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The study of many-body interacting systems has been a problem of interest in science for many years. Examples of particular interest include plasmas, hydrodynamics, gravitational systems, and coupled dynamical systems. The dynamics of these systems is self-consistent in the sense that the evolution of a given member of the system is determined by the collective effect of all the other members of the system. For example, in plasma physics the dynamics of an ensemble of charged particles is determined by the electromagnetic fields generated by the particles themselves. In hydrodynamics, an ensemble of point vortices evolves under the advection of the velocity field generated by the vortices themselves. Although the equations governing the above mentioned systems have been known for quite a long time, their self-consistent dynamics is not well-understood. In particular, a lot is known about the chaotic dynamics of a single particle in a given, time-dependent external potential. But, much less is known about the problem of self-consistent chaos in an ensemble of coupled particles. Our goal is to study this problem in the context of a Hamiltonian mean field model known as the single wave model (SWM). The SWM is a generic description of marginally stable Vlasov-Poisson plasmas and shear flows. From a dynamical systems perspective, the SWM has proved to be a useful laboratory to study a wide range of problems including: active transport, the formation and destruction of phase space coherent structures, self-consistent resonance overlap, self-consistent diffusion, and chaos in globally coupled symplectic maps, among others. The following list of projects describe these problems in more detail. We also consider the role of self-consistent Lagrangian chaos in the transition to Eulerian turbulence in shear flows, and the problem of self-consistent chaotic scattering in MHD (Magnetohydrodynamic) flows which is a problem of interest in the study of magnetically confined plasmas.