Finite symmetries of quantum character stacks

For a finite group $D$, we study categorical factorisation homology on oriented surfaces equipped with principal $D$-bundles, which `integrates' a (linear) balanced braided category $\mathcal{A}$ with $D$-action over those surfaces. For surfaces with at least one boundary component, we identify the value of factorisation homology with the category of modules over an explicit algebra in $\mathcal{A}$, extending the work of Ben-Zvi, Brochier and Jordan to surfaces with $D$-bundles. Furthermore, we show that the value of factorisation homology on annuli, boundary conditions, and point defects can be described in terms of equivariant representation theory. Our main example comes from an action of Dynkin diagram automorphisms on representation categories of quantum groups. We show that in this case factorisation homology gives rise to a quantisation of the moduli space of flat twisted bundles.Comment: 38 pages, 14 figures, comments welcom

The Treaty of Lisbon: A Second Look at the Institutional Innovations

This book examines the institutional innovations that are gradually being introduced as a result of the Treaty of Lisbon

CFD study of oil-jet gear interaction flow phenomena in spur gears

Oil-jet lubrication and cooling of high-speed gears is frequently employed in aeronautical systems, such as novel high-bypass civil aero engines based on the geared turbofan technology. Using such oil-jet system, practitioners aim to achieve high cooling rates on the flanks of the highly thermally loaded gears with minimum oil usage. Thus, for an optimal design, detailed knowledge about the flow processes is desired. These involve the oil exiting the nozzle, the oil impacting on the gear teeth, the oil spreading on the flanks, the subsequent oil fling-off, as well as the effect of the design parameters on the oil flow. Better understanding of these processes will improve the nozzle design phase, e.g. regarding the nozzle positioning and orientation, as well as the nozzle sizing and operation. Most related studies focus on the impingement depth to characterize the two-phase flow. However, the level of information of this scalar value is rather low for a complete description of the highly dynamic three-dimensional flow. Motivated by the advancements in numerical methods and the computational resources available nowadays, the investigation of the oil-jet gear interaction by means of computational fluid dynamics (CFD) has come into focus lately. In this work, a numerical setup based on the volume-of-fluid method is presented and employed to investigate the two-phase flow phenomena occurring in the vicinity of the gear teeth. The setup consists of a single oil-jet impinging on a single rotating spur gear. By introducing new metrics for characterizing the flow phenomena, extensive use of the possibilities of modern CFD is made, allowing a detailed transient and spatially resolved flow analysis. Thus, not only the impingement depth, but also the temporal and spatial evolution of wetted areas on the gear flanks, as well as the evolution of the oil volume in contact with the gear flanks are extracted from the simulation data and compared in a CFD study. The study consists of 21 different simulation cases, whereby the effect of varying the jet velocity, the jet inclination angle, the jet diameter, and the gear speed are examined. Consistent results compared to a simplified analytical approach for the impinging depth are obtained and the results for the newly introduced metrics are presented

Numerische Simulation der Ölstrahl-Zahnrad-Interaktion bei Flugtriebwerken mit hohem Nebenstromverhältnis: Stand der Forschung

Anforderungen aus der Flugtriebwerksentwicklung erfordern eine noch effizientere Gestaltung des Ölsystems zur Kühlung und Schmierung von schnelllaufenden Untersetzungsgetrieben. Deshalb unternehmen Wissenschaftler weltweit Anstrengungen, um die bei hohen Drehzahlen angewandte Ölstrahlschmierung und -kühlung zu erforschen. Fortschritte bei den CFD Methoden und gestiegene Rechenkapazitäten führen zu einem gestiegenen Einsatz numerischer Methoden zur Untersuchung der Ölstrahl-Zahnrad-Interaktion, wobei hauptsächlich die Volume-of-Fluid und die Smoothed Particle Hydrodynamics Methode eingesetzt werden. In diesem Übersichtsartikel wird der Stand der Forschung in diesem Bereich dargestellt und die Vor- und Nachteile der eingesetzten Methoden skizziert

Identifying and Characterizing Types of Balance Recovery Strategies Among Females and Males to Prevent Injuries in Free-Standing Public Transport Passengers

Free-standing passengers on public transport are subjected to perturbations during non-collision incidents caused by driver maneuvers, increasing the risk of injury. In the literature, the step strategy is described as a recovery strategy during severe perturbations. However, stepping strategies increase body displacement, ultimately subjecting passengers to higher risk of impacts and falls on public transport. This study investigates the influence of different recovery strategies on the outcome of balance recovery of free-standing public transport passengers, challenged in postural balance by the non-uniform vehicle dynamics. From high-speed video recordings, a qualitative investigation of the balance responses of volunteer participants in a laboratory experiment was provided. On a linearly moving platform, 24 healthy volunteers (11 females and 13 males) were subjected to perturbation profiles of different magnitude, shape and direction, mimicking the typical acceleration and deceleration behavior of a bus. A methodology categorizing the balancing reaction to an initial strategy and a recovery strategy, was used to qualitatively identify, characterize and, evaluate the different balance strategies. The effectiveness of different strategies was assessed with a grading criterion. Statistical analysis based on these ordinal data was provided. The results show that the current definition in the literature of the step strategy is too primitive to describe the different identified recovery strategies. In the volunteers with the most successful balancing outcome, a particularly effective balance recovery strategy not yet described in the literature was identified, labeled the fighting stance. High jerk perturbations seemed to induce faster and more successful balance recovery, mainly for those adopting the fighting stance, compared to the high acceleration and braking perturbation profiles. Compared to the pure step strategy, the characteristics of the fighting stance seem to increase the ability to withstand higher perturbations by increasing postural stability to limit body displacement

Human Response to Longitudinal Perturbations of Standing Passengers on Public Transport During Regular Operation

This study investigates the response of standing passengers on public transport who experience balance perturbations during non-collision incidents. The objective of the study was to analyse the effects of the perturbation characteristics on the initial responses of the passengers and their ability to maintain their balance. Sled tests were conducted on healthy volunteers aged 33.8 +/- 9.2 years (13 males, 11 females) standing on a moving platform, facilitating measurements of the initial muscle activity and stepping response of the volunteers. The volunteers were exposed to five different perturbation profiles representing typical braking and accelerating manoeuvres of a public transport bus in the forward and backward direction. The sequence of muscle activations in lower-extremity muscles was consistent for the perturbation pulses applied. For the three acceleration pulses combining two magnitudes for acceleration (1.5 and 3.0 m/s(2)) and jerk (5.6 and 11.3 m/s(3)), the shortest muscle onset and stepping times for the passengers to recover their balance were observed with the higher jerk value, while the profile with the higher acceleration magnitude and longer duration induced more recovery steps and a higher rate of safety-harness deployment. The tendency for a shorter response time was observed for the female volunteers. For the two braking pulses (1.0 and 2.5 m/s(2)), only the lower magnitude pulse allowed balance recovery without compensatory stepping. The results obtained provide a reference dataset for human body modelling, the development of virtual test protocols, and operational limits for improving the safety of public transportation vehicles and users

New Insights in the Primary Breakup Process of Prefilming Airblast Atomizers by SPH Predictions

Smoothed Particles Hydrodynamics (SPH) simulations of the primary breakup process have been conducted using a planar prefilming airblast atomizer geometry that has been investigated experimentally. Despite the fact that a 2D study is conducted, most of the breakup phenomena are captured by the simulations. A variation of the liquid mass flow effects the simulated air flow and spray in the same way as indicated by experimental results. Using this numerical approach new insights in the primary breakup process are obtained, which can be received only difficultly in experiments. The presence of liquid at the trailing edge of the prefilmer is quantified from a side view perspective. In addition, the influence of a variation of the liquid mass flow on the liquid film and the presence of liquid at the trailing edge are characterized. Furthermore, three different wetting modes of the trailing edge are observed: The non-wetting mode which is characterized by one film wave per breakup event as well as the unstable and stable accumulation modes which are related to two film waves per breakup event. Finally, it is demonstrated that the liquid film waves and the breakup of the ligaments are slightly decoupled by the accumulation of liquid at the trailing edge

Three-dimensional SPH simulation of a twin-fluid atomizer operating at high pressure [in press]

In the context of biofuel production, a twin-fluid atomizer is investigated by the means of the Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) method. This configuration consists of a round liquid jet discharging at low velocity into a quiescent cavity. The liquid is atomized by a high-speed turbulent co-flow. This configuration has been studied experimentally as well. In order to reflect the experimental conditions, the liquid is a mixture of Glycerol and water and a constant viscosity is set to 200 mPa s. The ambient pressure is 11 bar and the gas velocity is 58.3 m/s, leading to a gas Reynolds number of 137 000 and a Weber number of 1375. The three-dimensional numerical domain consists of the twin-fluid nozzle and a cavity of 30 mm length and 17.4 mm diameter. The spatial resolution is 33 \textmu m, which leads to 208 million of particles. The simulation is run for 45 ms of physical time using 2000 CPU. The results show that the fiber-mode breakup is well captured by the method. The shape and the dynamics of the fragmented liquid lumps are in very good qualitative agreement with the experimental observations. Further quantitative analyses are performed in terms of time average of the liquid phase, and time evolution of the spray characteristics at the exit of the cavity. Finally, due to the Lagrangian nature of the SPH method, the breakup sequence of each liquid elements can be monitored and collected. Hence, the fragmentation spectrum of this configuration is also presented

Auslander-Buchweitz approximation theory for triangulated categories

We introduce and develop an analogous of the Auslander-Buchweitz approximation theory (see \cite{AB}) in the context of triangulated categories, by using a version of relative homology in this setting. We also prove several results concerning relative homological algebra in a triangulated category \T, which are based on the behavior of certain subcategories under finiteness of resolutions and vanishing of Hom-spaces. For example: we establish the existence of preenvelopes (and precovers) in certain triangulated subcategories of \T. The results resemble various constructions and results of Auslander and Buchweitz, and are concentrated in exploring the structure of a triangulated category \T equipped with a pair (\X,\omega), where \X is closed under extensions and $\omega$ is a weak-cogenerator in \X, usually under additional conditions. This reduces, among other things, to the existence of distinguished triangles enjoying special properties, and the behavior of (suitably defined) (co)resolutions, projective or injective dimension of objects of \T and the formation of orthogonal subcategories. Finally, some relationships with the Rouquier's dimension in triangulated categories is discussed.Comment: To appear at: Appl. Categor. Struct. (2011); 22 page