We consider Prandtl's equations for the impulsively started disk and follow the process of the formation of the singularity in the complex plane using the singularity tracking method. We classify Van Dommelen and Shen's singularity as a cubic root singularity.We introduce a class of initial data which have a dipole singularity in the complex plane. These data are uniformly bounded in H 1 and lead to an earlier singularity formation. The presence of a small viscosity in the streamwise direction changes the behavior of the singularities.

Numerical solutions of the laminar Prandtl boundary-layer and NavierStokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions that can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and NavierStokes solutions and analyze the previous interactions from a different perspective.

We consider a generalization of the non-Hermitian PT symmetric Jaynes-Cummings Hamiltonian, recently introduced for studying optical phenomena with time-dependent physical parameters, that includes environment-induced decay. In particular, we investigate the interaction of a two-level fermionic system (such as a two-level atom) with a single bosonic field mode in a cavity. The states of the two-level system are allowed to decay because of the interaction with the environment, and this is included phenomenologically in our non-Hermitian Hamiltonian by introducing complex energies for the fermion system. We focus our attention on the occurrence of exceptional points in the spectrum of the Hamiltonian, clarifying its mathematical and physical meaning.

We propose an extended version of quantum dynamics for a certain system S, whose evolution is ruled by a Hamiltonian H, its initial conditions, and a suitable set ρ of rules, acting repeatedly on S. The resulting dynamics is not necessarily periodic or quasi-periodic, as one could imagine for conservative systems with a finite number of degrees of freedom. In fact, it may have quite different behaviors depending on the explicit forms of H, ρ as well as on the initial conditions. After a general discussion on this (H, ρ)-induced dynamics, we apply our general ideas to extend the classical game of life, and we analyze several aspects of this extension

We discuss the role of pseudo-fermions in the analysis of some two-dimensional models, recently introduced in connection with non self-adjoint hamiltonians. Among other aspects, we discuss the appearance of exceptional points in connection with the validity of the extended anti-commutation rules which define the pseudo-fermionic structure.