Localization phenomena (sometimes called ``{\it flea on the elephant}'') for the operator $L^\varepsilon=-\varepsilon^2 \Delta u + p(\xx) u$, $p(\xx)$ being an asymmetric double-well potential, are studied both analytically and numerically, mostly in two space dimensions within a perturbative framework. Starting from a classical harmonic potential, the effects of various perturbations are retrieved, especially in the case of two asymmetric potential wells.

Standard reaction-diffusion systems are characterized by infinite velocities and no persistence in the movement of individuals, two conditions that are violated when considering living organisms. Here we consider a discrete particle model in which individuals move following a persistent random walk with finite speed and grow with logistic dynamics. We show that, when the number of individuals is very large, the individual-based model is well described by the continuous reactive Cattaneo equation (RCE), but for smaller values of the carrying capacity important finite-population effects arise.

The protozoan parasite Trypanosoma cruz causes the Chagas disease, which final outcome can be morbidity or death. The complexity of this infection is due to the many kinds of players involved in the immune response and to the variety of host cells targeted by the parasite. We built an ordinary differential equation model which includes aspects of innate and adaptive immune response to study the T. cruzi infection. The model also includes cardiomyocytes to represent how the infection affects the heart.

A binary mixture saturating a horizontal porous layer, with large pores and uniformly heated from below, is considered. The instability of a vertical uid motion (throughflow) when the layer is salted by one salt (either from above or from below) is analyzed. Ultimately boundedness of solutions is proved, via the existence of positively invariant and attractive sets (i.e. absorbing sets). The critical Rayleigh numbers at which steady or oscillatory instability occurs, are recovered.

A reaction-diffusion system governing the prey-predator interaction with hunting cooperation is investigated. Definitive boundedness of solutions is proved via the existence of positive invariants and attractive sets. Linear stability of the coexistence equilibria is performed and conditions guaranteeing the occurrence of Turing instability are found. Numerical simulations on the obtained results are provided.

In this paper an in silico study of the behavior of an active polar emulsion is reported, focusing on the case of a highly off-symmetric ratio between the polar (active) and passive components, both for the extensile and contractile case. In absence of activity the system is characterized by an hexatic-ordered droplets phase. We find that small extensile activity is able to enhance the hexatic order in the array of droplets with respect to the passive case, while increasing activity aster-like rotating droplets appear.

In this paper, we deal with a group variable in size of pedestrians moving in a unknown confined environment and searching for an exit. Pedestrian dynamics are simulated by means of a recently introduced microscopic (agent-based) model, characterized by an exploration phase and an egress phase. First, we study the model to reveal the role of its main parameters and its qualitative properties.

Many scientific applications require the solution of large and sparse linear systems of equations using Krylov subspace methods; in this case, the choice of an effective preconditioner may be crucial for the convergence of the Krylov solver. Algebraic MultiGrid (AMG) methods are widely used as preconditioners, because of their optimal computational cost and their algorithmic scalability. The wide availability of GPUs, now found in many of the fastest supercomputers, poses the problem of implementing efficiently these methods on high-throughput processors.