We discuss the intriguing ability of minimal kinetic theory to describe a broad variety of complex non-equilibrium flows across scales of motion. It is argued that, besides major computational progress, minimal kinetic theory also provides a new conceptual framework to investigate the complexities of flowing matter far from equilibrium.

The vortex-body interaction problem, that characterizes the flow field of a rudder placed downstream of a single-blade marine rotor, is investigated by numerical simulations.

A critical issue in image restoration is noise removal, whose state-of-art algorithm, NonLocal Means, is highly demanding in terms of computational time. Aim of the present paper is to boost its performance by an efficient algorithm tailored to GPU hardware architectures. This algorithm adapts itself to several variants of the methodologies in terms of different strategies for estimating the involved filtering parameter, type of noise affecting data, multicomponent signals, spatial dimension of the images. Numerical experiments on brain Magnetic Resonance images are provided.

We present a Lattice Boltzmann method for the simulation of a wide range of Knudsen regimes. The method is assessed in terms of normalised discharge for flow across parallel plates and three-dimensional flows in porous media. Available analytical solutions are well reproduced, supporting the the method as an appealing candidate to bridge the gap between the hydrodynamic regime and free molecular motion.

We investigate Poiseuille channel flow through intrinsically curved media, equipped with localized metric perturbations. To this end, we study the flux of a fluid driven through the curved channel in dependence of the spatial deformation, characterized by the parameters of the metric perturbations (amplitude, range, and density). We find that the flux depends only on a specific combination of parameters, which we identify as the average metric perturbation, and derive a universal flux law for the Poiseuille flow.

We study the conformational freedom of a protein made by two rigid domains connected by a flexible linker. The conformational freedom is represented as an unknown probability distribution on the space of allowed states. A new algorithm for the calculation of the maximum allowable probability is proposed, which can be extended to any type of measurements. In this paper we use pseudo contact shifts and residual dipolar coupling. We reconstruct a single central tendency in the distribution and discuss in depth the results.

The theoretical understanding of Gartner's "hype curve" is an interesting open question in deciding the strategic actions to adopt in presence of an incoming technology. In order to describe the hype behaviour quantitatively, we propose a mathematical approach based on a rate equation, similar to that used to describe quantum level transitions. The model is able to describe the hype curve evolution in many relevant conditions, which can be associated to various market parameters.

The effects of compressibility on Rayleigh-Taylor instability (RTI) are investigated by inspecting the interplay between thermodynamic and hydrodynamic nonequilibrium phenomena (TNE, HNE, respectively) via a discrete Boltzmann model. Two effective approaches are presented, one tracking the evolution of the local TNE effects and the other focusing on the evolution of the mean temperature of the fluid, to track the complex interfaces separating the bubble and the spike regions of the flow.

A sharp integrability condition on the right-hand side of the p-Laplace system for all its solutions to be continuous is exhibited. Their uniform continuity is also analyzed and estimates for their modulus of continuity are provided. The relevant estimates are shown to be optimal as the right-hand side ranges in classes of rearrangement-invariant spaces, such as Lebesgue, Lorentz, Lorentz-Zygmund, and Marcinkiewicz spaces, as well as some customary Orlicz spaces