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K. Simon

Publications and source records attributed to K. Simon.

4 recordsLinked to original sources

36Cl Concentrations from Polar Ice Cores Set New Constraints on the Carrington Event

The Carrington event of 1859 CE is considered as one of the largest geomagnetic storms of the observational era, and often used as a benchmark for a worst-case scenario. Yet, there exists no robust evidence of an associated solar energetic particle event of a significant magnitude, based on measurements of cosmogenic radionuclides 10Be and 14C from ice cores and tree rings, respectively. In this study, we present two 36Cl records from Greenland with 2-year and 4-year resolution from the EGRIP and NGRIP ice-core sites, together with semi-annual 10Be data from EGRIP, as well as annual 10Be and 36Cl concentrations from the Dome Summit Site, Law Dome, East Antarctica. We observe no significant 36Cl concentration increase around 1859 CE in the three records. This allows us to rule out an extreme solar energetic particle event hitting Earth associated with the Carrington event in terms of fluence above 30 MeV. Based on these ice core 36Cl measurements, we can suggest two scenarios: i) a soft SEP event with a maximum fluence above 30 MeV up to three times larger than any Space Age event or, ii) the possibility that there was no Earth-bound SEP event.

astro-ph.SR

Fractal dimensions of continuous piecewise linear iterated function systems

We consider iterated function systems on the real line that consist of continuous, piecewise linear functions. Under a mild separation condition, we show that the Hausdorff and box dimensions of the attractor are equal to the minimum of 1 and the exponent which comes from the most natural system of covers of the attractor.

math.DS

Special families of piecewise linear iterated function systems

This paper investigates the dimension theory of some families of continuous piecewise linear iterated function systems. For one family, we show that the Hausdorff dimension of the attractor is equal to the exponential growth rate obtained from the most natural covering system. We also prove that for Lebesgue typical parameters, the 1-dimensional Lebesgue measure of the underlying attractor is positive, if this number is bigger than 1 and all the contraction ratios are positive.

math.DS

Piecewise linear iterated function systems on the line of overlapping construction

In this paper we consider Iterated Function Systems (IFS) on the real line consisting of continuous piecewise linear functions. We assume some bounds on the contraction ratios of the functions, but we do not assume any separation condition. Moreover, we do not require that the functions of the IFS are injective, but we assume that their derivatives are separated from zero. We prove that if we fix all the slopes but perturb all other parameters, then for all parameters outside of an exceptional set of less than full packing dimension, the Hausdorff dimension of the attractor is equal to the exponent which comes from the most natural system of covers of the attractor.

math.DS