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We study sequences of periodic orbits and the associated phase space dynamics in a 4-D sym-plectic map of interest to the problem of beam stability in circular particle accelerators. The increasing period of these orbits is taken from a sequence of rational approximants to an incom-mensurate pair of irrational rotation numbers of an invariant torus. We find(More)
The last decade several cellular automata (CA) models have been developed in order to explain the solar flare statistics derived from observations. These models simulate the storage/release process using simple evolution rules, neglecting the details of the processes. The main advantage of this approach is the treatment of a large number of elementary(More)
The purpose of this tutorial is to introduce the main concepts behind normal and anomalous diffusion. Starting from simple, but well known experiments, a series of mathematical modeling tools are introduced, and the relation between them is made clear. First, we show how Brownian motion can be understood in terms of a simple random walk model. Normal(More)
We show that the Cellular Automaton (CA) model for Solar flares of Lu and Hamilton (1991) can be understood as the solution to a particular partial differential equation (PDE), which describes diffusion in a localized region in space if a certain instability threshold is met, together with a slowly acting source term. This equation is then compared to the(More)
Solar ares frequently radiate in the 1{3 GHz range, the lowest frequency microwaves, but not much is known about the spectral shape of these emissions. We present a catalogue of selected bursts observed with a new spectrometer at ETH Zurich in the years 1989{1993. The original data set includes 268 events of various types. Featureless broadband continua(More)
Electron and proton acceleration in three-dimensional electric and magnetic fields is studied through test particle simulations. The fields are obtained by a three-dimensional magnetohydrodynamic simulation of magnetic reconnection in slab geometry. The nonlinear evolution of the system is characterized by the growth of many unstable modes and the initial(More)
The formation and evolution of active regions are inherently complex phenomena. Magnetic fields generated at the base of the convection zone follow a chaotic evolution before reaching the solar surface. In this article, we use a two-dimensional probabilistic cellular automaton to model the statistical properties of the magnetic patterns formed on the solar(More)
A setup is introduced which can be superimposed onto the existing solar flare cellular automata (CA) models, and which specifies the interpretation of the model's variables. It extends the CA models, yielding the magnetic field, the current, and an approximation to the electric field, in a way that is consistent with Maxwell's and the MHD equations.(More)
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