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In the first part of my work I have investigated the ageing properties of the first passage time distributions in a one-dimensional subdiffusive continuous time random walk with power law distributed waiting times of the form $\psi(\tau) \sim \tau^{-1-\alpha}$ with $0<\alpha<1$ and $1<\alpha<2$. The age or ageing time $t_a$ is the time span from the start of the stochastic process to the start of the observation of this process (at $t=0$). I have calculated the results for a single target and two targets, also including the biased case, where the walker is driven towards the boundary by a constant force. I have furthermore refined the previously derived results for the non-ageing case and investigated the changes that occur when the walk is performed in a discrete quenched energy landscape, where the waiting times are fixed for every site. The results include the exact Laplace space densities and infinite (converging) series as exact results in the time space. The main results are the dominating long time power law behavior regimes, which depend on the ageing time. For the case of unbiased subdiffusion ($\alpha < 1$) in the presence of one target, I find three different dominant terms for ranges of $t$ separated by $t_a$ and another crossover time $t^{\star}$, which depends on $t_a$ as well as on the anomalous exponent $\alpha$ and the anomalous diffusion coefficient $K_{\alpha}$. In all three regimes ($t \ll t_a$, $t_a \ll t \ll t^{\star}$, $t \gg t^{\star}$) one finds power law decay with exponents depending on $\alpha$. The middle regime only exists for $t_a \ll t^{\star}$. The dominant terms in the first two regimes (ageing regimes) come from the probability distribution of the forward waiting time, the time one has to wait for the stochastic process to make the first step during the observation. When the observation time is larger than the second crossover time $t^{\star}$, the first passage time density does not show ageing and the non-ageing first passage time dominates. The power law exponents in the respective regimes are $-\alpha$ for strong ageing, $-1-\alpha$ in the intermediate regime, and $-1-\alpha/2$ in the final non-ageing regime. A similar split into three regimes can be found for $1<\alpha<2$, only with a different second crossover time $t^*$. In this regime the diffusion is normal but also age-dependent. For the diffusion in quenched energy landscapes one cannot detect ageing. The first passage time density shows a quenched power law $^\sim t^{-(1+2\alpha)/(1+\alpha)}$. For diffusion between two target sites and the biased diffusion towards a target only two scaling regimes emerge, separated by the ageing time. In the ageing case $t \ll t_a$ the forward waiting time is again dominant with power law exponent $-\alpha$, while the non-ageing power law $-1-\alpha$ is found for all times $t \gg t_a$. An intermediate regime does not exist. The bias and the confinement have similar effects on the first passage time density. For quenched diffusion, the biased case is interesting, as the bias reduces correlations due to revisiting of the same waiting time. As a result, CTRW like behavior is observed, including ageing. Extensive computer simulations support my findings.
The second part of my research was done on the subject of ageing Scher-Montroll transport, which is in parts closely related to the first passage densities. It explains the electrical current in an amorphous material. I have investigated the effect of the width of a given initial distribution of charge carriers on the transport coefficients as well as the ageing effect on the emerging power law regimes and a constant initial regime. While a spread out initial distribution has only little impact on the Scher-Montroll current, ageing alters the behavior drastically. Instead of the two classical power laws one finds four current regimes, up to three of which can appear in a single experiment. The dominant power laws differ for $t \ll t_a, t_c$, $t_a \ll t \ll t_c$, $t_c \ll t \ll t_a$, and $t \gg t_a,t_c$. Here, $t_c$ is the crossover time of the non-aged Scher-Montroll current. For strongly aged systems one can observe a constant current in the first regime while the others are dominated by decaying power laws with exponents $\alpha -1$, $-\alpha$, and $-1-\alpha$. The ageing regimes are the 1st and 3rd one, while the classical regimes are the 2nd and the 4th. I have verified the theory using numerical integration of the exact integrals and applied the new results to experimental data.
In the third part I considered a single file of subdiffusing particles in an energy landscape. Every occupied site of the landscape acts as a boundary, from which a particle is immediately reflected to its previous site, if it tries to jump there. I have analysed the effects single-file diffusion a quenched landscape compared to an annealed landscape and I have related these results to the number of steps and related quantities. The diffusion changes from ultraslow logarithmic diffusion in the annealed or CTRW case to subdiffusion with an anomalous exponent $\alpha/(1+\alpha)$ in the quenched landscape. The behavior is caused by the forward waiting time, which changes drastically from the quenched to the annealed case. Single-file effects in the quenched landscape are even more complicated to consider in the ensemble average, since the diffusion in individual landscapes shows extremely diverse behavior. Extensive simulations support my theoretical arguments, which consider mainly the long time evolution of the mean square displacement of a bulk particle.
The spatial and temporal control over presentation of protein-based biomolecules such as growth factors and hormones is crucial for in vitro applications to mimic the complex in vivo environment. We investigated the interaction of a model protein lysozyme (Lys) with poly(L-lysine)/hyaluronic acid (PLL/HA) multilayer films. We focused on Lys diffusion as well as adsorption and retention within the film as a function of the film deposition conditions and post-treatment. Additionally, an effect of Lys concentration on its mobility was probed. A combination of confocal fluorescence microscopy, fluorescence recovery after photobleaching, and microfluidics was employed for this investigation. Our main finding is that adsorption of PLL and HA after protein loading induces acceleration and reduction of Lys mobility, respectively. These results suggest that a charge balance in the film to a high extent governs the protein-film interaction. We believe that control over protein mobility is a key to reach the full potential of the PLL/HA films as reservoirs for biomolecules depending on the application demand. (C) 2016 The Authors. Published by Elsevier B.V.
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.
The present work offers an explanation on how the long-range interaction of dislocations influences their movement, and therefore the strain, during creep of metals. It is proposed that collective motion of dislocations can be described as a fractional Brownian motion. This explains the noisy appearance of the creep strain signal as a function of time. Such signal is split into a deterministic and a stochastic part. These terms can be related to two kinds of dislocation motions: individual and collective, respectively. The description is consistent with the fractal nature of strain-induced dislocation structures predicated in previous works. Moreover, it encompasses the evolution of the strain rate during all stages of creep, including the tertiary one. Creep data from Al99.8% and Al3.85%Mg tested at different temperatures and stresses are used to validate the proposed ideas: it is found that different creep stages present different diffusion characters, and therefore different dislocation motion character.
Even though the effects of insect pests on global agricultural productivity are well recognised, little is known about movement and dispersal of many species, especially in the context of global warming. This work evaluates how temperature and light conditions affect different movement metrics and the feeding rate of the large lupine beetle, an agricultural pest responsible for widespread damage in leguminous crops. By using video recordings, the movement of 384 beetles was digitally analysed under six different temperatures and light conditions in the laboratory. Bayesian linear mixed-effect models were used to analyse the data. Furthermore, the effects of temperature on the daily diffusion coefficient of beetles were estimated by using hidden Markov models and random walk simulations. Results of this work show that temperature, light conditions, and beetles' weight were the main factors affecting the flight probability, displacement, time being active and the speed of beetles. Significant variations were also observed in all evaluated metrics. On average, beetles exposed to light conditions and higher temperatures had higher mean speed and flight probability. However, beetles tended to stay more active at higher temperatures and less active at intermediate temperatures, around 20 degrees C. Therefore, both the diffusion coefficient and displacement of beetles were lower at intermediate temperatures. These results show that the movement behaviour and feeding rates of beetles can present different relationships in the function of temperature. It also shows that using a single diffusion coefficient for insects in spatially explicit models may lead to over- or underestimation of pest spread.