Abstract Many simple natural phenomena are characterized by complex motion that appears random at first glance, but often displays underlying patterns and behavior can be clustered in groups. The movement of small pieces paper falling through the air is one these systems whose complete mathematical description seems unworkable. Understanding types thus demands automated experimentation capable ...

We consider a two-parameter family of cylindrical force-free equilibria, modeled to match numerical simulations of relativistic force-free jets. We study the linear stability of these equilibria, assuming a rigid impenetrable wall at the outer cylindrical radius R j. We find that equilibria in which the Lorentz factor γ(R) increases monotonically with increasing radius R are stable. On the othe...

We explain how Itô Stochastic Differential Equations on manifolds may be defined as 2-jets of curves. We use jets as a natural language to express geometric properties of SDEs and show how jets can lead to intuitive representations of Itô SDEs, including three different types of drawings. We explain that the mainstream choice of Fisk-StratonovichMcShane calculus for stochastic differential geom...