Consider the mean field limit of a model for multiple HTTP sources multiplexed through a drop-tail router. The limit may exhibit two stationary regimes. In the fluid regime the flows are independent, there are no packet losses and the average throughput is high. In the turbulent regime the flows are synchronized, there are periodic congestion epochs with packet losses and the average throughput...

We consider the evolution of a set carried by a space periodic incompressible stochastic flow in a Euclidean space. We report on three main results obtained in [8, 9, 10] concerning long time behaviour for a typical realization of the stochastic flow. First, at time t most of the particles are at a distance of order √ t away from the origin. Moreover, we prove a Central Limit Theorem for the ev...

Recently found unstable time-periodic solutions to the incompressible Navier-Stokes equation are reviewed to discuss their relevance to plane Couette turbulence and isotropic turbulence. It is shown that the periodic motion embedded in the Couette turbulence exhibits a regeneration cycle of near-wall coherent structures, which consists of formation and breakdown of streamwise vortices and low-v...

The present paper is a review of counterexamples to the “Hamiltonian Seifert conjecture” or, more generally, of examples of Hamiltonian systems having no periodic orbits on a compact energy level. We begin with the discussion of the “classical” and volume– preserving Seifert conjectures. Then the constructions of counterexamples to the Hamiltonian Seifert conjecture in dimensions greater than o...

The periodic orbit conjecture states that, on closed manifolds, the set of lengths orbits a non-vanishing vector field all whose are admits an upper bound. This is known to be false in general due counterexample by Sullivan. However, it satisfied under geometric condition being geodesible. In this work, we use recent characterization Eulerisable flows (or more generally admitting strongly adapt...

In this paper, we study the classical problem of wind in steady atmospheric Ekman layer with constant eddy viscosity. Different from well-known homogeneous system [14,20], retain turbulent fluxes and establish a new nonhomogeneous first order differential equations involving term horizontal dependent. We present existence uniqueness periodic solutions show Hyers-Ulam stability results for syste...

The main purpose of this paper is mathematical analysis on time-periodic flows electrons and holes in semiconductors. appear a situation that alternating-current voltages are applied to devices. In paper, we study the drift-diffusion model for semiconductors three-dimensional bounded domain investigate existence stability solutions. We first derive uniform-in-time estimates time-global solution...