Tracking fronts and interfaces is a fundamental task in several real world applications of mathematical modelling. The most widely used and successful technique for tracking front propagation is the so-called Level-Set Method (LSM). However, many applications require to track fronts embedded into a random environment. The LSM is generalized to describe such random situations according to the probability density function (PDF) of the displacement of interface particles around the average frontline determined by the ordinary LSM. The correct determination of the PDF, which describes the physics of the specific underlying process, is therefore of paramount importance for any applications.
The research follows three general themes:
- Mathematical investigation and theoretical development
- Development of models for anomalous diffusion in the framework of Fractional Calculus
- Applications in turbulent premixed combustion, wildland fire propagation and groundwater infiltration.