Sketch of the relaxation process. The hatched region in the unstable configuration (a) marks the excess amount of heat to be moved, and the hatched region in the relaxed state (b) marks the amount of heat received in the relaxation event. The dashed line connects the temperatures at the grid sites and represents the local temperature profile.
Spatial mean of (a) the temperature and of (b) the absolute normalized scale length as a function of time, for heating only in stable states and for continuous heating, and with two different heating intensities. The horizontal dashed line in (b) shows the instability threshold , while the arrows mark the transition of the system to the SOC state.
Temperature profiles during the SOC state for (a) different values of and , and (b) for different values of , all with loading only in stable configurations.
Temperature profiles for central heating (dotted-dashed), and for simultaneous central and off-axis heating (dashed), both with heating only in stable states, and for central, continuous heating (solid).
Distributions (normalized histograms) of the total heat fluxes per avalanche [(a), (c), and (e)] and total heat-out-fluxes per avalanche [(b), (d), and (f)], for different loading intensities [(a) and (b)], for different thresholds [(c) and (d)], and for different diffusivities [(e) and (f)], together with power-law fits (dashed lines). [The distributions are shifted in the vertical direction for better visualization, and in each subfigure error bars (red) are shown for reference in one case.]
Power-law indices and from the power-law fits to the distributions of the total internal fluxes and the total out-fluxes , respectively, in Fig. 5.
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