Mean--field electrodynamics: Critical analysis of various analytical approaches to the mean electromotive force

There are various analytical approaches to the mean electromotive force $\cal E =$ crucial in mean--field electrodynamics, with $\vec{u}$ and $\vec{b}$ being velocity and magnetic field fluctuations. In most cases the traditional approach, restricted to the second--order correlation approximation, has been used. Its validity is only guaranteed for a range of conditions, which is narrow in view of many applications, e.g., in astrophysics. With the intention to have a wider range of applicability other approaches have been proposed which make use of the so--called $\tau$--approximation, reducing correlations of third order in $\vec{u}$ and $\vec{b}$ to such of second order. After explaining some basic features of the traditional approach a critical analysis of the approaches of that kind is given. It is shown that they lead in some cases to results which are in clear conflict with those of the traditional approach. It is argued that this indicates shortcomings of the $\tau$--approaches and poses serious restrictions to their applicability. These shortcomings do not result from the basic assumption of the $\tau$--approximation. Instead, they seem to originate in some simplifications made in order to derive $\cal E$ without really solving the equations governing $\vec{u}$ and $\vec{b}$. A starting point for a new approach is described which avoids the conflict.Comment: 32 pages, no figures; accepted by Geophys. Astrophys. Fluid Dynam. A quenching formula for \alpha and a section on comparisons with numerical simulations added; references amended; changes in presentation and languag

Contributions to the theory of a two-scale homogeneous dynamo experiment

The principle of the Karlsruhe dynamo experiment is closely related to that of the Roberts dynamo working with a simple fluid flow which is, with respect to proper Cartesian co-ordinates x, y and z, periodic in x and y and independent of z. A modified Roberts dynamo problem is considered with a flow more similar to that in the experimental device. Solutions are calculated numerically, and on this basis an estimate of the excitation condition of the experimental dynamo is given. The modified Roberts dynamo problem is also considered in the framework of the mean-field dynamo theory, in which the crucial induction effect of the fluid motion is an anisotropic alpha-effect. Numerical results are given for the dependence of the mean-field coefficients on the fluid flow rates. The excitation condition of the dynamo is also discussed within this framework. The behavior of the dynamo in the nonlinear regime, i.e. with backreaction of the magnetic field on the fluid flow, depends on the effect of the Lorentz force on the flow rates. The quantities determining this effect are calculated numerically. The results for the mean-field coefficients and the quantities describing the backreaction provide corrections to earlier results, which were obtained under simplifying assumptions.Comment: 12 pages, 9 figures, accepted for publication in Phys. Rev.

The Mean Electromotive Force for MHD Turbulence: the Case of a Weak Mean Magnetic Field and Slow Rotation

The mean electromotive force in the framework of mean--field magnetohydrodynamics is found with a particular attention to the effect of a mean rotation of the fluid on the mean electromotive force. Anisotropy of the turbulence due to gradients of its intensity or its helicity are admitted. The mean magnetic field is considered to be weak enough to exclude quenching effects. Magnetic fluctuations with a zero mean magnetic field are taken into account. The Omega x J -effect works in the same way with velocity fluctuations and magnetic fluctuations. A contribution to the electromotive force connected with the symmetric parts of the gradient tensor of the mean magnetic field was found in the case of rotation, resulting from velocity or magnetic fluctuations. The implications of the results for the mean electromotive force for mean--field dynamo models are discussed with special emphasis to dynamos working without alpha-effect.Comment: 19 pages, REVTEX4, submitted to Geophys. Astrophys. Fluid Dynamic

Model-Driven Engineering Method to Support the Formalization of Machine Learning using SysML

Methods: This work introduces a method supporting the collaborative definition of machine learning tasks by leveraging model-based engineering in the formalization of the systems modeling language SysML. The method supports the identification and integration of various data sources, the required definition of semantic connections between data attributes, and the definition of data processing steps within the machine learning support. Results: By consolidating the knowledge of domain and machine learning experts, a powerful tool to describe machine learning tasks by formalizing knowledge using the systems modeling language SysML is introduced. The method is evaluated based on two use cases, i.e., a smart weather system that allows to predict weather forecasts based on sensor data, and a waste prevention case for 3D printer filament that cancels the printing if the intended result cannot be achieved (image processing). Further, a user study is conducted to gather insights of potential users regarding perceived workload and usability of the elaborated method. Conclusion: Integrating machine learning-specific properties in systems engineering techniques allows non-data scientists to understand formalized knowledge and define specific aspects of a machine learning problem, document knowledge on the data, and to further support data scientists to use the formalized knowledge as input for an implementation using (semi-) automatic code generation. In this respect, this work contributes by consolidating knowledge from various domains and therefore, fosters the integration of machine learning in industry by involving several stakeholders.Comment: 43 pages, 24 figure, 3 table

Electrical interferences in SFRA measurements

Power transformers are still among the most costly and critical components in an electrical power network. Thus, the importance of a reliable condition assessment of these assets increases due to the aging of transformer fleets. The Sweep Frequency Response Analysis (SFRA) has become an important standard test and provides comprehensive information about the mechanical and electrical integrity of the active part of power transformers. Electrical as well as geometrical changes in the magnetic core, the winding assembly and the clamping structure can be detected by a comparison of an actual measurement with a reference measurement. In contrast to traditional diagnostic methods, the SFRA is sensitive to external electrical interferences which may limit the comparability and can consequently lead to misinterpretation of the measurement results. For an optimum suppression of narrowband and broadband noise, software-based as well as hardware-based techniques can be utilized. This article discusses the theory of different noise sources and noise suppression techniques. Different case studies show the efficacy of measurements even in harsh conditions

Electrical interferences in SFRA measurements

Power transformers are still among the most costly and critical components in an electrical power network. Thus, the importance of a reliable condition assessment of these assets increases due to the aging of transformer fleets. The Sweep Frequency Response Analysis (SFRA) has become an important standard test and provides comprehensive information about the mechanical and electrical integrity of the active part of power transformers. Electrical as well as geometrical changes in the magnetic core, the winding assembly and the clamping structure can be detected by a comparison of an actual measurement with a reference measurement. In contrast to traditional diagnostic methods, the SFRA is sensitive to external electrical interferences which may limit the comparability and can consequently lead to misinterpretation of the measurement results. For an optimum suppression of narrowband and broadband noise, software-based as well as hardware-based techniques can be utilized. This article discusses the theory of different noise sources and noise suppression techniques. Different case studies show the efficacy of measurements even in harsh conditions

Model-Driven Engineering for Artificial Intelligence - A Systematic Literature Review

Objective: This study aims to investigate the existing body of knowledge in the field of Model-Driven Engineering MDE in support of AI (MDE4AI) to sharpen future research further and define the current state of the art. Method: We conducted a Systemic Literature Review (SLR), collecting papers from five major databases resulting in 703 candidate studies, eventually retaining 15 primary studies. Each primary study will be evaluated and discussed with respect to the adoption of (1) MDE principles and practices and (2) the phases of AI development support aligned with the stages of the CRISP-DM methodology. Results: The study's findings show that the pillar concepts of MDE (metamodel, concrete syntax and model transformation), are leveraged to define domain-specific languages (DSL) explicitly addressing AI concerns. Different MDE technologies are used, leveraging different language workbenches. The most prominent AI-related concerns are training and modeling of the AI algorithm, while minor emphasis is given to the time-consuming preparation of the data sets. Early project phases that support interdisciplinary communication of requirements, such as the CRISP-DM \textit{Business Understanding} phase, are rarely reflected. Conclusion: The study found that the use of MDE for AI is still in its early stages, and there is no single tool or method that is widely used. Additionally, current approaches tend to focus on specific stages of development rather than providing support for the entire development process. As a result, the study suggests several research directions to further improve the use of MDE for AI and to guide future research in this area

Mean-field concept and direct numerical simulations of rotating magnetoconvection and the geodynamo

A comparison is made between mean-field models and direct numerical simulations of rotating magnetoconvection and the geodynamo. The mean-field coefficients are calculated with the fluid velocity taken from the direct numerical simulations. The magnetic fields resulting from mean-field models are then compared with the mean magnetic field from the direct numerical simulations