Two color free-electron laser and frequency beating.

We review the theory of two color high gain free-electron laser emission, derive the integral equation characterizing the evolution of the optical intensities, and provide a description of the relevant dynamics. The characteristic feature of this regime is the existence of a mutual bunching, whose origin and role are discussed.

Cancer metabolism and the dynamics of metastasis.

Cancer growth dynamics, commonly simulated with a Gompertzian model, is analyzed in the framework of a more recent and realistic model. In particular, we consider the setting of a tumor embedded in a host organ and investigate their interaction. We assume that, at least in some cases, tumor metastasis may be triggered by an 'energetic crisis', when the tumor exceeds the 'carrying capacity' of the host organ.