@phdthesis{Dahlke2020,
  author    = {Dahlke, Sandro},
  title     = {Rapid climate changes in the arctic region of Svalbard},
  doi       = {10.25932/publishup-44554},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-445542},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xv, 123},
  year      = {2020},
  abstract  = {Over the last decades, the Arctic regions of the earth have warmed at a rate 2-3 times faster than the global average- a phenomenon called Arctic Amplification. A complex, non-linear interplay of physical processes and unique pecularities in the Arctic climate system is responsible for this, but the relative role of individual processes remains to be debated. This thesis focuses on the climate change and related processes on Svalbard, an archipelago in the North Atlantic sector of the Arctic, which is shown to be a "hotspot" for the amplified recent warming during winter. In this highly dynamical region, both oceanic and atmospheric large-scale transports of heat and moisture interfere with spatially inhomogenous surface conditions, and the corresponding energy exchange strongly shapes the atmospheric boundary layer. In the first part, Pan-Svalbard gradients in the surface air temperature (SAT) and sea ice extent (SIE) in the fjords are quantified and characterized. This analysis is based on observational data from meteorological stations, operational sea ice charts, and hydrographic observations from the adjacent ocean, which cover the 1980-2016 period. It is revealed that typical estimates of SIE during late winter range from 40-50\% (80-90\%) in the western (eastern) parts of Svalbard. However, strong SAT warming during winter of the order of 2-3K per decade dictates excessive ice loss, leaving fjords in the western parts essentially ice-free in recent winters. It is further demostrated that warm water currents on the west coast of Svalbard, as well as meridional winds contribute to regional differences in the SIE evolution. In particular, the proximity to warm water masses of the West Spitsbergen Current can explain 20-37\% of SIE variability in fjords on west Svalbard, while meridional winds and associated ice drift may regionally explain 20-50\% of SIE variability in the north and northeast. Strong SAT warming has overruled these impacts in recent years, though. In the next part of the analysis, the contribution of large-scale atmospheric circulation changes to the Svalbard temperature development over the last 20 years is investigated. A study employing kinematic air-back trajectories for Ny-{\AA}lesund reveals a shift in the source regions of lower-troposheric air over time for both the winter and the summer season. In winter, air in the recent decade is more often of lower-latitude Atlantic origin, and less frequent of Arctic origin. This affects heat- and moisture advection towards Svalbard, potentially manipulating clouds and longwave downward radiation in that region. A closer investigation indicates that this shift during winter is associated with a strengthened Ural blocking high and Icelandic low, and contributes about 25\% to the observed winter warming on Svalbard over the last 20 years. Conversely, circulation changes during summer include a strengthened Greenland blocking high which leads to more frequent cold air advection from the central Arctic towards Svalbard, and less frequent air mass origins in the lower latitudes of the North Atlantic. Hence, circulation changes during winter are shown to have an amplifying effect on the recent warming on Svalbard, while summer circulation changes tend to mask warming. An observational case study using upper air soundings from the AWIPEV research station in Ny-{\AA}lesund during May-June 2017 underlines that such circulation changes during summer are associated with tropospheric anomalies in temperature, humidity and boundary layer height. In the last part of the analysis, the regional representativeness of the above described changes around Svalbard for the broader Arctic is investigated. Therefore, the terms in the diagnostic temperature equation in the Arctic-wide lower troposphere are examined for the Era-Interim atmospheric reanalysis product. Significant positive trends in diabatic heating rates, consistent with latent heat transfer to the atmosphere over regions of increasing ice melt, are found for all seasons over the Barents/Kara Seas, and in individual months in the vicinity of Svalbard. The above introduced warm (cold) advection trends during winter (summer) on Svalbard are successfully reproduced. Regarding winter, they are regionally confined to the Barents Sea and Fram Strait, between 70°-80°N, resembling a unique feature in the whole Arctic. Summer cold advection trends are confined to the area between eastern Greenland and Franz Josef Land, enclosing Svalbard.},
  language  = {en}
}
@phdthesis{HernandezAnguizola2020,
  author    = {Hernandez Anguizola, Eloy Luis},
  title     = {Numerical simulations in multimode fibres for astronomical spectroscopy},
  doi       = {10.25932/publishup-47236},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472363},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xvi, 114},
  year      = {2020},
  abstract  = {The goal of this thesis was to thoroughly investigate the behavior of multimode fibres to aid the development of modern and forthcoming fibre-fed spectrograph systems. Based on the Eigenmode Expansion Method, a field propagation model was created that can emulate effects in fibres relevant for astronomical spectroscopy, such as modal noise, scrambling, and focal ratio degradation. These effects are of major concern for any fibre-coupled spectrograph used in astronomical research. Changes in the focal ratio, modal distribution of light or non-perfect scrambling limit the accuracy of measurements, e.g. the flux determination of the astronomical object, the sky-background subtraction and detection limit for faint galaxies, or the spectral line position accuracy used for the detection of extra-solar planets. Usually, fibres used for astronomical instrumentation are characterized empirically through tests. The results of this work allow to predict the fibre behaviour under various conditions using sophisticated software tools to simulate the waveguide behaviour and mode transport of fibres. The simulation environment works with two software interfaces. The first is the mode solver module FemSIM from Rsoft. It is used to calculate all the propagation modes and effective refractive indexes of a given system. The second interface consists of Python scripts which enable the simulation of the near- and far-field outputs of a given fibre. The characteristics of the input field can be manipulated to emulate real conditions. Focus variations, spatial translation, angular fluctuations, and disturbances through the mode coupling factor can also be simulated. To date, complete coherent propagation or complete incoherent propagation can be simulated. Partial coherence was not addressed in this work. Another limitation of the simulations is that they work exclusively for the monochromatic case and that the loss coefficient of the fibres is not considered. Nevertheless, the simulations were able to match the results of realistic measurements. To test the validity of the simulations, real fibre measurements were used for comparison. Two fibres with different cross-sections were characterized. The first fibre had a circular cross-section, and the second one had an octagonal cross-section. The utilized test-bench was originally developed for the prototype fibres of the 4MOST fibre feed characterization. It allowed for parallel laser beam measurements, light cone measurements, and scrambling measurements. Through the appropriate configuration, the acquisition of the near- and/or far-field was feasible. By means of modal noise analysis, it was possible to compare the near-field speckle patterns of simulations and measurements as a function of the input angle. The spatial frequencies that originate from the modal interference could be analyzed by using the power spectral density analysis. Measurements and simulations yielded similar results. Measurements with induced modal scrambling were compared to simulations using incoherent propagation and once again similar results were achieved. Through both measurements and simulations, the enlargement of the near-field distribution could be observed and analyzed. The simulations made it possible to explain incoherent intensity fluctuations that appear in real measurements due to the field distribution of the active propagation modes. By using the Voigt analysis in the far-field distribution, it was possible to separate the modal diffusion component in order to compare it with the simulations. Through an appropriate assessment, the modal diffusion component as a function of the input angle could be translated into angular divergence. The simulations gave the minimal angular divergence of the system. Through the mean of the difference between simulations and measurements, a figure of merit is given which can be used to characterize the angular divergence of real fibres using the simulations. Furthermore, it was possible to simulate light cone measurements. Due to the overall consistent results, it can be stated that the simulations represent a good tool to assist the fibre characterization process for fibre-fed spectrograph systems. This work was possible through the BMBF Grant 05A14BA1 which was part of the phase A study of the fibre system for MOSAIC, a multi-object spectrograph for the Extremely Large Telescope (ELT-MOS).},
  language  = {en}
}
@phdthesis{Krivenkov2020,
  author    = {Krivenkov, Maxim},
  title     = {Spin textures and electron scattering in nanopatterned monolayer graphene},
  doi       = {10.25932/publishup-48701},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-487017},
  school      = {Universit{\"a}t Potsdam},
  pages     = {x, 176},
  year      = {2020},
  abstract  = {The current thesis is focused on the properties of graphene supported by metallic substrates and specifically on the behaviour of electrons in such systems. Methods of scanning tunneling microscopy, electron diffraction and photoemission spectroscopy were applied to study the structural and electronic properties of graphene. The purpose of the first part of this work is to introduce the most relevant aspects of graphene physics and the methodical background of experimental techniques used in the current thesis. The scientific part of this work starts with the extensive study by means of scanning tunneling microscopy of the nanostructures that appear in Au intercalated graphene on Ni(111). This study was aimed to explore the possible structural explanations of the Rashba-type spin splitting of ~100 meV experimentally observed in this system — much larger than predicted by theory. It was demonstrated that gold can be intercalated under graphene not only as a dense monolayer, but also in the form of well-periodic arrays of nanoclusters, a structure previously not reported. Such nanocluster arrays are able to decouple graphene from the strongly interacting Ni substrate and render it quasi-free-standing, as demonstrated by our DFT study. At the same time calculations confirm strong enhancement of the proximity-induced SOI in graphene supported by such nanoclusters in comparison to monolayer gold. This effect, attributed to the reduced graphene-Au distance in the case of clusters, provides a large Rashba-type spin splitting of ~60 meV. The obtained results not only provide a possible mechanism of SOI enhancement in this particular system, but they can be also generalized for graphene on other strongly interacting substrates intercalated by nanostructures of heavy noble d metals. Even more intriguing is the proximity of graphene to heavy sp-metals that were predicted to induce an intrinsic SOI and realize a spin Hall effect in graphene. Bismuth is the heaviest stable sp-metal and its compounds demonstrate a plethora of exciting physical phenomena. This was the motivation behind the next part of the current thesis, where structural and electronic properties of a previously unreported phase of Bi-intercalated graphene on Ir(111) were studied by means of scanning tunneling microscopy, spin- and angle-resolved photoemission spectroscopy and electron diffraction. Photoemission experiments revealed a remarkable, nearly ideal graphene band structure with strongly suppressed signatures of interaction between graphene and the Ir(111) substrate, moreover, the characteristic moir{\´e} pattern observed in graphene on Ir(111) by electron diffraction and scanning tunneling microscopy was strongly suppressed after intercalation. The whole set of experimental data evidences that Bi forms a dense intercalated layer that efficiently decouples graphene from the substrate. The interaction manifests itself only in the n-type charge doping (~0.4 eV) and a relatively small band gap at the Dirac point (~190 meV). The origin of this minor band gap is quite intriguing and in this work it was possible to exclude a wide range of mechanisms that could be responsible for it, such as induced intrinsic spin-orbit interaction, hybridization with the substrate states and corrugation of the graphene lattice. The main origin of the band gap was attributed to the A-B symmetry breaking and this conclusion found support in the careful analysis of the interference effects in photoemission that provided the band gap estimate of ~140 meV. While the previous chapters were focused on adjusting the properties of graphene by proximity to heavy metals, graphene on its own is a great object to study various physical effects at crystal surfaces. The final part of this work is devoted to a study of surface scattering resonances by means of photoemission spectroscopy, where this effect manifests itself as a distinct modulation of photoemission intensity. Though scattering resonances were widely studied in the past by means of electron diffraction, studies about their observation in photoemission experiments started to appear only recently and they are very scarce. For a comprehensive study of scattering resonances graphene was selected as a versatile model system with adjustable properties. After the theoretical and historical introduction to the topic of scattering resonances follows a detailed description of the unusual features observed in the photoemission spectra obtained in this work and finally the equivalence between these features and scattering resonances is proven. The obtained photoemission results are in a good qualitative agreement with the existing theory, as verified by our calculations in the framework of the interference model. This simple model gives a suitable explanation for the general experimental observations. The possibilities of engineering the scattering resonances were also explored. A systematic study of graphene on a wide range of substrates revealed that the energy position of the resonances is in a direct relation to the magnitude of charge transfer between graphene and the substrate. Moreover, it was demonstrated that the scattering resonances in graphene on Ir(111) can be suppressed by nanopatterning either by a superlattice of Ir nanoclusters or by atomic hydrogen. These effects were attributed to strong local variations of tork function and/or destruction of long-range order of thephene lattice. The tunability of scattering resonances can be applied for optoelectronic devices based on graphene. Moreover, the results of this study expand the general understanding of the phenomenon of scattering resonances and are applicable to many other materials besides graphene.},
  language  = {en}
}
@phdthesis{Mandal2020,
  author    = {Mandal, Partha Sarathi},
  title     = {Controlling the surface band gap in topological states of matter},
  doi       = {10.25932/publishup-48045},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-480459},
  school      = {Universit{\"a}t Potsdam},
  pages     = {122},
  year      = {2020},
  abstract  = {In the present study, we employ the angle-resolved photoemission spectroscopy (ARPES) technique to study the electronic structure of topological states of matter. In particular, the so-called topological crystalline insulators (TCIs) Pb1-xSnxSe and Pb1-xSnxTe, and the Mn-doped Z2 topological insulators (TIs) Bi2Te3 and Bi2Se3. The Z2 class of strong topological insulators is protected by time-reversal symmetry and is characterized by an odd number of metallic Dirac type surface states in the surface Brillouin zone. The topological crystalline insulators on the other hand are protected by the individual crystal symmetries and exhibit an even number of Dirac cones. The topological properties of the lead tin chalcogenides topological crystalline insulators can be tuned by temperature and composition. Here, we demonstrate that Bi-doping of the Pb1-xSnxSe(111) epilayers induces a quantum phase transition from a topological crystalline insulator to a Z2 topological insulator. This occurs because Bi-doping lifts the fourfold valley degeneracy in the bulk. As a consequence a gap appears at ⌈¯, while the three Dirac cones at the M̅ points of the surface Brillouin zone remain intact. We interpret this new phase transition is caused by lattice distortion. Our findings extend the topological phase diagram enormously and make strong topological insulators switchable by distortions or electric field. In contrast, the bulk Bi doping of epitaxial Pb1-xSnxTe(111) films induces a giant Rashba splitting at the surface that can be tuned by the doping level. Tight binding calculations identify their origin as Fermi level pinning by trap states at the surface. Magnetically doped topological insulators enable the quantum anomalous Hall effect (QAHE) which provide quantized edge states for lossless charge transport applications. The edge states are hosted by a magnetic energy gap at the Dirac point which has not been experimentally observed to date. Our low temperature ARPES studies unambiguously reveal the magnetic gap of Mn-doped Bi2Te3. Our analysis shows a five times larger gap size below the Tc than theoretically predicted. We assign this enhancement to a remarkable structure modification induced by Mn doping. Instead of a disordered impurity system, a self-organized alternating sequence of MnBi2Te4 septuple and Bi2Te3quintuple layers is formed. This enhances the wave-function overlap and gives rise to a large magnetic gap. Mn-doped Bi2Se3 forms similar heterostructure, but only a nonmagnetic gap is observed in this system. This correlates with the difference in magnetic anisotropy due to the much larger spin-orbit interaction in Bi2Te3 compared to Bi2Se3. These findings provide crucial insights for pushing lossless transport in topological insulators towards room-temperature applications.},
  language  = {en}
}
@phdthesis{Christ2020,
  author    = {Christ, Simon},
  title     = {Morphological transitions of vesicles exposed to nonuniform spatio-temporal conditions},
  doi       = {10.25932/publishup-48078},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-480788},
  school      = {Universit{\"a}t Potsdam},
  pages     = {viii, 105},
  year      = {2020},
  abstract  = {Giant unilamellar vesicles are an important tool in todays experimental efforts to understand the structure and behaviour of biological cells. Their simple structure allows the isolation of the physical elastic properties of the lipid membrane. A central physical property is the bending energy of the membrane, since the many different shapes of giant vesicles can be obtained by finding the minimum of the bending energy. In the spontaneous curvature model the bending energy is a function of the bending rigidity as well as the mean curvature and an additional parameter called the spontaneous curvature, which describes an internal preference of the lipid-bilayer to bend towards one side or the other. The spontaneous and mean curvature are local properties of the membrane. Additional constraints arise from the conservation of the membrane surface area and the enclosed volume, which are global properties. In this thesis the spontaneous curvature model is used to explain the experimental observation of a periodic shape oscillation of a giant unilamellar vesicle that was filled with a protein complex that periodically binds to and unbinds from the membrane. By assuming that the binding of the proteins to the membrane induces a change in the spontaneous curvature the experimentally observed shapes could successfully be explained. This involves the numerical solution of the differential equations as obtained from the minimization of the bending energy respecting the area and volume constraints, the so called shape equations. Vice versa this approach can be used to estimate the spontaneous curvature from experimentally measurable quantities. The second topic of this thesis is the analysis of concentration gradients in rigid conic membrane compartments. Gradients of an ideal gas due to gravity and gradients generated by the directed stochastic movement of molecular motors along a microtubulus were considered. It was possible to calculate the free energy and the bending energy analytically for the ideal gas. In the case of the non-equilibrium system with molecular motors, the characteristic length of the density profile, the jam-length, and its dependency on the opening angle of the conic compartment have been calculated in the mean-field limit. The mean field results agree qualitatively with stochastic particle simulations.},
  language  = {en}
}
@phdthesis{Mardoukhi2020,
  author    = {Mardoukhi, Yousof},
  title     = {Random environments and the percolation model},
  doi       = {10.25932/publishup-47276},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472762},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xxii, 103},
  year      = {2020},
  abstract  = {Percolation process, which is intrinsically a phase transition process near the critical point, is ubiquitous in nature. Many of its applications embrace a wide spectrum of natural phenomena ranging from the forest fires, spread of contagious diseases, social behaviour dynamics to mathematical finance, formation of bedrocks and biological systems. The topology generated by the percolation process near the critical point is a random (stochastic) fractal. It is fundamental to the percolation theory that near the critical point, a unique infinite fractal structure, namely the infinite cluster, would emerge. As de Gennes suggested, the properties of the infinite cluster could be deduced by studying the dynamical behaviour of the random walk process taking place on it. He coined the term the ant in the labyrinth. The random walk process on such an infinite fractal cluster exhibits a subdiffusive dynamics in the sense that the mean squared displacement grows as ~t2/dw, where dw, called the fractal dimension of the random walk path, is greater than 2. Thus, the random walk process on the infinite cluster is classified as a process exhibiting the properties of anomalous diffusions. Yet near the critical point, the infinite cluster is not the sole emergent topology, but it coexists with other clusters whose size is finite. Though finite, on specific length scales these finite clusters exhibit fractal properties as well. In this work, it is assumed that the random walk process could take place on these finite size objects as well. Bearing this assumption in mind requires one address the non-equilibrium initial condition. Due to the lack of knowledge on the propagator of the random walk process in stochastic random environments, a phenomenological correspondence between the renowned Ornstein-Uhlenbeck process and the random walk process on finite size clusters is established. It is elucidated that when an ensemble of these finite size clusters and the infinite cluster is considered, the anisotropy and size of these finite clusters effects the mean squared displacement and its time averaged counterpart to grow in time as ~t(d+df (t-2))/dw, where d is the embedding Euclidean dimension, df is the fractal dimension of the infinite cluster, and , called the Fisher exponent, is a critical exponent governing the power-law distribution of the finite size clusters. Moreover, it is demonstrated that, even though the random walk process on a specific finite size cluster is ergodic, it exhibits a persistent non-ergodic behaviour when an ensemble of finite size and the infinite clusters is considered.},
  language  = {en}
}
@phdthesis{Landau2020,
  author    = {Landau, Livnat},
  title     = {Mechanical stimulation of in-vitro tissue growth using magnetic beads},
  pages     = {112},
  year      = {2020},
  abstract  = {Cells and tissues are sensitive to mechanical forces applied to them. In particular, bone forming cells and connective tissues, composed of cells embedded in fibrous extracellular matrix (ECM), are continuously remodeled in response to the loads they bear. The mechanoresponses of cells embedded in tissue include proliferation, differentiation, apoptosis, internal signaling between cells, and formation and resorption of tissue. Experimental in-vitro systems of various designs have demonstrated that forces affect tissue growth, maturation and mineralization. However, the results depended on different parameters such as the type and magnitude of the force applied in each study. Some experiments demonstrated that applied forces increase cell proliferation and inhibit cell maturation rate, while other studies found the opposite effect. When the effect of different magnitudes of forces was compared, some studies showed that higher forces resulted in a cell proliferation increase or differentiation decrease, while other studies observed the opposite trend or no trend at all. In this study, MC3T3-E1 cells, a cell line of pre-osteoblasts (bone forming cells), was used. In this cell line, cell differentiation is known to accelerate after cells stop proliferating, typically at confluency. This makes this cell line an interesting subject for studying the influence of forces on the switch between the proliferation stage of the precursor cell and the differentiation to the mature osteoblasts. A new experimental system was designed to perform systematic investigations of the influence of the type and magnitude of forces on tissue growth. A single well plate contained an array of 80 rectangular pores. Each pore was seeded with MC3T3-E1 cells. The culture medium contained magnetic beads (MBs) of 4.5 μm in diameter that were incorporated into the pre-osteoblast cells. Using an N52 neodymium magnet, forces ranging over three orders of magnitude were applied to MBs incorporated in cells at 10 different distances from the magnet. The amount of formed tissue was assessed after 24 days of culture. The experimental design allowed to obtain data concerning (i) the influence of the type of the force (static, oscillating, no force) on tissue growth; (ii) the influence of the magnitude of force (pN-nN range); (iii) the effect of functionalizing the magnetic beads with the tripeptide Arg-Gly-Asp (RGD). To learn about cell differentiation state, in the final state of the tissue growth experiments, an analysis for the expression of alkaline phosphatase (ALP), a well - known marker of osteoblast differentiation, was performed. The experiments showed that the application of static magnetic forces increased tissue growth compared to control, while oscillating forces resulted in tissue growth reduction. A statistically significant positive correlation was found between the amount of tissue grown and the magnitude of the oscillating magnetic force. A positive but non-significant correlation of the amount of tissue with the magnitude of forces was obtained when static forces were applied. Functionalizing the MBs with RGD peptides and applying oscillating forces resulted in an increase of tissue growth relative to tissues incubated with "plain" epoxy MBs. ALP expression decreased as a function of the magnitude of force both when static and oscillating forces were applied. ALP stain intensity was reduced relative to control when oscillating forces were applied and was not significantly different than control for static forces. The suggested interpretation of the experimental findings is that larger mechanical forces delay cell maturation and keep the pre-osteoblasts in a more proliferative stage characterized by more tissue formed and lower expression of ALP. While the influence of the force magnitude can be well explained by an effect of the force on the switch between proliferation and differentiation, the influence of force type (static or oscillating) is less clear. In particular, it is challenging to reconcile the reduction of tissue formed under oscillating forces as compared to controls with the simultaneous reduction of ALP expression. To better understand this, it may be necessary to refine the staining protocol of the scaffolds and to include the amount and structure of ECM as well as other factors that were not monitored in the experiment and which may influence tissue growth and maturation. The developed experimental system proved well suited for a systematic and efficient study of the mechanoresponsiveness of tissue growth, it allowed a study of the dependence of tissue growth on force magnitude ranging over three orders of magnitude, and a comparison between the effect of static and oscillating forces. Future experiments can explore the multiple parameters that affect tissue growth as a function of the magnitude of the force: by applying different time-dependent forces; by extending the force range studied; or by using different cell lines and manipulating the mechanotransduction in the cells biochemically.},
  language  = {en}
}
@phdthesis{Sposini2020,
  author    = {Sposini, Vittoria},
  title     = {The random diffusivity approach for diffusion in heterogeneous systems},
  doi       = {10.25932/publishup-48780},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-487808},
  school      = {Universit{\"a}t Potsdam},
  year      = {2020},
  abstract  = {The two hallmark features of Brownian motion are the linear growth < x2(t)> = 2Ddt of the mean squared displacement (MSD) with diffusion coefficient D in d spatial dimensions, and the Gaussian distribution of displacements. With the increasing complexity of the studied systems deviations from these two central properties have been unveiled over the years. Recently, a large variety of systems have been reported in which the MSD exhibits the linear growth in time of Brownian (Fickian) transport, however, the distribution of displacements is pronouncedly non-Gaussian (Brownian yet non-Gaussian, BNG). A similar behaviour is also observed for viscoelastic-type motion where an anomalous trend of the MSD, i.e., <x2(t)> ~ ta, is combined with a priori unexpected non-Gaussian distributions (anomalous yet non-Gaussian, ANG). This kind of behaviour observed in BNG and ANG diffusions has been related to the presence of heterogeneities in the systems and a common approach has been established to address it, that is, the random diffusivity approach. This dissertation explores extensively the field of random diffusivity models. Starting from a chronological description of all the main approaches used as an attempt of describing BNG and ANG diffusion, different mathematical methodologies are defined for the resolution and study of these models. The processes that are reported in this work can be classified in three subcategories, i) randomly-scaled Gaussian processes, ii) superstatistical models and iii) diffusing diffusivity models, all belonging to the more general class of random diffusivity models. Eventually, the study focuses more on BNG diffusion, which is by now well-established and relatively well-understood. Nevertheless, many examples are discussed for the description of ANG diffusion, in order to highlight the possible scenarios which are known so far for the study of this class of processes. The second part of the dissertation deals with the statistical analysis of random diffusivity processes. A general description based on the concept of moment-generating function is initially provided to obtain standard statistical properties of the models. Then, the discussion moves to the study of the power spectral analysis and the first passage statistics for some particular random diffusivity models. A comparison between the results coming from the random diffusivity approach and the ones for standard Brownian motion is discussed. In this way, a deeper physical understanding of the systems described by random diffusivity models is also outlined. To conclude, a discussion based on the possible origins of the heterogeneity is sketched, with the main goal of inferring which kind of systems can actually be described by the random diffusivity approach.},
  language  = {en}
}
@phdthesis{Knigge2020,
  author    = {Knigge, Xenia},
  title     = {Einzelmolek{\"u}l-Manipulation mittels Nano-Elektroden und Dielektrophorese},
  doi       = {10.25932/publishup-44313},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-443137},
  school      = {Universit{\"a}t Potsdam},
  pages     = {106, xxxii},
  year      = {2020},
  abstract  = {In dieser Arbeit wurden Nano-Elektroden-Arrays zur Einzel-Objekt-Immobilisierung mittels Dielektrophorese verwendet. Hierbei wurden fluoreszenzmarkierte Nano-Sph{\"a}ren als Modellsystem untersucht und die gewonnenen Ergebnisse auf biologische Proben {\"u}bertragen. Die Untersuchungen in Kombination mit verschiedenen Elektrodenlayouts f{\"u}hrten zu einer deterministischen Vereinzelung der Nano-Sph{\"a}ren ab einem festen Gr{\"o}ßenverh{\"a}ltnis zwischen Nano-Sph{\"a}re und Durchmesser der Elektrodenspitzen. An den Proteinen BSA und R-PE konnte eine dielektrophoretische Immobilisierung ebenfalls demonstriert und R-PE Molek{\"u}le zur Vereinzelung gebracht werden. Hierf{\"u}r war neben einem optimierten Elektrodenlayout, das durch Feldsimulationen den Feldgradienten betreffend gesucht wurde, eine Optimierung der Feldparameter, insbesondere von Spannung und Frequenz, erforderlich. Neben der Dielektrophorese erfolgten auch Beobachtungen anderer Effekte des elektrischen Feldes, wie z.B. Elektrolyse an Nano-Elektroden und Str{\"o}mungen {\"u}ber dem Elektroden-Array, hervorgerufen durch Joulesche W{\"a}rme und AC-elektroosmotischen Fluss. Zudem konnte Dielektrophorese an Silberpartikeln beobachtet werden und mittels Fluoreszenz-, Atom-Kraft-, Raster-Elektronen-Mikroskopie und energiedispersiver R{\"o}ntgenspektroskopie untersucht werden. Schließlich wurden die verwendeten Objektive und Kameras auf ihre Lichtempfindlichkeit hin analysiert, so dass die Vereinzelung von Biomolek{\"u}len an Nano-Elektroden nachweisbar war. Festzuhalten bleibt also, dass die Vereinzelung von Nano-Objekten und Biomolek{\"u}len an Nano-Elektroden-Arrays gelungen ist. Durch den parallelen Ansatz erlaubt dies, Aussagen {\"u}ber das Verhalten von Einzelmolek{\"u}len mit guter Statistik zu treffen.},
  language  = {de}
}
@phdthesis{Graetz2020,
  author    = {Gr{\"a}tz, Fabio M.},
  title     = {Nonlinear diffusion in granular gases and dense planetary rings},
  school      = {Universit{\"a}t Potsdam},
  pages     = {101},
  year      = {2020},
  abstract  = {Small moonlets or moons embedded in dense planetary rings create S-shaped density modulations called propellers if their masses are smaller than a certain threshold, alternatively they create a circumferential gap in the disk if the embedded body's mass exceeds this threshold (Spahn and Sremčević, 2000). The gravitational perturber scatters the ring particles, depletes the disk's density, and, thus, clears a gap, whereas counteracting viscous diffusion of the ring material has the tendency to close the created gap, thereby forming a propeller. Propeller objects were predicted by Spahn and Sremčević (2000) and Sremčević et al. (2002) and were later discovered by the Cassini space probe (Tiscareno et al., 2006, Sremčević et al., 2007, Tiscareno et al., 2008, and Tiscareno et al., 2010). The ring moons Pan and Daphnis are massive enough to maintain the circumferential Encke and Keeler gaps in Saturn's A ring and were detected by Showalter (1991) and Porco (2005) in Voyager and Cassini images, respectively. In this thesis, a nonlinear axisymmetric diffusion model is developed to describe radial density profiles of circumferential gaps in planetary rings created by embedded moons (Grätz et al., 2018). The model accounts for the gravitational scattering of the ring particles by the embedded moon and for the counteracting viscous diffusion of the ring matter back into the gap. With test particle simulations it is shown that the scattering of the ring particles passing the moon is larger for small impact parameters than estimated by Goldreich and Tremaine (1980). This is especially significant for the modeling of the Keeler gap. The model is applied to the Encke and Keeler gaps with the aim to estimate the shear viscosity of the ring in their vicinities. In addition, the model is used to analyze whether tiny icy moons whose dimensions lie below Cassini's resolution capabilities would be able to cause the poorly understood gap structure of the C ring and the Cassini Division. One of the most intriguing facets of Saturn's rings are the extremely sharp edges of the Encke and Keeler gaps: UVIS-scans of their gap edges show that the optical depth drops from order unity to zero over a range of far less than 100 m, a spatial scale comparable to the ring's vertical extent. This occurs despite the fact that the range over which a moon transfers angular momentum onto the ring material is much larger. Borderies et al. (1982, 1989) have shown that this striking feature is likely related to the local reversal of the usually outward-directed viscous transport of angular momentum in strongly perturbed regions. We have revised the Borderies et al. (1989) model using a granular flow model to define the shear and bulk viscosities, ν and ζ, in order to incorporate the angular momentum flux reversal effect into the axisymmetric diffusion model for circumferential gaps presented in this thesis (Grätz et al., 2019). The sharp Encke and Keeler gap edges are modeled and conclusions regarding the shear and bulk viscosities of the ring are discussed. Finally, we explore the question of whether the radial density profile of the central and outer A ring, recently measured by Tiscareno and Harris (2018) in the highest resolution to date, and in particular, the sharp outer A ring edge can be modeled consistently from the balance of gravitational scattering by several outer moons and the mass and momentum transport. To this aim, the developed model is extended to account for the inward drifts caused by multiple discrete and overlapping resonances with multiple outer satellites and is then used to hydrodynamically simulate the normalized surface mass density profile of the A ring. This section of the thesis is based on studies by Tajeddine et al. (2017a) who recently discussed the common misconception that the 7:6 resonance with Janus alone maintains the outer A ring edge, showing that the combined effort of several resonances with several outer moons is required to confine the A ring as observed by the Cassini spacecraft.},
  language  = {en}
}