We investigate the effects of nanoparticles on the onset of varicose and whipping instabilities in the dynamics of electrified jets. In particular, we show that the non-linear interplay between the mass of the nanoparticles and electrostatic instabilities, gives rise to qualitative changes of the dynamic morphology of the jet, which in turn, drastically affect the final deposition pattern in electrospinning experiments.

We present a multi-layer mathematical model to describe the transdermal drug release from an iontophoretic system. The Nernst-Planck equation describes the basic convection-diffusion process, with the electric potential obtained by solving the Laplace's equation. These equations are complemented with suitable interface and boundary conditions in a multi-domain. The stability of the mathematical problem is discussed in different scenarios and a finite-difference method is used to solve the coupled system.

In an attempt to study the accuracy and utility of 'coarse grained' models for methane-clathrate systems, molecular-dynamics simulations were run for three different potential models. One was fully atomistic of TIP4P water and fully atomistic methane, the next model was atomistic SPC water and coarse-grained UA methane, whilst the final model was the fully coursed-grained mW model. All models were run at two different sizes (8 and 64 fully-occupied sI clathrate unit cells) at 250 K and 60 bar.

We study a variational problem for simultaneous video inpainting and motion estimation. We consider a functional proposed by Lauze and Nielsen [25] and we study, by means of the relaxation method of the Calculus of Variations, a slightly modified version of this functional. The domain of the relaxed functional is constituted of functions of bounded variation and we compute a representation formula of the relaxed functional. The representation formula shows the role of discontinuities of the various functions involved in the variational model.

Protected Areas are subject to long-term modifications associated with climate and environmental change, enhancing the risk of ecosystem collapse, tipping points and unexpected responses to droughts, fires, floods and other individual events.

The large H2020 project ECOPOTENTIAL (2015-2019, 47 partners, contributing to GEO and GEOSS http://www.ecopotential-project.eu/) is devoted to making best use of remote sensing and in situ data to improve future ecosystem benefits, adopting the view of ecosystems as one physical system with their environment, focusing on geosphere-biosphere interactions, Earth Critical Zone dynamics, Macrosystem Ecology and cross-scale interactions, the effect of extreme events and using Essential (Climate, Biodiversity and Ocean) Variables as descriptors of change.

Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of a crowd is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviors. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviors.