@phdthesis{Spallanzani2022,
  author    = {Spallanzani, Roberta},
  title     = {Li and B in ascending magmas: an experimental study on their mobility and isotopic fractionation},
  doi       = {10.25932/publishup-56061},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-560619},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xiv, 131},
  year      = {2022},
  abstract  = {This research study focuses on the behaviour of Li and B during magmatic ascent, and decompression-driven degassing related to volcanic systems. The main objective of this dissertation is to determine whether it is possible to use the diffusion properties of the two trace elements as a tool to trace magmatic ascent rate. With this objective, diffusion-couple and decompression experiments have been performed in order to study Li and B mobility in intra-melt conditions first, and then in an evolving system during decompression-driven degassing. Synthetic glasses were prepared with rhyolitic composition and an initial water content of 4.2 wt\%, and all the experiments were performed using an internally heated pressure vessel, in order to ensure a precise control on the experimental parameters such as temperature and pressure. Diffusion-couple experiments were performed with a fix pressure 300 MPa. The temperature was varied in the range of 700-1250 °C with durations between 0 seconds and 24 hours. The diffusion-couple results show that Li diffusivity is very fast and starts already at very low temperature. Significant isotopic fractionation occurs due to the faster mobility of 6Li compared to 7Li. Boron diffusion is also accelerated by the presence of water, but the results of the isotopic ratios are unclear, and further investigation would be necessary to well constrain the isotopic fractionation process of boron in hydrous silicate melts. The isotopic ratios results show that boron isotopic fractionation might be affected by the speciation of boron in the silicate melt structure, as 10B and 11B tend to have tetrahedral and trigonal coordination, respectively. Several decompression experiments were performed at 900 °C and 1000 °C, with pressures going from 300 MPa to 71-77 MPa and durations of 30 minutes, two, five and ten hours, in order to trigger water exsolution and the formation of vesicles in the sample. Textural observations and the calculation of the bubble number density confirmed that the bubble size and distribution after decompression is directly proportional to the decompression rate. The overall SIMS results of Li and B show that the two trace elements tend to progressively decrease their concentration with decreasing decompression rates. This is explained because for longer decompression times, the diffusion of Li and B into the bubbles has more time to progress and the melt continuously loses volatiles as the bubbles expand their volumes. For fast decompression, Li and B results show a concentration increase with a δ7Li and δ11B decrease close to the bubble interface, related to the sudden formation of the gas bubble, and the occurrence of a diffusion process in the opposite direction, from the bubble meniscus to the unaltered melt. When the bubble growth becomes dominant and Li and B start to exsolve into the gas phase, the silicate melt close to the bubble gets depleted in Li and B, because of a stronger diffusion of the trace elements into the bubble. Our data are being applied to different models, aiming to combine the dynamics of bubble nucleation and growth with the evolution of trace elements concentration and isotopic ratios. Here, first considerations on these models will be presented, giving concluding remarks on this research study. All in all, the final remarks constitute a good starting point for further investigations. These results are a promising base to continue to study this process, and Li and B can indeed show clear dependences on decompression-related magma ascent rates in volcanic systems.},
  language  = {en}
}
@phdthesis{Hennig2022,
  author    = {Hennig, Theresa},
  title     = {Uranium migration in the Opalinus Clay quantified on the host rock scale with reactive transport simulations},
  doi       = {10.25932/publishup-55270},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-552700},
  school      = {Universit{\"a}t Potsdam},
  pages     = {161},
  year      = {2022},
  abstract  = {Humankind and their environment need to be protected from the harmful effects of spent nuclear fuel, and therefore disposal in deep geological formations is favoured worldwide. Suitability of potential host rocks is evaluated, among others, by the retention capacity with respect to radionuclides. Safety assessments are based on the quantification of radionuclide migration lengths with numerical simulations as experiments cannot cover the required temporal (1 Ma) and spatial scales (>100 m). Aim of the present thesis is to assess the migration of uranium, a geochemically complex radionuclide, in the potential host rock Opalinus Clay. Radionuclide migration in clay formations is governed by diffusion due to their low permeability and retarded by sorption. Both processes highly depend on pore water geochemistry and mineralogy that vary between different facies. Diffusion is quantified with the single-component (SC) approach using one diffusion coefficient for all species and the process-based multi-component (MC) option. With this, each species is assigned its own diffusion coefficient and the interaction with the diffuse double layer is taken into account. Sorption is integrated via a bottom-up approach using mechanistic surface complexation models and cation exchange. Therefore, reactive transport simulations are conducted with the geochemical code PHREEQC to quantify uranium migration, i.e. diffusion and sorption, as a function of mineralogical and geochemical heterogeneities on the host rock scale. Sorption processes are facies dependent. Migration lengths vary between the Opalinus Clay facies by up to 10 m. Thereby, the geochemistry of the pore water, in particular the partial pressure of carbon dioxide (pCO2), is more decisive for the sorption capacity than the amount of clay minerals. Nevertheless, higher clay mineral quantities compensate geochemical variations. Consequently, sorption processes must be quantified as a function of pore water geochemistry in contact with the mineral assemblage. Uranium diffusion in the Opalinus Clay is facies independent. Speciation is dominated by aqueous ternary complexes of U(VI) with calcium and carbonate. Differences in the migration lengths between SC and MC diffusion are with +/-5 m negligible. Further, the application of the MC approach highly depends on the quality and availability of the underlying data. Therefore, diffusion processes can be adequately quantified with the SC approach using experimentally determined diffusion coefficients. The hydrogeological system governs pore water geochemistry within the formation rather than the mineralogy. Diffusive exchange with the adjacent aquifers established geochemical gradients over geological time scales that can enhance migration by up to 25 m. Consequently, uranium sorption processes must be quantified following the identified priority: pCO2 > hydrogeology > mineralogy. The presented research provides a workflow and orientation for other potential disposal sites with similar pore water geochemistry due to the identified mechanisms and dependencies. With a maximum migration length of 70 m, the retention capacity of the Opalinus Clay with respect to uranium is sufficient to fulfill the German legal minimum requirement of a thickness of at least 100 m.},
  language  = {en}
}
@phdthesis{Šustr2020,
  author    = {Šustr, David},
  title     = {Molecular diffusion in polyelectrolyte multilayers},
  doi       = {10.25932/publishup-48903},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-489038},
  school      = {Universit{\"a}t Potsdam},
  pages     = {106},
  year      = {2020},
  abstract  = {Research on novel and advanced biomaterials is an indispensable step towards their applications in desirable fields such as tissue engineering, regenerative medicine, cell culture, or biotechnology. The work presented here focuses on such a promising material: polyelectrolyte multilayer (PEM) composed of hyaluronic acid (HA) and poly(L-lysine) (PLL). This gel-like polymer surface coating is able to accumulate (bio-)molecules such as proteins or drugs and release them in a controlled manner. It serves as a mimic of the extracellular matrix (ECM) in composition and intrinsic properties. These qualities make the HA/PLL multilayers a promising candidate for multiple bio-applications such as those mentioned above. The work presented aims at the development of a straightforward approach for assessment of multi-fractional diffusion in multilayers (first part) and at control of local molecular transport into or from the multilayers by laser light trigger (second part). The mechanism of the loading and release is governed by the interaction of bioactives with the multilayer constituents and by the diffusion phenomenon overall. The diffusion of a molecule in HA/PLL multilayers shows multiple fractions of different diffusion rate. Approaches, that are able to assess the mobility of molecules in such a complex system, are limited. This shortcoming motivated the design of a novel evaluation tool presented here. The tool employs a simulation-based approach for evaluation of the data acquired by fluorescence recovery after photobleaching (FRAP) method. In this approach, possible fluorescence recovery scenarios are primarily simulated and afterwards compared with the data acquired while optimizing parameters of a model until a sufficient match is achieved. Fluorescent latex particles of different sizes and fluorescein in an aqueous medium are utilized as test samples validating the analysis results. The diffusion of protein cytochrome c in HA/PLL multilayers is evaluated as well. This tool significantly broadens the possibilities of analysis of spatiotemporal FRAP data, which originate from multi-fractional diffusion, while striving to be widely applicable. This tool has the potential to elucidate the mechanisms of molecular transport and empower rational engineering of the drug release systems. The second part of the work focuses on the fabrication of such a spatiotemporarily-controlled drug release system employing the HA/PLL multilayer. This release system comprises different layers of various functionalities that together form a sandwich structure. The bottom layer, which serves as a reservoir, is formed by HA/PLL PEM deposited on a planar glass substrate. On top of the PEM, a layer of so-called hybrids is deposited. The hybrids consist of thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) -based hydrogel microparticles with surface-attached gold nanorods. The layer of hybrids is intended to serve as a gate that controls the local molecular transport through the PEM-solution-interface. The possibility of stimulating the molecular transport by near-infrared (NIR) laser irradiation is being explored. From several tested approaches for the deposition of hybrids onto the PEM surface, the drying-based approach was identified as optimal. Experiments, that examine the functionality of the fabricated sandwich at elevated temperature, document the reversible volume phase transition of the PEM-attached hybrids while sustaining the sandwich stability. Further, the gold nanorods were shown to effectively absorb light radiation in the tissue- and cell-friendly NIR spectral region while transducing the energy of light into heat. The rapid and reversible shrinkage of the PEM-attached hybrids was thereby achieved. Finally, dextran was employed as a model transport molecule. It loads into the PEM reservoir in a few seconds with the partition constant of 2.4, while it spontaneously releases in a slower, sustained manner. The local laser irradiation of the sandwich, which contains the fluorescein isothiocyanate tagged dextran, leads to a gradual reduction of fluorescence intensity in the irradiated region. The release system fabricated employs renowned photoresponsivity of the hybrids in an innovative setting. The results of the research are a step towards a spatially-controlled on-demand drug release system that paves the way to spatiotemporally controlled drug release. The approaches developed in this work have the potential to elucidate the molecular dynamics in ECM and to foster engineering of multilayers with properties tuned to mimic the ECM. The work aims at spatiotemporal control over the diffusion of bioactives and their presentation to the cells.},
  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{Kneier2019,
  author    = {Kneier, Fabian},
  title     = {Subsea permafrost in the Laptev Sea},
  school      = {Universit{\"a}t Potsdam},
  pages     = {220},
  year      = {2019},
  abstract  = {During lower sea levels in glacial periods, deep permafrost formed on large continental shelf areas of the Arctic Ocean. Subsequent sea level rise and coastal erosion created subsea permafrost, which generally degrades after inundation under the influence of a complex suite of marine, near-shore processes. Global warming is especially pronounced in the Arctic, and will increase the transition to and the degradation of subsea permafrost, with implications for atmospheric climate forcing, offshore infrastructure, and aquatic ecosystems. This thesis combines new geophysical, borehole observational and modelling approaches to enhance our understanding of subsea permafrost dynamics. Three specific areas for advancement were identified: (I) sparsity of observational data, (II) lacking implementation of salt infiltration mechanisms in models, and (III) poor understanding of the regional differences in key driving parameters. This study tested the combination of spectral ratios of the ambient vibration seismic wavefield, together with estimated shear wave velocity from seismic interferometry analysis, for estimating the thickness of the unfrozen sediment overlying the ice-bonded permafrost offshore. Mesoscale numerical calculations (10^1 to 10^2 m, thousands of years) were employed to develop and solve the coupled heat diffusion and salt transport equations including phase change effects. Model soil parameters were constrained by borehole data, and the impact of a variety of influences during the transgression was tested in modelling studies. In addition, two inversion schemes (particle swarm optimization and a least-square method) were used to reconstruct temperature histories for the past 200-300 years in the Laptev Sea region in Siberia from two permafrost borehole temperature records. These data were evaluated against larger scale reconstructions from the region. It was found (I) that peaks in spectral ratios modelled for three-layer, one-dimensional systems corresponded with thaw depths. Around Muostakh Island in the central Laptev Sea seismic receivers were deployed on the seabed. Derived depths of the ice-bonded permafrost table were between 3.7-20.7 m ± 15 \%, increasing with distance from the coast. (II) Temperatures modelled during the transition to subsea permafrost resembled isothermal conditions after about 2000 years of inundation at Cape Mamontov Klyk, consistent with observations from offshore boreholes. Stratigraphic scenarios showed that salt distribution and infiltration had a large impact on the ice saturation in the sediments. Three key factors were identified that, when changed, shifted the modelled permafrost thaw depth most strongly: bottom water temperatures, shoreline retreat rate and initial temperature before inundation. Salt transport based on diffusion and contribution from arbitrary density-driven mechanisms only accounted for about 50 \% of observed thaw depths at offshore sites hundreds to thousands of years after inundation. This bias was found consistently at all three sites in the Laptev Sea region. (III) In the temperature reconstructions, distinct differences in the local temperature histories between the western Laptev Sea and the Lena Delta sites were recognized, such as a transition to warmer temperatures a century later in the western Laptev Sea as well as a peak in warming three decades later. The local permafrost surface temperature history at Sardakh Island in the Lena Delta was reminiscent of the circum-Arctic regional average trends. However, Mamontov Klyk in the western Laptev Sea was consistent to Arctic trends only in the most recent decade and was more similar to northern hemispheric mean trends. Both sites were consistent with a rapid synoptic recent warming. In conclusion, the consistency between modelled response, expected permafrost distribution, and observational data suggests that the passive seismic method is promising for the determination of the thickness of unfrozen sediment on the continental Arctic shelf. The quantified gap between currently modelled and observed thaw depths means that the impact of degradation on climate forcing, ecosystems, and infrastructure is larger than current models predict. This discrepancy suggests the importance of further mechanisms of salt penetration and thaw that have not been considered - either pre-inundation or post-inundation, or both. In addition, any meaningful modelling of subsea permafrost would have to constrain the identified key factors and their regional differences well. The shallow permafrost boreholes provide missing well-resolved short-scale temperature information in the coastal permafrost tundra of the Arctic. As local differences from circum-Arctic reconstructions, such as later warming and higher warming magnitude, were shown to exist in this region, these results provide a basis for local surface temperature record parameterization of climate and, in particular, permafrost models. The results of this work bring us one step further to understanding the full picture of the transition from terrestrial to subsea permafrost.},
  language  = {en}
}
@phdthesis{Roder2018,
  author    = {Roder, Phillip},
  title     = {Kombination von Fluoreszenzmikroskopie und Rasterkraftmikroskopie zur Aufkl{\"a}rung physiologischer Prozesse in lebenden Zellen},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-419806},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xvi, 113},
  year      = {2018},
  abstract  = {Innerhalb dieser Doktorarbeit wurde eine neuartige Mikromanipulationstechnik f{\"u}r die lokale Fl{\"u}ssigkeitsabgabe am komplexen Dr{\"u}sengewebe der Schabe P. americana charakterisiert und f{\"u}r die damit verbundene gezielte Manipulation von einzelnen Zellen in einem Zellkomplex (Gewebe) angewandt. Bei dieser Mikromanipulationstechnik handelt es sich um die seit 2009 bekannte nanofluidische Rasterkraftmikroskopie (FluidFM = fluidic force microscopy). Dabei werden sehr kleine mikrokan{\"a}lige Rasterkraftspitzen bzw. Mikro-/Nanopipetten mit einer {\"O}ffnung zwischen 300 nm und 2 µm verwendet, mit denen es m{\"o}glich ist, sehr kleine Volumina im Pikoliter- bis Femtoliter-Bereich (10-12 L - 10-15 L) gezielt und ortsgenau abzugeben. Das Ziel dieser Arbeit war die Analyse zellul{\"a}rer Prozesse, wie z. B. Zell-Zell-Kommunikation oder Signalweiterleitung, zwischen benachbarten Zellen unter Zuhilfenahme der Fluoreszenzmikroskopie. Mit dieser Methode k{\"o}nnen die Zellen und ihre Bestandteile mittels vorheriger Farbstoffbeladung unter einem Mikroskop mit hohem Kontrast optisch dargestellt werden. Mit Hilfe der Fluoreszenzmikroskopie sollten schlussendlich die zellul{\"a}ren Reaktionen innerhalb des Gewebes nach der lokalen Manipulation visualisiert werden. Zun{\"a}chst wurde die Anwendung des Systems an Luft und w{\"a}ssriger Umgebung beschrieben. In diesem Zusammenhang wurde eine Reinigungs- und Beladungsmethode entwickelt, mit der es m{\"o}glich war, die kostspieligen Mikro-/Nanopipetten zu reinigen und anschließend mehrmals wiederzuverwenden. Hierzu wurde eine alternative Methode getestet, mit der das Diffusionsverhalten von Farbstoffmolek{\"u}len in unterschiedlichen Medien untersucht werden kann. Des Weiteren wurden die Systemparameter optimiert, welche n{\"o}tig sind, um zwischen der Probenoberfl{\"a}che und der Pipette einen guten Pipetten{\"o}ffnungs-abschluss zu erhalten. Dieser Abschluss ist essentiell, damit die abgegebene Fl{\"u}ssigkeit ausschließlich in der Abgaberegion mit der Probe wechselwirkt und die darauffolgenden Reaktionen nur innerhalb des Gewebes erfolgen, da ansonsten die Zell-Zell-Signalweiterleitung zwischen den Zellen nicht eindeutig nachvollzogen werden kann. Diese interzellul{\"a}re Kommunikation wurde anhand zweier sekund{\"a}rer Botenstoffe (Ca2+ und NO) untersucht. Hierbei war es m{\"o}glich einzelne lokale Reaktionen zu detektieren, welche sich {\"u}ber weitere Zellen ausbreiteten. Schlussendlich wurde die Fertigung einer speziellen Injektionspipette beschrieben, welche an zwei biologischen Systemen getestet wurde.},
  language  = {de}
}
@phdthesis{Kruesemann2016,
  author    = {Kr{\"u}semann, Henning},
  title     = {First passage phenomena and single-file motion in ageing continuous time random walks and quenched energy landscapes},
  school      = {Universit{\"a}t Potsdam},
  pages     = {122},
  year      = {2016},
  abstract  = {In der Physik gibt es viele Prozesse, die auf Grund ihrer Komplexit{\"a}t nicht durch physikalische Gleichungen beschrieben werden k{\"o}nnen, beispielsweise die Bewegung eines Staubkorns in der Luft. Durch die vielen St{\"o}ße mit Luftmolek{\"u}len f{\"u}hrt es eine Zufallsbewegung aus, die so genannte Diffusion. Auch Molek{\"u}le in biologischen Zellen diffundieren, jedoch befinden sich in einer solchen Zelle im selben Volumen viel mehr oder viel gr{\"o}ßere Molek{\"u}le. Das beobachtete Teilchen st{\"o}ßt dementsprechend {\"o}fter mit anderen zusammen und die Diffusion wird langsamer, sie wird subdiffusiv. Mit der Zeit kann sich die Charakteristik der Subdiffusion {\"a}ndern; dies wird als (mikroskopisches) Altern bezeichnet. Ich untersuche in der vorliegenden Arbeit zwei mathematische Modelle f{\"u}r eindimensionale Subdiffusion, einmal den continuous time random walk (CTRW) und einmal die Zufallsbewegung in einer eingefrorenen Energielandschaft (QEL=quenched energy landscape). Beide sind Sprungprozesse, das heißt, sie sind Abfolgen von r{\"a}umlichen Spr{\"u}ngen, die durch zufallsverteilte Wartezeiten getrennt sind. Die Wartezeiten in der QEL sind r{\"a}umlich korrelliert, w{\"a}hrend sie im CTRW unkorrelliert sind. Ich untersuche in der vorliegenden Arbeit verschiedene statistische Gr{\"o}ßen in beiden Modellen. Zun{\"a}chst untersuche ich den Einfluss des Alters und den Einfluss der Korrellationen einer QEL auf die Verteilung der Zeiten, die das diffundierendes Teilchen ben{\"o}tigt, um eine (r{\"a}umliche) Schwelle zu {\"u}berqueren. Ausserdem bestimme ich den Effekt des Alters auf Str{\"o}me von (sub)diffundierenden Partikeln, die sich auf eine absorbierende Barriere zubewegen. Zuletzt besch{\"a}ftige ich mich mit der Diffusion einer eindimensionalen Anordnung von Teilchen in einer QEL, in der diese als harte Kugeln miteinander wechselwirken. Dabei vergleiche ich die gemeinsame Bewegung in einer QEL und als individuelle CTRWs miteinander {\"u}ber die Standartabweichung von der Startposition, f{\"u}r die ich das Mittel {\"u}ber mehrere QELs untersuche. Meine Arbeit setzt sich zusammen aus theoretischen {\"U}berlegungen und Berechnungen sowie der Simulation der Zufallsprozesse. Die Ergebnisse der Simulation und, soweit vorhanden, experimentelle Daten werden mit der Theorie verglichen.},
  language  = {en}
}
@phdthesis{Mulansky2012,
  author    = {Mulansky, Mario},
  title     = {Chaotic diffusion in nonlinear Hamiltonian systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63180},
  school      = {Universit{\"a}t Potsdam},
  year      = {2012},
  abstract  = {This work investigates diffusion in nonlinear Hamiltonian systems. The diffusion, more precisely subdiffusion, in such systems is induced by the intrinsic chaotic behavior of trajectories and thus is called chaotic diffusion''. Its properties are studied on the example of one- or two-dimensional lattices of harmonic or nonlinear oscillators with nearest neighbor couplings. The fundamental observation is the spreading of energy for localized initial conditions. Methods of quantifying this spreading behavior are presented, including a new quantity called excitation time. This new quantity allows for a more precise analysis of the spreading than traditional methods. Furthermore, the nonlinear diffusion equation is introduced as a phenomenologic description of the spreading process and a number of predictions on the density dependence of the spreading are drawn from this equation. Two mathematical techniques for analyzing nonlinear Hamiltonian systems are introduced. The first one is based on a scaling analysis of the Hamiltonian equations and the results are related to similar scaling properties of the NDE. From this relation, exact spreading predictions are deduced. Secondly, the microscopic dynamics at the edge of spreading states are thoroughly analyzed, which again suggests a scaling behavior that can be related to the NDE. Such a microscopic treatment of chaotically spreading states in nonlinear Hamiltonian systems has not been done before and the results present a new technique of connecting microscopic dynamics with macroscopic descriptions like the nonlinear diffusion equation. All theoretical results are supported by heavy numerical simulations, partly obtained on one of Europe's fastest supercomputers located in Bologna, Italy. In the end, the highly interesting case of harmonic oscillators with random frequencies and nonlinear coupling is studied, which resembles to some extent the famous Discrete Anderson Nonlinear Schroedinger Equation. For this model, a deviation from the widely believed power-law spreading is observed in numerical experiments. Some ideas on a theoretical explanation for this deviation are presented, but a conclusive theory could not be found due to the complicated phase space structure in this case. Nevertheless, it is hoped that the techniques and results presented in this work will help to eventually understand this controversely discussed case as well.},
  language  = {en}
}
@phdthesis{Klumpp2003,
  author    = {Klumpp, Stefan},
  title     = {Movements of molecular motors : diffusion and directed walks},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-0000806},
  school      = {Universit{\"a}t Potsdam},
  year      = {2003},
  abstract  = {Bewegungen von prozessiven molekularen Motoren des Zytoskeletts sind durch ein Wechselspiel von gerichteter Bewegung entlang von Filamenten und Diffusion in der umgebenden L{\"o}sung gekennzeichnet. Diese eigent{\"u}mlichen Bewegungen werden in der vorliegenden Arbeit untersucht, indem sie als Random Walks auf einem Gitter modelliert werden. Ein weiterer Gegenstand der Untersuchung sind Effekte von Wechselwirkungen zwischen den Motoren auf diese Bewegungen. Im einzelnen werden vier Transportph{\"a}nomene untersucht: (i) Random Walks von einzelnen Motoren in Kompartimenten verschiedener Geometrien, (ii) station{\"a}re Konzentrationsprofile, die sich in geschlossenen Kompartimenten infolge dieser Bewegungen einstellen, (iii) randinduzierte Phasen{\"u}berg{\"a}nge in offenen r{\"o}hrenartigen Kompartimenten, die an Motorenreservoirs gekoppelt sind, und (iv) der Einfluß von kooperativen Effekten bei der Motor-Filament-Bindung auf die Bewegung. Alle diese Ph{\"a}nomene sind experimentell zug{\"a}nglich, und m{\"o}gliche experimentelle Realisierungen werden diskutiert.},
  language  = {en}
}