The Apulian Castel del Monte has a distinct floor plan that is based upon three concentric octagons. This is why the proportions of the floor plan are based upon the Silver Ratio. However, this proporational system requires measurements which have irrational numbers that are very difficult to work with on a construction site. For this reason, the design of the building was converted into a modular system during the early construction planning phase. The modular system operates with whole numbers while preserving the intended design concept. The ratio of 17 to 7 is of fundamental importance here.

Numerical homogenization includes methods for solving multiscale problems. The goal here is to solve the underlying problem on a macroscale, taking into account the influence of a heterogeneous microscale. Numerical homogenization methods thus provide a better understanding of the macroscopic problem while at the same time reducing the numerical effort compared to a complete analysis of the microscale. The Finite Element Heterogeneous Multiscale Method is one of these numerical homogenization methods and, through a complete a priori error analysis, provides a new and at the same time significant contribution to numerical homogenization by two-scale finite element methods. In this work and the publications on which it is based, the implementation of the Finite Element Heterogeneous Multiscale Method for vector-valued problems in the field of elasticity was described and numerous other aspects were examined. These include i) Confirmation of the a priori convergence statements for linear elasticity using numerous examples with different regularity with different coupling conditions of the two scales and linear and quadratic shape functions. ii) Comparison of the Finite Element Heterogeneous Multiscale Method with the FE² method. Although both methods are based on different approaches, the quantitative agreement of the results was shown using numerous examples, so that the a priori convergence statements can also be transferred to the FE² method. iii) While error analyzes in the literature usually deal with errors on the macroscale, this work also examined errors on the microscale. For this purpose, a distinction was made between the discretization error and a resolution error that takes the resolution of the microscale into account. iv) An investigation of the error estimation on the heterogeneous microscale provided an adapted error estimator algorithm with which the quality of the error estimation on the microscale can be significantly improved. v) Different adaptive and uniform mesh coarsening algorithms that can be used as a preprocessor to reduce the microscale degrees of freedom were examined based on their effects on the discretization and resolution errors. vi) In order to reduce the high numerical effort of non-linear two-scale problems, which results from the repeated solution of nested macro and micro equation systems, a new solution algorithm was introduced that can significantly speed up the calculations.

This paper pushes for a reframing of Anthropology as a collaborative and situated practice grounded in relationships rather than extraction. Using the metaphor of the fissure (raja) as both concept and method, it explores how research with/in communities unsettles disciplinary boundaries and challenges the coloniality of knowledge production. The text proposes a constellation of orientations -decolonial vigilance, feminist reflexivity, embodied attention, sensory attunement, and ontological openness- that operate as ethical and political commitments rather than fixed techniques. Through examples that traverse various disciplines, it shows how different media can be reimagined as tools for collective inquiry and transformation. The paper concludes by calling for creativity, solidarity and hope in order to sustain plural, accountable, and co-created forms of knowledge.

Quantum metrology and quantum thermodynamics are two relatively young fields that, in the spirit of the second quantum revolution, apply quantum theory to address fundamental questions and to develop technological applications. While the research in these fields is predominantly conducted with discrete, finite-dimensional quantum systems in mind, this thesis makes the case for continuous variable mechanical degrees of freedom. In the first of three projects, we present two realizations of the Otto cycle with a planar rotor as the working medium. As a mechanical system, the planar rotor has a well-defined classical analogue that allows the identification of genuine quantum effects by comparing classical and quantum machine. Here, we mainly focus on the parameter regimes, where the machine admits a certain operation mode, i.e. an engine, a refrigerator, or a heater. In the first realization, we find a systematic disadvantage of the quantum machine. The opposite is true for the second realization: It can be shown that the classical machine can, in general, not be run in a useful operation mode. The quantum machine, on the other hand, admits an engine operation mode for sufficiently cold temperatures of the cold bath. The second project is devoted to the dynamics of a quantum system subjected to a thermal gas. In contrast to repeated interaction models, we consider any gas particle as a motional degree of freedom. We Employ quantum mechanical scattering theory to derive a low-density limit master equation, including gases with internal structure. Then, the thermodynamic consistency of the master equation is shown. A comparison with repeated interaction models makes evident that the inclusion of motional degrees of freedom of the gas plays a curial role for the consistency. Finally, we consider a nonequilibrium scenario, where the internal and motional degrees of freedom of the gas are thermal with respect to different temperatures. We show that, under the influence of this gas, the ergotropy of the system can increase. In the last project, we apply quantum metrology on the measurement of magnetic moments in an electron microscope. We consider two types of sample, one that is static and does not change under the influence of the electron and another one that is described by a quantum system and experiences quantum backaction. For both samples, we derive the scattering operator from first principles. Then, two metrological tasks are considered: First, the sensing of the strength of the magnetic moment. We derive the Fisher information in several bases and find that momentum measurements are already optimal in the case without backaction. With backaction included, a measurement of angular momentum is optimal. The second task, we consider, is the optimal discrimination of the scattered and unscattered motional electron state. We derive the trace distance and find the experimentally achievable basis with the highest classical trace distance, which is still significantly worse than the theoretical optimum.