheric layers.
In this work, we performed transmission spectroscopy by spectrophotometry of three
Hot Jupiter exoplanets. When we began the work on this thesis, optical transmission
spectra have been available for two exoplanets. Our main goal was to advance the current
sample of probed objects to learn by comparative exoplanetology whether certain
absorption features are common. We selected the targets HAT-P-12b, HAT-P-19b and
HAT-P-32b, for which the detection of atmospheric signatures is feasible with current
ground-based instrumentation. In addition, we monitored the host stars of all three objects
photometrically to correct for influences of stellar activity if necessary.
The obtained measurements of the three objects all favor featureless spectra. A variety
of atmospheric compositions can explain the lack of a wavelength dependent absorption.
But the broad trend of featureless spectra in planets of a wide range of temperatures,
found in this work and in similar studies recently published in the literature, favors an
explanation based on the presence of condensates even at very low concentrations in the
atmospheres of these close-in gas giants. This result points towards the general conclusion
that the capability of transmission spectroscopy to determine the atmospheric composition
is limited, at least for measurements at low spectral resolution.
In addition, we refined the transit parameters and ephemerides of HAT-P-12b and HATP-
19b. Our monitoring campaigns allowed for the detection of the stellar rotation period
of HAT-P-19 and a refined age estimate. For HAT-P-12 and HAT-P-32, we derived upper
limits on their potential variability. The calculated upper limits of systematic effects of
starspots on the derived transmission spectra were found to be negligible for all three
targets.
Finally, we discussed the observational challenges in the characterization of exoplanet
atmospheres, the importance of correlated noise in the measurements and formulated
suggestions on how to improve on the robustness of results in future work.
Synchronization is a fundamental phenomenon in nature. It can be considered as a general property of self-sustained oscillators to adjust their rhythm in the presence of an interaction.
In this work we investigate complex regimes of synchronization phenomena by means of theoretical analysis, numerical modeling, as well as practical analysis of experimental data.
As a subject of our investigation we consider chimera state, where due to spontaneous symmetry-breaking of an initially homogeneous oscillators lattice split the system into two parts with different dynamics. Chimera state as a new synchronization phenomenon was first found in non-locally coupled oscillators system, and has attracted a lot of attention in the last decade. However, the recent studies indicate that this state is also possible in globally coupled systems. In the first part of this work, we show under which conditions the chimera-like state appears in a system of globally coupled identical oscillators with intrinsic delayed feedback. The results of the research explain how initially monostable oscillators became effectivly bistable in the presence of the coupling and create a mean field that sustain the coexistence of synchronized and desynchronized states. Also we discuss other examples, where chimera-like state appears due to frequency dependence of the phase shift in the bistable system.
In the second part, we make further investigation of this topic by modeling influence of an external periodic force to an oscillator with intrinsic delayed feedback. We made stability analysis of the synchronized state and constructed Arnold tongues. The results explain formation of the chimera-like state and hysteric behavior of the synchronization area. Also, we consider two sets of parameters of the oscillator with symmetric and asymmetric Arnold tongues, that correspond to mono- and bi-stable regimes of the oscillator.
In the third part, we demonstrate the results of the work, which was done in collaboration with our colleagues from Psychology Department of University of Potsdam. The project aimed to study the effect of the cardiac rhythm on human perception of time using synchronization analysis. From our part, we made a statistical analysis of the data obtained from the conducted experiment on free time interval reproduction task. We examined how ones heartbeat influences the time perception and searched for possible phase synchronization between heartbeat cycles and time reproduction responses. The findings support the prediction that cardiac cycles can serve as input signals, and is used for reproduction of time intervals in the range of several seconds.
The mystery of the origin of cosmic rays has been tackled for more than hundred years and is still not solved. Cosmic rays are detected with energies spanning more than 10 orders of magnitude and reaching energies up to ~10²¹ eV, far higher than any man-made accelerator can reach. Different theories on the astrophysical objects and processes creating such highly energetic particles have been proposed.
A very prominent explanation for a process producing highly energetic particles is shock acceleration. The observation of high-energy gamma rays from supernova remnants, some of them revealing a shell like structure, is clear evidence that particles are accelerated to ultrarelativistic energies in the shocks of these objects. The environments of supernova remnants are complex and challenge detailed modelling of the processes leading to high-energy gamma-ray emission.
The study of shock acceleration at bow shocks, created by the supersonic movement of individual stars through the interstellar medium, offers a unique possibility to determine the physical properties of shocks in a less complex environment. The shocked medium is heated by the stellar and the shock excited radiation, leading to thermal infrared emission. 28 bow shocks have been discovered through their infrared emission. Nonthermal radiation in radio and X-ray wavelengths has been detected from two bow shocks, pointing to the existence of relativistic particles in these systems. Theoretical models of the emission processes predict high-energy and very high-energy emission at a flux level in reach of current instruments. This work presents the search for gamma-ray emission from bow shocks of runaway stars in the energy regime from 100MeV to ~100TeV.
The search is performed with the large area telescope (LAT) on-board the Fermi satellite and the H.E.S.S. telescopes located in the Khomas Highland in Namibia. The Fermi-LAT was launched in 2008 and is continuously scanning the sky since then. It detects photons with energies from 20MeV to over 300 GeV and has an unprecedented sensitivity. The all-sky coverage allows us to study all 28 bow shocks of runaway stars listed in the E-BOSS catalogue of infrared bow shocks. No significant emission was detected from any of the objects, although predicted by several theoretical models describing the non-thermal emission of bow shocks of runaway stars.
The H.E.S.S. experiment is the most sensitive system of imaging atmospheric Cherenkov telescopes. It detects photons from several tens of GeV to ~100TeV. Seven of the bow shocks have been observed with H.E.S.S. and the data analysis is presented in this thesis. The analyses of the very-high energy data did not reveal significant emission from any of the sources either.
This work presents the first systematic search for gamma-ray emission from bow shocks of runaway stars. For the first time Fermi-LAT data was specifically analysed to reveal emission from bow shocks of runaway stars. In the TeV regime no searches for emission from theses objects have been published so far, the study presented here is the first in this energy regime. The level of the gamma-ray emission from bow shocks of runaway stars is constrained by the calculated upper limits over six orders in magnitude in energy.
The upper limits calculated for the bow shocks of runaway stars in the course of this work, constrain several models. For the best candidate, ζ Ophiuchi, the upper limits in the Fermi-LAT energy range are lower than the predictions by a factor ~5. This challenges the assumptions made in this model and gives valuable input for further modelling approaches.
The analyses were performed with the software packages provided by the H.E.S.S. and Fermi collaborations. The development of a unified analysis framework for gamma-ray data, namely GammaLib/ctools, is rapidly progressing within the CTA consortium. Recent implementations and cross-checks with current software frameworks are presented in the Appendix.
Galaxies are observational probes to study the Large Scale Structure. Their gravitational motions are tracers of the total matter density and therefore of the Large Scale Structure. Besides, studies of structure formation and galaxy evolution rely on numerical cosmological simulations. Still, only one universe observable from a given position, in time and space, is available for comparisons with simulations. The related cosmic variance affects our ability to interpret the results. Simulations constrained by observational data are a perfect remedy to this problem. Achieving such simulations requires the projects Cosmic flows and CLUES. Cosmic flows builds catalogs of accurate distance measurements to map deviations from the expansion. These measures are mainly obtained with the galaxy luminosity-rotation rate correlation. We present the calibration of that relation in the mid-infrared with observational data from Spitzer Space Telescope. Resulting accurate distance estimates will be included in the third catalog of the project. In the meantime, two catalogs up to 30 and 150 Mpc/h have been released. We report improvements and applications of the CLUES' method on these two catalogs. The technique is based on the constrained realization algorithm. The cosmic displacement field is computed with the Zel'dovich approximation. This latter is then reversed to relocate reconstructed three-dimensional constraints to their precursors' positions in the initial field. The size of the second catalog (8000 galaxies within 150 Mpc/h) highlighted the importance of minimizing the observational biases. By carrying out tests on mock catalogs, built from cosmological simulations, a method to minimize observational bias can be derived. Finally, for the first time, cosmological simulations are constrained solely by peculiar velocities. The process is successful as resulting simulations resemble the Local Universe. The major attractors and voids are simulated at positions approaching observational positions by a few megaparsecs, thus reaching the limit imposed by the linear theory.
Despite remarkable progress made in the past century, which has revolutionized our understanding of the universe, there are numerous open questions left in theoretical physics. Particularly important is the fact that the theories describing the fundamental interactions of nature are incompatible. Einstein's theory of general relative describes gravity as a dynamical spacetime, which is curved by matter and whose curvature determines the motion of matter. On the other hand we have quantum field theory, in form of the standard model of particle physics, where particles interact via the remaining interactions - electromagnetic, weak and strong interaction - on a flat, static spacetime without gravity. A theory of quantum gravity is hoped to cure this incompatibility by heuristically replacing classical spacetime by quantum spacetime'. Several approaches exist attempting to define such a theory with differing underlying premises and ideas, where it is not clear which is to be preferred. Yet a minimal requirement is the compatibility with the classical theory, they attempt to generalize. Interestingly many of these models rely on discrete structures in their definition or postulate discreteness of spacetime to be fundamental. Besides the direct advantages discretisations provide, e.g. permitting numerical simulations, they come with serious caveats requiring thorough investigation: In general discretisations break fundamental diffeomorphism symmetry of gravity and are generically not unique. Both complicates establishing the connection to the classical continuum theory. The main focus of this thesis lies in the investigation of this relation for spin foam models. This is done on different levels of the discretisation / triangulation, ranging from few simplices up to the continuum limit. In the regime of very few simplices we confirm and deepen the connection of spin foam models to discrete gravity. Moreover, we discuss dynamical, e.g. diffeomorphism invariance in the discrete, to fix the ambiguities of the models. In order to satisfy these conditions, the discrete models have to be improved in a renormalisation procedure, which also allows us to study their continuum dynamics. Applied to simplified spin foam models, we uncover a rich, non--trivial fixed point structure, which we summarize in a phase diagram. Inspired by these methods, we propose a method to consistently construct the continuum theory, which comes with a unique vacuum state.
The H.E.S.S. array is a third generation Imaging Atmospheric Cherenkov Telescope (IACT) array. It is located in the Khomas Highland in Namibia, and measures very high energy (VHE) gamma-rays. In Phase I, the array started data taking in 2004 with its four identical 13 m telescopes. Since then, H.E.S.S. has emerged as the most successful IACT experiment to date. Among the almost 150 sources of VHE gamma-ray radiation found so far, even the oldest detection, the Crab Nebula, keeps surprising the scientific community with unexplained phenomena such as the recently discovered very energetic flares of high energy gamma-ray radiation. During its most recent flare, which was detected by the Fermi satellite in March 2013, the Crab Nebula was simultaneously observed with the H.E.S.S. array for six nights. The results of the observations will be discussed in detail during the course of this work. During the nights of the flare, the new 24 m × 32 m H.E.S.S. II telescope was still being commissioned, but participated in the data taking for one night. To be able to reconstruct and analyze the data of the H.E.S.S. Phase II array, the algorithms and software used by the H.E.S.S. Phase I array had to be adapted. The most prominent advanced shower reconstruction technique developed by de Naurois and Rolland, the template-based model analysis, compares real shower images taken by the Cherenkov telescope cameras with shower templates obtained using a semi-analytical model. To find the best fitting image, and, therefore, the relevant parameters that describe the air shower best, a pixel-wise log-likelihood fit is done. The adaptation of this advanced shower reconstruction technique to the heterogeneous H.E.S.S. Phase II array for stereo events (i.e. air showers seen by at least two telescopes of any kind), its performance using MonteCarlo simulations as well as its application to real data will be described.