Alessandro P. S. de Moura

Effective dynamics in Hamiltonian systems with mixed phase space

An adequate characterization of the dynamics of Hamiltonian systems at physically relevant scales has been largely lacking. Here we investigate this fundamental problem and we show that the finite-scale Hamiltonian dynamics is governed by effective dynamical invariants, which are significantly different from the dynamical invariants that describe the asymptotic Hamiltonian dynamics. The effective invariants depend both on the scale of resolution and the region of the phase space under consideration, and they are naturally interpreted within a framework in which the nonhyperbolic dynamics of the Hamiltonian system is modeled as a chain of hyperbolic systems.

Three‐dimensional effects in active chaotic flows

We study the dynamics of active particles advected by 3‐dimensional open incompressible flows. We find that 3D reactive flows have fundamentally novel dynamical features, not found in 2D systems. In particular, we argue that that the reaction’s productivity per reaction step can be enhanced, with respect to the 2D case, while the productivity per unit time in some 3D flows goes to zero in the limit of high mixing rates, in contrast to the 2D behavior, in which the productivity goes to a finite constant.