In this page, I gather some (not all, many do not deserve being spread) projects I have done in the past few years. Maybe someone will find them useful when attacking the same topics... Who knows...

• A multidimensional model for the Ca2+ ion dynamics in the astrocytes [report]
  

  Astrocytes are an important kind of cell in the central nervous system, often acting as a regulatory device. For example, the glutamate stimulus indirectly modifies the calcium concentration by increasing the availability of inositol trisphosphate which stimulates the endoplasmatic reticulum to release calcium ions into the cytoplasm. The increase of calcium triggers the release of arachidonic acid from the membrane, with many consequences on the blood flow in the surrounding tissues. We provide a highly simplified space-extended model to study the dynamics of Ca2+ions released thanks to inositol trisphosphate. It accounts for the calcium fluxthrough transmembrane calcium channels induced by the difference of concentration and for the calcium release from the channels localized over the endoplasmatic reticulum membrane, modulated by the level of inositol trisphosphate produced by the glutamate receptors. This phenomena are modeled in terms of time varying lo-cal boundary conditions and the concentrations of both species satisfy a diffusion equation. We propose a discretization of our model by Finite Differences in time and Finite Elements in space.

• SimpleQuadTree [slides / .zip with documentation / GitHub]

  Programming project in C++ for the course "Algorithms and Parallel Computing" @ Politecnico di Milano. The aim of the project was twofold:

  1. Construct highly adaptive Cartesian non-uniform meshes on which one can perform numerical quadrature and eventually implement numerical solvers for PDEs, mainly based on the Finite Volume method.

  2. Implement a simple method to compress digital images, which recognizes large areas of almost uniform color.

  

   

• Lotus Effect and Partial Differential Equations (in French) [.zip with report and codes]

  Project related with the course "Simulation numérique d’équations aux dérivées partielles" at the Ecole polytechnique, whose aim was to establish a framework, based on Partial DIfferential Equation, to account for the Lotus effect. Moreover, we dealt with the numerical simulation of the Allen-Cahn and the Cahn-Hillard equation in 2D using simple Finite Difference schemes.