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Abstract: For a set $\mathcal{Q}$ of points in the plane and a real number $δ$ ≥ 0, let $\mathbb{G}_δ(\mathcal{Q})$ be the graph defined on $\mathcal{Q}$ by connecting each pair of points at distance at most $δ$. We consider the connectivity of $\mathbb{G}_δ(\mathcal{Q})$ in the best scenario when the location of a few of the points is uncertain, but we know for each uncertain point a line segment that contains it. More precisely, we consider the following optimization problem: given a set $\mathcal{P}$ of $n$ – $k$ points in the plane and a set $\mathcal{S}$ of $k$ line segments in the plane, find the minimum $δ$ ≥ 0 with the property that we can select one point $p_s$ ∈ $s$ for each segment $s$ ∈ $\mathcal{S}$ and the corresponding graph $\mathbb{G}_δ(\mathcal{P} ∪ \{p_s$ | $s ∈ \mathcal{S}\})$ is connected. It is known that the problem is NP-hard. We provide an algorithm to exactly compute an optimal solution in $\mathcal{O}( f (k)n$ ${\rm log}$ $n)$ time, for a computable function $f$ (·). This implies that the problem is FPT when parameterized by $k$. The best previous algorithm uses $\mathcal{O}((k!)^kk^{k+1} · n^{2k})$ time and computes the solution up to fixed precision.
Keywords: computational geometry, uncertainty, geometric optimization, fixed parameter tractability, parametric search
Published in DKUM: 21.10.2025; Views: 0; Downloads: 1
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Abstract: We present a novel approach to numerical modelling of thermal nanofluids based on the Euler–Lagrange method. This approach overcomes the challenge of extremely fine temporal discretization, which previous Euler–Lagrange nanofluid numerical models struggled to address, while also avoiding the need for too many Lagrangian nanoparticles. A numerical uncertainty assessment method is adapted for the proposed approach. The model is validated with a simple verification case and applied to simulate a closed natural circulation loop heat exchanger operating with heating power ranging from 10 W to 50 W and nanoparticle volume fractions of 0.5% to 2%, using an Al2O3–water nanofluid. Results are compared with experimental temperature measurements and an Euler–Euler implementation of the same nanofluid. The model is also applied to simulate the natural convection inside a vertical enclosure, studied experimentally by other authors. The proposed novel approach demonstrates agreement with both experimental data and the Euler–Euler implementation, effectively capturing the overall behaviour of nanofluids. We establish, that the interplay of multiple transport phenomena, that occur in nanofluid operated devices, can be difficult to completely reproduce numerically within the framework of current modelling assumptions.
Keywords: Euler–Lagrange nanofluid modelling, numerical uncertainty assessment, natural convection loop simulation, nanoparticle concentration analysis, nanofluid heat transfer
Published in DKUM: 17.06.2025; Views: 0; Downloads: 7
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Abstract: This thesis focuses on improving the simulation, estimation, and accuracy of parameter identification in lithium-ion battery models. The key objective was to enhance a previously developed program by transitioning it to an object-oriented design, making it more efficient, user-friendly, and modular. Additionally, efforts were made to optimize the parameter estimation process by upgrading the cost function used during simulations and integrating real-world battery measurement data, specifically for the LGM50 battery type. The first step in the thesis involved reworking the codebase to an object-oriented structure, which improved not only the code’s clarity but also its extensibility and efficiency. With this change, the program was better suited for future improvements and became more accessible for other users through simplified installation procedures. This was accompanied by the implementation of unit testing to ensure the reliability of the code. Experiments were conducted across a range of discharge rates (from 0.05C to 1C) to evaluate the performance of the model under different conditions. These tests helped to identify trends in how the model responded to changes in operational parameters. Additionally, a dynamic pulse test was performed, which allowed for more precise estimation of the parameters. The results of these tests demonstrated the robustness of the methodology, especially under dynamic conditions. A major innovation introduced in this thesis was the development of a new cost function, which led to noticeable improvements in parameter estimation accuracy, particularly under high discharge rates and when estimating multiple parameters simultaneously. This new cost function proved especially effective in more complex scenarios, where the original cost function struggled to maintain the same level of accuracy. The program’s capabilities were further extended by incorporating real experimental data. Using a constant discharge profile for the LGM50 battery, the results showed some challenges when dealing with real-world data, particularly due to issues in measurement or data preprocessing. Nonetheless, the model consistently produced solutions, although the accuracy was influenced by the quality of the input data. The thesis concludes by highlighting the success of the improvements made, both in terms of the program’s structure and the precision of its estimations. However, it also emphasizes the importance of improving the quality of real-world data to fully leverage the model’s potential in practical applications. This work lays a foundation for future developments in battery modeling, providing a framework that is adaptable for further research and practical use.
Keywords: Machine Learning, Lithium-Ion Batteries, Parameter Estimation, Uncertainty Quantification, Real-experimental data
Published in DKUM: 03.03.2025; Views: 0; Downloads: 45
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Abstract: The paper studies the effects of foreign (the US, the UK and the Chinese) and domestic economic policy uncertainty (EPU) shocks on unemployment in Germany, France, Italy and Spain. The analysis is run separately for the rates of adult and youth unemployment. Impulse responses derived from vector autoregressive models show that the magnitudes of the responses of the adult and youth segments of the labour market are quite different. Following an uncertainty shock, the youth unemployment rate increases significantly more than the adult unemployment rate. This is the case for France, Italy and Spain. The German labour market seems to be resistant to foreign (except Chinese) and domestic EPU shocks, while the remaining labour markets, foremost the Spanish and Italian ones, are susceptible to uncertainty shocks, especially to the US EPU shocks.
Keywords: economic policy uncertainty, youth unemployment, adult unemployment, spillover effects, impulse responses
Published in DKUM: 26.09.2023; Views: 370; Downloads: 46
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Abstract: The aim of this doctoral dissertation was to develop a general methodology for sustainable integration of company's supply networks into nearby regional networks by i) integrating renewables, thereby increasing company's energy self-sufficiency, ii) by performing multi-objective synthesis in order to obtain economically efficient and yet environmentally benign or even unburdening solutions, and iii) to perform dynamic and stochastic synthesis under uncertainties in dynamically changing market conditions in order to obtain more reliable and realistic solutions. The research work is directly interlinked with a large-scale European meat producing company Perutnina Ptuj d.d., which is located in the heart of Slovenia. The aim of the first part was to integrate renewables into companies’ supply-networks at regional level in order to maximize the self-sufficiencies of their energy supplies. This concerns companies’ activities from the use of natural resources to supplying their final products to the customers being interlinked with their regional networks. A Mixed-Integer Linear Programming (MILP) model has been developed for the integration of both the companies’ and surrounding regional supply-networks and the utilization of different types of renewables as sources for the companies’ energy supplies. The potential renewable energy sources, which are located within companies surrounding region are solar, biomass, organic and animal wastes. The result indicates that by sufficient integration of renewables into companies’ supply networks, profitable and yet energy self-sufficient solutions can be obtained. The second part presents the multi-objective synthesis of a company’s supply-network by integrating renewables and accounting for several environmental footprints. A previously developed model for achieving energy self-sufficiency by integrating renewables into companies’ supply-networks has been extended for the evaluation of environmental impacts, such as energy, carbon, nitrogen, and water footprints. The achievement of an energy self-sufficient supply-network has been considered whilst significantly reducing environmental impacts. Direct (burdening) and indirect (unburdening) effects that form total effects on the environment are considered for the evaluation of environmental footprints. This approach identifies those alternative energy production technologies that are more profitable and environmentally more benign with significant unburdening capabilities. The results showed significant unburdening of the environment in terms of carbon and nitrogen footprints; however, higher burdening in terms of the water footprint. The third part presents a multi-objective MILP synthesis of a dynamic supply-network under uncertainty applied to the company. The previously-developed multi-objective model for achieving energy self-sufficiency by integrating renewables into companies’ supply-networks has now been extended to account for the dynamic consideration of variable supply and demand over the year, for uncertainties related to products’ demand and sun radiation, and for multi-objective optimisation, in order to obtain the most sustainable company’s supply-network. The sustainable synthesis of a company’s network is performed regarding the integration of the renewables such as biomass and other wastes, and solar energy. The obtained solutions are those reflecting maximal profit, reflecting constantly-changing dynamic market conditions, accounting for several uncertain parameters, and protecting the environment.
Keywords: Company's supply network, Renewables, Environmental Impacts, Dynamic synthesis, Flexibility, Multi-objective optimisation, Uncertainty
Published in DKUM: 21.07.2017; Views: 1694; Downloads: 185
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