Uncertainty Relations in the Madelung Picture

Madelung showed how the complex Schrödinger equation can be rewritten in terms of two real equations, one for the phase and one for the amplitude of the complex wave function, where both equations are not independent of each other, but coupled. Although these equations formally look like classical hydrodynamic equations, they contain all the information about the quantum system. Concerning the quantum mechanical uncertainties of position and momentum, however, this is not so obvious at first sight. We show how these uncertainties are related to the phase and amplitude of the wave function in position and momentum space and, particularly, that the contribution from the phase essentially depends on the position–momentum correlations. This will be illustrated explicitly using generalized coherent states as examples.

Multiscale Mixed Hydrodynamics in Line Contacts

In the hydrodynamic line contact, there is a very thin layer physically adsorbed to the solid surface. When the surface separation is sufficiently small, the Hertzian contact zone will be completely filled with the boundary layer, while in most of the inlet zone still occurs continuum hydrodynamics, which lies between the mated adsorbed layers. The present paper studies this mixed hydrodynamics by a multiscale analysis. The boundary layer flows are simulated from the flow factor approach model; The intermediate continuum fluid flow is simulated from the continuum fluid model. The flow equations are given respectively for the boundary layers and for the intermediate continuum fluid. The final governing equation has been obtained relating the surface separation to the solid surface speeds and the carried load. The calculation results show that for a high rolling speed the hydrodynamic behavior in the contact agrees with the classical hydrodynamic theory; However for a critically low rolling speed it gives the surface separation greatly higher than that calculated from the classical hydrodynamic theory, showing the significant adsorbed layer effect.

The hydraulic resistance paradox in rapid narrow pipe waterflow

In this work we present experimental results of cross-sectional speed of water flow in narrow cylindrical metal tubes at high pressure gradients up to 1.1 GPa$$\cdot$$ · m−1. The measurement draws attention to the paradoxical behaviour of flowing water in internal diameters less than 250 $$\upmu$$ μ m. At constant pressure gradient, its cross-section speed decreases with decreasing diameter in accordance with the classical hydrodynamic prediction for turbulent flow in rough cylindrical tube. However for very low diameters below 250 $$\upmu$$ μ m, the cross-section speed rises again and reaches almost the maximum theoretical value of the outflow speed for the appropriate pressure without energy loss caused by contraction or hydraulic friction. Our contribution describes mainly experimental character of the new phenomenon and its motivation is to promptly provide the material for further study to the professional public.

On Quantum Extensions of Hydrodynamic Lattice Gas Automata

We consider quantum extensions of classical hydrodynamic lattice gas models. We find that the existence of local conserved quantities strongly constrains such extensions. We find the only extensions that retain local conserved quantities correspond to changing the local encoding of a subset of the bits. These models maintain separability of the state throughout the evolution and are thus efficiently classically simulable. We then consider evolution of these models in the case where any of the bits can be encoded and measured in one of two local bases. In the case that either encoding is allowed, the models are efficiently classically simulable. In the case that both encoding and measurement is allowed in either basis, we argue that efficient classical simulation is unlikely. In particular, for classical models that are computationally universal such quantum extensions can encode Simon’s algorithm, thus presenting an obstacle to efficient classical simulation.

A panoply of Schwinger-Keldysh transport

We classify all possible allowed constitutive relations of relativistic fluids in a statistical mechanical limit using the Schwinger-Keldysh effective action for hydrodynamics. We find that microscopic unitarity enforces genuinely new constraints on the allowed transport coefficients that are invisible in the classical hydrodynamic description; they are not implied by the second law or the Onsager relations. We term these conditions Schwinger-Keldysh positivity and provide explicit examples of the various allowed terms.

PROBLEMS OF NONSTATIONARY FILTRATION

he article deals with the classical hydrodynamic theory of filtration. Discusses models of soil, fluid and nature of fluid flow that formed the basis for the creation of the classic filtration theory. Also discusses the assumptions made for the linearization of the equations. Evaluated the scope of the classical filtration theory. Proposed a new model of filtration through a porous medium, based on the application of the laws of theoretical mechanics. It is based on the classical model of soil: the soil is composed of capillaries with ..parallel axes, in which the liquid moves. For tasks of infiltration equations of motion. Considered special cases of unsteady motion of a finite volume of liquid. Numerical example a machine experiment.

Parallel and perpendicular cascades in solar wind turbulence

MHD-scale fluctuations in the velocity, magnetic, and density fields of the solar wind are routinely observed. The evolution of these fluctuations, as they are transported radially outwards by the solar wind, is believed to involve both wave and turbulence processes. The presence of an average magnetic field has important implications for the anisotropy of the fluctuations and the nature of the turbulent wavenumber cascades in the directions parallel and perpendicular to this field. In particular, if the ratio of the rms magnetic fluctuation strength to the mean field is small, then the parallel wavenumber cascade is expected to be weak and there are difficulties in obtaining a cascade in frequency. The latter has been invoked in order to explain the heating of solar wind fluctuations (above adiabatic levels) via energy transfer to scales where ion-cyclotron damping can occur.Following a brief review of classical hydrodynamic and magnetohydrodynamic (MHD) cascade theories, we discuss the distinct nature of parallel and perpendicular cascades and their roles in the evolution of solar wind fluctuations.