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.

A mathematical model and the simulation of subsoil decontamination by bioventing will be presented. The bases for the model construction are the following: (1) the pollutant is considered as immobile and confined in the unsaturated zone; (2) only oxygen is injected in the subsoil by wells; (3) the bacteria acting the pollutant removal are immobile and their growth depends on oxygen and pollutant concentration.

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.

One of the most popular discrete approximating polynomials is the Lagrange interpolation polynomial and the Jacobi zeros provide a particularly convenient choice of the interpolation knots on [?1, 1]. However, it is well known that there is no point system such that the associate sequence of Lagrange polynomials, interpolating an arbitrary function f, would converge to f w.r.t. any weighted uniform or L1 norm.

Bioventing is a clean-up technology essentially used to remove hydrocarboon from polluted subsoil by the action of microorganism. The model is based on the theory of fluid flows in porous media and on the mathematical description of population dynamics. The numerical results of a simplified model will be described.

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.

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.

Using covariance identities based on the Clark-Ocone representation formula we derive Gaussian density bounds and tail estimates for the probability law of the solutions of several types of stochastic differential equations, including Stratonovich equations with boundary condition and irregular drifts, and equations driven by fractional Brownian motion. Our arguments are generally simpler than the existing ones in the literature as our approach avoids the use of the inverse of the Ornstein-Uhlenbeck operator.

Broader comprehension of gene expression regulatory mechanisms can be gained from a global analysis of how transcription and degradation are coordinated to orchestrate complex cell responses. The role of messenger RNA (mRNA) turnover modulation in gene expression levels has become increasingly recognized.