arXiv subjects

Reinhard Prix

Publications and source records attributed to Reinhard Prix.

62 records · Page 4Linked to original sources

arXiv2005

Variational description of multi-fluid hydrodynamics: Coupling to gauge fields

In this work we extend our previously developed formalism of Newtonian multi-fluid hydrodynamics to allow for coupling between the fluids and the electromagnetic and gravitational field. This is achieved within the convective variational principle by using a standard minimal coupling prescription. In addition to the conservation of total energy and momentum, we derive the conservation of canonical vorticity and helicity, which generalize the corresponding conserved quantities of uncharged fluids. We discuss the application of this formalism to electrically conducting systems, magnetohydrodynamics and superconductivity. The equations of electric conductors derived here are more general than those found in the standard description of such systems, in which the effect of entrainment is overlooked, despite the fact that it will generally be present in any conducting multi-constituent system.

physics.flu-dyn↗

arXiv2005

Relativistic numerical models for stationary superfluid Neutron Stars

We have developed a theoretical model and a numerical code for stationary rotating superfluid neutron stars in full general relativity. The underlying two-fluid model is based on Carter's covariant multi-fluid hydrodynamic formalism. The two fluids, representing the superfluid neutrons on one hand, and the protons and electrons on the other, are restricted to uniform rotation around a common axis, but are allowed to have different rotation rates. We have performed extensive tests of the numerical code, including quantitative comparisons to previous approximative results for these models. The results presented here are the first ``exact'' calculations of such models in the sense that no approximations (other than that inherent in a discretized numerical treatment) are used. Using this code we reconfirm the existence of prolate-oblate shaped configurations. We studied the dependency of the Kepler rotation limit and of the mass-density relation on the relative rotation rate. We further demonstrate how one can simulate a (albeit fluid) neutron-star ``crust'' by letting one fluid extend further outwards than the other, which results in interesting cases where the Kepler limit is actually determined by the outermost but slower fluid.

gr-qc↗

arXiv2002

Adiabatic oscillations of non-rotating superfluid neutron stars

We present results concerning the linear (radial and non-radial) oscillations of non-rotating superfluid neutron stars in Newtonian physics. We use a simple two-fluid model to describe the superfluid neutron star, where one fluid consists of the superfluid neutrons,while the second fluid contains all the comoving constituents (protons, electrons). The two fluids are assumed to be "free" in the sense of absence of vortex-mediated forces like mutual friction or pinning, but they can be coupled by the equation of state, in particular by entrainment.We calculate numerically the eigen-frequencies and -modes of adiabatic oscillations, neglecting beta-reactions that would lead to dissipation.We find a doubling of all acoustic-type modes (f-modes, p-modes), and confirm the absence of g-modes in these superfluid models. We show analytically and numerically that only in the case of non-stratified background models (i.e. with no composition gradient) can these doublets of acoustic modes be separated into two distinct families, which are characterised by either co- or counter-moving fluids respectively, and which are sometimes referred to as "ordinary" and "superfluid" modes. In the general, stratified case, however, this separation is not possible, and these acoustic modes can not be classified as being either purely "ordinary" or "superfluid". We show how the properties of the two-fluid modes change as functions of the coupling by entrainment. We find avoided mode-crossings for the stratified models, while the crossings are not avoided in the non-stratified, separable case. The oscillations of normal-fluid neutron stars are recovered as a special case simply by locking the two fluids together.In this effective one-fluid case we find the usual singlet f- and p-modes, and we also find the expected g-modes.

astro-ph↗

arXiv2001

Relativistic solution of Iordanskii problem in multi-constituent superfluid mechanics

Flow past a line vortex in a simple perfect fluid or superfluid gives rise to a transverse Magnus force that is given by the well known Joukowski lift formula. The problem of generalising this to multiconstituent superfluid models has been controversial since it was originally posed by the work of Iordanski in the context of the Landau 2-constituent model for He-4 at finite temperature. The present work deals not just with this particular case but with the generic category of perfect multiconstituent models including the kind proposed for a mixture of He-4 and He-3 by Andreev and Bashkin. It is shown here (using a relativistic approach) that each constituent will provide a contribution proportional to the product of the corresponding momentum circulation integral with the associated asymptotic current density.

cond-mat↗

arXiv2000

Covariant Vortex In Superconducting-Superfluid-Normal Fluid Mixtures with Stiff Equation of State

The integrals of motion for a cylindrically symmetric stationary vortex are obtained in a covariant description of a mixture of interacting superconductors, superfluids and normal fluids. The relevant integrated stress-energy coefficients for the vortex with respect to a vortex-free reference state are calculated in the approximation of a ``stiff'', i.e. least compressible, relativistic equation of state for the fluid mixture. As an illustration of the foregoing general results, we discuss their application to some of the well known examples of ``real'' superfluid and superconducting systems that are contained as special cases. These include Landau's two-fluid model, uncharged binary superfluid mixtures, rotating conventional superconductors and the superfluid neutron-proton-electron plasma in the outer core of neutron stars.

gr-qc↗

arXiv1999

Bogomol'nyi Limit For Magnetic Vortices In Rotating Superconductor

This work is the sequel of a previous investigation of stationary and cylindrically symmetric vortex configurations for simple models representing an incompressible non-relativistic superconductor in a rigidly rotating background. In the present paper, we carry out our analysis with a generalized Ginzburg-Landau description of the superconductor, which provides a prescription for the radial profile of the normal density within the vortex. Within this framework, it is shown that the Bogomol'nyi limit condition marking the boundary between type I and type II behavior is unaffected by the rotation of the background.

cond-mat.supr-con↗

arXiv1999

Slowly Rotating Two-Fluid Neutron Star Model

We study stationary axisymmetric configurations of a star model consisting of two barotropic fluids, which are uniformly rotating at two different rotation rates. Analytic approximate solutions in the limit of slow rotation are obtained with the classical method of Chandrasekhar, which consists of an expansion of the solution in terms of the rotation rate, and which is generalized to the case of two fluids in order to apply it to the present problem. This work has a direct application to neutron star models, in which the neutron superfluid can rotate at a different speed than the fluid of charged components. Two cases are considered, the case of two non-interacting fluids, and the case of an interaction of a special type, corresponding to the vortices of the neutron superfluid being completely pinned to the second fluid. The special case of the equation of state P~rho^2 is solved explicitly as an illustration of the foregoing results.

astro-ph↗

arXiv1999

Energy of Magnetic Vortices in Rotating Superconductor

We carry out a systematic analytic investigation of stationary and cylindrically symmetric vortex configurations for simple models representing an incompressible non-relativistic superconductor in a rigidly rotating background. It is shown that although the magnetic and kinetic contributions to the energy per unit length of such a vortex are separately modified by the background angular velocity, its effect on the total energy per unit length cancels out. For a type II superconductor threaded by a parallel array of such vortices, this result implies that the relevant macroscopic magnetic field strength H will not be equal to the large scale average of the local magnetic induction B (as has previously been suggested) but instead that H will simply be equal to the external London field that characterizes the value of B outside the vortices.

cond-mat.supr-con↗