A nonlinear stability theory is presented for three-dimensional transition in the wake of a circular cylinder up to Reynolds number 300. The primary input to the theory is the linear and the nonlinear stability results of Barkley and Hen-derson. Based on symmetric bifurcation theory, normal form equations are proposed to describe (to lowest order) the nonlin-ear interaction of three-dimensional...

Periodically driven nontrivial quantum states open another door to engineer topological phases in solid systems by light. Here we show, based on the Floquet-Bloch theory, that the on-resonant linearly and circularly polarized infrared light brings in the exotic Floquet quantum spin Hall state and half-metal in two-dimensional Metal-organic frameworks (2D MOFs) because of the unbroken and broken...

We present a numerical scheme for the analysis of periodic dielectric waveguides using Floquet-Bloch theory. The problem of finding the fundamental propagation modes is reduced to a nonlinear eigenvalue problem involving Dirichlet-to-Neumann maps. This approach leads to much smaller matrix problems than the ones that have appeared previously. By an increase of the discretization fineness, any d...

For a periodic Hamiltonian, periodic dynamical invariants may be used to obtain non-degenerate cyclic states. This observation is generalized to the degenerate cyclic states, and the relation between the periodic dynamical invariants and the Floquet decompositions of the time-evolution operator is elucidated. In particular, a necessary condition for the occurrence of cyclic non-adiabatic non-Ab...

We develop a consistent mathematical theory of weakly nonlinear periodic dielectric media for the dimensions one, two and three. The theory is based on the Maxwell equations with classical quadratic and cubic constitutive relations. In particular, we give a complete classification of different nonlinear interactions between Floquet–Bloch modes based on indices which measure the strength of the ...

Stability of a switched system that consists of a set of linear time invariant subsystems and a periodic switching rule is investigated. Based on the Floquet theory, necessary and sufficient conditions are given for exponential stability. It is shown that there exists a slow switching rule that achieves exponential stability if at least one of these subsystems is asymptotically stable. It is al...