Ricerc@Sapienza

In this paper we will consider oscillations of square viscoelastic membranes by adding to the wave equation another term, which takes into account the memory. To this end, we will study a class of integrodifferential equations in square domains. By using accurate estimates of the spectral properties of the integrodifferential operator, we will prove an inverse observability inequality.

We present modeling strategies that describe the motion and interaction of groups of pedestrians in obscured spaces.We start off with an approach based on balance equations in terms of measures and then we exploit the descriptive power of a probabilistic cellular automaton model. Based on a variation of the simple symmetric random walk on the square lattice, we test the interplay between population size and an interpersonal attraction parameter for the evacuation of confined and darkened spaces.

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.

We construct families of positive solutions for competitive and cooperative systems
which blow-up and concentrate at different points of the domain.
This problem can be seen as a generalization for systems of a Brezis–
Nirenberg type problem.

We propose a numerical method for stationary Mean Field Games defined on a network.
In this framework a correct approximation of the transition conditions at the vertices plays a crucial
role. We prove existence, uniqueness and convergence of the scheme and we also propose a least squares
method for the solution of the discrete system. Numerical experiments are carried out.

This research aims at ascertaining the existence and characteristics of natural long-term capture orbits around a celestial body of potential interest. The problem is investigated in the dynamical framework of the three-dimensional circular restricted three-body problem. Previous numerical work on two-dimensional trajectories provided numerical evidence of Conley’s theorem, proving that long-term capture orbits are topologically located near trajectories asymptotic to periodic libration point orbits. This work intends to extend the previous investigations to three-dimensional paths.

Cells, tissues and organs of astronauts aboard the International Space Station (ISS) are exposed to the damaging effects of microgravity and cosmic radiation. Space Agencies are forced to find effective therapeutic countermeasures to safeguard astronauts’ health. Since retina is one of the most vulnerable target, we undertook a project entitled The Coenzyme Q10 (CoQ10) as countermeasure for retinal damage onboard the International Space Station: the CORM project, funded by the Italian Space Agency (ASI) and launched in the summer 2017.

Microsecond pulsed electric fields (?sPEFs) with amplitude of tens of kV/m are used to permeabilize the plasma membrane whereas nanosecond pulsed electric fields of MV/m also permeabilize cell internal structures, such as the endoplasmic reticulum. In this work, a numerical realistic model of cell and its reticulum has been realized to study the use of ?sPEFs also for the permeabilization of this internal structure

Nano-systems, often used in biomedical applications for the treatment of a broad category of illnesses, represent one of the nanomedicine approaches recently proposed to target specific drugs only in the region where the disease has been developed. Recently the use of this technique has been proposed with electropulsation, hence taking advantage of the enhanced permeabilization of the cell membrane and simultaneously control the release of the encapsulated drug by the nano-system.