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- ItemGalilean Bulk-Surface Electrothermodynamics and Applications to Electrochemistry(Basel : MDPI, 2023) Müller, Rüdiger; Landstorfer, ManuelIn this work, the balance equations of non-equilibrium thermodynamics are coupled to Galilean limit systems of the Maxwell equations, i.e., either to (i) the quasi-electrostatic limit or (ii) the quasi-magnetostatic limit. We explicitly consider a volume (Formula presented.), which is divided into (Formula presented.) and (Formula presented.) by a possibly moving singular surface S, where a charged reacting mixture of a viscous medium can be present on each geometrical entity (Formula presented.). By the restriction to the Galilean limits of the Maxwell equations, we achieve that only subsystems of equations for matter and electromagnetic fields are coupled that share identical transformation properties with respect to observer transformations. Moreover, the application of an entropy principle becomes more straightforward and finally helps estimate the limitations of the more general approach based the full set of Maxwell equations. Constitutive relations are provided based on an entropy principle, and particular care is taken in the analysis of the stress tensor and the momentum balance in the general case of non-constant scalar susceptibility. Finally, we summarise the application of the derived model framework to an electrochemical system with surface reactions.
- ItemTopology- and Geometry-Controlled Functionalization of Nanostructured Metamaterials(Basel : MDPI, 2023) Fomin, Vladimir M.; Marquardt, Oliver[no abstract available]
- ItemFeedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise(Basel : MDPI, 2022) Djurdjevac Conrad, Nataša; Köppl, Jonas; Djurdjevac, AnaWe introduce an agent-based model for co-evolving opinions and social dynamics, under the influence of multiplicative noise. In this model, every agent is characterized by a position in a social space and a continuous opinion state variable. Agents’ movements are governed by the positions and opinions of other agents and similarly, the opinion dynamics are influenced by agents’ spatial proximity and their opinion similarity. Using numerical simulations and formal analyses, we study this feedback loop between opinion dynamics and the mobility of agents in a social space. We investigate the behaviour of this ABM in different regimes and explore the influence of various factors on the appearance of emerging phenomena such as group formation and opinion consensus. We study the empirical distribution, and, in the limit of infinite number of agents, we derive a corresponding reduced model given by a partial differential equation (PDE). Finally, using numerical examples, we show that a resulting PDE model is a good approximation of the original ABM.
- ItemSemiconductor laser linewidth theory revisited(Basel : MDPI, 2021) Wenzel, Hans; Kantner, Markus; Radziunas, Mindaugas; Bandelow, UweMore and more applications require semiconductor lasers distinguished not only by large modulation bandwidths or high output powers, but also by small spectral linewidths. The theoretical understanding of the root causes limiting the linewidth is therefore of great practical relevance. In this paper, we derive a general expression for the calculation of the spectral linewidth step by step in a self-contained manner. We build on the linewidth theory developed in the 1980s and 1990s but look from a modern perspective, in the sense that we choose as our starting points the time-dependent coupled-wave equations for the forward and backward propagating fields and an expansion of the fields in terms of the stationary longitudinal modes of the open cavity. As a result, we obtain rather general expressions for the longitudinal excess factor of spontaneous emission (K-factor) and the effective α-factor including the effects of nonlinear gain (gain compression) and refractive index (Kerr effect), gain dispersion, and longitudinal spatial hole burning in multi-section cavity structures. The effect of linewidth narrowing due to feedback from an external cavity often described by the so-called chirp reduction factor is also automatically included. We propose a new analytical formula for the dependence of the spontaneous emission on the carrier density avoiding the use of the population inversion factor. The presented theoretical framework is applied to a numerical study of a two-section distributed Bragg reflector laser.
- ItemTopology- and Geometry-Controlled Functionalization of Nanostructured Metamaterials(Basel : MDPI, 2023) Fomin, Vladimir M.; Marquardt, Oliver[No abstract available]
- ItemOn the Regularity of Weak Solutions to Time-Periodic Navier–Stokes Equations in Exterior Domains(Basel : MDPI, 2022) Eiter, ThomasConsider the time-periodic viscous incompressible fluid flow past a body with non-zero velocity at infinity. This article gives sufficient conditions such that weak solutions to this problem are smooth. Since time-periodic solutions do not have finite kinetic energy in general, the well-known regularity results for weak solutions to the corresponding initial-value problem cannot be transferred directly. The established regularity criterion demands a certain integrability of the purely periodic part of the velocity field or its gradient, but it does not concern the time mean of these quantities.
- ItemDecomposition of a Cooling Plant for Energy Efficiency Optimization Using OptTopo(Basel : MDPI, 2022) Thiele, Gregor; Johanni, Theresa; Sommer, David; Krüger, JörgThe operation of industrial supply technology is a broad field for optimization. Industrial cooling plants are often (a) composed of several components, (b) linked using network technology, (c) physically interconnected, and (d) complex regarding the effect of set-points and operating points in every entity. This leads to the possibility of overall optimization. An example containing a cooling tower, water circulations, and chillers entails a non-linear optimization problem with five dimensions. The decomposition of such a system allows the modeling of separate subsystems which can be structured according to the physical topology. An established method for energy performance indicators (EnPI) helps to formulate an optimization problem in a coherent way. The novel optimization algorithm OptTopo strives for efficient set-points by traversing a graph representation of the overall system. The advantages are (a) the ability to combine models of several types (e.g., neural networks and polynomials) and (b) an constant runtime independent from the number of operation points requested because new optimization needs just to be performed in case of plant model changes. An experimental implementation of the algorithm is validated using a simscape simulation. For a batch of five requests, OptTopo needs 61 (Formula presented.) while the solvers Cobyla, SDPEN, and COUENNE need 0.3 min, 1.4 min, and 3.1 min, respectively. OptTopo achieves an efficiency improvement similar to that of established solvers. This paper demonstrates the general feasibility of the concept and fortifies further improvements to reduce computing time.
- ItemStability of Weak Solutions to Parabolic Problems with Nonstandard Growth and Cross–Diffusion(Basel : MDPI, 2021) Erhardt, André H.We study the stability of a unique weak solution to certain parabolic systems with nonstandard growth condition, which are additionally dependent on a cross-diffusion term. More precisely, we show that two unique weak solutions of the considered system with different initial values are controlled by their initial values.