Stationary solutions of liquid two-layer thin film models

We investigate stationary solutions of a thin-film model for liquid two-layer flows in an energetic formulation that is motivated by its gradient flow structure. The goal is to achieve a rigorous understanding of the contact-angle conditions for such two-layer systems. We pursue this by investigating a corresponding energy that favors the upper liquid to dewet from the lower liquid substrate, leaving behind a layer of thickness $h_*$. After proving existence of stationary solutions for the resulting system of thin-film equations we focus on the limit $h_*\to 0$ via matched asymptotic analysis. This yields a corresponding sharp-interface model and a matched asymptotic solution that includes logarithmic switch-back terms. We compare this with results obtained using $\Gamma$-convergence, where we establish existence and uniqueness of energetic minimizers in that limit

Automatic detection of service initiation signals used in bars

Loth S, Huth K, de Ruiter J. Automatic detection of service initiation signals used in bars. Frontiers in Psychology. 2013;4: 557.Recognizing the intention of others is important in all social interactions, especially in the service domain. Enabling a bartending robot to serve customers is particularly challenging as the system has to recognize the social signals produced by customers and respond appropriately. Detecting whether a customer would like to order is essential for the service encounter to succeed. This detection is particularly challenging in a noisy environment with multiple customers. Thus, a bartending robot has to be able to distinguish between customers intending to order, chatting with friends or just passing by. In order to study which signals customers use to initiate a service interaction in a bar, we recorded real-life customer-staff interactions in several German bars. These recordings were used to generate initial hypotheses about the signals customers produce when bidding for the attention of bar staff. Two experiments using snapshots and short video sequences then tested the validity of these hypothesized candidate signals. The results revealed that bar staff responded to a set of two non-verbal signals: first, customers position themselves directly at the bar counter and, secondly, they look at a member of staff. Both signals were necessary and, when occurring together, sufficient. The participants also showed a strong agreement about when these cues occurred in the videos. Finally, a signal detection analysis revealed that ignoring a potential order is deemed worse than erroneously inviting customers to order. We conclude that (a) these two easily recognizable actions are sufficient for recognizing the intention of customers to initiate a service interaction, but other actions such as gestures and speech were not necessary, and (b) the use of reaction time experiments using natural materials is feasible and provides ecologically valid results

Epitaxial thin films of binary Eu-compounds close to a valence transition

Intermetallic binary compounds of europium reveal a variety of interesting phenomena due to the interconnection between two different magnetic and 4f electronic (valence) states, which are particularly close in energy. The valence states or magnetic properties are thus particularly sensitive to strain-tuning in these materials. Consequently, we grew epitaxial EuPd$_2$ (magnetic Eu$^{2+}$) and EuPd$_3$ (nonmagnetic Eu$^{3+}$) thin films on MgO(001) substrates using molecular beam epitaxy. Ambient X-ray diffraction confirms an epitaxial relationship of cubic Laves-type (C15) EuPd$_2$ with an (111)-out-of plane orientation, whereby four distinct in-plane crystallographic domains develop. For simple cubic EuPd$_3$ two different out-of-plane orientations can be obtained by changing the substrate annealing temperature under ultra-high vacuum conditions from 600{\deg} C to 1000{\deg} C for one hour. A small resistance minimum evolves for EuPd$_3$ thin films grown with low temperature substrate annealing, which was previously found even in single crystals of EuPd$_3$ and might be attributed to a Kondo or weak localization effect. Absence of influence of an applied magnetic fields and magnetotransport measurements suggest always a nonmagnetic ground state for EuPd$_3$ thin films, i. e., a purely trivalent Eu valence, as previously found in EuPd3 single crystals. For EuPd$_2$ magnetic ordering below ~72 K is observed, quite similar to single crystal behaviour. Additional field dependent measurements of the magnetoresistance and the Hall effect show hysteresis effects below ~0.4 T and an anomalous Hall effect below ~70 K, which saturates around 1.4 T, thus proving a ferromagnetic ground state of the divalent Eu

Gradient flow perspective of thin-film bilayer flows

We study gradient flow formulations of thin-film bilayer flows with triple-junctions between liquid/liquid/air. First we highlight the gradient structure in the Stokes free-boundary flow and identify its solutions with the well known PDE with boundary conditions. Next we propose a similar gradient formulation for the corresponding thin-film model and formally identify solutions with those of the corresponding free-boundary problem. A robust numerical algorithm for the thin-film gradient flow structure is then provided. Using this algorithm we compare the sharp triple-junction model with precursor models. For their stationary solutions a rigorous connection is established using Gamma-convergence. For time-dependent solutions the comparison of numerical solutions shows a good agreement for small and moderate times. Finally we study spreading in the zero-contact angle case, where we compare numerical solutions with asymptotically exact source-type solutions

Gradient flow perspective of thin-film bilayer flows

We study gradient flow formulations of thin-film bilayer flows with triple-junctions between liquid/liquid/air. First we highlight the gradient structure in the Stokes free-boundary flow and identify its solutions with the well-known PDE with boundary conditions. Next we propose a similar gradient formulation for the corresponding thin-film model and formally identify solutions with those of the corresponding free-boundary problem. A robust numerical algorithm for the thin-film gradient flow structure is then provided. Using this algorithm we compare the sharp triple-junction model with precursor models. For their stationary solutions a rigorous connection is established using [Gamma]-convergence. For time-dependentsolutions the comparison of numerical solutions shows a good agreement for small and moderate times. Finally we study spreading in the zero-contact angle case, where we compare numerical solutions with asymptotically exact source-type solutions

Stationary solutions for two-layer lubrication equations

We investigate stationary solutions of flows of thin liquid bilayers in an energetic formulation which is motivated by the gradient flow structure of its lubrication approximation. The corresponding energy favors the liquid substrate to be only partially covered by the upper liquid. This is expressed by a negative spreading coefficient which arises from an intermolecular potential combining attractive and repulsive forces and leads to an ultra-thin layer of thickness ε. For the corresponding lubrication models existence of stationary solutions is proven. In the limit ε to 0 matched asymptotic analysis is applied to derive sharp-interface models and the corresponding contact angles, i.e. the Neumann triangle. In addition we use Γ-convergence and derive the equivalent sharp-interface models rigorously in this limit. For the resulting model existence and uniqueness of energetic minimizers are proven. The minimizers agree with solutions obtained by matched asymptotics

Digitale Drehtür Hessen – Förderung mathematisch interessierter Kinder und Jugendlicher

Das Projekt „Digitale Drehtür Hessen“ richtet sich als Enrichment-Angebot an mathematisch interessierte Schüler*innen der Primarstufe und Sekundarstufe I. Hierzu wird das Enrichment-Triad-Modell nach Renzulli (1981), siehe auch Rogalla (2009) oder auch Greiten (2016), adaptiert und digital umgesetzt. Im Projekt werden eigene Interessen weiterentwickelt und in fachlichen Kursangeboten aufgegriffen. Die Förderung findet parallel zum Regelunterricht statt. In der Pilotphase, bis voraussichtlich Sommer 2022, arbeiten mehrere Fächer der Justus-Liebig-Universität Gießen und verschiedene Schulen gemeinsam an der Realisierung dieses Angebots. Ab Sommer/Herbst 2022 soll das hessenweite Angebot, koordiniert vom Zentrum für Lehrerbildung Gießen und dem hessischen Kultusministerium, erfolgen

Magnetic properties of multi-domain epitaxial EuPd2_2 thin films

Europium intermetallic compounds show a variety of different ground states and anomalous physical properties due to the interactions between the localized 4f electrons and the delocalized electronic states. Europium is also the most reactive of the rare earth metals which might be the reason why very few works are concerned with the properties of Eu-based thin films. Here we address the low-temperature magnetic properties of ferromagnetic EuPd$_2$ thin films prepared by molecular beam epitaxy. The epitaxial (111)-oriented thin films grow on MgO (100) with eight different domain orientations. We analyze the low-temperature magnetic hysteresis behavior by means of micromagnetic simulations taking the multi-domain morphology explicitly into account and quantify the magnetic crystal anisotropy contribution. By ab initio calculations we trace back the microscopic origin of the magnetic anisotropy to thin film-induced biaxial strain

Efficiency and timing performance of the MuPix7 high-voltage monolithic active pixel sensor

The MuPix7 is a prototype high voltage monolithic active pixel sensor with 103 times 80 um2 pixels thinned to 64 um and incorporating the complete read-out circuitry including a 1.25 Gbit/s differential data link. Using data taken at the DESY electron test beam, we demonstrate an efficiency of 99.3% and a time resolution of 14 ns. The efficiency and time resolution are studied with sub-pixel resolution and reproduced in simulations.Comment: 7 pages, 13 figures, submitted to Nucl.Instr.Meth.

Seeking Attention: Testing a Model of Initiating Service Interactions

Loth S, Huth K, de Ruiter J. Seeking Attention: Testing a Model of Initiating Service Interactions. In: Hernández-López M de la O, Fernández Amaya L, eds. A Multidisciplinary Approach to Service Encounters. Studies in Pragmatics. Vol 14. Amsterdam: Brill; 2015: 229-247