Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier–Stokes equation for viscous fluid flow. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out...

In this set of lectures I will describe how one can use ideas of dynamical systems theory to give a quite complete picture of the long time asymptotics of solutions of the two-dimensional Navier-Stokes equation. I will discuss the existence and properties of invariant manifolds for dynamical systems defined on Banach spaces and review the theory of Lyapunov functions, again concentrating on the...

The dynamics of the fluid fields in a large class of causal dissipative fluid theories is studied. It is shown that the physical fluid states in these theories must relax (on a time scale that is characteristic of the microscopic particle interactions) to ones that are essentially indistinguishable from the simple rel-ativistic Navier-Stokes descriptions of these states. Thus, for example, in t...

[Abstract] A theoretical analysis of electronic-resonance-enhanced (ERE) coherent anti-Stokes Raman scattering (CARS) of NO is discussed. The time-dependent density matrix equations for the nonlinear ERE-CARS process are derived and manipulated into a form suitable for direct numerical integration (DNI). In the ERE-CARS configuration considered in this paper, the pump and Stokes beams are far f...

Cheyne-Stokes breathing has been induced in 30 dogs by inserting a circulatory delay system between the heart and the brain to prolong the transit time of blood from the lungs to the brain. The duration of each cycle of Cheyne-Stokes breathing increased proportionately with the volume of the delay system and decreased as the perfusion pressure to the brain was increased. Periodic variations in ...

We consider incompressible viscous flows between two transversely vibrating solid walls and construct an asymptotic expansion of solutions of the Navier–Stokes equations in the limit when both the amplitude of the vibration and the thickness of the oscillatory boundary layers (the Stokes layers) are small and have the same order of magnitude. Our asymptotic expansion is valid up to the flow bou...