We investigate the role of hydrodynamic interactions on the decision-making and leader-identification processes within a group of fifty small-size active individuals, immersed in a viscous fluid at very low Reynolds number, . A fraction of the individuals is informed about the spatial location of the target, and moves accordingly along a privileged trajectory. The rest of the group has no access to this information, but may draw indirect benefit by following the trajectory of the informed individuals, through a process of leader-identification.

We consider a simple model for signal transport in the cytoplasm. Following some recent experimental evidences, the standard diffusion model is supplemented by advection operated through an attachement/detachement mechanism along microtubules. This model is given by a system of partial differential equations which are cast in different dimensions and connected by suitable exchange rules. A numerical scheme is introduced and some simulations are presented and discussed to show the performances of our model.

We propose a numerical method to solve the Wigner equation in quantum systems of spinless, non-relativistic particles. The method uses a spectral decomposition into L-2(R-d) basis functions in momentum-space to obtain a system of first-order advection-reaction equations. The resulting equations are solved by splitting the reaction and advection steps so as to allow the combination of numerical techniques from quantum mechanics and computational fluid dynamics by identifying the skew-hermitian reaction matrix as a generator of unitary rotations.

The identification of the basic mechanisms responsible for cardiovascular diseases stands as one of the most challenging problems in modern medical research including various mechanisms which encompass a broad spectrum of space and time scales. Major implications for clinical practice and pre-emptive medicine rely on the onset and development of intraluminal thrombus in which effective clinical therapies require synthetic risk predictors/indicators capable of informing real-time decision-making protocols.

In this paper, we demonstrate that vertically vibrating a plate in a cornstarch suspension causes the suspension to vigorously ratchet up the plate. We show that this is a necessary consequence of the fact that cornstarch in water is shear thickening: when the plate moves up it opposes gravity and so the fluid stiffens; when it moves down it works with gravity and so the fluid flows. This produces asymmetric ratcheting that opposes gravity.

We correct an error in the proof of Theorem 4.1 of the paper "Boundedness of solutions to anisotropic variational problems" [Comm. Part. Diff. Eq. 36 (2011); 470-486].

The formation of methane-hydrate precursors at large planar water-methane interfaces has been studied using massively parallel molecular dynamics in systems of varying size from around 10 000 to almost 7 x 10(6) molecules. This process took two distinct steps. First, the concentration of solvated methane clusters increases just inside the aqueous domain via slow diffusion from the methane-water interface, forming "clusters" of solvated methane molecules.

Beside geographical and physical characteristics of the environment, mostly temperature changes drive glacier dynamical evolution with subglacial and supraglacial water release or approaching a metastable state. The appearance of subglacial lakes filling bedrock depressions, glacier sliding, crevasses formation and calving are linked climate change sensitive macro-phenomena, where interactions between the interfacing phases are crucial. We shall discuss the mathematical modelling and the numerical simulation of one of the above glacier problems with moving boundary. References A.