We investigate chaos synchronization of small-scale motions in the three-dimensional turbulent energy cascade, via pseudospectral simulations of the incompressible Navier-Stokes equations. The modes of the turbulent velocity field below about 20 Kolmogorov dissipation lengths are found to be slaved to the chaotic dynamics of larger-scale modes. The dynamics of all dissipation-range modes can be...

We consider a generalized model of cell population dynamics with n different phenotypes. Both the Markov branching process and the ODE system are presented, and exploited to investigate the dynamics of the phenotypic proportions. We will give a sufficient and necessary condition under which the phenotypic proportions satisfy the Kolmogorov forward equations of an n-state Markov chain. In genera...