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On strong sharp phase transition in the random connection model
No full textWe consider a random connection model (RCM) driven by a Poisson process . We derive exponential moment bounds for an arbitrary cluster, provided that the intensity of is below a certain critical intensity . The associated subcritical regime is characterized by a finite mean cluster size, uniformly in space. Under an exponential decay assumption on the connection function, we also show that the cluster diameters are exponentially small as well. In the important stationary marked case and under a uniform moment bound on the connection function, we show that coincides with , the largest for which does not percolate. In this case, we also derive some percolation mean field bounds. These findings generalize some of the recent results. Even in the classical unmarked case, our results are more general than what has been previously known. Our proofs are partially based on some stochastic monotonicity properties, which might be of interest in their own right
Core plasma fueling by fast inward particle transport after hydrogen pellet injection in Wendelstein 7-X
No full textA large database of more than 1000 individual cryogenic hydrogen pellets injected into Wendelstein 7-X for plasma fueling was analyzed to improve the understanding of the three phases of the process: the ablation, deposition and transport of the pellet material. Kilohertz-sampled electron density and temperature measurements revealed a more complex drift behavior than predicted by numerical code simulation. It could be explained by the poloidal plasma E x - drift rotation, which plays a significant role in stellarators, but was not previously considered in pellet injection codes like HPI2. The drift results in a fast poloidal rotation of the pellet material around the plasma core, leading to an almost homogeneous deposition over the involved flux surfaces regardless of magnetic high and low field side injection geometry. Additionally, a novel fast inward directed transport mechanism (‘FIT-effect’) was observed. The effect occurs on timescales of tens of milliseconds and cannot be explained by neoclassical transport or diffusion. It might be linked to the turbulence pinch recently found in Wendelstein 7-X. When the FIT-effect occurs, the pellet particles are rapidly transferred from the deposition flux surfaces to the plasma core, causing the plasma density profile to peak, which is beneficial for confinement in Wendelstein 7-X. The large pellet injection database was statistical analyzed with regard to pellet and plasma parameters, which delivered some starting points towards developing an understanding of the physics behind the FIT-effect. The results indicate, that plasma core fueling via pellet injection is largely independent of the injection geometry in stellarators under certain conditions, reducing the technical complexity of the injection system
Pre-Filtered Numerical Integration for Machine Tool Vibration Measurements
No full textAccurate knowledge of spindle displacement is essential for assessing the dynamic behavior and machining performance of machine tools, as relative tool–workpiece motion directly affects surface quality and dimensional accuracy. In practice, however, spindle vibrations are commonly measured using accelerometers. Therefore, the displacement has to be calculated from accelerometer data. A major challenge in deriving displacement from acceleration measurements is the accumulation of low-frequency noise and offsets during numerical integration, which leads to unrealistic drift and unphysical displacement signals. As a result, direct double integration of raw acceleration data is not suitable for reliable machine tool vibration analysis with respect to displacements. This paper addresses this problem by applying pre-filtered numerical integration of acceleration signals, following the methodology proposed by Hofmann (2013). High-pass Butterworth filtering with varying cutoff frequencies is applied prior to double integration to suppress low-frequency disturbances while preserving relevant dynamic content. The proposed approach is experimentally validated on a milling machine spindle using broadband impulse hammer excitation. Reconstructed displacement signals are directly compared with reference measurements obtained from a laser interferometer in both the time and frequency domains. The results show that a high-pass cutoff frequency of approximately 10~Hz provides the best agreement with the reference data, enabling physically meaningful spindle displacement reconstruction from accelerometer measurements
Correctness-by-Construction for Pancake Programs
No full textIn sicherheitskritischen Umgebungen werden häufig Betriebssysteme eingesetzt. Daher müssen sie strikte Anforderungen an ihre funktionale Korrektheit erfüllen, was sie zu einem geeigneten Ziel für die Anwendung formaler Techniken macht, beispielsweise für formale Verifikation. Bestehende Forschungsarbeiten, zum Beispiel die Arbeiten zum seL4-Mikrokernel, zeigen, dass die Verifikation von Systemsoftware zeitaufwändig und kostspielig ist. Die Systemprogrammiersprache Pancake geht dieses Problem durch ihr Sprachdesign an, das einen verifizierten Compiler umfasst, der auf einer im interaktiven Theorembeweiser HOL4 formalisierten Semantik basiert.
Die bestehenden formalen Techniken für Systemprogrammiersprachen beschränken sich jedoch auf Post-Hoc-Ansätze, das heißt die Verifikation einer abgeschlossenen Implementierung gegen eine Spezifikation. Da diese Spezifikation in der Regel bereits vor der Implementierung bekannt ist, besteht hier Verbesserungspotenzial. Im Gegensatz zu Post-Hoc-Ansätzen nutzen Refinement-basierte Techniken wie Correctness-by-Construction (CbC) dieses Wissen, indem sie die Spezifikation als Ausgangspunkt für korrektheitserhaltende Refinement-Schritte verwenden, was zu einem Programm führt, das die ursprüngliche Spezifikation a priori erfüllt. Die Refinement-Schritte in CbC bestehen in der benutzergeführten Anwendung formal bewiesener Refinement-Regeln, welche die Auswahl korrekter Refinement-Schritte vereinfachen.
In dieser Arbeit stellen wir einen CbC-Kalkül für eine Turing-vollständige Teilmenge der Systemprogrammiersprache Pancake vor, der es Entwicklern ermöglicht, Pancake-Programme zu implementieren, indem sie eine Hoare-Spezifikation unter Verwendung von 26 Refinement-Regeln zu einem Pancake-Programm zu verfeinern. Unser CbC-Kalkül ist in HOL4 implementiert und nutzt die formale Semantik von Pancake, um beweisbare Ende-zu-Ende-Korrektheit zu erreichen. Um die Machbarkeit unseres Ansatzes zu zeigen, präsentieren wir eine Implementierung der linearen Suche als Fallstudie sowie einen Ansatz zur Automatisierung der Refinement-Beweise
Towards a Service-Oriented Infrastructure for Distributed Systems with Heterogeneous AI Accelerators
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