Erscheinungsjahr 2022

This paper considers the structure consisting of the set of all words over a given alphabet together with the subword relation, regular predicates, and constants for every word. We are interested in the counting extension of first-order logic by threshold counting quantifiers. The main result shows that the two-variable fragment of this logic can be decided in twofold exponential alternating time with linearly many alternations (and therefore in particular in twofold exponential space as announced in the conference version (Kuske and Schwarz, in: MFCS’20, Leibniz International Proceedings in Informatics (LIPIcs) vol. 170, pp 56:1-56:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020) of this paper) provided the regular predicates are restricted to piecewise testable ones. This result improves prior insights by Karandikar and Schnoebelen by extending the logic and saving one exponent in the space bound. Its proof consists of two main parts: First, we provide a quantifier elimination procedure that results in a formula with constants of bounded length (this generalises the procedure by Karandikar and Schnoebelen for first-order logic). From this, it follows that quantification in formulas can be restricted to words of bounded length, i.e., the second part of the proof is an adaptation of the method by Ferrante and Rackoff to counting logic and deviates significantly from the path of reasoning by Karandikar and Schnoebelen.

Muscle fatigue as a defense body mechanism against overload is a result of the products of incomplete oxygen oxidation such as reactive oxygen species. Hence, C60 fullerene as a powerful nanoantioxidant can be used to speed up the muscle recovery process after fatigue. Here, the residual effect of C60 fullerene on the biomechanical and biochemical markers of the development of muscle soleus fatigue in rats for 2 days after 5 days of its application was studied. The known antioxidant N-acetylcysteine (NAC) was used as a comparison drug. The atomic force microscopy to determine the size distribution of C60 fullerenes in an aqueous solution, the tensiometry of skeletal muscles, and the biochemical analysis of their tissues and rat blood were used in this study. It was found that after the cessation of NAC injections, the value of the integrated muscle power is already slightly different from the control (5%-7%) on the first day, and on the second day, it does not significantly differ from the control. At the same time, after the cessation of C60 fullerene injections, its residual effect was 45%-50% on the first day, and 17%-23% of the control on the second one. A significant difference (more than 25%) between the pro- and antioxidant balance in the studied muscles and blood of rats after the application of C60 fullerene and NAС plays a key role in the long-term residual effect of C60 fullerene. This indicates prolonged kinetics of C60 fullerenes elimination from the body, which contributes to their long-term (at least 2 days) compensatory activation of the endogenous antioxidant system in response to muscle stimulation, which should be considered when developing new therapeutic agents based on these nanoparticles.

We present a highly efficient simulation method for the calculation of three-dimensional quasi-static interface shapes under the influence of electric fields. The method is especially useful for the simulation of microfluidic systems driven by electrowetting on dielectrics because it accounts automatically and inherently for the highly non-trivial interface shape in the vicinity of the triple-phase contact. In particular, the voltage independence of the local contact angle predicted based on analytical considerations is correctly reproduced in all our simulations. For the calculation of the shape of the interface, the geometry is triangulated and the mesh nodes are shifted until the system energy becomes minimal. The same mesh is also used to calculate the electric field using the boundary-element method. Therefore, only the surface of the geometry needs to be meshed, and no volume meshes are involved. The method can be used for the simulation of closed systems with a constant volume (e.g., droplet-based microfluidics) while preserving the volume very precisely as well as open systems (e.g., the liquid-air interface within micro-cavities or capillaries). Additional effects, such as the influence of gravitational forces, can easily be taken into account. In contrast to other efficient simulations, such as the volume-of-fluid, level-set, or phase-field methods, ideally, sharp interfaces are obtained. We calculate interface shapes for exemplary systems and compare with analytical as well as experimental results.

During the impregnation of reinforcement fabrics in liquid composite molding processes, the flow within fiber bundles and the channels between the fiber bundles usually advances at different velocities. This so-called “dual-scale flow” results in void formation inside the composite material and has a negative effect on its mechanical properties. Semi-empirical models can be applied to calculate the extent of the dual-scale flow. In this study, a methodology is presented that stops the impregnation of reinforcement fabrics at different filling levels by using a photo-reactive resin system. By means of optical evaluation, the theoretical calculation models of the dual-scale flow are validated metrologically. The results show increasingly distinct dual-scale flow effects with increasing pressure gradients. The methodology enables the measurability of microscopic differences in flow front progression to validate renowned theoretical models and compare simulations to measurements of applied injection processes.

Magnetorheological fluid (MR) based dampers have been established as an alternative to classical hydraulic dampers with proportional electromagnetic valves under vibration processes which demand adaptive damping forces. Almost all MR-dampers are spatially 1-Degree-of-Freedom (DOF) dampers, having only one axis or direction of damping force generation. In many technical applications there exist movements in more than one spatial DOF, eventually necessitating more than one damper. Because of this, the damping is required not only in one but in more spatial directions, yet adjustable. In this work, a new design of a spatial 3DOF MR damper is proposed to allow damping in three directions within one damping device. The underlying motivation is to spatially integrate three damping directions in one device to potentially reduce installation space compared to three separate 1 DOF dampers. The basic idea of the construction is to use one fluid chamber with several spatially distributed control elements at different positions of the fluid chamber. The control elements are electromagnets, generating the magnetic field in the fluid at different positions so that in total 3 spatial DOFs can be damped individually. Experiments and investigation are made, where the damper's behavior are analyzed not only in one single DOF but also in more than one DOF. It is shown, that the damping concept can generate damping in all three spatial DOFs, both individually or together. Moreover, the damping can be generated to be dominant in one specific direction, meanwhile minimum in the other direction orthogonal to it.