Linear stability analysis of a horizontal phase boundary separating two miscible liquids

The evolution of small disturbances to a horizontal interface separating two miscible liquids is examined. The aim is to investigate how the interfacial mass transfer affects development of the Rayleigh-Taylor instability and propagation and damping of the gravity-capillary waves. The phase-field approach is employed to model the evolution of a miscible multiphase system. Within this approach, the interface is represented as a transitional layer of small but nonzero thickness. The thermodynamics is defined by the Landau free energy function. Initially, the liquid-liquid binary system is assumed to be out of its thermodynamic equilibrium, and hence, the system undergoes a slow transition to its thermodynamic equilibrium. The linear stability of such a slowly diffusing interface with respect to normal hydro- and thermodynamic perturbations is numerically studied. As a result, we show that the eigenvalue spectra for a sharp immiscible interface can be successfully reproduced for long-wave disturbances, with wavelengths exceeding the interface thickness. We also find that thin interfaces are thermodynamically stable, while thicker interfaces, with the thicknesses exceeding an equilibrium value, are thermodynamically unstable. The thermodynamic instability can make the configuration with a heavier liquid lying underneath unstable.We also find that the interfacial mass transfer introduces additional dissipation, reducing the growth rate of the Rayleigh Taylor instability and increasing the dissipation of the gravity waves. Moreover, mutual action of diffusive and viscous effects completely suppresses development of the modes with shorter wavelengths

Why hyperbolic theories of dissipation cannot be ignored: Comments on a paper by Kostadt and Liu

Contrary to what is asserted in a recent paper by Kostadt and Liu ("Causality and stability of the relativistic diffusion equation"), experiments can tell apart (and in fact do) hyperbolic theories from parabolic theories of dissipation. It is stressed that the existence of a non--negligible relaxation time does not imply for the system to be out of the hydrodynamic regime.Comment: 8 pages Latex, to appear in Phys.Rev.

Toroidal metrics: gravitational solenoids and static shells

In electromagnetism a current along a wire tightly wound on a torus makes a solenoid whose magnetic field is confined within the torus. In Einstein's gravity we give a corresponding solution in which a current of matter moves up on the inside of a toroidal shell and down on the outside, rolling around the torus by the short way. The metric is static outside the torus but stationary inside with the gravomagnetic field confined inside the torus, running around it by the long way. This exact solution of Einstein's equations is found by fitting Bonnor's solution for the metric of a light beam, which gives the required toroidal gravomagnetic field inside the torus, to the general Weyl static external metric in toroidal coordinates, which we develop. We deduce the matter tensor on the torus and find when it obeys the energy conditions. We also give the equipotential shells that generate the simple Bach-Weyl metric externally and find which shells obey the energy conditions.Comment: To appear in Class. Quantum Gra

Semiquantum thermodynamics of complex ferrimagnets

High-quality magnets such as yttrium iron garnet (YIG) are electrically insulating and very complex. By implementing a quantum thermostat into atomistic spin dynamics we compute YIG's key thermodynamic properties, viz., the magnon power spectrum and specific heat, for a large temperature range. The results differ (sometimes spectacularly) from simple models and classical statistics, but agree with available experimental data

Size of Fireballs Created in High Energy Lead-Lead Collisions as Inferred from Coulomb Distortions of Pion Spectra

We compute the Coulomb effects produced by an expanding, highly charged fireball on the momentum distribution of pions. We compare our results to data on Au+Au at 11.6 A GeV from E866 at the BNL AGS and to data on Pb+Pb at 158 A GeV from NA44 at the CERN SPS. We conclude that the distortion of the spectra at low transverse momentum and mid-rapidity can be explained in both experiments by the effect of the large amount of participating charge in the central rapidity region. By adjusting the fireball expansion velocity to match the average transverse momentum of protons, we find a best fit when the fireball radius is about 10 fm, as determined by the moment when the pions undergo their last scattering. This value is common to both the AGS and CERN experiments.Comment: Enlarged discussion, new references added, includes new analysis of pi-/pi+ at AGS energies. 12 pages 5 figures, uses LaTex and epsfi

Chaotic flow and efficient mixing in a micro-channel with a polymer solution

Microscopic flows are almost universally linear, laminar and stationary because Reynolds number, $Re$, is usually very small. That impedes mixing in micro-fluidic devices, which sometimes limits their performance. Here we show that truly chaotic flow can be generated in a smooth micro-channel of a uniform width at arbitrarily low $Re$, if a small amount of flexible polymers is added to the working liquid. The chaotic flow regime is characterized by randomly fluctuating three-dimensional velocity field and significant growth of the flow resistance. Although the size of the polymer molecules extended in the flow may become comparable with the micro-channel width, the flow behavior is fully compatible with that in a table-top channel in the regime of elastic turbulence. The chaotic flow leads to quite efficient mixing, which is almost diffusion independent. For macromolecules, mixing time in this microscopic flow can be three to four orders of magnitude shorter than due to molecular diffusion.Comment: 8 pages,7 figure

Gravitational energy

Observers at rest in a stationary spacetime flat at infinity can measure small amounts of rest-mass+internal energies+kinetic energies+pressure energy in a small volume of fluid attached to a local inertial frame. The sum of these small amounts is the total "matter energy" for those observers. The total mass-energy minus the matter energy is the binding gravitational energy. Misner, Thorne and Wheeler evaluated the gravitational energy of a spherically symmetric static spacetime. Here we show how to calculate gravitational energy in any static and stationary spacetime for isolated sources with a set of observers at rest. The result of MTW is recovered and we find that electromagnetic and gravitational 3-covariant energy densities in conformastatic spacetimes are of opposite signs. Various examples suggest that gravitational energy is negative in spacetimes with special symmetries or when the energy-momentum tensor satisfies usual energy conditions.Comment: 12 pages. Accepted for publication in Class. Quantum Gra

Inertial frame rotation induced by rotating gravitational waves

We calculate the rotation of the inertial frames within an almost flat cylindrical region surrounded by a pulse of non-axially-symmetric gravitational waves that rotate about the axis of our cylindrical polar coordinates. Our spacetime has only one Killing vector. It is along the z-axis and hypersurface orthogonal. We solve the Einstein equations to first order in the wave amplitude and superpose such linearized solutions to form a wave pulse. We then solve the relevant Einstein equation to second order in the amplitude to find the rotation of inertial frames produced by the pulse. The rotation is without time delay. The influence of gravitational wave angular momentum on the inertial frame demonstrates that Mach's principle can not be expressed in terms of the influence of the stress-energy-momentum tensor alone but must involve also influences of gravitational wave energy and angular momentum.Comment: Scheduled to appear in Class. and Quantum Grav. July 2008, "inertial" added in titl