Sonia Kovalevsky Lecture

2014 Lecturer: Irene M. Gamba

The evolution of complex interactions in non-linear kinetic systems

Recent developments in statistical transport modeling, ranging from rarefied gas dynamics, collisional plasmas and electron transport in nanostructures, to self-organized or social interacting dynamics, share a common description based in a Markovian framework of birth and death processes. Under the regime of molecular chaos propagation, their evolution is given by kinetic equations of non-linear collisional (integral) Boltzmann type. We will present an overview of analytical issues and novel numerical methods for these equations that preserve the expected conserved properties of the described phenomena, while enabling rigorous stability, convergence and error analysis.