Ricerc@Sapienza

We combine two existing estimators of the local Hurst exponent to improve both the goodness of fit and the computational speed of the algorithm. An application with simulated time series is implemented, and a Monte Carlo simulation is performed to provide evidence of the improvement. The estimation of the Hurst exponent of a time series is a recurring problem of great interest in many fields: finance, biology, hydrology, ecology, and signal processing, to quote a few.

The presence of obstacles modifies the way in which particles diffuse. In cells, for instance, it is observed that, due to the presence of macromolecules playing the role of obstacles, the mean-square displacement of biomolecules scales as a power law with exponent smaller than one. On the other hand, different situations in grain and pedestrian dynamics in which the presence of an obstacle accelerates the dynamics are known.

Particle diffusion is modified by the presence of barriers. In cells macromolecules, behaving as obstacles, slow down the dynamics so that the meansquare displacement of molecules grows with time as a power law with exponent smaller than one. In different situations, such as grain and pedestrian dynamics, it can happen that an obstacle can accelerate the dynamics. In the framework of very basic models, we study the time needed by particles to cross a strip for different bulk dynamics and discuss the effect of obstacles.

Molecular dynamics (MD) simulations have proved to be a useful tool for unveiling many aspects of pore formation in lipid membranes under the influence of external electric fields. In order to compare the size-related properties of pores in bilayers of various compositions, generated and maintained under different physical and chemical conditions, reference metrics are needed for characterizing pore geometry and its evolution over time.