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.

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.

It is shown that the combination of generalized Van der Waals equations of state with high-order discrete velocity lattices, permits to simulate the dynamics of liquid droplets at air-water density ratios, with very moderate levels of spurious currents near the droplet interface. Satisfactory agreement with experimental data on droplet collisions at density ratios of order thousand is reported.

Cooperativity effects have been proposed to explain the non-local rheology in the dynamics of soft jammed systems. Based on the analysis of the free-energy model proposed by L. Bocquet, A. Colin and A. Ajdari, Phys. Rev. Lett., 2009, 103, 036001, we show that cooperativity effects resulting from the nonlocal nature of the fluidity (inverse viscosity) are intimately related to the emergence of shear-banding configurations.

Cavitation in a liquid moving past a constraint is numerically investigated by means of a free-energy lattice Boltzmann simulation based on the van der Waals equation of state. The fluid is streamed past an obstacle, and depending on the pressure drop between inlet and outlet, vapor formation underneath the corner of the sack-wall is observed. The circumstances of cavitation formation are investigated and it is found that the local bulk pressure and mean stress are insufficient to explain the phenomenon.

We analyze the dynamics of small particles vertically confined, by means of a linear restoring force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic turbulent velocity field. The model that we introduce and study is possibly the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy, or any other mechanism, maintain themselves in a shallow horizontal layer below the free surface of oceans or lakes.

Partial integro-differential equation (PIDE) formulations are often preferable for pricing options under models with stochastic volatility and jumps. In this talk, we consider the numerical approximation of such models. On one hand, due to the non-local nature of the integral term, we propose to use Implicit-Explicit (IMEX) Runge-Kutta methods for the time integration to solve the integral term explicitly, giving higher order accuracy schemes under weak stability time-step restrictions.

We present a general model of drug release from a drug delivery device and the subsequent transport in biological tissue. The model incorporates drug diffusion, dissolution and solubility in the polymer coating, coupled with diffusion, convection and reaction in the biological tissue. Each layer contains bound and free drug phases so that the resulting model is a coupled two-phase two-layer system of partial differential equations. One of the novelties is the generality of the model in each layer.