A lattice Boltzmann formulation for relativistic fluids is presented and numerically validated through quantitative comparison with recent hydrodynamic simulations of relativistic fluids. In order to illustrate its capability to handle complex geometries, the scheme is also applied to the case of a three-dimensional relativistic shock wave, generated by a supernova explosion, impacting on a massive interstellar cloud.

An analytical solution for solving the transient drug diffusion in adjoining porous wall layers faced with a drug-eluting stent is presented. The endothelium, intima, internal elastic lamina and media are all treated as homogeneous porous media and the drug transfer through them is modelled by a set of coupled partial differential equations. The classical separation of variables method for a multi-layer configuration is used. The model addresses the concept of penetration depth for multi-layer solids that is useful to treat the wall thickness by estimating a physical bound for mass diffusion.

We consider a rather simple algorithm to address the fascinating field of numerical extrapolation of (analytic) band-limited functions. It relies on two main elements: namely, the lower frequencies are treated by projecting the known part of the signal to be extended onto the space generated by ``Prolate Spheroidal Wave Functions" (PSWF, as originally proposed by Slepian), whereas the higher ones can be handled by the recent so--called ``Compressive Sampling" (CS, proposed by Cand\`es) algorithms which are independent of the largeness of the bandwidth.

We study the inverse problem of determining the conformational freedom of two protein domains from residual dipolar coupling (RDC) measurements. For each paramagnetic ion attached to one of the domains we obtain a magnetic susceptibility tensor ? from the RDC of couples of atoms of that domain, and a mean paramagnetic susceptibility tensor ?¯ from the RDC of couples of atoms of the other domain. The latter is an integral average of rotations of ? which depends on the conformational freedom of the two domains.

We analyse the effect of the mechanical response of the solid phase during liquid/solid phase change by numerical simulation of a benchmark test based on the well known and debated experiment of melting of a pure gallium slab counducted by Gau & Viskanta in 1986. The adopted mathematical model includes the description of the melt flow and of the solid phase deformations.

Magnetic tomography is an ill-posed and ill-conditioned inverse problem since, in general, the solution is non-unique and the measured magnetic field is affected by high noise. We use a joint sparsity constraint to regularize the magnetic inverse problem. This leads to a minimization problem whose solution can be approximated by an iterative thresholded Landweber algorithm.