A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics

We present a new variational framework for dissipative general relativistic fluid dynamics. The model extends the convective variational principle for multi-fluid systems to account for a range of dissipation channels. The key ingredients in the construction are i) the use of a lower dimensional matter space for each fluid component, and ii) an extended functional dependence for the associated volume forms. In an effort to make the concepts clear, the formalism is developed in steps with the model example of matter coupled to heat considered at each level. Thus we discuss a model for heat flow, derive the relativistic Navier-Stokes equations and discuss why the individual dissipative stress tensors need not be spacetime symmetric. We argue that the new formalism, which notably does not involve an expansion away from an assumed equilibrium state, provides a conceptual breakthrough in this area of research and provide an ambitious list of directions in which one may want to extend it in the future. This involves an exciting set of problems, relating to both applications and foundational issues.Comment: 21 pages RevTex, 3 pdf figures, matches the published version. arXiv admin note: text overlap with arXiv:1107.1005 by other author

The time evolution of marginally trapped surfaces

In previous work we have shown the existence of a dynamical horizon or marginally trapped tube (MOTT) containing a given strictly stable marginally outer trapped surface (MOTS). In this paper we show some results on the global behavior of MOTTs assuming the null energy condition. In particular we show that MOTSs persist in the sense that every Cauchy surface in the future of a given Cauchy surface containing a MOTS also must contain a MOTS. We describe a situation where the evolving outermost MOTS must jump during the coalescence of two seperate MOTSs. We furthermore characterize the behavior of MOTSs in the case that the principal eigenvalue vanishes under a genericity assumption. This leads to a regularity result for the tube of outermost MOTSs under the genericity assumption. This tube is then smooth up to finitely many jump times. Finally we discuss the relation of MOTSs to singularities of a space-time.Comment: 21 pages. This revision corrects some typos and contains more detailed proofs than the original versio

String Effects on Fermi--Dirac Correlation Measurements

We investigate some recent measurements of Fermi--Dirac correlations by the LEP collaborations indicating surprisingly small source radii for the production of baryons in $e^+e^-$-annihilation at the $Z^0$ peak. In the hadronization models there are besides the Fermi--Dirac correlation effect also a strong dynamical (anti-)correlation. We demonstrate that the extraction of the pure FD effect is highly dependent on a realistic Monte Carlo event generator, both for separation of those dynamical correlations which are not related to Fermi--Dirac statistics, and for corrections of the data and background subtractions. Although the model can be tuned to well reproduce single particle distributions, there are large model-uncertainties when it comes to correlations between identical baryons. We therefore, unfortunately, have to conclude that it is at present not possible to make any firm conclusion about the source radii relevant for baryon production at LEP

The nonlinear development of the relativistic two-stream instability

The two-stream instability has been mooted as an explanation for a range of astrophysical applications from GRBs and pulsar glitches to cosmology. Using the first nonlinear numerical simulations of relativistic multi-species hydrodynamics we show that the onset and initial growth of the instability is very well described by linear perturbation theory. In the later stages the linear and nonlinear description match only qualitatively, and the instability does not saturate even in the nonlinear case by purely ideal hydrodynamic effects.Comment: 15 pages, 9 figure

The dynamics of neutron star crusts: Lagrangian perturbation theory for a relativistic superfluid-elastic system

The inner crust of a mature neutron star is composed of an elastic lattice of neutron-rich nuclei penetrated by free neutrons. These neutrons can flow relative to the crust once the star cools below the superfluid transition temperature. In order to model the dynamics of this system, which is relevant for a range of problems from pulsar glitches to magnetar seismology and continuous gravitational-wave emission from rotating deformed neutron stars, we need to understand general relativistic Lagrangian perturbation theory for elastic matter coupled to a superfluid component. This paper develops the relevant formalism to the level required for astrophysical applications.Comment: 31 pages, double spacing, minor typos fixe

A Strong Maximum Principle for Weak Solutions of Quasi-Linear Elliptic Equations with Applications to Lorentzian and Riemannian Geometry

The strong maximum principle is proved to hold for weak (in the sense of support functions) sub- and super-solutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for $C^0$ spacelike hypersurfaces in a Lorentzian manifold. As one application a Lorentzian warped product splitting theorem is given.Comment: 37 pages, 1 figure, ams-latex using eepi

Resource effective control of Elymus repens

Preliminary results show that there is room for improvement within existing control methods of couch grass (Elymus repens (L.) Gould). It may be possible to reduce the number of stubble cultivations during autumn by timing the treatment, and to reduce the cultivation depth by using a goose foot cultivator (5 cm) instead of a disc cultivator (10 cm), without sacrificing couch grass control efficiency. The first year of the experiment, the use of a goose foot cultivator resulted in less nitrogen leaching than cultivation by disc. A reduced number of stubble cultivations potentially reduces nutrient loss, fuel consumption and the workload of the farmer. Our experiments with cover crops to control couch grass in cereals has yet to prove significant effects on couch grass control, but cover crops combined with goose foot hoeing did reduce nitrogen leaching by more than a third compared to cultivation by disc. Further data is necessary to see if the system can be used to effectively control couch grass without significant yield losses. Regardless, it can reduce nitrogen leaching and potentially provide other ecosystem services, e.g. control weeds other than couch grass

Blowup of Jang's equation at outermost marginally trapped surfaces

The aim of this paper is to collect some facts about the blowup of Jang's equation. First, we discuss how to construct solutions that blow up at an outermost MOTS. Second, we exclude the possibility that there are extra blowup surfaces in data sets with non-positive mean curvature. Then we investigate the rate of convergence of the blowup to a cylinder near a strictly stable MOTS and show exponential convergence near a strictly stable MOTS.Comment: 15 pages. This revision corrects some typo

R-mode oscillations and rocket effect in rotating superfluid neutron stars. I. Formalism

We derive the hydrodynamical equations of r-mode oscillations in neutron stars in presence of a novel damping mechanism related to particle number changing processes. The change in the number densities of the various species leads to new dissipative terms in the equations which are responsible of the {\it rocket effect}. We employ a two-fluid model, with one fluid consisting of the charged components, while the second fluid consists of superfluid neutrons. We consider two different kind of r-mode oscillations, one associated with comoving displacements, and the second one associated with countermoving, out of phase, displacements.Comment: 10 page

The dynamics of dissipative multi-fluid neutron star cores

We present a Newtonian multi-fluid formalism for superfluid neutron star cores, focussing on the additional dissipative terms that arise when one takes into account the individual dynamical degrees of freedom associated with the coupled "fluids". The problem is of direct astrophysical interest as the nature of the dissipative terms can have significant impact on the damping of the various oscillation modes of the star and the associated gravitational-wave signatures. A particularly interesting application concerns the gravitational-wave driven instability of f- and r-modes. We apply the developed formalism to two specific three-fluid systems: (i) a hyperon core in which both Lambda and Sigma^- hyperons are present, and (ii) a core of deconfined quarks in the colour-flavour-locked phase in which a population of neutral K^0 kaons is present. The formalism is, however, general and can be applied to other problems in neutron-star dynamics (such as the effect of thermal excitations close to the superfluid transition temperature) as well as laboratory multi-fluid systems.Comment: RevTex, no figure