Dynamical percolation on general trees

H\"aggstr\"om, Peres, and Steif (1997) have introduced a dynamical version of percolation on a graph $G$. When $G$ is a tree they derived a necessary and sufficient condition for percolation to exist at some time $t$. In the case that $G$ is a spherically symmetric tree, H\"aggstr\"om, Peres, and Steif (1997) derived a necessary and sufficient condition for percolation to exist at some time $t$ in a given target set $D$. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time $t\in D$, in the case that the underlying tree is not necessary spherically symmetric. This answers a question of Yuval Peres (personal communication). We present also a formula for the Hausdorff dimension of the set of exceptional times of percolation.Comment: 24 pages; to appear in Probability Theory and Related Field

Sub-arcsecond imaging with the International LOFAR Telescope I. Foundational calibration strategy and pipeline

The International LOFAR Telescope is an interferometer with stations spread across Europe. With baselines of up to ~2000 km, LOFAR has the unique capability of achieving sub-arcsecond resolution at frequencies below 200 MHz. However, it is technically and logistically challenging to process LOFAR data at this resolution. To date only a handful of publications have exploited this capability. Here we present a calibration strategy that builds on previous high-resolution work with LOFAR. It is implemented in a pipeline using mostly dedicated LOFAR software tools and the same processing framework as the LOFAR Two-metre Sky Survey (LoTSS). We give an overview of the calibration strategy and discuss the special challenges inherent to enacting high-resolution imaging with LOFAR, and describe the pipeline, which is publicly available, in detail. We demonstrate the calibration strategy by using the pipeline on P205+55, a typical LoTSS pointing with an 8 h observation and 13 international stations. We perform in-field delay calibration, solution referencing to other calibrators in the field, self-calibration of these calibrators, and imaging of example directions of interest in the field. We find that for this specific field and these ionospheric conditions, dispersive delay solutions can be transferred between calibrators up to ~1.5° away, while phase solution transferral works well over ~1°. We also demonstrate a check of the astrometry and flux density scale with the in-field delay calibrator source. Imaging in 17 directions, we find the restoring beam is typically ~0.3′′ ×0.2′′ although this varies slightly over the entire 5 deg2 field of view. We find we can achieve ~80–300 μJy bm−1 image rms noise, which is dependent on the distance from the phase centre; typical values are ~90 μJy bm−1 for the 8 h observation with 48 MHz of bandwidth. Seventy percent of processed sources are detected, and from this we estimate that we should be able to image roughly 900 sources per LoTSS pointing. This equates to ~ 3 million sources in the northern sky, which LoTSS will entirely cover in the next several years. Future optimisation of the calibration strategy for efficient post-processing of LoTSS at high resolution makes this estimate a lower limit

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)

Sub-arcsecond imaging with the International LOFAR Telescope. I.: Foundational calibration strategy and pipeline

InstrumentationGalaxie