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Friction stir welding is a modern welding technology with which the joining partners are welded in the solid state. The technology is often employed in the aerospace industry due to the excellent mechanical properties of the weld. Process disturbances can cause irregularities in the weld quality. It is still a challenge to avoid part fit-up deviations as a result of part misalignments and tolerances. Several publications have investigated the effect of alignment discrepancies on the weld quality, for example, by introducing a gap between parts, a tool offset, or linearly misaligned sheets. Depending on the application, the effects of simultaneously occurring alignment discrepancies on the weld quality could be critical. In this work, three alignment discrepancies were investigated (gap, linearly misaligned sheets, tool offset). The weld quality was determined using tensile tests. Process data such as the process forces and the spindle torque were also measured during the welding experiments. The results showed that each of the alignment discrepancies had a negative impact on the weld quality. The simultaneous occurrence resulted in an even lower weld quality. Some alignment discrepancies can probably be detected in the future using process data (e.g., the lateral force).

Abstract.: We investigate the dynamical properties of delay differential equations with large delay. Starting from a mathematical discussion of the singular limit τ → ∞, we present a novel theoretical approach to the stability properties of stationary solutions in such systems. We introduce the notion of strong and weak instabilities and describe a method that allows us to calculate asymptotic approximations of the corresponding parts of the spectrum. The theoretical results are illustrated by several examples, including the control of unstable steady states of focus type by time delayed feedback control and the stability of external cavity modes in the Lang-Kobayashi system for semiconductor lasers with optical feedback.

We investigate the dynamical properties of delay differential equations with large delay. Starting from a mathematical discussion of the singular limit τ → ∞, we present a novel theoretical approach to the stability properties of stationary solutions in such systems. We introduce the notion of strong and weak instabilities and describe a method that allows us to calculate asymptotic approximations of the corresponding parts of the spectrum. The theoretical results are illustrated by several examples, including the control of unstable steady states of focus type by time delayed feedback control and the stability of external cavity modes in the Lang-Kobayashi system for semiconductor lasers with optical feedback.

We investigate the geometrical properties of the attractor for semilinear scalar parabolic PDEs on a bounded interval with Neumann boundary conditions. Using the nodal properties of the stationary solutions which are determined by an ordinary boundary value problem, we obtain crucial information about the long-time behavior for the full PDE. Especially, we prove an exact criterion for the intersection of strong-stable and strong-unstable manifolds in the finite dimensional Morse-Smale flow on the attractor.

Ohne Zusammenfassung:

BackgroundThe age-thrombus score-index of microcirculatory resistance (ATI) score is a diagnostic tool recently applied by our group in ST elevation myocardial infarction (STEMI). It is able to predict suboptimal myocardial reperfusion early in the revascularisation process thus facilitating the triage of alternative or additional therapies to the conventional approach with stenting. We aimed to validate the ATI score against cardiac magnetic resonance imaging (cMRI).MethodsThe ATI score was calculated using age (>50=1 point), pre-stenting index of microcirculatory resistance (IMR) (>40 and <100=1 point; ≥100=2 points) and angiographic thrombus score (4=1 point; 5=3 points)]. cMRI scan was performed within 48 hours from admission and at 6 months follow up to assess the extent of infarct size (IS%) and microvascular obstruction (MVO%).ResultsThe ATI score was calculated prospectively in 80 STEMI patients. cMRI scanning was performed within 48 hours in all patients and in 50 patients at six months follow up. ATI score was closely related to final IS% (ATI0-1: 18.0% [9.0–24.5], ATI2-3: 28.5% [12.8–43.0] and ATI4-5-6: 41.2% [22.0–44.4] p: 0.001) and with MVO% (ATI0-1: 0.0% [0.0–0.9], ATI2-3: 0.7% [0.0–2.5] and ATI4-5-6: 4.1% [1.2–10.7], p<0.001). ATI score predicted final IS% at six months follow up (ATI0-1: 12.7% [4.5–22.0], ATI2-3-: 20.0% [6.4–25.6] and ATI4-5-6: 34.0% [22.2–46.5], p: 0.02).ConclusionsThe ATI score applied prior to stenting in patents with STEMI, can predict the likelihood of MVO% and IS% both acutely and at six months follow up cMRI.