The features of equatorial motion of an extended body in Kerr spacetime are investigated in the framework of the Mathisson-Papapetrou-Dixon model. The body is assumed to stay at quasiequilibrium and respond instantly to external perturbations. Besides the mass, it is completely determined by its spin, the multipolar expansion being truncated at the quadrupole order, with a spin-induced quadrupole tensor. The study of the radial effective potential allows us to analytically determine the innermost stable circular orbit shift due to spin and the associated frequency of the last circular orbit.

In the present work the numerical simulation of breaking wave processes is discussed. A detailed analysis is performed using Smoothing Particle Hydrodynamics (SPH) models as well as a mesh-based Level-Set Finite Volume Method (LS-FVM). Considerations on the numerical dissipation involved in such models are discussed within the frameworks of weakly compressible and incompressible ssumptions. The breaking wave processes are simulated using both mono- and two-phases models. Due to the extensive test-cases discussed, the present analysis is limited to a bi-dimensional framework.

Bioventing is a technology used to remove some kinds of pollutants from the subsoil and it is based on the capability of some bacteria species to biodegrade contaminants. The biochemical reaction requires, among other things, oxygen and, therefore, oxygen is inflated into the subsoil by wells. The mathematical model describes the movement of the different fluids which are present in the subsoil - air, water, pollutants, oxygen and so on - and the bacteria population dynamics.

We establish a comparison result for solutions to nonlinear fully anisotropic elliptic problems by means of anisotropic symmetrization. As consequence we deduce a priori estimates for norms of the relevant solutions.

We investigate the effects of dissipative air drag on the dynamics of electrified jets in the initial stage of the electrospinning process. The main idea is to use a Brownian noise to model air drag effects on the uniaxial elongation of the jets. The developed numerical model is used to probe the dynamics of electrified polymer jets at different conditions of air drag force, showing that the dynamics of the charged jet is strongly biased by the presence of air drag forces. This study provides prospective beneficial implications for improving forthcoming electrospinning experiments.

A novel, coarse-grained, single-framework 'Eulerian' model for blood flow in the microvascular circulation is presented and used to estimate the variations in flow properties that accrue from all of the following: (i) wall position variation, associated with the endothelial cells' (ECs) shape, (ii) glycocalyx layer (GL) effects and (iii) the particulate nature of blood. We stress that our new model is fully coupled and uses only a single Eulerian computational framework to recover complex effects, dispensing altogether with the need for, e.g. re-meshing and advected sets of Lagrangian points.

In this paper 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.

The influence of an arbitrary spin orientation on the quadrupolar structure of an extended body moving in a Schwarzschild spacetime is investigated. The body dynamics is described by the Mathisson-Papapetrou-Dixon model, without any restriction on the motion or simplifying assumption on the associated spin vector and quadrupole tensor, generalizing previous works.

In the present work the simulation of water impacts is discussed. The investigation is mainly focused on the energy dissipation involved in liquid impacts in both the frameworks of the weakly compressible and incompressible models. A detailed analysis is performed using a weakly compressible Smoothed Particle Hydrodynamics (SPH) solver and the results are compared with the solutions computed by an incompressible mesh-based Level-Set Finite Volume Method (LS-FVM). Impacts are numerically studied using single-phase models through prototypical problems in 1D and 2D frameworks.