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Localisation of deformation is a ubiquitous feature in continental rift dynamics and observed across drastically different time and length scales. This thesis comprises one experimental and two numerical modelling studies investigating strain localisation in (1) a ductile shear zone induced by a material heterogeneity and (2) in an active continental rift setting. The studies are related by the fact that the weakening mechanisms on the crystallographic and grain size scale enable bulk rock weakening, which fundamentally enables the formation of shear zones, continental rifts and hence plate tectonics. Aiming to investigate the controlling mechanisms on initiation and evolution of a shear zone, the torsion experiments of the experimental study were conducted in a Patterson type apparatus with strong Carrara marble cylinders with a weak, planar Solnhofen limestone inclusion. Using state-of-the-art numerical modelling software, the torsion experiments were simulated to answer questions regarding localisation procedure like stress distribution or the impact of rheological weakening. 2D numerical models were also employed to integrate geophysical and geological data to explain characteristic tectonic evolution of the Southern and Central Kenya Rift. Key elements of the numerical tools are a randomized initial strain distribution and the usage of strain softening. During the torsion experiments, deformation begins to localise at the limestone inclusion tips in a process zone, which propagates into the marble matrix with increasing deformation until a ductile shear zone is established. Minor indicators for coexisting brittle deformation are found close to the inclusion tip and presumed to slightly facilitate strain localisation besides the dominant ductile deformation processes. The 2D numerical model of the torsion experiment successfully predicts local stress concentration and strain rate amplification ahead of the inclusion in first order agreement with the experimental results. A simple linear parametrization of strain weaking enables high accuracy reproduction of phenomenological aspects of the observed weakening. The torsion experiments suggest that loading conditions do not affect strain localisation during high temperature deformation of multiphase material with high viscosity contrasts. A numerical simulation can provide a way of analysing the process zone evolution virtually and extend the examinable frame. Furthermore, the nested structure and anastomosing shape of an ultramylonite band was mimicked with an additional second softening step. Rheological weakening is necessary to establish a shear zone in a strong matrix around a weak inclusion and for ultramylonite formation.
Such strain weakening laws are also incorporated into the numerical models of the
Southern and Central Kenya Rift that capture the characteristic tectonic evolution. A three-stage early rift evolution is suggested that starts with (1) the accommodation of strain by a single border fault and flexure of the hanging-wall crust, after which (2) faulting in the hanging-wall and the basin centre increases before (3) the early-stage asymmetry is lost and basinward localisation of deformation occurs. Along-strike variability of rifts can be produced by modifying the initial random noise distribution. In summary, the three studies address selected aspects of the broad range of mechanisms and processes that fundamentally enable the deformation of rock and govern the localisation patterns across the scales. In addition to the aforementioned results, the first and second manuscripts combined, demonstrate a procedure to find new or improve on existing numerical formulations for specific rheologies and their dynamic weakening. These formulations are essential in addressing rock deformation from the grain to the global scale. As within the third study of this thesis, where geodynamic controls on the evolution of a rift were examined and acquired by the integration of geological and geophysical data into a numerical model.
The development of novel programmable materials aiming to control friction in real-time holds potential to facilitate innovative lubrication solutions for reducing wear and energy losses. This work describes the integration of light-responsiveness into two lubricating materials, silicon oils and polymer brush surfaces.
The first part focusses on the assessment on 9-anthracene ester-terminated polydimethylsiloxanes (PDMS-A) and, in particular, on the variability of rheological properties and the implications that arise with UV-light as external trigger. The applied rheometer setup contains an UV-transparent quartz-plate, which enables radiation and simultaneous measurement of the dynamic moduli. UV-A radiation (354 nm) triggers the cycloaddition reaction between the terminal functionalities of linear PDMS, resulting in chain extension. The newly-formed anthracene dimers cleave by UV-C radiation (254 nm) or at elevated temperatures (T > 130 °C). The sequential UV-A radiation and thermal reprogramming over three cycles demonstrate high conversions and reproducible programming of rheological properties. In contrast, the photochemical back reaction by UV-C is incomplete and can only partially restore the initial rheological properties. The dynamic moduli increase with each cycle in photochemical programming, presumably resulting from a chain segment re-arrangement as a result of the repeated partial photocleavage and subsequent chain length-dependent dimerization. In addition, long periods of radiation cause photooxidative degradation, which damages photo-responsive functions and consequently reduces the programming range. The absence of oxygen, however, reduces undesired side reactions. Anthracene-functionalized PDMS and native PDMS mix depending on the anthracene ester content and chain length, respectively, and allow fine-tuning of programmable rheological properties. The work shows the influence of mixing conditions during the photoprogramming step on the rheological properties, indicating that material property gradients induced by light attenuation along the beam have to be considered. Accordingly, thin lubricant films are suggested as potential application for light-programmable silicon fluids.
The second part compares strategies for the grafting of spiropyran (SP) containing copolymer brushes from Si wafers and evaluates the light-responsiveness of the surfaces. Pre-experiments on the kinetics of the thermally initiated RAFT copolymerization of 2-hydroxyethyl acrylate (HEA) and spiropyran acrylate (SPA) in solution show, first, a strong retardation by SP and, second, the dependence of SPA polymerization on light. Surprisingly, the copolymerization of SPA is inhibited in the dark. These findings contribute to improve the synthesis of polar, spiropyran-containing copolymers. The comparison between initiator systems for the grafting-from approach indicates PET-RAFT superior to thermally initiated RAFT, suggesting a more efficient initiation of surface-bound CTA by light. Surface-initiated polymerization via PET-RAFT with an initiator system of EosinY (EoY) and ascorbic acid (AscA) facilitates copolymer synthesis from HEA and 5-25 mol% SPA. The resulting polymer film with a thickness of a few nanometers was detected by atomic force microscopy (AFM) and ellipsometry. Water contact angle (CA) measurements demonstrate photo-switchable surface polarity, which is attributed to the photoisomerization between non-polar spiropyran and zwitterionic merocyanine isomer. Furthermore, the obtained spiropyran brushes show potential for further studies on light-programmable properties. In this context, it would be interesting to investigate whether swollen spiropyran-containing polymers change their configuration and thus their film thickness under the influence of light. In addition, further experiments using an AFM or microtribometer should evaluate whether light-programmable solvation enables a change in frictional properties between polymer brush surfaces.
The echo chamber model describes the development of groups in heterogeneous social networks. By heterogeneous social network we mean a set of individuals, each of whom represents exactly one opinion. The existing relationships between individuals can then be represented by a graph. The echo chamber model is a time-discrete model which, like a board game, is played in rounds. In each round, an existing relationship is randomly and uniformly selected from the network and the two connected individuals interact. If the opinions of the individuals involved are sufficiently similar, they continue to move closer together in their opinions, whereas in the case of opinions that are too far apart, they break off their relationship and one of the individuals seeks a new relationship. In this paper we examine the building blocks of this model. We start from the observation that changes in the structure of relationships in the network can be described by a system of interacting particles in a more abstract space.
These reflections lead to the definition of a new abstract graph that encompasses all possible relational configurations of the social network. This provides us with the geometric understanding necessary to analyse the dynamic components of the echo chamber model in Part III. As a first step, in Part 7, we leave aside the opinions of the inidividuals and assume that the position of the edges changes with each move as described above, in order to obtain a basic understanding of the underlying dynamics. Using Markov chain theory, we find upper bounds on the speed of convergence of an associated Markov chain to its unique stationary distribution and show that there are mutually identifiable networks that are not apparent in the dynamics under analysis, in the sense that the stationary distribution of the associated Markov chain gives equal weight to these networks.
In the reversible cases, we focus in particular on the explicit form of the stationary distribution as well as on the lower bounds of the Cheeger constant to describe the convergence speed.
The final result of Section 8, based on absorbing Markov chains, shows that in a reduced version of the echo chamber model, a hierarchical structure of the number of conflicting relations can be identified.
We can use this structure to determine an upper bound on the expected absorption time, using a quasi-stationary distribution. This hierarchy of structure also provides a bridge to classical theories of pure death processes. We conclude by showing how future research can exploit this link and by discussing the importance of the results as building blocks for a full theoretical understanding of the echo chamber model. Finally, Part IV presents a published paper on the birth-death process with partial catastrophe. The paper is based on the explicit calculation of the first moment of a catastrophe. This first part is entirely based on an analytical approach to second degree recurrences with linear coefficients. The convergence to 0 of the resulting sequence as well as the speed of convergence are proved. On the other hand, the determination of the upper bounds of the expected value of the population size as well as its variance and the difference between the determined upper bound and the actual value of the expected value. For these results we use almost exclusively the theory of ordinary nonlinear differential equations.
Plate tectonics describes the movement of rigid plates at the surface of the Earth as well as their complex deformation at three types of plate boundaries: 1) divergent boundaries such as rift zones and mid-ocean ridges, 2) strike-slip boundaries where plates grind past each other, such as the San Andreas Fault, and 3) convergent boundaries that form large mountain ranges like the Andes. The generally narrow deformation zones that bound the plates exhibit complex strain patterns that evolve through time. During this evolution, plate boundary deformation is driven by tectonic forces arising from Earth’s deep interior and from within the lithosphere, but also by surface processes, which erode topographic highs and deposit the resulting sediment into regions of low elevation. Through the combination of these factors, the surface of the Earth evolves in a highly dynamic way with several feedback mechanisms. At divergent boundaries, for example, tensional stresses thin the lithosphere, forcing uplift and subsequent erosion of rift flanks, which creates a sediment source. Meanwhile, the rift center subsides and becomes a topographic low where sediments accumulate. This mass transfer from foot- to hanging wall plays an important role during rifting, as it prolongs the activity of individual normal faults. When rifting continues, continents are eventually split apart, exhuming Earth’s mantle and creating new oceanic crust. Because of the complex interplay between deep tectonic forces that shape plate boundaries and mass redistribution at the Earth’s surface, it is vital to understand feedbacks between the two domains and how they shape our planet.
In this study I aim to provide insight on two primary questions: 1) How do divergent and strike-slip plate boundaries evolve? 2) How is this evolution, on a large temporal scale and a smaller structural scale, affected by the alteration of the surface through erosion and deposition? This is done in three chapters that examine the evolution of divergent and strike-slip plate boundaries using numerical models. Chapter 2 takes a detailed look at the evolution of rift systems using two-dimensional models. Specifically, I extract faults from a range of rift models and correlate them through time to examine how fault networks evolve in space and time. By implementing a two-way coupling between the geodynamic code ASPECT and landscape evolution code FastScape, I investigate how the fault network and rift evolution are influenced by the system’s erosional efficiency, which represents many factors like lithology or climate. In Chapter 3, I examine rift evolution from a three-dimensional perspective. In this chapter I study linkage modes for offset rifts to determine when fast-rotating plate-boundary structures known as continental microplates form. Chapter 4 uses the two-way numerical coupling between tectonics and landscape evolution to investigate how a strike-slip boundary responds to large sediment loads, and whether this is sufficient to form an entirely new type of flexural strike-slip basin.
Salt deposits offer a variety of usage types. These include the mining of rock salt and potash salt as important raw materials, the storage of energy in man-made underground caverns, and the disposal of hazardous substances in former mines. The most serious risk with any of these usage types comes from the contact with groundwater or surface water. It causes an uncontrolled dissolution of salt rock, which in the worst case can result in the flooding or collapse of underground facilities. Especially along potash seams, cavernous structures can spread quickly, because potash salts show a much higher solubility than rock salt. However, as their chemical behavior is quite complex, previous models do not account for these highly soluble interlayers. Therefore, the objective of the present thesis is to describe the evolution of cavernous structures along potash seams in space and time in order to improve hazard mitigation during the utilization of salt deposits.
The formation of cavernous structures represents an interplay of chemical and hydraulic processes. Hence, the first step is to systematically investigate the dissolution and precipitation reactions that occur when water and potash salt come into contact. For this purpose, a geochemical reaction model is used. The results show that the minerals are only partially dissolved, resulting in a porous sponge like structure. With the saturation of the solution increasing, various secondary minerals are formed, whose number and type depend on the original rock composition. Field data confirm a correlation between the degree of saturation and the distance from the center of the cavern, where solution is entering. Subsequently, the reaction model is coupled with a flow and transport code and supplemented by a novel approach called ‘interchange’. The latter enables the exchange of solution and rock between areas of different porosity and mineralogy, and thus ultimately the growth of the cavernous structure. By means of several scenario analyses, cavern shape, growth rate and mineralogy are systematically investigated, taking also heterogeneous potash seams into account. The results show that basically four different cases can be distinguished, with mixed forms being a frequent occurrence in nature. The classification scheme is based on the dimensionless numbers Péclet and Damköhler, and allows for a first assessment of the hazard potential. In future, the model can be applied to any field case, using measurement data for calibration.
The presented research work provides a reactive transport model that is able to spatially and temporally characterize the propagation of cavernous structures along potash seams for the first time. Furthermore, it allows to determine thickness and composition of transition zones between cavern center and unaffected salt rock. The latter is particularly important in potash mining, so that natural cavernous structures can be located at an early stage and the risk of mine flooding can thus be reduced. The models may also contribute to an improved hazard prevention in the construction of storage caverns and the disposal of hazardous waste in salt deposits. Predictions regarding the characteristics and evolution of cavernous structures enable a better assessment of potential hazards, such as integrity or stability loss, as well as of suitable mitigation measures.
The key to reduce the energy required for specific transformations in a selective manner is the employment of a catalyst, a very small molecular platform that decides which type of energy to use. The field of photocatalysis exploits light energy to shape one type of molecules into others, more valuable and useful.
However, many challenges arise in this field, for example, catalysts employed usually are based on metal derivatives, which abundance is limited, they cannot be recycled and are expensive. Therefore, carbon nitrides materials are used in this work to expand horizons in the field of photocatalysis.
Carbon nitrides are organic materials, which can act as recyclable, cheap, non-toxic, heterogeneous photocatalysts. In this thesis, they have been exploited for the development of new catalytic methods, and shaped to develop new types of processes.
Indeed, they enabled the creation of a new photocatalytic synthetic strategy, the dichloromethylation of enones by dichloromethyl radical generated in situ from chloroform, a novel route for the making of building blocks to be used for the productions of active pharmaceutical compounds.
Then, the ductility of these materials allowed to shape carbon nitride into coating for lab vials, EPR capillaries, and a cell of a flow reactor showing the great potential of such flexible technology in photocatalysis.
Afterwards, their ability to store charges has been exploited in the reduction of organic substrates under dark conditions, gaining new insights regarding multisite proton coupled electron transfer processes.
Furthermore, the combination of carbon nitrides with flavins allowed the development of composite materials with improved photocatalytic activity in the CO2 photoreduction.
Concluding, carbon nitrides are a versatile class of photoactive materials, which may help to unveil further scientific discoveries and to develop a more sustainable future.