### About

My current research primarily focuses on modeling and simulation of traffic flow. Modeling traffic flow is a difficult task, as complex as human behaviour. In the absence of first principles, models are formulated by observation, and are evaluated by their ability to reproduce familiar traffic scenarios and by their success to fit real data. At the macroscopic level, traffic flow is described by car flow density and average velocity, and is modelled by PDE's that are reminiscent of gas dynamics. At the most fundamental level, the equations express car mass conservation. Equilibrium models use a closure rule called the fundamental diagram, that describes how flow velocity adjusts to local flow density. These models are scalar nonlinear conservation laws. Dynamic models are richer, they formulate rules by which cars accelerate, and yield 2x2 non-linear hyperbolic systems with relaxation and diffusion terms for in-lane flow. Conditions for lane changing may be formulated and yield mass/momentum exchange terms between lanes. These models raise a whole host of fascinating questions that are theoretical, numerical and ultimately hopefully practical. I am currently working on the development, analysis and implementation of non-deterministic models to account for variability in driving styles and reactions, on suitable numerical methods and on comparison with real data.