99 research outputs found
One-dimensional reduction of viscous jets. I. Theory
We build a general formalism to describe thin viscous jets as one-dimensional
objects with an internal structure. We present in full generality the steps
needed to describe the viscous jets around their central line, and we argue
that the Taylor expansion of all fields around that line is conveniently
expressed in terms of symmetric trace-free tensors living in the two dimensions
of the fiber sections. We recover the standard results of axisymmetric jets and
we report the first and second corrections to the lowest order description,
also allowing for a rotational component around the axis of symmetry. When
applied to generally curved fibers, the lowest order description corresponds to
a viscous string model with circular sections. However, when including the
first corrections we find that curved jets generically develop elliptic
sections. Several subtle effects imply that the first corrections cannot be
described by a rod model, since it amounts to selectively discard some
corrections. For completeness, we also recover the constitutive relations for
forces and torques in rod models and exhibit a missing term in the lowest order
expression of viscous torque. Given that our method is based on tensors, the
complexity of all computations has been beaten down by using an appropriate
tensor algebra package such as {\it xAct}, allowing us to obtain a
one-dimensional description of curved viscous jets with all the first order
corrections consistently included. Finally, we find a description for straight
fibers with elliptic sections as a special case of these results, and recover
that ellipticity is dynamically damped by surface tension. An application to
toroidal viscous fibers is presented in the companion paper [Pitrou, Phys. Rev.
E 97, 043116 (2018)].Comment: 41 pages, 1 figur
Isotropization of the universe during inflation
A primordial inflationary phase allows one to erase any possible anisotropic
expansion thanks to the cosmic no-hair theorem. If there is no global
anisotropic stress, then the anisotropic expansion rate tends to decrease. What
are the observational consequences of a possible early anisotropic phase? We
first review the dynamics of anisotropic universes and report analytic
approximations. We then discuss the structure of dynamical equations for
perturbations and the statistical properties of observables, as well as the
implication of a primordial anisotropy on the quantization of these
perturbations during inflation. Finally we briefly review models based on
primordial vector field which evade the cosmic no-hair theorem.Comment: 9 pages, 3 figures. Invited review article for the French Academy of
Scienc
Quantization of perturbations during inflation in the 1+3 covariant formalism
This note derives the analogue of the Mukhanov-Sasaki variables both for
scalar and tensor perturbations in the 1+3 covariant formalism. The possibility
of generalizing them to non-flat Friedmann-Lemaitre universes is discussed.Comment: 4 pages: v2 has minor changes to match published versio
xPand: An algorithm for perturbing homogeneous cosmologies
In this paper, we develop in detail a fully geometrical method for deriving
perturbation equations about a spatially homogeneous background. This method
relies on the 3+1 splitting of the background space-time and does not use any
particular set of coordinates: it is implemented in terms of geometrical
quantities only, using the tensor algebra package xTensor in the xAct
distribution along with the extension for perturbations xPert. Our algorithm
allows one to obtain the perturbation equations for all types of homogeneous
cosmologies, up to any order and in all possible gauges. As applications, we
recover the well-known perturbed Einstein equations for
Friedmann-Lemaitre-Robertson-Walker cosmologies up to second order and for
Bianchi I cosmologies at first order. This work paves the way to the study of
these models at higher order and to that of any other perturbed Bianchi
cosmologies, by circumventing the usually too cumbersome derivation of the
perturbed equations.Comment: 21 pages, 2 figure
One-dimensional reduction of viscous jets. II. Applications
In a companion paper [Pitrou, Phys. Rev. E 97, 043115 (2018)], a formalism
allowing to describe viscous fibers as one-dimensional objects was developed.
We apply it to the special case of a viscous fluid torus. This allows to
highlight the differences with the basic viscous string model and with its
viscous rod model extension. In particular, an elliptic deformation of the
torus section appears because of surface tension effects, and this cannot be
described by viscous string nor viscous rod models. Furthermore, we study the
Rayleigh-Plateau instability for periodic deformations around the perfect
torus, and we show that the instability is not sufficient to lead to the torus
breakup in several droplets before it collapses to a single spherical drop.
Conversely, a rotating torus is dynamically attracted toward a stationary
solution, around which the instability can develop freely and split the torus
in multiple droplets.Comment: 10 pages, 5 figure
A precise numerical estimation of the magnetic field generated around recombination
We investigate the generation of magnetic fields from non-linear effects
around recombination. As tight-coupling is gradually lost when approaching
, the velocity difference between photons and baryons starts to
increase, leading to an increasing Compton drag of the photons on the
electrons. The protons are then forced to follow the electrons due to the
electric field created by the charge displacement; the same field, following
Maxwell's laws, eventually induces a magnetic field on cosmological scales.
Since scalar perturbations do not generate any magnetic field as they are
curl-free, one has to resort to second-order perturbation theory to compute the
magnetic field generated by this effect. We reinvestigate this problem
numerically using the powerful second-order Boltzmann code SONG. We show that:
i) all previous studies do not have a high enough angular resolution to reach a
precise and consistent estimation of the magnetic field spectrum; ii) the
magnetic field is generated up to ; iii) it is in practice
impossible to compute the magnetic field with a Boltzmann code for scales
smaller than . Finally we confirm that for scales of a few , this magnetic field is of order , many orders
of magnitude smaller than what is currently observed on intergalactic scales.Comment: 6 pages, 3 figure
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