## 500 Naturwissenschaften und Mathematik

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Electric trains are considered one of the most eco-friendly and safest means of transportation. Catenary poles are used worldwide to support overhead power lines for electric trains. The performance of the catenary poles has an extensive influence on the integrity of the train systems and, consequently, the connected human services. It became a must nowadays to develop SHM systems that provide the instantaneous status of catenary poles in- service, making the decision-making processes to keep or repair the damaged poles more feasible. This study develops a data-driven, model-free approach for status monitoring of cantilever structures, focusing on pre-stressed, spun-cast ultrahigh-strength concrete catenary poles installed along high-speed train tracks. The pro-posed approach evaluates multiple damage features in an unfied damage index, which leads to straightforward interpretation and comparison of the output. Besides, it distinguishes between multiple damage scenarios of the poles, either the ones caused by material degradation of the concrete or by the cracks that can be propagated during the life span of the given structure. Moreover, using a logistic function to classify the integrity of structure avoids the expensive learning step in the existing damage detection approaches, namely, using the modern machine and deep learning methods. The findings of this study look very promising when applied to other types of cantilever structures, such as the poles that support the power transmission lines, antenna masts, chimneys, and wind turbines.

Das Kernthema dieser Arbeit ist die Beschäftigung mit den Folgen des Uranbergbaus in dem Gebiet um die ehemalige Abbauregion der Wismut SAG/SDAG in Ronneburg (Ostthüringen). Dieses Thema wird unter historischen, sozialen, kulturanthropologischen und künstlerischen Aspekten betrachtet und in den Zusammenhang mit den weltweiten Voraussetzungen der Nuklearindustrie und Auswirkungen des Uranbergbaus und seiner Folgen gestellt. Die Arbeit legt dar, wie eine Uranbergbaufolgelandschaft entsteht und welches Wissen ist für ein angemessenes Verständnis des Phänomens wichtig ist. Es wird untersucht, ob Kunst bezüglich der Uranbergbaufolgelandschaft einen relevanten Beitrag leisten kann bzw. in welcher Form dies versucht wurde, bzw. stellte Arbeiten vor, die verwandete Themen bearbeitet haben. In Kombination dieser beiden Hauptaspekte geht die Arbeit der Frage nach, welche Faktoren die Uranbergbaufolgelandschaft prägen und ob es sinnvolle Beteiligungsfelder für künstlerisches Forschen oder Handeln gibt sowie welche Bedingungen hierfür erfüllt werdenmüssten. Die Kernthese der Arbeit ist, dass künstlerische Arbeiten im Themenfeld des Uranbergbaus unter bestimmten Bedingungen relevante Beiträge leisten können.

The growing complexity of modern practical problems puts high demand on mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice is becoming particularly important. Methods for model comparison and model choice typically used in practical applications nowadays are computationbased, and thus time consuming and computationally costly. Therefore, it is necessary to develop other approaches to working abstractly, i.e., without computations, with mathematical models. An abstract description of mathematical models can be achieved by the help of abstract mathematics, implying formalisation of models and relations between them. In this paper, a category theory-based approach to mathematical modelling is proposed. In this way, mathematical models are formalised in the language of categories, relations between the models are formally defined and several practically relevant properties are introduced on the level of categories. Finally, an illustrative example is presented, underlying how the category-theory based approach can be used in practice. Further, all constructions presented in this paper are also discussed from a modelling point of view by making explicit the link to concrete modelling scenarios.

The main purpose of the thesis is to ensure the safe demolition of old guyed antenna masts that are located in different parts of Germany. The major problem in demolition of this masts is the falling down of the masts in unexpected direction because of buckling problem. The objective of this thesis is development of a numerical models using finite element method (FEM) and assuring a controlled collapse by coming up with different time setups for the detonation of explosives which are responsible for cutting down the cables. The result of this thesis will avoid unexpected outcomes during the demolition processes and prevent risk of collapsing of the mast over near by structures.

Utilizing Modern FIB/SEM Technology and EDS for 3D Imaging of Hydrated Alite and its Pore Space
(2021)

The exploration of cementitious materials using scanning electron microscopes (SEM) is mainly done using fractured or polished surfaces. This leads to high-resolution 2D-images that can be combined using EDX and EBSD to unveil details of the microstructure and composition of materials. Nevertheless, this does not provide a quantitative insight into the three-dimensional fine structure of for example C-S-H phases.
The focused ion beam (FIB) technology can cut a block of material in thin layers of less than 10 nm. This gives us a volume of 1000 μm³ with a voxel resolution of down to 4 x 4 x 10 nm³. The results can be combined with simultaneously acquired EDX data to improve image segmentation. Results of the investigation demonstrate that it is possible to obtain close-to-native 3D-visualisation of the spatial distribution of unreacted C3S, C-S-H and CH. Additionally, an optimized preparation method allows us to quantify the fine structure of C-S-H phases (length, aspect ratio, …) and the pore space.

Chemical glass frosting processes are widely used to create visual attractive glass surfaces. A commonly used frosting bath mainly contains ammonium bifluoride (NH4HF2) mixed with hydrochloric acid (HCl). The frosting process consists of several baths. Firstly, the preliminary bath to clean the object. Secondly, the frosting bath which etches the rough light scattering structure into the glass surface. Finally, the washing baths to clean the frosted object. This is where the constituents of the preceding steps accumulate and have to be filtered from the sewage. In the present contribution, phosphoric acid (H3PO4) was used as a substitute for HCl to reduce the amount of ammonium (NH4+) and chloride (Cl−) dissolved in the waste water. In combination with magnesium carbonate (MgCO3), it allows the precipitation of ammonium within the sewage as ammonium magnesium phosphate (MgNH4PO4). However, a trivial replacement of HCl by H3PO4 within the frosting process causes extensive frosting errors, such as inhomogeneous size distributions of the structures or domains that are not fully covered by these structures. By modifying the preliminary bath composition, it was possible to improve the frosting result considerably. To determine the optimal composition of the preliminary bath, a semi-automatic evaluation method has been developed. This method renders the objective comparison of the resulting surface quality possible.

Die Auswirkungen der durch den Kapitalismus befeuerten Umweltzerstörung werden immer deutlicher erkennbar. Unsere Gesellschaft ist nun damit konfrontiert, dass ihre kulturelle Identität, aber auch ihr Wohlstand sowohl eng mit Konsum und Wirtschaftswachstum als auch mit der Gesundheit der Natur verbunden sind. Es scheint ein geeigneter Moment, um die Perspektive zu wechseln und einer neuen Form des Wachstums eine Chance zu geben. Pilze sind eine von der Region unabhängige, natürlich vorkommende Ressource, die lokal angebaut und verarbeitet werden kann, ohne die Umwelt zu belasten. Pilze sind klimafreundlich, müllvermeidend und in bestehende natürliche Kreisläufe inkludierbar. Kurzum, Pilze sind cool, doch das wissen nicht Viele. Das sollte sich ändern. Mit Myzelwachstum gegen das Wachstumsparadigma.

This work presents a robust status monitoring approach for detecting damage in cantilever structures based on logistic functions. Also, a stochastic damage identification approach based on changes of eigenfrequencies is proposed. The proposed algorithms are verified using catenary poles of electrified railways track. The proposed damage features overcome the limitation of frequency-based damage identification methods available in the literature, which are valid to detect damage in structures to Level 1 only. Changes in eigenfrequencies of cantilever structures are enough to identify possible local damage at Level 3, i.e., to cover damage detection, localization, and quantification. The proposed algorithms identified the damage with relatively small errors, even at a high noise level.

In the last two decades, Peridynamics (PD) attracts much attention in the field of fracture mechanics. One key feature of PD is the nonlocality, which is quite different from the ideas in conventional methods such as FEM and meshless method. However, conventional PD suffers from problems such as constant horizon, explicit algorithm, hourglass mode. In this thesis, by examining the nonlocality with scrutiny, we proposed several new concepts such as dual-horizon (DH) in PD, dual-support (DS) in smoothed particle hydrodynamics (SPH), nonlocal operators and operator energy functional. The conventional PD (SPH) is incorporated in the DH-PD (DS-SPH), which can adopt an inhomogeneous discretization and inhomogeneous support domains. The DH-PD (DS-SPH) can be viewed as some fundamental improvement on the conventional PD (SPH). Dual formulation of PD and SPH allows h-adaptivity while satisfying the conservations of linear momentum, angular momentum and energy. By developing the concept of nonlocality further, we introduced the nonlocal operator method as a generalization of DH-PD. Combined with energy functional of various physical models, the nonlocal forms based on dual-support concept are derived. In addition, the variation of the energy functional allows implicit formulation of the nonlocal theory. At last, we developed the higher order nonlocal operator method which is capable of solving higher order partial differential equations on arbitrary domain in higher dimensional space. Since the concepts are developed gradually, we described our findings chronologically.
In chapter 2, we developed a DH-PD formulation that includes varying horizon sizes and solves the "ghost force" issue. The concept of dual-horizon considers the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly with arbitrary particle discretization. All three peridynamic formulations, namely bond based, ordinary state based and non-ordinary state based peridynamics can be implemented within the DH-PD framework. A simple adaptive refinement procedure (h-adaptivity) is proposed reducing the computational cost. Both two- and three- dimensional examples including the Kalthoff-Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method.
In chapter 3, a nonlocal operator method (NOM) based on the variational principle is proposed for the solution of waveguide problem in computational electromagnetic field. Common differential operators as well as the variational forms are defined within the context of nonlocal operators. The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease, which is necessary for the eigenvalue analysis of the waveguide problem. The present formulation is applied to solve 1D Schrodinger equation, 2D electrostatic problem and the differential electromagnetic vector wave equations based on electric fields.
In chapter 4, a general nonlocal operator method is proposed which is applicable for solving partial differential equations (PDEs) of mechanical problems. The nonlocal operator can be regarded as the integral form, ``equivalent'' to the differential form in the sense of a nonlocal interaction model. The variation of a nonlocal operator plays an equivalent role as the derivatives of the shape functions in the meshless methods or those of the finite element method. Based on the variational principle, the residual and the tangent stiffness matrix can be obtained with ease. The nonlocal operator method is enhanced here also with an operator energy functional to satisfy the linear consistency of the field. A highlight of the present method is the functional derived based on the nonlocal operator can convert the construction of residual and stiffness matrix into a series of matrix multiplications using the predefined nonlocal operators. The nonlocal strong forms of different functionals can be obtained easily via the concept of support and dual-support. Several numerical examples of different types of PDEs are presented.
In chapter 5, we extended the NOM to higher order scheme by using a higher order Taylor series expansion of the unknown field. Such a higher order scheme improves the original NOM in chapter 3 and chapter 4, which can only achieve one-order convergence. The higher order NOM obtains all partial derivatives with specified maximal order simultaneously without resorting to shape functions. The functional based on the nonlocal operators converts the construction of residual and stiffness matrix into a series of matrix multiplication on the nonlocal operator matrix. Several numerical examples solved by strong form or weak form are presented to show the capabilities of this method.
In chapter 6, the NOM proposed as a particle-based method in chapter 3,4,5, has difficulty in imposing accurately the boundary conditions of various orders. In this paper, we converted the particle-based NOM into a scheme with interpolation property. The new scheme describes partial derivatives of various orders at a point by the nodes in the support and takes advantage of the background mesh for numerical integration. The boundary conditions are enforced via the modified variational principle. The particle-based NOM can be viewed a special case of NOM with interpolation property when nodal integration is used. The scheme based on numerical integration greatly improves the stability of the method, as a consequence, the operator energy functional in particle-based NOM is not required. We demonstrated the capabilities of current method by solving the gradient solid problems and comparing the numerical results with the available exact solutions.
In chapter 7, we derived the DS-SPH in solid within the framework of variational principle. The tangent stiffness matrix of SPH can be obtained with ease, and can be served as the basis for the present implicit SPH. We proposed an hourglass energy functional, which allows the direct derivation of hourglass force and hourglass tangent stiffness matrix. The dual-support is {involved} in all derivations based on variational principles and is automatically satisfied in the assembling of stiffness matrix. The implementation of stiffness matrix comprises with two steps, the nodal assembly based on deformation gradient and global assembly on all nodes. Several numerical examples are presented to validate the method.

Broadband dielectric measurement methods based on vector network analyzer coupled with coaxial transmission line cell (CC) and open-ended coaxial probe (OC) are simply reviewed, by which the dielectric behaviors in the frequency range of 1 MHz to 3 GHz of two practical geomaterials are investigated. Kaolin after modified compaction with different water contents is measured by using CC. The results are consistent with previous study on standardized compacted kaolin and suggest that the dielectric properties at frequencies below 100 MHz are not only a function of water content but also functions of other soil state parameters including dry density. The hydration process of a commercial grout is monitored in real time by using OC. It is found that the time dependent dielectric properties can accurately reveal the different stages of the hydration process. These measurement results demonstrate the practicability of the introduced methods in determining dielectric properties of soft geomaterials.