This paper summarizes a function-based approach to model and animate 2D and 3D flows. We use periodic functions to create cyclical animations that represent 2D and 3D flows. These periodic functions are constructed with an extremely simple algorithm from a set of oriented lines. The speed and orientation of the flow are described directly by the orientation and the lengths of these oriented lin...

Abstract The structure of locally soluble periodic groups in which every abelian subgroup is cyclic was described over 20 years ago. We complete the aforementioned characterization by dealing with non-periodic case. also describe finite all subgroups are cyclic.

Hamiltonian dynamical systems tend to have infinitely many periodic orbits. For example, for a broad class of symplectic manifolds almost all levels of a proper smooth Hamiltonian carry periodic orbits. The Hamiltonian Seifert conjecture is the existence problem for regular compact energy levels without periodic orbits. Very little is known about how large the set of regular energy values witho...

We study generation of magnetic fields involving large spatial scales by time-and space-periodic small-scale parity-invariant flows. The anisotropic magnetic eddy diffusivity tensor is calculated by the standard procedure involving expansion of magnetic modes and their growth rates in power series in the scale ratio. Our simulations, conducted for flows with random harmonic composition and expo...

We discuss the Smith iteration for solving large-scale sparse projected discrete-time periodic Lyapunov equations which arise in periodic state feedback problems and in model reduction of periodic descriptor systems. Two algorithms are presented in this paper. The first one works with the cyclic lifted representation of the corresponding projected discrete-time periodic Lyapunov equations. In t...