A two-phasemathematical model describing the dynamics of a substance between two coupled media of different properties and dimensions is presented. A system of partial differential equations describes the diffusion and the binding/unbinding processes in both layers. Additional flux continuity at the interface and clearance conditions into systemic circulation are imposed. An eigenvalue problem with discontinuous coefficients is solved and an analytical solution is given in the form of an infinite series expansion.

Bioventing is a technology used to abate the presence of pollutants in the subsoil. Microorganisms biodegrade the pollutant but the biochemical reaction requires oxygen and so an air ow is induced in the subsoil by means of injection and/or extraction wells. Costs, final result and decontamination time are reliant on contaminant type, soil permeability and several other factors, but oxygen subsoil concentration plays a very important role.

Large-scale simulations of blood flow allow for the optimal evaluation of endothelial shear stress for real-life case studies in cardiovascular pathologies. The procedure for anatomic data acquisition, geometry and mesh generation are particularly favorable if used in conjunction with the Lattice Boltzmann method and the underlying cartesian mesh. The methodology allows to accommodate red blood cells in order to take into account the corpuscular nature of blood in multi-scale scenarios and its complex rheological response, in particular, in proximity of the endothelium.

A mathematical model describing the bioventing technique for the decontamination of pol- luted subsoil will be presented. Bioventing is a biological technique: bacteria remove the contaminant transforming it and oxygen is consumed in the reaction. The numerical model is based on the fluid flow theory in porous media and bacteria population dynamics and it describes: pollutant degradation, oxygen and bacteria concentration. The mathematical model will be numerically solved and the results of some experiments will be presented.

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.

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 derive an integration by parts formula for functionals of de- terminantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a conguration-valued diffusion process which is non-colliding and admits the distribution of the determinantal process as reversible law. In particular, this approach allows us to build a concrete example of the associated diffusion process, providing an illustration of the results of [4] and [30]. 1

Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 1950s with the Kierstead, Slobodkin, and Skellam (KiSS) model, namely a continuous reaction-diffusion equation for a population growing on a patch of finite size L surrounded by a deadly environment with infinite mortality, i.e., an oasis in a desert. The main outcome of the model is that only patches above a critical size allow for population persistence.