Michal Branicki

TL;DR: It is demonstrated that each contact-electrified piece develops a net charge of either positive or negative polarity, and each surface supports a random “mosaic” of oppositely charged regions of nanoscopic dimensions that accommodate significantly more charge per unit area than previously thought.

TL;DR: In this paper, the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval is considered and a variety of examples, some with explicit solutions, that illustrate in a concrete manner the issues and phenomena that arise in the setting of finite-time dynamical systems.

TL;DR: A large number of new theoretical and computational phenomena which arise in the emerging statistical-stochastic framework for quantifying and mitigating model error in imperfect predictions, such as the existence of information barriers to model improvement, are developed and reviewed here with the intention to introduce mathematician, applied mathematicians, and scientists to these remarkable emerging topics with increasing practical importance.

TL;DR: In this paper, the suitability of truncated polynomial chaos expansions (PCE) and truncated GramCharlier Expansions (GrChE) as possible methods for uncertainty quantification (UQ) in nonlinear systems with intermittency and positive Lyapunov exponents is examined.

TL;DR: In this article, a method for determining the geometry of a class of 3D invariant manifolds in non-autonomous (aperiodically time-dependent) dynamical systems is presented.