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Abstract: A Monte-Carlo approach to solving a stochastic jump transition model foractive-region energy Wheatland and Glukhov, Astrophys. J. 494, 1998;Wheatland, Astrophys. J. 679, 2008 is described. The new method numericallysolves the stochastic differential equation describing the model, rather thanthe equivalent master equation. This has the advantages of allowing moreefficient numerical solution, the modelling of time-dependent situations, andinvestigation of details of event statistics. The Monte-Carlo approach isillustrated by application to a Gaussian test case, and to the class offlare-like models presented in Wheatland 2008, which are steady-state modelswith constant rates of energy supply, and power-law distributed jump transitionrates. These models have two free parameters: an index $\delta $, whichdefines the dependence of the jump transition rates on active-region energy,and a non-dimensional ratio $\overline{r}$ of total flaring rate to rate ofenergy supply. For $\overline{r}\ll 1$ the non-dimensional mean energy$<\overline{E}>$ of the active-region satisfies $<\overline{E}> \gg 1$,resulting in a power-law distribution of flare events over many decades inenergy. The Monte-Carlo method is used to explore the behavior of thewaiting-time distributions for the flare-like models. The models with$\delta eq 0$ are found to have waiting times which depart significantly fromsimple Poisson behavior when $<\overline{E}> \gg 1$. The original model fromWheatland and Glukhov 1998, with $\delta=0$ no dependence of transitionrates on active-region energy, is identified as being most consistent withobserved flare statistics.



Author: M.S. Wheatland

Source: https://arxiv.org/







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