Quantum fluid mechanics

This proves that the pseudoparticles in the quantum fluid obey classical mechanics in the classical limit. 

Quantum efficiencies Quantum efficiency Quantum electronics Quantum fluids Quantum mechanics Quantum size effect Quantumwell... 

Below we shall start with our problem — namely the prediction of the properties of a molecular liquid — first at the quantum mechanical and then at the statistical level up to hydrodynamic limit. We shall then conclude by showing the feasibility of using molecular dynamics to solve problems of fluid mechanics and the results obtained by using water as a solvent for DNA in the presence of counterions. 

It is impossible to read much of the literature on viscosity without coming across some reference to the equation of motion. In the area of fluid mechanics, this equation occupies a place like that of the Schrodinger equation in quantum mechanics. Like its counterpart, the equation of motion is a complicated partial differential equation, the analysis of which is a matter for fluid dynamicists. Our purpose in this section is not to solve the equation of motion for any problem, but merely to introduce the physics of the relationship. Actually, both the concentric-cylinder and the capillary viscometers that we have already discussed are analyzed by the equation of motion, so we have already worked with this result without explicitly recognizing it. The equation of motion does in a general way what we did in a concrete way in the discussions above, namely, describe the velocity of a fluid element within a flowing fluid as a function of location in the fluid. The equation of motion allows this to be considered as a function of both location and time and is thus useful in nonstationary-state problems as well. 

The second contribution spans an even larger range of length and times scales. Two benchmark examples illustrate the design approach polymer electrolyte fuel cells and hard disk drive (HDD) systems. In the current HDDs, the read/write head flies about 6.5 nm above the surface via the air bearing design. Multi-scale modeling tools include quantum mechanical (i.e., density functional theory (DFT)), atomistic (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational fluid mechanics, and system optimization) levels. 

While an understanding of the molecular processes at the fuel cell electrodes requires a quantum mechanical description, the flows through the inlet channels, the gas diffusion layer and across the electrolyte can be described by classical physical theories such as fluid mechanics and diffusion theory. The equivalent of Newton s equations for continuous media is an Eulerian transport equation of the form... 

In this section we discuss how shock compression produces electronic and vibrational excitations that can cause chemical reactions. It is an outline for a theory that connects the fluid-mechanical picture of shock compression to the quantum mechanical picture of chemical reaction dynamics. 

It is not implausible that there are worlds whose ultimate constituents are Newtonian particles conforming to Newtonian-like laws, worlds whose ultimate constituents are fluids obeying classical fluid mechanics, worlds whose ontology and laws are those of Bohmian quantum mechanics, all of which contain configurations that realize the nomological/causal specifications associated with at least some mental properties. 

Depending on the nature and the size of the objects considered, mechanics is divided into several branches mechanics of fluids, mechanics of solids, quantum mechanics (dealing with particles and waves), etc. A peculiar branch is the mechanic of the point when objects have a negligible volume or are sufficiently homogeneous and symmetric for allowing their modeling by a geometrical point. 

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The similarity in form between the two real equations implied by the single-body spin-0 Schrddinger equation in the position representation (wave mechanics) and the equations of fluid mechanics with potential flow in its Eulerian formulation was first pointed out by Madelung in 1926 [1]. In this analogy, the probability density is proportional to the fluid density, and the phase of the wave function is a velocity potential. A novel feature of the quantum fluid is the appearance of quantum stresses, which are usually represented through the quantum potential. To achieve mathematical equivalence of the models, the hydrodynamic variables have to satisfy... 

However, this apparent simplicity hides tremendous complexity of the cell components structure and function. Obviously, the first working PEFC prototypes were constructed by the trial-and-error method. However, a significant market penetration requires that the cells must be cheap, efficient, and long-living. Nowadays, it is evident that the solution of these problems demands concerted efforts of specialists in electrochemistry, quantum chemistry, physics, fluid mechanics, mechanical, and chemical engineering. 

Linear response theory [152] is perfectly suited to the study of fluid structures when weak fields are involved, which turns out to be the case of the elastic scattering experiments alluded to earlier. A mechanism for the relaxation of the field effect on the fluid is just the spontaneous fluctuations in the fluid, which are characterized by the equilibrium (zero field) correlation functions. Apart from the standard technique used to derive the instantaneous response, based on Fermi s golden rule (or on the first Bom approximation) [148], the functional differentiation of the partition function [153, 154] with respect to a continuous (or thermalized) external field is also utilized within this quantum context. In this regard, note that a proper ensemble to carry out functional derivatives is the grand ensemble. All of this allows one to gain deep insight into the equilibrium structures of quantum fluids, as shown in the works by Chandler and Wolynes [25], by Ceperley [28], and by the present author [35, 36]. In doing so, one can bypass the dynamics of the quantum fluid to obtain the static responses in k-space and also make unexpected and powerful connections with classical statistical mechanics [36]. 

Chandler D and Wolynes P 1979 Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids J. Chem. Rhys. 70 2914... 

C. Similarities Between Potentiai Fluid Dynamics and Quantum Mechanics... 

In writing the Lagrangean density of quantum mechanics in the modulus-phase representation, Eq. (140), one notices a striking similarity between this Lagrangean density and that of potential fluid dynamics (fluid dynamics without vorticity) as represented in the work of Seliger and Whitham [325]. We recall briefly some parts of their work that are relevant, and then discuss the connections with quantum mechanics. The connection between fluid dynamics and quantum mechanics of an electron was already discussed by Madelung [326] and in Holland s book [324]. However, the discussion by Madelung refers to the equations only and does not address the variational formalism which we discuss here. 

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