We apply the phase-reduction analysis to examine synchronization properties of periodic fluid flows. The dynamics of unsteady flows are described in terms of the phase dynamics reducing the high-dimensional fluid flow to its single scalar phase variable. We characterize the phase response to impulse perturbations, which can in turn quantify the influence of periodic perturbations on the unstead...

The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic time-periodic parameters are discussed in the framework of squeezed state. It is shown that the cyclic and quasicyclic squeezed states correspond to the periodic and quasiperiodic solutions of an effective Hamiltonian defined on an extended phase space, respectively. The geometric phase of the cycli...

[14]. More precisely, we have this error term if we can choose three closed orbits of least periods l1, l2, l3 such that θ = (l1 − l2)/(l2 − l3) is diophantine, i.e., there exists C > 0 and β > 0 such that |qθ − p| ≥ Cq−(1+β) for all p ∈ Z and q ∈ N. In this paper we shall consider compact groups extensions of hyperbolic flows. Let G be a compact Lie group. Let φ̂t : Λ̂ → Λ̂ be a topologically wea...

We construct doubly periodic Stokes flows in two dimensions using elliptic functions. This method has advantages when the doubly periodic lattice of obstacles has less than maximal symmetry. We find the mean flow through an arbitrary lattice in response to a pressure gradient in an arbitrary direction, and show in a typical example that the shorter of the two period lattice vectors is an “easy ...