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To determine the size of an extensive air shower it is not necessary to have knowledge of the function that describes the fall-off of signal size from the shower core (the lateral distribution function). In this paper an analysis with a simple Monte Carlo model is used to show that an optimum ground parameter can be identified for each individual shower. At this optimal core distance, $r_mathrm{opt}$, the fluctuations in the expected signal, $S(r_mathrm{opt})$, due to a lack of knowledge of the lateral distribution function are minimised. Furthermore it is shown that the optimum ground parameter is determined primarily by the array geometry, with little dependence on the energy or zenith angle of the shower or choice of lateral distribution function. For an array such as the Pierre Auger Southern Observatory, with detectors separated by 1500 m in a triangular configuration, the optimum distance at which to measure this characteristic signal is close to 1000 m.
The size of the giant component in the configuration model, measured by the asymptotic fraction of vertices in the component, is given by a well-known expression involving the generating function of the degree distribution. In this note, we argue tha
Using data from more than ten-years of observations with the Akeno Giant Air Shower Array (AGASA), we published a result that the energy spectrum of ultra-high energy cosmic rays extends beyond the cutoff energy predicted by Greisen, and Zatsepin and
We observe a correlation between the slope of radio lateral distributions, and the mean muon pseudorapidity of 59 individual cosmic-ray-air-shower events. The radio lateral distributions are measured with LOPES, a digital radio interferometer co-loca
Airless planetary bodies are covered by a dusty layer called regolith. The grain size of the regolith determines the temperature and the mechanical strength of the surface layers. Thus, knowledge of the grain size of planetary regolith helps to prepa
Stellar photometry in nine fields around the giant elliptical galaxy M87 in the Virgo cluster is obtained from archival images of the Hubble Space Telescope. The resulting Hertzsprung--Russell diagrams show populated red-giant and AGB branches. The p