238 research outputs found
Statistics of initial density perturbations in heavy ion collisions and their fluid dynamic response
An interesting opportunity to determine thermodynamic and transport
properties in more detail is to identify generic statistical properties of
initial density perturbations. Here we study event-by-event fluctuations in
terms of correlation functions for two models that can be solved analytically.
The first assumes Gaussian fluctuations around a distribution that is fixed by
the collision geometry but leads to non-Gaussian features after averaging over
the reaction plane orientation at non-zero impact parameter. In this context,
we derive a three-parameter extension of the commonly used Bessel-Gaussian
event-by-event distribution of harmonic flow coefficients. Secondly, we study a
model of N independent point sources for which connected n-point correlation
functions of initial perturbations scale like 1/N^(n-1). This scaling is
violated for non-central collisions in a way that can be characterized by its
impact parameter dependence. We discuss to what extent these are generic
properties that can be expected to hold for any model of initial conditions,
and how this can improve the fluid dynamical analysis of heavy ion collisions.Comment: 35 pages, 5 figures, published versio
Characterization of initial fluctuations for the hydrodynamical description of heavy ion collisions
Event-by-event fluctuations in the initial conditions for a hydrodynamical
description of heavy-ion collisions are characterized. We propose a
Bessel-Fourier decomposition with respect to the azimuthal angle, the radius in
the transverse plane and rapidity. This allows for a complete characterization
of fluctuations in all hydrodynamical fields including energy density,
pressure, fluid velocity, shear stress and bulk viscous pressure. It has the
advantage that fluctuations can be ordered with respect to their wave length
and that they can be propagated mode-by-mode within the hydrodynamical
formalism. Event ensembles can then be characterized in terms of a functional
probability distribution. For the event ensemble of a Monte Carlo Glauber
model, we provide evidence that the latter is close to Gaussian form, thus
allowing for a particularly simple characterization of the event distribution.Comment: 40 pages, 16 figure
Mode-by-mode fluid dynamics for relativistic heavy ion collisions
We propose to study the fluid dynamic propagation of fluctuations in
relativistic heavy ion collisions differentially with respect to their
azimuthal, radial and longitudinal wavelength. To this end, we introduce a
background-fluctuation splitting and a Bessel-Fourier decomposition of the
fluctuating modes. We demonstrate how the fluid dynamic evolution of realistic
events can be build up from the propagation of individual modes. We describe
the main elements of this mode-by-mode fluid dynamics, and we discuss its use
in the fluid dynamic analysis of heavy ion collisions. As a first illustration,
we quantify to what extent only fluctuations of sufficiently large radial wave
length contribute to harmonic flow coefficients. We find that fluctuations of
short wave length are suppressed not only due to larger dissipative effects,
but also due to a geometrical averaging over the freeze-out hyper surface. In
this way, our study further substantiates the picture that harmonic flow
coefficients give access to a coarse-grained version of the initial conditions
for heavy ion collisions, only.Comment: 6 pages, 5 figures, published versio
Präbiotische Synthese der Pyrimidinnukleoside sowie Entwicklung eines neuen Mechanismus zur Stickstofffixierung aus redox-neutraler Atmosphäre
Backreaction effects on the matter side of Einstein's field equations
Recently, we have derived a novel and compact expression for how
perturbations in the matter fields of the cosmological fluid can lead to
deviations from the standard Friedmann equations. Remarkably, the dissipative
damping of velocity perturbations by bulk and shear viscosity in the dark
sector can modify the expansion history of the universe on arbitrarily large
scales. In universes in which this effect is sufficiently sizeable, it could
account for the acceleration of the cosmological expansion. But even if dark
matter should be less viscous and if the effect would be correspondingly
smaller, it may have observable consequences in the era of precision cosmology.
Here, we review the origin of this backreaction effect and possibilities to
constrain it further.Comment: 4 pages, to be published in the Moriond Proceedings 201
Nonlinear evolution of density and flow perturbations on a Bjorken background
Density perturbations and their dynamic evolution from early to late times
can be used for an improved understanding of interesting physical phenomena
both in cosmology and in the context of heavy-ion collisions. We discuss the
spectrum and bispectrum of these perturbations around a longitudinally
expanding fireball after a heavy-ion collision. The time-evolution equations
couple the spectrum and bispectrum to each other, as well as to higher-order
correlation functions through nonlinear terms. A non-trivial bispectrum is thus
always generated, even if absent initially. For initial conditions
corresponding to a model of independent sources, we discuss the linear and
nonlinear evolution is detail. We show that, if the initial conditions are
sufficiently smooth for fluid dynamics to be applicable, the nonlinear effects
are relatively small.Comment: 32 pages, 17 figures, published versio
Large scale structure from viscous dark matter
Cosmological perturbations of sufficiently long wavelength admit a fluid
dynamic description. We consider modes with wavevectors below a scale for
which the dynamics is only mildly non-linear. The leading effect of modes above
that scale can be accounted for by effective non-equilibrium viscosity and
pressure terms. For mildly non-linear scales, these mainly arise from momentum
transport within the ideal and cold but inhomogeneous fluid, while momentum
transport due to more microscopic degrees of freedom is suppressed. As a
consequence, concrete expressions with no free parameters, except the matching
scale , can be derived from matching evolution equations to standard
cosmological perturbation theory. Two-loop calculations of the matter power
spectrum in the viscous theory lead to excellent agreement with -body
simulations up to scales Mpc. The convergence properties in the
ultraviolet are better than for standard perturbation theory and the results
are robust with respect to variations of the matching scale.Comment: 30 pages, 7 figure
How (non-) linear is the hydrodynamics of heavy ion collisions?
We provide evidence from full numerical solutions that the hydrodynamical
evolution of initial density fluctuations in heavy ion collisions can be
understood order-by-order in a perturbative series in deviations from a smooth
and azimuthally symmetric background solution. To leading linear order, modes
with different azimuthal wave numbers do not mix. Quadratic and higher order
corrections are small and can be understood as overtones with corresponding
wave numbers.Comment: 8 pages, 4 figure
A perturbative approach to the hydrodynamics of heavy ion collisions
Initial fluctuations in hydrodynamic fields such as energy density or flow
velocity give access to understanding initial state and equilibration physics
as well as thermodynamic and transport properties. We provide evidence that the
fluid dynamic propagation of fluctuations of realistic size can be based on a
background-fluctuation splitting and a systematic perturbative expansion in the
fluctuating fields. Initial conditions are characterized by a Bessel-Fourier
expansion for single events, event-by-event correlations and probability
distributions. The evolution equations can be solved order-by-order in the
expansion which allows to study the fluid dynamical propagation of single
modes, the study of interaction effects between modes, the determination of the
associated particle spectra and the generalization of the whole program to
event-by-event correlations and distributions.Comment: poceedings of the XXIV Quark Matter conference (2014
Backreaction from inhomogeneous matter fields during large-scale structure formation
We study how inhomogeneities of the cosmological fluid fields backreact on
the homogeneous part of energy density and how they modify the Friedmann
equations. In general, backreaction requires to go beyond the pressureless
ideal fluid approximation, and this can lead to a reduced growth of
cosmological large scale structure. Since observational evidence favours
evolution close to the standard growing mode in the linear regime, we focus on
two-component fluids in which the non-ideal fluid is gravitationally coupled to
cold dark matter and in which a standard growing mode persists. This is
realized, e.g. for a baryonic fluid coupled to cold dark matter. We calculate
the backreaction for this case and for a wide range of other two-fluid models.
Here the effect is either suppressed because the non-ideal matter properties
are numerically too small, or because they lead to a too stringent UV cut-off
of the integral over the power spectrum that determines backreaction. We
discuss then matter field backreaction from a broader perspective and
generalize the formalism such that also far-from-equilibrium scenarios relevant
to late cosmological times and non-linear scales can be addressed in the
future.Comment: 11 pages, 3 figure
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