A comparison between first-order microscopic and macroscopic differential models of crowd dynamics is established for an increasing number N of pedestrians. The novelty is the fact of considering massive agents, namely, particles whose individual mass does not become infinitesimal when N grows. This implies that the total mass of the system is not constant but grows with N. The main result is that the two types of models approach one another in the limit N -> ?, provided the strength and/or the domain of pedestrian interactions are properly modulated by N at either scale.

We study a quasilinear parabolic equation of forward-backward type, under assumptions on the nonlinearity which hold for a wide class of mathematical models, using a pseudo-parabolic regularization of power type.We prove existence and uniqueness of positive solutions of the regularized problem in a space of Radon measures. It is shown that these solutions satisfy suitable entropy inequalities. We also study their qualitative properties, in particular proving that the singular part of the solution with respect to the Lebesgue measure is constant in time.

We present an axisymmetric lattice Boltzmann model based on the Kupershtokh et al. multiphase model that is capable of solving liquid-gas density ratios up to 10(3). Appropriate source terms are added to the lattice Boltzmann evolution equation to fully recover the axisymrnetric multiphase conservation equations. We validate the model by showing that a stationary droplet obeys the Young-Laplace law, comparing the second oscillation mode of a droplet with respect to an analytical solution and showing correct mass conservation of a propagating density wave.

By using direct numerical simulations (DNS) at unprecedented resolution, we study turbulence under rotation in the presence of simultaneous direct and inverse cascades. The accumulation of energy at large scale leads to the formation of vertical coherent regions with high vorticity oriented along the rotation axis. By seeding the flowwithmillions ofinertialparticles,wequantify -- forthefirsttime -- theeffects ofthose coherent vertical structures on the preferential concentration of light and heavy particles.

We introduce a new particle shape which shows preferential rotation in three dimensional homogeneous isotropic turbulence. We call these particles chiral dipoles because they consist of a rod with two helices of opposite handedness, one at each end. 3D printing is used to fabricate these particles with a length in the inertial range and their rotations are tracked in a turbulent flow between oscillating grids.

Planktonic copepods are small crustaceans that have the ability to swim by quick powerful jumps. Such an aptness is used to escape from high shear regions, which may be caused either by flow perturbations, produced by a large predator (i.e., fish larvae), or by the inherent highly turbulent dynamics of the ocean. Through a combined experimental and numerical study, we investigate the impact of jumping behavior on the small-scale patchiness of copepods in a turbulent environment.

We present the formulation of a kinetic mapping scheme between the Direct Simulation Monte Carlo (DSMC) and the Lattice Boltzmann Method (LBM) which is at the basis of the hybrid model used to couple the two methods in view of efficiently and accurately simulate isothermal flows characterized by variable rarefaction effects. Owing to the kinetic nature of the LBM, the procedure we propose ensures to accurately couple DSMC and LBM at a larger Kn number than usually done in traditional hybrid DSMC--Navier-Stokes equation models.

In this article, we study in detail the fluid dynamics system proposed in Clarelli et al. (2013, J. Math. Biol., 66, 1387-1408) to model the formation of cyanobacteria biofilms. After analysing the linear stability of the unique non-trivial equilibrium of the system, we introduce in the model the influence of light and temperature, which are two important factors for the development of a cyanobacteria biofilm.

We study the initial-boundary value problem (Formula presented.) with measure-valued initial data. Here ? is a bounded open interval, ?(0)=?(?)=0, ? is increasing in (0,?) and decreasing in (?,?), and the regularising term ? is increasing but bounded. It is natural to study measure-valued solutions since singularities may appear spontaneously in finite time. Nonnegative Radon measure-valued solutions are known to exist and their construction is based on an approximation procedure. Until now nothing was known about their uniqueness.