For healthy eaters, Super Bowl parties' bent toward rich, calorie-laden foods compete with our desire to shed some holiday pounds and return to regular diet regimens. Whether supplying eco-beer selections for guests or bringing refreshments to a gathering, armchair players can score green points both in terms of natural ingredients and supporting the domestic economy and environment.
Other American microbrews deploy varied eco-solutions. Dave's BrewFarm, in Wilson, Wisconsin, for instance, obtains most of its energy via a wind-powered generator. Goats "mow" the grass outside the Anderson Valley Brewing plant in Boonville, California.
Odell Brewing Company, in Fort Collins, Colorado, practices waste reduction and recycling and uses renewable energy sources. The 100 percent wind-powered brewery also encourages employees to bike to work and/or carpool, and uses biodiesel-powered delivery trucks (the biodegradable fuel emits 78 percent less CO2 than standard fuel).
Five of the 2014 Good Food Awards' winning beers—exceeding the criteria of recycling water, local sourcing and banning genetically modified ingredients—are Port City Brewing Co., Alexandria, Virginia; Deschutes Brewery, Bend, Oregon; Bear Republic Brewing Co., Healdsburg, California; Victory Brewing Co., Downingtown, Pennsylvania; and Ninkasi Brewing Co., Eugene, Oregon (GoodFoodAwards.org).
ChasingGreen.org offers information on many other U.S. craft breweries that operate in sustainable ways, including the Brooklyn Brewery, Brooklyn, New York; New Belgium Beer, Fort Collins, Colorado; and the Great Lakes Brewing Co., Cleveland, Ohio.
If none of these brews is yet a current favorite, seek them out at a specialty beverage retailer that stocks from multiple regions in order to score a touchdown for us and the Earth. Some just may become part of local fans' first-string beverage "team" after the game is over.


text:
Matt Stone (født 26. maj 1971) er den ene af skaberne bag tv-serien South Park. Han har skabt serien sammen med Trey Parker.

Lægger stemme til følgende figurer i South Park:

 Kyle Broflovski og hans far Gerald
 Kenny McCormick og hans far Stuart
 Leopold "Butters" Stotch
 Jimbo Kern
 Terrance Henry Stoot (blot kaldet Terrance)
 Jesus
 Saddam Hussein
 Tweek Tweak
 Father Maxi (South Parks præst)
 John McCain

Eksterne henvisninger

Manuskriptforfattere fra USA
Filmproducere fra USA
Filmskuespillere fra USA
Emmy-vindere
Personer fra Colorado
Personer fra Texas
Tegnefilmsdubbere fra USA
South Park

redpajama_set_name: RedPajamaWikipedia


The Archdiocese of Detroit is committed to providing safe environments and fostering continuous improvement in every organization that sponsors activities and/or provides services to children and youth. the Archdiocese intends to create communities of informed adults who model appropriate behavior, are vigilant to the warning signs of abuse and take action to prevent abuse and improve safety. Likewise, the Archdiocese is determined to ensure that facilities, grounds and procedures promote optimal safety.
Participate in a Protecting God's Children workshop within 6 months of a staff or volunteer assignment, if the potential exists for contact with children or youth.
Numbers 1 and two above apply to incumbent staff and volunteers. However, their participation in a Protecting God's Children® workshop shall be required within six (6) months of the issuance of this policy.
Volunteers under 18 years of age should be paired with an adult or another teen and regularly supervised by an adult. Employees or volunteers, aged 16 and older, will attend the Protecting God's Children® workshop and will undergo a criminal background check. Staff and volunteers age 16 to 18 are required to have parental permission to attend the workshop and have the criminal background check.


One reason why the history of computers interests me is probably because I can relate to it more than I can to all the excesses of the past kings and their queens. The fact that I'm using a particular computer today makes it interesting to know about developments in the recent past leading to this model. It sometimes also helps me predict the future and take decisions.


text:
Q: How to commit partial changes from another branch than the original - git disclaimer: I am relatively new to Git so this may seem to be a confusing question from the title, so apologies in advance.
While working on a project I had created 2 branches (lets name them b1 and b2). b1 was created to define a specific translation file, whereas b2 was responsible for implementing that file in the project.
During my work, I failed to realize that the work was to be divided into 2 branches, and so defined the file, as well as implemented it in the same branch and later commit the changes to the repository (We are required to make only one commit per branch, therefore the solution here is not applicable for me)
One naive solution could be to copy everything again to the other branch manually and remove the unrelated files from the branch b2, as well as delete unrelated files from b1, and then amend the commit at b1, but there are too many files that would need to be copied and deleted manually. Is there a cleaner solution to this? If so what are the steps needed to achieve this?
Thanks in advance!

A: I would suggest branching b2 off b1. that way, b2 will have your implementation and the translation file. now you can just delete the translation file while keeping the implementation file.
you can do this:
git checkout b1

and then:
git checkout -b b2 #this will lead to b2 branching off from b1

redpajama_set_name: RedPajamaStackExchange


text:
Watch the 2018 World Cup Online, How to Stream Live for Free
by John Anthony
The 2018 FIFA World Cup is scheduled to take place in Russia starting on June 14. The worldwide football/soccer event will run for approximately 30 days and see 32 national teams compete for the top prize. The first match pits Russia's team against Saudi Arabia, followed the next day by Egypt vs Uruguay. No matter where you live, or which team you're rooting for, you don't want to miss this World Cup!
Since most soccer and football fans can't attend the event in person, the best way to catch all the action is to stream the 2018 World Cup online. Several television networks will air select matches on a time delay, but if you want full and free access to every game and every goal, you'll need a reliable method of streaming it online. Today, we're covering some of the best methods of watching the 2018 World Cup online for free, so read on!
Streaming FIFA 2018 World Cup Online: Use a VPN
It doesn't matter how you access your online streams, it's always a good idea to have a reliable virtual private network active whenever you go online. VPNs encrypt your data to help keep it safe from prying eyes, while masking your identity with an anonymous IP address. This effectively defeats most government surveillance efforts and hacker spies looking to monitor your online activities.
VPNs are mission-critical tools for accessing worldwide videos and sports streams. Each time you connect, you can choose a proxy server located in a different country through which you can route your internet traffic. This fools websites and streaming services into thinking you've changed regions, allowing you to bypass region blocks on Netflix, Hulu, BBC iPlayer, and various streaming sites around the world.
We recommend using IPVanish for watching the 2018 World Cup. The service delivers top tier speeds to servers around the world, allowing you to log in and utilize a lag-free connection no matter where you live. The company runs a network of over 950 servers in 60 different countries, as well, which means you'll never have trouble finding a great connection.
Most VPNs struggle to deliver fast speeds with strong security. IPVanish bucks that trend by providing both in ample supply. The service delivers top tier speeds to servers around the world, allowing you to log in and utilize a lag-free connection no matter where you live. The company runs a network of over 950 servers in 60 different countries, as well, which means you'll never have trouble finding a great connection. For security, IPVanish protects your entire connection to the internet with strong 256-bit AES encryption, a zero logging policy on all traffic, DNS leak protection, and an automatic kill switch. You can use the service with full access to torrents, P2P networks, and Kodi add-ons, as well, all while staying completely hidden online!
Learn more about this excellent VPN by checking out our full IPVanish review.
EXCLUSIVE DEAL: Save a massive 60% here on the IPVanish annual plan, taking the monthly price down to only $4.87/mo
Easiest Ways to Watch the World Cup Online
The World Cup is the most-watched sporting event in the world. It only comes around every four years, but when it does, broadcasters pay attention. This means there are several legitimate resources available for streaming the World Cup for free, several of which are extremely easy to get started with.
Fox Sports on Twitter
Announced January 2018, Fox Sports is teaming up with Twitter to produce an exclusive 27 episode show set to air alongside the World Cup. The live content will stream on Twitter and be available to users in the U.S. for free. It includes commentary, real-time highlights, recaps, reviews, previews, and much more. For users located elsewhere in the world, a VPN like IPVanish can grant access to these U.S.-only streams by connecting to an American proxy server.
Stream on Fox
Fox TV owns the broadcast rights for the 2018 FIFA World Cup in the United States and much of North America. If you have a TV, even just a simple receiving antenna, you should be able to tune into your local Fox affiliate station and stream World Cup matches as soon as they air.
To watch the World Cup online with Fox, you'll need to grab the app for iOS, Android, and streaming/gaming consoles, or use the company's sports website service. Both provide access to live matches as well as highlights, making it surprisingly easy to keep track of the latest games.
A drawback to using the Fox online streaming services is that some users may be asked to log in using their cable subscription details. This can be limiting for anyone outside of the U.S. as well as citizens that don't use cable. If you have an existing cable subscription, however, you can access all of Fox's coverage for free.
Watch on Telemundo
Spanish-language soccer fans, especially those living in Latin America, will have full access to World Cup games thanks to the Telemundo broadcasting service. The streams will be released with full Spanish commentary powered by NBC. No cable subscription details should be required to access this content, though you may need a reliable VPN set to a Latin American country in order to stream from the Telemundo website.
Use Free Trials to Watch the World Cup for Free
Popular online streaming services are eager to let people try out their offerings. To that end, many of them have free trials you can sign up for, some of which last for weeks at a time! Below are some of the better trial offers you can take advantage of for some free FIFA World Cup streams.
Sling is getting in on the football action with a full page dedicated to the 2018 World Cup. The service itself is an inexpensive "a la carte" TV streaming service that lets users sign up and subscribe to only the channels they're interested in. This means you can snag access to the World Cup and dozens of dedicated sports and movie channels for next to nothing.
If you want free soccer streams, all you have to do is sign up for Sling's seven day free trial. This gives you a solid week to watch FIFA for free, including on the Sling TV apps available for mobile, gaming devices, and tons of other platforms. It's not a wide enough window to let you watch the entire event, but if you're only interested in a few teams, it might do the trick!
Sony's PlayStation Vue service operates a lot like Sling TV, only with a slightly stronger focus on subscription plans instead of per-channel payments. This lets Vue users access loads of free content for a small monthly price, including broadcast networks, movie channels, and plenty of live sports resources for the World Cup.
PlayStation Vue offers a seven day free trial for its entire service, with a current 20% off the first two months of core subscriptions. This lets you watch a full week of FIFA for free and get a hefty discount for the remaining weeks. Note that PlayStation Vue is only available in the United States, which can be an unfortunate limiting factor for worldwide soccer fans.
Hulu with Live TV offers a good variety of broadcast and cable channels accessible to most customers in the U.S. and Japan. The content is hidden behind a paywall, of course, but thanks to a free seven day trial, anyone can sign up to test things out and stream all the sports and World Cup content they like, all for free.
YouTube has recently gotten in on the TV streaming game with its own dedicated monthly subscription service. Like its competitors above, you'll have access to dozens of channels, including multiple sports resources that will stream the World Cup. The free trial lasts for seven days and subscriptions can be canceled at any time, giving you a nearly-free option for watching tons of soccer this summer.
Use Kodi to Watch the World Cup for Free
Do network broadcasts and free trials still feel too constricting? Don't worry, there are a few other options to get your soccer fix for free. The best is to install Kodi, the free media center software with support for third party extensions. Find the right resources and you can stream every kick and every goal, all for free.
World Cup Matches on the Maverick Repository
The Maverick repository has become one of the best ways to watch all kinds of free sports streams on Kodi. NFL games, basketball, hockey, tennis, and much more, all available from a single repository! We'll cover the best add-ons to access World Cup streams for free below. Before you jump in, follow the steps below to add the repository to your system.
Installing the Maverick Repo
Maverick is a fast installation, just like any piece of unofficial Kodi content. Once you add the zip file to your system you'll be able to install as many of its add-ons as you like. Follow the steps below first, then choose which add-ons you need and install them individually.
Open Kodi and click the gear icon to enter the System menu.
Go to System Settings > Add-ons.
Toggle the slider next to the Unknown sources option. Make sure it's white and to the right, allowing you to install third party repos.
Accept the warning message that pops up.
Open a web browser and go to the official Maverick repository.
Download repository.maverickrepo-3.4.zip and save it somewhere convenient.
Back in Kodi, go to the main menu and choose Add-ons.
Click the box icon and select Install from Zip File.
Navigate to where you saved repository.maverickrepo.zip
From the open box menu, choose Install from repository.
Scroll down and open the MaverickTV repository.
Enter the Video add-ons folder.
From here you can install the add-ons you like, one by one. See the selections below for our favorite choices.
SportsDevil remains one of the best all-around sports streaming resources for Kodi. It's fast, free, and it comes with dozens of reliable sources for every sport under the sun. Whether you're an NFL fan or an NBA junkie, you'll be able to find plenty of content through SportsDevil.
Soccer and World Cup aficionados will enjoy some of the biggest selection of streaming sources to boot. Not only does SportsDevil's main links support full soccer categories, but there are two dedicated sections made especially for soccer. These links vary in terms of reliability, but with some persistence, you'll usually be able to find a good stream. You'll want to stick with the Live Sports category along with the reliable streams listed below.
LiveFootball.ws – A simple streaming source that shows games as they air. Confirmed to be showing at least some World Cup matches this year.
LiveFootballVideo.com – Another soccer service showing World Cup games as they air.
Bundesliga-Streams.net – A variety of live sports organized by starting time, including soccer/football categories.
Dimsports.eu – A large resource with nearly 20 unique sports categories, including football.
To install SportsDevil just follow the instructions above for adding the Maverick repo, then choose SportsDevil from the add-ons list.
Project Mayhem Sports
The Maverick repository's flagship add-on happens to be an incredible resource for live sports, especially football/soccer and the World Cup. The extension includes dozens of reliable channels from around the world, such as BT Sports, Sky Sports, Bein Sports, and Pac 12. You'll also get Premiere League channels and dedicated sections for sports highlights, martial arts, and fitness videos.
For free World Cup content, all you have to do is run the add-on, then check through the top streaming channels and see who's broadcasting. You might even get an HD stream so you can enjoy soccer in gorgeous high quality!
Install Project Mayhem Sports by following the repo instructions above, then select the add-on by name from the list.
Joker Sports – Live Sports Channels
Joker Sports is a wonderfully complete streaming add-on that includes live access to dozens of sports resources around the world. Once you install it you'll be able to dive straight into Pac 12 content, Bein channels, BT Sport, Sky, and dozens more. Joker Sports also includes support for U.S.-based cable channels like NBC and ESPN, though reliability can be spotty on occasion.
For free FIFA World Cup streams, Joker Sports offers several possible options, most of which are unsorted and can be found in the add-ons Live Sports folder. Unfortunately, there's no way to tell if any of these channels will stream World Cup content until the event is live. If the above methods fail, however, Joker Sports is good to have installed as a backup.
To install Joker Sports, follow the Maverick repository install guide above. You'll then find Joker Sports on the list of add-ons.
UK Turk Playlists
The old reliable standby UK Turk Playlists is a powerful add-on with hundreds of amazing streaming resources. It delivers live sports, TV shows, new and classic movies, and lots more, all organized into categories and channels just waiting to keep you entertained.
Some of UK Turk's sports content is geared towards soccer and should show World Cup content as it airs. Even if it doesn't, you won't be wasting your time installing UK Turk, as it's one of the best all-purpose add-ons in the Kodi ecosystem.
Make sure you're ready for the games by following our guide on how to install UK Turk Playlists.
The World Cup is one of the largest sporting events in the world, second only to the Olympics. It attracts millions of fans eager to cheer on their country and team. Gaining access to free online World Cup streams has gotten easier and easier as the years go by. With all the options above, you won't have any trouble keeping track of every single goal.
Who's your favorite to win this World Cup? Need help getting any of our recommendations to work? Leave us a comment below!
← How To Use Green Address On Linux → How to Stream the World Cup 2018 Russia for Free, No Cable Subscription Needed

redpajama_set_name: RedPajamaCommonCrawl


text:
Hypognatha jacaze  è un ragno appartenente alla famiglia Araneidae.

Etimologia
Il nome della specie deriva dal nome della località brasiliana di rinvenimento dell'olotipo maschile: Jacareacanga (probabilmente traslitterato male come Jacazeranga)

Caratteristiche
L'olotipo maschile rinvenuto ha dimensioni: cefalotorace lungo 1,32mm, largo 1,09mm; opistosoma lungo 2,3mm, largo 2,2mm.

Distribuzione
La specie è stata reperita nel Brasile centrosettentrionale: nei pressi del comune di Jacareacanga, nello stato del Pará.

Tassonomia
Al 2014 non sono note sottospecie e dal 1996 non sono stati esaminati nuovi esemplari.

Note

Bibliografia
   (pag.128)

Altri progetti

Collegamenti esterni

Hypognatha
Taxa classificati da Herbert Walter Levi


text:
\section{INTRODUCTION} \label{intro}
After the seminal papers by A. Kolmogorov in 1941, it is well established that, apart from small corrections due to intermittency
\cite{frisch1995t},
the energy spectrum, $E(k)$, of the velocity fluctuations for high Reynolds number hydrodynamic turbulence shows a power  law
of the form $E(k)=C\;  P^{2/3} \;  k^{-5/3}$, where $C$ is the dimensionless Kolmogorov  constant and $P$ is
the flux of energy in the wave number space. This is a very strong result that has been  confirmed experimentally and
  numerically by the direct numerical integration of the Navier-Stokes equation. It can be  obtained
via dimensional considerations or as a solution of phenomenological turbulence
closures \cite{frisch1995t}. However, so far, this result has not been obtained
analytically from the Navier-Stokes equation.
Many decades after the work by Kolmogorov,
it has been discovered by Zakharov in 1965
that systems of weakly nonlinear, dispersive, random waves
behave qualitatively in a similar way as hydrodynamical turbulence \cite{zakh65}.
Namely,
the nonlinear interaction of waves can produce other waves with different
wavelengths and so on, generating a {\it cascade} process
leading to power-law wave spectra similar to the Kolmogorov spectrum.
Because of such an analogy, they  are called Kolmogorov-Zakharov (KZ) spectra, and the entire field
is known as Weak Wave Turbulence (WWT).
Description of WWT turns out to be more accessible
than of the hydrodynamic turbulence because nonlinearity
 in the dynamical equations, although still crucial, is small.
 In the WWT framework, a systematic approach
based on averaging the dynamical equations leads to
a Boltzmann-like  equation known as the
{\it wave kinetic equation}
 which describes the evolution of the spectrum of
  the turbulent wave field \cite{zakharov41kst}.
One remarkable property of WWT is that, in
contrast to hydrodynamic turbulence, the KZ spectra have been found as
exact stationary solutions of the wave kinetic equation \cite{zakh65,zakharov1967ess}.
Unlike the thermodynamic solutions,
for which  the integrand in the collision integral is identically zero,
the KZ solutions
correspond to non-trivial
states for which
a source, a sink and a window of transparency (inertial range) are required.
 Since this discovery, weak wave turbulence has found applications for a
 vast variety of  physical systems ranging from quantum to astrophysical scales,
 see books \cite{zakharov41kst,nazarenko-book} and references therein.

In this paper, we consider nonlinear dispersive  waves described by Gross-Pitaevskii equation (GPE),
\begin{equation}
i\frac{\partial \psi}{\partial t}+\nabla^2\psi +\sigma |\psi|^2\psi=0.
\label{nls0}
\end{equation}
This partial differential equation
has attracted the attention of many researchers:
it describes
propagation of optical pulses in  nonlinear media \cite{sulem1899nse} and
weakly interacting boson gases at very low temperatures called Bose-Einstein condensates
(BEC) \cite{dalfovo1999theory}.
In the present paper we will be concerned with the latter case and we will focus on the three-dimensional (3D) systems.
  Complex wave function
$ \psi $  is called {\it order parameter} and $ \sigma = \pm1$, depending on the physics of the problem:
  the defocusing case, $ \sigma=-1$, represents repulsive bosons, while the focusing, $ \sigma=1 $, considers an attractive
  interaction.
GPE has recently attracted the attention of many fluid dynamicists because BEC is a good example of superfluid,
i.e. a fluid with zero viscosity.
Indeed, using the Madelung transformation, the GPE can be mapped onto an Euler equation
which differs from the classical one only by an extra
term named  quantum pressure. Therefore, numerical computations of the 3D defocusing GPE
 have become a tool for investigating superfluids and quantum fluids dynamics.
Phenomena such as the vortex reconnections \cite{koplik1993vrs}, formation of a condensate \cite{berloff2002ssn},
and formation of power-law spectra  \cite{nore1997dkt, kobayashi2005kss, kobayashi2005kol, proment:051603} have been observed.

The purpose of this paper is to revisit and investigate the turbulence characteritics in the defocusing 3D GPE
with particular attention to the forced and dissipated case. An interesting issue to be addressed is
verification of the  WWT theory which offers a solid theoretical tool for predicting statistical
quantities in systems of dispersive, weakly interacting waves. As it will be shown
in the next section, when the nonlinearity becomes large, the predictions of the WWT theory fail
 and the concept of  {\it critical balance} (CB) has to be introduced in order to
explain the observed spectra.

This paper is organized as follows. In section \ref{theory} we present the theoretical background
 on the GPE model revisiting some mathematical aspects, including  quantum vortices and the
 general properties of quantum turbulence. In section \ref{fd-GPE} we introduce the
 forced-dissipated GPE and present predictions for steady turbulent states: in
 particular we discuss the WWT for the  four-wave and the three-wave regimes
  and the CB conjecture. Section \ref{numerics} is dedicated to presenting numerical
  results in three different regimes: free condensation at large scales ({\bf RUN 1}),
  dissipation  by friction at low wave numbers ({\bf RUN 2}),
  and dissipation  by hypo-viscosity at low wave numbers ({\bf RUN 3}).
  Finally, section \ref{conclusion} contains the conclusions.

\section{Theoretical background} \label{theory}
In this paper, we will consider the defocusing GPE model,
\begin{equation}
\imath \frac{\partial \psi(\mathbf{x}, t)}{\partial t} + \nabla^2 \psi(\mathbf{x}, t) - |\psi(\mathbf{x}, t)|^2\psi(\mathbf{x}, t)=0,
\label{gpe}
\end{equation}
where the nonlinearity comes from the self-interactions proportional  to the gas density $ \rho(\mathbf{x}, t)=|\psi(\mathbf{x}, t)|^2 $;
this term is a consequence of considering local interactions between bosons.
The system is conservative and its Hamiltonian is
\begin{equation}
H=\int \left( |\nabla \psi(\mathbf{x}, t)|^2 + \frac{1}{2}|\psi(\mathbf{x}, t)|^4 \right) d\mathbf{x} = H_{lin}(t) + H_{nl}(t).
\end{equation}
In the latter relation the total energy $ H $ has been split into a part responsible for the linear dynamics, $ H_{lin}(t) = \int |\nabla\psi(\mathbf{x}, t)|^2 d\mathbf{k} $, and the one describing the  nonlinear interactions, $ H_{nl}(t) =1/2 \int |\psi(\mathbf{x}, t)|^4 d\mathbf{k} $.
In the following, we will use the  energy densities defined as  $ \mathcal{E}_{lin}=H_{lin}/V $ and $ \mathcal{E}_{nl}=H_{nl}/V $ where $ V $ is the total volume.
The system conserves a second quantity, the mass $ M $, defined as
\begin{equation}
M=\int {|\psi(\mathbf{x}, t)|^2} d\mathbf{x} = \int \rho(\mathbf{x}, t) d\mathbf{x}.
\end{equation}

An important quantity that characterizes the system is the healing length $ \xi $: it physically  estimates the distance over which the field $ \psi(\mathbf{x}, t) $ recovers its bulk value when subject to a localized perturbation. This definition refers to the case of a single perturbation in a uniform field but can be extended to even  highly perturbed statistical  systems as
\begin{equation}
\xi = \frac{1}{\sqrt{\langle \rho \rangle}},
\end{equation}
where $ \langle \cdot \rangle $ denotes the spatial averaging, i.e. $ \langle \rho \rangle = M/V $.  The healing length $ \xi $ measures on average the scale at which the nonlinear term becomes comparable with the linear one. Dual to  the scale $\xi$ is  wave number
$ k_{\xi}=2\pi \sqrt{\langle \rho \rangle} $.

The GPE has been widely studied in the fluid dynamics framework. Indeed, the  Madelung transformation, $ \psi(\mathbf{x}, t)=\sqrt{\rho(\mathbf{x}, t)}e^{\imath \theta(\mathbf{x}, t)}$, maps the GPE for the complex field  into the system of two equations,
\begin{equation}
\begin{split}
& \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0 \\
&\rho \left( \frac{\partial v_j}{\partial t} + v_k \frac{\partial v_j}{\partial x_k} \right) = -\frac{\partial p}{\partial x_j} + \frac{\partial \Sigma_{jk}}{\partial x_k},
\label{eq:fd-NLSE}
\end{split}
\end{equation}
for the real density field $ \rho(\mathbf{x}, t) $ and a real velocity field $ \mathbf{v}(\mathbf{x}, t) = 2\nabla\theta(\mathbf{x}, t) $.
The first equation represents a continuity equation for a compressible fluid and the second equation is a momentum conservation law.
 The  terms in the r.h.s of the latter equation can be thought as a pressure $ p=\rho^2 $ and a ``quantum stress" tensor, $\Sigma_{jk}= \rho \frac{\partial^2  (\ln \rho)}{\partial x_j \partial x_k} $. The quantum stress term
 becomes important at scales of the order of $ \xi $.
 The system (\ref{eq:fd-NLSE}) describes an inviscid and irrotational fluid flow.

\subsection{Quantum vortices}
Even if the fluid is irrotational, particular types of vortex solutions exist. This is true  if the region occupied by
 the irrotational flow is not simply connected, e.g., if  there are phase defects in the field
 at locations of the zero density.

Moreover, differently from classical fluids, such vortices carry quantized circulation and therefore are called {\it quantum vortices}.
To better understand  their structure, we first consider a two-dimensional (2D)
system. A necessary condition to assure the continuity of the complex field $ \psi $ is that the phase changes by $ \Delta \theta = 2\pi n $, where $ n \in \mathcal{N} $, around a vortex. As the velocity field $ \mathbf{v} $ is proportional to the gradient of the phase, it is easy to see that the circulation around a vortex is quantized,
\begin{equation}
\mathcal{C} = \oint \mathbf{v} \cdot d\mathbf{l} = 2 \oint \nabla \theta \cdot d\mathbf{l} = 2 \Delta \theta.
\end{equation}
In Fig. \ref{vortex-phase} and Fig. \ref{vortex-density} we show respectively the phase field $ \theta(\mathbf{x}, t) $ and the density field $ \rho(\mathbf{x}, t) $ in the neighborhood of a 2D vortex embedded in a uniform density field.
\begin{figure}
\begin{minipage}[l]{0.36\linewidth}
\includegraphics[scale=0.5]{fig01.pdf}
\caption{$ \theta(\mathbf{x}, t) $ near a 2D vortex. \label{vortex-phase}}
\includegraphics[scale=0.48]{fig02.pdf}
\caption{$ \rho(\mathbf{x}, t) $ near a 2D vortex. \label{vortex-density}}
\end{minipage}
\begin{minipage}[r]{0.58\linewidth}
\includegraphics[scale=0.28]{fig03.pdf}
\caption{Plot of the low density region $ \rho(\mathbf{x}, t) $ below a certain threshold in a freely decay simulation. \label{vortices}}
\end{minipage}
\end{figure}
The vortex core size is of the order of $ \xi $ because, by definition, the healing length  measures the size of a generic order-one
fluctuation on the uniform condensate solution. By measuring circulation it is possible to distinguish between
clockwise and anti-clockwise vortices.
Note another important difference from the classical fluids arising from the presence of the
quantum stress: vortices with the opposite sign can approach each other and  annihilate.

In 3D, the vortices are more complicated objects consisting of continuous lines or loops with different topologies. These structures can oscillate producing Kelvin waves \cite{kozik:060502}, be transported by the fluid or induce a fluid motion, and reconnect \cite{koplik1993vrs, alamri:215302}. The vortex energy is proportional, in the leading order, to its length and it can be transferred to the fluid via sound waves \cite{leadbeater2001sou}. Examples of all these vortex motions is shown in Fig. \ref{vortices}: here we plot a snapshot of low density regions,
associated with the vortex cores, obtained in a numerical computation of the GPE in a periodic cubic box with
twelve vortices as initial condition \cite{url:proment-qt}.

\subsection{Quantum Turbulence}
Vortex-vortex dynamics (collective dynamics of vortex bundles, reconnections of vortex lines), vortex-sound (radiation and scattering of sound by vortices) and sound-sound  interactions (acoustic wave turbulence) and the dynamics of the vortex itself (Kelvin waves, vortex rings) represent the ingredients of quantum turbulence (QT).
When forced at the scales larger than the mean inter-vortex separation $\ell \gg \xi$, QT cascade starts as the classical
Richardson cascade characteristic of Navier-Stokes turbulence until it reaches the scale  $\ell$. At scales $\le \ell$ the
discreteness of the quantized vortex field becomes essential, and the further cascade to lower scales is very different than the
one in the classical fluids with continuous vorticity  \cite{vinen-nimela, PhysRevB.61.1410, PhysRevB.64.134520}. After some reconnections and other crossover processes
 near the transitional  scale  $\ell$ \cite{lvov_naz_rud1,lvov_naz_rud2},
the energy cascade is be carried to the scales  $\le \ell$ by Kelvin wave cascade until,
 at a very low scale, it is radiated into sound
 \cite{vinen-nimela, PhysRevB.61.1410, PhysRevB.64.134520, PhysRevLett.92.035301, boffetta, KW_rec, KW-dam, LN-spectrum}.

In the recent years, GPE has become a popular model for studying QT by using numerical simulations \cite{nore1997dkt, berloff2002ssn, kobayashi2005kss, kobayashi2005kol, yepez:084501, PhysRevLett.104.075301}. The pioneering paper of Nore et al. \cite{nore1997dkt} showed similarities between the 3D GPE and the classical Navier-Stokes turbulence, including observations of the famous Kolmogorov $5/3$-spectrum.
This spectrum was observed for scales $>\ell $ (with $\ell > \xi$), which agrees with the view that at this scales the discreteness of the vortex lines is inessential, and the turbulence picture is basically classical Kolmogorov.
However, in several follow-up works  \cite{kobayashi2005kss, kobayashi2005kol, yepez:084501} the $5/3$-spectrum was reported to extend
to the smaller scales, between $\ell $ and $\xi$, where the classical Kolmogorov picture is not expected to be valid theoretically.
Later in our paper we will comment on this apparent paradox.

 Numerical quantities usually measured in QT can be defined in the fluid dynamic framework. Namely, the
 total energy is divided into kinetic, quantum and internal energy of the system as follows \cite{nore1997dkt},
\begin{equation}
H = E_{kin}(t) + E_{qu}(t) + E_{int}(t),
\end{equation}
where $ E_{kin}(t) = \frac{1}{2} \int \left( \sqrt{\rho} \mathbf{v} \right)^2 d\mathbf{x} $ is the kinetic energy , $ E_{qu}(t) = \frac{1}{2} \int \left(2\nabla\sqrt{\rho} \right)^2 d\mathbf{x} $ is the quantum energy
 and  $ E_{int}(t) = \frac{1}{2} \int  \rho^2 d\mathbf{x} = H_{nl}(t) $ the internal energy.
Moreover, the quantity in the integrand of the kinetic energy is usually divided, using the Helmholtz's theorem, into a solenoidal (incompressible) and an irrotational (compressible) vector fields,
\begin{equation}
\sqrt{\rho}\mathbf{v} =  (\sqrt{\rho}\mathbf{v})^i + (\sqrt{\rho}\mathbf{v})^c.
\end{equation}
The incompressible part, satisfying  $ \nabla \cdot (\sqrt{\rho}\mathbf{v})^i=0 $, is associated to the vortex dynamics; the compressible part, which satisfies $ \nabla \times (\sqrt{\rho}\mathbf{v})^c=0 $, is related to the  sound waves. Note that the mentioned
 above results of  papers \cite{nore1997dkt, kobayashi2005kss, kobayashi2005kol, yepez:084501} for the $ k^{-5/3} $ power-law behavior
refer to the spectrum of the incompressible kinetic energy $ E_{kin}^i $.

\section{Forced-dissipated GPE}\label{fd-GPE}
The aim of this research is to study the steady turbulent states in the GPE model, with particular interest in observing cascades from large scales to small ones. Therefore, in the spirit of classical turbulence, we build a sustained system by including a forcing and a dissipation terms in  the GPE:
\begin{equation}
\imath \frac{\partial \psi(\mathbf{x}, t)}{\partial t} + \nabla^2 \psi(\mathbf{x}, t) - |\psi(\mathbf{x}, t)|^2\psi(\mathbf{x}, t)= \mathcal{F} + \mathcal{D},
\label{gpe-fd}
\end{equation}
where the forcing $ \mathcal{F} $ injects mass and energy, while the dissipation $ \mathcal{D} $ removes them. As a consequence, the mass and the energy are no longer constants of motion. However, if a steady turbulent state is reached, the quantities $ \dot{H}(t) $ and $ \dot{M}(t) $ are zero.
In such a steady state, the mass and the energy get transferred  from the forcing to the dissipation scales, being approximately conserved
while cascading though the inertial ranges (see  \ref{ap:fluxes}).

\subsection{Weak wave turbulence predictions}
The WWT furnishes some prediction for wave spectra in steady states. In order to
introduce WWT, let us put the system into a 3D periodic box and write the equation (neglecting $ \mathcal{F} $ and $ \mathcal{D} $) in Fourier space:
\begin{equation}
\imath \frac{\partial \tilde{\psi}(\mathbf{k}_1, t)}{\partial t} - \omega(\mathbf{k}_1) \tilde{\psi}(\mathbf{k}_1, t) =
\sum_{\mathbf{k}_{2}, \mathbf{k}_{3}, \mathbf{k}_{4} \in \mathbb{Z}^3}
 \tilde{\psi}^\ast(\mathbf{k}_2, t) \tilde{\psi}(\mathbf{k}_3, t) \tilde{\psi}(\mathbf{k}_4, t) \delta(\mathbf{k}_1 + \mathbf{k}_2 -\mathbf{k}_3-\mathbf{k}_4) .
\label{eq:bbgky}
\end{equation}
Here $\tilde{\psi}_i \equiv  \tilde{\psi}(\mathbf{k}_i, t) $ is the Fourier transform
of ${\psi}(\mathbf{x}, t) $ and $\omega(\mathbf{k})={k}^2 $ is the dispersion relation of the system
(hereafter $k=|\mathbf{k}|$).
The WWT theory, taking the limits of infinite-box limit, small nonlinearity,
and assuming space homogeneity and
random  phases and amplitudes (RPA) of the initial  wave amplitudes,
provides a statistical closure.
The closure predicts the behavior of statistical quantities such as correlators $ \langle \tilde{\psi}_1 \tilde{\psi}_2 ... \tilde{\psi}_n \tilde{\psi}_{n+1}^\ast \tilde{\psi}_{n+2}^\ast ... \tilde{\psi}_{n+m}^\ast \rangle  $, where the average is performed over the random initial
data.
In this framework the simplest non-trivial correlator is the second order one,
\begin{equation}
 \langle  \hat \psi_i^\ast \hat \psi_j \rangle = \langle  |\hat \psi_i| |\hat \psi_j| e^{\imath \left(\theta_i-\theta_j \right)} \rangle = n_i \delta (\mathbf{k}_i-\mathbf{k}_j),
\end{equation}
where the quantity $ n_i \equiv n(\mathbf{k}_i,t) $ is called {\it wave-action} spectrum.
The RPA assumption allows one to close the system by the Wick decomposition,
a mechanism which splits the higher order correlators as sums of products of second order correlators
\cite{cln0,cln1,cln2}.
This procedure, when applied to the GPE model, leads to the following four-wave {\it kinetic equation}
for the evolution of the wave-action spectrum \cite{dyachenko:1992hc},
\begin{eqnarray}\label{kin4}
\frac{\partial n_1}{\partial t} & = &4 \pi \int n_1 n_2 n_3 n_ 4 \left( \frac{1}{n_1} + \frac{1}{n_2} - \frac{1}{n_3} - \frac{1}{n_4} \right) \nonumber \\
& & \times \delta(\mathbf{k}_1+\mathbf{k}_2-\mathbf{k}_3-\mathbf{k}_4) \delta(\omega_1+\omega_2-\omega_3-\omega_4) d\mathbf{k}_{234} , \label{kineticequation}
\end{eqnarray}
where $d\mathbf{k}_{234} \equiv d\mathbf{k}_{2} d\mathbf{k}_{3} d\mathbf{k}_{4}$.

This is an integro-differential equation which models ``wave collisions'', in analogy with Boltzmann kinetic equation for the
particle collisions.
Physically, it says that for times much longer that the  fast wave periods   $ T_i = 2\pi/\omega_i $, the wave amplitudes
 $ \tilde{\psi}_i $ are effectively coupled  only if they satisfy the following resonant conditions,
\begin{equation}
\begin{split}
&\mathbf{k}_1+\mathbf{k}_2=\mathbf{k}_3+\mathbf{k}_4 \\
&\omega_1+\omega_2=\omega_3+\omega_4.
\end{split}
\end{equation}
Equation  (\ref{kineticequation})  has the following  invariants, $ M=\int n(\mathbf{k}, t) d\mathbf {k} $, $ {\bf P}=\int \mathbf{k} n(\mathbf{k}, t)d\mathbf{k} $, and $ E=\int \omega(\mathbf{k}) n(\mathbf{k}, t) d\mathbf{k} $ that are respectively the total number of particles (or the mass), the momentum and the energy. Moreover, the dynamics described by the  kinetic equation is irreversible in time and an entropy measure can be defined.
Three trivial functions that cancel the integrand in  (\ref{kineticequation}) are $ n_k^{(1)}= A $, $ n_k^{(2)}= (\mathbf{B} \cdot \mathbf{k})^{-1} $ and $ n_k^{(3)}=C k^{-2} $ with $ A, \mathbf{B},  $ and $ C $ constants. By combining these solutions, the general thermodynamic solution takes the form:
\begin{equation}
\label{eq:RJ}
n_k^{(RJ)} = \frac{T}{\mu +(\mathbf{u}\cdot\mathbf{k})+ k^2},
\end{equation}
where $ \mu $ is a  chemical potential constant, $ \mathbf{u} $ is a constant macroscopic velocity and $ T $ is a temperature of the system. In an isotropic field, the macroscopic velocity is zero and the relation \eqref{eq:RJ} assumes the form  known in literature as Rayleigh-Jeans (RJ)
thermodynamic equilibrium distribution. As the distribution is not convergent for large $ k $'s, the temperature and the chemical potential can be evaluated based on the known  mass and energy of the system only by introducing an ultraviolet cutoff, as proposed in \cite{PhysRevLett.95.263901}.

 In presence of an external forcing and damping, besides the  RJ distribution, two other steady   solutions may exist, namely the KZ spectra discussed in the introduction.
   These solutions

   have the form of a power-law  $ n_k = c k^{-\alpha} $, where

    $ c $ is a dimensional constant. They can be obtained analytically by applying a change of integration variables known as  the Zakharov transformation \cite{zakharov41kst}, or by a dimensional analysis
\cite{connaughton2003dimensional}.
The value of the exponent $ \alpha $ depends on the particular wave model. KZ solutions correspond to constant fluxes of positive
conserved quantities in
 the scale space (turbulent cascades).

The GPE model has two positive invariants, the mass $M$ and the energy $E$.
It can be shown (see \ref{ap:fluxes}) that energy has a direct cascade,
i.e. from large to small scales, while the mass cascade is inverse, from small to large scales.
The corresponding KZ exponents are respectively $ \alpha_E=3 $ and $ \alpha_M=7/3 $.
Hereafter in this work, we present results in terms of the one-dimensional spectrum  $ n_{1D}(k) $, obtained from $ n(k) $
by integrating out the angular variables, i.e.  $ n_{1D}(k) = 4 \pi k^2 n_k $.
In this notation the KZ solutions are
\begin{equation}
\begin{split}
&n_{1D}^{(E)}(k)= 4\pi c^{(E)} k^{-1} \\
&n_{1D}^{(M)}(k)=4\pi c^{(M)} k^{-1/3}.
\end{split}
\label{eq:KZ}
\end{equation}
These solutions represent respectively constant fluxes of $M$ and $E$ and, therefore, they are sustained by an external  forcing and a dissipation. Even tough the KZ spectra are found for infinite inertial ranges,

 they are expected
   in finite systems provided the scales of $ \mathcal{F} $ and $ \mathcal{D} $ are widely separated in Fourier space and
   provided the interactions of the wave modes are local.

   The locality of the KZ solutions (\ref{eq:KZ}) is checked  in  \ref{ap:locality}: the energy cascade turns out to be marginally nonlocal and its locality is restored by  a logarithmic correction, while the  inverse particle cascade is local.

\subsection{Transition to three-wave interactions}
Equation (\ref{kin4}) describes a four-wave interaction process which is responsible for the direct and the inverse cascades. When the inverse cascade is not damped at low $k$'s, it  leads to accumulation of  particles at these scales which can alter the four-wave dynamics.
Respectively, the {\it zero-mode} $ n_{\mathbf{k}=0}(t) $ (related to the uniform part of the field $ \psi $ in physical space) will grow, which
can be interpreted as a Bose-Einstein condensation process.
When the condensate fraction becomes large,  the kinetic equation   (\ref{kin4})  ceases to be valid.
Suppose that a large fraction of the wave-action is present at the zero-mode,
thereby $ \psi(\mathbf{x}, t)=c(t) + \epsilon\phi(\mathbf{x}, t) $, where $ \phi $ represents
small fluctuations ($ \epsilon \ll 1 $). By substituting this ansatz into GPE (\ref{nls0}), we find,
at the order $ \epsilon^0 $, the evolution equation for the {\it condensate fraction},
\begin{equation}
\imath \frac{\partial c}{\partial t} - |c|^2 c=0.
\end{equation}
Its  solution is $ c(t)=c_0 e^{-\imath c_0^2 t} $, where $c_0$ is a real positive constant.
Thus, the condensate amplitude  rotates in the complex plane with an
 angular velocity proportional to its square modulus.
In the next order in $\epsilon$, we obtain a linear equation for the fluctuations on  the condensate background:
\begin{equation}
\imath \frac{\partial \phi}{\partial t}(\mathbf{x}, t) + \nabla^2 \phi(\mathbf{x}, t) - 2c_0^2 \phi(\mathbf{x}, t) + c_0 e^{-2\imath c_0^2 t} \phi^\ast (\mathbf{x}, t)=0.
\label{phi}
\end{equation}
Diagonalizing the linear dynamics in Fourier space, one can show that the linear wave modes
oscillate at  the Bogoliubov frequency \cite{dyachenko:1992hc,zakharov2005dbe},
\begin{equation}
\omega(\mathbf{k})=\pm {k} \sqrt{{k}^2+2c_0^2}.
\label{eq:bogoliubov}
\end{equation}
In the limit of small $ k $'s or  strong condensate fraction $c_0$, when $k^2 \ll c_0^2$,
the fluctuations are acoustic waves with the speed of sound $ \omega/k \approx \sqrt{2c_0^2} $.

In the next order in $\epsilon$, when  weak nonlinearity is taken into account for the fluctuations,
 it is possible to use the WWT theory and derive a kinetic equation describing  three-wave interactions of the Bogoliubov sound
  \cite{dyachenko:1992hc,zakharov2005dbe}:
\begin{equation}
\frac{\partial n_1}{\partial t} = \int (R_{231} - R_{123} - R_{312}) d\mathbf{k}_{12},
\label{eq:3wave}
\end{equation}
where
\begin{equation}
R_{123} = 2\pi |V_{123}|^2 \delta(\mathbf{k}_1-\mathbf{k}_2-\mathbf{k}_3) \delta(\omega_1-\omega_2-\omega_3) (n_2 n_3 - n_1n_2 - n_1 n_3)
\end{equation}
and the analytical form of the scattering matrix $V_{123}$ is given in \cite{zakharov2005dbe}.
Equation (\ref{eq:3wave}) describes  three-wave interactions $ 1 \leftrightarrows 2 $  which conserve only the energy
 and not the mass. Thus, only the energy cascade KZ solution is relevant to this regime.
For the large-scale (strong condensate) limit $k^2 \ll c_0^2$, the
 direct cascade KZ spectrum takes the form $ E_{1D}(k) \sim k^{-3/2} $ predicted by Zakahrov and Sagdeev for the
  3D acoustic WWT \cite{zakharov1970sat}. Because most of the wave-action in this case is in the condensate, the 1D energy spectrum is $ E_{1D}^{(E)}(k) \sim c_0^2 n_{1D}^{(E)}(k) $ \cite{zakharov2005dbe}. Therefore, the wave-action spectrum for the energy cascade in the acoustic
  regime is
\begin{equation}
n_{1D}^{(E)}(k) \sim k^{-3/2}.
\end{equation}

\subsection{Critical balance conjecture}
In some physical situations, wave turbulence fails to be weak, and the wave spectrum saturates at a critical shape such that the linear term is of the same size as the nonlinear term for each mode ${\bf k}$. Such a \em critical balance \em appears to be typical for a wide range of
physical systems, ranging from Magneto-Hydrodynamic turbulence \cite{goldreich1995tti}, to the rotating and stratified geophysical systems \cite{nazarenko-cb-paper}.
The most famous example is the Phillips spectrum of the gravity water waves \cite{phillips:367511, korotkevich:074504}, in which case the saturation at the critical value occurs due to wave breaking.

In the GPE model, similar situation may occur when an equivalent of wave breaking process is active in the system. Namely, we will see that when the low-${\bf k}$ range is over-dissipated by strong hypo-viscosity ({\bf RUN 3}), the inverse particle cascade tends to accumulate at low ${\bf k}$'s ({\it infrared bottleneck}) until a critical balance is reached and the spectrum is saturated.
Indeed, for the inverse cascade to exist the wave turbulence must be weak, because only then the Fj{\o}rtoft argument works (see \ref{fjortoft}). However, when the linear and the nonlinear terms, locally in Fourier space, are of the same order, the inverse cascade stops and so does
the infrared bottleneck  accumulation. This is precisely the mechanism of reaching the critical balance condition in this case.

Now we present an estimate for the critical balance spectrum in the GPE model.
Equating the linear and the nonlinear terms in Fourier space gives
\begin{equation}
\begin{array}{rcl}
k^2 |\tilde{\psi}_k|   & \sim & |\tilde{\psi}_k|^3 k^6 \\
\Rightarrow \; k^{-4} & \sim & |\tilde{\psi}_k|^2.
\end{array}
\end{equation}
Note that we have replaced each $ d\mathbf{k} $ integration  by $ k^3 $ thereby assuming that only the wave amplitudes with similar $k$'s
 are correlated in Fourier space.
Thus, for the 1D wave-action spectrum  in the critical balance regime, we have
\begin{equation}
n_{1D}^{(CB)}(k) \sim k^{-2}.
\end{equation}

\section{The numerical experiments}\label{numerics}
As we want to understand the basic properties of the GPE turbulence,
 we choose to deal with the simplest configuration: triple periodic boundary condition and uniform mesh grid. With this choice we can use the discrete Fourier transforms which are numerically fast \cite{press:1992rm, url:fftw}. In our numerics the complex wave field $ \psi $ is a double precision variable defined in space over $ 256^3 $ points. The simulation box has side $ L=256 $ and so the Fourier space width is $ L_k = 2\pi $ with resolution $ \Delta k=2\pi/256 $. Without considering for the moment the forcing and the dissipation
  terms, the GPE model (\ref{nls0}) can be written in the physical space as a sum of a linear operator $ \mathcal{L} $ and a nonlinear one $ \mathcal{G} $
\begin{equation}
\imath \frac{\partial \psi}{\partial t} = \mathcal{L} \psi + \mathcal{G} \psi,
\end{equation}
where $ \mathcal{L} = -\nabla^2 $ and $ \mathcal{G} = |\psi|^2 $. We then use a split step method to solve separately the contributions
 of the two operators in time. This choice is very useful because the linear operator has the exact solution in Fourier space, $ \tilde{\psi}(\mathbf{k}, t+\Delta t)=\tilde{\psi}(\mathbf{k}, t) e^{-\imath |\mathbf{k}|^2 \Delta t} $, while the nonlinear one, due to the conservation of the mass in the system, has the analytic solution $ \psi(\mathbf{x}, t+\Delta t)=\psi(\mathbf{x}, t) e^{-i |\psi(\mathbf{x}, t)|^2 \Delta t} $ in the physical space. At each time step $ \Delta t $, we first evaluate the linear part in Fourier space and then use this temporary solution to solve the nonlinear part in the physical space. With this choice, the numerical error in the algorithm is only due to the time-splitting \cite{bao:2006zk}. The time step is always $ \Delta t =0.5 $, chosen to be of the order of the shortest linear time $ 2\pi/\omega_{max} $.

Concerning the forcing and the dissipation, it appears
 convenient to control $ \mathcal{F} $ and $ \mathcal{D} $ directly in Fourier space to gain a wide inertial range.
  The forcing term acts to inject mass and energy in the system. In all simulations, $ \mathcal{F} $ modifies the first (linear)
  calculation half-step  as  follows,
\begin{equation}
\tilde{\psi}(\mathbf{k}, t+\Delta t)= \left\{
\begin{array}{ll}
\tilde{\psi}(\mathbf{k}, t) e^{-\imath |\mathbf{k}|^2 \Delta t} + A f_0 e^{\imath \varphi(\mathbf{k}, t)}, \ \ & k_{\min} \le |\mathbf{k}| \le k_{\max} \\
\tilde{\psi}(\mathbf{k}, t) e^{-\imath |\mathbf{k}|^2 \Delta t}, & |\mathbf{k}|<k_{\min} \cup |\mathbf{k}|>k_{\max},
\end{array}
\right.
\label{eq:forcing}
\end{equation}
where $ A \simeq 1.62 \times 10^{-3} $. Thus the pumping add mass and energy in the ring region $ k_{\min} \le |\mathbf{k}| \le k_{\max} $ with the function $ \varphi(\mathbf{k}, t) $ uniformly distributed in $ [0, 2\pi) $ and statistically independent at each $\bf  k $-space and
each time step. We choose the forcing  at relatively large scales, with $ k_{\min}=9 \Delta k $ and $ k_{\max}=10 \Delta k $.
A dissipation at high wave numbers is added to halt the direct cascade and to prevent termalization effects.
We find that an hyper-viscous term $ \mathcal{D}_h = \imath\nu_h(\nabla^2)^8 \psi(\mathbf{x}, t) $, where $ \nu_h=2 \times 10^{-6} $,
is effective in absorbing the high-$k$ spectrum and in preventing the aliasing and the bottleneck effects.
This term is also added to the linear operator to evaluate it efficiently in Fourier space.
Finally, different types of dissipations at the large scales can be chosen.
In this manuscript we report three different setups, briefly summarized in Table \ref{tab:cases},
whose results are discussed in the following.
\begin{table}
\begin{center}
\begin{tabular}{| c | c | c | c |}
\hline
cases & forcing & dissipation at low $ k $'s & dissipation at high $ k $'s \\
\hline
{\bf RUN 1} & $ f_0=0.1 $ & none &  $ \mathcal{D}_{h}=\imath \nu_h (\nabla^2)^8 \psi(\mathbf{x}, t) $ \\
{\bf RUN 2} & $ f_0=0.1 $ & $ \hat{\mathcal{D}}_{l}=\imath \theta(k^\star-|\mathbf{k}|)\tilde{\psi}(\mathbf{k}, t) $ &  $ \mathcal{D}_{h}=\imath \nu_h (\nabla^2)^8 \psi(\mathbf{x}, t) $ \\
{\bf RUN 3} &  various & $ \mathcal{D}_{l}=\imath \nu_l (\nabla^{-2})^8 \psi(\mathbf{x}, t) $ &  $ \mathcal{D}_{h}=\imath \nu_h (\nabla^2)^8 \psi(\mathbf{x}, t) $ \\
\hline
\end{tabular}
\end{center}
\caption{Summary of the different numerical simulations performed. Here the hat operator $ \hat{\cdot} $ stands for the Fourier-space
 operator, $ \nu_h = 2 \times 10^{-6} $, $ \nu_l =1 \times 10^{-18} $, $ \mu = 1 \times 10{-4} $, $ k^\star=9 \Delta k $ and the forcing is defined in (\ref{eq:forcing}).}
\label{tab:cases}
\end{table}

\subsection{{\bf RUN 1} - free condensate growth}
Here, we study the evolution of the GPE system, initially empty, without any dissipation at low $ \mathbf{k} $'s.
At every time step, the forcing term inputs  mass $ \Delta M(t) $ and energy $ \Delta E(t) $, so that $M$ and $E$
 start to grow. Even if the forcing is acting at a particular wave-number range,
  the nonlinear interactions cause mass and energy  transfers in Fourier space.
  We have chosen the forcing coefficient $ f_0 $ such that the transfers become efficient for the
  time step considered, namely it chosen to be sufficiently  big to prevent sandpile effects characteristic to
  mesoscopic turbulence \cite{nazarenko:2006ta,zakharov:2005jt}.
   One can see in Fig. \ref{in-spectra} that at early stages of the simulation the wave-action
   spectrum $ n_{1D}(k, t) $ evolves and spreads over the wave-numbers space:
   the energy and the particles undergo a direct and an inverse cascades respectively.
\begin{figure}
\includegraphics[scale=1.6]{fig04.pdf}
\caption{Wave-action spectrum $ n_{1D}(k, t) $ during initial stages of simulation. The time unit $ \tau $ refers to the linear time of the forcing scale.\label{in-spectra}}
\end{figure}
After an initial transient time, the linear energy density $ \mathcal{E}_{lin}(t) $ stops to grow, as clearly visible in Fig. \ref{hv-energy}. Linear energy weights at the high wave number part of the spectrum and this saturation is an evidence that its
transfer to the
 small scales is now absorbed by the hyper-viscosity. On the contrary, as no dissipation is present at the large scales,
  the inverse particle cascade is not arrested and the  nonlinear energy density $ \mathcal{E}_{nl}(t) $ continues to increase.
\begin{figure}
\includegraphics[scale=1.6]{fig05.pdf}
\caption{Linear $ \mathcal{E}_{lin}(t) $  and nonlinear $ \mathcal{E}_{nl}(t) $ energy densities during the {\bf RUN 1}. \label{hv-energy}}
\end{figure}

\subsubsection{Spectra}
In Fig. \ref{spectrum-hv} we present the 1D
wave-action spectrum at two different stages after the stabilization of the linear energy.
The spectrum plotted with dashed line is taken at early stages, when the linear and the nonlinear energy
densities are comparable: at this point there is a good agreement with the WWT $ k^{-1} $ prediction, which is also plotted.
\begin{figure}
\includegraphics[scale=1.6]{fig06.pdf}
\caption{Wave-action spectrum $ n_{1D}(k, t) $ at two different stages of {\bf RUN 1}.
 The four-wave and the three-wave WWT
 predictions are also indicated by the lines with slopes $-1$ and $-3/2$ respectively.
  Inset: evolution of the condensate component $ c_0(t) $.\label{spectrum-hv}}
\end{figure}
The condensate component $ c_0(t) $ continues to increase during the simulation, as shown in inset to Fig. \ref{spectrum-hv},
 and  a well defined series of peaks appears in the wave-action spectrum at the final stage (continuous line).
 Such behavior is a clear sign  of three-wave interactions, as reported in \cite{falkovich1988efc}.
Note that the late stage spectrum is consistent with the three-wave Zakharov-Sagdeev WWT prediction $ k^{-3/2} $.
The acoustic three-wave regime is also confirmed by evaluating the dispersion relation by measuring the wavenumber-frequency Fourier transform.
The result, presented in Fig. \ref{dispersion-hv}, shows the presence of two branches (one for the Bogoliubov mode and another for its conjugate) shifted by the condensate velocity oscillation $ c_0^2 $, in excellent agreement with the corresponding Bogoliubov dispersion (\ref{eq:bogoliubov}).
\begin{figure}
\includegraphics[scale=1.6]{fig07.pdf}
\caption{Dispersion relation at the final stage of {\bf RUN 1}, when the condensate fraction is strong. The white dashed line is the Bogoliubov dispersion (only the upper branch). Inset: a zoom on the small $ k $'s zone to appreciate the shift due to the presence of the condensate.\label{dispersion-hv}}
\end{figure}

The observed evolution of the spectrum can be summarized  as follows. (a) At initial times  the condensate wave amplitude $ \tilde{\psi}_{\mathbf{k}=0} (t) $ is of the same order as the amplitude of other modes and the dynamics is well described by the four-wave WWT regime. (b) As the inverse cascade is not halted, mass accumulates at low $ \mathbf{k} $'s and strong turbulence takes place in this transition. (c) Finally when the zero-mode becomes dominant over the fluctuations the wave turbulence is again weak and well described by the three-wave WWT.

\subsubsection{Condensation and density PDF}

 To access further information about  the statistics of the transition from the four-wave to the three-wave regime during the condensation process, in Fig. \ref{fig:1_desity_pdfs} we show the probability density function (PDF) of the density field $ \rho $ at initial and final stages.
\begin{figure}
\includegraphics[scale=1.6]{fig08.pdf}
\caption{Probability density function of the density field $ \rho $ at different time: early stages ($ t_a $) and final stage ($ t_b $) in {\bf RUN 1}. A normal distribution with mean $ \mu $ and standard deviation $ \sigma $ are indicated.\label{fig:1_desity_pdfs}}
\end{figure}
At early stages the density remains small with a lot of low density regions present, which indicates presence of numerous ``ghost'' (weakly nonlinear)  vortices. In fact, in the ideal four-wave WWT dynamics, the wave field would be nearly Gaussian, and the respective density $\rho$ would have an exponential (Rayleigh) PDF, which would be a straight line (with a negative slope) in Fig. \ref{fig:1_desity_pdfs}. We see a significant deviation from the Rayleigh behavior, which means that even at an early stage (at time $t_a$ when the four-wave KZ spectrum is reported) the statistics already differed from the Gaussian.
The development of a maximum on the PDF of $\rho$ is a signature of the emerging condensate.
 As the inverse cascade is not halted the condensate density keeps growing in time. At final stages (at time $t_b$ when the three-wave KZ spectrum is reported) the density field shows a normal distribution behavior in the core of the PDF with  a tail remaining at low density regions corresponding to vortices (which are now strongly nonlinear).
  Note that the mean value of $\rho$ at this time (0.428) is much greater than the standard deviation (0.055) which means that the condensate
    density is much stronger that the  Boboliubov fluctuations about the mean density. This is a clear sign of the three-wave WWT.

\subsubsection{Vortices and velocity PDF}

     Now let us focus on the vortex component represented by the low-$\rho$ PDF tail at $t=t_b$. By plotting the iso-surfaces with small density threshold ($ \rho_{thr}=0.1 $) only one quantum vortex is found in the computational box. We plot in Fig. \ref{fig:1_vortex} its evolution, showing only a part of the total box. The vortex has a ring shape and it propagates in the direction of the ring axis. The  vortex core radius is consistent with the healing length estimate $ \xi \simeq 1.5 = 1.5 \Delta x $.
  Propagating Kelvin waves can be observed on the vortex line. We will argue below that these waves are crucial for understanding the $5/3$-spectrum of the incompressible kinetic energy.
\begin{figure}
\includegraphics[scale=0.4]{fig09.pdf}
\caption{Snapshots of iso-surfaces of low density region with threshold $ \rho_{thr}=0.1 $ (the mean density is $ \langle \rho \rangle \simeq 0.43 $). The box is $ 1/2\times 1/2 \times 1/4 $ the computational domain. The frames are taken approximately every $ 3 \tau $.\label{fig:1_vortex}}
\end{figure}

In Fig. \ref{fig:1_pdf_vel} we plot the PDF of the single velocity  components (the data are normalized in order to compare
 different distributions). \begin{figure}
\includegraphics[scale=1.6]{fig10.pdf}
\caption{Probability density function of the single velocity components at the final stage in {\bf RUN 1}. Inset: zoom on
  the positive tail of the distribution in log-log coordinates.\label{fig:1_pdf_vel}}
\end{figure}
The velocity PDF appears to have a dominant Gaussian core, which is consistent with the three-wave WWT.
In addition, the velocity PDF power-law  tail  with exponent
 $ -3 $ is another signature of the thin vortex lines, whose velocity field falls off inversely proportional to the distance
  from the line at short distances. Such power-law velocity PDF's where observed
 in superfluid turbulence  experimentally  \cite{paoletti:154501} and numerically \cite{PhysRevLett.104.075301} and interpreted as
   an evidence of quantum vortices.

\subsubsection{Incompressible energy spectrum}

Spectra of the compressible and the incompressible kinetic energy at late time ($t=t_b$) are presented in Fig. \ref{fig:1_kin_spectra}.
\begin{figure}
\includegraphics[scale=1.6]{fig11.pdf}
\caption{Compressible and incompressible kinetic energy spectra measured at final stage of simulation in {\bf RUN 1}. A $ k^{-5/3} $ showin classical Kolmogorov prediction is also plotted.\label{fig:1_kin_spectra}}
\end{figure}
The compressible part is dominant and has the same features as the ones already discussed for the wave-action spectrum: it shows  the peaks
(harmonics of the forcing scale) and it follows the  Zakharov-Sagdeev spectrum (with exponent $-3/2+2 =1/2$).
 The incompressible spectrum formally coincides with the classical Kolmogorov $ 5/3 $-law.
  But we have seen in Fig. \ref{fig:1_vortex} that only one quantized vortex ring remains in the system at this time, so it is impossible
  for the Kolmogorov theory, developed for the continuous classical vorticity fields, to be relevant in this case.
  Resolution to this paradox is suggested in \cite{lvov-et-al-5/3}. In short, the $ -5/3 $ slope is produced
  by an energy cascade carried by Kelvin waves (seen in
  Fig. \ref{fig:1_vortex}).
  It turns out \cite{LN-spectrum}
  that the Kelvin wave energy spectrum also has exponent $ -5/3 $ and the coincidence with the Kolmogorov
  exponent is purely coincidental (the Kelvin-wave and the Kolmogorov spectra have different pre-factors).

\subsection{{\bf RUN 2} - friction at large scales}
In the previous run no steady turbulent state has been reached because of the presence of the inverse cascade.
To stay in the four-wave weak turbulence regime  and to
avoid the condensate growth, an effective friction term at large scales will now be added.
This term is written directly in Fourier space and results in
\begin{equation}
\hat{\mathcal{D}}_l = \imath \mu \theta(k^\star-|\mathbf{k}|) \tilde{\psi},
\end{equation}
where $ \theta $ is the Heaviside step function, $ k^\star = 9 \Delta k $ is the lowest forced wave-number and $ \mu=1 \times 10^{-4} $ is a friction coefficient. This coefficient is optimally chosen to stop the inverse cascade without altering the direct energy cascade. With this choice both the nonlinear and the linear energy densities reach a constant value during the simulation, as plotted in Fig. \ref{hvf-energy}.
\begin{figure}
\includegraphics[scale=1.6]{fig12.pdf}
\caption{Linear $ \mathcal{E}_{lin}(t) $ and nonlinear $ \mathcal{E}_{nl}(t) $ energy density evolution in the presence of large scale friction ({\bf RUN 2}). \label{hvf-energy}}
\end{figure}
The final stage wave-action spectrum, presented in Fig. \ref{spectrum-hvf}, agrees with the $ k^{-1} $ four-wave WWT prediction. The condensate growth, shown in the inset, is halted by the friction. Agreement with the four-wave WWT may seem surprising because, according to
 Fig. \ref{hvf-energy}, the nonlinear energy exceeds the linear one. Our explanation is that the nonlinear energy  mostly
 resides in the condensate and forcing scales, whereas in the direct cascade range the modes are weakly nonlinear.
\begin{figure}
\includegraphics[scale=1.6]{fig13.pdf}
\caption{Wave-action spectrum $ n_{1D}(k, t) $ at final stage of simulation in the presence of friction. The WWT four-wave prediction $ k^{-1} $ is
shown by the straight line. The inset shows the condensate evolution $ c_0(t) $. \label{spectrum-hvf}}
\end{figure}

We now turn our attention to the statistically
steady state distributions in the physical space. The PDF of the density field $ \rho $, not showed here,
looks similar to early stage distribution presented in Fig. \ref{fig:1_desity_pdfs}.
Here the average density is $ \langle \rho \rangle \simeq 8.31\cdot 10^{-2} $, which corresponds to healing length $ \xi \simeq 3.5 \Delta x $. The low density regions in the computational box are plotted in Fig. \ref{density-fric}.
\begin{figure}
\includegraphics[scale=0.4]{fig14.pdf}
\caption{Low density region of the density field, threshold $ \rho_{thr}=0.015 $, in presence of friction ({\bf RUN 2}).\label{density-fric}}
\end{figure}
A big fuzzy ring structure is present in the top of the figure. It is probably a single ring with large fluctuations, which create secondary small
vortex loops near the main vortex.
Besides this ring, other uniform bubble-like low density regions are present in the box. These are small scale ghost vortices
 which are weakly nonlinear and short-lived (their typical  size is close to the resolution scale).
Thus we see that even though the wave field is mostly random, the coherent vortex structures are also seen in this
regime.

The system in the fluid dynamics framework presents quite unexpected results, still remaining to be explained.
 The PDFs of the  velocity components are plotted in Fig. \ref{pdf_vel-fric}.
\begin{figure}
\includegraphics[scale=1.6]{fig15.pdf}
\caption{Probability density function of  velocity components in the presence of friction ({\bf RUN 2}). Inset: zoom in log, log scale of the positive PDFs branch.\label{pdf_vel-fric}}
\end{figure}
The PDF is isotropic and Gaussian in the core, but it has a power-law tail  $\sim v_i^{-5.3} $.
We still do not have a theoretical explication for this exponent, although the power-law PDF tail with a different
exponent (-1) was previously predicted for WWT in \cite{cln0}.
The compressible and the incompressible kinetic energy spectra are presented in Fig. \ref{fig:2_kin_en}.
\begin{figure}
\includegraphics[scale=1.6]{fig16.pdf}
\caption{Compressible and incompressible kinetic energy spectra in a steady state with friction ({\bf RUN 2}).\label{fig:2_kin_en}}
\end{figure}
The compressible spectrum does not show peaks (as in {\bf RUN 1}) indicating that this turbulence is not
acoustic. The incompressible spectrum shows
 a power-law behavior with exponent close to $ 1/3 $. Again, no theoretical explanation could be proposed.

\subsection{{\bf RUN 3} - hypo-viscosity dissipation}
One can devise to stop the inverse cascade with a different type of dissipation at low $ k $'s.
For this, let us now choose a hypo-viscosity of the form
\begin{equation}
\mathcal{D}_l=\imath (\nabla^{-2})^8 \psi(\mathbf{x}, t).
\end{equation}
As this operator is singular in $ \mathbf{k}=0 $, we will separately remove, at each time step, the zero-mode in Fourier space. This choice still allows to reach steady turbulent states, but unexpectedly leads to different results with respect to {\bf RUN 2}. In Fig. \ref{spectrum-all-hlv} we present various steady state spectra evaluated with  different levels of the forcing $ f_0 $.
\begin{figure}
\includegraphics[scale=1.6]{fig17.pdf}
\caption{Wave-action spectra $ n_{1D}(k, t) $ at the final stage of the simulation in the presence of  hypo-viscosity ({\bf RUN 3}) for different forcing coefficients: $ f_0=0.05 $ {\bf (A)}, $ f_0=0.1 $ {\bf (B)}, $ f_0=0.5 $ {\bf (C)}, $ f_0=1.0 $ {\bf (D)}, $ f_0=2 $ {\bf (E)}, $ f_0=3 $ {\bf (F)}. The $ k^{-1} $ WWT and $ k^{-2} $ CB predictions are also shown. \label{spectrum-all-hlv}}
\end{figure}
What emerges clearly  is that the spectra still have a power-law behavior in the inertial range, but
 it does not follow the WWT four-wave prediction $ k^{-1} $. Instead, we see the $ k^{-2} $ critical balance prediction
 for the wide range of the forcing amplitudes.

Our interpretation is the following.
The hypo-viscosity causes an infrared bottleneck that alters the dynamics at the
scales near the forcing: there the linear and the nonlinear energies become comparable.
At this point the Fj{\o}rtoft argument can no longer apply  and the
critical balance condition propagates into
 all the inertial range causing the observed $ k^{-2} $ spectra. This suggestion is
 corroborated by the measurement of the ratio between nonlinear and linear energies $ \eta={H_{nl}}/{H_{lin}} $
 evaluated for various forcing coefficients $ f_0 $  illustrated in Fig. \ref{energy_ratio-hlv}.
\begin{figure}
\includegraphics[scale=1.6]{fig18.pdf}
\caption{Energy ratio $ \eta=H_{nl}/H_{lin} $ with respect to different forcing coefficients $ f_0 $ in the presence of hypo-viscosity ({\bf RUN 3}). For informations about labels see caption in Fig. \ref{spectrum-all-hlv}. \label{energy_ratio-hlv}}
\end{figure}
 From these results it is clear that, for a wide range of the forcing coefficients (almost two orders of magnitude),
 the energy ratio $ \eta $ remains always order one.

As in the previous runs, we  look at the density field in the
 physical space to visualize vortices and other turbulent structures.
 For this we choose the case ({\bf D}) when $ f_0=1.0 $ (all other cases look similar).
  Again, the PDF of the density is similar to the early stage PDF in Fig. \ref{fig:1_desity_pdfs},
   and this is natural because there is no condensate in the present system.
   The mean density is $ \langle \rho \rangle \simeq 4.31 \cdot 10^{-1} $ and so $ \xi \simeq 1.5 \Delta x $.
In Fig. \ref{density-hypo} we show the low density regions in the physical space
with a threshold $ \rho_{thr}=0.05 $.
 This figure is qualitatively different from the previous ones (Fig.  \ref{fig:1_vortex} and Fig. \ref{density-fric}).
 Now very thin vortex structures fill completely the computational box and form a ``vortex tangle''.
\begin{figure}
\includegraphics[scale=0.4]{fig19.pdf}
\caption{Low density regions with threshold of $ \rho_{thr}=0.05 $ are plotted at the final stage with the presence of hypo-viscosity with $ f_0=1.0 $ ({\bf RUN 3}). \label{density-hypo}}
\end{figure}

The one point PDF's of the single velocity components are plotted in Fig. \ref{pdf_vel-hypo}.
\begin{figure}
\includegraphics[scale=1.6]{fig20.pdf}
\caption{PDF of single velocity components in the presence of hypo-viscosity with $ f_0=1.0 $ ({\bf RUN 3}). Inset: zoom  of the positive branch of the PDF in log-log coordinates.\label{pdf_vel-hypo}}
\end{figure}
The PDF's, which show isotropy, are strongly non-Gaussian: the power-law behavior of $ v^{-3} $ is observed.
This result  is  interesting because similar behavior was observed
experimentally in \cite{paoletti:154501} and numerically in
\cite{PhysRevLett.104.075301} and explained by presence of thin quantized vortex lines.
We emphasize  the $ v^{-3} $ PDF behavior is dominant and not present just in the tail as in the {\bf RUN 1}.
This is because we have much more strong vortex lines in the {\bf RUN 3} than in the {\bf RUN 1}.
Indeed, as the condensate fraction is removed by this type of dissipation,
it is thus natural to think that the vortices fill the system at all scales and highly influence the velocity field.
These vortex lines undergo frequent reconnections resulting in a sound emission.
The incompressible kinetic energy spectra, for all the forcing amplitudes, are illustrated in Fig. \ref{fig:3_kin_en}.
\begin{figure}
\includegraphics[scale=1.6]{fig21.pdf}
\caption{Incompressible kinetic energy spectra for different forcing amplitude $ f_0 $ in presence of hypo-viscosity ({\bf RUN 3}). For information about the labels see caption in Fig. \ref{spectrum-all-hlv}.\label{fig:3_kin_en}}
\end{figure}
No evidence of  $ -5/3 $ law is found in this (critical balanced) regime.
All spectra have a power-law behavior in the inertial range with exponent near $ -1 $. A theoretical explanation of this exponent is
 still lacking.

\section{Conclusions}\label{conclusion}
In this paper, we have analyzed the turbulent states in the forced-dissipated 3D GPE model by  using the  direct numerical simulations.
Introduction of the forcing and the damping is aimed at achieving statistically stationary turbulent cascades.
We have focused our attention on the direct energy cascade by introducing a pumping term at relatively
large scales and by  using hyper-viscosity  at small scales. We have studied three regimes with different
dampings at the scales larger than the forcing scale:
no dissipation ({\bf RUN 1}), a friction ({\bf RUN 2}) and a hypo-viscosity ({\bf RUN 3}).

{\bf RUN 1} is performed without any dissipation at large scales and so the inverse cascade,
predicted by the WWT theory, causes condensation at the $k=0$ mode. This alters the four-wave
dynamics  and the system, after a strongly turbulent transient, becomes dominated by weak three-wave dynamics
of acoustic  fluctuations  on background of  a strong coherent condensate. The long-time evolution in this
case is characterized
by the appearance of a large quantum vortex ring in the numerical box. Kelvin waves propagate on this vortex ring,
 which causes the incompressible kinetic energy spectrum to follow the  $ -5/3 $ law.
 We argue that the classical turbulence picture developed for the continuous vorticity fields is
 inapplicable; the fact that the Kelvin wave turbulence has the same spectrum as
the classical Kolmogorov spectrum is coincidental, as it arises from completely different physical
processes \cite{LN-spectrum,lvov-et-al-5/3}. The vortex ring in this regime coexists with the random
acoustic waves engaged in the three-wave interactions. The vortex shows up as a $v^{-3}$ tail on
the velocity PDF while the random waves make up the Gaussian core of this PDF.

In {\bf RUN 2} and {\bf RUN 3} we have introduced a dissipation term at large scales
in order to stop the inverse cascade and to reach statistically steady states.
The characteristics of these states depend strongly on the choice of the low-$k$ damping.
If a friction is introduced ({\bf RUN 2}), the growth of the condensate is halted and the
wave-action spectrum follows the four-wave WWT prediction. A large fuzzy vortex ring surrounded by
  small ghost vortices appears in the final stage of the computation.
 If the dissipation is an hypo-viscosity ({\bf RUN 3}), the final steady spectra,
 evaluated for a wide range of forcing coefficient, agree with the critical balance prediction.
 In this regime the computational box appears to be filled by a vortex tangle - a chaotic set
 of strongly nonlinear
 vortex lines. The velocity PDF exhibits, both in the core and on the tails,
 a power-law behavior $v^{-3}$ characteristic to such vortex lines.

In Summary, our numerical results clearly show that  the turbulent state in the direct cascade range
 is strongly affected by the choice of damping in the inverse cascade range.
Most realistic configuration for the existing BEC experiments is configuration of {\bf RUN 1}.
Indeed, while the hyper-viscosity can be physically understood as an evaporative cooling mechanism,
no large-scale damping mechanisms have ever been proposed.
On the other hand, to study the nontrivial QT states predicted by the {\bf RUN 2} and the {\bf RUN 3} of the present paper,
it would be interesting to explore possibilities to damp the lowest-momentum modes in BEC experiments.

\section{Acknowledgments}
We thank Al Osborne and Victor L'vov for always stimulating discussions and for suggestions. We are also grateful to Guido Boffetta, Filippo De Lillo and Stefano Musacchio for precious advises on classical turbulence and numerics. We appreciate the work of FFTW developers in providing an excellent package to perform FFT algorithm.

redpajama_set_name: RedPajamaArXiv


text:
The Netherlands Proteomics Centre (NPC) is a Dutch research center in the field of proteomics. The research is focused on the proteome, the entire set of proteins expressed by a genome, cell, tissue or organism.

The NPC was established by Prof. Dr. Albert Heck in 2003 and is located in the city of Utrecht. NPC is part of the Netherlands Genomics Initiative (NGI).

Cooperating institutions

Within NPC there is a cooperation between seven universities, four academic medical centers and a number of biotechnology companies:

 Utrecht University (UU)
 University Medical Center Utrecht (UMCU)
 University of Groningen (RUG)
 Leiden University (LU)
 Leiden University Medical Center (LUMC)
 Delft University of Technology (TU Delft)
 Radboud University Nijmegen (RUN)
 University of Amsterdam (UvA)
 Academic Medical Center (AMC)
 Wageningen University and Research Centre (WUR/PRI)
 Erasmus MC
 Dutch Cancer Institute (NKI)
 Dutch Vaccin Institute (NVI)
 AMOLF
 Hubrecht Institute

Board
 Prof. Dr. Albert Heck
 Dr. Werner Most
 Prof. Dr. Geert Kops
 Prof dr. Hermen Overkleeft
 Prof. Dr. Bert Poolman
 Prof. Dr. Rob Liskamp

References

External links
  Website of the Netherlands Proteomics Centre

Proteomics organizations
Research institutes in the Netherlands
Utrecht University


Viper is a very bright, high drive, independent dog from our Verona x Chester litter. We did not originally intend to keep a puppy from this litter as we were hoping to keep a chocolate puppy from Verona's next litter, but Viper was too special to resist. From a young age, she had the most intelligent, focused 'Keep Me!' eyes. As a stand-out puppy in an exceptional litter, we are excited to see what the future holds for this little smarty pants.
Viper is training for agility, rally, dock diving and nosework and is doing very well – she has earned her C-WAGS scent patrol title and WON the BC Championship semi-pro X-treme Air dock jumping competition with a personal best jump of 18'9″ on her debut weekend of dock competition. Viper continues to progress in dock diving, and in 2017 was handled to several new personal bests including a 6'2″ in high jump and a 7th overall finish overall at the Canadian Championships. Viper is probably best known for her wonderful social temperament with both dogs and people and her ultra keen nose. She has siblings titled and/or excelling in training for rally, obedience, agility, field trials, hunt tests and search and rescue.
Viper's first litter was born in early 2017, sired by Harvey. Those puppies are doing great things in obedience, agility and dock diving and one is an emotional support dog. The breeding was repeated in 2018 with puppies going to a similar variety of homes.


The Office of Diversity and Inclusion works to foster a diverse and inclusive campus community.
The Office of Multicultural Affairs provides resources and support for students, including mentoring opportunities and programs celebrating the many cultures represented at Wake Forest.
The LGBTQ Center provides education, advocacy, and support to the entire campus community around issues of sexual orientation and gender identity.
The Office of Sustainability works closely with a sustainability working group composed of key partners across campus to craft and implement strategic goals.
The Faculty Senate is an elected body that advises the Board of Trustees and recommends the recipients of honorary degrees.
The Staff Advisory Council serves as a forum for staff to exchange ideas about policies and issues affecting Wake Forest University employees and to offer feedback to the President on these issues.


text:
Olympus Introduces New FL-900R Flagship External Flash Unit
Olympus has updated their flash offerings with the all new FL-900R Electronic Flash for use with their PEN and OM-D camera lines.
Some of the highlights of this new flash include increased coverage with a generous guide number of 58m, weather-sealed construction to match their OM-D line (dust-proof, splash-proof and freeze-proof down to -10°C), a fast recycle time of just 2.5 seconds, and remote wireless functionality.
See the Olympus press release below for more details.
LIGHT FOR THE SPEED OF LIFE: THe NEW HIGH-INTENSITY FLAGSHIP ELECTRONIC FLASH FL-900R
New high-intensity flash has a maximum guide number of 58[1] and the fastest sequential shooting tracking performance in its class2
CENTER VALLEY, Pa., September 19, 2016 -- Olympus responds to the needs of advanced photographers with the new flagship FL-900R Electronic Flash, a high-intensity flash with a maximum guide number of 58 and 10 fps sequential shooting tracking speed when paired with the new OM-D® E-M1 Mark II camera body, the fastest in its class.The compact, lightweight Micro Four Thirds® system-compliant flash is dust-proof, splash-proof and freeze-proof (-10°C)3 and pairs with the weatherproof E-M1 Mark II, E-M1, E-M5 Mark II cameras and M.ZUIKO® PRO lenses to give users peace of mind when shooting in a wide variety of extreme conditions.
The FL-900R Electronic Flash produces optimal lighting even in challenging environments when combined with the camera's built-in TruePic image processor and TTL metering. Photographers are able to cover an angle of view for a focal length range of 12-100mm (24-200mm in 35mm equivalent) and 7mm-10mm (14-20mm in 35mm equivalent) when using the built-in wide panel.
Charging time has been reduced to approximately 2.5 seconds, which provides fast sequential shooting and tracking performance that enables split-second capture of fast-moving subjects. When paired with the Olympus OM-D E-M1 Mark II, the FL-900R is compatible with various Olympus shooting modes, including Wireless RC mode, High-Res Shot, Focus Stacking, Focus Bracketing, Movie Mode (with LED light) and Multi-Flash Mode, for a wide range of photographic expression.
Main Features Details
1. Flagship flash with a maximum guide number of 58m
The Olympus FL-900R Electronic Flash, a high-intensity flash with a maximum guide number of 58m, makes use of an Olympus camera's TruePic image processor and TTL metering to provide optimal lighting in a wide variety of shooting conditions. When using the built-in wide panel, the flash covers an angle of view for a focal length range of 12-100mm (24mm-200mm in 35mm equivalent) and 7-10mm (14-20mm in 35mm equivalent).
2. 10 fps sequential shooting tracking performance, the fastest in its class
Charging circuits have been optimized for nickel metal hydride (Ni-MH) rechargeable batteries to reduce the recycle time to approximately 2.5 seconds, enabling 10 fps sequential shooting and tracking performance to capture split-second motion and fast-moving subjects.
3. Compact, lightweight, weather-resistant performance with excellent mobility and reliability
The FL-900R is dustproof, splashproof and freezeproof (-10°C) and, when combined with the E-M1 Mark II, E-M1, E-M5 Mark II and M.ZUIKO PRO lenses, users can take advantage of its compact, lightweight design to shoot in a range of harsh environments.
4. Versatile shooting features
a. Wireless RC Mode
Wireless control capabilities make high-intensity, multi-flash photography seamless. From the camera, you can control up to four flash groups, select whether or not a group fires, compensate for flash output, and adjust various settings. The flash is also equipped with a wireless remote function and may be attached to the hot shoe of a camera to be used as the commander flash when using the commander function. An IR filter is also included for when visible light from the commander flash is not necessary.
b. Multi Flash Mode
Multi Flash Mode is available on the new E-M1 Mark II for capturing subject motion. When the FL-900R is paired with the E-M1 Mark II, users are able to set the flash output, the interval and the number of times the flash fires to capture subject motion in a single image.
c. Compatible with High-Res Shot, Focus Stacking and Focus Bracketing
The FL-900R also supports unique Olympus functions including High-Res Shot, Focus Stacking and Focus Bracketing. Because the FL-900R recycles so quickly, shorter shooting intervals are now available on these functions.
d. LED light for video capture
The built-in LED light with a maximum power of 100 lux at 1m supports video capture and is compatible with lenses with a focal length of 12mm (24mm in 35mm equivalent) or higher.
Sales Outline
Planed Ship Date
Electronic Flash
FL-900R
U.S. Pricing and Availability
The Olympus FL-900R Electronic Flash will be available beginning in October 2016 for an estimated street price of $579.99 USD and $729.99 CAD. For a complete list of specifications, visit the Olympus website at: http://www.getolympus.com/accessories/fl-900r.html
Journalists interested in more information, review units and high-resolution images of the Olympus FL-900R Electronic Flash should contact Colin Brown, MullenLowe Public Relations, [email protected], 617-226-9749, or Jennifer Colucci, Olympus America Inc., [email protected]olympus.com, 484-896-5719, or visit the Olympus website: http://asset.olympusamerica.com/login/.
ABOUT OLYMPUS AMERICA INC.
Olympus America Inc. is a leading provider of digital imaging and audio technology solutions noted for its precision optics and groundbreaking technologies.
For more than 90 years, Olympus has innovated and developed best-in-class products that expand the boundaries of product design and functionality, empowering consumers and professionals alike to capture their stories. These include:
Professional and Consumer Interchangeable Lens Cameras
Related Underwater Products and Accessories
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For more information about Olympus and our award-winning products, please visit www.getolympus.com or connect with us and other fans like you through our social and photographic communities: @getolympus on Facebook, Twitter, Tumblr, YouTube, Pinterest, Instagram and Flickr.
Specifications and design are subject to change without any notice or obligation on the part of the manufacturer. All trademarks and registered trademarks listed herein are the property of their respective holders, in the U.S. and/or other countries.
© 2016 Olympus America Inc.
[1] In meters at ISO100.
2 As of September 1, 2016, based on Olympus internal research, when using the OM-D E-M1 Mark II at a flash ratio of 1/32, with a clip on flash with a guide number of 50 or higher guide number powered by AA batteries.
3 Low temperatures may reduce battery performance and duration.


Under a blue sky and one of the hottest days of the Championships so far, the 2011 470 World Championship title contenders, Medal Race teams and nineteen Olympic qualifying nations were confirmed. Perfect sailing conditions ranging between 12-17 knots were delivered by the Fremantle Doctor out on Success Course for the 80 boats from thirty-nine nations in the 470 Men fleets. The temperature which had heated up a notch or two was matched by the intensity of racing amongst the teams in the concluding two races of the final series.
The December 2011 Issue of Sail Racing Magazine is crammed full of exciting and exclusive content and now available for download via the iPad/iPhone Apple Newsstand or to view online in our browser version.
Film 1 concentrates on the very heavy artillery employed against Sewastopol. Film 2 covers the Wehrmacht on several fronts and together the film provide film footage not seen since the war when it was used for propaganda and training. An interesting DVD that will be a much valued addition to any DVD war film collection.


I aim to eat mostly local, seasonal food. We get most of our food from our CSA (farm share) and for the past several months, have had seemingly endless supplies of all the root veggies. Beets, potatoes, parsnips, carrots, turnips, radishes, rutabaga, sweet potatoes, celeriac, kohlrabi... and I am sure I'm forgetting more!
These dirt-born veggies end up raw in salads, cooked in soups, sauces, and even baked into cookies (the best Sweet Potato Cookies here)!
You can use whatever veggies you'd like, but I used parsnips, sweet potatoes, carrots, and turnip.
I was instantly attracted to Nina's Honey, and I think it's pretty obvious why. If you're confused, allow me to introduce myself: My name is Morgan and I am OBSESSED with dogs!
As much as I love winter food, I'm getting reeaalllly over this cold weather and am ready to lighten up. I am loving the fresh bright flavors that the lime zest and herbs bring - I can feel spring coming (despite the 2 feet of snow outside)!!!
This dish is great on it's own, served as a side, with quinoa, or on a bed of greens. It's actually quite easy but looks impressive. Take it to a party and I guarantee it will be the first empty dish.
Toss the chopped veggies with the avocado oil, sea salt, and garlic powder. Roast on parchment paper at 400 for 25-35 minutes, until soft and beginning to turn golden brown.
In a bowl, mix the olive oil, honey, lime zest and juice, herbs, sea salt and pepper. Toss the roasted veggies with the herb dressing and serve.


Live the instant, moment by moment, without the painful past; with no hindrances of the future. Relax the Mind. Empty it of all kind of thoughts, wishes, passions, etc. Do not accept inside your mind any thought.
Before the Flame of Gold can burn with a serene light, the "lamp" must be well cared for, sheltered from all winds! The earthly thoughts must drop dead at the doors of the temple!
The mind must be quiet inside, outside and in the centre. Thus, in deep ?Meditation?, and with the mind totally relaxed, you will experience the "Real". Give in to your inner, profound God, totally oblivious of the mundane. During meditation keep the eyelids closed. So your physical vehicle will slumber delightfully. Meditation without slumber destroys the brain and upsets the mind. Deep Meditation, properly combined with slumber, leads to ecstasy, to SHAMADI. Combine sleep with Meditation in harmonic proportions.
Never forget the "Law of Balance". "You really need 50% of sleep and 50% of meditation". PRACTICE MEDITATION when you feel predispose to naturally sleep. The baker who wants to make bread must know how to combine the appropriate quantities of flour and water. If he mixes more water than needed for the flour, the dough will not become bread; the same if he mixes too much flour with the water. In a similar way works the process of Meditation. If we give into more sleep than meditation, we will fall into unconsciousness. If we force more meditation than sleep, we will ruin the mind and the brain; if we do not know how to combine harmoniously sleep and meditation, we will achieve that that is called SHAMADI, ECSTASY. Who pretends to meditate by radically eliminating sleep, is like the man who tries to start a car by violently stepping on the brakes.
Another example will clarify all this: imagine a rider on a horse. If the rider want the horse to walk, must let the rends as bit loose; but if instead he pulls of them, at the same time will hurt the animal that will feel uneasy, and the horse will stop, neigh, and might even thrust the rider over its head. Something similar will happen to the "devout" that will try to meditate eliminating sleep.
Mental relaxation must be perfect. Any idea, thought, wishes, etc., that in a given moment crosses the mind produces stress, and this is not relaxing. Perfect relaxation of the mind exclude wishes, ideas, thoughts, remembrances, passions, etc. To empty the Mind, make it a bottomless well, this really relaxes it. The superficial mind is like a puddle by the road; when the water evaporates under the solar rays, it only remains rotten lime. The Mind deeply and marvellously relaxed is like an unfathomable lake, in where they live innumerable creatures and there is abundant life.
When some one throws a pebble in a peaceful, serene lake ripples are produced from the centre were the pebble fell to the periphery, it's the reaction of the water to the impact coming from the outside world. Similarly, we can say that the relaxed Mind is like a peaceful, serene lake, where it is reflected the Universe's panorama.
The impacts coming from the exterior world, at falling in the mind, cause ripples that go from its centre to the periphery. Those ripples agitate the mind of the Ascetic and lead them to failure. The Mind must be controlled from its centre, so it will not react to the impacts coming from the outside world.
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More Americans are giving President Barack Obama a thumbs-up. In fact, the president's approval rating climbed to 46.4 percent in the first three months of 2015—a 3-percentage-point increase from the previous quarter, USA Today reports. It was his best quarter since mid-2013, according to the Gallup poll.
A separate CNN/ORC survey (pdf) found a similar trend. CNN reports that 48 percent of Americans approve of how Obama is running the country, while 47 percent disapprove. It's the first time since May 2013 that more Americans approve than disapprove of Obama.
Both polls point to the economy as the primary reason for the upward trend. Falling gas prices at the end of 2014 helped people keep more money in their pockets. CNN said that more Americans are feeling positive about their personal finances. Forty-two percent of those polled said they're better off financially than they were one year ago.
If this trend continues, Obama could soon pass the elusive 50 percent mark. USA Today notes that the average presidential approval rating since 1945 is 53.3 percent. The last time Obama's approval rating was that high was in the period leading up to his re-election victory and his second inauguration.
When put in perspective, Obama's numbers are nestled between those of his immediate predecessors, according to CNN. President George W. Bush had a 36 percent approval rate at the same point in his presidency, while President Bill Clinton reached the 60 percent mark.


Power Rundown: China Too Risky?
American exec Chip Starnes, who was held hostage in China by his employees over a pay dispute, has paid a ransom of up to $600,000 in cash for his freedom. CNBC's Jane Wells and Kayla Tausche discuss.


Are you looking for Hypnotherapy Oak Park and would wish to understand if we can help you to beat ones issue and help you back onto the route of success?
Just like so many others that we have worked well with throughout time, it is completely understandable to be increasingly inquisitive with hypnosis and the correct way it can easily assistance you to transform one's life.
Hypnotherapy Oak Park is effective with re-training the unconscious mind. The subconscious mind is the most successful area of our mind. It is the part that is intuitive, imaginative, and instinctive. It is definitely the region of the mind that is definitely to blame for our routines, fearful reactions and automated operations similar to our own inhaling and exhaling, sweating and heartbeat.
Although our subconscious mind is fairly robust, it often has frustration recognising expressions. That is certainly the reason why you can easily make clear to a tiny kid or certainly to anyone that a spider is absolutely nothing to fear. On a conscious level that particular person will probably fully fully grasp and very likely agree.
Nevertheless, on a unconscious level they can certainly not agree. However this is precisely why the automatic fear reaction is nevertheless prompted, even after extended conversations in relation to spiders being very much tinier (and that they literally fear us etc).
The anxious response is initiated by way of the unconscious region of the mind that did not really grasp the reality of spiders. The conscious part of the mind that does have an awareness of it may find it hard to have an effect on the programmed anxiety response, simply in the way it can not influence our own drive against behavior such as cigarette smoking and eating too much. That means that we can speak with subconscious region from the mind as a way to achieve a permanent change if we want to obtain long-lasting success.
A hypnotherapist is trained to lead a person into a trance. A state of hypnosis 'turns down' the conscious mind permitting higher admittance for the unconscious region. A effective hypnotist is then able to communicate together with the unconscious mind applying metaphors, visualizations, and deliberate crystal clear language.
A prepared hypnotherapist may then convey to the unconscious mind that a spider is nothing to be feared. They could possibly by way of example instruct the person to picture a spider dancing around like a clown, making it look as preposterous as plausible. They may perhaps use exceptional progressive very clear language to likewise relay this communication. If that is completed efficiently, it can send a powerful concept to the subconscious mind that a spider isn't threatening, down in a solution that it knows. At the time the subconscious mind understands this, it will certainly no longer trigger the automatic anxiousness reaction and a phobia is then healed.
When people can properly communicate with an individual's unconscious mind, an individual can certainly help to make many miraculous modifications to an individual's life. People may improve pretty much just about any dependence and any kind of issue. You can easily develop into alot more optimistic, increased successful, and even more fulfilled with lifestyle.
If you're near Oak Park and you might have had more than enough with your struggle of daily life and wish to alter one self, and take pleasure in the enjoyment you are entitled to, then you need to make contact with us here to learn much more today.