The Non-Abelian Self-Dual String and the (2,0)-Theory

We argue that the relevant higher gauge group for the non-abelian generalization of the self-dual string equation is the string 2-group. We then derive the corresponding equations of motion and discuss their properties. The underlying geometric picture is a string structure, i.e. a categorified principal bundle with connection whose structure 2-group is the string 2-group. We readily write down the explicit elementary solution to our equations, which is the categorified analogue of the 't Hooft-Polyakov monopole. Our solution passes all the relevant consistency checks; in particular, it is globally defined on $\mathbb{R}^4$ and approaches the abelian self-dual string of charge one at infinity. We note that our equations also arise as the BPS equations in a recently proposed six-dimensional superconformal field theory and we show that with our choice of higher gauge structure, the action of this theory can be reduced to four-dimensional supersymmetric Yang-Mills theory.Comment: v3: 1+42 pages, presentation improved, typos fixed, published versio

Towards an M5-Brane Model I: A 6d Superconformal Field Theory

We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the string Lie 2-algebra as a gauge structure, which we motivated in previous work. The kinematical data contains a connection on a categorified principal bundle, which is the appropriate mathematical description of the parallel transport of self-dual strings. Our action can be written down for each of the simply laced Dynkin diagrams, and each case reduces to a four-dimensional supersymmetric Yang--Mills theory with corresponding gauge Lie algebra. Our action also reduces nicely to an M2-brane model which is a deformation of the ABJM model. While this action is certainly not the desired M5-brane model, we regard it as a key stepping stone towards a potential construction of the (2,0)-theory.Comment: 1+39 pages, v3: minor improvements, published versio

Unusual synchronization phenomena during electrodissolution of silicon: the role of nonlinear global coupling

The photoelectrodissolution of n-type silicon constitutes a convenient model system to study the nonlinear dynamics of oscillatory media. On the silicon surface, a silicon oxide layer forms. In the lateral direction, the thickness of this layer is not uniform. Rather, several spatio-temporal patterns in the oxide layer emerge spontaneously, ranging from cluster patterns and turbulence to quite peculiar dynamics like chimera states. Introducing a nonlinear global coupling in the complex Ginzburg-Landau equation allows us to identify this nonlinear coupling as the essential ingredient to describe the patterns found in the experiments. The nonlinear global coupling is designed in such a way, as to capture an important, experimentally observed feature: the spatially averaged oxide-layer thickness shows nearly harmonic oscillations. Simulations of the modified complex Ginzburg-Landau equation capture the experimental dynamics very well.Comment: To appear as a chapter in "Engineering of Chemical Complexity II" (eds. A.S. Mikhailov and G.Ertl) at World Scientific in Singapor

Analysis Of The Relevance Of Models, Influencing Factors And The Point In Time Of The Forecast On The Prediction Quality In Order-Related Delivery Time Determination Using Machine Learning

One of the main objectives of manufacturing companies that structure their manufacturing system according to the workshop principle is to meet the delivery dates communicated to the customer. One approach to avoid large delivery time buffers to stabilize liability of communicated delivery dates is to improve the forecasting quality of the initially determined planned delivery dates. In this context, machine learning methods are a promising approach for the dynamic, order-related forecasting of delivery times. In the development process of machine learning based applications for delivery time forecasting companies are challenged by the following questions: which influencing factors must be considered? Which machine learning models generate the best forecast quality? At what point in the production process does the application of machine learning methods for delivery time forecasting make sense from an economic perspective? Existing approaches do not adequately address these questions. In most cases, only few process steps are considered and only throughput times are forecasted instead of delivery times. The information available at the point in time when the delivery time is forecasted is not discussed. The considered input factors influencing the delivery time are reduced to the company's internal supply chain and therefore do not allow for a satisfactory forecast quality of the delivery time. External influencing factors are often not included. Therefore, this paper describes the influence of different machine learning models, different points in time for the forecasting itself and included influencing factors on the achievable forecast quality. The influence is determined by applying machine learning methods on delivery time forecasting to five real-world use cases