Learn how to make a Christmas garland that will take your Christmas fireplace mantle decor to another level with this step-by-step tutorial.
As promised in last week's blue and white Christmas home tour, here is the tutorial for making my Christmas garland.
Ever since I wrote last year's post on decorating a fireplace mantel that has a TV above it, I have been planning to go all out on creating a garland for my mantel this year.
So this tutorial has been a whole year in the making!!
You might be wondering what was so life-changing about that post? While I was looking for garland inspiration, I found Regina Gust's website with her absolutely gorgeous holiday decor. I decided right then and there that I wanted a garland like one of those to go over my fireplace.
Unfortunately, last year it was a little too close to Christmas when I discovered her amazing website, so I promised myself that I would make one this year…and I did!
Keep reading to find out how to make a Christmas garland to go over your fireplace mantel.
– 2 types of ribbon that are at least 2 1/2″ wide. If you can get wired ribbon, it is a little easier to position (but not absolutely necessary). I matched the color of the ribbons to one of my ornaments.
Note: This is the list of what I used for my garland, but you can use whatever works with your decor (and whatever you have on hand).
– 50 round ornaments – I used about 25 4″ ornaments and 25 2 1/2″ ornaments in a mixture of blue, white and gold colors. Most of them came from this ornament set*.
One of the things I really like about Regina's garlands is that they go all the way to the ground. So I was looking for either a long garland or shorter ones that I could join together.
I originally bought these sparkly garlands from Michael's (everyone knows I like a little sparkle!) And I do like them, but I realized that the garland needs to have "pose-able" branches in order to move them where you need them. So these ones were out.
After searching through a bunch of different stores, I found exactly what I was looking for – an 18-foot garland with lights*. Even better, it was the least expensive option I found!
This isn't the fullest garland you can find. It's actually pretty scrawny! But for this project, I wasn't too worried about that. All of the extra decorations will fill it out!
If your garland didn't come with lights, you'll want to add them add this point.
Just thread them in and around the garland branches just like you would with a Christmas tree.
I know it seems a little backward to hang the garland before you put anything on it, but I think it's easier this way.
For this, you will need at least 2 (and possibly 3) command hooks*. They will hold the garland on your mantel and can be removed later without causing any damage to the finish.
I went for the ones that can hold 5 pounds…this garland will be heavy by the time we're finished!
Position the first hook close to one end of the mantel, about 1″ from the wall. Stick it onto the mantel with the hook end closer to the front of the mantel.
Repeat the process on the other end of the mantel.
The third hook will be used to hold the garland up in the middle if you want to do that. If you're not sure what you want to do, you can wait to attach this one. I didn't decide that I wanted it up in the middle until after I had put most of the ornaments on the garland.
Then hook the garland around the command hook on each side of the mantel.
Make sure that the garland is evenly hung on both sides. You may need to fiddle with it a bit to make sure that the ends are even and that it drapes like you want it in the front. It will get pulled down some by the weight of the ornaments so you don't want too much of a swag at the front.
Important Note: Make sure that the light plug is at the end closest to the electric socket. I plugged my garland in at this point to make sure I had it right.
Now that the garland is hung, it's time to start the fun part! The decorating!
The first thing to put on the garland is the tulle.
To attach the tulle, simply wrap one of the garland branches around the tulle.
Then move up the garland a foot or two and wrap another one of the garland branches around the tulle. Keep the tulle pretty loose between each tie point.
Keep going until you have reached the other end of the garland.
Take the 2 ribbons and wrap a branch around them to tie them on to the garland. I attached them in the same location as the tulle.
Keep going up and around the garland with the ribbon, the same way that you did with the tulle.
Try to alternate sides with the ribbon…so that the blue ribbon starts on the right side of the garland at the bottom, then is on the left side of the garland for the next section, then goes back to the right side on so on.
The gold ribbon does the same criss-cross pattern in the opposite direction.
Keep going until you reach the other end of the garland.
Add the clip on poinsettias.
At a minimum, I would put them in the corners of the mantel and the center of the swag.
But I also did 3 of them down each side of the garland.
Try to have some facing up and some down to give it a random feel.
Cut the multi-branch pearl picks into smaller pieces. Wire cutters are the easiest way to do this.
Stick the picks in behind the poinsettia clips.
I also added some poinsettia flower picks in between the larger flowers.
Now you get to add all of the 4″ round ornaments, long ornaments and the ginger jars.
These are all hung using thread or ribbon so that they hang down from the garland.
I also decided at this point to bring the middle of the garland up to the mantel instead of having it hang down.
To do this, I attached the third command hook in the center of the middle close to the front edge. The the garland hooks around it just like it did on the sides.
Use standard ornament hooks to add some of the smaller ornaments to the garland.
Then add some of the ornaments close into the garland by attaching them with alligator clips.
Try to make sure that the clip is hidden behind the ornament when you attach it.
Combining some of the balls in groups of 2 or 3 on the garland adds color to the garland.
Add the leaf picks into the garland to fill in any empty spots.
I added some ginger jars in the corners of the mantel to add some height beside the TV and tie the whole look together.
With all of the ornaments on the garland, the lights mostly show up behind it…which almost makes it look like it's floating.
I really like the way the ornaments hang down in front of the fireplace. Which also pulls your eye down and distracts a little from the TV.
After decorating the tree in the same blue and white colors, it definitely is the focal point of my living room.
I even have a great spot in front of the fireplace for my blue and white garden seat.
It definitely doesn't look like the same scrawny garland that I started with!
So there you have it. My steps for making a Christmas garland to go over your fireplace mantel.
Hopefully, you have found some inspiration to create a version that will take your Christmas decor over the top!
If you are looking for some other ideas, try out these easy and inexpensive ways to decorate for Christmas.
Have comments or questions on how to make a Christmas garland? Tell us in the section below.
You've outdone yourself with this grande mantel décor. Way to go and Happy holidays .
Thanks, Victoria! It's my favorite part of my Christmas decor this year 🙂 Happy holidays!


text:
Q: NodeJS and Dygraphs I try to draw a (Dy)graph ... currently running NodeJs - a little bit of HTML.
My question is: My data is stored in a postgreSQL DB...How do i load the data from my datasource and into my NODEJS FILE? All example by DyGraphs...is inline or loading from a text file...i have million of data point - so the solution should have performance like no. 1 criteria...
If you would approach this in a very different way - another way to construct and build this code - please tell me! My only demand is it runs NodeJS...
HTML FILE

NODEJS FILE:
function draw_chart() {

    new Dygraph(
        document.getElementById("demodiv"),
        "chart.csv"
        );
}

A: Solution: I never use the database. DyGraphs already suppport .cvs files out-of-the box. So instead i make my calculations server side, and at the client i make a request for the .csv file directly from within the dygraph object...local path or URL - DyGraphs is happy with both :-)

redpajama_set_name: RedPajamaStackExchange


Here is a photograph from 1954, the second time in the modern era when the Plays were performed. It was taken by professional photographer Will Acton, who had a shop in King's Square, York. A set of black and white photographs by him of the Plays that year has been donated to the NCEM by his grandson Paul Acton. The photographs do not have titles, this seems to be Pilate with his wife Percula, here with their household beadle. If so, the actors are: Pilate - Alec de Little; Percula - Moira Reed; Beadle - Philip Clarke.
Below right for comparison are Pilate, Procula and the Beadle as performed on a wagon in 2010. This photograph was taken outside St William's College by the Director of the York Settlement Community Players, Graham Sanderson, who donated it to the NCEM archive. The actors are: Pilate - Maurice Crichton; Percula - Vicki Hill; Beadle - Matt Pattison.
Below left is a scene from 1980, when live sheep were among the actors. This was scanned from one of the postcards in Anne Blincoe's extensive collection. Cain (Alan Inglis) is threatening his brother Abel (John Ramsden).
We would love more rehearsal photographs. Some donated by Gweno Williams of 1984 include this amusing one from Museum Gardens.
angels (one soon to be a devil) having fun in the Minster Millennium production. It was donated by Jude Brereton, Administrator that year.
Linda Terry loaned for scanning an album from that year: here she is backstage, left.
Below right is Herod from a 'Yorkshire Mysteries' production in 1987, a picture donated by Simon Tompsett.
In 2012 a team of local people took photographs, which were given to the NCEM by York Theatre Royal.
In March 2013 the NCEM was given a copy of a video (VHS format) of the 1988 production in Museum Gardens.
We are delighted to have 2016 pictures such as this below from Anthony Chappell-Ross. and of rehearsals and performances in 2018 by John Saunders and Michael Oakes.
And we recently received this photo of Alan Dobie as Christ in 1963.
Here is a scary 2018 image.
Back to Archive page with search mechanism.


This is both my first crafster contest and the first time I'm posting my own project. Here it is, my mini mushroom pincushion with inch worm! The mushroom head is made out of a bit of scrap fleece, and the spots are just some white scrap fabric that I sewed on. I like how the white ravelled a little bit when I sewed. The head is stuffed with just a tiny bit of polyester filling. The stem is a cork that I carved down. The little inch worm is made of home made play dough that I baked at a low temperature in the oven to dry it out before I painted it.
Here's a head on view.
And one showing the size. It's actually a bit smaller than it looks because of the angle of the camera.
And finally, it actually having pins in it.
What a neat way to use a cork. I'll be more tempted next time to keep the cork and craft with it.
I love the worm you made too. Nice touch.
I agree - I think the frayed white fabric adds a great touch!! This is super duper cute and a very clever way to use a cork. The teeny tiny inch worm is also adorable.
Ahh so cute and very creative! The little worm is adorable!
Your little wormie is so cute!!! Nice job on the mushroom too.
Thanks! I really wanted to do a gnome with it, but it seems gnomes are done (better) by a lot of other people. I had a lot of fun doing it. You can't even tell that one night while I was working on it I dropped the whole mushroom in my tea. Good thing cork floats.


We're on a quest to try all 50 of the world's best bars. Every year, the William Reed Business Media ranks the top 50 bars in the world (note they're from the UK, so the list tends to skew UK/Singapore). It's a great excuse to travel.
We will be updating the list with links to our reviews!


text:
\section{Introduction}

The nature of dark energy, {\em i.e.}~ the source of the current accelerated expansion of the Universe, is one of the deepest mysteries in contemporary cosmology. Although the simplest explanation is the presence of an (unnaturally) tiny cosmological constant, it is important to explore other scenarios both from the point of view of fundamental theory as well as from a phenomenological perspective.

The simplest model of dynamical dark energy is provided by a canonical single scalar field, minimally coupled to gravity, or {\em quintessence} \citep{FerreiraJoyce1997, WangSteinhardt1998, ZlatevWangSteinhardt1999}. In general, however, Lagrangians with non-canonical kinetic terms lead as well to viable models \citep{ArmendarizPiconMukhanovSteinhardt2000}. In the absence of a compelling theory, \citet{CreminelliEtal2009} recently developed an effective theory for the perturbations in generic quintessence models\footnote{Usually this name is reserved for theories of canonical scalar fields with a potential, but we will call quintessence a generic scalar field minimally coupled to gravity.}. On cosmological scales, the relevant parameter space is two-dimensional, consisting of the equation of state parameter $w = p/\rho$ and of the speed of sound of perturbations, $c_s^2 = \delta p/\delta \rho$ where $p$ and $\rho$ are, respectively, the pressure and the density in the velocity orthogonal gauge. Canonical scalar fields have perturbations with $c_s = 1$, so they will not cluster appreciably on sub-horizon scales and their only observationally relevant effect is the modification of the expansion history and of the linear growth factor of dark matter perturbations.

On the other hand, the opposite case of a very small, {\em i.e.}~ negligible, speed of sound is also very interesting. From a theoretical point of view, it is ``technically natural'', since it can be thought of as a deformation of the Ghost Condensate theory \citep{ArkaniHamedEtal2004A}, in which limit one recovers an exact shift symmetry. Moreover, if the background has $w < -1$, the only way of having a stable theory, free of ghosts and gradient instabilities, is to require a tiny speed of sound $|c_s| \lesssim 10^{-15}$ \citep{CreminelliEtal2009}. In this work we will focus on models characterized by a vanishing speed of sound: from an observational point of view, models of clustering quintessence have an important effect on structure formation, since perturbations now actively participate in the gravitational collapse and virialization of structures at low redshift, along with dark matter \citep{CreminelliEtal2010,LimSawickiVikman2010}.

Most of recent investigations on the observational effects of a clustering quintessence focused so far on the linear regime \citep{DeDeoCaldwellSteinhardt2003, WellerLewis2003, HuScranton2004, BeanDore2004, Hannestad2005, CorasanitiGiannantonioMelchiorri2005, Takada2006, Torres-RodriguezCress2007, SaponeKunz2009, SaponeKunzAmendola2010}. At the linear level, however, it is difficult to distinguish peculiar effects due to dark energy perturbations from the effects due to the background energy density and expansion history. In fact, it is reasonable to expect that the assumption of an {\em inhomogeneous} dark energy component might have specific consequences on the nonlinear evolution of structures, both at small scales, in terms of the gravitational collapse of virialized objects, as well as at larger scales, in terms of corrections to the linear solutions of large-scale structure correlation functions in the mildly nonlinear regime.

Analytical investigations on the effects of dark energy on the nonlinear evolution of structures are, at this stage, particularly relevant. In the first place, the implementation of numerical simulations for some quintessence models is particularly challenging and necessarily involves approximations. The comparison with theoretical predictions can therefore provide an essential test. In addition, for some specific models, as for instance the one considered here, numerical results are not yet available. In the second place, future large-scale structure observations will provide large data-sets with significant information in the mildly nonlinear regime: restricting our analysis to ``linear scales'' will severely limit their scientific exploitation, particularly in the case of weak lensing observations.

For a clustering quintessence, a first step in the prediction of nonlinear effects has been taken in \citet{CreminelliEtal2010}, focusing on the extension of spherical collapse model. In the limit of zero speed of sound, pressure gradients are negligible and dark energy perturbations are comoving with the dark matter, so that the spherical halo behaves like a closed FRW universe, allowing for an exact solution. They found small modifications to the critical threshold of collapse and to the {\em dark matter} mass function. However, larger effects are expected on the {\em total} mass function, that is including the quintessence perturbation component to the virialized halos. Indeed, the relative quintessence contribution to the total halo mass is proportional to the ratio between quintessence and dark matter energy densities, {\em i.e.}~$\sim (1 + w)\,\Omega_Q/ \Omega_m$ and it is therefore particularly relevant at low redshift.

Following instead a perturbative approach to the study of density correlators in the mildly nonlinear regime, \citet{SefusattiVernizzi2011} recognized that the relevant quantity for gravitational evolution is the \emph{total} density contrast, defined as a weighted sum of dark matter and dark energy overdensities. Indeed, any measurable cosmological quantity is related gravitationally to the total density fluctuations with no possibility to distinguish in large-scale structure observations between the two components. This work shows that it is possible to write down a closed set of fluid equations for the total density and for the common velocity which take the form of the standard Eulerian equations for the dark matter, with a simple correction to the linear term in the velocity divergence of the continuity equation given by the time-dependent factor $C = 1 + (1+w) \Omega_Q/\Omega_m$. The equations of motions are solved at second order in standard Eulerian Perturbation Theory \citep[EPT, see][for a review]{BernardeauEtal2002}. The second order solution allows to derive the tree-level expression for the density bispectrum, but third order solutions are required to compute the next-to-leading order (one-loop) correction to the power spectrum.

Other, more accurate, methods, along with standard EPT, have been proposed in recent years to predict the nonlinear matter power spectrum as well as higher-order correlation functions. As a theoretical motivation, on small scales the EPT perturbative expansion for density correlators is not well defined, because it presents large cancellations between contributions of the same order. However, it has been shown that classes of higher-order corrections can be resummed, leading to a well-established perturbative scheme known, in its first formulation, as Renormalized Perturbation Theory \citep[RPT, ][]{CrocceScoccimarro2006B, CrocceScoccimarro2006A, CrocceScoccimarro2008, BernardeauCrocceScoccimarro2008, BernardeauCrocceSefusatti2010}. Complementary methods are given by the Renormalization Group approach \citep[RG, ][]{MatarresePietroni2007, MatarresePietroni2008}, the path-integral formalism of \citet{Valageas2007}, closure theory \citep{TaruyaHiramatsu2008}, Lagrangian resummation \citep{Matsubara2008A, Matsubara2008B, Matsubara2008Berr, Matsubara2011}, and the Time-RG approach \citep[Time-RG, ][]{Pietroni2008, LesgouguesEtal2009, BartoloEtal2010}.

In this paper, we will apply the Time-RG method to the equations of motion for the total density perturbations derived in \citet{SefusattiVernizzi2011}. Since this approach is based on differential equations {\em in time} for the matter power spectrum and bispectrum directly derived from the equations of motion of the matter and velocity field, it is particularly straightforward to adapt it to the evolution of the total density fluctuations in a model where the quintessence field has a vanishing speed of sound. In this case, in fact, the only modification to the equations of motion amounts to an extra time-dependent factor in the continuity equation.

We will compare the nonlinear corrections to the total density power spectrum for clustering quintessence with the matter density power spectrum for $\Lambda$CDM and smooth quintessence models. We will focus in particular on the relative nonlinear corrections, that is the ratio between nonlinear and linear power spectrum, showing that the effect of a vanishing speed of sound is relatively small. However, and precisely for this reason, since at low redshift the effect on the {\em linear growth factor} of quintessence perturbations is instead particularly relevant, we will point out that the typical relation between the amplitude of linear fluctuation and the corresponding nonlinear correction, exploited by fitting formulas like \texttt{halofit} \citep{SmithEtal2003}, is not respected in the clustering quintessence model. For instance, for models with $w>-1$, the nonlinear corrections at redshift zero will be significantly smaller than those na\" ively expected from the corresponding linear power spectrum. This fact can have interesting consequences for detectability of quintessence perturbations, particularly in weak lensing observations, that will be explored in future works.

The paper is organized as follows. In Section 2 we write down the equations of motion and discuss their linear solution. In Section 3 we describe the time-RG approach and the non-linear evolution of the power spectrum. Our results are presented in Section 4, while Section 5 is devoted to our conclusions and future prospects. In an appendix we briefly discuss the accuracy and validity of the Time-RG method.

\section{Equations of motion and linear solutions}
\label{sec:eom}

We will consider the case of a two-fluid system coupled gravitationally, following the description given by \citet{SefusattiVernizzi2011} and adopting their notation. The quintessence component is described by a constant equation of state, $w=\bar{p}_Q/\bar{\rho}_Q$ and vanishing speed of sound, $c_{s}=0$. Under these assumptions, the matter and quintessence perturbations are comoving and therefore share the same velocity field. The relevant degrees of freedom are the matter and quintessence density contrasts, respectively $\delta_m$ and $\delta_Q$, and their common velocity $\vec v$. The equations of motion are given by two continuity equations corresponding to the two components,
\begin{align}
&\frac{\partial \delta_m}{\partial \tau}  + \vec \nabla \cdot \big[ (1+\delta_m) \vec v \big] = 0 \label{continuity_m}\,,\\
&\frac{\partial \delta_Q}{\partial \tau}  -3 w {\cal H} \delta_Q+ \vec \nabla \cdot \big[ (1+w+\delta_Q) \vec v\big] = 0 \label{continuity_Q}\,,
\end{align}
and one Euler equation,
\begin{equation}
\frac{\partial {\vec{ v}}}{\partial \tau}  + {\cal H} \vec v+ (\vec v \cdot \vec \nabla) \vec v =-\vec \nabla \Phi\;, \label{euler_common}
\end{equation}
where $\tau$ is the conformal time and ${\cal H}=d\ln a/d \tau$. In addition, we consider the Poisson equation relating the energy density to the gravitational potential $\Phi$,
\begin{equation}
\nabla^2 \Phi = \frac{3}{2}\, {\cal H}^2\, \Omega_m \left( \delta_m +  \delta_Q \frac{\Omega_Q}{\Omega_m} \right)\,,
\end{equation}
where the relative mean densities of both matter and quintessence are given by $\Omega_\alpha=\Omega_\alpha(\tau)\equiv\bar{\rho}_\alpha/(\bar{\rho}_m+\bar{\rho}_Q)$ with $\alpha=m$, $Q$.
As customary, we define the velocity divergence $\theta\equiv\vec \nabla \cdot \vec v$, fully describing the peculiar velocity $\vec v$ up to shell crossing \citep{BernardeauEtal2002}. In Fourier space, assuming the notations $q_i \equiv | \vec q_i|$ and $\vec q_{ij}\equiv\vec q_i+\vec q_j$, the continuity equations become
\begin{align}
&\frac{\partial \delta_{m,\vec k}}{\partial \tau}  + \theta_{\vec k} = -\!\!\int\!\! d^3 q_1 d^3 q_2\, \delta_D (\vec k - \vec q_{12})\,\alpha(\vec q_1, \vec q_2)\, \theta_{\vec q_1} \delta_{m,\vec q_2} \label{continuity_m_FS}\,,\\
&\frac{\partial \delta_{Q,\vec k}}{\partial \tau}  -3 w {\cal H} \delta_{Q,\vec k}+ (1+w) \theta_{\vec k} = -\!\!\int\!\! d^3 q_1 d^3 q_2\, \delta_D (\vec k - \vec q_{12})\,\alpha(\vec q_1, \vec q_2)\, \theta_{\vec q_1} \delta_{Q,\vec q_2} \label{continuity_Q_FS}\,,
\end{align}
with
\begin{equation}
\alpha(\vec q_1, \vec q_2)  \equiv  1 + \frac{\vec q_1 \cdot \vec q_2}{q_1^2}  \;.  \label{alpha_def}
\end{equation}
The Poisson equation can be used to replace the gravitational potential in the Euler equation to obtain for the latter, in Fourier space
\begin{equation}
\frac{\partial \theta_{\vec k}}{\partial \tau} + {\cal H}\, \theta_{\vec k} + \frac32\, \Omega_m {\cal H}^2 \left( \delta_{m,\vec k} + \delta_{Q,\vec k}\, \frac{\Omega_Q}{\Omega_m} \right) = -\!\!\int\!\! d^3 q_1 d^3 q_2\, \delta_D (\vec k - \vec q_{12})\,\beta(\vec q_1, \vec q_2)\, \theta_{\vec q_1} \,\theta_{\vec q_2}\;, \label{euler_sum}
\end{equation}
with
\begin{equation}
\beta(\vec q_1, \vec q_2)\equiv \frac{q_{12}^2 \,\vec q_1 \cdot \vec q_2 }{2\, q_1^2\, q_2^2}\;.\label{beta_def}
\end{equation}
As pointed out by \citet{SefusattiVernizzi2011}, it is convenient to combine matter and quintessence perturbations into a {\em total density contrast} defined as
\begin{equation} \label{tdc}
\delta \equiv \frac{\delta \rho}{\bar \rho_m} = \delta_m +  \delta_Q \frac{\Omega_Q}{\Omega_m}\;,
\end{equation}
which is bounded from below as $\delta>-1-\Omega_Q/\Omega_m$, instead of the usual $\delta>-1$.
In fact, any clustering observable is affected only by the gravitational effects of the total energy density, while the individual matter and quintessence components are {\em not}---even indirectly---accessible by observations. The gravitational potential, responsible for both weak lensing effects and galaxy clustering is given, in terms of the total density perturbations $\delta$, by
\begin{equation}
\nabla^2 \Phi = 4 \pi\, G\, a^2 \bar \rho_m\, \delta \;. \label{poisson_2}
\end{equation}
For this reason, we will focus in this work on the nonlinear evolution of the total density perturbations defined by eq.~(\ref{tdc}). Clearly, other definitions of such quantity, differing by an overall time-dependent factor, are possible. This definition has the advantage of recovering standard expressions when quintessence perturbations are not present. Introducing the quantity
\begin{equation}\label{eq:C}
C(\tau) \equiv  1+ (1+w)\frac{\Omega_Q(\tau)}{\Omega_m(\tau)}\;,
\end{equation}
we can rewrite the equations of motion for the total density contrast $\delta$ and the velocity divergence $\theta$ as
\begin{align}
&\frac{\partial \delta_{\vec k}}{\partial \tau}  + C  \theta_{\vec k} = -\!\!\int\!\! d^3 q_1 d^3 q_2\, \delta_D (\vec k - \vec q_{12})\,\alpha(\vec q_1, \vec q_2) \theta_{\vec q_1} \delta_{\vec q_2} \label{continuity_tot}\,,\\
&\frac{\partial \theta_{\vec k}}{\partial \tau} + {\cal H} \theta_{\vec k} + \frac{3}{2} \Omega_m {\cal H}^2 \delta_{\vec k} = - \!\!\int\!\! d^3 q_1 d^3 q_2\, \delta_D (\vec k - \vec q_{12})\,\beta(\vec q_1, \vec q_2) \theta_{\vec q_1} \theta_{\vec q_2}\;. \label{euler_tot}
\end{align}
Notice that setting $C=1$ reduces the system to the usual smooth quintessence scenario with $\delta=\delta_m$. On the other hand, the effect of quintessence perturbations is expected to be relevant at late times and for significant departures from $w=-1$, with a sign depending on the sign of $1+w$ \citep{WellerLewis2003, CreminelliEtal2009}.

\begin{figure}[t]
\begin{center}
{\includegraphics[width=0.49\textwidth]{fig_C}}
{\includegraphics[width=0.49\textwidth]{fig_D1_vs_D1LCDM}}
\caption{{\em Left panel}: The function $C(z)$, eq.~(\ref{eq:C}), as a function of redshift for $w=-1.2$ ({\em blue, dot-dashed curves}), $w=-1.1$ ({\em blue, long-dashed curves}), $w=-1$ ($\Lambda$CDM, {\em black, continuous curves}), $w=-0.9$ ({\em red, short-dashed curves}) and $w=-0.8$ ({\em red, dotted curves}). The vertical line indicates the redshift of equality between matter and quintessence for a $\Lambda$CDM cosmology, {\em i.e.}~~$z_{eq}=0.37$ for the assumed $\Omega_{m,0}=0.279$. {\em Right panel}: ratio of linear growth factor $D$ to the same quantity in the $\Lambda$CDM model as a function of redshift, assuming $w=-1.1$ ({\em blue, long-dashed curves}) and $w=-0.9$ ({\em red, short-dashed curves}), with thick and thin curves corresponding respectively to the clustering and smooth cases. The two panels reproduce Fig.~1 and the bottom left panel of Fig.~2 of \citet{SefusattiVernizzi2011}.}
\label{fig:CD}
\end{center}
\end{figure}
Since the function $C(z)$ is uniquely responsible for the correction to the equations of motion induced by the clustering of quintessence, and therefore particularly relevant to our problem, we plot it as a function of redshift for a few values of the equation of state $w$ in the left panel of Fig.~\ref{fig:CD}, reproducing Fig.~1 in \citet{SefusattiVernizzi2011}. In particular we consider the following values and corresponding graphic notations, assumed throughout the paper, for the quintessence equation of state: $w=-1.2$ ({\em blue, dot-dashed curves}), $w=-1.1$ ({\em blue, long-dashed curves}), $w=-1$ ($\Lambda$CDM, {\em black, continuous curves}), $w=-0.9$ ({\em red, short-dashed curves}) and $w=-0.8$ ({\em red, dotted curves}). In addition, when needed, thin lines indicate smooth quintessence results as opposed to thick lines corresponding to the clustering case. Here and in the rest of the paper we assume a flat Universe with $\Omega_{m,0}=0.279$, ``0'' denoting quantities at $z=0$. In the $\Lambda$CDM scenario, this implies a redshift of equality between matter and cosmological constant components equal to $z_{eq}\simeq 0.37$, shown by the vertical line in Fig.~\ref{fig:CD}. For all results involving the initial power spectrum in the next sections we further assume $\Omega_b=0.046$, $h=0.7$, $n_s=0.96$ and $\sigma_8=0.8$ for the $\Lambda$CDM case. We fixed the normalization of the primordial power spectrum to be the same for all models, so that the actual value of $\sigma_8$ for models different from $\Lambda$CDM in fact depends on the value of the linear growth factor at redshift zero.

The linear solutions to the equations of motion of matter and quintessence perturbations and their observational consequences have been studied in several works \citep{DeDeoCaldwellSteinhardt2003, WellerLewis2003, BeanDore2004, HuScranton2004, CorasanitiGiannantonioMelchiorri2005, Hannestad2005, Takada2006, Torres-RodriguezCress2007, SaponeKunz2009, SaponeKunzAmendola2010}. In particular, \citet{SefusattiVernizzi2011} find, for the total overdensity $\delta$, an integral solution to the linear growth factor $D(z)$ completely analogous to the one obtained in $\Lambda$CDM cosmologies (but absent in smooth quintessence scenarios), given by
\begin{equation}
D(a) = \frac52\, H_0^2\, \Omega_{m,0}\, H(a)\! \int_0^a\!\! \frac{C(\tilde a)}{[\tilde a\, H(\tilde a)]^3} d \,\tilde a\;. \label{int_sol}
\end{equation}
The corresponding linear growth factor for matter perturbations alone is given by
\begin{equation}
D_m(a)=\int_0^a\left[\frac52 -\frac32\frac{D(\tilde{a})}{\tilde{a}}\right]\Omega_m(\tilde{a})\,d\, \tilde{a}\;,
\end{equation}
but we will not consider the evolution of matter perturbations alone when quintessence perturbations are present, focusing instead on the total density fluctuations throughout the paper.

In order to make this work as much self-contained as possible and to help in the interpretations of our results in section~\ref{sec:results}, we show, in the right panel of Fig.~\ref{fig:CD}, the ratio of linear growth factor $D$ to the same quantity in the $\Lambda$CDM model as a function of redshift, assuming $w=-1.1$ ({\em blue, long-dashed curves}) and $w=-0.9$ ({\em red, short-dashed curves}), with thick and thin curves corresponding respectively to the clustering and smooth cases. It is crucial to remark that while the high-redshift behavior is similar and asymptotically equal in the $c_s=0$ as in the $c_s=1$ scenarios, the growth of quintessence perturbations strongly affects the low-$z$ behavior leading to a turn-around and larger or smaller values for the growth factor w.r.t. $\Lambda$CDM, corresponding, respectively to $w=-0.9$ or $w=-1.1$. For a detailed discussion of the phenomenology of the linear growth of total density fluctuations see \citet{SefusattiVernizzi2011}.

\section{Non-linear evolution and the Time-RG approach}
\label{sec:nonlinear}

In this section we study the nonlinear evolution of the total density perturbations in terms of the nonlinear corrections to the total density power spectrum. In this respect, as we will see, the Time-Renormalization Group approach of \citet{Pietroni2008} is particularly apt at extending the linear theory predictions, due to the specific form of the correction induced by clustering quintessence on the equations of motion.

We use, as time variable, $\eta\equiv \ln D$ with $D$ corresponding to the growing mode, and rescale the velocity divergence $\theta$ in the following way:
\begin{equation}
\Uptheta \equiv  - \frac{C }{{\cal H} f} \theta \;, \label{Theta_def}
\end{equation}
where $f\equiv d\ln D/ d\ln a$ is the linear growth rate. The linear solutions for the density and velocity are then given by
\begin{equation}
\Uptheta^{\rm lin}_{\vec k} (\eta) =  \delta_{\vec k}^{\rm lin} (\eta)= D (\eta) \delta^{\rm in}_{\vec k} \;,  \label{theta_lin}
\end{equation}
$\delta^{\rm in}_{\vec k}$ corresponding to the initial conditions.
In the new variables, the equations of motion become
\begin{align}
&\frac{\partial \delta_{\vec k}}{\partial \eta} -   \Uptheta_{\vec k} = \!\!\int\!\! d^3 q_1 d^3 q_2\, \delta_D (\vec k - \vec q_{12})\,\frac{\alpha(\vec q_1, \vec q_2)}C \Uptheta_{\vec q_1} \delta_{\vec q_2} \label{continuity_tot_eta}\,,\\
&\frac{\partial \Uptheta_{\vec k}}{\partial \eta} - \Uptheta_{\vec k} +\frac32 \frac{\Omega_m\,C}{f^2} (\Uptheta_{\vec k} - \delta_{\vec k}) = \!\!\int\!\! d^3 q_1 d^3 q_2\, \delta_D (\vec k - \vec q_{12})\, \frac{\beta(\vec q_1, \vec q_2)}C \Uptheta_{\vec q_1} \Uptheta_{\vec q_2}\;. \label{euler_tot_eta}
\end{align}
Again, the only difference with the standard equations of motions for matter perturbations in the $\Lambda$CDM or smooth quintessence scenarios is given by the presence of the function $C(z)$, different from unity at small redshift.

\citet{SefusattiVernizzi2011} studied the nonlinear solutions to these equations of motion in the standard Eulerian Perturbation Theory (EPT) framework, finding the second-order solution for the density and velocity fields.
Such corrections are sufficient to compute the tree-level expression for the total density bispectrum, but the first nonlinear (one-loop) correction to the power spectrum requires the knowledge of the third order solution for $\delta_{\vec k}$ and $\Uptheta_{\vec k}$.

In this work we will follow, however, a different approach. The idea at the basis of the Time-RG method is to take ensemble averages of the continuity and Euler equations, obtaining a hierarchy of differential equations in time for the density and velocity correlation functions \citep{Pietroni2008}. Because of nonlinearities, the equations for the $n$-th order correlation will involve the $(n+1)$-th order one, so one has to truncate the hierarchy at some order: since we are interested in the non-linear power spectrum, it has been shown that a good approximation is given by setting the connected 4-point function, or {\em trispectrum}, to zero.

It is convenient to rewrite the fluid equations in terms of the doublet \citep{Scoccimarro1998}
\begin{equation}
\begin{pmatrix}
\phi_{1, \vec k}(\eta) \\
\phi_{2, \vec k}(\eta)
\end{pmatrix} \equiv
e^{-\eta}
\begin{pmatrix}
\delta_{\vec k}(\eta) \\
\Uptheta_{\vec k}(\eta)
\end{pmatrix} \; ,
\end{equation}
so that eqs.~\eqref{continuity_tot_eta}-\eqref{euler_tot_eta} become
\begin{equation}
\label{eq:master}
\partial_\eta \phi_{a, \vec k}(\eta) + \Omega_{ab}(\eta)\,\phi_{b, \vec k}(\eta)
= \frac{e^\eta}{C(\eta)}\,\gamma_{abc}(\vec k; -\vec q_{1},-\vec q_{2})\, \phi_{b, \vec q_1}(\eta) \phi_{c, \vec q_2}(\eta) \; ,
\end{equation}
where we have defined the time-dependent, inverse``propagator''
\begin{equation}
\Omega_{ab}(\eta) \equiv
\begin{pmatrix}
1 & -1 \\
-\frac{3}{2}\,\frac{\Omega_{m}\,C}{f^2} & \frac{3}{2}\,\frac{ \Omega_{m}\,C}{f^2}
\end{pmatrix}\;,
\end{equation}
and the vertex function is given by
\begin{gather}
\gamma_{121}(\vec k; \vec q_1, \vec q_2) = \gamma_{112}(\vec k; \vec q_2, \vec q_1) = \delta_D(\vec k+\vec q_{12})\, \alpha(\vec q_1, \vec q_2)/2 \\
\gamma_{222}(\vec k; \vec q_1, \vec q_2) = \delta_D(\vec k+\vec q_{12})\, \beta(\vec q_1, \vec q_2) \; ,
\end{gather}
with all other components being equal to zero.

Following \citet{Pietroni2008}, we now consider derivatives of the correlation functions, and using eq.~\eqref{eq:master} we find the Time-RG hierarchy
\begin{align}
\partial_\eta \avg{\phi_a \phi_b} =& -\Omega_{ac} \avg{\phi_c \phi_b} - \Omega_{bc} \avg{\phi_c \phi_a}
+ \frac{e^\eta}{C} \gamma_{acd} \avg{\phi_c \phi_d \phi_b} + \frac{e^\eta}{C} \gamma_{bcd} \avg{\phi_c \phi_d \phi_a} \\
\partial_\eta \avg{\phi_a \phi_b \phi_c} =& -\Omega_{ad} \avg{\phi_a \phi_ b \phi_c} - \Omega_{bd} \avg{\phi_a \phi_d \phi_c}
-\Omega_{cd} \avg{\phi_a \phi_b \phi_d} \nonumber \\
&+ \frac{e^\eta}{C} \gamma_{ade} \avg{\phi_d \phi_e \phi_b \phi_c} + \frac{e^\eta}{C} \gamma_{bde} \avg{\phi_a \phi_d \phi_e \phi_c}
+ \frac{e^\eta}{C} \gamma_{cde} \avg{\phi_a \phi_b \phi_d \phi_e} \\
\partial_\eta \avg{\phi_a \phi_b \phi_c \phi_d} =& \dots
\end{align}
We truncate the hierarchy setting $\avg{\phi_a \phi_b \phi_c \phi_d}_c = 0$ and, using the definitions of the power spectrum and bispectrum
\begin{align}
&\avg{\phi_{a, \vec k_i} \phi_{b, \vec k_j}} = \delta_D(\vec k_{ij}) P_{ab}(k_i) \; , \\
&\avg{\phi_{a, \vec k_i} \phi_{b, \vec k_j} \phi_{c, \vec k_l}} = \delta_D(\vec k_{ijl}) B_{abc}(k_i,k_j,k_l) \; ,
\end{align}
our system of equations can be rewritten as
\begin{align}
&\partial_\eta P_{ab}(k) = -\Omega_{ac} P_{cb}(k) - \Omega_{bc} P_{ac}(k)
+ \frac{e^\eta}{C} \frac{2 \pi}{k} \left[ I_{acd, bcd}(k) + I_{bcd, acd}(k) \right] \\
&\partial_\eta I_{acd,bef}(k) = - \Omega_{bg} I_{acd,gef}(k) - \Omega_{eg} I_{acd,bgf}(k) - \Omega_{fg} I_{acd,beg}(k)
+ 2 \frac{e^\eta}{C} A_{acd,bef}(k) \; ,
\end{align}
where we have introduced, for convenience, the following functions:
\begin{gather}
I_{acd,bef}(k) \equiv \int_0^{\infty} \!\!\textrm{d} q\, q\, \int_{|q-k|}^{q+k}\!\! \textrm{d} p\, p\, \frac{1}{2}\, \left[ \gamma_{acd}(k,q,p) B_{bef}(k,q,p)
+ (q \leftrightarrow p) \right] \; , \\
A_{acd,bef}(k) \equiv \int_0^{\infty}\!\! \textrm{d} q\, q\, \int_{|q-k|}^{q+k}\!\! \textrm{d} p\, p\, \frac{1}{2}\, \bigg\{ \gamma_{acd}(k,q,p)
\big[ \gamma_{bgh}(k,q,p) P_{ge}(q) P_{hf}(p) + \gamma_{egh}(q,p,k) P_{gf}(p) P_{hb}(k) \nonumber \\
+ \gamma_{fgh}(p,k,q) P_{gb}(k) P_{he}(q) \big] + (q \leftrightarrow p) \bigg\} \; .
\end{gather}
The derivation is therefore the same as the one of \citet{Pietroni2008} for the standard case of matter perturbations, with the only difference given by the function $C(\eta)\ne 1$} accounting for the total density field.

Having specified the dynamics, we need to set up the initial conditions. We start the numerical evaluations at the initial redshift $z_{in} = 50$ and we choose $P_{ab}(k,\eta_{in})$ as the linearly evolved power spectrum, while we set $B_{abc}(k,\eta_{in}) = 0$ for Gaussian initial conditions.

\section{Results}
\label{sec:results}

In this section we present our results for the nonlinear power spectrum of the total density perturbations, both in smooth and clustering quintessence cosmologies, computed in the TRG approach.

\begin{figure}[t!]
\begin{center}
{\includegraphics[width=0.49\textwidth]{fig_P_w0p1_z0}}
{\includegraphics[width=0.49\textwidth]{fig_P_w0p2_z0}}\\
{\includegraphics[width=0.49\textwidth]{fig_P_w0p1_z0_ratio}}
{\includegraphics[width=0.49\textwidth]{fig_P_w0p2_z0_ratio}}\\
{\includegraphics[width=0.49\textwidth]{fig_P_w0p1_z0_ratioB}}
{\includegraphics[width=0.49\textwidth]{fig_P_w0p2_z0_ratioB}}
\caption{{\em Upper panels}: nonlinear power spectrum at $z=0$ in the $\Lambda$CDM cosmology and for $w=-0.9$ and $-1.1$ ({\em left}) and $w=-0.8$ and $-1.2$ ({\em right}). Thick lines correspond to the clustering case while thin lines correspond to the smooth case. {\em Middle panels}: ratios to the $\Lambda$CDM nonlinear power spectrum. {\em Lower panels}: ratio of the nonlinear to linear power spectrum in the clustering case divided by the same ratio for the smooth case, illustrating the effect of clustering quintessence on the nonlinear corrections. The dotted vertical line indicates the value of the wavenumber below which the TRG prediction is accurate at 1\% level in the $\Lambda$CDM case, that is $k=0.15\, h \, {\rm Mpc}^{-1}$.}
\label{fig:Pz0}
\end{center}
\end{figure}
As previously mentioned, all our predictions assume the same {\em initial} power spectrum, so that the evolved results will differ both in the linear and nonlinear regimes. Fig.~\ref{fig:Pz0},~\ref{fig:Pz0p5} and \ref{fig:Pz1} show our results at redshift $z=0$, $0.5$ and $1$, respectively. Each figure includes, in the upper panels, the total power spectrum as a function of $k$. The middle panels present the ratio of the power spectrum in the quintessence cosmologies to the $\Lambda$CDM case. Finally, in order to highlight the peculiar effect of a vanishing speed of sound on the nonlinear evolution alone, the lower panels show the {\em ratio} of the {\em ratios} of the nonlinear to linear power spectrum of the clustering to the smooth case, for a given value of the equation of state. In each figure, the left panels consider the cases $w=-1.1$ ({\em blue, long-dashed lines}) and $w=-0.9$ ({\em red, short-dashed lines}) while the right panels show the results for $w=-1.2$ ({\em blue, dot-dashed lines}) and $w=-0.8$ ({\em red, dotted lines}).
The dotted vertical line indicates the value of the wavenumber below which the TRG prediction is accurate at 1\% level in the $\Lambda$CDM case. For the three redshift considered such scale is given by $k=0.15\, h \, {\rm Mpc}^{-1}$, $k=0.18\, h \, {\rm Mpc}^{-1}$ and $k=0.34\, h \, {\rm Mpc}^{-1}$, respectively. We determine these values by a direct comparison with numerical simulations, as detailed in Appendix~\ref{app:accuracy}.

We remark from the start that the corrections induced at the nonlinear level by both smooth and clustering quintessence are of the order of the predictions accuracy for $|w+1|\simeq 0.1$ and only slightly larger for $|w+1|\simeq 0.2$. However, it is reasonable to expect the validity of the theoretical predictions to be more extended when ratios between nonlinear power spectra are considered, as it will be the case in the interpretation of our results. In this respect, our results are providing, in the first place, a qualitative picture of the behavior of the nonlinear power spectrum. We anticipate, nonetheless, that improved theoretical methods are possible and will be considered in future works.

\begin{figure}[t]
\begin{center}
{\includegraphics[width=0.49\textwidth]{fig_P_w0p1_z0p5}}
{\includegraphics[width=0.49\textwidth]{fig_P_w0p2_z0p5}}\\
{\includegraphics[width=0.49\textwidth]{fig_P_w0p1_z0p5_ratio}}
{\includegraphics[width=0.49\textwidth]{fig_P_w0p2_z0p5_ratio}}\\
{\includegraphics[width=0.49\textwidth]{fig_P_w0p1_z0p5_ratioB}}
{\includegraphics[width=0.49\textwidth]{fig_P_w0p2_z0p5_ratioB}}
\caption{Same as Fig.~\ref{fig:Pz0} but at redshift $z=0.5$.}
\label{fig:Pz0p5}
\end{center}
\end{figure}

Let us focus on the comparison with the $\Lambda$CDM power spectrum, in the linear regime at redshift zero, shown by the middle panels of Fig.~\ref{fig:Pz0}. In the $c_s=1$ cases, shown by the thin curves, the different cosmic expansion history for $w<-1$ with respect to $w>-1$ results in a lower or, respectively, larger growth of dark matter perturbations. The corresponding nonlinear corrections follow the expectations as again, respectively, lower or larger the nonlinear corrections in the $\Lambda$CDM case.

The behavior of the power spectrum of the {\em total perturbations} is strikingly different. In fact, the opposite effect on the linear growth of clustering versus smooth quintessence corresponds to the results already shown in Fig.~\ref{fig:CD}, where $D(z)$ is given as a function of redshift. The growth of the total perturbations at small redshift is affected by appearance and growth of quintessence perturbations for $w<-1$, while the opposite effect is at place for $w>-1$. However, taking as an example the $w>-1$ case, despite a larger linear growth factor, the nonlinear corrections are significantly smaller with respect to $\Lambda$CDM. Looking at the lower panels, we notice that, relative to the linear power spectrum, the nonlinear corrections are even smaller in the clustering quintessence case, than in the smooth one. The additional corrections induced by the clustering of quintessence are of the order of a few percents in the mildly nonlinear regime for $|w+1|\sim 0.2$ and they are roughly proportional to the departure from $w=-1$.

\begin{figure}[t]
\begin{center}
{\includegraphics[width=0.49\textwidth]{fig_P_w0p1_z1}}
{\includegraphics[width=0.49\textwidth]{fig_P_w0p2_z1}}\\
{\includegraphics[width=0.49\textwidth]{fig_P_w0p1_z1_ratio}}
{\includegraphics[width=0.49\textwidth]{fig_P_w0p2_z1_ratio}}\\
{\includegraphics[width=0.49\textwidth]{fig_P_w0p1_z1_ratioB}}
{\includegraphics[width=0.49\textwidth]{fig_P_w0p2_z1_ratioB}}
\caption{Same as Fig.~\ref{fig:Pz0} but at redshift $z=1$.}
\label{fig:Pz1}
\end{center}
\end{figure}
The peculiar relation between the linear solution and nonlinear corrections can be explained qualitatively taking into account the results for the second-order solution in standard PT for the total density contrast derived by \citet{SefusattiVernizzi2011}. It is possible to show that in the clustering quintessence case some of the terms contributing to such corrections are proportional to the product of the total density growth factor $D$ with the matter growth factor, $D_m$, that is $\delta^{(2)}_{\vec k}\sim D\,D_m$, while in the standard scenarios one typically has $\delta^{(2)}_{\vec k}\sim D^2$. This means that the nonlinear evolution of the total fluctuations is in a large part determined by the nonlinear evolution of the matter density alone, leading to a suppression of the nonlinear evolution with respect to the one expected from the value of the growth factor alone in standard scenarios.

At higher redshift, the effects of quintessence are clearly milder. In particular, at $z=0.5$, Fig.~\ref{fig:Pz0p5}, a vanishing speed of sounds has the effect, for instance assuming $w=-0.8$, of increasing the growth factor by 10\% with respect to the $c_s=1$ case, and reducing the nonlinear correction by less than 1\% at $k\simeq 0.2\, h \, {\rm Mpc}^{-1}$. Again, the interesting feature is given by the opposite effect on the linear and on the {\em relative} nonlinear growth. At $z=1$, Fig.~\ref{fig:Pz1}, the relevant effect is on the linear growth alone since nonlinear corrections due to quintessence clustering are essentially negligible.

\begin{figure}[t]
\begin{center}
{\includegraphics[width=0.49\textwidth]{fig_P_halofit_ratios_z0}}
{\includegraphics[width=0.49\textwidth]{fig_P_halofit_ratios_z1}}\\
{\includegraphics[width=0.49\textwidth]{fig_P_halofit_ratios_B_z0}}
{\includegraphics[width=0.49\textwidth]{fig_P_halofit_ratios_B_z1}}\\
\caption{{\em Upper panels}: ratio of the ratio between the nonlinear quintessence power spectrum to the $\Lambda$CDM power spectrum predicted by \texttt{halofit} assuming the simple linear prediction, to the ratio of the same quantities computed in the TRG approach at redshift $z=0$ ({\em left panel}) and $z=1$ ({\em right panel}). {\em Lower panels}: ratio of the ratios between the nonlinear quintessence power spectrum for $c_s=1$ to the one for $c_s=0$ predicted by \texttt{halofit} to the ratio of the same quantities computed in the TRG approach. Again, at redshift $z=0$ ({\em left panel}) and $z=1$ ({\em right panel}.}
\label{fig:halofit}
\end{center}
\end{figure}
Because of the peculiar relation between the linear growth factor in clustering quintessence cosmologies and the corresponding nonlinear corrections, simple tools like the \texttt{halofit} fitting function \citep{SmithEtal2003} cannot be directly used for the prediction of the nonlinear power spectrum of the total density perturbations. Still, it is useful to compare such predictions with the Time-RG ones. In fact, \texttt{halofit} provides the expected nonlinear evolution of the power spectrum based on the linear one and, specifically, on the combination of the amplitude of the initial perturbations and their linear growth. To illustrate this point, in the upper panels of Fig.~\ref{fig:halofit} we show a comparison ({\em i.e.} the ratio) between, in turn, the ratio of the nonlinear power spectrum in a quintessence cosmology and the $\Lambda$CDM nonlinear power spectrum computed using \texttt{halofit} and the same quantity computed in the TRG approach. We consider, in particular, the results at redshift $z=0$ ({\em left panel}) and $z=1$ ({\em right panel}). We notice for instance that, due to the larger value of the growth factor at redshift zero, corresponding to a larger value for $\sigma_8$, in the clustering quintessence case, \texttt{halofit} over-predicts (under-predicts) the nonlinear evolution by up to 5\% at $k\simeq 0.2\, h \, {\rm Mpc}^{-1}$ for $w=-0.8$ ($w=-1.2$). And a much larger discrepancy can be expected at smaller scales. In general, while in the smooth quintessence case the errors are relatively small (below 1\%) on the scales of interest, in the clustering case they can be still of a few percents for $k\simeq 0.4$ even at $z=1$.
It is reasonable to expect that a simple modification to the \texttt{halofit} prescription, perhaps computing the one-halo contribution simply in terms of the {\em matter} linear power spectrum, can extend its validity to the clustering models.  We do not investigate this issue further in this work.

In standard scenarios it is reasonable to expect that to larger values for the linear power spectrum correspond larger nonlinear corrections. As we have seen, such expectations can be disattended, to a certain extent, if quintessence clusters. In the lower panels of Fig.~\ref{fig:halofit} we show instead the ratio between, in turn, the ratio of the nonlinear power spectrum in a quintessence cosmology with $c_s=1$ to the one for $c_s=0$ computed using \texttt{halofit} and the same quantity computed in the TRG approach at redshift $z=0$ ({\em left panel}) and $z=1$ ({\em right panel}). The difference between the two calculations can be taken to a first approximation as the difference expected for the nonlinear corrections for the two values of the sound speed assuming the same linear power spectrum. If indeed the observed density fluctuations result from two comoving fluid as those of the system considered here, the difference in the nonlinear evolution can be as large as ten percent at $z=0$ and still a few percent at $z=1$ for $|w+1|\simeq 0.2$ and approximately proportional to $w+1$.

Before concluding this section, it is interesting to quantify, within the limits of our approximations, the effect that the additional nonlinear evolution induced by the quintessence perturbations has on the position of the acoustic peaks in the total power spectrum. Typically, nonlinear corrections partially smooth out the acoustic features present in the initial power spectrum and induce a shift in the position of the maximum of the correlation function \citep[see, for instance][]{CrocceScoccimarro2008}. We consider here simply the position of the power spectrum maximum at about $k\simeq 0.072\, h \, {\rm Mpc}^{-1}$ in the ratio of $P(k)$ with respect to a wiggle-less power spectrum in the Time-RG predictions for clustering and smooth quintessence. We find that, at redshift zero, for $w=-0.8$ the position of the peak changes by a $0.5\%$ in the clustering with respect to the smooth case, in fact being closer to the linear theory value, due to the relatively smaller nonlinear growth. For $w=-1.2$, the shift of the maximum between the smooth and clustering quintessence cases is of $0.6\%$ with quintessence perturbations increasing the overall shift with respect to linear theory. At redshift $z=0.5$ the shift is much smaller, below $0.1\%$ for $|w+1|\simeq 0.2$. We remind the reader that these results are obtained assuming the same initial power spectrum and the same value of $\Omega_{m,0}$ for all different models varying only the dark energy equation of state parameter $w$, leading therefore to different values of the linear power spectrum amplitude at redshift zero, {\em i.e.}~ different values of $\sigma_8$.

\section{Conclusions}
\label{sec:conclusions}

We studied the nonlinear evolution of the total density power spectrum in cosmologies where the acceleration of the Universe is due to a quintessence field with vanishing speed of sound. As noted in \citet{SefusattiVernizzi2011}, under this assumption, matter and quintessence perturbations are comoving and it is possible to define total density perturbations as a weighted sum of the individual matter and quintessence overdensities. This quantity is particularly relevant since it is directly related to cosmological observables such as cosmic shear or the galaxy power spectrum, while there is no way of distinguishing dark matter from quintessence perturbations as they both only interact gravitationally with baryonic matter.

We compute the nonlinear power spectrum of total matter and quintessence density in the Time-RG approach introduced by \citet{Pietroni2008}. This method is particularly suitable to this problem since the effect of a clustering quintessence field results in a modification of the standard equations of gravitational instability in terms of a single time-dependent factor in the continuity equation, \eqref{continuity_tot}, given by the function $C(z)=1+(1+w)\Omega_Q(z)/\Omega_m(z)$. In the TRG framework, continuity and Euler equations are used to obtain differential equations in time for the density correlators, making the extension to the total density including quintessence with a vanishing speed of sound straightforward.

Assuming the same initial power spectrum, the difference in the linear growth of the {\em total} density fluctuations between the clustering, $c_s=0$, and the smooth, $c_s=1$, quintessence case is significant at low redshift, being up to 5\% for $|w+1|\simeq 0.1$ at redshift zero. We have shown, however, that the difference between corresponding nonlinear corrections, that is the ratio between nonlinear and linear power spectrum in each case, is relatively small at mildly nonlinear scales, of the order of 1\% at $k=0.15\, h \, {\rm Mpc}^{-1}$ and redshift zero. This fact is quite interesting because the large difference in the linear regime typically corresponds to larger, by a factor of a few, nonlinear corrections in standard cosmologies with clustering of dark matter alone. The matter component plays a predominant role in the nonlinear evolution of the coupled system and nonlinear corrections to the total power spectrum are in fact very close to those present for the smooth case. As shown by the middle panels of Fig.~\ref{fig:Pz0}, a quintessence cosmology with $w>-1$ and $c_s=0$, leads to a larger growth factor and therefore a larger linear power spectrum with respect to a $\Lambda$CDM cosmology. {\em At the same time}, however, it presents a {\em smaller} power spectrum then $\Lambda$CDM at nonlinear scales due to a suppressed nonlinear evolution (which is in fact very close to the one obtained in the smooth quintessence case). For $c_s=1$, on the other hand, $w>-1$ leads to a smaller linear growth and a correspondingly smaller nonlinear evolution, as usually expected. This peculiar behavior of gravitational instabilities in the presence of dark energy perturbations might have some specific observational consequences that will be the subject of forthcoming work.

During completion of this work, we became aware of a similar work in preparation, \citet{AnselmiBallesterosPietroni2011}, whose contents are not known to us at the time of writing.

\bigskip
{\bf Acknowledgments}\\

We thank Filippo Vernizzi and Rom\'an Scoccimarro for useful discussions and Mart\`in Crocce and Vincent Desjacques for providing the RPT predictions and simulations data for the Appendix. E.S. acknowledges support by the European Commission under the Marie Curie Inter European Fellowship and he is grateful to the Center for Cosmology and Particle Physics of New York University for kind hospitality during the completion of this project.
The work of G.D'A. is supported by a James Arthur Fellowship. We are grateful to the organizers of the PONT 2011 conference, where part of this project has been completed.

redpajama_set_name: RedPajamaArXiv


In 280 days, I get to marry my best friend—the man I admire more than anyone else in the world.
And some people are surprised he's black.
When Ray Holden and I started dating during my sophomore year, I don't think I fully understood racism. To me, it was an abstract—a deep feeling that people masked (sometimes successfully, sometimes not). But it was "out there," not something I experienced myself.
Now I have, at least to an extent.
When people see Ray and me together, the reactions are mixed. Sometimes we get warm smiles of approval. Other times we're snubbed and given sideways glances.
The first time I felt the disapproval of others stung. Suddenly, racism had a face. Sometimes the face was white, sometimes it was black. A coworker would ask me why I was dating a black guy. In public, Ray would hear a couple of random black men call him "white boy" as he and my family walked by.
Her question led to a wonderful conversation (not to mention a sweet friendship), and I was able to tell her our story. I love Ray for his person. I love that he surprised me on Labor Day by showing up to my 8 a.m. class with my favorite Starbucks drink. I love him for his character, for the way he treats other people, for his strength and his gentleness.
So, when it comes to our relationship and our commitment to each other, ethnicity just isn't a factor. Our faith is. His character is. In the most vital ways, because of our love for Christ and for each other, we're the same, not different.
Ethnicity just isn't a factor. Our faith is.
I remember when I first learned this lesson. I was a teenager in Ohio, and my youth pastor, Joe Tyrpak, took our youth group on a mission exposure trip in Cleveland. We visited a mosque and a synagogue. We attended a Roman Catholic service and a liberal Protestant service (during which the female pastor celebrated homosexuality and denied the Trinity). The people in the Catholic church and the liberal church looked just like me—but we could not have been more different!
One of the most frequent questions I get asked is, "What do your parents think?" Usually I just tell them that race isn't a relevant factor in our family. My dad is actually the one who set us up, and my mom is thrilled that I'm going to marry a wonderful man who loves me, serves me and cares for me better than I deserve.
I'm not crazy about the term "interracial dating" or "interracial marriage." We're both human (Acts 17:26). More importantly, we're both Christians (Galatians 3:27-28). And our ethnic differences are beautiful. Opposition can be challenging, but we work through it, and it brings us even closer together.
I couldn't be more excited to marry my best friend. And we're praying that our union will be a small example of the creativity of God and the barrier-breaking power of the Gospel.


1Doctoral Student, Aalto University, School of Engineering, Otakaari 4, 00076 AALTO, Finland and, +372 56 455 953, ergo.pikas@aalto.fi.
2Professor of Construction and Project Management, University of Huddersfield, United Kingdom, l.koskela@hud.ac.uk.
3Doctoral Student, Department of Civil Engineering, Technical University of Denmark, Denmark, nitr@byg.dtu.dk.
4Research Director of the Project Production Systems Laboratory at the Univ. of California, Berkeley. ballard@ce.berkeley.edu.
5Tallinn University of Technology, Faculty of Civil Engineering, Ehitajate tee 5, 19086 Tallinn, Estonia. roode.liias@ttu.ee.
The purpose of this article is to understand the academic landscape on collaboration in design, its characteristics and related concepts for promoting collaboration within in the project based production systems. We aim to answer to the following three questions: How to define collaboration in design and why individuals need to collaborate during design? What characterizes effective collaboration in design? Which concepts support the development of collaboration in design? For shedding light on this subject, a literature review is conducted and applicability to Architecture, Engineering and Construction industry and project delivery are discussed. In this study, it was found that collaboration is a complex phenomenon, which explains the diversity of views and many complimentary concepts in organizational and design literature. Collaboration requires the management of material and knowledge boundaries, in order to develop common goals, processes and product. Lean construction concepts, methods and tools have helped the teams to develop collaborative design and construction practices.
Design collaboration, collaboration, boundaries, bridging boundaries, crossing boundaries.
Pikas, E. , Koskela, L. , Treldal, N. , Ballard, G. & Liias, R. 2016, ' Collaboration in Design – Justification, Characteristics and Related Concepts' In:, 24th Annual Conference of the International Group for Lean Construction. Boston, USA, 20-22 Jul 2016.


Right now, we are looking for a Roaming Support Engineer for the International Voice and Roaming Area. I am Maria Jansson Rådström, the leader of our team of Telia Carrier Voice and Roaming in Sweden.
As a member of my team you will have the responsibility for trouble shooting, operations and configuration of our roaming services. Preparing and establishing connections for new roaming partners will also be part of and a key role in your daily work. You will also implement network elements for the roaming services. You will also have a direct contact with our external customers, internal development engineers, project managers and managers to ensure a fast and high quality Service Assurance process.
We work in a constantly changing environment with new technologies and challenges. We do have an important role being the bridge between Development and Operations using a DevOps mindset in our daily work.
It is a job that calls for someone who understand technology, processes and people. You will also be coaching and act as an internal consultant for colleagues within other parts of our organisation. The position will also include on call duty outside office hours.
We are on a journey to become the new generation telco, which means that you need to be open-minded and part of our change journey. To really enjoy your job here, you need to be forward thinking, customer obsessed and have a passion for new technologies, trends, patterns and frameworks.


text:
President Museveni commends faith groups for supporting OWC
President Yoweri Museveni yesterday received and held a meeting with a 60-strong delegation of members of the Inter-Religious Council in Uganda, led by their Chairman, Sheikh Shaban Ramadhan Mubajje who is Chief Mufti of Uganda. He told his guests that leadership entails caring about others.
Today's meeting was a follow-up on recent familiarization tour by the religious leaders to the Districts of Ibanda, Kiruhuura and Masaka that involved the monitoring of the NRM Government's Operation Wealth Creation Programme.
"I am impressed with your enthusiasm and commitment to support the Government efforts towards poverty eradication in the country. Leadership is about caring for others. I launched the drive to eradicate poverty from Nyabushozi and the neighbouring area on the 25th December 1966. I started off by identifying the cause of nomadism among the people of the area. The first cause was the search for pasture and the second was to escape the dangers of ticks against the cattle. The solution was to ensure availability of pasture and effective control of ticks," he said.
He informed his guests that by 1989 the NRM Government had succeeded with poverty eradication among the cattle keepers. He, therefore, expressed conviction about finding a poverty solution for crop growers. He said that in 1995/96 the Government launched the 4-acres agriculture production programme under which wananchi are encouraged to allocate an acre of land to coffee growing, another one acre to the cultivation of fruits, while the third acre should be dedicated to food crops and the fourth acre for pasture growing to facilitate zero grazing.
Mr. Museveni commended religious leaders for taking off time to tour various farmers who have been transformed through modern farming activities. He expressed happiness that there are good working relations between them and the Government. He reminded them that faith organizations are also affected by the poverty among their congregations adding that there is no way the development projects of religious groups can prosper when the followers are wallowing in poverty.
The President pledged to facilitate the Inter Religious Council with a budget of Shs.5 billion to facilitate the promotion of wealth creation among the believers. He urged the religious leaders to lead the people by example and proposed that religious leaders should execute their wealth creation efforts through the Parishes set up by Government.
Mr. Museveni commended Kampala Archbishop, the Most Rev. Dr. Cyprian Kizito Lwanga for establishing the Wekembe group in Luwero District under a model of a SACCO. He expressed his conviction that progress would be recorded because the Government is working well with religious institutions in the country. He called on the Members of Parliament to think more about the promotion and development of the welfare of 40 million Ugandans instead of working to increase their remunerations. He stressed the crucial need to budget in a disciplined manner.
Mr. Museveni agreed to arrange a meeting with the Inter Religious Council three times a year and also agreed to a suggestion that official vehicles be purchased tax-free for religious institutions to enable them carry out pastoral work. The President agreed to the request to convene a meeting of about 1,000 religious leaders in July this year to sensitize them on the Operation Wealth Creation programme.
The Inter-Religious Council Chairman, Sheikh Shaban Ramadhan Mubajje, on his part, saluted President Museveni for facilitating their recent tour of Ibanda, Kiruhuura and Masaka Districts recently and said it enlightened them over the means of eradicating poverty from wananchi. He also echoed President Museveni's call on the people to discard the negative practices of land fragmentation.
Sheikh Mubaje stressed the need to consolidate the prevailing peace in the country. He noted that agriculture is a game changer towards driving Uganda to a middle class income society
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BREAKING NEWS, RELIGION
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redpajama_set_name: RedPajamaCommonCrawl


text:
SYNONYM

#### According to
The Catalogue of Life, 3rd January 2011

#### Published in
Stirp. Agri. Femison. 5: 67 (1827)

#### Original name
null

### Remarks
null

redpajama_set_name: RedPajamaGithub


text:
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text:
Shrimp Trawler
Suzannah Smith Miles
Virginia Greene
From Edisto and Beaufort to McClellanville and Georgetown, each morning during shrimp season the air fills with the deep-dieseled rumble of these hard-working boats as they head out to sea for a long day of trawling. This is a tough, take-it-on-the-chin, often thankless profession beset with pitfalls—bad weather, engine problems, the breakdown of a $5 part or worse: a torn net. Yet thanks to them we enjoy a ready supply of one of the most delectable items found in Lowcountry cuisine—sweet, delicate, just-caught shrimp straight from the docks
Built for Trouble - These strong, working boats with flat sterns and high-hulled bows are designed to take the repeated punishment of rough weather and rolling seas. The average size is in the 55- to 78-foot range, but some boats are as small as 25 feet.
Rock & Roll - Trawling is done at a low speed across continuous swells from the ocean which cause the boat to pitch and roll. To ease this rolling motion, triangular-shaped stabilizers attached to the end of the outriggers are lowered into the water. These hydrofoils steady the boat's pitch.
Pulling the Load - Trawling is accomplished by pulling a net—also called "trawl"—through water behind a boat. A "bottom trawl" allows the net to brush across the ocean floor; a "midwater trawl," as the name implies, is not as deep. A trawl typically lasts from 30 minutes to three hours, depending on conditions.
Bye-bye Bycatch - A drag often includes "bycatch," such as squid, crabs, jellyfish, sharks, and small fish that need to be returned to the water. To relieve bycatch and protect species, two devices are required by law: the Turtle Exclusion Device, which keeps large sea turtles from getting trapped in the net and drowning, and the Bycatch Reduction Device, designed to release small "trash" fish.
Laws & Order - Shrimping is one of the most carefully regulated of all maritime occupations. Each year (usually in May) the opening date of the commercial shrimping season is determined by South Carolina Department of Natural Resources according to weather and shrimp growth cycle.
Blessed -The 32nd annual Blessing of the Fleet Festival takes place on April 28 at Mount Pleasant Memorial Waterfront Park.
Hiberian Hall
On March 18, 1839, the Irish organization known as the Hibernian Society laid the first cornerstone for a new hall at 105 Meeting Street. The building has survived fire, war, the 1886 earthquake, politics, and innumerable St. Patrick's Day celebrations.
Wood Duck
Explorer John Lawson—who visited South Carolina in 1700—gives an apt introduction to Aix sponsa, whose nicknames include "wood duck," "summer duck," and "Carolina duck." The creature "has a great topping, is pied and very beautiful," he wrote.
Huguenot Church
Since 1687, the French Protestants known as Huguenots and their descendants have worshipped at the corner of Church and Queen. The edifice that stands today (the congregation's third) was the first Gothic Revival building constructed in Charleston.
South Carolina Department of Natural Resources / Festival / Shrimp / Park / Waterfront Park / Fish / Crabs / sharks / turtles / ONE / Shrimping
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text:
Ingathering of the Jews
July 7, 2017 /in Rabbi Blog /by Kerry M.
What is the third largest sporting event in the world? You wouldn't believe it, but the Maccabiah (this year is its 20th) is it!
Thousands of Jewish youth have gathered in the Holy Land to compete in sports- as Jews. South Africa is fielding a large contingent with Cape Town making an impressive showing. We wish each delegate much success!
Welcome and Mazel Tov to Alan & Kim Feldman who are celebrating their son Joseph's Bar Mitzvah this week, in our Shul. The Feldman's hail from Melbourne but heard so much about our Shul from brother Evan & Lara, they decided to do the Barmy at Marais Rd Shul! (Also most of their family is in SA…) Mazel Tov to grandparents Robin & Merle Feldman and Looky & Freda Braude of Pretoria & Johannesburg respectively. Mazel Tov, Mate!
Mazel Tov to Avin & Lauren Lieberman and Michael & Helen Lieberman who are celebrating their son & grandson, Matthew's Bar Mitzvah this Shabbas. Much nachas!
Gideon Wolman was a Shul 'all-rounder'. He could lead the service, shoot off any Haftorah and was always happy to help someone in need. His passing this week is a shock to our community, his many friends & work colleagues- and of course his family. Our condolences to his mother, Tilly Wolman, and siblings Geoffrey & Michelle.
The fast of "17th of Tammuz" falls out this Tuesday. Fast begins at 6:31am & ends 6:11pm. This ushers in the 3 Weeks of mourning for the destruction of both Temples in Yerushalayim & the terrible exiles which followed & which- almost 2000 years later- we still find ourselves in.
The Talmud notes that, "those who mourn the Temple's destruction, will merit to rejoice in its rebuilding". Click here for more info.
May we merit the rebuilding of G-d's Beit Hamikdash & the revelation of Hashem's One-ness in all the world, through the coming of Mashiach, speedily!
Did you miss the JLI Israel course? No worries! Chabad House is running the course July 26- August 30 with lecturer Rebbetzin Nicole Green. Email reception@chabad.co.za to book your spot.
Shabbat Shalom & happy reading,
http://www.maraisroadshul.com/wp-content/uploads/2015/07/marias-logo.png 0 0 Kerry M. http://www.maraisroadshul.com/wp-content/uploads/2015/07/marias-logo.png Kerry M.2017-07-07 08:11:082017-07-07 08:11:08Ingathering of the Jews
Balak in a Nutshell The one ingredient


Wings for Autism™ events continue to spread across the country!
Cape Abilities, Cape Air™ ,the Barnstable Municipal Airport and the Transportation Security Administration (TSA) are excited to bring the inaugural Wings for Autism™ program to Cape Cod on Saturday, September 17, from 9am-Noon.
This unique event, which was initiated in Massachusetts in 2011 by the Charles River Center and Massport™, is a free program specifically designed to support individuals with autism, creating a travel test run to help ease the stress of airline travel.
Visit http://www.capeabilities.org/wings/ for more information and to register.


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