Effect of Ergodic and Non-Ergodic Fluctuations on a Charge Diffusing in a Stochastic Magnetic Field

In this paper, we study the basic problem of a charged particle in a stochastic magnetic field. We consider dichotomous fluctuations of the magnetic field where the sojourn time in one of the two states are distributed according to a given waiting-time distribution either with Poisson or non-Poisson statistics, including as well the case of distributions with diverging mean time between changes of the field, corresponding to an ergodicity breaking condition. We provide analytical and numerical results for all cases evaluating the average and the second moment of the position and velocity of the particle. We show that the field fluctuations induce diffusion of the charge with either normal or anomalous properties, depending on the statistics of the fluctuations, with distinct regimes from those observed, e.g., in standard Continuous-Time Random Walk models.

Uncertainty assessment based on scenarios derived from static connectivity metrics

The approach presented in this paper characterises the uncertainty related to the outputs of a sequential Gaussian simulation. The input data set was a random subset of a complete CT slice. To outline possible, characteristically different groups of realisations within the outputs, we performed a distance-based classification of the realisations based on their derived connectivity features. Global metrics of connectivity also called geo-body or geoobject connectivity is derivative properties related to the overall structure of the simulated field. Based on these attributes stochastic images, which show the same characteristics from a statistical point of view become distinguishable. The scenarios generated this way are able to bridge the gap of information content between the individual stochastic images and the entirety of the pooled realisations. Scenarios are also capable of highlighting the groups of most probable outcomes from the realisations while screening the effect of ergodic fluctuations of the individual stochastic images. They yield a more realistic representation of the smaller scale heterogeneities than the individual stochastic images. In this sense, our approach is able to resolve the question of how many realisations to choose for the assessment of uncertainty. Besides, it eliminates subjectivity and supports reproducible decision-making when the task is to select stochastic images for dynamic simulation.