Molecular hydrodynamic theory of the velocity autocorrelation function

The velocity autocorrelation function (VACF) encapsulates extensive information about a fluid's molecular-structural and hydrodynamic properties. We address the following fundamental question: How well can a purely hydrodynamic description recover the molecular features of a fluid as exhibited by the VACF? To this end, we formulate a bona fide hydrodynamic theory of the tagged-particle VACF for simple fluids. Our approach is distinguished from previous efforts in two key ways: collective hydrodynamic modes are modeled by \emph{linear} hydrodynamic equations; the fluid's static kinetic energy spectrum is identified as a necessary initial condition for the momentum current correlation. Our formulation leads to a natural physical interpretation of the hydrodynamic VACF as a superposition of quasinormal hydrodynamic modes weighted commensurately with the static kinetic energy spectrum, which appears to be essential to bridging continuum hydrodynamical behavior and discrete-particle kinetics. Our methodology yields VACF calculations quantitatively on par with existing approaches for liquid noble gases and alkali metals; moreover, our hydrodynamic model for the self-intermediate scattering function extends the applicable domain to low densities where the Schmidt number is of order unity, enabling calculations for gases and supercritical fluids.Comment: 14 pages, 3 figures; 5 appendices, 2 appendix figures; improved method/results for Fig. 3 w/ appendix 4; added new results w/ procedure in appendix 5. (v2: 11 pages, 3 figures, 3 appendices

Inappropriateness of the finite Larmor radius model for the tilting mode in field reversed configurations

Numerical results are presented of the finite Larmor radius (FLR) treatment of the tilting mode as described by Seyler and Barnes. We have two principal results. First, the FLR theory of tilting has singularities at the magnetic axis that make application of the theory unphysical. Second, numerical results will be presented showing that for current experiments the magnetic moments of the ions are poorly conserved at the tips of the flux surfaces in an FRC, ad therefore there is a priori reason to view an FLR theory as suspect for global modes in FRCs

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F. Robert Henderson et al., Increasing Eastern Bluebirds in Kansas, Kansas State University, November 1990

Ion kinetic effects on the tilt mode in FRCs

Theory and simulations have shown that field reversed configurations (FRG's) should be unstable magnetohydrodynamically to the tilting mode, yet tilting seldom is seen in the experiments. Profile effects (within MHD) and ion finite larmor radius (FLR) effects have been prosed to explain the observed stability of FRC's. The present work seeks to test both of these effects

Role of confined phonons in thin film superconductivity

We calculate the critical temperature $T_c$ and the superconducting energy gaps $\Delta_n$ of a thin film superconductor system, where $\Delta_n$ is the superconducting energy gap of the $n$-th subband. Since the quantization of both the electron energy and phonon spectrum arises due to dimensional confinement in one direction, the effective electron-electron interaction mediated by the quantized confined phonons is different from that mediated by the bulk phonon, leading to the modification of $T_c$ in the thin film system. We investigate the dependence of $T_c$ and $\Delta_n$ on the film thickness $d$ with this modified interaction.Comment: 4 pages, 2 figure

Pervasive melt percolation reactions in ultra-depleted refractory harzburgites at the Mid-Atlantic Ridge, 15° 20′N : ODP Hole 1274A

Author Posting. © The Authors, 2006. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Contributions to Mineralogy and Petrology 153 (2007): 303-319, doi:10.1007/s00410-006-0148-6.ODP Leg 209 Site 1274 mantle peridotites are highly refractory in terms of lack of residual clinopyroxene, olivine Mg# (up to 0.92) and spinel Cr# (~0.5), suggesting high degree of partial melting (>20%). Detailed studies of their microstructures show that they have extensively reacted with a pervading intergranular melt prior to cooling in the lithosphere, leading to crystallization of olivine, clinopyroxene and spinel at the expense of orthopyroxene. The least reacted harzburgites are too rich in orthopyroxene to be simple residues of low-pressure (spinel field) partial melting. Cu-rich sulfides that precipitated with the clinopyroxenes indicate that the intergranular melt was generated by no more than 12% melting of a MORB mantle or by more extensive melting of a clinopyroxene-rich lithology. Rare olivine-rich lherzolitic domains, characterized by relics of coarse clinopyroxenes intergrown with magmatic sulfides, support the second interpretation. Further, coarse and intergranular clinopyroxenes are highly depleted in REE, Zr and Ti. A two-stage partial melting/melt-rock reaction history is proposed, in which initial mantle underwent depletion and refertilization after an earlier high pressure (garnet field) melting event before upwelling and remelting beneath the present-day ridge. The ultra-depleted compositions were acquired through melt re-equilibration with residual harzburgites.Funding for this research was provided by Centre National de la Recherche Scientifique-Institut National des Sciences de l’Univers (Programme Dynamique et Evolution de la Terre Interne)