We derive the hydrodynamic limit of a kinetic equation where interactions in velocity are modelled by linear operator (Fokker-Planck or Linear Boltzmann) and force Vlasov term is stochastic process with high amplitude short-range correlation. In scales regime we consider, scalar second-order partial differential equation. Compared to deterministic case, also observe phenomenon enhanced diffusion.

We show how the recently developed theory of geodesic transport barriers for fluid flows can be used to uncover key invariant manifolds in externally forced, one-degree-of-freedom mechanical systems. Specifically, invariant sets in such systems turn out to be shadowed by least-stretching geodesics of the Cauchy–Green strain tensor computed from the flow map of the forced mechanical system. This...

In this paper, periodic motions in a periodically excited, Duffing oscillator with a time-delayed displacement are investigated through the Fourier series, and the stability and bifurcation of such periodic motions are discussed through eigenvalue analysis. The time-delayed displacement is from the feedback control of displacement. The analytical bifurcation trees of period-1 motions to chaos i...

TheDuffing oscillator has become a classical paradigm for illustrating the remarkable jump phenomenon and other nonlinear behaviour [1,2]. The understanding gained on the basis of this low-order nonlinear systemhas helped in the development of reducedorder models of complex mechanical systems ranging from microscales to macroscales [3,4]. The nondimensional Duffing equation with damping and ext...