A first step toward higher order chain rules in abelian functor calculus

One of the fundamental tools of undergraduate calculus is the chain rule. The notion of higher order directional derivatives was developed by Huang, Marcantognini, and Young, along with a corresponding higher order chain rule. When Johnson and McCarthy established abelian functor calculus, they proved a chain rule for functors that is analogous to the directional derivative chain rule when $n = 1$. In joint work with Bauer, Johnson, and Riehl, we defined an analogue of the iterated directional derivative and provided an inductive proof of the analogue to the chain rule of Huang et al. This paper consists of the initial investigation of the chain rule found in Bauer et al., which involves a concrete computation of the case when $n=2$. We describe how to obtain the second higher order directional derivative chain rule for abelian functors. This proof is fundamentally different in spirit from the proof given in Bauer et al. as it relies only on properties of cross effects and the linearization of functors

Influence of functional rider and horse asymmetries on saddle force distribution during stance and in sitting trot

Asymmetric forces exerted on the horse's back during riding are assumed to have a negative effect on rider–horse interaction, athletic performance, and health of the horse. Visualized on a saddle pressure mat, they are initially blamed on a nonfitting saddle. The contribution of horse and rider to an asymmetric loading pattern, however, is not well understood. The aim of this study was to investigate the effects of horse and rider asymmetries during stance and in sitting trot on the force distribution on the horse's back using a saddle pressure mat and motion capture analysis simultaneously. Data of 80 horse-rider pairs (HRP) were collected and analyzed using linear (mixed) models to determine the influence of rider and horse variables on asymmetric force distribution. Results showed high variation between HRP. Both rider and horse variables revealed significant relationships to asymmetric saddle force distribution (P < .001). During sitting trot, the collapse of the rider in one hip increased the force on the contralateral side, and the tilt of the rider's upper body to one side led to more force on the same side of the pressure mat. Analyzing different subsets of data revealed that rider posture as well as horse movements and conformation can cause an asymmetric force distribution. Because neither horse nor rider movement can be assessed independently during riding, the interpretation of an asymmetric force distribution on the saddle pressure mat remains challenging, and all contributing factors (horse, rider, saddle) need to be considered

A machine learning route between band mapping and band structure

The electronic band structure (BS) of solid state materials imprints the multidimensional and multi-valued functional relations between energy and momenta of periodically confined electrons. Photoemission spectroscopy is a powerful tool for its comprehensive characterization. A common task in photoemission band mapping is to recover the underlying quasiparticle dispersion, which we call band structure reconstruction. Traditional methods often focus on specific regions of interests yet require extensive human oversight. To cope with the growing size and scale of photoemission data, we develop a generic machine-learning approach leveraging the information within electronic structure calculations for this task. We demonstrate its capability by reconstructing all fourteen valence bands of tungsten diselenide and validate the accuracy on various synthetic data. The reconstruction uncovers previously inaccessible momentum-space structural information on both global and local scales in conjunction with theory, while realizing a path towards integrating band mapping data into materials science databases

The Great Lakes School of Turfgrass Science: A Nine-State Online Collaboration to Improve the Turfgrass Short Course

Increasing costs and decreasing numbers of university Extension faculty have made it difficult to provide quality turfgrass short course education. In response, faculty from nine institutions collaborated to develop the Great Lakes School of Turfgrass Science. This 12-week online course provides students with unique learning experiences through a combination of assigned readings, quizzes, lectures, and live instructor discussion. Student attendance increased and costs decreased relative to traditional in-person short courses. Additionally, student feedback has been overwhelmingly positive. These results demonstrate that online courses such as this can provide an effective and flexible source of knowledge that meets the busy schedules of students and instructors

Computational Prediction of Primary Breakup in Fuel Spray Nozzles for Aero-Engine Combustors

[EN] Primary breakup of liquid fuel in the vicinity of fuel spray nozzles as utilized in aero-engine combustors is numerically investigated. As grid based methods exhibit a variety of disadvantages when it comes to the prediction of multiphase flows, the ”Smoothed Particle Hydrodynamics“ (SPH)-method is employed. The eligibility of the method to analyze breakup of fuel has been demonstrated in recent publications by Braun et al, Dauch et al and Koch et al [1, 2, 3, 4]. In the current paper a methodology for the investigation of the two-phase flow in the vicinity of fuel spray nozzles at typical operating conditions is proposed. Due to lower costs in terms of computing time, 2D predictions are desired. However, atomization of fluids is inherently three dimensional. Hence, differences between 2D and 3D predictions are to be expected. In course of this study, predictions in 2D and based on a 3D sector are presented. Differences in terms of gaseous flow, ligament shape and mixing are assessed.This work was performed on the computational resource ForHLR Phase II funded by the Ministry of Science, Research and Arts Baden-Württemberg and DFG (”Deutsche Forschungsgemeinschaft“). In addition the authors would like to thank Rolls-Royce Deutschland Ltd & Co KG for the outstanding cooperation. The authors also are grateful for many lively and fruitful discussions with Simon Holz.Dauch, T.; Braun, S.; Wieth, L.; Chaussonnet, G.; Keller, M.; Koch, R.; Bauer, H. (2017). Computational Prediction of Primary Breakup in Fuel Spray Nozzles for Aero-Engine Combustors. En Ilass Europe. 28th european conference on Liquid Atomization and Spray Systems. Editorial Universitat Politècnica de València. 806-813. https://doi.org/10.4995/ILASS2017.2017.4693OCS80681

Hybridized intervalley moir\ue9 excitons and flat bands in twisted WSe(2)bilayers

The large surface-to-volume ratio in atomically thin 2D materials allows to efficiently tune their properties through modifications of their environment. Artificial stacking of two monolayers into a bilayer leads to an overlap of layer-localized wave functions giving rise to a twist angle-dependent hybridization of excitonic states. In this joint theory-experiment study, we demonstrate the impact of interlayer hybridization on bright and momentum-dark excitons in twisted WSe(2)bilayers. In particular, we show that the strong hybridization of electrons at the ? point leads to a drastic redshift of the momentum-dark K-? exciton, accompanied by the emergence of flat moire exciton bands at small twist angles. We directly compare theoretically predicted and experimentally measured optical spectra allowing us to identify photoluminescence signals stemming from phonon-assisted recombination of layer-hybridized dark excitons. Moreover, we predict the emergence of additional spectral features resulting from the moire potential of the twisted bilayer lattice