Bewegungen von prozessiven molekularen Motoren des Zytoskeletts sind durch ein Wechselspiel von gerichteter Bewegung entlang von Filamenten und Diffusion in der umgebenden Lösung gekennzeichnet. Diese eigentümlichen 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. <br /> <br /> Im einzelnen werden vier Transportphänomene untersucht: <br /> (i) Random Walks von einzelnen Motoren in Kompartimenten verschiedener Geometrien, <br /> (ii) stationäre Konzentrationsprofile, die sich in geschlossenen Kompartimenten infolge dieser Bewegungen einstellen,<br /> (iii) randinduzierte Phasenübergänge in offenen röhrenartigen Kompartimenten, die an Motorenreservoirs gekoppelt sind, und <br /> (iv) der Einfluß von kooperativen Effekten bei der Motor-Filament-Bindung auf die Bewegung. Alle diese Phänomene sind experimentell zugänglich, und mögliche experimentelle Realisierungen werden diskutiert. / Movements of processive cytoskeletal motors are characterized by an interplay between directed motion along filament and diffusion in the surrounding solution. In the present work, these peculiar movements are studied by modeling them as random walks on a lattice. An additional subject of our studies is the effect of motor-motor interactions on these movements. <br /> <br /> In detail, four transport phenomena are studied: <br /> (i) Random walks of single motors in compartments of various geometries, <br /> (ii) stationary concentration profiles which build up as a result of these movements in closed compartments, <br /> (iii) boundary-induced phase transitions in open tube-like compartments coupled to reservoirs of motors, and <br /> (iv) the influence of cooperative effects in motor-filament binding on the movements. All these phenomena are experimentally accessible and possible experimental realizations are discussed.

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To understand the mechanism of a pressure-induced structural phase transition, it is important to know which bonding changes lead to the stabilization of the new structure. A useful approach in this regard is the quantum chemical topology, which provides a large variety of indicators for the characterization of interatomic interactions. In this work, a number of topological indicators are used to analyze the bonding changes during the pressure-induced phase transition from the cubic diamond (cd) to the β-Sn-type structure of the elements of the 14th group of the periodic table. The ability of these indicators to reflect the presence of the cd → β-Sn transition in experiment for Si, Ge and Sn and its absence for carbon is investigated. Furthermore, the effect of pressure on the interatomic interactions in the cd- and β-Sn-type structures is examined. It is observed that the energy change along the cd → β-Sn transformation pathway correlates with the evolution of certain parameters of the electron density and the electron localizability indicator (ELI-D). Accordingly, criteria of structural stability were formulated based on characteristics of interatomic interactions. These results can serve as guidelines for the investigation of other solid-state phase transformations by the topological methods.

Modeling the interaction of a silicon (Si) surface with a pointed asperity is a crucial step towards the understanding of several phenomena related to machining of this important semiconductor. If subjected to pressure or contact loading, Si undergoes a series of stress-driven phase transitions accompanied by large volume changes. We developed a finite deformation constitutive model that captures the semiconductor-to-metal (cd-Si ➙ β-Si) and metal-to-amorphous (β-Si ➙ a-Si) transitions within the framework of thermodynamics with internal variables. The model was implemented as a user material subroutine for the finite element code Abaqus/Std. in analogy to pressure sensitive, rate independent, non-associated, non-smooth multisurface plasticity. Material parameters were identified from indentation load-displacement curves in (111)-Si using a Berkovich indenter tip. The constitutive model was verified by successfully predicting the load-displacement curves for different indenters, the residual surface profile, as well as the size and shape of the transformation zone under the indenter tip as compared to TEM results.

In the study of strongly interacting condensed-matter systems controlled microscopic theories hold a key position. Spin-wave theory, large-N expansion, and $epsilon$-expansion are some of the few successful cornerstones. In this doctoral thesis work, we have developed a novel large-$d$ expansion method, $d$ being the spatial dimension, to study model Hamiltonians hosting a quantum phase transition between a paramagnet and a magnetically ordered phase. A highlight of this technique is that it can consistently describe the entire phase diagram of the above mentioned models, including the quantum critical point. Note that most analytical techniques either efficiently describe only one of the phases or suffer from divergences near the critical point. The idea of large-$d$ formalism is that in this limit, non-local fluctuations become unimportant and that a suitable product state delivers exact expectation values for local observables, with corrections being suppressed in powers of $1/d$. It turns out that, due to momentum summation properties of the interaction structure factor, all diagrams are suppressed in powers of $1/d$ leading to an analytic expansion. We have demonstrated this method in two important systems namely, the coupled-dimer magnets and the transverse-field Ising model. Coupled-dimer magnets are Heisenberg spin systems with two spins, coupled by intra-dimer antiferromagnetic interaction, per crystallographic unit cell (dimer). In turn, spins from neighboring dimers interact via some inter-dimer interaction. A quantum paramagnet is realized for a dominant intra-dimer interaction, while a magnetically ordered phase exists for a dominant (or of the same order as intra-dimer interaction) inter-dimer interaction. These two phases are connected by a quantum phase transition, which is in the Heisenberg O(3) universality class. Microscopic analytical theories to study such systems have been restricted to either only one of the phases or involve uncontrolled approximations. Using a non-linear bond-operator theory for spins with S=$1/2$, we have calculated the $1/d$ expansion of static and dynamic observables for coupled dimers on a hypercubic lattice at zero temperature. Analyticity of the $1/d$ expansion, even at the critical point, is ensured by correctly identifying suitable observables using the mean-field critical exponents. This method yields gapless excitation modes in the continuous symmetry broken phase, as required by Goldstone\'s theorem. In appropriate limits, our results match with perturbation expansion in small ratio of inter-dimer and intra-dimer coupling, performed using continuous unitary transformations, as well as the spin-wave theory for spin-$1/2$ in arbitrary dimensions. We also discuss the Brueckner approach, which relies on small quasiparticle density, and derive the same $1/d$ expansion for the dispersion relation in the disordered phase. Another success of our work is in describing the amplitude (Higgs) mode in coupled-dimer magnets. Our novel method establishes the popular bond-operator theory as a controlled approach. In $d=2$, the results from our calculations are in qualitative agreement with the quantum Monte Carlo study of the square-lattice bilayer Heisenberg AF spin-$1/2$ model. In particular, our results are useful to identify the amplitude (Higgs) mode in the QMC data. The ideas of large-$d$ are also successfully applied to the transverse-field Ising model on a hypercubic lattice. Similar to bond operators, we have introduced auxiliary Bosonsic operators to set up our method in this case. We have also discussed briefly the bilayer Kitaev model, constructed by antiferromagnetically coupling two layers of the Kitaev model on a honeycomb lattice. In this case, we investigate the dimer quantum paramagnetic phase, realized in the strong inter-layer coupling limit. Using bond-operator theory, we calculate the mode dispersion in this phase, within the harmonic approximation. We also conjecture a zero-temperature phase diagram for this model.

To understand the mechanism of a pressure-induced structural phase transition, it is important to know which bonding changes lead to the stabilization of the new structure. A useful approach in this regard is the quantum chemical topology, which provides a large variety of indicators for the characterization of interatomic interactions. In this work, a number of topological indicators are used to analyze the bonding changes during the pressure-induced phase transition from the cubic diamond (cd) to the β-Sn-type structure of the elements of the 14th group of the periodic table. The ability of these indicators to reflect the presence of the cd → β-Sn transition in experiment for Si, Ge and Sn and its absence for carbon is investigated. Furthermore, the effect of pressure on the interatomic interactions in the cd- and β-Sn-type structures is examined. It is observed that the energy change along the cd → β-Sn transformation pathway correlates with the evolution of certain parameters of the electron density and the electron localizability indicator (ELI-D). Accordingly, criteria of structural stability were formulated based on characteristics of interatomic interactions. These results can serve as guidelines for the investigation of other solid-state phase transformations by the topological methods.

Complex networks are employed as a mathematical description of complex systems in many different fields, ranging from biology to sociology, economy and ecology. Dynamical processes in these systems often display phase transitions, where the dynamics of the system changes qualitatively. In combination with these phase transitions certain components of the system might irretrievably go extinct. In this case, we talk about absorbing transitions. Developing mathematical tools, which allow for an analysis and prediction of the observed phase transitions is crucial for the investigation of complex networks. In this thesis, we investigate absorbing transitions in dynamical networks, where a certain amount of diversity is lost. In some real-world examples, e.g. in the evolution of human societies or of ecological systems, it is desirable to maintain a high degree of diversity, whereas in others, e.g. in epidemic spreading, the diversity of diseases is worthwhile to confine. An understanding of the underlying mechanisms for emergence and persistence of diversity in complex systems is therefore essential. Within the scope of two different network models, we develop an analytical approach, which can be used to estimate the prerequisites for diversity. In the first part, we study a model for opinion formation in human societies. In this model, regimes of low diversity and regimes of high diversity are separated by a fragmentation transition, where the network breaks into disconnected components, corresponding to different opinions. We propose an approach for the estimation of the fragmentation point. The approach is based on a linear stability analysis of the fragmented state close to the phase transition and yields much more accurate results compared to conventional methods. In the second part, we study a model for the formation of complex food webs. We calculate and analyze coexistence conditions for several types of species in ecological communities. To this aim, we employ an approach which involves an iterative stability analysis of the equilibrium with respect to the arrival of a new species. The proposed formalism allows for a direct calculation of coexistence ranges and thus facilitates a systematic analysis of persistence conditions for food webs. In summary, we present a general mathematical framework for the calculation of absorbing phase transitions in complex networks, which is based on concepts from percolation theory. While the specific implementation of the formalism differs from model to model, the basic principle remains applicable to a wide range of different models.

In our experiments, the icing temperature of small water volumes placed on different pyroelectric single crystals (SrxBa1−xNb2O6, LiNbO3, and LiTaO3) was determined using two measurement setups: (1) the sessile droplet and (2) ring system method. In the first method, a free-standing water droplet was exposed to several external factors in the air environment. This was found to lead to higher icing temperatures compared to the second method where the water was more isolated from external factors such as evaporation. In the second method, the material of the ring system was found to be an important factor determining the freezing temperature of the enclosed water. A recommendation for the application of both methods is given, their advantages and disadvantages depending on the purpose of measurement, and their reproducibility for practical applications. In addition to this, the correlation between pyroelectricity and icing temperature, with regard to several types of internal and external factors affecting water freezing, is also discussed in the paper.

Verändern Photoreaktionen eingelagerter Substanzen die Klärtemperatur flüssigkristalliner Polyelektrolyt-Tensid-Komplexe? Komplexe (Salze) aus Polyaminen und Alkylsulfonsäuren bilden mit Wasser einen hexagonalen Flüssigkristall, der sich beim Erwärmen in eine optisch isotrope Phase umwandelt. In diese Demethylionenalkylsulfonate genannten Komplexe werden Bisthienylcyclopentene mit Alkylsulfonatseitenketten zwar ortsfest eingelagert, deren Photozyklisierung verschiebt das Gleichgewicht jedoch nur wenig von der hexagonalen zur isotropen Phase. Hingegen verläuft die Photozyklisierung der Bisthienylcyclopentene im festen Komplex teilweise deutlich langsamer als in Lösungen. / Can photoreactions of embedded substances change phase transition temperatures of polyelectrolyte surfactant complexes? Complexes made from polyamines and alkyl sulfonates form an hexagonal liquid crystal in presence of water, which is converted to optical isotropic phase by heating. These complexes resembling those of ionenes are called demethyl-ionene alkyl sulfonates. Bisthienylcyclopentenes bearing alkyl sulfonate side chains are incorporated into these complexes and keep their locations over prolonged periods of time, but the photocyclization of the chromophore only slightly shifts the equilibrium from hexagonal liquid crystal towards the optical isotropic phase. Conversely, the photocyclization of bisthienylcyclopentenes partially proceeds appreciably slower within the solid complex than in solution.

The ferroelectricity in fluorite oxides has gained increasing interest due to its promising properties for multiple applications in semiconductor as well as energy devices. The structural origin of the unexpected ferroelectricity is now believed to be the formation of a non-centrosymmetric orthorhombic phase with the space group of Pca2₁. However, the factors driving the formation of the ferroelectric phase are still under debate. In this study, to understand the effect of annealing temperature, the crystallization process of doped HfO₂ thin films is analyzed using in situ, high-temperature X-ray diffraction. The change in phase fractions in a multiphase system accompanied with the unit cell volume increase during annealing could be directly observed from X-ray diffraction analyses, and the observations give an information toward understanding the effect of annealing temperature on the structure and electrical properties. A strong coupling between the structure and the electrical properties is reconfirmed from this result.